Natural History Museum Library
000163832
‘
PHILOSOPHICAL
TRANSACTIONS
OP THE
ROYAL SOCIETY
OF
LONDON,
FOR THE YEAR MDCCCLXXV.
YOL. 165.
LONDON:
PRINTED BY TAYLOB AND FRANCIS, RED LION COURT, FLEET STREET.
MDCCCLXXVI.
CONTENTS
OF VOL. 165.
PART I.
I. Contributions to the Developmental History of the Mollusca. By E. Ray Lankester,
M.A., Fellow of Fxeter College, Oxford. Communicated by George Rolleston,
F.B.S., Linacre Professor of Physiology page 1
II. Researches on Explosives. — Fired Gunpowder. By Captain Noble ( late R.A.),
F.R.S., F.B.A.S., F.C.S., &c., and F. A. Abel, F.R.S., President C.S., &c. 49
III. On the Atmospheric Lines of the Solar Spectrum, illustrated by a Map drawn on
the same scale as that adopted by Kirchhoee. By J. B. N. Hennessey, F.R.A.S.
Communicated by Professor Stokes, Sec. R.S. 157
IV. Contributions to Terrestrial Magnetism. — No. XIV. By General Sir Edward
Sabine, R.A., K.C.B., F.B.S 161
V. Addition to the Paper on “ Volcanic Energy: an attempt to develop its true Origin and
Cosmical Relations.” By Robert Mallet, A.M., C.E., F.R.S., M.R.I.A. 205
VI. Research on the Smallpox of Sheep. By E. Klein, M.D. , Assistant Professor at the
Laboratory of the Brown Institution , London. Communicated by John Simon,
F.R.S., D.C.L., Medical Officer of the Privy Council and of the Local Government
Board 215
VII. Description of the Living and Extinct Races of Gigantic Land-Tortoises. —
Parts I. & II. Introduction, and the Tortoises of the Galapagos Islands. By
Dr. Albert Gunther, F.R.S., V.P.Z.S., Keeper of the Zoological Department of
the British Museum 251
[ t* ]
VIII. On the Development of the Teeth of the Newt , Frog , Slowworm, and Green Lizard.
By Charles S. Tomes, M.A. Communicated by John Tomes, F.B.S. page 285
IX. On the Structure and Development of the Teeth of Ophidia. By Charles S. Tomes,
M.A. Communicated by John Tomes, F.B.S. 297
X. On Polishinq the Specula of Beflectinq Telescopes. By W. Lassell, F.B.S.,
V.P.B.A.S., LL.D. . .' 303
PART II.
XI. On the Tides of the Arctic Seas. By the Bev. Samuel Haughton, M.D. Dubl., D.C.L.
Oxon ., F.B.S., Fellow of Trinity College, Dublin. — Part IY. On the Tides of
Northumberland Sound, at the Northern Outlet of Wellington Channel . 317
XII. On the Tides of the Arctic Seas. By the Bev. Samuel Haughton, M.D. Dubl.,
D.C.L. Oxon., F.B.S., Fellow of Trinity College, Dublin. — Part V. On the Tides
of Befuge Cove, Wellington Channel 331
XIII. On the Tides of the Arctic Seas. By the Bev. Samuel Haughton, M.D. Dubl.t
D.C.L. Oxon., F.B.S., Fellow of Trinity College , Dublin. — Part VI. Tides of Port
Kennedy, in Bellot Strait 339
XIV. On the Mathematical Expression of Observations of Complex Periodical Pheno-
mena; and on Planetary Influence on the Earth's Magnetism. By Charles
Chambers, F.B.S., and F. Chambers 361
XV. Beduction of Anemograms taken at the Armagh Observatory in the years 1857-63.
By T. R. Robinson, D.D., F.B.S., F.A.S., &c 403
XVI. The Croonian Lecture. — Experiments on the Brain of Monkeys (Second Series).
By David Ferrier, M.A., M.D. , Professor of Forensic Medicine, King's College.
Communicated by Dr. Sanderson, V.P.B.S 433
XVII. On a Class of Identical Delations in the Theory of Elliptic Functions. By
J. W. L. Glaisher, M.A., Fellow of Trinity College, Cambridge. Communicated
by James Glaisher, F.B.S. 489
XVIII. On Bepulsion resulting from Badiation. — Part II. By William Crookes,
F.B.S. &c 519
XIX. On the Structure and Development of Myriothela. By Professor Allman, M.D. ,
LL.D., F.B.S., President of the Linnean Society 549
[ V ]
XX. Spectroscopic Observations of the Sun. By J. Norman Lockyer, F.R.S., and
G. M. Seabroke, F.R.A.S. page 577
XXI. Tables of Temperatures of the Sea at different Depths beneath the Surface,
reduced and collated from the various observations made between the years 1749
and 1868, discussed. With Map and Sections. By Joseph Prestwich, M.A.,
F.B.S., F.G.S. 587
675
XXII. A Memoir on Prepotentials. By Professor Cayley, F.B.S.
Index ....
775
LIST OF ILLUSTRATIONS.
Plates 1 to 12. — Mr. E. Ray Lankester on the Developmental History of the Mollusca.
Plates 13 to 24. — Captain Noble and Mr. F. A. Abel on Fired Gunpowder.
Plate 25. — Mr. J. B. N. Hennessey on the Atmospheric Lines of the Solar Spectrum.
Plates 26 to 28. — 'General Sir Edward Sabine on Terrestrial Magnetism.
Plates 29 to 32. — Dr. E. Klein on the Smallpox of Sheep.
Plates 33 to 45. — Dr. A. Gunther on Gigantic Land-Tortoises.
Plates 46 & 47. — Mr. C. S. Tomes on the Development of the Teeth of the Newt, Frog,
Slowworm, and Green Lizard.
Plate 48. — Mr. C. S. Tomes on the Structure and Development of the Teeth of Ophidia.
Plate 49. — No Plate.
Plates 50 to 52. — Mr. W. Lassell on Polishing the Specula of Reflecting Telescopes.
Plates 53 & 54. — Messrs. C. and F. Chambers on the Mathematical Expression of
Observations of Complex Periodical Phenomena.
Plates 55 to 58. — Professor Allman on the Structure and Development of Myriothela.
Plates 59 to 64. — Messrs. Lockyer and Seabroke on Spectroscopic Observations of the
Sun.
Plates 65 to 68. — Mr. J. Prestwick on Submarine Temperatures.
PHILOSOPHICAL
TRANSACTIONS
OF THE
ROYAL SOCIETY
OF
LONDON.
FOR THE YEAR MDCCCLXXV.
VOL. 165— PART I.
LONDON:
PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET.
MDCCCLXXV.
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a 2
[ iv ]
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CONTENTS.
PART I.
I. Contributions to the Developmental History of the Mollusca. By E. Ray Lankester,
M.A., Fellow of Fxeter College , Oxford. Communicated by George Rolleston,
F.B.S. , Linacre Professor of Physiology page 1
II. Besearches on Explosives. — Fired Gunpowder. By Captain Noble ( late B.A.),
F.B.S. , F.B.A.S., F.C.S., &c., and F. A. Abel, F.B.S. , President C.S., &c. 49
III. On the Atmospheric Lines of the Solar Spectrum, illustrated by a Map drawn on
the same scale as that adopted by Kirchhoff. By J. B. N. Hennessey, F.B.A.S.
Communicated by Professor Stokes, Sec. B.S 157
IV. Contributions to Terrestrial Magnetism. — No. XIV. By General Sir Edward
Sabine, B.A., K.C.B. , F.B.S 161
V. Addition to the Paper on “ Volcanic Energy: an attempt to develop its true Origin and
Cosmical Belations.” By Robert Mallet, AM., C.E., F.B.S., M.B.I.A. 205
VI. Besearch on the Smallpox of Sheep. By E. Klein, M.D., Assistant Professor at the
Laboratory of the Brown Institution, London. Communicated by John Simon,
F.B.S., D.C.L., Medical Officer of the Privy Council and of the Local Government
Board 215
VII. Description of the Living and Extinct Paces of Gigantic Land-Tortoises. —
Parts I. & II. Introduction , and the Tortoises of the Galapagos Islands. By
Dr. Albert Gunther, F.B.S., V.P.Z.S., Keeper of the Zoological Department of
the British Museum 251
VIII. On the Development of the Teeth of the Newt, Frog, Slowworm, and Green Lizard.
By Charles S. Tomes, M.A. Communicated by John Tomes, F.B.S. . . 285
IX. On the Structure and Development of the Teeth of Ophidia. By Charles S. Tomes,
M.A. Communicated by John Tomes, F.B.S 297
X. On Polishing the Specula of Beflecting Telescopes. By W. Lassell, F.B.S.,
V.P.B.A.S., LL.D 303
LIST OF ILLUSTRATIONS.
Plates 1 to 12. — Mr. E. Ray Lankester on the Developmental History of the Mollusca.
Plates 13 to 24. — Captain Noble and Mr. F. A. Abel on Fired Gunpowder.
Plate 25. — Mr. «T. B. N. Hennessey on the Atmospheric Lines of the Solar Spectrum.
Plates 26 to 28. — General Sir Edward Sabine on Terrestrial Magnetism.
Plates 29 to 32. — Dr. E. Klein on the Smallpox of Sheep.
Plates 33 to 45. — Dr. A. Gunther on Gigantic Land-Tortoises.
Plates 46 & 47. — Mr. C. S. Tomes on the Development of the Teeth of the Newt, Frog,
Slowworm, and Green Lizard.
Plate 48. — Mr. C. S. Tomes on the Structure and Development of the Teeth of Ophidia.
Plate 49. — No Plate.
Plates 50 to 52. — Mr. W. Lassell on Polishing the Specula of Reflecting Telescopes.
PHILOSOPHICAL TRANSACTIONS.
I. Contributions to the Developmental History of the Mollusca. By E. Rat Lankester,
M.A., Fellow of Exeter College , Oxford. Communicated by George Rolleston,
F.R.S. , Linacre Professor of Physiology.
Received January 19, — Read March 12, 1874.
No. I. The Early Development of Pisidium pusillum.
In the months of April and May 1871 I obtained a supply of the freshwater bivalve
Pisidium pusillum, from a muddy little stream near Jena, in Saxe Weimar.
The fact that the development of the eggs of this mollusk takes place within a pair
of brood-cavities formed at the root of the inner gill-lamella on each side, enables the
observer very readily to obtain embryos in different stages of development.
Leydig and O. Schmidt had previously to this described the development of species
of Cyclas, which genus really embraces Pisidium. Leydig studied Cyclas cornea ,
Schmidt studied Cyclas calyculata. At the period when their studies were made the
questions of histogenesis were not quite in the same position as they are to-day ; and
accordingly in their papers little will be found relating to the topics now discussed.
Moreover, on account of the greater transparency of the eggs of Pisidium , I have been
able to work at them with an objective of as high magnifying-power as Hartnack’s
No. 10 a immersion.
I propose in the present communication to take up the figures in the accompanying
Plates in the order in which they present themselves as developmental stages, and thus to
combine an account of the changes and their significance with a description of the Plates.
Plate 1. fig. 1 represents an ovum from the oviduct of Pisidium pusillum at the
breeding-season. The egg-cell is not yet fully grown, and is seen to lie in close appo-
sition to a coiled highly refringent mass, which is a secretion of adjacent cells, and is
assimilated by the egg-cell as “ deutoplasm,” in consequence of which its “ body,” which
is now pellucid, becomes granular, as seen in fig. 3 *.
Plate 1. fig. 2 represents a number of such ova with adjacent masses of deutoplasm
and spermatozoa. The genus Cyclas is hermaphrodite, and so is Pisidium. Whether
* March 7th, 1875. — I should prefer to speak of such matter uniformly as “food-material” in all eggs
where it occurs.
MDCCCLXXY.
2
MR. E. RAY LANKESTER ON THE
self-impregnation occurs is not definitely ascertained, but it seems possible. Leydig
was unable to give a satisfactory account of the arrangement of the ducts and generative
glands from a study of the large Cyclas. cornea , and I have not attempted to enter upon
this question with the much smaller Pisidium.
Plate 1. fig. 3 is drawn from an egg removed from the brood-pouch. It is now gra-
nular in the body owing to the inception of deutoplasm, and has undergone impregnation.
This is inferred from the fact that it is enclosed in a transparent envelope or egg-shell
of membranous consistency. The nucleus and nucleolus seen now in the egg may or
may not be the original germinal vesicle and spot of the egg-cell. Though these
structures disappear in some eggs, it cannot be asserted that they may not be persistent
in others. One point of interest in this and other eggs figured on the Plate is the
presence of the membranous envelope to the egg, which was not found by either Leydig
or Schmidt in their studies on Cyclas.
This fact has been especially insisted upon with regard to Cyclas , and it is therefore
important to note the presence of the envelope in Pisidium. It is very delicate, and is
ruptured and discarded after the first stages of development.
Plate 1 . fig. 15 shows a similar egg in its envelope ; in this egg two nucleoli are
present in the nucleus (1 germinal spots and vesicle).
Plate 1. fig. 16 gives a surface- view of the first pair of cleavage-grooves. They are
seen to embrace the whole egg.
Plate 1. fig. 17. The cleavage-grooves are now four meridional, and the first circum-
ferential is beginning to make its appearance. These two views are taken so as to
exhibit the grooved surface of the yelk.
Plate 1. fig. 4 exhibits the four nuclei of the four first cleavage-segments.
Plate 1. figs. 5 & 6. The cleavage-products have increased largely in number, so
that the egg is now a ball of embryonic cells or a polyplast.
Plate 1. figs. 7 & 8 exhibit a very important condition of the early development.
A deep in-pushing of the surface of the polyplast is obvious, the result being the invagi-
nation of a part of the superficial cells, in the same way as a woven nightcap is tucked
in to make it assume the form of a cap. The occurrence of this primitive invagination
of the embryonal polyplast has been demonstrated by Kowalevsky in Ascidia and
Amjphioxus , and has now been recognized in some members of all the large groups of the
animal kingdom. The process results in the production of a form which I proposed*
* Annals and Magazine of Natural History, May 1873.
The formation of a Gastrula by invagination is obviously indicated though not recognized by the author, in
LoviN’s admirable studies on the development of Mollusca, as also in Karl Yogt’s memoir on the development
of Actceon. In the Nudibranchs and in Limax lhave observed and drawn the Gastrula in course of formation
by invagination (see Contribution No. III.).
Dec. 1874. — Also in Lymnceus (see Quart. Journ. Mic. Sci., October 1874) and in Paluclina vivipara.
March 7th, 1875. — Though the name Gastrula is expressive, I am at this moment inclined to prefer the
original term Planula, on account of the ascribing of a mouth by Professor Haeckel to his typical Gastrula.
The orifice of invagination, when it occurs, is not known to be a mouth. I propose to call it the blastopore.
DEVELOPMENTAL HISTORY OP THE MOLLUSCA.
3
to call the Planula, but which Professor Haeckel has better termed the Gastrula ,
reserving the former name for a condition of the Gastrula which sometimes presents
itself in which there is no aperture of invagination. The Gastrula thus formed consists
of an outer and an inner layer of cells, forming a wall which encloses a cavity (the
primitive gastric cavity) which communicates with the exterior by the aperture of
invagination. The two layers of cells are thus respectively the representatives of the
ectoderm and endoderm of Ccelenterata, and further of the epiblast and the hypoblast
of the developing Vertebrate.
Up to this point the membranous envelope of the egg is intact ; but now it disappears,
since the egg increases very largely in size (Plate 3. figs. 9, 10, 11). This increase in
size is due to the rapid growth of the outer layer of cells, which expands and separates
itself entirely from contact with the invaginated layer, excepting at the part corresponding
to the lips of the orifice of invagination. The orifice entirely closes, and the primitive
gastric cavity remains as a small shut sac formed by well-marked cellular elements,
affixed to one part of the large expanding epiblast, ectoderm, or outer cell-layer (see
fig. 10). The space between the two primitive layers is occupied by a colourless trans-
parent liquid. A surface-view of an embryo in this stage is given in fig. 9, figs. 10 & 11
being deeper views of the same embryo.
The surface-cells are seen to lie closely packed, with a small quantity of granular
matter surrounding each large clear nucleus. The granular matter represents the body
of each cell, and is apparently in this condition not distinctly demarcated for each indi-
vidual element ; so that the epiblast is in the condition of a granular protoplasm with
numerous closely packed imbedded nuclei. The clear pellucid nuclei present one, two,
three, or four nucleoli, and are in process of multiplication by fission.
When the focus of the microscope is so adjusted as to bring an optical section of the
embryo into view, we get the appearance given in fig. 10 ; the invaginated hypoblast is
seen as a small oblong mass (Jiy) at one pole of the oval embryo, and the wall formed by
the epiblast, which is only one cell thick, is seen in section.
But now closer examination shows here and there fusiform or branched cells {me)
attached to the inner surface of the epiblastic wall. More careful focusing, so as
to bring this surface precisely into view, gives the appearance represented in fig. 11,
where a larger number of these subjacent branched cells are visible.
These branched cells are the commencement of the mesoblast. The great space between
the invaginated hypoblast and the epiblastic wall is the mesoblastic cavity, that cavity
which is the distinguishing characteristic of the higher groups of the animal kingdom,
and which becomes ultimately blood-sinus, peritoneal cavity, or hsemolymph-system.
The minutest details as to the mode of origin of these first mesoblastic cells would be
of the greatest interest in the present state of our knowledge as to the origin of the
middle layer of the Vertebrate embryo, and I accordingly have paid especial attention
to it.
Plate 1. figs. 12 & 13 give more highly magnified views of parts of the embryo
b 2
4
ME. E. EAT LANKESTEE ON THE
seen in figs. 9, 10, 11. There can, I think, be little doubt, after an examination of these
figures and fig. 11, that some of these mesoblastic cells are proliferated from the epiblastic
wall. In particular I may draw attention to fig. 13, where the continuity of some of
the branching corpuscles of the mesoblast with the granular matter surrounding the
large nuclei of the epiblast, two of which are seen (ep) in the figure, is obvious. It is
perhaps necessary again to mention that these different views (figs. 10-13) are taken
from the same embryo (without shifting its position) by altering the focus, a power of
1100 diameters being employed so as to obtain a series of optical sections.
It is a more doubtful matter as to whether any of the mesoblastic cells are derived
from the invaginated block of hypoblastic corpuscles. In figs. 11 & 13 I would draw
attention to the corpuscles marked p, which appear to be in the act of detaching
themselves from the hypoblast, whilst the corpuscle (pd) has the appearance of a hypo-
blastic cell undergoing quadruple division.
It is not desirable here to summarize or discuss the various views now current as to
the origin of the mesoblast. It is sufficient to say that the derivation of a portion of
the mesoblast from the epiblast, and of another portion from the hypoblast is in accord-
ance with the view most recently adopted, from various considerations, by Professor
Eknst Haeckel*. At the same time we are by no means yet in a position to assert
that the mesoblast has uniformly the same origin in the various classes of the animal
kingdom, nor in all members of the same class, though this uniformity should be our
working hypothesis.
Plate 2. fig. 18 represents in optical section an embryo somewhat more advanced
than that of figs. 9-11, and with a consequently larger development of mesoblastic cor-
puscles in the cavity lying between epiblast and hypoblast.'
Plate 2. fig. 19 exhibits this in optical section taken just below the epiblastic
surface.
Plate 2. fig. 20 advances to a later stage. The hypoblast is now seen to be assuming
a definite form. Seen thus in optical section, it appears as a bilobed mass supported by
a peduncle, rp. This peduncle f develops subsequently into the rectum, and may there-
fore be designated the “ rectal peduncle.”
The cells or nucleated corpuscles of the mesoblast have greatly augmented in number,
and in this particular view those especially are obvious which, accumulating at the
pole opposite to the attachment of the rectal peduncle, lay the foundation of the foot ( f ).
Plate 2. fig. 21 shows epiblast and hypoblast in optical section, and is introduced
to demonstrate the mobility of the walls of the vesicular embryo. Active movement
does not occur; but slow changes of long and short diameter are noticeable at this
period of development.
Plate 2. figs. 22 & 23 represent an embryo in two slightly differing depths of optical
* Die Gastrsea-Theorie, die phylogenetische Classification des Thierreichs, und die Homologie der Keimblatter.
Jena, September 1873.
t I bave elsewhere applied the term “ pedicle of invagination ” to this same group of cells.
DEVELOPMENTAL HISTOEY OE THE MOLLUSCA.
5
section. In fig. 22 the hypoblast is in section, showing clearly the character of its
cells and their arrangement. In fig. 23 its somewhat irregular outgrowths (Jiy) are
seen, and their relation to groups of the branched mesoblastic corpuscles.
The most important fact shown by these two drawings is the arrangement of certain
of the mesoblastic branched corpuscles {me) in strings or groups, binding, as it were,
others of the cells into groups. The large cells {x) of these figures are not distinguish-
able in form and character from the epiblastic cells in immediate contact with which
they lie, and from which, with little doubt, they have been derived. They apparently
furnish the primitive elements of the foot ; but whether they are to be considered
distinctly as mesoblastic elements or as epiblastic I cannot decide. Supposing that
they give rise to muscular tissue, they establish a very close connexion between the
“ Hautfaserblatt ” and the epiblast, which is paralleled in Hydra and in the higher
Ccelenterata. On the other hand, it is possible that the strings of branched corpuscles
(derived at an earlier period from the epiblast) which traverse these groups of large
cells are the real foundations of the muscular tissue, and that the large cells serve only
as so much material for their appropriation, or as the primitive elements of the nerve-
ganglia.
Plate 2. fig. 24 is not so far advanced in development as figs. 22, 23. It presents two
features of interest with regard to the mesoblast. First, several large fusiform
corpuscles of the mesoblast are seen attached by one extremity to the mass of the
hypoblast, and by the other connected with groups of mesoblastic cells. In connexion
with a similar condition in the corresponding stage of development of Aplysia, to be
described in a further communication, this has considerable interest ; and so has the
second feature, which also is presented by Ajplysia , viz. the ciliation of the surface of
some of these mesoblastic cells (ci). In this particular embryo a few cilia were seen
also on the outer surface of the epiblast, as indicated in the figure.
The ciliation of the mesoblastic cavity is a common phenomenon in adult Vermes
{Gejphyrea and some Annelids), and has even been observed in a sporadic form in some
Vertebrata exclusive of the ciliation of the Fallopian tube (Klein’s observations on the
peritoneum of the Frog).
Plate 2. figs. 25, 26 bring us to a later stage and more definite differentiation of
parts than we have yet considered. They represent the same embryo, seen first in
section and then from the surface. The rudimentary alimentary cavity {al) is seen
hanging from its rectal peduncle as in fig. 20. It will hardly be right any further
to speak of this mass as simply “ hypoblast for it is by no means clear what
changes have gone on, and there may be elements now present which represent the
“ Darmfaserblatt.” The rudimentary alimentary sac is seen to have definite lobes now
which will shortly develop into the two large juxtaposed chambers which constitute the
bulk of the alimentary canal during the embryonic condition in Pisidium. The epiblast
(ej>) is seen not to be sharply marked off from a number of cells or corpuscles accumu-
lated beneath its wall, both laterally (me) and at that pole which represents the foot (f).
6
MR. E. RAT LANKESTER ON THE
Plate 2. fig. 26 is important, because it shows the way in which the mouth first
makes its appearance, and its relation to the “ rectal peduncle.” Plate 2. figs. 25
& 26 represent the same embryo unmoved, but the focus slightly changed : hence it
is obvious that the mouth (o) is about to eat its way into the epiblast’s wall in order to
reach the enlarging rudimentary alimentary cavity — quite independently of the original
point of invagination ; this is, indeed, as mentioned above, long since closed, and sub-
sequently in its neighbourhood the rectum, at first csecal, opens to the exterior.
Plate 2. figs. 27, 28 represent an embryo in the same stage of development, two
views somewhat differently focused being given. They serve to confirm the disposition
of parts ascertained from fig. 25. But in fig. 28 the focus is so arranged as to bring a
larger number of mesoblastic corpuscles into view; in particular, above the mass of
large cells at f, there is an indication of the strings of branched corpuscles which
have already been seen in the phase drawn in fig. 23.
Plate 2. fig. 29 shows the commencement of the oral invagination and the develop-
ment of cilia on the surface round this invagination. Cilia have, however, previously
made their appearance.
Plate 3. fig. 30 takes a leap forward ; but the gap is to some extent filled by
figs. 32 & 33. The individual cells are no longer represented as in the optical sections
of previous stages, but a general superficial view of the embryo is presented. The
surface of the embryo has now become considerably differentiated. The ciliated region
marked f is the foot, which is now contractile and takes on special growth. The
plications in its side (mn) indicate the commencement of the mantle-flap, whilst the
most important differentiation of the surface is the oblong or saddle-like patch ( sh )
formed of large elongate epidermal cells arranged along the sides of a groove. This
remarkable saddle-like patch is the commencement of the secreting surface which
gives rise to the shell, or rather pair of shells. I have traced its gradual extension from
this commencement in later stages ; but the constancy of its first appearance as a
groove surrounded by peculiar elongate cells is the feature to which most importance
must be attached. It will be seen from my observations on Aplysia that the first
commencement of the shell of the larva or “ veliger form ” is there of precisely the
same nature, viz. a groove surrounded by elongate secreting cells. In Aplysia , and also
in Neritina , this groove is sufficiently deep to be entitled to the title of “ gland ” or
“ follicle.” It is of the same order of structures precisely as the byssal gland, and gives
rise to a chitinous plug in Aplysia and Neritina. In Pisidium, as will be seen from
Plate 4. figs. 38 a, 39, the two calcareous valves do not make their earliest appearance
in close contact one with the other. The central portion of the shell-gland is not
concerned with them ; and since it is precisely that point which in the Gasteropods cited
gives rise to a chitinous plug, may we not see in the ligament of the bivalve, which
occupies so precisely the required position, the homogen of that production \
At present I am not prepared to go further with this subject than to suggest that
were the open groove of the shell-area to become closed in so as to form a sac, and
DEVELOPMENTAL HISTORY OE THE MOLLUSCA.
7
were it then to continue its chitinous secretion, we should have produced an internal
chitinous rod like the pen of Loligo. A reference to what I have said on the deve-
lopment of the pen in another communication will show that I have not yet got the
detailed demonstration of the mode of development of the “ pen ” of the Decapodous
Cephalopods, which is required to substantiate the supposed relationship now suggested*.
Fig. 31 shows another embryo with the foot-surface turned to the right instead of
the left. The focus is somewhat deeper, showing, instead of the ciliated surface and
commencing mantle-flap, the rudimentary alimentary canal al and rp. The pharynx
(ph) is seen lined with cilia ; it now is about the stage of development at which it
opens into the gastric chamber, al. The groove of the shell-gland is well seen ( sh ) in
this figure.
Fig. 31 a. Mouth-region ( o ) of an embryo at a somewhat earlier period, more highly
magnified. Surface-view.
Plate 3. figs. 32, 33, represent tw’o views of an embryo less fully formed than that
of fig. 30, but still showing the shell-gland remarkably well (sh). The embryo is also
remarkable for the distinctness with which it exhibits the condition of the alimentary
canal with its two central lobes or gastric chambers, and fore and aft the pharynx and
the rectal peduncle.
Though the foot is developed to so slight an extent in this specimen and the body-
walls generally were so thin and transparent as to suggest some abnormality of deve-
lopment, yet at the point marked f in the figure, slow movements of contraction and
expansion were going on. From this phase onward, in fact, the foot exhibits muscular
movements.
Plate 3. figs. 34, 35, 36 go together, giving different views of three embryos of very
nearly the same stage of development — that is to say, a little in advance of the embryo
of fig. 31. The foot has now grown out as a very prominent conical mass, and being
covered with vibratile cilia and capable of considerable alteration of form, becomes the
chief locomotive organ. The embryos in this condition move about freely in the brood-
pouch, and feed on the material supplied to them from its walls. The pharynx (ph)
now actively functions, expanding widely and bringing in material to its cavity by
means of its ciliate lining, then contracting sharply, and passing on its contents to the
left gastric chamber. Hence the food passes by a slow circular movement into the
adjacent right gastric chamber, and thence to the rectum. As yet, however, there is
* Dee. 1874. — This evidence I subsequently obtained in the spring of 1874 at Naples. The pen-sac of
Loligo does develop as an open pit, which becomes closed in, and it corresponds in position with the shell-
gland, the existence of which I have now demonstrated in Pisidium, Ajplysia, Pleurobranchidium, Neritinci,
Limnceus, and Paludina. M. Hermanx Eol has, subsequently to the publication of my first observations on
this matter (which were made in 1871 and 1872), observed the structure which I term the “ shell-gland ” in
certain Pteropod embryos. Although there is a correspondence between the pen-sac of Cephalopods and the
shell-gland of other mollusks, I have, in the Quart. Journ. Microsc. Science, Oct. 1874, adduced reasons
(based on palaeontological facts) for considering them not to be identical structures. . See also the same Journal
for January 1875.
8
ME. E. EAT LANKESTEE ON THE
no anal opening. The arrangement of these parts is seen best in the diagram, Plate 4.
fig. 51.
The mantle (mn) originates simply as a continuation of the rim of the pharynx, carried
along each side of the foot, as is well seen in fig. 35.
Plate 3. fig. 35 a gives in a diagrammatic way a view of the border of the pharynx
surrounding the oral opening ( o ), and the similar border of the commencing mantle-flap
surrounding the foot (f).
In Plate 3. fig. 36 an embryo of this period is seen in approximately complete optical
section. The shell-gland, which belongs of course really to the surface, is introduced
( sh ), showing the double appearance which it has when focused thus, being in reality
saddle-shaped, and extending on each side of the embryo a little way. In both this
section and in Plate 3. figs. 30 & 35, certain large cells are conspicuous ( y ), which lie
above the pharynx in what ought to be the cephalic region. I merely draw attention
to them, but cannot offer any explanation of their late differentiation. They present
the appearance of the earlier embryonic cells, and soon after this stage disappear.
It is perhaps well briefly to mention (what becomes obvious from the study of this
development in full) that there is nothing which corresponds to the velum of the
“ veliger form ” of Gasteropod development, though some marine Lamellibranchs, pro-
bably most, do exhibit a veliger stage. And it is even still more curious to note that
not even at the earliest stage, when such a differentiation of parts might make itself
apparent for a brief period, is there any thing which indicates or corresponds in the
remotest degree morphologically to a head. There is a gap between the region marked
y in fig. 35 and the pharynx, which might be filled by a head with paired eyes and
tentacles. These have been as completely suppressed as though they had been cut
away, and the sides of the wound so formed healed without leaving a trace.
In the section fig. 36 the differentiation of the cell-elements in the foot is to be
observed, and the attachment of some of these fusiform muscular corpuscles to the
stomach-wall. The lumen in the rectal peduncle is obvious, but it is also certain that
the peduncle is as yet imperforate at its termination. A mass of tissue projecting
inwards from the epiblast by the side of the rectal peduncle marked B is the rudiment
of one of the paired “ segmental organs,” or organs of Bojanus, of the mollusk. In
Plate 4. figs. 44 & 45 much more highly magnified views of similar in-buddings from the
epidermal layer, which occupied similar positions in other embryos, are given. The
position occupied subsequently by what are clearly enough the rudimentary Bojanian
organs, makes it highly probable that these buds are their first commencement. In
fig. 37 the same bud-like process is marked B.
Plate 3. fig. 37 is of value as a step in this developmental history, for it helps to
connect the phase just described with that which perhaps may be best understood by
looking at figs. 39 & 43. Up to this point the embryo usually and readily presents a
more or less accurate profile view of itself, lying on the glass slip with the foot to the
right and the pharynx to the left, or vice versa. But the result of the immediately
DEVELOPMENTAL HISTOET OF THE MOLLTJSCA.
9
ensuing growth is that the embryo cannot be got to tilt over on its side as in the earlier
state. It persistently presents a strictly dorsal, haemal, or umbonal aspect, or an equally
symmetrical, ventral, oral, or pedal aspect.
Fig. 37 represents an embryo which is nearing this change, but has yet to develop a
great margin of mantle-flap, which is the efficient cause of this change of habitual
attitude. In the later stage the observer is at first puzzled as to what has become of
the shell-gland and its groove. In fig. 37 some indication is afforded as to what develop-
ment it is undergoing ( sh ). It becomes very much less obvious than hitherto, owing to
the relative development of other parts and to the flattening of the arched surface on
which it formerly sat as a saddle. Its area is at the same time very greatly increasing —
that is to say, the cells all round the original oval patch of columnar epidermal cells are
acquiring the same character, and ultimately the cells of the general surface of the
mantle will assume the same character. The very large growth of the gastric cavity
at this stage is remarkable. The whole embryo is of course now continually increasing
in size, which is not indicated in the figures ; but the gastric chamber or pair of chambers
have dilated into one great bilobed sac, to which the rectal peduncle forms but a small
appendage. Up to this period the cellular elements of the walls of the gastric chamber
have not presented any noticeable feature, ciliated on their inner surface, and apparently
consisting of but a single series (though possibly a second series maybe present but not
obvious) of corpuscular elements. In the stage to which we are about to pass, they
appear to take on the most extraordinary activity ; and it becomes quite clear that what
has up to this point functioned as an aproctous alimentary canal is a mere larval affair,
and not even the rudiment of a part of the permanent digestive chamber. The cells or
corpuscles of its walls proliferate and arrange themselves in new masses to form the
permanent alimentary tract, and its glandular appendage the liver. The pharynx and
the rectal peduncle are, however, unaffected by this process of re-formation.
In Plate 3. fig. 37 the blind termination of the rectum is clearly seen.
In Plate 3. fig. 38 it is again obvious ( rc ) ; and in this figure the first rudiments of
the shell-valves, which now become evident, are introduced. The lower of the two is
seen lying in contact with a part of the shell-gland (sh), which is in optical section, and
extends really across the whole area occupied by the two shells.
Plate 4. fig. 39 gives a dorsal or umbonal view of an embryo in the next stage of
development — that in which the mantle has freely developed its large border. The
length of the foot has now greatly increased, and the shell-valves are larger and more
nearly approximating at their umbones than in figs. 38 & 38 a. Showing through
the mantle-surface beneath the shells are the two lobes of the gastric chamber, now
undergoing those curious developments of its cell-elements of which mention has just
been made.
Plate 4. figs. 40, 41, 42 represent a series of the modifications which the cell-
elements of the gastric chamber undergo. They are taken from different embryos of
three successive ages. A number of large pellucid nuclei first make their appearance,
MDCCCLXXV. c
10
MR. E. RAT LANKESTER ON THE
highly refringent, entirely devoid of structure, and very conspicuous. These are sur
rounded by a coarsely granular matter. What relation these nuclei hear to the original
elements of the hypoblast is not known. Nucleoli commence to appear in these nuclei
(Plate 4. fig. 41), and these enlarge very much, developing secondary and tertiary
nucleoli, whilst more than one primary nucleolus makes its appearance in each of the
original refringent bodies. The explanation of this sudden and striking cell-develop-
ment requires more extended study, but it looks like a rapid process of endogenous
proliferation.
Plate 4. fig. 43 is chiefly interesting as showing the position of the mouth (o) and
the form of the mantle ( mn ). The great gastric chamber obscures the full view of the
root of the foot, which is seen lying symmetrically between the flaps of the mantle
behind the mouth.
Plate 4. fig. 38 a sufficiently explains itself. Fig. 43 h gives a view of detached cel-
lular masses lying within the faintly indicated wall of the gastric chamber at a stage
corresponding to that of fig. 37. Their significance is obscure.
Plate 4. figs. 44 & 45 have been already alluded to as giving highly enlarged views
of processes from the epidermis budding inward, which appear to be the foundations of
the organ of Bojanus of one side. They are seen in their natural position close to the
rectal peduncle in Plate 3. figs. 36 & 37, B.
Plate 4. fig. 46 again brings us a large step forward in the developmental history
of Pisidium ; and beyond the stage here presented I have not followed it. The shell-
valves ( v ) have increased largely in size ; the mantle-border (mn), hanging like a skirt all
round the foot, covers it more and more. But the new feature which marks this stage
of development is the appearance of the rudiments of the branchige (hr). On each side
they are seen as four blunt processes springing from a line which runs towards the mouth
from the angle formed posteriorly by the junction of the foot with the mantle. They
now appear confined to this region at the posterior root of the foot; but later, as
appears from Leydig’s researches on Cyclas cornea , extend in the direction of their basal
line towards the mouth — that is to say, new buds make their appearance along this line
on each side of the foot, progressing from the posterior to the anterior pedal region.
The origin of the gill-lamellse of the Lamellibranchiata as short stump-like tentacles
which become ciliated has long since been worked out by Loven. Its significance
has been, I am inclined to think, overlooked. In relation to this matter' I will now
merely draw attention to the close general agreement of the disposition of these tentacular
branchiae, the foot, the mouth, and the anus in this embryo Pisidium (see Plate 4.
fig. 52), with the disposition of tentacles, epistoma, mouth, and anus in a Hippocrepian
Polyzoon, or more strikingly with the same parts in the exceedingly interesting form
Phabdojpleura, as worked out by M. G. O. Saks*, where, if the so-called “buccal shield”
be taken as the equivalent of the Lamellibranch’s foot, the homology of the gill-tentacles
in the two cases cannot appear doubtful.
* Quart. Journ. Micr. Sci., Jan. 1874.
DEVELOPMENTAL HISTOBY OE THE MOLLUSCA.
11
The mass of the central portion of the alimentary canal and its glands has in the
present stage of development become dark granular, and its details very obscure.
Anteriorly to the umbones of the shell-valves in the middle line appears a vesicle (?;)
which lies below the surface, but is not imbedded in the tissue of the alimentary tract.
One might take it for the commencing pericardium or cardiac ventricle, but that those
structures certainly in later life lie posteriorly to the umbones.
Plate 4. fig. 47 presents the same specimen as that of fig. 46, seen from the pedal
aspect instead of the umbonal aspect.
The drawing is not made so as to give a definite plane of optical section, but parts
are allowed to show themselves in virtue of the partial translucency of the embryo.
Plate 4. fig. 48 gives a more highly magnified view of the problematical vesicle, v,
of figs. 47, 46.
Plate 4. fig. 49. The same vesicle from another specimen, in which it is less strongly
marked.
Plate 4. fig. 50 represents an embryo a very little younger than that of Plate 4.
figs. 46 & 47 (less developed by one gill-process), drawn with the camera lucida. The
arrangement of the dark and clear masses in the central mass of tissue belonging to the
alimentary tract is of interest as indicating an approaching differentiation into the coils
of the intestine and the glandular adjacent liver. The rectum ( rp ) is here obvious, its
walls having become thin and translucent as compared with their former condition, when
we spoke of them as “ the rectal peduncle.” The anus is now perforate. At Ir the
lumen of the rectum as it opens into the now much modified gastric chamber is seen.
On either side the rectum two coiled tubes (B), the exact disposition of which it is
impossible to make out on account of their delicacy and the not too great transparency
of the body-wall, are to be observed. The position and character of these delicate
structures renders it exceedingly probable that they are the future organs of Bojanus,
and are developed from the rudiments marked B in earlier figures.
In front of the shell-valves in this figure (50) a transverse striation lying below the
surface Ad marks the commencing differentiation of the anterior adductor muscle.
Plate 4. figs. 51 & 52 represent, somewhat schematically, an earlier and the present
phase of the development of Pisidium.
In figure 51 the arrows indicate the direction of ciliary currents, by which matters
(chiefly or perhaps entirely liquid matter) are passed round the two lobes of the gastric
chamber.
At this stage my observations on Pisidium cease. There are some structures the
rudiments of which I was continually in search of, which seem to deserve mention on
account of their absence. For instance, the byssal gland figured by Leydjg in the foot
of Cyclas cornea at an early period (quite within the period here gone over) was absent.
No trace of any thickenings or invaginations to lay the foundation of the otocysts,
nor of the cephalic, pedal, or branchial ganglia, was to be detected.
c 2
12
ME. E. EAT LANKESTEE ON THE
A study of the later phases of Pisidimn pusillum would no doubt throw some light
on the origin of these structures as well as on the origin of the labial tentacles, the
nature of which, especially in relation to the branchiae, requires investigation.
Explanation of the lettering of the figures in Plates 1, 2, 3, 4.
a. Anus.
al. Central portion of the alimentary tract.
Ad. Anterior adductor muscle.
B. Rudiments of Bojanus’s organs.
hr. Branchial buds.
ci. Cilia.
ci'. Cilia of the mesoblastic cavity.
chy. Lumen of the hypoblastic invagination.
ep. Epiblast.
/. Foot.
hy. Hypoblast formed by invagination.
Ir. Lumen of the rectum.
me. Mesoblastic cells.
mn. Mantle-flap or border.
o. Mouth.
p. Cells apparently in the act of budding off from the hypoblast to form meso-
blastic elements.
pd. One of these cells dividing into four.
ph. Pharynx.
rp. Rectal peduncle of the hypoblast.
rc. Ctecal termination of the alimentary canal.
sh. Shell-groove or shell-gland.
v. Problematic vesicle.
x. Large cells doubtful as to being epiblastic or mesoblastic.
y. Large cells persisting until late development in the epipharyngeal region.
DEVELOPMENTAL HISTORY OE THE MOLLUSCA.
13
No. II. The Early Development of two Species of Aplysia (Aplysia depilans and
Pleurobranchidium, sp.).
At Naples, in the winter of 1871-72, I searched for the ova of some Gasteropodous
mollusk which would by their transparency permit the same kind of study with high
powers as to the early phenomena of development as those of Pisidium had previously
enabled me to carry on. Generally the ova of Mollusca are so highly charged with
finely granular matter, and the limits of the individual embryonic cells so little defined,
that it is impossible to do much with them on account either of opacity or of in-
definiteness. The eggs of some Nudibranchs afforded interesting results as to the mode
of formation of the “ Gastrula ” by invagination, which form the subject of a further
communication ; but the particular ova which seemed most favourable for study, on
account of transparency, clean definition of parts, and unlimited abundance, were those
of Aplysia. I kept the eggs of two species of this genus (or rather species of Aplysia
and of the subgenus Pleurobranchidium) under examination from time to time during
several months. The eggs occur in masses, which resemble vermicelli, and are known
by that name to the Neapolitan fishermen. The object of my work did not lead me to
identify the precise species of Aplysia to which my observations refer. I am, however,
able to identify the egg-coils ; and it is sufficient for all questions of histological and
embryological interest to distinguish these as the larger and the smaller species of
Aplysia (A. major and A. minor). I am nearly certain that my A. major is the common
big A. depilans. It is the largest Aplysia which is common in the Bay of Naples. On
the other hand, all I can say of my A. minor is that it is a much smaller species than
the former ; and from comparison of eggs laid by a Pleurobranchidium , I take it to be a
species of that subgenus. The egg-coils are distinguished by their size. Those of
A. major are about one tenth of an inch in diameter, whilst those of A. minor are but
two thirds of that width. The coils are, further, very completely distinguished by struc-
ture involving a numerical character. The substance of the coils is a crisp gelatinous
material, in which are closely packed spherical capsules (Plate 5. fig. 1, a). These
capsules are of nearly the same size in the two species — a very little larger in the larger
species. But whereas in the larger species each capsule contains from thirty to forty
ova, each one of which undergoes development up to a far-advanced stage, in the
smaller species each capsule contains but from five to seven ova, each one of which
develops and finally emerges from the capsule as a swimming embryo.
In the case of the smaller species, I kept the eggs from the earliest condition of
cleavage to the liberation of the veliger embryos ; but when once free I could no longer
retain them in my tank, since they were carried away by the stream of sea-water which
it was necessary to use to ensure aeration. The constant injection of a fine jet of air
into a small vessel of sea-water might obviate the difficulty which the water-stream
always presents in the treatment of minute swimming embryos.
In the case of the larger species, I never actually hatched any of the embryos, though
the condition of Plate 6. fig. 37 cannot be far from that in which the embryo escapes.
14
ME. E. EAT LANKESTEE ON THE
The ova and embryos were removed from the capsules for examination by cutting
across the egg-rope. Numbers were always thus extruded on to the glass slip used,
and a certain amount of liquid with them. A small piece of paper being placed at
one corner to protect them from pressure, the thin cover-glass was placed over them.
Abortive Embryos of larger Aplysia. — This is perhaps the place to mention a curious
feature in the history of the larger Aplysia. The egg-capsules in this form contain as
many as thirty or forty ova. They all advance in development to the condition presented
in Plate 6. fig. 24, with well-developed rudimentary shell, velum, &c. But at this
stage numbers of loose shells are to be found in the capsules, and the embryos are fewer
in number. I at first thought that this was a case of casting a larval shell, as observed
by Krohn in some Pteropods ; but it soon became apparent that the embryos to which
these shells belonged had disappeared. In some cases the embryos in a capsule were
reduced to ten only. It is remarkable that just after this period the digestive canal
of the embryos is fit to function — the mouth opens, and the primitive stomach-sac is
ready to receive food.
It seems most probable that we have here, then, a parallel to the case of certain
Gasteropods ( Purpura , Buccinum , Neritina ), in which out of many true ova included in
an egg-capsule only one develops, feeding on the others when it has attained digestive
capacities. In this large Aplysia the destruction and appropriation of the weaker
embryos is not consummated until they have all considerably advanced in development,
and then a desperate struggle and subsequent cannibalism takes place.
It is possible to suggest as an explanation of what occurred, in the egg-cords of
A. major kept by me, that abnormal conditions brought on an unhealthy condition
leading to the death of a number of the embryos ; but this does not seem to be likely,
though it should be borne in mind as possible.
Nothing of the kind occurred in A. minor , though kept under precisely the same con-
ditions in the same tank with a constant stream of sea-water. This is contrary to the
hypothesis of a diseased condition. One of the chief features of interest in the obser-
vations which follow is the comparison which they afford of the development of two
very closely similar species, which, notwithstanding their marked identity in adult form,
yet exhibit very curious divergences in the details of their early development.
Development of Aplysia major. — Plate 5. fig. 1 represents an ovum from an egg-rope
or egg-coil, in which all were at this very early phase of development. The upper part
of the egg is seen to be coarsely granular and of a yellow tint ; the lower pole is paler
and more transparent. The lower pole corresponds, as will be seen, to the cleavage-
patch of Loligo , the yellow part to the residual yelk* — though here, as in most
Mollusca Gasteropoda, there is not a complete segregation of cleavage-yelk from food-
* March 5th, 1875. — The term “ residual yelk ” I made use of in a portion of this memoir relating to
the development of the Cephalopod Loligo. I have withdrawn the greater part of that section in order to
incorporate observations made in the spring of 1874. In reference to the use of terms descriptive of parts of
the yelk I may refer to my paper in Quart. Journ. Micr. Sci., April 1875.
DEVELOPMENTAL HISTOEY OE THE MOLLUSCA.
15
yelk, and consequently the yellow mass or residual yelk shares in the first cleavage.
In both species of Aplysia it is only this one cleavage which the coloured or residual
yelk undergoes. In other Gasteropods, e. g. Neritina, it cleaves a second time, so as to
form four masses; whilst in other cases, as also in the Batrachia among Vertebrata, we
know that yelk which corresponds to what is here called “ residual” (that is, yelk which
does not itself build up structure) may exhibit a very extensive cleavage, and the
corpuscular or cell-elements therefrom resulting be nevertheless gradually broken down
and absorbed.
At the lower pole of the egg (Plate 5. fig. 1) a shrunken vesicle, marked B,, is
seen escaping from the colourless yelk. It appears to be the remains of the germinal
vesicle, and has been frequently observed by others in a variety of mollusks, being
sometimes spoken of as the “ Richtungsblaschen.” Plate 5. figs. 2, 3 represent the results
of the first two cleavage-furrows. The yellow yelk is in the condition of two larger
balls, the white yelk in the condition of two smaller balls.
Plate 5. fig. 4. The yellow yelk divides no further; but the white yelk now presents
four masses instead of two.
Plate 5. figs. 5, 6, 7. These continue to multiply and spread over the two balls
of yellow yelk, which they finally enclose. Clear pellucid nuclei of large size occur in
the yellow spheres of A. minor at this period (compare the figures, Plate 7), but,
curiously enough, are altogether absent here.
Plate. 5. fig. 8 shows some of the klastoplasts or cleavage-products of the white yelk
after their complete investment of the two spheres of residual yelk. These cleavage-
products not only invest the yellow masses, but are piled up at one pole, the original
cleavage-pole. I sought here for some indication of the 6r«s£rwZa-invagination ; but
obtained no evidence of it. In a recent paper, Dr. Emil Selenea has contrasted the
process of invagination as “ embole,” with that of overgrowth (such as occurs here and
in Loligo ) as “ epibole.” It is not yet clear how far they are equivalent processes or
reciprocally exclusive * The presence of a large mass of “ deutoplasm ” or food-yelk is
what, more than any thing else, seems to necessitate epibole ; and we require much more
numerous and detailed accounts than we at present possess of the origin of the hypo-
blast in various animals before asserting that the enclosure of the mass of residual yelk
(containing often or invariably some formative as well as nutritive material) by the
marginal increase of the cap of small cleavage-products is essentially the same thing
as the enclosure of the hypoblast by invagination. If it were so we should certainly
have, in cases of epibole, to look for the exact equivalents of the invag’inated hypoblastic
corpuscles in corpuscles arising from or making themselves apparent in the mass of
residual or coloured yelk. In cases where this enclosed residual yelk does not give rise
to the hypoblast (the chick, osseous fish, Loligo 1), but in which the latter is derived by
a process of “ lamination ” from the enclosing mass of cleavage-cells, there can be no
* March 7th, 1875. — At the present moment I incline altogether to the view sustained by Kowalevsky in
his invaluable researches on Euaxes and Lumiricus, to the effect that these two processes are one and the same.
16
ME. E. EAT LANKESTEE ON THE
morphological identity between the enclosed portion of the embryo resulting from
epibole and the enclosed portion resulting from embole. But, on the other hand, in
those cases of epibole where, as in Aplysia , and more strikingly in Neritina , there is
clearly formative material mixed with the enclosed nutritive mass as indicated by its
cleavage, we may look for a segregation of that formative material to form hypoblastic
elements ; and if such takes place, the enclosed mass of this case of epibole becomes a
true equivalent of the enclosed mass of embole. Nevertheless it must be remembered
that it has not been demonstrated in any one case that the hypoblast has such an origin,
and that in the frog we have corpuscular elements resulting from segmentation, which
serve no other purpose than that of nutritive evanescent yelk.
The ascertainment, then, of the further arrangements and dispositions of the
embryonic cells of Ajplysia has great general interest. The difficulties of observation,
however, entirely prevent any one set of observations from being at all conclusive as to
these questions.
Plate 5. fig. 9 shows an embryo in which the surface-layer of cells has condensed
so as to form a firm “ epiblast,” consisting of but one row of cell-elements ( ejp). The
yellow yelk ( ry ) has commenced to break up, no longer retaining its definite spherical
form, and between the two masses of yellow granular material a mass of colourless
closely aggregated cells has forced itself ( x ). This strongly contrasts with the corre-
sponding phase in Ajylysia minor , where the yelk-spheres retain their form unchanged
(Plate 7. fig. 3). The yelk-spheres may be said in A. major to have now fused with
the cells (%), for there is no demarcation or limit to the two masses ; the individual yellow
angular granules of the yellow yelk retain their sharp outlines, but the matrix in which
they were imbedded seems either to have segregated and become indistinguishable from
cells formed at the original cleavage-pole, or to have been assimilated by those cells,
which have now worked their way between and right into the two yellow spheres.
Plate 5. fig. 9 is a median optical section.
Plate 5. fig. 10 gives the same embryo focused more superficially.
Plate 5. fig. 11. There is now some differentiation in the mass of cells (#), which,
as already explained, may contain corpuscles derived from the yellow spheres, or may
be solely the remnant of the colourless cleavage-yelk after the separation of the
epiblast (<?p). We notice now first of all the formation of a distinct cavity (c), which
must be identified with the mesoblastic cavity of Pisidium , and more generally of
all the embryos of higher animals. But in addition to this the outer cells of the mass
(x) have taken on definite character, and form a dense layer, with fine processes passing
from them to the epiblastic wall. The comparison of this with the similar stage in
Pisidium is instructive.
In this and the preceding figure a pair of cells ( mn ) projecting from the epiblast
are obvious. These two cells constantly appear in this stage of development in various
Nudibranchs. They are seen when followed out to be the first commencement of the
mantle-flap, and indicate approximately a point at which the anus subsequently is
DEVELOPMENTAL HISTORY OF THE MOLLUSCA.
17
placed in the fully formed veliger larva. Plate 5. fig. 9 is in median section, whilst
fig. 11 is somewhat more superficial.
Plate 5. fig. 12 gives a surface-view of the same embryo, indicating the condition of
the surface-cells at this period, as seen in the living condition.
Plate 5. fig. 13 exhibits another embryo in the same plane of optical section
(approximately) as that given in fig. 9. The differentiation of the outer lot of the
original cell-mass ( x ) to form a markedly denser layer {me) is shown. In this specimen
minute actively vibrating cilia were detected among the cells (ci). They may correspond
to the mesoblastic cilia described in the preceding contribution in Pisidium, or may
be only the forerunners of the general ciliation of the gastric cavity. This latter view
is the more probable, since it is undoubtedly from cells occupying the position ci that
the epithelium of the chief alimentary cavity must be formed in this species of Aplysia.
At the point marked slip a thickening of the epiblast is indicated, which is the
commencement of the secreting-area of the shell or shell-patch, as it is convenient to
call it. In the Aplysia minor it will be seen how strongly developed this patch
becomes, so that it readily is detached from the embryo with its delicate circular
secretion — the rudimentary shell. It corresponds with the shell-groove of Pisidium.
Plate 5. fig. 14. The same plane of optical section of a more advanced embryo.
The ring of cilia (vv) which now appears, indicating the velum, is seen at the points where
it is traversed by the plane of section. At ot the first indication of the otocysts, that
of the right side, is seen. In Plate 5. figs. 17 & 18 the earliest commencement of
this organ is more fully exhibited. It originates as a vacuolation of a spot in the
epiblast near to the commencing oral invagination. It never communicates with the
exterior ; and by the unequal development of surrounding parts it is gradually trans-
ferred from this primitive position to that which it subsequently occupies in the foot.
I shall speak of this again in describing the same stage in A. minor.
In Plate 5. fig. 14 the epiblast is also seen to be considerably thickened at the
uppermost point, v. It is here that the inward growth to form mouth and pharynx
rapidly takes place. The history of mesoblast and hypoblast is to some extent affected
by what is shown in the lower part of the figure. Between the darker wall-marked ime. ,
which seems to correspond with me of fig. 13, and the shell-patch there now appears a
mass of cells ( pme ), the origin of which is quite uncertain. A similar mass appears at a
corresponding period in Ap. minor , and they must have one of two origins ; either they
have been “delaminated” (proliferated) from the epiblastic mass of the shell-patch, or
they are segregated from me of fig. 13. It is really of considerable importance to deter-
mine which view is correct ; for this mass {pme) appears to be concerned, most certainly
in the case of A. minor , in building up the intestinal portion of the alimentary canal,
perhaps only furnishing its outer walls. In A. major the position of this mass of
cells does not permit one so readily to follow out its connexion with the alimentary
canal as in A. minor. These two tracts of cell-aggregates I distinguish as inner meso-
blast ( ime ) and parietal mesoblast {pme), without attributing definitely a particular
MDCCCLXXV. D
18
ME. E. EAY LANKESTEE ON THE
origin to them, or a particular further development, exceping so far as that it is obvious
that ime forms the chief bulk of the wall of the primitive gastric sac of A. major , though
probably not its lining epithelium.
Plate 5. fig. 15 is another and very similar embryo, in which the same arrangement
of parts is observed.
Plate 5. fig. 16 is an embryo a very little further advanced and a little turned on
its axis. The “clearing up” or “hollowing out” of the primitive gastric cavity is now
advancing, though not yet is there any thing like a well-defined space there, but merely
a looseness and fluidity of material, such as accompanies the formation of a cavity by
absorption.
Plate 5. figs. 17, 18 have been already referred to. They exhibit on a larger scale
the earliest indication of the otocysts ; fig. 17 that of the right-hand side, fig. 18 that of
the left-hand side. This first rudiment of the otocyst developing in the epiblast may
be termed the “ otocystic vacuole.”
Plate 5. fig. 19 takes the development a step beyond fig. 16. The alimentary cavity
( al ) is much more distinctly marked, and the mass of tissue which has grown inward
from the epiblast to form the pharynx (ph) is in conjunction with it. The foot (f) is
beginning to push itself forward, and the velum ( v ) is becoming elevated into a kind
of cap.
A main point of interest in this stage of development, as compared with A. minor ,
is that the yellow yelk-granules are constituents of the mass which forms the wall of
the primitive alimentary cavity. In A. minor they remain outside it entirely, persisting
as the original nucleated yellow yelk-spheres, absolutely unchanged morphologically
until the embryo is of large size and freely swimming with its alimentary canal highly
developed ; they dwindle by absorption of their material and become relatively minute
bodies as the embryo increases in size, but they do not , as in A. major , enter into
the actual substance of the wall of the alimentary canal.
A close parallel to this is seen in the development of two allied Oligochsetous Anne-
lids described by Kowalevsky, Euaxes and Lumbricus. In the former there is a
large quantity of nutritive matter in the form of angular granules mixed with the egg as
laid. This granular matter, by the process of segregation and invagination (by epibole),
becomes confined to the central part of the embryo. The large cells of which this mass is
formed differentiate to form the glandular lining of the alimentary canal, enclosing a
number of the large cells as “ contents” to the alimentary cavity, which are gradually
absorbed. The primitive hypoblastic wall of the alimentary cavity is thus formed
by protoplasmic elements, each of which is distended with coarse angular granules,
which are only gradually absorbed. This is parallel to the case of Aplysia major.
In Lumbricus the egg is much smaller and comparatively free from an admixture of
coarse deutoplasmic particles. The hypoblastic wall of the alimentary canal, when
developed, is also free from them, and consists of pellucid columnar cells. This agrees
with A. minor, excepting (and this is an important distinction, for which it is not easy to
DEVELOPMENTAL HISTOEY OF THE MOLLUSCA.
19
find a parallel outside the class Mollusca) that in A. minor there is a quantity of
granular nutritive yelk, which, though not forming part of the substance of the hypo-
blastic corpuscles, nor yet enclosed within the alimentary cavity, remains in contact
with the developing alimentary canal lying outside its cavity *, as is seen on a very
much larger scale in Loligo.
Plate 5. fig. 21 displays the shell-patch when seen from above. It has now grown
to some thickness, as may also be remarked in fig. 20. The patch is in the fresh
condition, and its constituent cell-elements are not discernible; but the important
feature which it exhibits is the groove or slight invagination. It thus presents the
most striking correspondence with the grooved shell-patch of the Lamellibranch Pisidium
described in the preceding contribution.
Plate 5. fig. 22 is a portion of the foot of such an embryo as fig. 20, on which a
little fresh water has been allowed to act. This separates and brings into view the con-
stituent cell-elements of the epiblast.
Plate 6. figs. 23, 24. We now pass to a much more advanced embryo. The
shell is well marked and shovel-shaped. It is in this phase that I found so many of the
shells loose in the egg-capsules and packed one within the other, the embryos to which
they belonged having become broken up, either by a normal process or owing to some
injurious conditions.
The embryos now become very difficult to examine. The slightest pressure is apt to
cause them to fall out of the shell, and endosmotic action swells out the body-wall in
the way seen in fig. 23. At the same time the velum being now well grown, they swim
about with incessant activity. A slight pressure is sufficient to rupture the embryo
and separate the foot and velum from the rest, as seen in fig. 35. Such fragments show
well, however, the true form of the velum at this period. In figs. 23, 24 the focus is so
arranged as to give a surface-view of the mass of the alimentary cavity. The strongly
marked sulcus results from the original separation of the yellow yelk-masses.
Plate 6. fig. 25, 26, 27, 28 are different views of the shells at this stage of growth.
The narrower end has the brownish-yellow colour belonging to chitinous substance.
Plate 6. fig. 29 is a somewhat more advanced embryo, the focus taking a plane below
the surface of the wall of the alimentary cavity. The tract of the pharynx is now very
sharply marked out, though at present it is only a plug of ingrown epiblast, and not a
tubular body. In the velum-area a thickening of the epiblast is seen forming a distinct
boss or lobe, which appears to be the commencement of the cephalic nerve-ganglion.
The shell is not represented in fig. 29.
Plate 6. fig. 30 represents the alimentary cavity of the same embryo, more superficially
focused, so as to display the sulcus and the disposition of the yelk-granules.
* March. 7th, 1875. — Therefore in the mesohlastic cavity. Such a position being occupied by a part of the
endoderm or hypoblast, suggests a comparison with the development of Sagitta, where the mesohlastic cavity
has been shown by Kowalevsky to be simply an outgrowth of the primitive endoderm, as in Echinoderms
according to Mecznikow.
20
MR. E. RAY LANKESTER ON THE
Plate 6. fig. 31. The operculum appears on the lower surface of the whole length
of the foot (op), and the mouth (o) is commencing to break through the pharyngeal
plug. The otocyst ( ot ) is now seen to have become quite detached from the epiblast in
which it originated. The original vacuolar cavity is surrounded by regularly disposed
columnar cell-elements. It is still free from any solid contents.
Plate 6. fig. 32 is a portion of the body-wall more highly magnified, to show (fa)
fusiform cells lying just below its surface, which appear to be the muscular elements of
the parietes.
Plate 6. fig. 33 represents the left face of such an embryo as that of fig. 31. It
is focused high, so that the surface of the alimentary mass is in view, and also the
surface of the cephalopedal region. This brings into view the fold dv (descending
border of the velum), by which the edge of the velum is continued on each side on to
the foot. The embryo is now becoming markedly unilateral in its external features, as
may be seen by comparing the next figure with the present.
Plate 6. fig. 34 represents a similar view to that given in fig. 33, but now it is of the
right side of the embryo. It is on this (the right side), as in other Nudibranchs, that
the two cells already so early distinguished (mn) develop into a prominent mass, at
which point subsequently the anal termination of the alimentary canal develops, and
from which there grows also a fold which partially overlaps the shell in this region, and
increases in extent so as to form the rudiment of a mantle-flap.
Plate 6. fig. 35 is a detached cephalopedal mass, or velum and foot, of the phase
represented in fig. 29. The horseshoe-shape of the velum with the mouth (o) lying
in its hollow is well exhibited.
Plate 6. fig. 36 represents an embryo further advanced. The shell is not here seen
of its proper proportionate size, on account of the position into which it has slipped.
The marked advance in this embryo consists in the clear definition of the cavity of
the double gastric sac ( al ), and its attachment to the body-wall by transverse muscular
fibre-cells.
Plate 6. fig. 37 is not quite so far advanced ; but greater detail is given of the cephalic
regions. In particular, fibres are seen passing backwards from the neighbourhood of
the cephalic ganglion ( ng ), which is now large. They may be muscular attachments to
the pharynx or nerves.
In Plate 6. figs. 36, 37, the furthest stage to which I have traced A. major is
given. The history so far furnishes interesting data for comparison with A. minor
and with other Mollusca, though I have fully stated the doubts and guesses connected
with the interpretation of much which is figured. In this, as in other cases, the figures
must at any rate serve as a basis of fact, interpret them how we may. In a subject so
vague and tentative as the embryology of the lower animal classes must for some time
remain, the best contribution which one can expect as yet to offer towards unravelling
the complicated phenomena, is the observation and record of fact — a contribution which
can best be effected by few words and copious drawings.
DEVELOPMENTAL HISTOEY OF THE MOLLTJSCA.
21
The condition of the alimentary tract in the embryo of Aplysia major as we now
leave it is exceedingly interesting, and is never presented by the embryo of Aplysia
minor, nor by other Nudibranchs studied by me. It is in the condition of a pair of
freely communicating gastric chambers, or a double chamber which is connected by a
pharynx with the exterior, but is entirely devoid of rectum or anus. It would be
important to ascertain how these latter organs make their appearance. At the same
time, if the figures of the development of Pisidium pusillum are referred to, it will be
seen that at one time Pisidium is in a closely similar condition, having a perforate
pharynx leading into a double gastric chamber, which is suspended in a large body-
cavity, and though possessed of a so-named “ rectal peduncle ” due to the very earliest
feature of the development, yet this peduncle is relatively very small, and does not open
to the exterior.
Development of Aplysia minoi :—PleurobrancMdium, sp. — We must now go back to
the earliest stages of development, to compare them with those of the smaller species of
Aplysia figured in Plates 7 & 8 of this memoir.
Plate 7. fig. 1 represents a single ovum of A. minor in the condition exactly corre-
sponding to fig. 5 of Plate 5 of A. major.
Fig. 2 represents a condition further advanced, in that the colourless cleavage-
products have extended round the two yellow spheres. It corresponds exactly to fig. 7
of Plate 1 ; but we observe this difference between the two. In A. minor the yellow
yelk-spheres are, each of them, beginning to show evidence of a central pellucid nucleus.
Plate 7. fig. 3 brings us on to the stage corresponding with Plate 5. fig. 9 ; and now
the differences are more obvious between the two species. In the present species the
outermost cleavage-cells have “condensed,” if that expression is allowable, to form a very
clearly marked epiblast ( ep ). Already this is thickened at the aboral pole, to form the
basis of the shell-patch (slip). The two pioneer-cells of the mantle (mn) are prominent ;
and within we have, as in A. major , the yellow residual yelk-spheres (ry), and a mass of
undifferentiated cleavage-products (x). But the condition of the yellow masses is very
different to that of those in the same stage of A. major : their outline is strongly marked ;
they retain their circular contour, and possess each a large brilliant and colourless
nucleus. There is no question in this case of any breaking up of the yellow masses, or
of their possibly furnishing formative elements by segregation to take the sole or a part
of the work of building the hypoblast. They remain sharply defined, and keep their
granular angular particles compacted together throughout the subsequent stages of
development, although they become distorted and flattened by the pressure upon them
of other growing elements, and probably dwindle and thin out in consequence of the
absorption of some of their material.
Plate 7. fig. 3 is very carefully rendered in every detail, as seen under a Hartnack’s
10 d immersion. The figure represents an optical section in the median plane, and
the region which will give rise to the foot is turned to the right.
Plate 7. fig. 4 represents a similar view of an embryo a little further advanced, in
22
ME. E. EAY LANKESTEE ON THE
which the potential foot is to the left. In this figure a darker mass of cells (x) is distin-
guished from a paler group {,pme). There can be no doubt that the cleavage-corpuscles
enclosed by the epiblast are now in process of arranging themselves, to lay the founda-
tions of particular groups of organs ; but whether x in this case is to be regarded merely
as a mass of primitive cells from which pme have become detached, or as a group
destined to give rise to the hypoblast, subsequent phases of development do not enable
me to decide. I am inclined to take the latter vidw, especially on looking at the position
occupied by the mass x in fig. 5.
Plate 7. fig. 5 is a little further advanced than fig. 4. Already the circle of cilia
belonging to the velum are present, and the first invagination of the epiblast for the
pharynx (ph). The mass x is now clearly separate from pme ; and it is now time to
point out that the subsequent development of the embryo most fully agrees with the
view that this mass ( x ) coming into close relation with the yellow spheres, gives rise
to the hypoblast of the alimentary canal, whilst the mass pme, which is still in part
actually continuous with the epiblastic wall (see fig. 11), forms the muscular wall of the
alimentary canal, and especially develops the whole of its terminal part, being gradually
eaten into by the cavity of the alimentary canal by the growth of the hypoblast : that
is to say, in other words, the cavity of the main chamber or stomach is first formed by
the development of the mass x> whilst jpme forms the outer wall of the intestine, into
which an outgrowth from the stomach gradually extends. I do not wish to attach any
importance to these statements beyond that of suggestions ; for the investigation is a
very difficult one on account of the smallness of the embryos and their want of clearness
in detail of structure, though in this respect they are better than most molluscan embryos.
Plate 7. fig. 8 shows the pharynx further advanced (ph) ; the shell already exists as
a delicate pellicle ( sh ), and the foot (/) is beginning to push. Now is the earliest period
at which I have seen the otocyst ( ot ) in this species. On account of the position in which
the embryo is lying on the glass slip, the otocyst is not brought to the edge of the section,
but is seen lying in the foot. It is, however, still near the surface, and is in the
condition of a vacuole excavated in the thick epiblast of this part.
Plate 7. fig. 6 gives a much more superficial view of an embryo of the same stage
in a reversed and oblique position. The otocyst {ot) is seen near the surface in the
foot-region. But the most important feature in this drawing is the shell-patch and
shell-groove ( shgr ), which are seen here quite superficially. The close similarity of
this structure to the shell-groove of Pisidium cannot be overlooked. This is the earliest
stage also at which the pigment-spots (one on each side) (pg) are visible. They are
small superficial vesicles, at first circular in outline, containing four finely coloured pink
granules. They enlarge and become oval, whilst the number of granules which they
contain increases. I shall only speak of them as pigment-spots, for their function is
altogether obscure.
Plate 7. figs. 7, 9, 11 represent embryos of one and the same age, not quite so far
advanced as that of fig. 8. Their positions (accidentally assumed as they lay on the
DEVELOPMENTAL HISTOEY OE THE MOLLTJSCA.
23
glass slip) are a little different, and the plane of focus differs a little in each case, being,
however, nearly median, but more superficial in fig. 9 than in figs. 7 & 11. Plate 7.
figs. 7 & 9 are so disposed by focus and attitude as to catch strongly the shell-groove
and the thickened mass of tissue at the aboral pole. In fig. 11 the indentation or groove
itself is out of focus, but the thick epiblast (ep) is well shown, and the mass of adherent
cells (pme), which, as stated above, undoubtedly take a chief part in forming the intes-
tinal portion of the alimentary canal.
Plate 7. figs. 12, 13, 14, 15 show a great advance in the development of the foot and
of the pharynx. They are, however, chiefly of interest in relation to the groove of the
shell-patch, which they show with remarkable clearness. Figs. 12 & 15 present the
same embryo, with the least possible change of focus, fig. 12 being a very minute bit
higher than fig. 15. The result of this little change of plane on the appearance of
both pharynx and of shell-groove enables one to make out the direction and character
of these structures.
The shell-groove is perhaps the most important structure to which I have to draw
attention in this paper, and I may therefore now say a few more words about it. Is
this groove connected with the secretion of the shell 1 or is it perhaps an invagination
to give rise to a block of tissue connected subsequently with the rectum and anus'?
That question occurred to me ; and if the former supposition could not he supported,
the apparent analogy with the shell-groove of JPisidium would be a false one ; also
the possibility that this primitive groove in Mollusca generally may represent the
closed epidermal sac, in which the pen of Loligo is developed, would have no basis.
I am able definitely and conclusively to show that the “ shell-groove ” in Aplysia does
really belong to the shell, and in fact sometimes contains a plug of chitinous secretion,
an imbedded shell in fact, the possible homogen of the internal pen of Cephalopoda.
The specimens which gave this interesting result, and which also throw light on the
connexion of the rectal portion of the alimentary canal with the early aboral thick-
ening of the epiblast and the cell marked pme, are artificially produced deformities.
I was in the habit of keeping egg-coils of Aplysia minor in a basin, through which
there ran a constant current of sea-water. From the same egg-coil I cut from day to
day a small piece of the coil, in order to examine the embryos contained in its capsules.
I noticed that in some cases which had been left for several days untouched, the bit of
the coil near the cut edge had assumed an opaque and curiously pink appearance.
The capsules at this part on examination proved to contain most strange and irregular-
looking embryos, which were, however, in a high state of activity, moving about by
means of their cilia, as though their distorted conformation made little difference to
their vitality. Before proceeding further, I may, however, say that I did not succeed
in bringing such embryos on to an advanced stage of development. Two of these
embryos are represented in Plate 6. figs. A, B, C. Most were similar in condition to
that represented in figs. B, C; but some were as abortive and shapeless as that of
fig. A. Of that embryo I have nothing special to say beyond drawing attention to its
24
MR. E. RAT LANKESTER ON THE
rudimentary condition. All the deformed embryos agreed in this — that the yellow yelk-
spheres were gone ; whether they had been extruded (as I think most probable), or
whether they had been absorbed, I could not determine. In that drawn in figs. B, C,
and in others a simple yellow oily-looking body (ry) appeared to be the only remnant
of the yellow spheres; and from its position it suggests that the rest had escaped
through a rent in the epiblast. The mouth in these deformities was open, the alimen-
tary cavity complete and lined with cilia, its walls nevertheless quite free from any
of the yellow granules of the residual yelk. A peduncle of apparently solid, tissue (B)
passed from the lower part of the gastric sac to the side of the large thickened “ shell-
patch.” The condition of the shell-patch, as exhibited in the specimen figured and
in others, was most important ; for it had produced a thickened and brown-coloured
(chitinous 1) shell of small area, but relatively great solidity. A button or knob (pi)
continuous with this thick disk-like shell occupied the groove or indentation of the
shell-gland, forming thus an enclosed plug. Thus the real significance of the shell-
groove of the embryo is demonstrated by a pathological condition artificially induced.
In a subsequent part of this memoir will be found the description and figure of a
similar chitinous plug in connexion with the earliest rudiment of the shell in Neritina
Jluviatilis, which I studied at Oxford in May 1873.
The development of the alimentary tract in these deformities, in the absence of the
two yellow yelk-spheres, seems to show that it is independent of them in origin, its
ciliated lining being derived elsewhere than from material furnished by them. And,
again, the separate position and solid condition of the intestinal piece marked It agrees
well with what has been put forward above as to the origin of the two parts of the
alimentary canal. The gradual pushing of the ciliated lining of the gastric cavity (al)
along the solid piece B would give an intestine lined by “ hypoblast ” and built up
exteriorly by mesoblastic muscular elements.
Plate 7. figs. 10 & 16 show two planes of one embryo, the pigment-spot (pg) being
introduced into each as a fixed point of comparison. The foot and velum are now
taking definite shape, the former already provided with a very delicate operculum.
From the anterior horizontal border of the velum a fold ( dv ) descends on each side of
the foot as in A. major. In the deeper view (fig. 10) the letters int mark a part of
the cell-mass ( pme ) of fig. 11, now assuming development as part of the alimentary tract.
The figures on Plate 8 chiefly illustrate what can he ascertained of the development
of the alimentary canal.
Plate 8. fig. 18 is the most rudimentary shell, discoid in form, with an irregular
surface, hyaline and exceedingly delicate in texture.
Plate 8. fig. 19 is the shell-patch as detached by pressure sufficient to break the
embryo. The same structure was figured from A. major in Plate 5. fig. 21.
Plate 8. fig. 20 represents an embryo (of the same lot as that drawn in fig. 17) seen
from behind in such a position that the posterior border of the velum forms its upper-
boundary. Seen through is the pharynx ( ph ), and on each side (also seen through)
are the pigment-spots (pg).
DEVELOPMENTAL HISTOEY OF THE MOLLTJSCA.
25
Plate 8. fig. 21 represents a similar embryo seen from before, in such a position that
only the ciliated border of the velum is in view. The anterior margin of the foot here
forms the upper boundary of the figure. The want of bilateral symmetry due to the
development of the region in connexion with the early-appearing mantle-cells (inn) is
now apparent. The mass of tissue (int) is assuming form as alimentary canal, and is
overlaid by the flattened out, but not disintegrated yellow yelk-spheres. In other
specimens of this age the connexion of the intestinal rudiment with the region mn was
obvious. The continuity was so complete as to suggest the notion of an ingrowth or
invagination of the tissue at the point mn to form the mass int. We have, however,
seen that it is derived from the mass jyme of Plate 7. figs. 8 & 11. In Ajylysia major
no such structure as this int could be made out. The alimentary tract developed as a
double gastric chamber with the yellow yelk imbedded in its walls ; no trace of intestine
or rectal termination could be ascertained, the mass pme apparently giving rise only
to traversing muscular bands (if to any thing). The contrast with the present case is
very strong, and though possibly not rightly understood in the light of my present
observations, must furnish an interesting problem affecting general principles in
embryology.
The series of figures in Plate 8 now must be looked at in connexion with the alimen-
tary canal, and we can then pass through them again in connexion with other details of
velum, foot, nerve-ganglion, &c.
In figs. 17 & 22 certain of the cells which are to take part in the formation of the
alimentary canal, and which have hitherto been obscured by the relatively larger deve-
lopment of other parts, are seen to enlarge very greatly. The mass which they form is
marked int. In fig. 22, at the point A, the cells are so arranged as to enclose a space
as seen in the enlarged drawing (fig. 23) ; in fig. 24 a quite superficial view of the same
group of cells is given, and fig. 25 an intermediate view. It is seen from these drawings
that we have here large pellucid cells devoid of nucleus.
Plate 8. fig. 26 shows that these cells have not, in the stage represented in Plate 8.
fig. 22, attained their full growth. They are now individually of very large size, and
occupy a great part of the embryo. This has grown considerably in size, whilst the
relative bulk of the colourless elements of the alimentary tract and of the persisting
yellow yelk-masses is greatly changed. In fig. 26 attention must be drawn to what is
the most definite phenomenon to which one can point in this part of the development
of Aplysia minor — namely, the growth of some of the colourless cells into the substance
of the yellow yelk at the point marked in this figure int , resulting in the cutting off
of a piece of this material from the rest of the yellow residuary yelk. This detached
piece is marked dry. The detached piece does not retain its coarsely granular character,
but speedily becomes broken down in substance and changed in colour to a dirty brown.
This detached piece is rapidly invested by the colourless cells, and becomes, in the fully
formed veliger- larva, a sac-like mass lying by the side of the anus — almost certainly the
renal organ, the homogen of the Lamellibranch’s organ of Bojanus, and of the cuttle-
MDCCCLXXV. E
26
ME. E. EAT LANKESTEE ON THE
fish’s ink-bag. It does not follow because its foundations are thus laid that its lining
cell-layer is not derived from ingrowth of the epiblast, which is what one would look for.
In Plate 8. fig. 27 the large cells have given rise to smaller cells more closely packed,
and giving indications of the outlines of the coils of the alimentary canal (int), The
wall of the detached piece of yellow yelk has become clearly defined.
The steps of the passage to the condition of fig. 28, and from this to the phases repre-
sented in figs. 82 & 38, are so much obscured by difficulties of observation, that I doubt
whether it can be useful to attempt a rationale of them.
It is sufficient to point out that in Plate 8. fig. 28 the cavities are becoming more
clearly defined ; and whilst the embryo has increased in size, they continue to prepon-
derate more and more over the yellow yelk-masses.
Plate 8. fig. 29 represents the alimentary tract and surroundings of the same embryo,
focused at a somewhat higher level.
Plate 8. figs. 30 & 31 represent respectively the right lateral and the left lateral
aspects of a more advanced embryo. The part marked int is now clearly enough to be
identified as the chief gastric cavity, and its inner surface is covered with vibrating cilia.
The part marked int' is the rectum, which turns suddenly upon the gastric chamber.
It is this which was first sketched out by those cells which intruded themselves between
dry and ry. The rectum is not as yet perforate.
Plate 8. figs. 33 & 34 give a right and left lateral aspect respectively of an embryo
of Aplysia minor at the time of quitting the egg-capsule. The whole region of the
alimentary tract is now fully formed, though possibly there is no anal aperture at A as
yet. The residual yelk (ry) still remains, each original yellow sphere still retaining its
large clear nucleus, though now no longer a sphere, but rather a disk-like body. F rom
what appears to take place in other Nudibranchs, and indeed in the Cephalopoda also,
it is pretty certain that duct-forming outgrowths from the wall o£ the gastric cavity
penetrate these masses, and assimilating and absorbing their substance, establish in the
place occupied by them the molluscan liver.
Plate 8. fig. 32. In all the views given of the later growth of the Aplysia embryo the
oesophagus is obscured by the yellow yelk-masses which lie in the way of a lateral view ;
but when looked at from above, as in fig. 32, and rightly focused, the whole of the first
part of the alimentary canal may be very clearly made out as a ciliated tract running
from the mouth to the gastric cavity marked int in the figure, and passing between the
two yellow yelk-spheres.
In fig. 32 the embryo is closely drawn into its shell, and the plane of focus is near
the surface, so that the outline of the shell and the superficial extent of the yellow yelk-
masses is given to advantage. The figure represents the embryo after its escape from
the capsule.
We may now pass back for a moment to note the development of the nerve-
ganglion. As in A. major, this is seen, in Plate 8. fig. 22, making its appearance as a
thickening of the epiblast in the velar region. In Plate 8. fig. 26 it is large and
DEVELOPMENTAL HISTOKT OF THE MOLLUSCA.
27
sharply defined. In Plate 8. fig. 28 it has become fully differentiated from the overlying
tissue, and consists of a separate pair of rounded bodies (of which one only is seen in
this side view). In close connexion with it are other smaller rounded masses of the
same appearance {ng' and ng "). It seems very probable that these are outgrowths from
the primary nervous mass to form the pedal ganglia. The otocyst is seen in close rela-
tion with these supposed nervous masses. Of the otocyst it is merely necessary to point
out that the cells surrounding it gradually form for it a definite wall, and that then in
its centre appears a small otolith which gradually increases in size. It is not uncommon
for the otolith to make its appearance in one of the two otocysts before it does in the
other, as in Plate 10. fig. 5.
The muscle of the velum marked mv in Plate 8. fig. 22 is worth mention, since it
appears at an early period. It passes from the border of the velum to the foot. By
the contraction of this muscle the velum becomes doubled to some extent on itself, as
seen in figs. 30, 31, and the movement of the cilia stops.
The sudden stoppage of the cilia of the velum during life, and the erect sheaf-like
appearance which they assume, is quite different to the stoppage and disordered entan-
glement which they exhibit when the embryo is killed by acid. The rigid character of
the position of rest of these large cilia is exactly repeated in the case of the perianal
circlet of large cilia in such Annelidan embryos as that of Terebella.
The first trace of the great posteriorly placed retractor muscle may be made out in
embryos which are looked at from behind, when of about the same age as that of fig. 28.
The further differentiation of this finely fibrillar muscular band is seen in figs. 31 & 34,
M, M'. I was unable to observe the mode of development of this structure, though
in some Nudibranchs its differentiation from corpuscular elements lying beneath the
epiblast, and derived originally from it as a part of the parietal layer of the mesoblast,
is clear enough.
The matters of interest to which it has been the object of this part of the present
communication to draw attention are as follows : —
1. The primitive arrangement of the results of the cleavage-process.
2. The mode of development of the otocysts, by vacuolation of the epiblast.
3. The development of the cephalic-nerve ganglion-pair as a thickening of the
epiblast.
4. The “ shell-patch,” “ shell-groove,” and its plug.
5. Artificially produced monstrosities of the embryo.
6. Points of wide divergence in the development of the alimentary tract, and its rela-
tion to the yellow residual yelk-masses, between the two closely allied species here
spoken of as Ajplysia major and Aplysia minor.
28
MR. E. RAT LANKESTER ON THE
No. III. The Early Development of Tergipes, Polycera, Tethys, Neritina, Limax, and
Limnseus.
Tergipes. — The early history of the development of some of the Nudibranchs is of
considerable interest, since it clearly exhibits a Gastrula phase similar to that described
in my contribution on Pisidium, but which I could not discover in Aplysia. Carl
Vogt, in his memoir on the development of Actceon , has described and figured the
“ sillon ” which results from the invagination of the wall of the primitive blastosphere ;
but he did not distinctly recognize it as an invagination, nor are his figures sufficiently
large to give much information on the subject.
In Plate 9 the early development of a small Tergipes , the species of which I did not
identify, but which was common at Naples, is given. The invagination is very well
marked in this case, since there is relatively but a small amount of “ deutoplasm ”
present in the egg, that constant disturber of typical modes of development and of
satisfactory observation of the eggs by transmitted light.
Plate 9. fig. 1. The cleavage-cells do not present great disproportion in size.
Plate 9. fig. 2. Already in the centre there is a pit due to the tucking in of the
cleavage-products.
Plate 9. fig. 3 gives a later embryo in optical section. The invaginated group of
cells ( liy ) are seen lying within the wall-forming cells (ep). The cavity of the invaginated
group (C) still communicates with the exterior.
Plate 9. fig. 4 is an optical section at right angles to the preceding, so that the aper-
ture of invagination is not brought into view.
Plate 9. fig. 5. A surface-view of an embryo at the same stage, showing the long
groove formed by the aperture of invagination. This is the groove detected by Vogt
in Actceon. It closes up shortly, and the layers of the embryo proceed on their special
lines of development.
Plate 9. fig. 6 shows the embryo with the aperture of invagination or Gastrula-
mouth* now closed. The velar circlet of cilia has developed, and the two layers of the
embryo are breaking up into smaller and specially differentiated cells or corpuscles.
Plate 9. figs. 7, 8 show the separation of a middle layer (me) between the inner
and outer. It appears to be derived from the epiblast, to judge from the appearances
seen in Plate 9. fig. 7 ; but the hypoblast may also contribute to its formation.
Plate 9. fig. 9. Surface-view of the aboral pole of an embryo of the same stage as
the preceding, showing a fold or scar which is the remnant of the primitive invagination
aperture.
Plate 9. fig. 10 represents an embryo in which velum ( v ), foot ( f ), and shell (sh)
are already taking form. The pharyngeal invagination (o) is also indicated.
In this and preceding figures two small cells are marked It, which appear to be
“ Kichtungsblaschen they are well known in the development of Mollusca.
Plate 9. fig. 11 represents the embryo at a much more advanced stage ; the shell is
* March 7th, 1875. — Better called “ blastopore,” since it is not known to represent a mouth.
DEVELOPMENTAL HISTOEY OF THE MOLLTJSCA.
29
of a very peculiar boat-like form, and the velum is placed near the middle of it like a
pair of paddle-wheels. In fig. 11 such an embryo is seen from above. In fig. 12 the
outline of the same is drawn, in order to show the two muscular bands ( m ) which come
into view with a deeper focus. One of these is seen at fig. 12, a as displayed by a
Hartnack’s 10 a immersion.
Polycera and Tethys. — In Plate 10 figures are given of the embryos of Polycera qua-
drilineata and of Tethys at a time when they give evidence of a primitive invagination.
In Plate 10. figs. 1, 2, 3, three views are given of the embryo of Polycera , showing
the long groove of invagination, similar to the condition of Plate 9. fig. 5. The outer
cells are more transparent than the inner.
In Plate 10. figs. 10, 11, an early condition of the yelk-division of Tethys is pre-
sented. I am not able to figure the steps of invagination in this molluscan embryo ;
but the stage illustrated in figures 12 to 16 gives some evidence of the remains of an
aperture of invagination (i).
Plate 10. figs. 12 & 16 are left lateral views ; fig. 13 is a right lateral view; fig. 14
an aboral view ; fig. 15 an oral view of the same embryo.
These embryos are interesting to compare with the early stages of Aplysia described
in the preceding section of this communication. Especially the two mantle-rudiments
( mn ) are to be noted as making here an early appearance as in Aplysia *.
The remaining figures of Polycera embryos, viz. Plate 10. figs. 4-9, are chiefly of
interest for the sake of comparison with the corresponding “ veliger ” of Aplysia.
Plate 10. figs. 4 & 5 represent two views of a young stage in which the shell is just
beginning to appear. The curiously dark-coloured mass (q) I am not able to explain.
In Plate 10. fig. 5 it is seen that one otolith has formed before the other.
Plate 10. figs. 6-9 represent fully formed embryos nearly ready to escape from their
capsules. Fig. 6 is a right lateral view ; fig. 7 a back view ; fig. 8 a front view ;
fig. 9 a three-quarters profile view. A comparison of these figures with those of the
veliger of Aplysia minor will show the close correspondence even to the fusiform
muscle-cells which pass from the perianal mass (dry) to the body-wall.
Neritina Jluviatilis. — Plate 9. figs. 1-8 represent early stages in the development of
this mollusk. It is abundant in the river Thames at Godstow, near Oxford. After
searching in various spots I at last succeeded in obtaining the egg-capsules in quantity
from stones at the bottom of the river in front of the little inn near Godstow Priory.
The stones in this part of the river are covered with the broken remains of the capsules
deposited and hatched-out in former years. The fresh ones in the month of May stud
these stones in great numbers, each capsule being about the size of a large pin’s head.
The specimens obtained thence in 1873 were transferred to the histological laboratory of
* March 7th, 1875. — From observations made in December 1874 and communicated to me by my friend
Mr. F. M. Balfour, of Trinity College, Cambridge, it seems that the cells mn have not, as I supposed, the
same significance as in Aplysia, and that the part marked f in Plate 10. figs. 13 & 16 is not the foot but the
velum.
30
ME. E. EAY LANKESTEE ON THE
Exeter College, and kept there under a slow-running stream of water. Only one out of
the many ova contained in a capsule undergoes cleavage and further development.
The others break up and furnish nutritive material to the developing individual. This
phenomenon, which has been established in other Gasteropods, as by Claparede in
Neritina, connects itself at once with a view which has been with much justice put
forward by Gegenbaur — namely, that the glands in Mollusca and Vermes which secrete
“ deutoplasmic ” material which is appropriated by the growing ovarian egg, or is
enclosed with it in a capsule, are to be regarded as abortive portions of the ovary.
Thus the material which feeds the favoured egg-cell, whether it be presented in the
capsule or in the ovarian tubes, is one and the same by origin — namely, potential ova.
The easiest way of examining the contents of the capsules of Neritina I found to be
to open them under a dilute solution of osmic acid (T per cent.). This prevented the
breaking up of the various ova and the young embryo, which is likely to be caused by
other media, even by iodized serum.
In Plate 9. figs. 13, 14, 15, three stages of' cleavage are represented. In fig. 13 the
first division into two masses is commencing. The separation of formative and of food-
yelk is already quite obvious. The constitution of the clear straw-tinted food-yelk,
consisting as it does of spherical non-nucleated corpuscles, is a point of interest. When
cleavage has advanced to a further point, they assume a more homogeneous character.
Plate 9. figs. 16, 17 represent a polar and a lateral view of two embryos further
advanced. They are already actually of twice the diameter of the embryos 13-15. The
cleavage-cap of cells is gradually embracing the four spheres of residual colourless (not
coloured as is usual) yelk.
Plate 9. fig. 18. The enclosure is complete, and internal arrangements are in progress
which the opacity of this species does not permit the observer to follow. The four yelk-
spheres are still intact.
Plate 9. fig. 19 represents the phase which has most importance for the present
occasion. The embryo has greatly enlarged, and is assuming the well-known veliger
form. When caught at the right angle, the shell in a rudimentary state, as a delicate
disk, is seen to cover the thickened aboral surface. Claparede saw the shell at an early
period, but he did not detect what is of so much interest in connexion with what I have
described in Pisidium and in the deformed Aplysia minor — namely, the deep inden-
tation in this shell-patch or shell-secreting surface occupied by the plug of chitinous
material (pi), which in Aplysia I spoke of as the shell-plug.
Plate 9. fig. 20 gives a more highly magnified and cleanly focused view of the same
shell-plug and shell-patch.
Limax agrestis. — Plate 9. figs. 21 & 22 give two views of two different embryos of
Inmax agrestis. I kept a large number of ova of Limax and of Arion at Jena in April
1871, and followed out the development to a certain extent. I submit on this occasion
only the two drawings (figs. 21 & 22), because they establish the occurrence of the
Gastrula form developed by invagination in these Pulmonate Gasteropods.
DEVELOPMENTAL HISTOEY OP THE MOLLUSCA.
31
Fig. 21 is a day younger than fig. 22 ; the former gives a profile view, the latter is seen
from the surface with the aperture of invagination uppermost. The aperture ( i ) closes
entirely a clay later, and the development of the true mouth proceeds at another spot
still later. The sharp distinction between the invaginated cells ( [hy ) and the thick layer
of smaller epiblastic cells (ep) makes this Gastrula form one of the most typical among
Mollusca.
Limnceus stagnalis*. — Although I am unable to present at this time any drawings of
the development of this common Pulmonate, I must yet point out that it is one of the
most interesting and important in relation to the two new features of molluscan deve-
lopment pointed out in these contributions, viz. the invaginated Gastrula- phase and the
rudimentary shell-sac and plug.
In Limnceus stagnalis a Gastrula is developed by invagination, which is one of the
best marked in all the animal kingdom. Its aperture of invagination has been mistaken
by Lereboullet (who has well figured it without, as may be supposed, appreciating its
significance) for the mouth.
Similarly in the same mollusk, at a later stage, a thickened “ shell-patch ” develops,
which exhibits a very deeply marked groove or pit, the shell-groove. This has also been
seen and figured by Lereboullet, who has mistaken it for the commencing invagination
of the anus.
Thus Limnceus presents these two important developmental features in a strongly
marked condition.
* January 7, 1875. — The above was written in January 1874, and the facts to which it refers were
observed in the summer of 1871. In the summer of 1874 I took an opportunity of studying Limnceus in greater
detail, and published an account of its embryology in the Quart. Journ. Microsc. Sci., October 1874, with two
plates.
32
MR. E. RAT LANKESTER ON THE
General considerations relative to the observations contained in the preceding
Contributions (Nos. I., II., III.).
Before leaving the preceding records of observations to the consideration of the reader,
I may point out briefly their bearing on two matters of theoretical importance, viz. (1)
the origin and significance of what has been called the Gastrula phase of development,
and (2) the homologies or homogenies (as I should prefer to say) of the shells, ligaments,
and internal pens of the Mollusca. More facts have to be sought out and brought to
bear on these questions ; but whilst occupied in that further search, let me indicate the
anticipations which must guide and stimulate it. Before doing so I must mention that
there are a variety of other matters of interest in the facts recorded in the preceding
pages which cannot yet be brought into any theoretical structure, but which I have not
on that account kept back, as they will probably be of some service in their isolated
condition.
(1) Kowalevsky was the first to describe, in a precise manner, the formation of the
foundations of the alimentary tract in a developing embryo by invagination of the wall
of a simple primitive blastosphere, or hollow ball of embryonic cleavage-corpuscles.
He detected this mode of development in Amphioxus , and subsequently in Ascidia. By
later researches he was able to indicate the same mode of development in certain Vermes
( Sagitta , Lumbricus ); and he mentioned incidentally that he had observed a similar
development in the Heteropodous mollusk Atalanta. I was at this time studying
the development of Pisidium and Limax , and obtained evidence of the invagination of
the primitive blastosphere in those two widely separated mollusks. Subsequently at
Naples I found the same process occurring in Nudibranchs. The probable identity of
this process of invagination with that so well known in the Batrachians, especially
through Stricker’s admirable work on the subject, became clear, to those occupied with
embryological studies, from the facts established by Kowalevsky ; and the “ anus of
Ruscoui ” co aid now be recognized in the “ orifice of invagination ” present in members
of the three large groups of Vermes, Mollusca, and Vertebrata.
The embryonic form produced by this invagination-process is a simple sac, composed
of an ectoderm and endoderm, with an orifice connecting the exterior with the cavity
lined by the endoderm. It, in short, presents the typical structure of the simplest
Coelenterata, and corresponds exactly with the so-called Planula of the polyps and
corals. Hence we are tempted to see in this primitive invagination-form the repre-
sentative of the Ccelenterate phase of development of the whole animal kingdom. In
a paper published in May 1873*, containing the substance of lectures delivered in the
preceding October, I have discussed this notion at some length, and other points
connected with the attempt to work out the correspondences of the embryonal cell-
layers of the various groups of the animal kingdom. At the end of the year 1872,
Professor Haeckel’s splendid Monograph of the Calcareous Sponges appeared, in which
the same questions are methodically discussed. The name Gastrula is given by
* Annals & Mag. Nat. History.
DEVELOPMENTAL' HISTOEY OE THE MOLLUSCA.
33
Professor Haeckel to the embryonic form which I had proposed to designate by the
old name Planula ; and the multicellular blastosphere, from which the Gastrula is
developed, which I had proposed to speak of as a polyplast , he well christens the
Morula. Professor Haeckel was able to show in his monograph that the Calcareous
Sponges exhibit a beautifully definite Gastrula- larva, which swims freely by means of
cilia. Lieberkuhn, Miklucho-Maclay, and Oscar Schmidt had previously shown that
certain sponges exhibit such an embryonic form ; but Prof. Haeckel described it in
many cases, and showed fully its mode of development and structure.
This brings us to an important point in what ITaeckel calls the “ Gastroea theory
The Gastrula form of the Calcareous Sponges is not formed by invagination. Without
any opening in the blastosphere making its appearance, the cells constituting its walls
divide into an endoderm and an ectoderm ; then, and not until then, an orifice is formed
from the central cavity to the exterior by a breaking through at one pole. Careful
accounts of the development of Ccelenterata, with a view to determine the mode of
development of the Planula or Gastrula form in regard to the question of invagination,
are not to hand in a large number of cases. But, on the one hand, we have Kowxlevsky’s
account of the development of Pelagia and Actinia, in which the formation of a Gastrula
by invagination is described, as in the cases already cited among Vermes, Mollusca, and
Vertebrata; on the other hand, we have Allman’s observations on the Hydroids,
Schultze’s on Cordylophora, Kleinenberg’s on Hydra, Haeckel’s on the Siphonopliora,
and Hermann Fol’s on the Geryonidee, in which the ectoderm and endoderm of the
embryo (which is at first a Planula without mouth, then a Gastrula with a mouth)
are stated to arise from the splitting or “delamination” of a single original series of
cells forming the wall of the blastosphere. Hermann Fol’s observations are of especial
value, since he shows most carefully how, from the earliest period, even when the egg
is unicellular, its central part has the character of the endodermal cells, its, peripheral
part that of the ectodermal cells.
The question now arises, can the Gastrulce which arise by invagination be regarded
as equivalent to those which arise by internal segregation of an endoderm from an
ectoderm 1 and if so, which is the typical or ancestral mode of development 1 and what
relation has the orifice of invagination in the one case to the mouth which, later, breaks
its way through in the other 1
It is not within the scope of the present memoir to discuss these questions at length ;
but I may say that I am of opinion that we must regard the Gastrula- sac, with its
endoderm and ectoderm, as strictly equivalent (homogeneous, to use another expression)
in the two sets of cases. One of the two methods is the typical or ancestral method of
development, and the departure from it in the other cases is due to some disturbing-
condition. I believe that we shall be able to make out that disturbing element in the
condition of the egg itself as laid, in the presence in that egg of a greater or less amount
of the adventitious nutritive material which Edouard van Beneden calls “deutoplasm.”
* His most recent views on this matter are contained in a pamphlet dated June 1873, ‘ Die Gastrsea-Theorie."
MDCCCLXXV. F
34
ME. E. EAY LANKESTEE * ON THE
This and certain relations of bulk in the early-developed organs of the various embryos
considered, determine the development either by invagination or by delamination. The
relation of bulk to the process of invagination I may illustrate from a fact established
in the preceding contributions. In Loligo * the large otocysts each develop by a well-
marked invagination of the epiblast forming a deep pit, which becomes the cavity of
the cyst. In Aplysia the smaller otocysts each develop by a simple vacuolation of the
epiblast without invagination. Again, in Vertebrata the nerve-cord develops by a long-
invagination of the epiblast ; in Euaxes and Lumbricus the corresponding nerve-cord
develops by a thickening of the epiblast without any groove and canal of invagination.
The bulkier structures in these cases are seen to develop by invagination, the smaller
by direct segregation. Invagination therefore acts as an economy of material, a hollow
mass being produced instead of a solid mass of the same extent.
A. Gastrulee developed by invagination , or invaginate Gastrulee, with either (1) embole
or (2) epibole. — That the presence of a quantity of deutoplasmic matter, or of a partially
assimilated mass of such matter, in the original egg is not accompanied by well-marked
-invagination of the blastosphere, whilst the absence of much deutoplasm is the invariable
characteristic of eggs which develop a Gastrula by invagination, is shown by a com-
parison of Aplysia and Loligo with Pisidium and Limax , and of the Bird with the
Batrachian. In some cases, such as Selenka has characterized by the term “ epibole,” it
seems that the enclosure of the large yelk-mass by the overgrowth of cleavage-cells may
be held as an equivalent to the invagination of the large yelk-cells by “.embole and
the intermediate character which the development of Luaxes and of Lumbricus presents
in this respect, as described by Kowalevsky, tends very strongly to establish a transition.
B. Gastrulee developed by segregation , or segregate Gastrulee. — But the mode of
development of the Gastrula of Geryonidee, described with so much minuteness by Fol,
which is obviously the same as that of the Gastrulee of Spongiadee and most Hydroids,
is clearly no masked case of invagination. There is no question of “ epibole ” here, but
a direct and simple splitting of one cell into two ; so that what was a sac formed by a
layer of cells one deep, becomes a sac formed by a layer of cells two deep, or of two
layers each one deep. It is yet a question for much further inquiry as to how this
mode of forming a double-walled Gastrula can be derived from, or harmonized with,
the formation of Gastrulee by the embolic or epibolic forms of invagination.
It would certainly seem, at present, that the orifice of invagination of the invaginate
Gastrula must not be regarded as the equivalent of the later erupting mouth of the
segregate Gastrula f, which is the true permanent mouth of the Sponge or Ccelenterate.
* See Annals & Mag. Eat. History, Feb. 1873 ; also Proe. Eoy. Soc. no. 151, 1874, and Quart. Journal of
Microse. Sci. January 1875.
t In my paper in the ‘ Annals ’ for May 1873, I have inclined to the view that it may be so regarded.
In a paper written a year after the date of the present memoir, and published in the Quart. Journ. Micr.
Science, April 1875, I have proposed to retain the original term Planula instead of Gastrula, and to speak of
the orifice of invagination as the “blastopore.”
DEVELOPMENTAL HISTORY OE THE MOLLUSCA.
35
In no case is the orifice of invagination of the invaginate Gastrula known to persist
under any form. It appears solely to effect the invagination, and when that is effected
vanishes.
Enough has been said to show the importance of observations relating to the Gastrula
phase of development. In the preceding parts of this paper well-marked invaginate
Gastrulce are described from : —
1. Pisidium (Lamellibranch).
2. Tergipes (Nudibranch).
3. Polycera (Nudibranch).
4. Limax (Pulmonate).
5. Limnceus (Pulmonate).
In addition to these cases of the development of invaginate Gastrulce among Mollusca,
the examination of the very beautiful figures in the papers of Loven on molluscan
development leaves no doubt that he has observed invaginate Gastrulce in the following
cases, but has not understood their structure : —
6. Cardium (Lamellibranch).
7. Crenella (Lamellibranch).
Similarly, Karl Vogt’s observations on Actceon indicate the same state of things as I
have pointed out in Polycera ; and hence we may add
8. Actceon (Nudibranch),
and, finally, from Kowalevsky’s statement, though not accompanied by figure or
description,
9. Atalanta (Heteropod).
(2) The second matter of theoretical interest (namely, the early features in the develop-
ment of the shell) has not been previously discussed, since the structures described in
the paper as shell-patch, shell-groove, and shell-plug were unknown.
If, as seems justifiable, the Cephalopoda are to be regarded as more nearly repre-
senting the molluscan type than do the other classes, or, in other words, more closely
resemble the ancestral forms than they do, we might look in the course of the develop-
ment of the less typical Mollusca for some indication of a representative of the internal
pen of the higher Cephalopoda. We might expect to find some indication of the
connexion between this and the calcareous shell of other forms ; in fact the original
shell of all Mollusca should be an internal one, or bear indications of a possible deve-
lopment into that condition.
In Pisidium , in Aplysia, and in Neritina I have submitted evidence of the
existence of a specially differentiated patch of epidermic cells at the aboral pole, which
develops a deep furrow, groove, or pit in its centre, almost amounting to a sac-like
cavity opening to the exterior. The first (chitinous) rudiment of the shell appears as a
disk on the surface of this gland, but also in some cases the cavity or groove is filled by
a chitinous plug.
Let the walls of the sac close and the activity of its living cells continue, and we
f 2
36
ME. E. EAY LANKESTEE ON THE
have the necessary conditions for the growth of such a “ pen ” as that of the Decapo-
dous “ Cephalopods.”
At present the details of the development of the “ pen ” in the Cephalopoda are not
fully known *. I have evidence that it is formed in an enclosed sac-like diverticulum
of the epidermis, but have not yet ascertained the earliest condition of this sac. The
history of its development becomes surrounded with additional interest in relation to
the shell-gland of the other Mollusca.
The position of the groove of the shell-gland in Pisidium suggests a possible con-
nexion of its chitinous plug with the ligament, which it will be worth inquiring into
in other developmental histories of Lamellibranchs.
In Dentalium and Fissurella it appears to be exactly that region of the shell which
would correspond with the first-produced chitinous shell-disk and its plug, which is
altogether absent, leaving an open hole.
The internal shells of other Mollusca besides the cuttlefish are certainly not in
some cases (e. g. Aplysia ) primitively internal, but become enclosed by overspreading
folds of the mantle. But in the case of Limax and its allies, it is possible (though
requiring renewed investigation) that the shell is a primitively internal one, representing
the shell-plug.
There is yet one more possible connexion of this shell-gland and plug : this is the
chitinous secretion b'y which Terebratula and its allies fix themselves to rocks &c. The
position of the peduncle exactly corresponds to that of the shell-gland ; and an exami-
nation of Professor Morse’s recently published account of the development of Terebra-
tulina , leaves little doubt that at the pole of attachment, which very early develops its
function and fixes the embryo, an in-pushing occurs, and a kind of shallow gland is
formed, which gives rise to the horny cement. My own observations on the develop-
ment of Terebratula vitrea do not extend to so early a period as this.
It is perhaps scarcely necessary, in conclusion, to point out the close resemblance of
shell-gland and plug to the byssal gland and its secretion. They are closely similar
structures ; but there does not appear to be any reason for regarding them as “ serial
homologues,” or as more closely related than are, say, the hairs on the head of a man
with the hairs on his chest.
Explanation of the lettering of Plates 5, 6, 7, 8, 9, 10. (For explanation of the lettering
of Plates 1, 2, 3, 4 see page 12.)
al. Alimentary canal.
C. primitive gastric cavity.
c. Body-cavity or ccelon.
ci. Cilia.
* March 7th, 1875. — I may he permitted to refer to two papers published since the above was written,
in which my subsequent observations are related establishing the mode of origin of the Cephalopod’s pen-sac as
an open pit. They are contained in the Quart. Journal of Microsc. Science, October 1874 and January 1875.
DEVELOPMENTAL HISTORY OE THE MOLLUSCA.
37
dry. Detached portion of the residual yelk concerned in the formation of the renal organ.
v. Descending border of the velum.
ep. Epiblast or ectoderm.
f. Foot.
liy. Hypoblast or endoderm.
ime. Darmfaserblatt, or alimentary layer of mesoblast.
int. Intestine.
int'. Terminal portion of the intestine.
vi, m'. Detractor muscles.
me. Mesoblast.
mn. Mantle rudiment.
ng. Nerve-ganglion.
ng', ng". Secondary ganglionic masses (1 pedal ganglion) .
0. Mouth.
o'. Thickening which precedes the mouth.
ce. CEsophagus.
01. Orifice of invagination (blastopore).
op. Operculum.
ot. Otocyst.
pg. Pigment-vesicles of unknown function.
ph. Pharynx.
pi. Plug of the shell-gland or groove.
pme. Hautfaserblatt, or tegumentary (parietal) layer of the mesoblast.
g. Dark-coloured cell-mass of unknown significance.
R. Richtungsblaschen, or particles extruded from the cleaving egg-cell, frequently
recognizable as the remains of the germinal vesicle.
ry. Residual yelk.
sh. Shell. .
shgr. Shell-groove, or follicle of the shell-gland.
shp. Shell-patch, or primitive shell-secreting area.
x. Undifferentiated cells of the colourless (or segregate) yelk, enclosed by the epiblast.
In Plate 7. figs. 4, 5, 8, 11, the letter x is applied to a deep-lying dark-looking
mass of cells which lies between the two coloured residual yelk-spheres.
38
MR. E. RAY LANKESTER ON THE
No. IV. The growth of the Ovarian JEgg o/7 Loligo and Sepia.
The following observations were made during the months of February, March, and
April, at Naples, in 1872 *. The eggs of Loligo were obtained in abundance from the
fishermen, as the spring advanced becoming more common. They were preserved in a
basin into which a jet of sea- water was allowed to run continually; others were sunk
in a basket in the fishermen’s harbour at Santa Lucia. I chose the eggs of Loligo
rather than of Sepia for the purpose of commencing the study of the development of
the Cephalopoda, because the egg-envelopes are colourless, and the egg itself sufficiently
small to be transparent and easy to examine in the living state. The eggs of Sepia , on
the other hand, require very careful treatment, in order to remove the dark-coloured en-
velopes, and are even then unwieldy objects for examination with high powers in the
fresh state. The first part of the observations recorded below relate actually to the
ovarian egg of Sepia, on which I found it more convenient (from the size of the eggs
and from the fact that I possessed well-preserved ovaries of that genus) to carry out
inquiries as to the mode of building-up of the egg previous to fertilization, and as to the
significance of its basket-worked tunic. At the same time I have made many parallel
observations on the ovarian eggs of Loligo itself ; and I believe that it may be asserted
with full confidence, that the ovarian egg of Loligo differs from that of Sepia only in
the size to which it attains.
In examining the progressive development of the deposited eggs of Loligo , I adopted
the following method of manipulation. One of the finger-like colourless strings of the
eggs being taken, I removed the outer coating of gelatinous matter, so as to expose the
deeper gelatinous material which forms a separate capsule to each egg, the capsules
being grouped longitudinally in four series around a central gelatinous string or axis ;
then with the scissors one, two, or three eggs were easily detached in their capsules and
placed on the compressorium, which was allowed to press but very slightly on them.
In this way (the egg being an elongated ovoid) a lateral view was of course always
obtained. To obtain what I may call “ a polar view ” (that is, a view of the egg as
seen from above when it is made to stand on end) is by no means so easy. I found the
best way to be to cut a small diamond-shaped hole in a piece of cardboard, and, after
having removed as much of the gelatinous investment of the egg-capsule as possible, by
the aid of delicate forceps, to place the egg on end in the hole, with the pole to be
observed uppermost. Then, keeping it well moistened with sea-water, the little piece
of cardboard with the egg was placed in the compressorium, and the upper glass of that
* J an. 1875. — The portion of this memoir now published relates only to the ovarian ovum. It stands as
it was read in March 1874. The rest of the memoir relating to Loligo has been withdrawn for the purpose
of incorporating new observations. An abstract of my observations (both those of 1872 and 1874) relating to
the later development of Loligo, illustrated by two plates, is published in the Quart. Journ. Microsc. Science,
Jan. 1875. In 1874, owing to the arrangements of Dr. Dohrn’s zoological station, I was enabled to obtain
abundant supplies of Loligo embryos in all stages of development.
DEVELOPMENTAL HISTORY OF THE MOLLUSCA.
39
most useful instrument brought gently down so as to touch the upper pole of the egg.
The adhesion of the delicate egg to the glass was now sufficient to maintain it in the
erect position. The eggs were examined thus in the living condition, and, in some
cases, after the addition of dilute acetic acid. The method of hardening and cutting-
sections was not applied by me to the study of the deposited eggs* of Loligo , which, on
account of their great transparency, offer every facility for study in the fresh state with
even the highest powers* ; but the growth of the ovarian egg and its envelopes or
prseseminary development f has been followed by means of sections stained with car-
mine, cut from eggs hardened in absolute alcohol, and some in chromic acid, in the
usual way.
The Ovarian Ovum.
The ovary of Sepia and of Loligo at the breeding-time is an arborescent organ,
formed by a series of branches and twigs, on the ends of which the eggs are seen like
so many grapes on a bunch, but differing from a grape-bunch in the fact that the eggs
are of very various sizes (Plate 11. fig. 13). I do not propose here to go into the larger
anatomical features of the ovary, but to confine myself to the history of the growth of
the individual eggs as exhibited in the variously sized specimens which occur in one
and the same adult ovary. This, accordingly, excludes all question of the earlier
development of the ovary and the ultimate origin of its constituent cells, a matter which
must be treated of in due course in connexion with the later embryonic history of the
developing Cephalopod.
Limits of size of the Ovarian Egg in Sepia. — The observations which follow, unless
the contrary is stated, must be understood as relating to Sepia. The preparations to
which they refer, some of which are represented in Plates 11, 12, were made in the
histological laboratory of Exeter College during the present year (1873). The ovarian
eggs of both Loligo and Sepia were also made the subject of study by me at Naples
in the spring of 1872, when they were in the fresh condition.
The smallest eggs in the mature ovary of Sepia or of Loligo are to be found sessile
among the long peduncles or stalks which support riper eggs. The smallest observed
in Sepia were about -g-jjo of an inch in diameter. Before quitting the ovary the
egg attains to nearly a quarter of an inch in long diameter, and has more than a
hundred thousand times the bulk of these smallest egg-cells. The acquisition of new
material by the egg-corpuscle, in passing from this smaller to that larger condition, is
accompanied by structural arrangements, which are illustrated in Plates 11, 12.
First Stage of Ovarian Growth. — In Plate 11. fig. 14, the egg-corpuscle, with its nucleus
and nucleolus, surrounded by a moderately developed “ body ” (the best, since the most
indifferent, term which can be applied to that part of a nucleated plastid which is some-
* In the spring of 1874 I studied the development by means of hardening and cutting sections.
t Prsesemin ary = before the junction of the semen with the ovum. Postseminary = after the junction of the
semen with the ovum. Insemination = the junction of semen with ovum.
40
ME. E. EAY LANKESTEE ON THE
times called the protoplasm), is seen as stained by carmine imbibition. The egg is now
a little over of an inch in diameter. It is surrounded by branched connective-
tissue corpuscles, some three or four of which are closely applied to it. By simple plasmic
nutrition (that is, by assimilation of matters which reach it by osmotic action from the
blood) the egg-corpuscle now increases in size, especially that part of it which we
called the body, and which now begins to assume the characteristics of an egg-yelk,
viz. in the fact that it is taking on a special and excessive growth. With this increase
of size, it is to be observed that the egg has acquired a more definite envelope (fig. 15, oc.).
The egg continues to increase in bulk, and the “ body ” relatively more so than does
the nucleus, the nucleolus of which has now become broken down. The capsule
becomes now definitely pinched off from the surrounding tissue, and a peduncle forms
to it which henceforward increases in length with the growth of the egg itself.
Whilst the peduncle is forming, the connective-tissue corpuscles forming the capsule
have proliferated in such a way as to form a double layer surrounding the egg, which
henceforth we can distinguish as “inner” and “outer” capsular membranes (Plate 11.
fig. 16). The corpuscles of the outer capsular tissue do not become materially changed;
they increase in number, and form a firm connective-tissue tunic to the egg continuous
with the peduncle. But the corpuscles of the inner capsular membrane, lying in direct
contact with the naked surface of the growing egg-cell, take on a very different cha-
racter; they form a secreting epithelium of columnar corpuscles, which have, up to a
certain stage of the egg’s growth, the characters of “ goblet cells ” (see Plate 12.
figs. 27 & 28). Whilst the corpuscles of the inner capsular membrane are assuming this
definite character, blood-vessels are pushing their way along the peduncle, and ulti-
mately form a network lying between the inner and the outer membranes of the cap-
sule, with an artery and a vein carrying the blood to and from the egg along the axis
of the peduncle. The development of this vascular system is a gradual affair ; but in
an egg of the size seen in Plate 11. fig 5 it is already in operation. The development
of marked longitudinal ridges on the inner capsular membrane is one of the first results
of the penetration of the vascular system to the egg-capsule.
Second Stage of Ovarian Growth. — From this time forward the whole nutrition of the
egg-corpuscle is fundamentally changed. Whereas it could previously be spoken of as
a plasmic nutrition, it now becomes entirely dependent on the cells of the inner cap-
sular membrane and their nutrition by the elaborate network of blood-vessels. The
corpuscles of the inner capsule are continually growing afresh, undergoing a peculiar
metamorphosis of their protoplasm, and pouring out the metamorphosed matter into
the substance of the growing egg-cell, just as the goblet cells of a mucous membrane
produce their glairy secretion (see Plate 12. fig. 28). The nutrition thus becomes one
characterized by the assumption of visible semifluid material by the body nourished —
inceptive nutrition. At a later period, it appears that it again somewhat changes its
character. Whether the term “nutrition” is or is not applicable to such segregation
of matter as here goes on may be a matter for discussion ; but I am inclined to think
DEVELOPMENTAL HISTORY OE THE MOLLTJSCA.
41
that we have no reason to suppose that the matter (deutoplasm of Van Bekeden) thus
thrown into the original egg-protoplasm, together with the subsequently introduced
male contribution of spermatozoa, is not assimilated so as to form with it an organic
whole ; rather it seems probable that the original protoplasm of the egg-corpuscle feeds
on the matter brought to it, as does an Amoeba or other unicellular organism, and that
it is not until the final segregation of formative from food yelk on the completion of
the blastoderm, that we can say what has not been digested, i. e. what stands over for
the nutrition of the new generation of blastodermic cells.
With the development of vascularity in the peduncle and egg-capsule, longitudinal
ridges make their appearance, and are plainly seen as a definite pattern through the
outer egg-envelope. They increase very much in complexity as the egg increases in
size; and finally the surface of the egg presents a complete basketwork tracery,
which is shown in an incomplete condition in the Loligo' s egg (drawn in fig. 22), and
has been figured and described by Kolliker in his classical ‘ Entwickelungsgeschichte
der Cephalopoden,’ published at Zurich in 1844. It is at this point that my observa-
tions first come in contact with Kolliker’s, who starts from this condition of the egg.
Kolliker’s is the only memoir on the development of any Cephalopoda to which I
shall have to refer in the present paper, since there has been but one short notice on
the subject of Cephalopod embryology during the last thirty years. That notice is due
to Prof. Metschnikoff, but is only known to me by a French abstract — like the
Russian original, exceedingly short and devoid of illustration. I shall not have to refer
again to Metschnikoff’s paper, and there are but few points in Kolliker’s work which
come into contact with mine. At the time when Prof. Kolliker made his admirable
observations, many questions were in a very different condition to that which they hold
at present; and microscopes were not of their present efficiency. Moreover, Prof.
Kolliker has described the early stages of postseminary development from the exclu-
sive study of the eggs of Sejpia and Argonauta , and mainly studied them by means of
surface- views obtained with a low power of amplification.
The structure of the basketworked capsule in the ovarian egg of Sepia was figured
and investigated by Kolliker. He attributes the surface-pattern to the folding of the
vitelline membrane of the egg itself, and points out that the egg-capsule does not take
any part in it. He shows by a section of the egg, which is figured, that (what he mis-
takes for) the vitelline membrane is thrown into folds, which are pushed inward towards
the centre of the egg, forming in section a series of incomplete septa traversing the egg.
These disappear, Kolliker shows, as the egg advances to maturity, and finally the egg
escapes from its capsule with a perfectly smooth surface. If in the year 1842 our
present methods of cutting and clarifying tissues for study with the microscope had
been known, it would have been quite a simple matter for Kolliker to have ascer-
tained that he was mistaken in supposing that the membrane which is thrown into
folds is the vitelline membrane.
The eggs of Sepia and of Loligo do not present any thing comparable to a vitelline
MDCCCLXXV. G
42
MR. E. RAY LANKESTER ON THE
membrane. They lie perfectly naked within the egg-capsule. What Prof. Kollikek
identified with the then metaphysically important vitelline membrane, is certainly our
inner membrane of the capsule.
It is the inner membrane of the capsule which, on the extension of long vascular
trunks between it and the outer membrane, becomes longitudinally folded, in cor-
respondence with those vascular trunks ; and now, as the growth of the egg rapidly
advances, the growth of these inwardly projecting folds or double ridges goes on to an
immense extent. The whole cavity of the egg-capsule becomes parcelled out by them
(see Plate 11. figs. 7, 8, 9) ; they push into it from every side, and drive the germinal
vesicle to an extreme polar position (fig. 8, gv ). Each fold is thoroughly supplied
with blood-vessels, on which the rapid development of this great bulk of tissue, the
increase in the total size of the egg, and the active secretion from the goblet cells of
the whole of its inner surface depends. This folded inner capsular membrane, with
its extensive system of vessels penetrating among its folds or follicles, may be regarded
as a shut gland, constantly increasing in size and accumulating its secretion within its
cavity.
The blood-vessels which lie between the inner and outer capsular membranes have
their own walls well marked, and in sections are not necessarily adherent either to one
or the other. The main trunks are seen at their point of entrance from the peduncle
in fig. 19, Plate 12, and the surface-network which connects the venous and arterial
trunks at this pole. But besides vessels which may be seen thus on the surface, there
are those which branch from them and penetrate between the pushed-in folds of the
inner capsular membrane ; some of these ( hv ) are well seen in Plate 11. fig. 10, also fig. 9,
and more minutely in Plate 12. fig. 23, in which the definite wall of the vessel, with
its corpuscular elements, is distinguishable ; and it becomes obvious that there is nothing
like a lacunar blood-space between the two membranes of the egg-capsule. The com-
pleteness of this vascular supply, and the luxuriant growth of the inner capsular mem-
brane, indicate great activity in this portion of the egg. The egg and its capsule
attain nearly (Plate 11. fig. 8) if not quite full size, and still the septal ridges are every-
where occupying its cavity. It is true that into the channels or follicles between the
ridges the active pavement of muciparous cells has poured out a certain amount of
material, and the egg has thus enormously increased in bulk. But there is so much
space at present occupied by the ridges, that the egg itself cannot be said to have
attained any thing like half its volume.
Third Stage of Ovarian Growth. — This is effected by the gradual absorption of the
entire inner capsular membrane, accompanied by the most active proliferation of its
cells, which are thrown off in immense numbers to swell the yelk as the processes or
ridges on all sides dwindle away and finally disappear. In figs. 10 and 11 sections of
eggs are represented in this condition ; the folds of the inner capsular membrane, seen
in section as processes formed by two rows of cells, with frequently a blood-vessel
between them, are in course of degeneration ; and already a great mass has been added
DEVELOPMENTAL HISTOEY OF THE MOLLUSCA.
43
to the yelk from their proliferous surfaces. In fig. 23, Plate 12, a portion of the same
section, more highly magnified, is accurately represented, showing the cells in various
stages of incorporation with the yelk, as they pass from the proliferous surface of the
inner capsular membrane.
There does not appear to be any room at all for doubting that cells keep on passing
off from the surface of these folds of the inner capsular membrane into the yelk, just
as cells keep on passing away as scurf from the surface of the human epidermis. It is
a very different question as to whether they retain their vitality and individuality after
passing into the yelk. This question is now one of the very greatest importance in
embryology generally ; and without discussing the views of Professor His or his oppo-
nents, who have made the egg of the hen and of osseous fishes their study, I desire to
draw attention to the facts observed in the case of the Cephalopods Sepia and Loligo.
Of the cells which pass off or are proliferated into the yelk, so to speak, by far the
majority are undoubtedly metamorphosed and broken down into a condition chemically
lower than that of living protoplasm before they have long been there. Hence there
is not such a wide distinction between this third mode of the egg’s nutrition, which I
shall call “ corpuscular,” and the earlier form of inceptive nutrition, which may be
distinguished as secretional. In the latter a portion of the goblet cell or corpuscle
was metamorphosed and thrown into the egg-mass ; in the former it is a whole cell
which is thrown in and subsequently metamorphosed.
The stages of the egg’s nutrition may be thus grouped : —
1st stage Plasmic Osmotic.
2nd stage
3rd stage .
But the question arises whether all the cells which migrate thus in such immense
numbers into the egg-yelk are equally metamorphosed, and to be regarded as having
lost their independent vitality. It is, of course, open to any one to maintain that the
cells which lose all trace of their nucleus and become irregular, highly refracting
masses of indefinite outline are yet capable of resuming their original properties as
protoplasmic corpuscles, and that they are not really degenerated, but only temporarily
modified. Cells or corpuscles which subsequently appear and take part in the for-
mation of the tissues may then be ascribed to the retention of individuality and
protoplasmic properties by the cells proliferated from the inner capsular membrane. I
believe, however, that corpuscles which have undergone the changes above described
and indicated in the Plates (Plate 12. figs. 23 & 24) will be considered by most persons,
as by myself, to have passed irretrievably from the living condition to that of a meta-
morphic product. Strangely enough, however, as though to prevent our feeling any
assurance that the survival of such cells in an egg-mixture is rendered quite improbable
by the facts observed in Sepia and .Loligo, we find, both in the fully formed and the
immature ovarian eggs of Sepia , here and there scattered in the yelk, nucleated cells,
Gr 2
44
MR. E. EAT LANKESTER ON THE
which are undoubtedly exceptional individuals of the migrated capsular cells which have
not become fully metamorphosed. I have never observed more than fifteen of these in
one egg, and those widely scattered, and all of those did not possess nuclei (Plate 12.
fig. 25, also 24 & 26). They were observed only in Sepia, not in Loligo, and lying at
a depth in the yelk, apparently in a zone of less dense yelk than that of the surface.
Concerning these zones of yelk, or more strictly “ stratified shells ” (see Plate 11. fig. 12),
there will be a few words to say below.
Corpuscles like these nucleated corpuscles, but devoid of nucleus, and rounder or
hexagonal in shape, were often observed by me in the eggs of Sepia during its post-
seminary development, widely separate and quite accidental in mode of occurrence. It
may be possible to attribute great significance to these enduring cells ; but the most
satisfactory explanation of their occurrence seems to me that they are individuals which,
owing to very slight individual differences of constitution (the existence of which may
be assumed from the generality of the principle of variation), have delayed their vitelline
metamorphosis, to which, however, they gradually (as evidenced by those without nuclei
in older eggs) succumb.
The process of proliferation from the surface of the ridges of the inner capsular
membrane goes on pari passu with the dwindling of the ridges themselves, until at last
there is no trace of the ridges left. The capsule then bursts at the pole opposite to
that at which the peduncle is attached. The egg, with its surface free from all trace
of the ridges, escapes, perfectly naked and devoid of any thing in the form of capsule,
vitelline membrane, shell, or other envelope *. It falls into the wide membranous end of
the oviduct, where, during the breeding-season, a number of free, naked eggs of this
kind may be found. The mode of dehiscence I do not know in detail ; but, as in
Plate 11. fig. 1, it is not unusual to observe ovaries with many empty shrunken capsules
( c , c).
Condition of the Capsule after escape of the JEgg. — The capsule, as thus left by the
escape of the egg, consists of the outer capsular membrane, supported on its peduncle, of
the main trunks of the blood-vessels which ramified between the inner and outer capsule,
and of degenerating remains of some parts of the inner capsular membrane. These
remains of the inner capsular membrane undergo a yellow degeneration, so as to form a
true corpus luteum (Plate 11. fig. 21). The blood-vessels are easily traced on the inner
surface of the empty capsules, and at intervals there are scattered shrunken yellow-
coloured masses. Probably the whole capsule disappears before another breeding-
season, but on this point I have no evidence.
Condition of the Egg after escape from its Capsule. — The egg is now no longer
“ ovarian,” but is still for a brief space of time prseseminary — that is, unimpregnated by
the male element.
* March 13th, 1875. — Evidence of a very delicate structureless chorion, adherent to the surface of the yelk,
is obtained at a later period, when the superficial organs of the embryo are making their first appearance. It
separates then in shreds.
DEVELOPMENTAL HISTORY OF THE MOLLTJSCA.
45
In this phase it is, as far as the eye assisted by the microscope can ascertain, in the
fresh state, a homogeneous transparent viscid body, devoid of any special membrane to
protect its surface, but retaining its ovoid shape, owing to the greater density of its
superficial layer of substance. In this phase no marking of the surface to indicate the
former sites of the capsular ridges *, no trace of a germinal vesicle, can be seen. I have
not represented the egg at this period in the Plates ; for it would be purely negative as
seen by transmitted light, a simple ovoid outline and nothing more. I have traced the
germinal vesicle up to the condition of eggs, such as Plate 11. fig. 8, but not beyond.
I agree with Kolliker that it disappears ; but I have not traced the mode of its
disappearance. It is not unlikely that it is absorbed at the same time as are the
capsular ridges.
The homogeneous unfertilized egg which now lies in the upper portion of the ovi-
duct is not, however, devoid of all differentiation of structure.
In the first place, when hardened in absolute alcohol, cut in sections and stained with
carmine, a stratified arrangement of the substance of the egg becomes obvious (Plate 11.
fig. 12), as many as four bands of differing intensity of staining being demonstrable.
These apparently indicate differing density of the successive layers of yelk-substance,
and are possibly connected with the successive modes of yelk-nutrition which we have
distinguished. But, in addition to this, on breaking up a fresh specimen of an egg
belonging to this phase, and allowing the yelk to spread out on a glass slip, covering
and examining with a power of 600 diameters, it becomes obvious that the yelk is not
in its nature homogeneous. In this case (Plate 12. fig. 24), and at later stages, a
perfectly definite structure uniformly spread through the mass can be observed. It
is possible to distinguish highly refringent, irregular, somewhat botryoidal masses and
interspaces occupied by a less dense material, probably a liquid, the denser masses being
viscous solids. The liquid must be relatively very small in amount ; for it is only
when carefully spread out that the yelk-particles become obvious, and with the highest
powers they are seen as of a greenish tint, whilst the interspaces are pinkf. The
botryoidal denser matter must without doubt be directly traced to the metamorphosed
cells thrown in from the inner capsular membrane. The forms and sizes of the masses
assumed by this material when spread out are too indefinite to admit of measurements,
but may be best judged of by the figures. It is necessary again to observe that, in the
undisturbed egg, the particles are so densely packed that the mass has the appearance
of being quite homogeneous. It is not until the particles are allowed to move on one
another a little that the granular or botryoidal structure of the yelk becomes obvious.
* Such markings are sometimes to he seen.
t These colours are of course only due to the optical defects of high-power objectives.
46
MR. E. RAY LANKESTER ON THE
Explanation of Plates 11 & 12 (illustrating Loligo).
Figs. 1 to 11 are drawn to the same scale.
Fig. 1. One of the smallest eggs from the ovary of Sepia officinalis at the breeding-
season (April), inch diameter.
Fig. 2. A somewhat larger egg.
gv. Germinal vesicle and spot.
oc. First appearance of the egg-capsule.
Fig. 3. An egg further advanced.
oc. Egg-capsule.
bv. Blood-vessel.
Fig. 4. An egg still further advanced (same stage as fig. 18). The yelk has now
received considerable addition to its substance, and there can be distin-
guished : —
oc. The outer egg-capsule.
ic. The inner egg-capsule, consisting of columnar cells.
gv. Germinal vesicle.
Fig. 5. The egg now shows traces of the development of folds or plicse in its capsule.
Fig. 6. The folds are more clearly developed, and are seen here as focused in a. surface-
view of the egg. Their connexion with the blood-vessel (bv) is obvious.
Fig. 7. An egg, further advanced, in transverse section, to show the disposition of the
now greatly enlarged folds of the inner capsular membrane (ic). The outer
capsular membrane (oc) is seen to take no part in the formation of the
penetrating ridges. The stained nuclei of the capsular cells have not been
presented in this figure, but the carmine-stained matter occupying the cavity
between the ridges of the capsule is indicated by shading. This matter is
the yelk of the egg, which is being increased by the addition of new material
from the capsular cells. Actual section.
Fig. 8. A much larger egg (in longitudinal section), showing the disposition of the
ridges of the inner capsular membrane and the condition of the yelk-cavity.
It is to be noticed that though the whole egg has increased greatly in bulk,
the yelk-space has not as yet gained any thing as compared with the capsular
folds or ridges.
gv. Germinal vesicle.
bv. Blood-vessels in section, lying between the outer and inner capsular
membranes.
oc. Outer capsular membrane.
ic. Inner capsular membrane.
c. Yelk-cavity. Actual section.
DEVELOPMENTAL HISTOEY OE THE MOLLTJSCA.
47
Fig. 9. Transverse section of an egg not quite so far advanced. The nuclei of the cells
of the inner capsular membrane are given in the upper part of the figure.
Letters as in fig. 8. Actual section.
Fig. 10. Longitudinal section of a full-sized ovarian egg of Sepia. The process of
absorption of the inner capsular membrane and its ridges has advanced to
some extent. The germinal vesicle has also disappeared.
x. Dwindled inner capsular membrane, forming the periphery of the inner
capsule. Other letters as in fig. 8. Actual section.
Fig. 11. Portion of a transverse section of an egg in the same stage of growth.
Letters as in fig. 10. Actual section.
Fig. 12. Transverse section of a completely formed egg of Sepia, magnified only four
diameters, to show the existence in the yelk of three concentric zones of
differing density. Actual section.
Fig. 13. Portion of a ripe ovary of Sepia, showing ova of various sizes and some empty
capsules, c, c.
Fig. 14. One of the smallest egg-cells observed in the ovary of Sepia at breeding-time.
Cells like connective-tissue corpuscles are seen to be grouped so as to form
the capsule of the egg. Optical section.
Fig. 15. An egg somewhat further advanced — the capsule now definitely formed.
Optical section.
Fig. 16. The capsule has become pedunculate; but as yet there is no blood-vessel
traversing it.
ic. Inner, and
oc. Outer capsular membranes. Optical section.
Fig. 17. A more advanced egg, drawn in the fresh state. By its side is a very small
egg-cell. Letters as before. Optical section.
Fig. 18. The separation between inner and outer capsules and the characters of their
respective corpuscles have become definite. The blood-vessels ( iv ) in the
stalk of the egg-capsule have developed. Other letters as before. Optical
section.
Fig. 19. Actual arrangement of blood-vessels between the inner and outer capsular
membranes of a nearly fully-grown egg, as seen from the peduncular pole.
The artery and vein are seen applying themselves at the point of attachment
of the egg-stalk to the capsular surface, and spreading out in large longitu-
dinal trunks connected by a network of smaller vessels transversely.
Fig. 20. The peduncle of the egg drawn in fig. 6, in optical section, so as to show the
wall and contents of the blood-vessel ( bv ), the outer capsule (oc), and the
cells of the inner capsule — i. e. not in section, but focused so as to show them
lying in one plane.
Fig. 21. Portion of an empty capsule in the fresh state from the ovary of Sepia, showing
blood-vessel and yellow degeneration of capsular cells.
48
ON THE DEVELOPMENTAL HISTORY OE THE MOLLUSCA.
Fig. 22. Ovarian egg of Loligo , showing peduncle, capsular plications, and germinal
vesicle. Drawn from a specimen examined in the fresh state.
Fig. 23. Portion of a similar section to that drawn in fig. 10, Plate 11, but more highly
magnified (Hartnack’s No. 10 a immersion) in order to show the relation
of blood-vessels to the folds of the inner capsular membrane, and the passage
of cells bodily from the proliferous ridges into the yelk of the growing egg.
Fig. 24. Portion of the surface of a fresh egg of Sepia, after escape from the ovarian
capsule (i. e. uterine), showing modified cellular elements.
Fig. 25. Modified cells (derived from the inner capsular epithelium) observed beneath
the denser cortical substance of a fully formed or uterine egg of Sepia.
Fig. 26. Modified cells from a not fully formed ovarian egg of Sepia.
Fig. 27. Portion of the egg and capsule drawn in fig. 9, Plate 11, to show more fully
the condition of the inner capsular epithelium.
The egg is not fully grown , and the process of proliferation from and
absorption of the inner capsular ridges is not established as in the egg of
fig. 23 ; but the cells have the character of those found on thickly secreting
mucous surfaces, and some appear as goblet cells.
bv. Blood-vessel.
oc. Outer capsular membrane.
ic. Inner capsular membrane.
Fig. 28. More highly magnified view of goblet cells ( cc ) and simple connective-tissue
corpuscles ( bb ) from a portion of the same section.
[ 49 ]
II. Researches on Explosives. — Fired Gunpowder. By Captain Noble ( late R.A.)y
F.B.S., F.B.A.S., F.C.S., Ac., and F. A. Abel, F.R.S. , President C.S., Ac.
Eeceived May 18, — Bead June 18, 1874.
Contents.
Page
A. Introductory History 49
De la Hire. — Robins. — Hutton. — Rumford.
— Gay-Lussac. — Chevreul. — Graham. —
Piobert. — Cavalli. — Prussian Committee.
— Mayevski. — Rodman. — Bunsen and
Schischkoff. — Linck. — Karolyi. — Airy.
Fedorow. — Noble. — Bertbelot. — DeTro-
menec. — Roux and Sarrau.
B. Objects of Experiments 60
C. Methods of Experiment 61
1. Explosion-apparatus 61
2. Measurement of Pressure 62
3. Measurement of the Volume of the Per-
manent Gases ’ 63
4 . Measurement of Heat 63
5. Collection of Gaseous Products 63
6. Collection of Solid Products 64
D. Analysis of the Products of Explosion .... 65
1. Gaseous Products 65
2. Solid Residue. — Preparation of the Re-
sidue for Analysis 67
3. Analysis of Solid Residue 68
E. Composition of Gunpowders employed .... 7i
F. Examination of the Analytical Results .... 73
G. Volume of the Permanent Gases 88
H. Results of Explosion, deduced by calculation
from Analytical Data 89
I. Condition of the Products at the instant of
or shortly after Explosion 93
J . The possibility of dissociation among Gaseous
Products considered 94
Page
K. Tension of Fired Gunpowder observed in a
close vessel 95
L. Determination of Heat generated by the
Combustion of Gunpowder 99
M. Determination of volume of Solid Products
at ordinary temperatures 101
N. Pressure in close vessels, deduced from Theo-
retical Considerations 102
O. Determination of the Temperature of Explo-
sion of Gunpowder 104
P. Mean Specific Heat of Liquid Products .... 106
Q. Probable Expansion of non-gaseous Products
between zero and temperature of Ex-
plosion 106
R. Observed Pressures in the bores of Guns . . 107
S'. Effect of increments in the weight of the Shot
on the Combustion and Tension of Pow-
der in the bore of a Gun 121
T. Effect of Moisture upon the Combustion and
Tension of Powder 122
U. Loss of Heat by communication to the enve-
lope in which the charge is exploded . . 122
V. Pressure in the bores of Guns, derived from
theoretical considerations 124
W. Temperature of Products of Combustion in
bores of Guns 131
X. Work effected by Gunpowder 132
Y. Determination of Total Theoretic work of
Powder when indefinitely expanded . . 134
Z. Summary of Results 136
Abstract of Experiments 138
A. INTRODUCTORY HISTORY.
The investigations which form the subject of this memoir have occupied our attention
for a considerable time, having been commenced in 1868. They have been made
MDCCCLXXV. H
50
CAPTAIN NOBLE AND MR. P. A. ABEL ON EIRED GUNPOWDER.
collaterally with a series of experiments carried on by a Committee appointed by
the Secretary of State for War, with the view, among other objects, of determining
the most suitable description of powder for use in heavy ordnance, which is still con-
tinually increasing in size ; indeed our main object has been to endeavour to throw
additional light upon the intricate and difficult subject under investigation by that
Committee.
There are perhaps few questions upon which, till within quite a recent date, such
discordant opinions have been entertained as upon the phenomena and results which
attend the combustion of gunpowder. As regards the question alone of the pressure
developed, the estimates are most discordant, varying from the 1000 atmospheres of
Robins to the 100,000 atmospheres of Rumford; or even, discarding these extreme
opinions in favour of views which have been accepted in modern text-books as more
reliable, the difference between an estimate of 2200* and of 29,000f atmospheres is
sufficiently startling as regards a physical fact of so much importance. The views
regarding the decomposition of gunpowder are nearly as various ; and we therefore think
that a description and discussion of our own researches may be usefully preceded by a
short account of the labours of the previous investigators of this subject and of the
grounds upon which their conclusions were based.
In the year 1702, De la Hire, who, according to Robins, was the first writer on the
force of fired gunpowder, supposed that it was due to the increased elasticity of the air
contained in and between the grains, the function of the powder itself being merely
that of a heating agent. Robins (who, however, greatly underrated the temperature of
explosion) pointed out that the elasticity so acquired would not exceed 5 atmospheres,
and that such a pressure was not the t.wo-hundredth part of the effort necessary to
produce the observed effects.
Robins J, in 1743, read before the Royal Society a paper in which he described expe-
riments tending to show that gunpowder, when fired, generated permanent gases which,
at ordinary temperatures and atmospheric pressure, occupied a volume 236 times greater
than that of the unexploded powder. He made further experiments to show that, at
the temperature which he conceived to be that of explosion, the elasticity of the per-
manent gases would be increased fourfold, and hence the maximum pressure due to
fired gunpowder would be about 1000 atmospheres.
Robins considered that the whole of the powder (such as he employed) was fired before
the bullet was sensibly moved from its seat. He argued that, were such not the case,
a much greater effect would be realized from the powder when the weight of the bullet
was doubled, trebled, &c. ; but his experiments showed that in all these cases the work
done by the powder was nearly the same.
* Bloxam, C. L., ‘Chemistry, Inorganic and Organic,’ 18.67, p. 427. Owex, Lieut.-Col., R.A., ‘Principles
and Practice of Modern Artillery,’ 1871, p. 155.
t Piobekt, Gf., ‘ Traite d’Artillerie Theorique et Experimentale,’ 1859, pp. 354-360.
t New Principles of Gunnery, 1805, pp. 59-74.
CAPTAIN NOBLE AND MR. E. A. ABEL ON EIRED GUNPOWDER. 51
In 177.8 Dr. Hutton*, of Newcastle-on-Tyne, read before the Royal Society an
account of his celebrated researches in Gunnery; and in his 37 th tract are detailed the
experiments from which he deduced the maximum pressure of gunpowder to be about
twice that given by Robins, or a little more than 2000 atmospheres.
Hutton, like Robins, saw that the moving force of gunpowder was due to the elas-
ticity of the highly heated gases produced by explosion; and, upon the assumption that
the powder was instantaneously ignited, he gave formulae for deducing the pressure of
the gas and velocity of the projectile at any point of the bore. These formulae, the
principles of thermodynamics being then unknown, are erroneous, no account being
taken of the loss of temperature due to work performed ; but we shall have occasion to
point out that the error arising from this cause is not nearly so great as might be at
first supposed^.
In 1797 Count Rumford $ communicated to the Royal Society his experimental deter-
minations of the pressure of fired gunpowder ; his results, although conjecturally
corrected by more than one writer, have retained up to the present time their position
as the standard, if not the only, series of .experiments in which the pressure has been
obtained by direct observation.
In prosecuting his remarkable experiments Count Rumford had two objects in view:
first to ascertain the force exerted by exploded powder when it completely filled the
space in which it was exploded ; secondly , to determine the relation between the
density of the gases and the tension.
The apparatus used by Rumford consisted of a small strong wrought-iron vessel or
chamber 0-25 inch. (6-3 millims.)' in diameter, and containing a volume of ’0897 cubic
inch (T47 cub. centim.). It was terminated at one end by a small closed vent filled
with powder, so arranged that the charge could be fired by the application of a red-hot
ball ; at the other end it was closed by a hemisphere upon which any required weight
could be placed.
When an experiment was to be made, a given charge was placed in the vessel, and a
weight, considered equivalent to the resulting gaseous pressure, was applied to the
hemisphere. If, on firing, the weight was lifted, it was gradually increased until it was
just sufficient to confine the products of explosion, and the gaseous pressure was calcu-
lated from the weight found necessary.
The powder experimented with was sporting, of very fine grain ; and as it contained
only 67 per cent, nitre, it differed considerably from ordinary powder. Its specific gra-
vity (1-868) and gravimetric density (T08) were also very high; but in his experiments
Count Rumford appears to have arranged so that the weight of a given volume of gun-
* Mathematical Tracts, 1812, vol. iii. pp. 209-316.
f Huttos', in a note to the new edition of Robins’s ‘ Gunnery,’ published in 1805, mentions that the elastic
force of gunpowder was considered by John Bernoulli to he that of 100 atmospheres, while Daniel Bernoulli
considered it to he equal to about 10,000 atmospheres. — Robins, loc. cit. p. 57.
+ Philosophical Transactions, 1797, p. 222.
H 2
52
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GUNPOWDER.
powder was nearly exactly equal to that of the same volume of water, — that is to say,
the gravimetric density was about equal to unity.
The curve drawn on Plate 13 exhibits the results of the first and most reliable series
of Count Bumford’s observations. It shows the relation he believed to exist between
the density of the gas and its pressure, and is expressed by the empirical formula
^=l,841#1+'0004,,!, 'p being the tension and x the density of the gas.
The charges with which Bumford experimented were very small ; the largest, with
one exception (by which his vessel was destroyed), was 18 grains (1T7 grm.). The total
quantity of powder required to fill the vessel was about 28 grains (1-81 grm.). It will
be observed that, if the curve (Plate 13) were supposed to be true up to the point when the
chamber is completely filled, the pressure exhibited would be about 29,000 atmospheres.
But, high as this result is, Bumford considered it much below the truth. In addition to
the series the results of which are graphically represented, a second series was made,
the results of which were very discordant.
From Plate 13 it will be observed that, with a charge of 12 grains (0'78 grm.)
(equivalent to a mean density in the products of combustion of 0’428), the tension of
the gas was in the first experiment about 2700 atmospheres; but in this second series
the tension with the same charge was repeatedly found higher than 9000 atmospheres.
The discrepancies between the two series of experiments are not explained ; but, relying
upon the second series, and on the experiment by which the cylinder was destroyed,
Bumford calculated that the tension of exploded gunpowder, such as that employed by
him, when filling completely the space in which it is confined, is 101,021 atmospheres
(662 tons on the square inch)*. He accounts for this enormous pressure by ascribing
it to the elasticity of the steam contained in the gunpowder, the tension of which he
estimates as being doubled by every addition of temperature equal to 30° F. He further
considers the combustion of powder in artillery and small arms to be comparatively slow,
and that hence the initial tension he assumes is, in their case, not realized.
In 1823 Gay-Lussac appears to have communicated to the “Comite des Poudres et
Salpetres” a report of his experiments upon the decomposition of gunpowder f. Gay-
Lussac’s products were obtained by allowing small quantities of gunpowder to fall into
a tube arranged to receive the gases, and heated to redness. The collected permanent
gases, when analyzed, gave in 100 volumes 52‘6 volumes of carbonic anhydride, 5 of
carbonic oxide, and 42 -4 of nitrogen. Gay-Lussac gave the volume of these gases, at
a temperature of 0° C. and 760 millims. barometric pressure, as occupying 450 times
the space filled by the powder, the gravimetric density of which was *9. Piobert,
however, points out that Gay-Lussac’s results, thus stated, are not possible, and suggests
that, by an error, the quantity of gas actually found has been doubled.
Piobert’s suggestion is, from various corroborative circumstances, exceedingly pro-
* Rumford, loc. cit. p. 280.
t We have been unable to obtain the original of this report ; see, however, Piobert, loc. cit. p. 293.
CAPTAIN NOBLE AND ME. F. A. ABEL ON FIEED GUNPOWDEE.
53
bable, and is confirmed by the fact that Gay-Lussac himself estimated the permanent
gases at about 250 volumes.
In 1825 Chevreul* * * §, after drawing attention to the difference in the decomposition
of gunpowder when occurring explosively, as in the bore of a gun, and when taking
place slowly, as by ignition in open air, supposes the decomposition in the former case
to be represented by the equation
2K N03+S+C3=K2S + N2+3C02.
He points out that the actual constituents of gunpowder are employed in proportions
almost in exact accordance with this formula ; and the same view appears to have been
taken by Graham^, who further supposes that the potassium sulphide is converted into
sulphate on coming into contact with the air.
Chevreul gives potassium sulphide, sulphate, carbonate, cyanide, nitrate or hypo-
nitrite, and carbon as composing the solid residue of gunpowder when burnt slowly ; and
gives further, as the result of some experiments of his own, for the gaseous products in
100 volumes : —
Carbonic anhydride . .
, . 45-41 vols.
Nitrogen
. . 37-1)3 ,,
Nitrous oxide
. . 8-10 „
Sulph. hydrogen .
. . 0-59 „
Marsh-gas
. . 3-50 „
Carbonic oxide . . .
. . 4-87 „
Between the years 1831-36 a great number of very important experiments, chiefly
upon the combustion and inflammation of gunpowder, were made by General Piobert.
The results of these experiments, together with Piobert’s theoretical views, are contained
in his work on the properties and effects of gunpowder J.
Piobert considered that the velocity of inflammation of gunpowder, that is the trans-
mission of the ignition from one grain to another, when the charge was contained in a
close vessel or tube offering a high resistance, was very great ; but he did not§ consider
that the influence of the high temperature and great tension of the gases exercised a
sensible effect in increasing the rapidity of combustion of the individual grains.
It is somewhat difficult to collect his views upon the subject of the decomposition of
gunpowder ; and his work on this point must be taken more as a resume of the views of
chemists on the subject than as an expression of his own. He seems, however, to have
ascribed a great influence to the mode of ignition, even on the quantity of permanent
gases, and quotes results varying from 200 volumes to 650 volumes. ||, all taken at atmo-
spheric temperatures and pressure.
* Dictionnaire des Sciences Naturelles, tom. xxxv. p. 58.
f Encyclopaedia Britannica, Art. “ Gunpowder.”
± Piobert, G., ‘ Traite d’Artillerie, Proprietes et Effets de la Poudre/ 1859.
§ Loc. cit. pp. 158-162. || Loc. cit. p. 292.
54
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GUNPOWDER.
He states that, from theory*, the quantity of gas should be comprised between 330
and 350 volumes, and should amount in weight to three fifths of that of the powder.
As regards the tension of the products at the moment of explosion, he accepts as
tolerably correct the first series of Rumford’s experiments, and makes the pressure of
gunpowder, when fired in its own space, about 23,000 atmospheresf.
He further considers it possible that the presence $ of the vapour of water may add
to the explosive force of gunpowder. He shares Rumford’s views as to the solid
products being in the state of vapour at the moment of explosion ; he ascribes the high
tension he assumes to the difference in the behaviour of vapours and permanent .gases
when highly heated, and divides the phenomenon of explosion into two very distinct
epochs : — the first when the solid products are in the state of elastic vapours, adding
their tension to that of the permanent gases; the second epoch being when the perma-
nent gases act alone, the vapours being condensed.
In 1843 General Cavalli § proposed to apply to an experimental gun, at various
distances from the bottom of the bore, a series of small barrels of wrought iron, arranged
to throw a spherical bullet which would be acted upon by the charge of the gun while
giving motion to its projectile. By ascertaining the velocities of these bullets, Cavalli
considered that the tensions in the bore would be ascertained. This arrangement was
carried out with a “ canon de 16,” under his own superintendence, in 1845; and from
these experiments was deduced the theoretical thickness of the metal at various points
along the bore.
General Cavalli appears to have estimated at a very high rate the tensions realized
in the bores of guns. He || considered that, with the Belgian “ brisante ” powder of
1850, a tension of 24,000 atmospheres (158 tons per square inch) was actually realized,
while in the less inflammable powders the tension was, he considered, under 4000
atmospheres.
In 1854 a Prussian Artillery Committee made a series of experiments to determine
the pressure exerted by the powder in the bores of the 6- and 12-pounder smooth-bored
guns.
The plan adopted was a great improvement on that suggested by Cavalli, and was
as follows : —
In the powder-chamber a hole was drilled, and in this hole was fitted a small gun-
barrel of a length of, say, 8 inches. Now, if the gun be loaded, and if in the small side
barrel we place a cylinder whose longitudinal section is the same as that of the projec-
tile, when the gun is fired, on the assumption that the pressure in the powder-chamber is
uniform, the cylinder and the projectile will in equal times describe equal spaces, and
* Piobeet, loc. tit. p. 291. f Loc. tit. p. 359. + Log. tit. p. 316.
§ Revue de Technologie Militaire, tom. ii. p. 147.
|| Cavalli, Gen., ‘ Memoire sur les Eclatements des Canons &c.,’ 1867, p. 83.
Archiv fur die Offiziere der Koniglich Preussischen Ar tiller ie- und Ingenieur-Corps, tom. xxxiv. p. 2.
Revue de Technologie Militaire, tom. i. p. 9, tom. ii. p. 152.
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIRED GUNPOWDER.
55
after the cylinder has travelled 8 inches it will be withdrawn from the action of the
charge. If, then, we know the velocity of the cylinder, we know that of the projectile
■when it has travelled 8 inches. Again, if we make the section of the cylinder half that
of the projectile, it will describe in the same time double the space and have acquired
double the velocity, and so on ; so that, for example, if the section of the cylinder be
one eighth of that of the projectile, we shall, if we know the cylinder’s velocity, know
that of the projectile when it has travelled 1 inch.
The general results at which the Prussian Committee arrived were, that in the
6-pounders the maximum pressure realized was about 1100 atmospheres (7’2 tons per
square inch), and in the 12-pounders about 1300 atmospheres (8’5 tons per square inch).
They further found that, with every charge with which they experimented, two maxima
of tension were distinctly perceptible.
These experiments were made the subject of an elaborate memoir by the distinguished
Russian Artillerist General Mayevski*, who confirmed generally the results arrived at
by the Prussian Committee.
Between the years 1857 and 1859 Major Rodman made an extensive series of
experiments on gunpowder for the United States Government.
The chief objects of Rodman’s experiments were: — 1st, to ascertain the pressure
exerted on the bores of their then Service Guns ; 2nd, to determine the pressures in
guns of different calibres, the charges and projectiles in each calibre being so arranged
that an equal column or weight of powder was behind an equal column or weight of
shot ; 3rd, to investigate the effect produced on the gaseous tension in the bore of a
gun by an increment in the size of the grains of the powder ; and 4th, to determine
the ratio which the tension of fired gunpowder bore to its density.
In carrying out these experiments, Rodman made use of an instrument devised by
himself, and since extensively used on the Continent. It is represented in Plate 14.
fig. 1, and consists of a cylinder, A, communicating by a passage, B, with the bore
of the gun or interior of the vessel, the pressure existing in which it is desired to
measure.
In the cylinder is fitted the indicating-apparatus, consisting of a piece of copper, C,
against which is placed the knife D, shown in elevation and section. The pressure
of the gas acting on the base of the piston E causes the indenting-tool to make a cut
on the soft copper, and, by mechanical means, the pressure necessary to make a similar
cut in the copper can be determined.
A small cup at F prevents any gas passing the indenting-tool, while the little channel
G allows escape should any, by chance, pass.
Rodman considered that his experiments showed that the velocities obtained in large
guns with the service small-grained powder might be obtained, with a greatly diminished
* Revue de Technologie Militaire, tom. ii. p. 174.
t Experiments on Metal for Cannon and qualities of Cannon Powder. Boston, 1861.
56
CAPTAIN NOBLE AND ME. E. A. ABEL ON FIEED GUNPOWDEK.
strain on the gun, by the use of powder properly adapted in size of grain to the calibre
and length of bore proposed to be used.
Rodman’s conclusions on this head are extremely valuable, although, as has been
elsewhere pointed out*, some of his experimental results are open to grave criticism.
His experiments on the relation between the tension and density of powder (the powder
being placed in a strong shell and fired through a small vent) were not carried far enough
to be of much value ; but on Plate 13. fig. 2 we have represented his results in comparison
with those of Rumfokd.
Rodman also made an attempt to determine the pressure that would be exerted when
powder was exploded in its own space. He fired the charges, as before, through a vent
in a strong shell, and considered that the maximum pressure would be realized before
the shell burst. His results were very various, ranging from 4900 to 12,400 atmo-
spheres, the highest tension being obtained with the smallest charge. These anomalous
results were probably due to the distance from the charge at which his instrument was
placed, the products of combustion doubtless attaining a very high velocity before acting
on the piston.
In 1857 Bunsen and Schischkoff publishedf their very important researches on
gunpowder. Their experiments were directed, first, to determine the nature and pro-
portions of the permanent gases generated by the explosion of gunpowder ; secondly,
to determine the amount of heat generated by the transformation. With the aid of
these experimental data they deduced, from theoretical considerations, the temperature
of explosion, the maximum pressure in a close chamber, and the total theoretical work
which gunpowder is capable of performing on a projectile.
The powder in these experiments was not exploded, but deflagrated, by being allowed
to fall in an attenuated stream into a heated bulb in which, and in the tubes connected
with it, the products were collected.
The transformation, according to these experimenters, experienced by gunpowder in
exploding, is shown in the following scheme. It will be observed that the permanent
gases represented only about 31 per cent, of the weight of the powder, and occupied at
0° C. and 760 millims. only 193 cubic centims. — that is, approximately, 193 times the
volume occupied by the unexploded powder.
* Noble, “Tension of Fired Gunpowder,” Proc. Eoyal Institution, vol. vi. p. 282.
t Poggendokff’s ‘ Annalen,’ vol. cii. p. 325. A translation of Bunsen and Schischkoff’s memoir appeared
in the occasional papers of the Eoyal Artillery Institution, vol. i. p. 297 ; see also, at p. 312 of the same
volume, Mr. Abel’s remarks on Bunsen and Schischkoff’s results.
CAPTAIN NOBLE AND ME. F. A. ABEL ON FIEED GUNPOWDER.
57
Table I. — Showing the transformation experienced by Gunpowder after Bunsen
and Schischkoff.
| ^Residue 0-6806 grin.
f Nitre . . . ,
. .. •7899'’)
1 Sulphur .
. . . -0984
;
fC -0769
Charcoal ■
H -0041
l
[ O -0307 J
Gases 0-3138 grm.
0-9944
f K2 C03
k2s2o3 ....
K2so4
k2s
' KC NS
kno3
(NH4)2 CO ..
s
1C
grms.
, -1264
, -0327
. -4227
. -0213
, -0030
, -0372
, -0286
•0014
, -0073
cub. centims.
rsH2
, -0018-
1-16
0
•0014=
1-00
CO
•0094-
7-49
co2
•2012=
101-71
H
•0002=
2-34
N
•0998=
79-40
193-10
In Table III. a comparative statement is given of the foregoing results with those of
other recent experimenters and with those furnished by our investigations.
Bunsen and Schischkoff determined the number of units of heat generated by
combustion, by exploding a small charge of powder in a tube immersed in water. They
found that the combustion of a gramme of powder gave rise to 620 gramme-units of
heat ; and hence they calculated that the temperature of explosion, in a close chamber
impervious to heat, was 3340° C (5980° F.).
From the above data the pressure in a close vessel is deducible ; and they computed
that the maximum pressure which the gas can attain, which it may approximate to but
can never reach, is about 4374 atmospheres, or 29 tons on the square inch.
Bunsen and Schischkoff further computed the total theoretical work which a kilo-
gramme of gunpowder is capable of producing on a projectile at 67,400 kilogrammetres.
In the course of our paper we shall have frequent occasion to refer to these very
important researches.
In 1858 Dr. J. Linck* repeated, with Wurtemburg war-powder, Bunsen and
Schischkoff’s analysis of the products of combustion, which were obtained by the same
method. The composition of the powder used is given in Table II.
Linck’s results, which we have placed in the same Table as those of Bunsen and
Schischkoff, differed in several points from the results of the latter chemists, but chiefly
in the much smaller quantity of potassium sulphate found. Linck considered that 1
gramme of the powder used generated 218*3 cub. centims. of gas.
In 1863 M. von KAEOLYif examined the products of combustion of Austrian musket-
and ordnance-powder.
* Annalen der Chemie, vol. cix. p. 53.
f Poggendorff’s ‘ Annalen,’ April 1863. Philosophical Magazine, ser. 4, vol. xxvi. p. 266.
MDCCCLXXV. I
58
CAPTAIN NOBLE AND ME. F. A. ABEL ON FIRED GUNPOWDER,
M. von Karolyi’s method of obtaining the products of combustion consisted in
suspending in a spherical shell a small case containing a charge of the powder to be
experimented with. Before firing the charge, the air contained in the shell was
exhausted ; the powder was fired by electricity.
The arrangement will readily be understood from the sketch shown in fig. 3, Plate 15.
After combustion, the gases were obtained for examination by means of the stop-
cock, while the solid residue remaining in the shell was removed with water and filtered.
The composition of the powders used is given in Table II., and the results of analysis
in Table III. Yon Karolyi computed that the gases resulting from 1 gramme of small-
arm powder generated 226-6 cubic centims., and from 1 gramme of ordnance-powder
200*9 cub. centims.
The Astronomer Royal, Sir G. B. Aiey, in a paper* published in 1863, “On the
Numerical Expression of the Destructive Energy in the Explosions of Steam-boilers,
and on its comparison with the Destructive Energy of Gunpowder,” considers that “ the
destructive energy of 1 cubic foot of water (62-23 lb. =28*23 kilos.) at the temperature
which produces the pressure of 60 lb. to the square inch is equal to that of 1 pound of
gunpowder, and that the destructive energy of 1 cubic foot of water at the temperature
which produces the pressure of 60 lb. to the square inch, surrounded by hot iron, is
precisely equal to the destructive energy of 2 lb. of gunpowder as fired in a cannon.”
Aiey takes the energy of a kilogramme of powder as fired from a gun at 56,656
kilogrammetres= 82-894 foot-tons per lb. of powder; so that the total energy of
gunpowder would be somewhat less than double the above value. He states, however,
that this estimate does not pretend to be very accurate.
In 1869 were published, in the ‘Zeitschrift fiir Chemie’f, the results of some
experiments made by Colonel Fedoeow to determine whether the products varied
materially with the mode of combustion.
Fedoeow experimented (1) by firing a pistol with a blank charge into a glass tube
4 feet long, (2) and by firing a shotted 9-pounder bronze gun with 3 lb. of powder ; the
residues were in each case dissolved in water and analyzed.
The composition of the powder employed by Fedoeow is given in Table II., and his
analytical results are shown in Table III.
From the experiments with the gun, Fedoeow calculated that the gaseous products
were 82-6 cub. centims. N, 162-1 cub. centims. C02, and 14 cub. centims. S02 and O.
He considers that several successive reactions take place during combustion, that
potassium sulphate and carbonic anhydride are first formed, while the excess of carbon
reduces the sulphate to carbonate, hyposulphite, and carbonic anhydride.
In 1871 Captain Noble $, one of the present writers, in detailing to the Royal
Institution his earlier researches on the tension of fired gunpowder, stated that the
conclusion at which he had arrived from the results of his experiments, where the
* Philosophical Magazine, ser. 4, vol. xxvi. p. 329. , f Yol. v. p. 12.
t Proceedings of Royal Institution, yol. vi. p. 282.. Revue Scientifique, No. 48, p. 1125.
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GUNPOWDEE.
59
products of combustion were entirely or partially confined, was, that the maximum
pressure of fired gunpowder, of the usual gravimetric density, when unrelieved by
expansion, did not greatly exceed 6100 atmospheres (40 tons to the square inch).
Upon the same occasion a curve was exhibited, showing the relation between the
tension and the density of the exploded products. These results have been confirmed by
our present more extensive and exact investigations.
Captain Noble also stated that, by means of a special apparatus, which was fully
described at the time, he had not only determined the tension of the gases at various
densities, but had exploded considerable charges filling entirely the chambers of close
vessels, and had altogether retained and at pleasure discharged the gaseous and other
products of combustion *.
Berthelot f published, in 1872, a collection of theoretical papers upon the force of
powder and other explosive substances.
Berthelot does not attempt to evaluate the force of fired gunpowder, but evidently
accepts as tolerably correct J the tensions assigned by Rumford and Piobert, and accounts
for the discrepancy between their conclusions and those of the modern chemists by
assuming that the laws of Mariotte and Gay-Lussac lose all physical significance for
pressures so enormous as those developed in the combustion of gunpowder.
Berthelot is disposed § to think that dissociation plays a considerable role during the
expansion of the products in the bore of a gun. He supposes that the phenomena of
dissociation do not exercise their influence only during the period of maximum effect,
but that, during the expansion of the gases, a cooling effect is produced, by which a
more complete combination is effected and more heat disengaged.
Taking Bunsen and Schischkoff’s experiments as a basis, Berthelot expresses the
decomposition experienced by gunpowder by the equation ||
I6KNO3+6S+ 13C=5K2S04+2K2 C03+K2S+16N+11C02,
which he considers represents their results with sufficient exactness.
In 1873 M. de Tromenec^J communicated to the Academy of Sciences a short memoir
on the means of comparing the absolute force of varieties of powder. His method was
based upon the principle that, when a body is exploded without producing mechanical
effect, the “ force disponible ” is converted into heat, and that it is only necessary to
explode a given weight in a close vessel and determine the heat produced.
The apparatus used by De Tromenec was closed in much the same manner as was
'* In the present paper, in Section K, the results of some of Capt. Noble’s earlier experiments are given.
They accord, as will he seen, exceedingly well with the series we have discussed at length ; hut a few experi-
ments made with a fine-grained powder are excluded, both because the powder, being sporting, was not com-
parable with the fine-grain used in the present researches, and because the differences in their composition are
unknown, the sporting-powder not having been analyzed.
f Sur la Force de la Poudre. Paris, 1872. J Loc. cit. p. 80. § Loc. cit. p. 83.
|| Loc. cit. p. 91. Comptes Rendus de l’Academie des Sciences, tom. lxxvii. p. 126.
i 2
60
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIRED GUNPOWDER.
that employed by Captain Noble in his earlier experiments already alluded to. The
three kinds of powder experimented with gave results varying between 729 and 891
calories generated by the combustion of 1 kilogramme of powder.
In the same * number of the ‘ Comptes Rendus ’ in which De Tkomenec’s memoir is
given, appears a note by MM. Roux and Sarrau, in which, and in a subsequent notef,
are determined, with small charges, some of the points to which our own investigations
have been specially directed.
MM. Roux and Sarrau have given, for five species of powder, the number of
calories and volume of gas generated by a given weight of powder, and have from these
data calculated the temperature of combustion and tension of the gas.
With one of the powders, representing closely the composition of those chiefly
experimented with by us, the number of calories and volume of the gas agree nearly
exactly with the numbers found by ourselves. There is, however, a considerable differ-
ence in our determinations (both theoretical and experimental) of the tension of the gas
and also of the temperature of explosion, the temperature being estimated by Roux and
Sarrau at about 4200° C. and the tension at about 4700 atmospheres.
We shall return, however, to these points when discussing our own experiments.
B. OBJECTS OE EXPERIMENTS.
The chief objects which we had in view in making these investigations were : —
First. To ascertain the products of combustion of gunpowder fired under circum-
stances similar to those which exist when it is exploded in guns or mines.
Second. To ascertain the tension of the products of combustion at the moment of
explosion, and to determine the law according to which the tension varies with the
gravimetric density of the powder.
Third. To ascertain whether any, and, if so, what well-defined variation in the nature
or proportions of the products accompanies a change in the density or size of grains
of the powder.
Fourth. To determine whether any, and, if so, what influence is exerted on the
nature of the metamorphosis by the pressure under which the gunpowder is fired.
Fifth. To determine the volume of permanent gases liberated by the explosion.
Sixth. To compare the explosion of gunpowder fired in a close vessel with that of
similar gunpowder when fired in the bore of a gun.
Seventh. To determine the heat generated by the combustion of gunpowder, and
thence to deduce the temperature at the instant of explosion.
Eighth. To determine the work which gunpowder is capable of performing on a shot
in the bore of a gun, and thence to ascertain the total theoretical work, if the bore be
supposed of indefinite length.
* Comptes Rendus, tom. lxxvii. p. 138.
t Ibid. p. 478.
CAPTAIN NOBLE AND ME. F. A. ABEL ON FIEED GUNPOWDER.
61
C. METHODS OE EXPERIMENT.
1. Explosion-apparatus.
We propose, in the first place, to describe the principal apparatus used in these
investigations, and shall commence with that portion which is of primary importance,
viz. the vessel in which the explosions were produced. Two sizes of vessels were used,
the larger being capable of holding about 2J lb. (1 kilogramme) of powder, the other
being about half that capacity.
Both vessels were of the same general construction, and similar to that described in
Captain Noble’s Lecture at the Royal Institution already referred to. A drawing of
the apparatus is given in Plate 14. figs. 2 & 3.
A (see figs. 2 & 3) is a mild steel vessel of great strength, carefully tempered in oil,
in the chamber of which (B) the charge to be exploded is placed.
The main orifice of the chamber is closed by a screwed plug (C), called the firing-
plug, which is fitted and ground into its place with great exactness.
In the firing-plug itself is a conical hole, which is stopped by the plug D, also ground
into its place with great accuracy. As the firing-plug is generally placed on the top of
the cylinder, and as, before firing, the conical plug would drop into the chamber if not
held, it is retained in position by means of the set-screw S, between which and the
cylinder a small washer (W) of ebonite is placed. After firing, the cone is, of course,
firmly held, and the only effect of internal pressure is more completely to seal the
aperture. At E is the arrangement for letting the gases escape ; the small hole F
communicates with the chamber where the powder is fired, and perfect tightness is
secured by means of the mitred surface (G). When it is wished to let the gases escape,
the screw E is slightly withdrawn, and the gas passes into the passage H.
At K is placed the “ crusher-apparatus ” for determining the tension at the moment of
explosion.
When it is desired to explode a charge, the crusher-apparatus, after due preparation,
is first carefully screwed into its place, and the hole F closed. The cone in the firing-
plug is covered with the finest tissue-paper, to act as an insulator.
The two wires LL, one in the insulated cone, the other in the cylinder, are connected
by a very fine platinum wire passing through a small glass tube filled with mealed
powder. Upon completing connexion with a Daniell’s battery the charge is fired.
The only audible indication of the explosion is a slight click ; but frequently, upon
approaching the nose to the apparatus, a faint smell of sulphuretted hydrogen is
perceptible.
The difficulties we have . met with in using this apparatus are more serious than migh
at first sight appear.
In the first place, the dangerous nature of these experiments rendered the greatest
caution necessary, while, as regards the retention of the products, the application of
62
CAPTAIN NOBLE AND ME. F. A. ABEL ON FIEED GUNPOWDER.
contrivances of well-known efficacy for closing the joints, such as jpapier-mdchG wads
between disks of metal (a method which has been successfully employed with guns), are
inadmissible, because the destruction of the closing or cementing material used, by
the heat, would obviously affect the composition of the gas. Every operation con-
nected with the preparation of the apparatus for an experiment has to be con-
ducted with the most scrupulous care. Should any of the screws not he perfectly
home, so that no appreciable amount of gas can escape, the gases, instantly upon their
generation, will either cut a way out for themselves, escaping with the violence of an
explosion, or will blow out the part improperly secured, in either case destroying the
apparatus.
The effect produced upon the apparatus, when the gas has escaped by cutting a
passage for itself, is very curious. If, for example, one of the plugs has not been
sufficiently screwed home, so that the products of combustion escape between the male
and female threads, the whole of these threads at the point of escape present the
appearance of being washed away, the metal having been evidently in a state of fusion,
and carried over the surface of the plug by the rush of the highly heated products.
Again, the difficulty of opening the vessel after explosion, when large charges have
been used, is very great. This will be readily understood when the temperature and
pressure of explosion are considered. The exploding-chamber being filled with products
intensely heated and under an enormous pressure, there is an expansion of the interior
surface of the cylinder. Hence small portions of the fluid products become forced in
between the threads of the screws. These solidify into a substance of intense hardness,
which cements together the metal surfaces, and, on cooling, the contraction of the
cylinder puts such a pressure on the screw, that, in attempting to open it, seizure is
very difficult to avoid. In one or two cases it was found impossible to open the
cylinder until melted iron had been run round it, so as to cause it to expand.
This difficulty has been in a great measure avoided, in the more recent experiments,
by making the screws conical, so that when once started clearance is rapidly given, and
they are removed with comparative ease.
2. Measurement of Pressure.
The apparatus used for the measurement of the tension of the gas was precisely
similar to that which has been used by the Committee on Explosives, and consists of a
screw-plug of steel (Plate 14. figs. 4 & 5), which admits of a cylinder of copper or other
material (A) being placed in the small chamber (B). The entrance to the chamber is
closed by the movable piston (C), and the admission of the gas is prevented by the use
of the gas-check, D. When the powder is fired, the gas acts upon the base of the piston
and compresses the cylinder. The amount of compression of the cylinder serves as an
index to the force exerted, the relation between the amount of crush and the pressure
necessary to produce it being previously carefully determined.
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GUNPOWDER
63
3. Measurement of the Volume of the Permanent Gases.
The apparatus used for the measurement of the permanent gases is shown in Plate
15. figs. 1 & 2. A is a vessel the annular space (B) of which is filled with water ; on
the surface of this a thin film of oil is floated, to prevent any slight absorption of the
gas which might otherwise take place.
Immediately after the explosion of a charge, the gas from which it is desired to
measure, the cylinder (C) containing the products is placed on the table (D), and the
gasometer (E) is placed over the cylinder ; the height of the water on the glass scale (F)
being then registered, the escape-screw (G) of the cylinder is turned, by means of a
turncock passing through the stuffing-box (M).
When the gas has all escaped, the height indicated on the glass scale being again
registered, the cubic contents are known, and the thermometer (H) and height of
barometer being noted, the necessary data are available for reducing the volume of
the gas to a temperature of 0°C. and a barometric pressure of 760 millims.
4. Measurement of Heat.
To determine the heat generated by explosion, a charge of powder was weighed and
placed in one of the smaller cylinders described, which was kept for some hours in a
room of very uniform temperature. When the apparatus was throughout of the same
temperature, the thermometer was read, the cylinder closed, and the charge exploded.
Immediately after explosion the cylinder was placed in a calorimeter containing a
given weight of water at a measured temperature, the vessel being carefully protected
from radiation, and its calorific value in water having been previously determined.
The uniform transmission of heat through the entire volume of water was maintained
by agitation of the liquid, and the thermometer was read every five minutes until the
maximum was reached. The observations were then continued for an equal time to
determine the loss of heat in the calorimeter due to radiation, &c. ; the amount so
determined was added to the maximum temperature.
In this method there is a possible source of error ; the walls of the cylinder being of
very considerable thickness, it is obvious that, although the outer surface of the cylinder
must be of the same temperature as the water, it by no means follows that this is true
of the internal surface ; consequently the loss of heat due to radiation, &c. may be in
some degree compensated by a flow of heat from the interior.
We had reason, from some experiments we made, to believe that the error due to this
cause was very small ; and our views were confirmed by finding no appreciable rise of
temperature on placing some water from the calorimeter into the chamber of the
cylinder immediately after an experiment.
5. Collection of Gaseous Products.
To collect the gases for analysis, a small pipe was screwed into the escape-passage (H^
of the cylinder (Plate 14. figs. 2..&.3), and an india-rubber tube, terminating in a glass
64
CAPTAIN NOBLE AND ME. F. A. ABEL ON EIEED OUNPOWDEE.
nozzle, was led to a mercurial trough. Before the gas was taken, a sufficient quantity
was allowed to escape to clear the tubes of air; the gas was then collected in tubes
over mercury, and confined in the usual manner by sealing them with the blowpipe.
The gas was generally collected in from five to fifteen minutes from the time of
explosion. Owing to the dangerous nature of the experiments, and the precautions
necessary to be adopted in exploding such considerable charges of powder, it was not
generally possible to collect the gases more rapidly ; but a comparison of the analysis
of different tubes taken from the same experiment has shown that, at all events within
moderate limits, no change takes place in the composition of the gas by its continued
contact with the solid products.
6. Collection of Solid Products.
The collection of the solid products presented much more difficulty than that of
the gaseous products. On opening the cylinder, the whole of the solid products were
found collected at the bottom, there being generally an exceedingly thin (in fact, with
large charges, quite an inappreciable) deposit on the sides. Upon the firing-plug there
was usually a button of deposit, which differed considerably both in appearance and
in chemical composition from the rest. In the button a crystalline structure was
quite apparent, some of the crystals being large and transparent. The surface of the
deposit was generally perfectly smooth and of a very dark grey, almost black, colour.
This colour, however, was only superficial, and through the black could be perceived
what was probably the real colour of the surface, a dark olive-green. The surface of
the deposit, and the sides of the cylinders, had a somewhat greasy appearance, and were
indeed greasy to the touch. On the smooth surface were frequently observed very
minute particles, in appearance like soot, but of the greasy texture to which we have
alluded.
The removal of the deposit was generally attended with great difficulty, as it formed
an exceedingly hard and compact mass, which always had to be cut out with steel
chisels. Lumps would frequently break off, but a considerable portion flew off before
the chisel in fine dust. In various experiments, on examining the fracture as exhibited
by the lumps, the variation in physical appearance was very striking, there being
marked differences in colour, and also, frequently, a marked absence of homogeneity,
patches of different colours being interspersed with the more uniform shade of the
fracture. There was no appearance of general crystalline structure in the deposit ; but,
on examination with a microscope and sometimes with the naked eye, shining crystals
of metallic lustre (sulphide of iron) were observed. On the whole, the general appear-
ance of the deposit was attended with such considerable variations, that, for minute
details, we must refer to the account of the experiments themselves. The deposit
always smelt powerfully of sulphuretted hydrogen, and frequently strongly of ammonia.
It was always exceedingly deliquescent, and after a short exposure to the air became
black on the surface, gradually passing over into an inky-looking pasty mass. As in
CAPTAIN NOBLE AND ME. F. A. ABEL ON FIRED GUNPOWDER.
65
physical appearance, so in behaviour of the solid, when removed from the cylinder, there
were considerable differences between the experiments. The deposit was transferred
to thoroughly dried and warm bottles, and sealed up as rapidly as possible. In most
cases, during the very short time that elapsed while the transference was being made, no
apparent change took place ; but in some a great tendency to development of heat was
apparent ; and in one instance, in which a portion of the deposit (exhibiting this
tendency in a high degree) was kept exposed to the action of the air, the rise of tempe-
rature was so great that the paper on which it was placed became charred, and the
deposit itself changed colour with great rapidity, becoming a bright orange-yellow on
the surface.
This tendency to heating always disappeared when the deposit was confined in a bottle
and fresh access of air excluded.
The portion of the residue which could not be removed from the cylinder in a dry
state was dissolved out with water, the solution being reserved for examination in well-
closed bottles.
D. ANALYSIS OF THE PRODUCTS OF EXPLOSION.
1. Gaseous Products.
The method pursued for the analysis of the gaseous products of explosion presented
only one important point of difference from that pursued by Bunsen and Schischkoff.
The volume of gas at command being more considerable than was the case in the inves-
tigations of those chemists, it was found more convenient to have recourse to methods
for determining the sulphuretted hydrogen differing from that which they adopted —
namely, its estimation by oxidation of the sulphur in the ball of potassium hydrate
employed for absorbing the carbonic anhydride and sulphuretted hydrogen together.
In some instances the volume of this gas was ascertained by absorption with manganese
balls, but generally the following indirect method was pursued. The combined volume
of carbonic anhydride and sulphuretted hydrogen was determined in one portion of the
gas by means of potassium hydrate ; another portion of gas was then treated with a
small quantity of cupric sulphate, and the volume of carbonic anhydride determined in
the gas thus freed from sulphuretted hydrogen.
The following numerical data relating to the analysis of the gases obtained by the
explosion of 190-5 grms. of R. L. G. gunpowder (of Waltham-Abbey manufacture) in
five times its own space are given in illustration of the detailed result obtained : —
I.
Volume.
Tempe-
Pressure.
Volume corrected
rature.
for temperature
and pressure.
1 . Original volume of gas . . . .
144-4
13-3
0-7243
99-80
2. After absorption of C02 and SH2 .
78-2
13-3
0-6727
.50-16
3. After absorption of oxygen . .
76-9
14-4
0-6795
49-64
MDCCCLXXV.
K
66
CAPTAIN NOBLE AND MB. E. A. ABEL ON EIKED GUNPOWDER.
II.
Volume.
Tempe-
Pressure.
Volume corrected
rature.
for temperature
o
and pressure.
4. Volume of original gas after absorp-]
t 144-2
14-2
0-7293
99-97
tion of sulphuretted hydrogen .J
s
5. After absorption of C02 . . .
. 82-2
16-3
0-6672
51-76
6. After absorption of oxygen . .
. 80-6
18-8
0-6735
50-79
III.
7. Portion of 3 transferred to eu-'
i 174-8
15-4
0-1983
32-81
diometer J
f
8*. After addition of air ....
. 248-4
15-5
0-2712
63-75
9. After addition of oxygen . . .
. 319-5
15-6
0-3427
103-58
10. After explosion with oxyhydrogen'
i 310-8
15-8
0-3302
97-02
gas J
1
1 1 . After absorption of C02 . . .
. 291*6
18-3
0-3271
89-39
12. Portion of 11 transferred to clean.
| 301-5
18-6
0-3141
88-66
eudiometer J
13. After addition of hydrogen . .
. 550-8
18-9
0-5642
290-85
14. After explosion (dry) ....
. 416-0
18-8
0-4295
167-16
By calculation from the above data, the composition ^of this gas,
in volumes per
cent., was found to be as follows : —
Carbonic anhydride 46T7
Sulphuretted hydrogen 3' 91
Oxygen 0'52
Carbonic oxide 11’46
Marsh-gas 0"03
Hydrogen 2-72
Nitrogen 35' 18
The gas in each experiment was generally collected in three or four large tubes.
The contents in one tube sufficed, in most instances, for the complete analysis ; but the
results obtained were always controlled by determinations of several, if not of the
whole, of the constituents in the contents of another tube. Only in one instance were
the contents of different tubes, collected from one and the same experiment, found to
differ materially in composition ; in this particular instance the proportion of sulphu-
retted hydrogen in the different tubes was discordant. The mean of the results fur-
nished by the contents of the three tubes was taken to represent the composition of
the gas.
* Air was added to dilute the gas in this and one or two subsequent explosion experiments ; but this precau-
tion was found to be unnecessary, and was therefore not continued.
CAPTAIN NOBLE AND MB. E. A. ABEL ON FIEED GUNPOWDER.
67
2. Solid Residue. — Preparation of the Residue for Analysis.
The residue, as collected for analysis, consisted of one or more large masses, besides
a quantity in a more or less fine state of division which had been detached from the
sides of the vessel. The appearance presented by the large pieces themselves indicated
that they were by no means homogeneous, and they evidently differed in some respects
from the ^smaller particles just referred to ; moreover the foreign matters (metal and
glass) could not be expected to be uniformly distributed throughout the mass, and a
chemical examination of the latter clearly indicated that certain constituents existed in
different proportions in the upper and lower parts of the residue. For these reasons,
in order to insure the attainment of results correctly representing the composition of
the residue, it appeared indispensable to operate upon the entire quantity at one time,
with the view of determining the total amount of matter insoluble in water, and of
preparing a solution of uniform composition in which the several components of the
residue could be estimated. As the investigation proceeded, much inconvenience and
delay were experienced from the necessity of working with very large quantities (from
400 to 100 grms.), which rendered the filtrations and washings protracted operations,
and necessitated dealing with very large volumes of liquid. It was therefore attempted
to expedite the examination of the residues by so preparing them that only portions
might be operated upon at one time in conducting the individual determinations of
the constituents. The impossibility of pulverizing and mixing the residue by any ordi-
nary mode of proceeding, on account of the rapidity with which oxygen and water were
absorbed from the air, was demonstrated by two or three attempts. An arrangement
was therefore devised for performing the operation in an atmosphere of pure nitrogen.
The gas employed was prepared in the following manner : —
A gasometer filled with air was submitted to a gentle pressure, causing the air to
flow very slowly through a delivery-pipe to a porcelain tube filled with copper turnings
and raised to a red heat. To remove any traces of oxygen, the nitrogen passed from
the tube through two Woulfe’s bottles containing pyrogallic acid dissolved in a solu-
tion of potassium hydrate; and, finally, to remove moisture, it passed through two
U-tubes filled with pumicestone moistened with sulphuric acid. The nitrogen thus
obtained was collected in india-rubber bags ; the residue was placed in a closed mill,
connected by an india-rubber tube with the gas-bag, which was subjected to a consider-
able pressure to establish a plenum in the mill. The substance was then ground, and
allowed to fall into bottles, which were at once sealed. By this treatment a sufficient
degree of uniformity in different samples of any particular residue was generally
attained ; in some cases, however, the state of division of the substance was not suffi-
ciently fine to secure such intimacy of mixture as would preclude the occurrence of
discrepancies in the analytical results furnished by different samples. It was therefore
found necessary to return occasionally to the employment of the entire residue obtained
in one experiment for determining its composition.
K 2
68
CAPTAIN NOBLE AND MR. E. A. ABEL ON EIRED GUNPOWDER.
3. Analysis of the Solid Residue.
Qualitative analysis indicated that the proportions of the following substances had
to be determined in the solid residue.
a. Portion insoluble in water. — This consisted of steel (unavoidably detached from
the interior of the vessel during removal of the residue) and of small quantities of other
metals, besides glass, which were used in the construction of the electric igniting
arrangement. The weight of these substances was deducted from the residue, as foreign
to the research.
In addition to these substances, the residue insoluble in water contained generally
traces of charcoal, besides sulphur, which was combined with iron and portions of the
other metals, and the amount of which is included in the statement of results as free
sulphur , together with the proportion which was found, in combination with potassium,
in excess of the amount required to form the monosulphide.
b. Portion soluble in water. — In this, the chief portion of the residue, there existed
the potassium sulphide, sulphocyanate, hyposulphite, sulphate, carbonate, and nitrate,
besides ammonium carbonate, and, in very exceptional cases, potassium hydrate. The
estimation of the proportions in which these several constituents existed in the residue
was conducted as follows : —
c. Water contained in the residue. — It is obvious that the highly hygroscopic nature
of the powder-residue rendered it impossible to transfer the product of an explosion
from the iron cylinder to suitable receptacles for its preservation out of contact with
the atmosphere without some absorption of moisture, however expeditiously the opera-
tion was performed. Moreover any water produced during the explosion, or preexist-
ing in the powder, would necessarily be retained by the solid residue after explosion,
as the gas remained in contact with a large surface of this powerful desiccating agent
for some time before it could be collected. In some instances the water was expelled
from the residue by exposing it for some time to a slow current of hydrogen at 300° C.,
the gas and volatile matters being passed into solution of lead acetate, for the purpose
of retaining sulphur, and the weight of the dried residue determined. The amount of
residue, however, was generally too considerable for this operation to be satisfactorily
performed ; there was therefore no alternative in such cases but to assume that the
difference between the total weight of the residue and the combined weights of its
several solid constituents, ascertained in almost every instance by duplicate and check
determinations, represented the amount of water present in the substance*.
d. Separation of the portion insoluble in water , and determination of Sulphur in it. —
The separation was accomplished by thoroughly washing the entire residue, or about
7 grammes of the ground residue, with well-boiled water until no discoloration was
produced in the washings by lead acetate. Boiled water was employed to avoid oxi-
* If discrepancies existed between the results of determination of the several constituents and the check-
determinations, the water was estimated, as described, in a portion of the residue.
CAPTAIN NOBLE AND MR. F. A. ABEL ON FIRED GUNPOWDER.
69
datioii of any of the constituents. After drying and washing the residue, it was intro-
duced, with its filter, into a small flask ; a little potassium bichromate was added before
addition of nitric acid, to guard against violent reaction and the possibility of minute
quantities of sulphur escaping as sulphuretted hydrogen. The oxidation was completed
by the addition of potassium chlorate ; the liquid, after sufficient dilution, was filtered
and evaporated, the residue redissolved in water, with addition of chlorhydric acid, and
the sulphuric acid determined in the solution by the usual method.
The proportion of charcoal contained in the insoluble residue was, in most instances,
so small that no importance could be attached to any attempt to determine the quantity.
In a few cases its amount was determined by combustion.
e. Potassium monosulphide.-— The method pursued differed but very slightly from
that adopted by Bunsen and Sciiischkoff. The aqueous solution, separated from the
insoluble portion, was digested with pure ignited cupric oxide in a well-closed flask,
with occasional agitation, until it became colourless. The oxide containing sulphide
was then filtered off, thoroughly washed, and the sulphur was determined in it by oxi-
dation according to the method just described (d).
f. Potassium sulphate. — The filtrate obtained after the treatment with cupric oxide
just described (or a measured quantity of it, if the entire residue was operated upon at
one time) was mixed with chlorhydric acid and boiled to expel the sulphurous acid
resulting from the decomposition of hyposulphite ; the liquid was then separated by
filtration from liberated sulphur, and the sulphuric acid determined as barium sulphate.
g. Potassium hyposulphite. — The solution obtained by treatment, as above described,
of about 4 grammes of the residue (or a sufficient volume prepared from the entire
residue) was acidulated with acetic acid; 8 or 4 cub. centims. of starch solution were
added, and the hyposulphurous acid determined by means of a standard iodine solution.
h. Potassium sulphocyanate. — A solution of the residue, after separation of the
insoluble portion and the soluble sulphide, was carefully acidified with a measured
quantity of dilute chlorhydric acid, so as to avoid separation of sulphur. The oxida-
tion of the hyposulphite was then effected by the gradual addition of a very dilute
solution of ferric chloride until the liquid exhibited a permanent pink tint. A mea-
sured quantity of the ferric solution was afterwards gradually added until the greatest
attainable depth of colour was produced. To determine what was the amount of
sulphocyanate thus arrived at, a volume of water corresponding to that of the original
solution tested was mixed with equal volumes of the dilute chlorhydric acid and ferric
chloride to those used in the previous experiments. A solution of potassium sulpho-
cyanate of known strength was then gradually added until a depth of colour cor-
responding to that of the actual assay was produced.
i. Potassium carbonate. — After the usual treatment of a solution of the residue with
cupric oxide, pure manganous sulphate or chloride was added to the liquid in excess;
the resulting precipitate might generally be washed by decantation in the first instance ;
after complete washing it was transferred to a small flask suitably fitted for the libera-
70
CAPTAIN NOBLE AND MR. F. A. ABEL ON FIRED GUNPOWDER.
tion of carbonic anhydride from it, by addition of sulphuric acid, and for the transmis-
sion of the gas through small weighed absorption-tubes containing respectively sulphuric
acid, calcium chloride, and solution of potassium hydrate. The increase in weight of
the latter corresponded to the proportion of carbonic anhydride in the solid residue.
j. Potassium sulphide, potassium carbonate , and potassium hydrate. — Pure man-
ganous chloride or sulphate was added in excess to the aqueous solution of the residue,
and the amount of manganese, in the thoroughly washed precipitate, determined as
red oxide. If the amount obtained exceeded those which would be furnished by the
potassium sulphide and carbonate (deduced from the previous determinations), the excess
was taken to correspond to potassium hydrate existing in the residue. If it was less,
the sulphur existing as monosulphide of potassium was calculated from the weight of
the manganous oxide, and the difference between it and the sulphur found in the cupric
oxide (in determination e) was taken to represent excess of sulphur, or free sulphur,
and was added to the result of determination d, the necessary correction being made in
the number furnished by determination e.
k. Total amount of potassium. — The solution of the residue, after treatment with
cupric oxide, was evaporated with excess of sulphuric acid, and the residue repeatedly
treated with ammonium carbonate and ignited, until the weight of potassium sulphate
was constant. Or water and sulphuric acid were added to about 4 grms. of the residue,
and after boiling to expel sulphurous acid, two or three drops of nitric acid were added
to peroxidize the little iron in solution and excess of ammonia to precipitate the latter.
The precipitate and insoluble matters (glass &c.) were then filtered off, and the solu-
tion evaporated, the weight of potassium sulphate being ascertained by treatment of
the residue as already described. In this way the amount of potassium arrived at
indirectly, by the determinations of the several substancesjvith which it existed in com-
bination, was controlled by direct estimation.
l. Ammonium sesqidcarbonate. — The solution of about 12 grms. of the residue was
diluted to one litre the liquid was then carefully distilled until about 250 cub. centims.
remained in the retort, the distillate being allowed to pass into dilute chlorhydric acid.
As some minute quantities of potassium salt might have passed over, the distillate was
returned to a retort, mixed with excess of sodium carbonate and again distilled, the
product passing into dilute chlorhydric acid. This second distillate was evaporated,
and the ammonium determined as platinum salt with the usual precautions, the weight
of the latter being controlled by ignition and determination of the weight of the
platinum.
m. Potassium nitrate. — The portion of solution remaining in the retort, after the
first distillation above described, was acidified with sulphuric acid; a piece of thin
sheet zinc was then placed in the liquid and allowed to remain for a week, a small
quantity of sulphuric acid being occasionally added. After the lapse of that time the
zinc was removed, and the ammonia produced from any nitrate existing in the liquid
was determined exactly as at 1.
CAPTAIN NOBLE AND MR. F. A. ABEL ON FIRED GUNPOWDER.
71
E. COMPOSITION OF THE GUNPOWDERS EMPLOYED.
The method pursued in determining the proportions of proximate constituents in the
samples of gunpowder present but very few points of difference from those ordinarily
adopted, and need therefore not be detailed.
It may he mentioned, however, with reference to the determination of the proportion
of saltpetre, that a very appreciable amount of the most finely divided particles of the
charcoal generally passes through the filter during th'e final washings, however care-
fully the operation be conducted.
These last washings, which contain ‘only a very small proportion of the saltpetre, were
therefore evaporated separately, and the residue was carefully heated until the small
quantity of charcoal was completely oxidized. The resulting carbonate was then con-
verted into nitrate by careful treatment with dilute nitric acid, and the product added
to the remainder of the saltpetre previously extracted.
The composition of the charcoal contained in the powders was determined by com-
bustion, after as complete a separation of the other constituents as possible. There
was, of course, no difficulty in completely extracting the saltpetre ; but the sulphur
cannot be entirely removed from the charcoal by digestion and repeated washings with
pure carbon disulphide. The amount remaining was therefore always determined by
oxidation of the charcoal, and estimation of sulphuric acid produced ; the necessary
correction thus arrived at was made in the amount of charcoal used for analysis.
The latter was dried by exposing it for some time (in the platinum boat in which it
was to be burned) to a temperature of about 170° in a current of pure dry hydrogen; it
was allowed nearly to cool in this gas, and dry air was then passed over for some time,
the boat being afterwards rapidly transferred to a well-stoppered tube for weighing.
The dried charcoal was burned in a very slow current of pure dry oxygen, the resulting
products being allowed to pass over the red-hot cupric oxide, and finally over a layer of
about 8 inches of lead chromate, heated to incipient redness. The efficiency of this layer
in retaining all sulphurous acid was fully established by preliminary test experiments.
The following tabular statement (Table II.) gives the percentage composition of
the five samples'* of gunpowder employed in these investigations as deduced from the
analytical results.
In every instance at least two determinations were made of each constituent, the
means of closely concordant results being given in the Table.
This Table also includes the results of analysis by Bunsen and Schischkoff, Karolyi,
Linck, and Federow, of the gunpowders employed in their experiments.
* The authors are indebted to Colonel C. W. Youxghusbajo), R.A., F.R.S., the Superintendent of the
W altham- Abbey Gunpowder Works, for having selected and furnished to them the samples of English gun-
powder employed in their investigations.
72
CAPTATN NOBLE AND MR. F. A. ABEL ON EIRED GUNPOWDER,
Table II. — Results of Analysis of Gunpowders employed in these Investigations and of
those used by other Investigators.
Components per cent.
Description of Gunpowders employed in experiments.
Pebble powder.
Waltham Abbey.
Rifle Large-grain.
Waltham Abbey.
Rifle Pine-grain.
Waltham Abbey.
Fine-grain.
Waltham Abbey.
Spanish Spherical
Pebble powder.
Saltpetre
Potassium sulphate
Potassium chloride
Sulphur
f Carbon
fc:
[Ash
Water
74-67
0 09 •
1007
12-121
rs
0-23 J
095
74-95
015
10-27
10-86 j
in ™
0-25 J
Ml
75-04
014
9-93
10-67 1
°'52 1409
2-66 f 14 09
0-24 J
0-80
73-55
0- 36
10-02
11 -36V
0 49 1 , ..-a
2 57 f i459
017j
1- 48
75-30
027
0-02
1242
8-651
iSM1*4
0-63
0-65
Gunpowders employed by other Investigators.
Bunsen and
Schischkoff.
Sporting-powder.
Karolyi.
Austrian cannon-
powder.
Karolyi.
Austrian small-
arm powder.
Linck.
Wiirtemburg
cannon-powder.
Federow*.
Russian powder.
Saltpetre
Sulphur
f Carbon
Charcoal ... \ Imogen -
| Oxygen
l_Ash
Water
77-99
9-84
7-691
®'41 1 J1.J7
307 r 11 17
traces J
73-78
12-80
10-88 1
P82 13-39
0-31 J
7715
8-63
11-781
0- 42 14-27
1- 79 f 14
0-28 J
74-66
12-49
12-31 j
0-54 j 12-85
7418
9-89
10-75 1
0-43 e„
3-31 \ 14-83
0-34 J
1-10
It will be seen that the several English service-powders of Waltham-Abbey manu-
facture did not differ from each other very importantly in composition ; the most note-
worthy points of difference are the somewhat low proportion of saltpetre in the F. G.
powder and the slightly higher proportion of carbon in the pebble powder.
The charcoals contained in these powders presented some decided differences in com-
position, as is shown by the following comparative statement : —
Pebble.
R. L. G.
R. F. G.
F. G.
Carbon
. 85-26
80-32
75-72
77-88
Hydrogen
. 2-98
3-08
3-70
3-37
Oxygen
. 10-16
14-75
18-84
17-60
Ash . . .
. 1-60
1-85
1-74
1-15
coal in the P.
powder is
somewhat more
highly burned
than
R. L. G., and decidedly more than the F. G. charcoal; that contained in the R. F. G.
powder is prepared from a different wood to the others, which is known to furnish a
comparatively quick-burning charcoal. Although, however, the charcoals themselves
differ very decidedly from each other, it will be seen that the percentages of carbon in
the gunpowders do not present great differences, the widest being between the P. and
R. F. G. powders.
The Spanish spherical pebble powder was specially selected from various other foreign
* This is the only analysis of powder, by foreign investigators of the subject, in which the proportion of
water, existing as a constituent of the powder experimented with, is given.
CAPTAIN NOBLE AND MR. E. A. ABEL ON EIRED GUNPOWDER.
73
powders for purposes of experiment, on account of the comparatively wide differ-
ence presented in composition between it and the English powders, the proportion
of sulphur being high, and that of carbon being low. The charcoal in this powder
(made from hemp) had the following percentage composition : —
Carbon 76 '2 9
Hydrogen 3*31
Oxygen 14-87
Ash 5-53
The proportions of carbon and hydrogen are therefore similar to those existing in the
F. G. powder ; but the amount of ash in the hemp-charcoal is very high compared to
that contained in the charcoals from light woods used generally in the manufacture of
gunpowder.
All the powders used by the recent foreign experimenters differed very decidedly
both from each other and from the powders employed by us. The sporting-powder of
Bunsen and Schischkoff, and Karolyi’s small-arm powder, were of very exceptional
composition, while the Russian powder used by Federow was the only one resembling
our service-powders in composition.
F. EXAMINATION OF THE ANALYTICAL RESULTS.
Table III. gives the composition in volumes per cent, of the gases, and the percentage
composition of the solid products furnished by a number of experiments with the
different gunpowders, the charges exploded having occupied various spaces in the
explosion-chambers. This Table also includes the results obtained by other recent
experimenters in the analytical examination of the products of explosion of gunpowder.
Table IV. shows the composition by weights of the products of combustion furnished
by 1 gramme of gunpowder under the different circumstances of our experiments.
The complicated nature of the analysis of these products has rendered it impossible to
complete the examination of the entire series furnished by our experiments ; we trust,
however, at a future time to fill up the blanks * remaining in this tabular statement.]
* The majority of these blanks have been now filled up. — February 1875.
MDCCCLXXV.
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Table IV. — Showing the composition by weight of the products of combustion of 1 gramme of fired Gunpowder.
76
CAPTAIN NOBLE AND AIR. E. A. ABEL ON FIRED GUNPOWDER.
A comparison of the analytical data furnished by our examination of the products of
explosion of gunpowder with those obtained by Bunsen and Schischkoff and other
recent investigators of this subject, points to the following principal differences in the
results arrived at : —
As regards the gaseous products : the proportion of carbonic oxide is considerably
lower in Bunsen and Schischkoff’s analysis and in one of Karolyi’s than in the results
obtained by us ; this might, in the case of Bunsen and Schishkoff’s results, be ascribed
to the fact that the proportion which the saltpetre bears to the carbon in the English
powder is lower than in the powder used by them, and that the proportion of sulphur
is also lower. The Austrian cannon-powder employed by Karolyi, which is not widely
different from the English cannon (R L. G.) powder, as regards the proportion of salt-
petre and carbon, though containing a higher proportion of sulphur, furnished amounts
of carbonic anhydride and carbonic oxide more nearly approaching those obtained with
the English powder at a low pressure. But the other (small-arms) powder used by him
furnished almost as low an amount of carbonic oxide as obtained by Bunsen and Schisch-
koff, although the proportion of saltpetre to the carbon in this powder was about the
same as in the other used by him. This result may be ascribable to the smaller propor-
tion of sulphur existing in the former. The Wurtemburg powder used by Linck, which
was made apparently with a very highly burned charcoal, but contained a similar propor-
tion of saltpetre to the English powder and a high proportion of sulphur, also furnished
a comparatively very small quantity of carbonic oxide. The proportions of this gas and
of carbonic anhydride which it yielded were very similar to those obtained by Bunsen
and Schischkoff with a gunpowder of widely different composition, though the method
of experiment pursued in the two instances was the same. Although the proportion of
hydrogen contained in the powder with which Linck experimented was very low, the
amount of sulphuretted hydrogen which it furnished was remarkably high ; and in this
respect again the analysis differs greatly from that of the products similarly obtained by
Bunsen and Schischkoff. The proportions of water existing in the gunpowders used
by these several experimenters is not stated, but it must probably have been very con-
siderable in Linck’s powder.
The solid products of explosion obtained by Bunsen and Schischkoff, Linck, and
Karolyi differ remarkably from those furnished by our experiments. The potassium
sulphate obtained by them was in Linck’s analysis about double, and in those of
the other chemists more than double the highest amount we found*. The potassium
carbonate furnished in the German experiments was about half that produced in ours ;
and the proportion of potassium sulphide found in the greater number of powder-
residues which we examined was very greatly in excess of the results obtained by the
German experimenters. Linck found a large proportion of potassium hyposulphite in
the solid products obtained by him, while the other chemists found comparatively
* Excepting in the case of a Spanish powder, which differed widely in composition from the other experi-
mented with by ns. — February 1875.
CAPTAIN NOBLE AND ME. F. A. ABEL ON FIRED GUNPOWDER.
77
small amounts of this constituent ; in our results (which will presently be compared
among themselves) the hyposulphite was also found to vary in amount very greatly.
These fluctuations were found by us, in most cases, to bear definite relation to those of
the sulphide ; but this is not observed to be the case in the analyses of Linck and Bunsen
and Schischkoff on comparing them with ours.
The method pursued by these chemists for obtaining the products of decomposition
of powder was of a nature calculated to furnish very variable results, which can scarcely
be accepted as corresponding to those produced when gunpowder is exploded in an
absolutely closed space or in the bore of a gun.
By allowing the powder-grains to drop gradually into a heated open bulb, not only is
their decomposition accomplished under very different conditions to those attending the
explosion of a confined charge of powder, but the solid products are necessarily subjected
to further changes during their continued exposure to a high temperature and to the
action of fresh quantities of powder deflagrated in contact with them. An imperfect
metamorphosis of the powder-grains themselves and further secondary changes in the
composition of the residue deposited (which will vary in extent with the duration of the
experiment), the amount of heat applied externally, and the rate at which the powder-
grains are successively deflagrated appear to be inevitable results of this mode of opera-
tion. A comparison of Bunsen and Schischkofu’s results with those shortly afterwards
obtained by Linck in Bunsen’s laboratory, the same method being pursued for effecting
the decomposition of the powder, appears to demonstrate this conclusively.
The differences in the composition of the powders operated upon in the two investi-
gations would certainly not suffice to account for the important differences exhibited by
the results of analysis of the residues. The comparatively large proportion of potassium
sulphide, the much larger proportion of hyposulphite, and the considerably smaller pro-
portion of sulphate found by Linck appear to indicate that the operation of burning
the powder was conducted much more rapidly by him, a view which is supported by the
fact that, while he found a considerable proportion of ammonium carbonate in the
residue, none existed in the product obtained by Bunsen and Schischkoff, who, however,
found this constituent in the so-called powder-smoke which they collected in a long tube
through which the gas escaped.
Our experiments have demonstrated conclusively that, even when the conditions under
which the explosion of powder is effected in distinct operations are as closely alike as
possible, very exceptional results, as regards the composition of the solid residue, may
be obtained, experiments 7 & 17, 9 & 4, 14 & 70 being illustrations of this. Yet in no
instance, however apparently abnormal, did any considerable proportion of potassium
nitrate escape decomposition, the highest amounts discovered in the residues being 0'48
and 0’56 per cent, (experiments 1 & 8). These percentages existed in the products of
explosion of powder formed under the lowest pressure ; in only two instances, at
higher pressures, were similar proportions found. The existence of so large a pro-
portion as 5 per cent, of potassium nitrate in the residue obtained by Bunsen and
Schischkoff, the coexistence of 7 ’5 per cent, of hyposulphite and small quantities of
78
CAPTAIN NOBLE AND MB. F. A. ABEL ON EIKED GUNPOWDEB,
other oxidizable substances, and the existence also of a comparatively high proportion
of oxygen in the gaseous products appear to indicate the occurrence of reactions in
the course of the preparation of gas and residue, by the gradual deflagration of the
powder, which were distinct from those attending the ordinary explosion of powder in
a confined space.
The very considerable differences between the results of our analyses and of the expe-
riments of Bunsen and Schischkoff and of Linck appear therefore clearly ascribable
to the fact that the deflagration of gunpowder, as carried out by them, cannot be
expected to furnish results similar to those produced when a charge of powder is
exploded in a. confined space under considerable pressure and in one operation.
This conclusion receives support from the results of analysis of powder-residues
published by Federow. Those products which he collected from a cannon in which
3 lb. of powder were fired furnished analytical results much more nearly resembling
those obtained by us than those of Bunsen and Schischkoff ; the proportion of sulphate
was similar to that obtained in many of our experiments, and therefore very much
below that of the German experimenters, while the proportion of sulphide was very
considerably higher than the largest amount obtained by us — a result, we believe, not
difficult of explanation. In the residue collected in a glass tube by firing small
quantities of powder (blank charges) in a pistol, which therefore were not exploded
under any considerable pressure, and were consequently subjected to more gradual
change, the results were of very different nature, the proportion of sulphate being
comparatively very high, and that of the sulphide very low.
That the mode of operation pursued by Karolyi should have furnished results similar
to those obtained by Bunsen and Schischkoff’s method is at first sight somewhat
surprising, inasmuch as, by the arrangement which he adopted, the powder-charge was
exploded in an envelope (a small thin shell) offering some amount of initial resistance.
But as this explosion was accomplished in a capacious exhausted chamber, the pressure
developed upon the first ignition of the charge suffered a sudden reduction at the moment
that the shell was fractured, and most probably, therefore, before the entire charge
had exploded. Hence it might have been expected that some portions of the oxidizable
constituents of powder would escape oxidation, either entirely or partly, and that, at
any rate, the oxidation of the sulphur would not be effected to the complete extent
observed in operating according to Bunsen and Schischkoff’s plan. But it appears
that in one instance not a trace, and in another only 0T5 per cent., of potassium
sulphide was found in the solid products, the proportion of hyposulphite found being
at the same time much smaller than that observed by Bunsen and Schischkoff; so that
the sulphur-compounds obtained consisted chiefly of the highest product of oxidation,
and yet in each of the two experiments nearly 4 per cent, of charcoal and a large
proportion of hydrogen escaped oxidation altogether. In one experiment nearly 7 per
cent, of sulphur appears to have been left in an uncombined state.
In our experiments, in which the powder was exploded under more or less consider-
able and sustained pressure, the complete oxidation of the sulphur might certainly be
CAPTAIN NOBLE AND ME. F. A. ABEL ON FIBED GUNPOWDER.
79
expected to have been favoured to a much greater extent than in Karolyi’^ experi-
ments; yet in all but one experiment, made with a powder of exceptional composition,
the proportion of sulphate formed was very greatly below that found by Karolyi.
The irreconcilable nature of Karolyi’s analytical results, though probably in some
measure ascribable to the exceptional conditions under which he obtained his products,
does not appear satisfactorily accounted for thereby.
On examination and comparison with each other of the analytical results given in the
foregoing Tables, the following points suggest themselves : —
Excluding the results of a few explosions of marked exceptional character as regards
the solid products furnished, and those produced under the lowest pressure, which were
naturally expected to yield variable and discordant results, there is considerable
similarity, not only between the products furnished by pebble powder when exploded
under different conditions as regards pressure, but also between the results obtained
with this powder and with the sample of R. L. G. powder employed in the experi-
ments, which did not differ greatly in composition from it. The proportion of carbon
was slightly lower in the R. L. G. than in the pebble powder ; and this fact is in harmony
with the proportion by weight which the total gaseous constituents bear to the solid
in the products obtained with the two powders, it being somewhat the highest, in
most instances, in the case of the pebble powder. The proportion of carbonic oxide is
often rather higher in the gas obtained from the pebble powder than in that furnished
by the R. L. G. powder ; and this is in accordance with the fact that the proportion of
carbon is somewhat higher, while that of the saltpetre is a little lower, in the former
than in the latter. Excluding the results furnished by the experiments in which the
powder was, exploded in the largest space (in which, therefore, the gases were deve-
loped at the lowest pressures) it will be observed that with the slowest-burning-
powder (the pebble) the proportion of carbonic oxide decreases steadily, while that of
the anhydride increases, in proportion to the pressure developed at the time of explosion.
The proportion of carbonic anhydride is about the same in the gas from the two
gunpowders specified ; but that of the potassium carbonate is somewhat different, and
appears regulated by circumstances other than the composition of the powder, being-
highest in the residues furnished by the R. L. G. powder at the higher pressures, and
lowest in those of the same powder furnished at lower pressures. The amount of
carbonate furnished by the pebble powder under different conditions as to pressure
varies, on the other hand, comparatively little, except at the highest pressure*.
The occasional occurrence of a small quantity of marsh-gas, like that of oxygen, is
evidently an accidental result, being observed in some instances in the products
obtained at low pressures, and the reverse in other instances.
In the gaseous products from the F. G. powder formed at pressures up to 50 per
* In 90 per cent, space the amount of carbonate formed was nearly equal to the proportions found in the
residues from E. L. G. produced at the higher pressures. — February 1875.
80
CAPTAIN NOBLE AND ME. F. A. ABEL ON FIEED OUNPOWDEE.
cent, space, the carbonic oxide existed in proportions similar to those furnished by the
R. L. G. powder. If the relative proportions of potassium nitrate and carbon in the
powders furnished an indication of the proportions in which this gas should be formed,
this particular powder should have furnished a higher proportion of carbonic oxide than
the R. L. G., as it contains 0’5 per cent, more carbon and 1*4 per cent, less saltpetre
than the latter; but then the proportion of sulphur in it is lower by 0'25 per cent.;
moreover the charcoal in the F. G. was less highly burned, and therefore more rapidly
oxidizable, a circumstance which may have a decided influence upon the amount of
carbonic oxide produced by the explosion of gunpowder, distinct from that exerted by
the proportion in which the ingredients exist. The difference in the amounts of
carbonic oxide produced from this powder at the lower and the higher pressures is more
marked than in the case of the other powders, the quantity in this as in the pebble
powder decreasing decidedly as the pressure increases. The amount of carbonic anhydride
which it furnished at the highest pressure (the powder occupied 90 per cent, of the
space) is the largest found in any of the gaseous products*; but that produced when
the powder occupied 70 per cent, of the total space was very nearly as high, while the
amount obtained in the intermediate experiment (80 per cent, space) was decidedly
lower, and corresponded closely to the proportions produced at the same pressure
from R. L. G. and pebble powder.
In the experiments with P. and R. L. G. (excluding the explosions in 10 p. c. space)
the amount of sulphuretted hydrogen was highest at the lowest pressures ; in the case
of R. L. G. powder the proportion fell gradually with the increase of pressure,
excepting at the highest pressure ; with pebble a similar relation was indicated, though
much less regularly ; with F. G. it was still less apparent, and with all three powders
the proportion of this gas rose somewhat again at the highest pressure. With pebble
and F. G. the hydrogen exhibited a steady diminution with increase of pressure, and a
similar though less regular result was observable with R. L. G. It need be scarcely
stated that the proportions of sulphuretted hydrogen and of hydrogen are in no instance
sufficiently high to enter into account in a consideration of what are the chief reactions
which occur upon the explosion of powder f.
While the results, as regards gaseous products, furnished by the three gunpowders
* Except in the case of the Spanish powder, which furnished an equally high proportion. — February 1875.
f The additional analyses which we have made since this paper was presented to- the Eoyal Society enable
us to summarize the general results furnished by examination of the gaseous products as follows : — (a) with
all the powders the proportion of carbonic anhydride produced increases steadily and decidedly with the
pressure; (5) with the P. and F. G. powders the carbonic oxide decreases steadily as the pressure increases;
and the same is generally true as regards the E. L. G. powder, although the series of analyses exhibits some
violent fluctuations ; (c) the proportions of sulphuretted hydrogen and of hydrogen furnished by all the powders
fall somewhat as the pressures increase, though the diminution is not very decided or regular ; (cl) free oxygen
was in no case found in the products from P. powder ; in one instance it was found in those from E. L. G.,
and it occurred in four instances in those from F. G. — February 1875.
CAPTAIN NOBLE AND MB. E. A. ABEL ON EIRED GUNPOWDER.
81
above referred to were on the whole remarkably uniform, the composition of the solid
residues exhibited comparatively great variations. Certain general results appear,
however, to be well established by a number of the analyses. Excluding again those
experiments conducted at the lowest pressure, the proportion of potassium sulphate
produced in the several experiments, with the comparatively slow-burning pebble
powder, was remarkably uniform at various pressures, being, as already pointed out,
not more than one fourth the amount found in powder-residue by Bunsen and
Schischkofe. The proportion of sulphur not actually entering into the principal
reactions involved in the explosion of the powder was also, with two exceptions, very
uniform, being about 35 per cent, of the total amount contained in the powder. The
proportion of potassium carbonate obtained from pebble powder was somewhat less
uniform, but did not differ greatly in the different experiments with the same powder
exploded in different spaces, excepting at the highest pressure. With the more rapidly-
exploding R. L. G. powder, the sulphate formed at the lower pressures was nearly double
that obtained with pebble powder ; while at the highest pressures the amounts furnished
by the two powders did not differ greatly, the amount of sulphur excluded from the
chief reaction at those pressures, with R. L. G., being, however, more considerable
than was the case with pebble powder under similar conditions. With regard to
this part of the sulphur contained in the powder, which corresponds to what Bunsen
and Schischkoff term free sulphur, some portion of it almost always exists, not in
combination with potassium as polysulphide, but combined with iron, and is therefore
discovered in the residue left undissolvecl, upon treatment with water, of the solid
products removed from the chamber. This proportion of the sulphur is evidently at
once fixed, at the instant of explosion, by union with parts of the metal surfaces
presented by the interior of the vessel in which the operation is conducted. The
extent to which sulphur is thus abstracted from the powder-constituents, and precluded
from entering into the reactions which are established by the explosion, or follow
immediately upon it, must depend in some degree upon accidental circumstances, such
as variations in the mechanical condition (smoothness, brightness, &c.) of the metal
surfaces, and also upon the temperature developed at the instant of the explosion.
The circumstance that, in the statement of the results of Experiment 42, both potas-
sium oxide and sulphur are separately included is therefore explained by the above
fact. The larger proportion of the “ sulphur ” specified in the several analyses existed
as potassium polysulphide, and may therefore be styled free sulphur, as it did not take
part in the chief reactions.
The carbonate , like the sulphate, differed decidedly in amount in the residues
furnished by the R. L. G. powder exploded in the smaller and the larger spaces : in
the former it was equal to the lowest result furnished by the pebble powder ; in the
others its proportion was about 10 per cent, higher than in the pebble-residues, excepting
in one of them produced at the highest pressure. In the products obtained by the
explosion of the smallest-grain powder (F. G.) the variations in the proportions of
MDCCCLXXV. M
82
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GTTNPOWDEE.
carbonate are somewhat considerable ; the proportions of sulphate were, on the other
hand, much alike, except at the highest and lowest pressures. The proportion of hypo-
sulphite was generally high, and that of the sulphide low, as compared with the pro-
portions of these constituents in the other powder-residues just discussed. In two of
the residues from F. G., the proportion of sulphur Avhich did not enter into the principal
reactions is about the same as that found in the pebble-powder residues ; while in three
others only small quantities of free sulphur existed — in two of these there was free
potassium oxide. Two of the residues (Nos. 42 & 47) contained not a trace of potas-
sium sulphide discoverable by the most delicate test (sodium nitroprusside).
With respect to the proportions of potassium sulphide and potassium hyposulphite
found in the several residues analyzed, the following points appear to be worthy of
note.
1. In the residues obtained by exploding pebble, K. L. G., and F. G. under the lowest
pressures (the charges only occupying 10 per cent, of the total space), the proportion
of potassium hyposulphite is in all cases high, while that of the sulphide is corre-
spondingly low.
2. In the comparatively slow-burning pebble powder, the products of explosion of
which at different pressures exhibited great similarity in many respects, there is a
marked fluctuation in the proportion of hyposulphite ; and this corresponds to a fluctua-
tion, in the opposite direction, in the amount of sulphide found, while the sulphate
varies but little. A similar fluctuation and relation is observed, as regards these two
constituents, in the solid products of the experiments made with It. L. G. powder at
the lowest pressures, but not, or only to a slight extent, in the residues furnished by
the powder at higher pressures.
3. In most of the residues from F. G., the hyposulphite is large in amount and the
sulphide small : in two of these (Nos. 42 & 47), which did not contain a trace of
potassium sulphide, the proportion of hyposulphite was considerably higher than in
any of the other experiments*; and in these cases there was no free sulphur — that is to
say, no sulphur in the form of poly sulphide, the small proportion given under the head of
“ sulphur ” in the tabulated results being found in combination with iron derived from
the interior of the chamber.
The circumstance that the hyposulphite generally existed in large proportions when
the sulphide was small in amount, appeared at first sight to afford grounds for the
belief that its production might be ascribable to a secondary reaction resulting in the
oxidation of sulphide by carbonic anhydride, a view which might appear to receive
support from the following circumstance. The upper portion of the solidified mass in
the cylinder was found to contain a considerably larger proportion of hyposulphite
than the remainder, as is demonstrated by the following results of a separate examina-
tion of the top and the lower portion of the residues obtained by exploding a charge
* One residue furnished by P. powder (experiment 38) contained a similarly high amount and a very small
quantity of sulphide. — February 1875.
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GUNPOWDEB,
83
of 6804 grains (440*9 grms.) of R. L. G. powder, which occupied 90 per cent, of total
space in the chamber (Experiment 68): —
Residue.
Carbonate.
Sulphate.
Hyposulphite.
Sulphide.
Sulphur.
Top portion .
. 52*15
7*69
I7*I4
6*03
4*88
Lower portion
. 67*75
7*44
4‘34
7*30
10*09
Similar results were obtained by the separate examination of the top part of other*
residues. Again, one of the small drops or buttons of the fused solid products which
have been mentioned as being generally found upon the firing-plug in the cylinder (the
residue of this particular experiment contained a somewhat considerable proportion of
sulphide) was found to be quite free from sulphide, but contained hyposulphite.
Lastly, a mixture of potassium carbonate and sulphide, after exposure in a crucible for
30 minutes to a temperature of about 1700° C. in a Siemens furnace (in which the
atmosphere consisted of carbonic anhydride, carbonic oxide, and nitrogen), was found
to contain a small quantity of hyposulphite. The production of this substance, as the
result of a secondary reaction, should, however, be rendered evident by a marked
increase in the proportion of carbonic oxide in all instances in which a large amount
of hyposulphite was found ; and this was certainly not the case, as will be seen by a
comparison of the results of Experiments 8 and 7, 3 and 11, 19 and 17.
Potassium.
Experiment.
Carbonic
anhydride.
Carbonic
oxide.
carbonate.
sulphate.
-A.
hyposulphite.
sulphide.
8. Pebble
. *2577
•0519
•3115*
•0843
•H63
•0416
7. Pebble
. *2517
’°575
*3216
•0768
•0208
•1011
3. R.L.G.
. *2504
'°393
*3128
*1378
•O329
•0547
11. R.L.G.
. *2624
•0360
•2819
*1324
*I393
•0117
19. F.G. .
. *2678
*°339
•2615
*1268
•1666
•0196
17. F. G. .
. *2512
•0416
•3454
*1409
•0308
•0298
It appears, therefore, that the formation of hyposulphite cannot be regarded as due
to the occurrence of a secondary reaction between carbonic anhydride or carbonate and
sulphide produced upon the explosion of gunpowder, but that it must be formed either
during the primary reaction of the powder-constituents on each other (in other words,
by the direct oxidizing action of saltpetre), or by an oxidation of sulphide by liberated
oxygen following immediately upon the first change (which results in the formation of
a large quantity of sulphide), and being regulated in extent by the amount of oxygen
liberated at the moment of explosion. The view that hyposulphite must be, at any
rate in part, due to the oxidation of sulphide formed in the first instance, appears to
be supported by the circumstance that the proportion of the latter in the powder-residues
is as variable as that of the hyposulphite, and is generally low when the hyposulphite
is high. Moreover in our experiments the proportion of sulphate is, except possibly
in a few instances, apparently not affected by the amount of hyposulphite formed. On
the other hand, the amount of sulphur which exists either in combination with iron
84
CAPTAIN NOBLE AND MR. E. A. ABEL ON FIRED GUNPOWDER.
(and other metals derived from the exploding-apparatus) or as polysulphide of potas-
sium, and which therefore has not entered into the chief reactions, is generally low
where the hyposulphite is high, which appears to indicate that the latter is also formed
(at any rate occasionally) by an oxidation of free sulphur following immediately upon
the first reaction.
. In the products of decomposition of the powder examined by Bunsen and Schisch-
koff, which were obtained, at any rate to a considerable extent, by a continued pro-
cess of oxidation, the conversion of sulphur into the highest product (sulphate) was
effected to a very great extent, there being no free sulphur and only an exceedingly
small quantity of sulphide ; but when the deflagration and action of heat were arrested,
there was still a considerable proportion (7-5 per cent.) of hyposulphite existing in the
solid residue. The smoke, or portions of the solid products mechanically carried away
by the gases evolved and afterwards deposited, was found by those chemists also to
contain as much as 4-9 per cent, of hyposulphite, while neither sulphide nor free
sulphur were discovered (the sulphate being, on the other hand, considerably higher in
amount than in the residue itself) ; the gas which escaped contained a very appreciable
amount of free oxygen, and there was 5 per cent, of nitrate left in the residue when
the operation was arrested. Here, therefore, the view appears a very probable one
that the hyposulphite constituted an intermediate product of a reaction following upon
the production of sulphide in the first instance. In. Linck’ s experiment, conducted in
the same way, the process of deflagration being, however, apparently arrested at an
earlier stage, more than twice the amount of hyposulphite found by Bunsen and
Schischkoff existed in the residue, while there were still nearly 6 per cent, of sulphide
and 0'5 per cent, of sulphur unoxidized, and a considerably smaller amount of sulphate
formed. This difference between the results of two experiments conducted on the
same plan may certainly be partly ascribed to the difference in the composition of the
two gunpowders experimented with, as that used by Linck was nearly of normal com-
position, and contained nearly 3 per cent, more sulphur, and quite 3 per cent, less salt-
petre, than Bunsen and Schischkoff’s powder ; yet this very circumstance appears to
support the view that, at the first instant of explosion, sulphide is formed in consider-
able proportion, its immediate oxidation and the nature and extent of that oxidation
being regulated by the proportion of oxygen which is liberated at the time that the
sulphide is formed, the same also applying to the proportion of sulphur which at the
moment of explosion does not combine with potassium to form sulphide.
Potassium hyposulphite is stated to decompose at about 200° C. ; but it is evidently
formed at very much higher temperatures ; and the experiments of Bunsen and Schisch-
koff and of Linck demonstrated that it may remain undecomposed, or may continue
to be produced, in powder-residue which is maintained at a high temperature.
We ourselves have exposed portions of powder-residue obtained in our experiments
for lengthened periods to the heat of a Siemens furnace (1700° C.), and have still
detected small quantities of hyposulphite in the material after such exposure.
CAPTAIN NOBLE AND MR. E. A. ABEL ON EIRED GUNPOWDER.
85
It will be seen on comparing our analytical results with the pressures recorded in
the several experiments as being developed by the explosions, that the latter are not
affected by very great differences in the composition of the products, or by important
variations in the extent to which particular reactions appear to predominate over
others. The pressures developed by explosion of the pebble and R. L. G. powders,
under corresponding conditions as regards the relation of charge to total space, were
almost identical up to the highest density ; and the same was the case with F. G.
powder at the lower densities ; yet there were in several instances very considerable
differences between the products formed from the different powders under the same
pressures (or accompanied by the development of corresponding pressures), differences
which were certainly not to be accounted for by the respective constitution of those
powders.
The composition of the gases and residues obtained in Experiments 8, 7, and 17,
and 12, 11, and 19 (Tables III. & IV.) may be referred to in illustration of this.
A cursory inspection of the analytical results at once shows that the variations in
composition of the solid products furnished by the different powders, and even by the
same powder under different conditions, are much more considerable than in those of
the gaseous products ; and it is evident that the reactions which occur .among the
powder-constituents, in addition to those which result in the development of gas, of
fairly uniform composition (and very uniform as regards the proportions which it bears
to the solid), from powders not differing widely in constitution from each other, are
susceptible of very considerable variations, regarding the causes of which it appears
only possible to form conjectures. Any attempt to express, even in a comparatively
complicated chemical equation, the nature of the metamorphosis which a gunpowder
of average composition may be considered to undergo, when exploded in a confined
space, would therefore only be calculated to convey an erroneous impression as to the
simplicity, or the definite nature, of the chemical results and their uniformity under
different conditions, while it would, in reality, possess no important bearing upon an
elucidation of the theory of explosion of gunpowder.
The extensive experiments which the Committee on Explosive Substances has insti-
tuted, with English and foreign gunpowders of very various composition, have con-
clusively demonstrated that the influence exerted upon the action of fired gunpowder
by comparatively very considerable variations in the constitution of the gunpowder
(except in the case of small charges applied in firearms) is often very small as compared
with (or even more than counterbalanced by) the modifying effects of variations in the
mechanical * and physical properties of the powder ( i . e. in its density, hardness, the
* The desirability of applying these means to effecting modifications in the action of fired gunpowder was
pointed out by Colonel Boxer in a memorandum submitted to the War Office in 1859 ; and the first Govern-
ment Committee on Gunpowder, soon afterwards appointed (of which Colonel Boxer and Mr. Abel were mem-
bers), obtained successful results, which were reported officially in 1864, by limiting the alterations in the
manufacture of gunpowder intended for use in heavy guns to modifications in the form, size, density, and
86
CAPTAIN NOBLE AND MR. F. A. ABEL ON FIRED GUNPOWDER.
size and form of the grains or individual masses, &c.). Hence it is not surprising to
find that a fine-grain gunpowder, which differs much more in mechanical than in che-
mical points from the larger powder (R. L. G.) used in these experiments, should present
decided differences, not only in regard to the pressures which it develops under similar
conditions, but also as regards the proportions and uniformity of the products which
its explosion furnishes. On the other hand, the differences in regard to size of in-
dividual masses and other mechanical peculiarities between the R. L. G. and pebble
powders are, comparatively, not so considerable, and are in directions much less likely
to affect the results obtained by explosions in perfectly closed spaces.
Again, the analysis of solid residues furnished by different kinds of gunpowder which
presented marked differences in composition, did not establish points of difference which
could be traced to any influence exerted by such variations ; indeed the proportions of
the several products composing residues which were furnished by one and the same
powder, in distinct experiments made at different pressures, differed in several instances
quite as greatly as those found in some of the residues of different powders which pre-
sented decided differences in composition. This will be seen on comparing with each
other the analysis of certain residues of P. powder (e.g. experiments 7 and 12), of
R. L. G. powder (e.g. experiments 4 and 39), and of F. G. powder (experiments 17
and 42), and on then comparing the composition of the residues of F. G. and R. F. G.
obtained in experiments Tl and 18.
"When, however, the deviation from the normal composition of cannon-powder is
comparatively great, a decided influence is thereby exerted upon the proportions in
which the products of explosion are formed. Thus, in the Spanish pebble powder
specially selected by us for experiment on account of the considerable difference between
its composition and that of the English powders, the proportion which the saltpetre
bears to the carbon is comparatively high, while the amount of sulphur it contains is
very high. An examination of the gaseous products which it furnished shows that
the proportion of carbonic oxide is only one half the amount produced under precisely
the same conditions, as regards pressure, by R. F. G. powder, and about one third
the amount contained in the products furnished by pebble and R. L. G. powders under
nearly similar conditions. With respect to the solid products of explosion obtained
with the Spanish powder, they also present several points of great difference from the
products furnished by the powders of English manufacture. The amount of potassium
carbonate is very much lower than in any of the other residues examined, and the
sulphate very much exceeds in amount the largest proportion furnished by the English
powders. The proportion of sulphide is small, while that of hyposulphite is also not
considerable.
Although, for the reasons given in the foregoing, we cannot attempt to offer any
hardness of the individual grains or masses, the composition of the powder remaining unaltered. The Com-
mittee on Explosive Substances have adhered to this system in producing gunpowder suitable for the largest
ordnance of the present day.
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GUNPOWDEB.
87
thing approaching a precise expression of the chemical changes which gunpowder of
average composition undergoes when exploded in a confined space, we feel warranted
by the results of our experiments in stating, with confidence, that the chemical theory
of the decomposition of gunpowder, as based upon the results of Bunsen and Schisch-
koff, and accepted in recent text-books, is certainly as far from correctly representing
the general metamorphosis of gunpowder as was the old and long-accepted theory,
according to which the primary products were simply potassium sulphide, carbonic
anhydride, and nitrogen.
Moreover the following broad facts regarding the products furnished by the explo-
sion of gunpowder appear to us to have been established by the analytical results
given in this paper.
1. The proportion of carbonic oxide produced in the explosion of a gunpowder in
which the saltpetre and charcoal exist in proportions calculated, according to the old
theory, to produce carbonic anhydride only, is much more considerable than hitherto
accepted.
2. The amount of the potassium carbonate formed, under all conditions (as regards
nature of the gunpowder and pressure under which it is exploded), is very much larger
than has hitherto been considered to be produced, according to the results of Bunsen
and Schischkoff and more recent experimenters.
3. The potassium sulphate furnished by a powder of average normal composition is
very much smaller in amount than found by Bunsen and Schischkoff, Linck, and
Karolyi.
4. Potassium sulphide is never present in very considerable amount, though generally
in much larger proportion than found by Bunsen and Schischkoff ; and there appears
to be strong reason for believing that in most instances it exists in large amount as a
primary result of the explosion of gunpowder.
5. Potassium hyposulphite is an important product of the decomposition of gun-
powder in closed spaces, though very variable in amount. It appears probable (as
above pointed out) that its production is in some measure subservient to that of the
sulphide ; and it may perhaps be regarded as representing, at any rate to a considerable
extent, that substance in powder-residue — i. e. as having resulted, partially and to a
variable extent, from the oxidation, by liberated oxygen, of sulphide, which has been
formed in the first instance.
6. The proportion of sulphur which does not enter into the primary reaction on the
explosion of powder is very variable, being in some instances high, while, in apparently
exceptional results, the whole amount of sulphur contained in the powder becomes
involved in the metamorphosis. In the case of pebble powder, the mechanical con-
dition (size and regularity of grain) of which is perhaps more favourable to uniformity
of decomposition under varied conditions as regards pressure than that of the smaller
powders, the amount of sulphur which remains as potassium polysulphide is very uni-
form, except in the products obtained at the lowest pressure ; and it is noteworthy
88
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GUNPOWDEE.
that with R. L. G. powder, under the same conditions, comparatively little sulphur
escapes ; while in the case of F. G. powder, under corresponding circumstances, there
is no free sulphur at all.
7. But little can be said with regard to those products, gaseous and solid, which,
though almost always occurring in small quantities in the products, and though appa-
rently, in some instances, obeying certain rules with respect to the proportion in which
they are formed, as already pointed out, cannot be regarded as important results of the
explosion of powder. It may, however, be remarked that the regular formation of
such substances as potassium sulphocyanate and ammonium carbonate, the regular
escape of hydrogen and sulphydric acid from oxidation, while oxygen is occasionally
coexistent, and the frequent occurrence of appreciable proportions of potassium nitrate,
indicate a complexity as well as an incompleteness in the metamorphosis. Such com-
plexity and incompleteness are, on the one hand, a natural result of the great abrupt-
ness as well as the comparative difficulty with which the reactions between the
ingredients of the mechanical mixture take place ; on the other hand, they favour the
view that, even during the exceedingly brief period within which chemical activity
continues, other changes may occur (in addition to the most simple, which follow im-
mediately upon the ignition of the powder) when explosions take place at pressures
such as are developed under practical conditions.
The tendency to incompleteness of metamorphosis, and also to the development of
secondary reactions under favourable conditions, appears to be fairly demonstrated by
the results obtained in exploding the different powders in spaces ten times that which
the charges occupied (experiments 8, 1, and 16). It appears, however, that, even
under apparently the most favourable conditions to uniformity of metamorphosis
(namely in explosions produced under high pressures), accidental circumstances may
operate detrimentally to the simplicity and completeness of the reactions. But the
fact, indisputably demonstrated in the course of these researches, that such accidental
variations in the nature of the changes resulting from the explosion do not, even when
very considerable, affect the force exerted by fired gunpowder, as demonstrated by the
recorded pressures, &c., indicates that a minute examination into the nature of the pro-
ducts of explosion of powder does not necessarily contribute directly to a comprehen-
sion of the causes which may operate in modifying the action of fired gunpowder.
G. VOLUME OE THE PEEMANENT GASES.
The results of the experiments made to determine the quantity of permanent gases
generated by the explosion of the three service-powders which we have employed are
given in Nos. 58 to 62 and 64.
From a discussion of these results it appears that, in the case of pebble powder, the
combustion of 386-2 grammes gave rise respectively to 106,357-8, 105,716-2, and
107,335-8 cub. centims. of gas at a temperature of 0° C. and a barometric pressure of
760 millims. ; or, stating the result per gramme of powder, the combustion of 1 gramme
CAPTAIN NOBLE AND ME. F. A. ABEL ON FIBED GUNPOWDER.
89
pebble generated respectively 275"4, 273-7, and 277-9 cub. centims., or a mean of
2 75 ’68 cub. centims., at the above temperature and pressure .-
From the combustion of a similar quantity of E,. L. G. powder resulted 106,080-4,
103,676-5, and 104,606-7 cub. centims., or 274-7, 268-45, and 270*86 cub. centims. of
gas (mean=271*34 cub. centims.) per gramme of powder; while 99,694-9, 101,372-3,
99,164-8, and 100,289-0, or 262-4, 258-1, 256-8, and 259-68 (mean 259-2) cub. centims.
per gramme were yielded by the F. G. powder.
The difference in quantity of gas between the pebble and the R. L. G. is very
slight ; but there appears to be a decided difference in the quantity generated by F. G.
powder, the defect being much greater than can be accounted for by any errors of
observation.
The results of those experiments show that the quantity of permanent gases generated
by 1 gramme of the service pebble or It. L. G. powders is about 276 cub. centims. at 0° C.
and 760 millims. — that is, they occupy at this temperature and pressure about 276
times the volume of the unexploded powder.
The volume given off by F. G. is less, being about 260 volumes; and, if we may trust
to the single measurement we have made of the permanent gases of It. F. G. (in
experiment 80), the volume generated by this powder does not differ greatly from that
given off by F. G.
With the view of ascertaining whether a powder of a marked difference in composition,
such as the Spanish spherical pellet powder, gave the same quantity of permanent gases
as our service-powders, a measurement of the volume generated by this powder was made
(in experiment 81).
The quantity was found to be notably less, being only 232-7 volumes; but this
measurement was the result of one determination only.
H. RESULTS OF EXPLOSION, DEDUCED BY CALCULATION FROM ANALYTICAL DATA.
We are now in a position to apply two important tests to the results at which we
have arrived as regards composition of products and measurement of gases. From a
consideration of the analysis of the solid products of explosion, we are able to deduce
the total weight of the solid residue, and thence, by difference, the weight of the
gaseous products. On the other hand, from a consideration of the measurement of the
volume of the gaseous products, combined with their analysis, we can calculate the
weight of the gaseous and, by difference, that of the solid products ; and if these
calculations accord, a valuable corroboration of the accuracy of our results will be
obtained. We can also compare the amounts of the elementary substances in the
powder before and after combustion, and so obtain a still further corroboration of
accuracy.
We have applied these tests to all the analyses completed; and we proceed to give
two illustrations of the method — one applied to pebble, the other to F. G. powder.
In experiment 12, 411-085 grms. pebble powder were fired, and the products of
combustion collected and analyzed. The analysis of this powder has been already
MDCCCLXXV. N
90
CAPTAIN NOBLE AND MR. E. A. ABEL ON EIRED GUNPOWDER.
given; but for our present purpose it is convenient to give the proportions of the
components, as found by analysis, in their elementary form.
The pebble powder, then, consisted of : —
Percentage composition.
Composition by weight,
grammes.
K . .
. . . -2886
118-639
C . .
. . . -1212
49-824
S . ..
. . . -1007
41-396
H . .
. . . -0052
2-138
O . .
. . . -3742
153-828
N . .
. . . -1078
44-315
Ash .
. . . -0023
•945
1-0000 411-085
while the composition of the solid products of combustion was found to be : —
K2 C03 . .
. -55220
KCNS . . .
•00244
K2S203 .
. -14080
kno3 . . .
•00084
k2so4 . .
. -13200
(NH4)2C03 .
•00067
K2 s . . .
. -09700
s
Not estimated .
•06058
•01347
Now almost any practical method of weighing the solid residue would give us
inexact results, the weight of the vessel used for explosion being too great to allow of
sufficient accuracy if weighed in the vessel, and the hygroscopic nature of the residue,
as well as the difficulty of removing it, preventing its being weighed after removal.
But we can arrive at the weight in the following manner: — We know that the whole
of the potassium originally contained in the powder will be found in the solid residue ;
we further know that potassium enters into the composition of potassium carbonate,
hyposulphite, sulphate, sulphide, and sulphocyanate in the proportions respectively of
565, 411, 448, 709, and 402 parts out of every thousand. Hence if x be the weight
of the solid residue we have the following equation : —
{•565 X -55220+-411 x T4080+-448X T3200 + -709 X -09700
+ •402 X -00244 + -386 x -00084^=118-639,
118-639 grms. being the amount of potassium originally in the powder.
Hence x= solid products = 237-717 grms. =-5783, and by difference gaseous
products = 173-368 grms. = -4217.
We can now perform the inverse process, and, from the measurement of the gas
and the gaseous analysis, arrive at the weight of the solid products. Since 1 grm. of
pebble powder gave rise to 275-68 cub. centims. of permanent gases, 411-085 grms. will
generate 113,797-9 cub. centims. But the analysis of the permanent gases, in this
particular experiment, gave SH2 -0170 volume, CO -1395, C02 ‘4952, CH4 -0032,
H -0235, N -3216 volumes, while a cubic centimetre of these gases weighs respectively
•001523, -001254, -001971, -0000896, and -001254 grm. Hence we have as follows
CAPTAIN NOBLE AND ME. F. A. ABEL ON FIEED GTJNPOWDEB.
91
vols. .
cub. centims.
grms.
weight.
sh9 . .
. -0170=
1,934-6
2-946
•0163
CO . .
. -1395 =
15,874-8
19-907
•1104
co2 . .
. -4952 =
56,352-7
111-071
•6160
ch4 . .
. -0032 =
364-2
•261
•0015
H . . .
. -0235 =
2,674-3
•240.
•0013
N . . .
. -3216 =
36,597-4
45-893
•2545
1-0000
113,798-0
180-318
1-0000
Hence, taking the gas-measurement and analysis combined as the basis of calculation,
we have : —
Gaseous products = 180-318 grms. Solid products = 230-767 grms.
or, if we take the mean of the two determinations as more nearly representing the truth,
Solid products = 234-242 grms. = -5698
Gaseous products . . . . = 176-843 grms. = -4302
Resolving the solid products of combustion into their elements, we have the follow-
ing scheme : —
Grms.
1 K'
C.
S.
H.
O.
N.
k„co3
k^s203
k2so4
K, S
K'CNS
kno3
(NHJ,C03
c
129*348
32-981
30-920
22-721
•572
•197
•157
I 73-082
13-555
13-852
16-109
•230
•077
•078
11-253
•069
•020
11-115
5- 689
6- 612
•083
•095
•013
45-013
8-311
11-379
1
•189
•027
•046
s
14-190
3-155
14-190
1-263
Not estimated... .
Totals
234-241
116-983
11-342
39-047
•013
64-703
•262
Following the same plan with the gaseous products, and comparing the total weights of
the elements found with those existing in the powder before combustion, we have : —
Grms.
K.
C.
S.
H.
O.
N.
SH
2-882
2-712
0-170
o..;
CO
19-523
8-375
11-148
CO,..
108-936
29-740
79-196
ch:
•265
•199
•066
H 4
•230
•230
N
45-007
45-007 1
Total gaseous
176-843
38-314
2-712
•466
90-344
45-007
Total solid
i 234-241
116-983
11-342
39-047
•013
64-703
•262
Total found
411-084
116-983
49-656
4T759
*479
155-047
45-269
Total originally in
powder
411-085
118-639
49-824
41-396
2-138
153-828
45-
Errors
— 1-656
-0-168
+ •363
-1-659
+ 1-219
+ •269
n 2
92
CAPTAIN NOBLE AND ME. E. A. ABEL ON El RED GUNPOWDER.
If we perform similar calculations in the case of experiment 17, when 205-542 grms.
of F. G. were exploded, and the products found to he of the undermentioned
composition : —
Solid Products.
vV
Gaseous
Products.
r~
k2co3 .
. -5939
(NH4)2C03 .
. -0015
sh2 .
'i
Yol.
. -0376
K2 b2 Og .
. -0530
s . . . .
. -0572
co" .
. -1235
k2so4 .
. *2422
co2 .
. *4741
k2s . .
. -0512
ch4 .
KC NS .
. *0002
H . .
. -0413
kno3 .
. -0008
N . .
. -3235
we obtain: —
For solid products .... 119-554 grms. = ‘5817
For gaseous products . . . . 85‘987 grms. = '4188
or, resolving these products as before into their elements : —
Grms.
K.
C.
S.
H.
O.
X.
K,C03
71-003
40-117
6-177
24-709
k2 s2 o3
6-336
2-604
2-135
1-597
k“so4
28-956
12-Q72
5-328
10-656
k” s
6-121
4-340
1-781
KCNS
•024
•010
•003
•008
•003
kno3
•096
•037
•045
•013
(NH j2 CO,
•179
•022
•015
•090
•052
c :.
s
6-839
6-839
Total solid
119*554
60-080
6-202
16-091
•015
37-097
0-068
SH
3-164
2-977
•187
CO‘
8-556
3-671
4-885
CO
51-644
14-099
37-545
CH
H 4
•206
•206
N
22-417
22-417
Gaseous
85-987
17-770
2-977
•393
42-430
22-417
Solid
119-554
60-080
6-202
16-091
•015
37-097
0-068
Found originally in
205-541
60-080
23-972
19-068
•408
79-527
22-485
powder
205-542
58-662
23-349
20-760
1-336
79-031
22-700
Errors
+ 1-418
+ 0-623
-1-692
-•928
+ •496
-•215
It will be seen from this comparison that the results, when the nature of the
analysis is taken into consideration, accord with great exactness. The volume of the
gaseous products, calculated from the weight of the gases given in the first column of
the Table, would be about 279 cub. centims. at 0° C. and 760 millims. per gramme of
powder in the case of the pebble, and 267 cub. centims. in the case of the F. G. powder.
These volumes are slightly more than the measured volumes ; but it must be remembered
CAPTAIN NOBLE AND ME. F. A. ABEL ON EIEED GUNPOWDER.
93
that it is not difficult to conceive causes which might tend to make the mean measured
quantity of gas somewhat less than reality, while it is hardly possible that the reverse
can be the case.
For example, without doubt an appreciable quantity of gas is occluded, as indicated
by the conditions of the residues (see account of experiments Nos. 10 and 38) and by
the disengagement of gas generally observed upon addition of water to the residue. In
some instances also there may be, under the high pressure of explosion, a trifling
leakage from the apparatus.
One point we must not pass over without observation. The deficiency of hydrogen
in the products of explosion, although absolutely small, is relatively very large. The
question then arises as to whether the missing hydrogen may not be present in the
form of aqueous vapour. None was detected in the analysis of the gases ; but it is not
difficult to explain this fact, as the extremely hygroscopic property of the residue would
most effectually dry the gases — the absorption of the vapour by the residue being
actually demonstrated by the greasiness observed on the surface of the deposit and on
the sides of cylinder immediately on its being opened after explosion. The entire
proportion of water formed or preexisting must therefore have existed in the solid
residues, but its determination therein was obviously impracticable.
The amount of water present can, however, be calculated from the deficiency of
hydrogen shown in our Tables.
I. CONDITION OF PRODUCTS AT THE INSTANT OF OR SHORTLY AFTER EXPLOSION.
A careful examination of the contents of the cylinders after they were opened showed
that, at all events shortly after explosion, the solid products were in a fluid state. It
was of course impossible to open the cylinder while the solid products were still fluid ;
but it occurred to us that we might yet obtain valuable information as to the state of
the contents at different periods after the explosion. Accordingly, in experiment 40,
the cylinder being about two thirds filled with F. G., thirty seconds after the explosion
the vessel was tilted so as to make an angle of 45°. Two minutes later it was restored
to its first position.
On subsequent examination the deposit was found to be lying at the angle of 45°, and
the edges of the deposit were perfectly sharp and well defined.
In experiment 41, the cylinder, being about three fourths filled with 14. L. G., was
allowed to rest for one minute after explosion. It was then placed sharply at an angle
of 45°, and forty-five seconds later it was returned to its first position.
Upon opening it was found that when the cylinder was tilted over the deposit had
just commenced to congeal ; for upon the surface there had been a thin crust which the
more fluid deposit underneath had broken through. The deposit was lying at an
angle of 45°, but the crust through which the fluid had run was left standing like a
thin sheet of ice.
94
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GUNPOWDER.
Hence in this experiment, one minute after explosion, the non-gaseous products had
commenced to congeal, and forty-five seconds later they were solid.
In experiment 77, the cylinder, being completely full of pebble powder and fired,
was placed at an angle of 45° one minute after exptasion, and the position of the
cylinder was altered every fifteen seconds. It was found that at sixty and seventy-five
seconds after explosion the deposit was perfectly fluid, the evidence of each motion
of the cylinder being given by a wave of deposit. At ninety seconds it was rather
viscid ; at one hundred and five seconds the deposit hardly moved.
Hence in this experiment it was rather more than a minute and three quarters before
the non-gaseous products became solid ; and the conclusion from the experiments is
that, very shortly after explosion, the non-gaseous products are collected as a fluid at
the bottom of the exploding-vessel, and that some time elapses before these products
finally assume the solid form.
J. THE POSSIBILITY OE DISSOCIATION AMONG GASEOUS PRODUCTS CONSIDERED.
In the attempt to reconcile or account for the discordant estimates of the pressure
exerted by fired gunpowder, some authorities have supposed that the phenomena con-
nected with dissociation play an important part, and that, for example, the dissociation
of carbonic anhydride into carbonic oxide and oxygen may give rise to a considerable
increment of pressure.
Berthelot has enunciated the view that the tendency to dissociation at very high
temperatures possessed by compound gases operates in preventing the formation, at
the time of explosion, of certain of the constituents which exist in the ultimate gaseous
products, and that during the expansion in the bore of the gun and the concomitant
fall of temperature, the compound gases existing in those ultimate products are gra-
dually formed. He*, indeed, points out that the effects of dissociation must not be
exaggerated, and that the decomposing influence of high temperature in the case of an
explosion may be altogether or in part compensated by the inverse influence of pressure.
Having given this subject our careful consideration, we cannot even go so far as Ber-
thelot does in accepting the view that the results of explosion. of powder in a gun are
at all affected by dissociation, the occurrence of which we cannot consider probable even
when the pressure to which the gases are subjected in the bore of a gun is relieved to
the maximum extent.
It is perhaps, however, worth while examining what would be the effect on the
pressure if the particular case of dissociation to which we have alluded above actually
occurred.
Among the products of combustion of 1 gramme of powder is -28 grm. of C02 occu-
pying, at 0° C. and 760 millims. pressure, 142 cub. centims. ; now if we suppose this
C02 dissociated into CO and O, the 142 cub. centims. of C02 would become 213 cub.
* Berthelot, 1 Eorcede la Poudre &c.,’ 1872, p. 81.
CAPTAIN NOBLE AND MR. E. A. ABEL ON EIRED GUNPOWDER,
95
centims. of the mixed gases, and the total quantity of gas generated by a gramme of
powder (282 cub. centims.) would become 353 cub. centims.
On the other hand, the *28 gramme of C02 contains ‘0764 grm. C., which, burnt to
C02, gives rise to 611 gramme-units, or burnt to CO gives rise to 187 gramme-units.
Now if a given weight of carbonic oxide, in combining with another atom of oxygen
and burning to carbonic anhydride, generates 424 units of heat, it is obvious that the
reverse process, or dissociation of the carbonic anhydride into carbonic oxide and oxygen,
must absorb precisely the same amount of heat.
Hence the dissociation we have supposed would absorb 424 gramme- units of heat,
and the consequent loss of temperature would reduce the pressure in a degree that
would far more than compensate for the increment due to the increase of volume by
dissociation.
K. TENSION OP FIRED POWDER OBSERVED IN A CLOSE VESSEL.
As it Avas one of our principal objects to determine with as much accuracy as possible
not only the tension of fired gunpowder Avhen filling completely the space in which it
was exploded, but also to determine the law according to which the tension varied with
the density, it has been our endeavour to render both varied and complete the experi-
ments instituted to ascertain these important points.
In the first experiments described in this paper, as well as in the earlier series which
formed the basis of Captain Noble’s lecture delivered to the Royal Institution, the
method adopted to determine the variation of pressure was as follows : — The space in
which the powder was to be fired having been carefully established, the weight of the
powder to be experimented with which would accurately fill the space was ascertained,
and -j^-, &c. of the vessel was successively filled with powder, which Avas then
fired, and the resulting pressures determined.
Later on it was found that, as with each description of powder the gravimetric density
varied, it was more convenient to refer the pressure not, as at first, to a density arrived
at by taking the weight of powder which completely filled a given space as unity, but
to the specific gravity of water as unity. The densities given hereafter must therefore
be taken to represent the mean density of the powder inclusive of the interstitial spaces
between the grains, or, what is the same thing, the mean density of the products of
explosion referred to water as unity. The gravimetric density of the modern pebble
powders closely approximates to 1 * ; that of the old class of cannon-powders, such as
L. G., R. L. G., &c., varied generally betweenf '870 and *920; that of F. G. and
sporting-powders was still lower.
* This statement applies only to the powder taken in considerable bulk. In our explosion-vessels, the gravi-
metric density, when they were completely filled, did not exceed, with pebble powder, ‘92 or '93. The state-
ment, therefore, that the powder was fired in so many per cent, of space does not actually refer to the space
occupied in the chamber, but to a chamber of a size that would hold powder of our standard density.
f Boxer, Gen., R.A., ‘Treatise on Artillery,’ 1859, p. 21. Mordecai, Major, U.S.A., ‘Report on Gunpowder,’
Washington, 1845, p. 187.
96
CAPTAIN NOBLE AND MR. E. A. ABEL ON EIRED GUNPOWDER.
The results of the whole of our experiments, as far as they relate to tension, arranged
according to the three descriptions of the powder used and to the density of the products
of explosion, are given in Table V. The experiments numbered with an asterisk are
taken from the earlier series made by Captain Noble. They accord very well with the
present experiments ; but the powder used in the first series not having been analyzed,
we are not prepared to say that it was of exactly the same constitution as the corre-
sponding kind of powder used in the present experiments, although the difference could
of course be but very trifling, it being gunpowder of Waltham- Abbey manufacture, which,
as shown by the analyses given in Table II., varies very little in composition.
Table V. — Giving the pressures actually observed, in tons per square inch, with F. G.,
R. L. G., and Pebble powders for various densities of the products of Explosion.
Mean
density of
products
of explosion.
Nature of Powder.
Mean
density of
products
of explosion .
Nature of Powder.
F. G.
E.L.G.
Pebble.
F.G.
E. L. G.
Pebble.
Pressure in
tons per
square inch.
Pressure in
tons per
square inch.
Pressure in
tons per
square inch.
Pressure in
tons per
square inch.
Pressure in
tons per
square inch.
Pressure in
tons per
square inch.
. -0940
1-6
•5000
10-48
10-48
•1064
1-66
1*39
10-20
10-70
1-35
1-26
11-10
,,
0 96
1-28
*•5300
*u-8o
•1973
2-67
•5322
11-48
12-20
•2000
2-70
•6000
14-14
14-36
13-78
•2114
2-93
„
13-50
•2129
3-70
,,
14-80
„
3-58
*•6100
*15-6
„
3-00
*•6200
*16-8
•2963
6-40
•7000
18-2
19-54
18-60
•3000
5-40
„
+18*9
J17-00
•3171
4-90
*'75°°
*21-90
•3193
6-75
1 -8000
23-20
24-40
28-60
„
6-32
27-10
23-20
24-20
*•3800
*8-5
•9000
27-20
35 -6
33-40
*7.7
31-60
•3860
7-68
,,
31-40
•3947
8-1
1 *’9000
*33*i
•4258
9-34
8-40
*3°-7
„
9-10
*3 11 "9
•4615
8-68
! -9150
34-5
•4893
10-14
•9300
36-2
•4934
11-50
•9300
*340
§35 0
f R. E. G. powder. t Spanish spherical pellet. § Pellet.
We have laid down on Plate 16 the whole of these experiments. The pressures
given by the pebble and the R. L. G. are nearly identical ; we have therefore considered
them so, and have drawn but one curve to represent their mean results. The curve
representing the pressures given by the F. G., although nearly identical with the pebble
and R. L. G. at the lower densities, does not coincide at the higher densities. A separate
curve has therefore been drawn for this powder. The lower tension is perhaps accounted
CAPTAIN NOBLE AND MR. E. A. ABEL ON FIRED GUNPOWDER.
97
for by the difference between the quantity of permanent gas yielded by it and by the
other two powders.
The corrected values of the tension, in terms of the density of the different powders,
as indicated by the curves Plate 16, are given in the following Table: —
Table VI. — Showing the pressure corresponding to a given density of the products of
explosion of F. G., R. L. G., and Pebble powders, as deduced from actual observa-
tion, in a close vessel. The pressures are given in tons per square inch, atmospheres,
and kilogrammes per square centimetre.
Corresponding pressures for Pebble
and R. L. G-. powders.
Corresponding pressures for
F. Gr. powder.
Mean
density of
products
of explosion.
•05
•10
•15
•20
•25
•30
•35
•40
•45
•50
•55
•60
•65
•70
•75
•80
•85
•90
•95
1-00
In tons per
square inch.
0- 7o
1- 47
2- 33
3- 26
4- 26
5- 33
6- 49
7- 75
9-14
10-69
12-43
14-39
16-60
19-09
21-89
25-03
28-54
32-46
36-83
41-70
In
atmospheres.
107
224
355
496
649
812
988
1180
1392
1628
1893
2191
2528
2907
3333
3812
4346
4943
5608
6350
In kilos, per
square
centimetre.
1102
231-5
367-0
513-4
670 9
839-4
1028-1
1220-5
1439-5
1683-6
1957-6
2266-3
2614-3
3006 5
3447-5
3942-0
4495 0
51121
5800-4
6567-3
In tons per
square inch.
0- 70
1- 47
2- 33
3- 26
4- 26
5- 33
6- 49
7- 74
9-10
10-59
12-22
14-02
16-04
18-31
20-86
23-71
26-88
30-39
34-26
38-52
In
atmospheres.
107
224
355
497
650
812
988
1179
1387
1614
1863
2136
2445
2790
3179
3613
4096
4632
5190
5870
In kilos, per
square
centimetre.
110 2
231-5
367 0
513-4
670 9
839-4
1022 1
1219 0
1433-2
1667-8
1924-5
2208-0
2526-1
2883-6
3285-2
3734 1
4233-3
4786-1
5335-6
6066-5
In considering the pressures indicated, the question naturally arises as to how their
value would be affected if the charges were greatly increased; or, to put the question
in another form, it may be inquired whether the tensions indicated by our experi-
ments are materially affected by the cooling influence of the vessel in which the
explosion is conducted.
We think there are very strong grounds for assuming that the pressure is not mate-
rially affected by the above circumstances, except in cases where the density of the
products of explosion is low and the quantity of powder therefore very small as com-
pared with the space in which it is fired.
Thus it will be observed that the pressures obtained in experiment 2 and in experi-
ments 65, 66, and 68 compare very well (the density being about the same), although
the quantity of powder fired in the first case is only half of that fired in the last three
experiments.
mdccclxxv. o
98
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GTJNPOWDEK.
Again, if there were any considerable decrement of pressure due to loss of heat, we
should expect to find that the tension indicated would be higher when means are taken
to insure rapidity of combustion. Such, however, is not the case ; for if reference be
made to experiments 70 and 71, in which the charges were detonated by means of
mercuric fulminate, it will be observed that the tension realized in these experiments
was not materially higher than when the powder was fired in the ordinary way.
We may cite also, in support of our view, some interesting observations made .during
some earlier experiments in which charges of 10,500 grains (6'80-4 grms.) R L. G. and
pellet powder were fired in chambers entirely closed with the exception of a vent ‘2 inch
(5*08 millims.) in diameter.
With the former powder the pressure realized under these circumstances was 36 ‘2
tons per square inch (5513 atmospheres), with the latter 17-3 tons (2634 atmospheres).
This large difference was due to the slower combustion of the pellet powder, upon the
ignition of which, therefore, a large part of the products of combustion escaped by the
vent before the whole of the powder was fired. When, however, the same powders were
fired in vessels absolutely closed, the pressure indicated by the pellet powder was more
than doubled (being 35 tons per square inch, or 5330 atmospheres), while the pressure
indicated by the R. L. G. was practically the same (being 34 tons per square inch, or
5178 atmospheres).
From the experiments made by the Committee on Explosives, we are able to name
approximately the absolute time that would be consumed in burning a charge of R. L. G.
and of pebble, assuming that the powder be confined. With R. L. G. the time would
be approximately -00128 second, with pebble approximately -0052 second. Of course
these figures must vary greatly with different powders, as they depend not only on the
nature, size of grain, and density of the powder, but also on the mode of ignition. They
are interesting, however, as indicating the minuteness of the times involved and the
relatively much larger time required for the decomposition of the pebble powder. It
follows from the accordance of the pressures in the experiments just referred to, when
powders differing so considerably in rapidity of combustion are fired in close vessels, that
there is no very appreciable difference in pressure due to the longer time taken by the
pebble powder to consume under these conditions.
But the strongest, and at the same time an altogether independent, corroboration of
our view is derived from the experiments upon the pressures exerted in the bores of guns
by the action of the charge.
Not only do these pressures, as obtained by observation, agree with most remarkable
accuracy with the theoretical pressures deduced from the experiments in a close vessel,
but, when in large guns the tensions due to very different charges are compared, not
with reference to the position of the shot in the bore, but with reference to the mean
density of the products of explosion, a most striking accordance is found to exist. We
may therefore conclude that, where powders such as those we have experimented with
are employed, there is but a trifling correction to be made in the observed pressure when
CAPTAIN NOBLE AND MR. E. A. ABEL ON FIRED GUNPOWDER.
99
the powder entirely fills the space in which it is fired, or, indeed, whenever it occupies
a considerable percentage of that space. But though the pressure may not be seriously
affected when the generated gases are of a high density, it is more than probable
that some very appreciable correction should be made in the results we have observed
when experimenting with gases of low density. In this latter case the cooling influence
of the vessel would be greatly increased, not only from the higher ratio which the cooling-
surface bears to the charge, but also from the slowness of combustion due to the com-
paratively feeble pressure ; and we think the effect of slow combustion is clearly traceable
in the low tensions observed with pebble powder (see curve, Plate 16) at densities of
*1, -2, and -3, as compared with those given at corresponding densities by F. G. powder,
the combustion of which would be much more rapid. But we shall return to this point
when we compare our results with those demanded by theory.
Upon the same Plate (Plate 13) on which we have given curves representing the
experiments of Bumford and Hodman, there is also laid down a curve representing our
own experiments. The very high results obtained by Bumford are probably in great
measure attributable to his method of experiment. The charges being placed at one
end of his little vessel, while the weight to be lifted, so to speak, closed the muzzle, the
products of combustion acquired a high vis viva before striking the weight, and thus
indicated a much higher pressure than that due to the tension of the gas, just as in
Bobins’s well-known experiment a musket-barrel may be easily bulged or burst by a
bullet placed at some distance from the charge. That Bumford’s and even Piobert’s
corrected estimate of the tension of fired gunpowder was very excessive is of course
indisputably proved by our experiments, as the vessels in which they were made were
quite incapable of resisting pressures at all approaching those assigned by these eminent
authorities.
Bodman’s results are also too high, from a defect in the application of his system of
measurement, which has elsewhere * been pointed out; and his experiments on the ratio
of tension to density were not carried sufficiently far to admit of comparison in the
more important portion of the curve.
L. DETERMINATION OF HEAT GENERATED BY THE COMBUSTION OF GUNPOWDER.
The amount (that is the number of units) of heat liberated by the combustion of
gunpowder is determined from experiments Nos. 46, 47, 48, 49, and 63.
The powder used was the B. L. G. and F. G. ; but as it was found that there was
no material difference in the heat liberated, we have drawn no special distinction
between the experiments made with the two brands.
In each of the experiments Nos. 46, 48, and 63, 3800 grains (246-286 grms.) were
exploded ; and when the necessary reductions were made to convert the alterations in
temperature which were observed into their equivalents in water, it was found that in
experiment 48 the explosion of 246-286 grms. F. G. was sufficient to raise 173,077*4
* Noble, loc. cit. p. 25; Revue Scientifique, No. 48, p. 1138.
o 2
100
CAPTAIN NOBLE AND ME. E. A. ABEL ON FIEED GUNPOWDEB.
grms. of water through 1° C. In experiment 48 the explosion of the same quantity of
R. L. G. was equivalent to raising 172,569 grms. of water through 1° C., and in
experiment 63 to raising 171,500 grms. through 1°C. ; or, expressing these results in
a ditferent form, it appears that the combustion of a gramme of powder gave rise to
quantities of heat represented by raising a gramme of water through 702°-80 C.,
700C-69C., and 696°-50 C. respectively.
In experiments 47 and 49 the charge used was 393-978 grms.; and it was found
that in experiment 47 the heat generated by the explosion of the F. G. was sufficient
to raise 277,994T grms. of water through 1° C. ; and in experiment 49 the explosion of
the same quantity of R. L. G. generated heat represented by the raising of 278,185-5
grms. through 1° C., — or, in the two experiments, 1 gramme of powder gave rise
respectively to 705-61 and 706-09 gramme-units.
The mean of the whole of these experiments gives 702-34 gramme-units of heat
generated by the explosion of a gramme of powder, and we shall probably have a very
close approximation to the truth in assuming it at 705 gramme-units.
From this datum the temperature of explosion may be deduced, if we know the
mean specific heat of the products of combustion. We have only to divide 705 by the
specific heat, and the result is the required temperature.
The specific heat of all the gaseous products of combustion are known ; and they
have also been determined for the principal solid products at low temperatures, when
they are [of course] in the solid form.
Bunsen and Schischkoff, from their experiments, deduced the temperature of
explosion on the assumption that the specific heats of the solid products remain in-
variable over the great range of temperature through which they pass.
With every deference to those distinguished chemists we think their assumption is
quite untenable. Without, we believe, any known exception, the specific heat is
largely increased in passing from the solid to the liquid state. In the case of water
the specific heat is doubled ; the specific heats of bromine, phosphorus, sulphur, and
lead are increased from 25 to 40 per cent., and those of the nitrates of potassium and
sodium nearly 50 per cent., while it is more than probable that, even with liquids, the
specific heat increases very considerably with the temperature.
We shall, however, deduce from our experiments the temperature of explosion on
Bunsen and Schischkoff’s hypothesis, both with the view of enabling our results to
be compared with theirs, and for the purpose of fixing a high limit, to which it is
certain the temperature of explosion cannot reach. We shall afterwards endeavour to
estimate more accurately the true temperature.
The data necessary for computing the specific heat of a gramme of exploded powder
are given in the subjoined Table.
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GUNPOWDER,
101
Table VII. — Showing the specific heats and proportions of the products generated by
the combustion of gunpowder.
1.
Products of combustion.
Proportion'
in a
gramme.
3.
Specific
heat.
4.
Authority.
Products of
columns 2 & 3.
Solid *5684.
Potassium carbonate
•3382
•206
Kopp.
•06967
„ hyposulphite
•0355
•197
Pape.
•00700
„ sulphate
•0882
•196
Kopp.
•01729
„ sulphide
•0630
•108
Bunsen.
•00680
„ sulphocyanate
„ nitrate
•0009
•0006 !
•239
Kopp.
•00014
Ammonia carbonate
Sulphur
•0006
•0414
•171
Bunsen.
•00708
Carbon
•0000
•242
Regnault.
Gaseous -4316.
Sulphuretted hydrogen
•0113
[At constant
volume.
•184
Clausius.
•00208
Oxygen
•0000
•155
Carbonic oxide
•0447
•174
„
•00778
Carbonic anhydride
•2628
•172
•04520
Marsh-gas
•0005
•468
„
•00024
Hydrogen
•0010
2-411
„
•00241
Nitrogen
•1113
•173
”
•01925
1
•18494
Adding up the numbers in column 5, we obtain T8494 as the mean specific heat of
the products of explosion of a gramme of powder at ordinary temperatures ; and since,
as we have said, the temperature of explosion is obtained by dividing the gramme-units of
heat by the specific heat, we have the temperature of explosion=.I||i=38120C. ; and we
may accept this figure as indicating a temperature which is certainly not attained by
the explosion of gunpowder. We defer until further on the consideration of the
actual temperature.
M. DETERMINATION OE VOLUME OE SOLID PRODUCTS AT ORDINARY TEMPERATURES.
The space occupied by the solid products of combustion at temperatures but little
removed from 0° is deduced from experiments Nos. 46, 48, 49, 57, 58, 60, 61, and 62.
From these experiments it appears that
246-29 grms. R. L. G. gave rise to 76-46 cub. centims. solid residue.
33
33
F. G.
„ 67-26
33
33
393-98
33
R. L. G.
„ 123-12
33
33
386-21
33
F. G.
„ 115-34
33
33
33
R. L. G.
' „ 110-81
33
33
33
P.
„ 111-78
33
33
33
33
R. L. G.
„ 105-30
33
3 3
33
„
F.G.
„ 108-54
33
33
102
CAPTAIN NOBLE AND ME. P. A. ABEL ON EIEED GUNPOWDEE.
Or, stating the results per gramme of powder, it appears that in the several experi-
ments the solid products arising from the combustion of a gramme of powder occupied
respectively -3105, -2731, -3125, -2987, -2869, -2894, *2726, and -2810 cub. centim.
The mean of these figures is *2906 ; and we may thence conclude that at 0°C. the
solid residue of 1 gramme of burned powder occupies a volume closely approximating to
•29 cub. centim. ; therefore, since the solid products represent 57 percent, of the original
weight of the powder, it follows that at 0° C. the specific gravity of the residue is
about 1*4.
N. PEESSTJEE IN CLOSE YESSELS, DEDUCED FEOM THEOEETICAL CONSIDEEATIONS.
From the investigations we have described, it appears that in a close vessel, at the
moment of explosion, or at all events shortly afterwards, the results of the decompo-
sition of a given charge (say 1 gramme) of powder such as we have experimented with
are as follows : —
1. About 43 per cent, by weight of permanent gases, occupying, at 0°C. and under a
pressure of 760 millims., a volume of about 280 cub. centims.
2. About 57 per cent, by weight of liquid product, occupying, when in the solid form
and at 0°C., a volume of about -3 cub. centim.
Now, if we assume that the conditions known to exist shortly after explosion obtain
also at the moment of explosion, we are able, with the aid of our experiments, to com-
pute the pressure, temperature of explosion, and volume occupied by the permanent
gases. We propose to make these calculations, and then, by comparison with the
results obtained under the varied conditions adopted in our experiments, to form an
estimate of the correctness of our assumption. . And, first, to establish a relation between
the tension and the mean density of the products of explosion at the moment of
ignition, —
Let A B C D, Plate 15. fig. 4, represent the interior of the vessel, of volume v, in
which the experiments were made. Let C D E F represent the volume of a given
charge of powder placed in the vessel. Let & be the ratio which the volume CDEF
bears to A B C D, and let C D H G (vul suppose) be the volume occupied by the liquid
products at the moment and temperature of explosion.
It is obviously, for our present purpose, a matter of indifference whether we suppose
the liquid products collected, as in the figure, at the bottom of the vessel or mixed with
the permanent gases in a finely divided state.
Our conditions on explosion, then, are: — we have the space C D H G=y occupied
by the fluid residue, and the space A B IL 0=^(1 — «£) by the permanent gases.
Hence, since the tension of the permanent gases will vary directly as their density, we
have, if jp represent the pressure and D the density,
^=RD,
where R is a constant.
(1)
CAPTAIN NOBLE AND ME. E. A. ABEL ON FIEED GUNPOWDEE.
103
Now suppose the charge exploded in the chamber to be increased. In this case, not
only is the density of the permanent gases increased on account of a larger quantity being
generated, but the density is still further added to, from the gases being confined in a
smaller space ; the liquid residue CDHG being increased in a like proportion with the.
charge (D, in fact, varying as S ^), we have
or if p0 , &0 be corresponding known values of jp and &,
.. Po(l — «So) s
V— S0 !-«&•
(3)
In taking the tension of the permanent gases to vary directly as their density, we
have of course assumed that the temperature, whatever be the value of &, is the same.
In our experiments the charges exploded have varied in quantity from that necessary
to fill entirely the chamber to a small fraction of that quantity ; but whatever the charge
it is obvious that if the vessel be considered impervious to heat (and we have already
pointed out that only with the lower charges is there a material error due to this hypo-
thesis), the temperature at the moment of explosion would be the same ; for, as in the
case of Joule’s celebrated experiment, any heat converted into work by the expansion
of the gases would again be restored to the form of heat by the impact of the particles
against the sides of the vessel.
Returning to (3), the value of the constant a in this equation has yet to be found. If
from Table VI. we take out a second pair of corresponding values &15 a is determined
and will be found =*65, very nearly. Taking a=-65, and from Table VI. or the curve
Plate 16 taking &0=’6, p0=14'4 tons, equation (3) becomes
*=14-«8rhr W
Substituting in this equation successively values of § -05, T, T5, &c., we obtain com-
puted values of », which we compare with those derived directly from observation in
Table VIII.
104
CAPTAIN NOBLE AND ME, E. A. ABEL ON EIEED GUNPOWDER.
Table VIII. — Showing the comparison, in atmospheres and tons per square inch, between
the pressures actually observed in a close vessel and those calculated from the
f i (1 — «S0) &
formula p=p, —
1.
Density of pro-
ducts of com-
bustion.
Value ofp
deduced from
direct observa-
tion.
3.
Value of p
deduced from
equation (3) when
a=-65.
4.
Value of p
deduced from
equation (3) when
a -60.
5.
Value of p
deduced from
direct observa-
tion.
6.
Value ofp
deduced from
equation (3) when
«=-65.
7.
Value of p
deduced from
equation (3) when
«= 6.
Tons per
square inch.
Tons per
square inch.
Tons per
square inch.
Atmospheres.
Atmospheres.
Atmospheres.
•05
0-70
•758
•855
107
115
130
•10
1-47
1-565
1-765
224
238
269
•15
2-33
2-432
2-734
355
370
416
•20
3-26
3-363
3-771
496
512
574
•25
4-26
4-367
4-879
649
665
743
•30
5-33
5-452
6-071
812
830
924
•35
6-49
6-628
7-350
988
1009
1119
•40
7-75
7-908
,8-732
1180
1204
1330
*45
9-14
9-305
10-228
1392
1417
1557
•50
10-69
10-837
11-851
1628
1650
1805
•55
12-43
12-524
13-620
1893
1907
2074
•60
14-39
14-390
15-554
2191
2191
2369
*65
16-60
16-466
17-679
2528
2507
2692
•70
19-09
18-791
20-024
2907
2861
3049
•75
21-89
21-410
22-625
3333
3260
3445
•80
25-03
24-383
25-525
3812
3713
3887
•85
28-54
27-789
28-780
4346
4232
4383
•90
32-46
31-728
32-460
4943
4831
4943
•95
36-83
36-336
36-654
5608
5538
5582
1-00
41-70
41-698
41-477
6350
6350
6316
Now if the figures given in columns 2 and 5, being those derived from the obser-
vations themselves corrected by differencing, be compared with the values given in
columns 3 and 6, computed on the value a = -65 (that is, on the assumption that at the
temperature of explosion the liquid residue of 1 gramme of powder occupies -65 cub.
centim.), it will be found that the two columns are practically indentical, thus affording
a confirmation of the strongest nature of the correctness of our assumption. The close-
ness of agreement will he best seen by examining the graphical representations in
Plate 17. We have already, however, had more than once occasion to remark that there
is reason to suppose that the observed pressures are slightly in defect, at all events at
low densities. Other considerations have led us to the conclusion that a value of a
not far removed from ’6 would more nearly represent the truth, were all disturbing
influences removed. We have therefore added to the above Table the pressures com-
puted on this hypothesis ; and Plate 17 shows at a glance the comparison between the
three curves.
0. DETERMINATION OP THE TEMPERATURE OF EXPLOSION OP GUNPOWDER,
We are now in a position to compute the temperature of explosion.
CAPTAIN NOBLE AND ME. F. A. ABEL ON FIEED GUNPOWDER.
105
Since p, v, and t are, in the case of permanent gases, connected by the equation of
elasticity and dilatability,
pv=Rt (5)
(where R is a constant and t is reckoned from absolute zero), t will be known if p, v ,
and R be known.
Now if we assume a = *6, it follows that in the combustion of 1 gramme of powder
(gravimetric density =1) the gaseous products will, if the powder entirely fill the
chamber in which it is placed, occupy a space of *4 cub. centim. But we know that,
at 0° C. and under a barometric pressure of 760 millims., the gaseous products of
1 gramme occupy a space of about 280 cub. centims. Hence at 0° C., if the gaseous
products are compressed into a space of *4 cub. centim., we have a pressure of 700
atmospheres; and since absolute zero = — 274° C., we have, in the equation ^>0v0=Rf0,
the values ^o=700, w0=-4, t0=2 74;
.-. R=-^^ =1-0218.
Hence (5) becomes
pv=V0218t (6)
Now under the above conditions, but at the temperature of explosion, we have from
Table VIII. ^) = 6400 atmospheres, and, as before, v = *4. Therefore
t=
6400 x -4
1-0218
=2505;
(7)
and this is the temperature of explosion reckoned from absolute zero. Subtracting 274°
from this temperature to reduce the scale to Centigrade, we have temperature of explo-
sion =2231° C.
If we assume a=-65, the temperature of explosion deduced in the same way would be
1950° C. ; but this temperature, as we shall shortly show, would be somewhat too low.
We have now three points to consider: —
1. Is this temperature a probable one] and can any direct experimental facts be
adduced to corroborate this theoretical deduction ?
2. What is the mean specific heat of the solid or liquid products which the above
temperature implies ] and
3. Can any corroboration be given to the high rate of expansion of the solid residue
implied by assuming the value of a as =-6 ]
With regard to the direct estimation of the temperature of explosion, we have made
several experiments with the view of obtaining this result, by ascertaining the effects of
the heat developed on platinum. For example, in experiment 78 we introduced into the
charge of R. F. G. a coil of very fine platinum wire and also a piece of thin sheet plati-
num. After the explosion the sheet platinum was found much bent, but unmelted ; but
on examination with a microscope there were evident signs of a commencement of fusion
on the surface, and a portion of the fine platinum wire was found welded on to the sheet.
MDCCCLXXV. p
106
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED G-UNPOWDEE.
The coil of wire was not to be found, but portions of it were observed welded to the
sides of the cylinder.
Now we know that platinum is readily volatilized when exposed to the hydrogen-
blowpipe at a temperature of about 3200° C., and therefore, if the temperature of
explosion had approached this point, we should have expected the very fine wire to be
volatilized; remembering the low specific heat of platinum, we should furthermore have
been warranted in expecting more decided signs of fusion in the sheet metal.
Again, in experiments 84, 85, and 68, pieces of platinum wire -03 inch (0‘75 millim.)
in diameter and 4 inches (100 millims.) long were placed in the cylinder with consider-
able charges of It. L. G. and F. G. In none of these experiments did the platinum
melt, although, as in the case of the sheet platinum, there were signs of fusion on the
surfaces of the wires. In experiment 79, however, in which platinum wire was placed
with a corresponding charge of the Spanish powder, the wire was fused, with the exception
of a small portion. With this powder, indeed, which is of a very different composition
from the English powders and decidedly more rapidly explosive in its nature, it is quite
possible that a somewhat higher heat may have been attained. But, as in one case the
platinum wire was nearly fused, and in others it only showed signs of fusion, the con-
clusion we draw from the whole of these experiments on the fusion of the platinum is
that the temperature of explosion is higher than the melting-point of that metal, but
not greatly so. Now, according to Deville, the melting-point of platinum is nearly
2000° C. ; and hence we have a strong corroboration of the approximate accuracy of
the theoretical temperature of explosion at which we have arrived, viz. 2231° C.
P. MEAN SPECIFIC HEAT OF LIQUID PEODUCTS.
We have already given the specific heat of the liquid products when in the solid form.
If we assume the temperature above specified to be correct, a mean specific heat of the
liquid product of ’4090, or a total mean specific heat of the entire products of -3094,
would result, being an increment of about 67 per cent. ; and this, judging from the
analogy of the case we have cited, does not appear an improbable conclusion.
Q. PEOBABLE EXPANSION OF NON-GASEOUS PEODUCTS BETWEEN ZEEO AND
TEMPEEATUEE OF EXPLOSION.
So far as we are aware there were, prior to our experiments, no data existing as to
the behaviour of the non-gaseous products of combustion at the high temperature
involved, except perhaps the experiment made by Bunsen and Schischkoff, who exposed
on platinum foil the solid residue in an oxyhydrogen jet, and concluded, from there
being no ebullition, that at the temperature of 3300° C. the tension of the resulting
vapour did not reach one atmosphere. Taking the circumstances into account, we may
indeed doubt if the residue itself actually reached the temperature we have uamed ;
but the experiment would at all events prove that, at the temperature which we find to
be that developed by explosion, the solid or liquid products are not in the state of
vapour, or at least that the small portion volatilized had but an insignificant tension.
CAPTAIN" NOBLE AND ME. F. A. ABEL ON FIEED G-UNPOWDEE.
107
To test, however, the behaviour of the residue for ourselves, we placed in one of
Siemens’s gas-furnaces, the temperature, of which was estimated at about 1700° C.,
several crucibles containing powder-residue. The behaviour of the residue was in all
cases the same ; at first there was a little spirting (probably due to escape of water), which,
however, soon diminished, and in time the contents of the crucibles became perfectly
quiet, but up to the end of the experiment only a very slight volatilization could be
observed. In the case of three of the crucibles, two of which contained powder-residue,
the other a mixture of potassium carbonate and liver of sulphur, when removed from
the furnace after being exposed to the full heat for about a quarter of an hour, the
volumes of the contents in the highly heated state were observed without difficulty.
The contraction in cooling was evidently very great, especially at first. The contents
set at a temperature of between 700° and 800° C., and when cool the expansion was
measured by calibration with mercury. The first crucible gave an expansion of 77-8
per cent, between 0°C. and 1700° C. ; the second (potass, carb. and liver of sulphur) an
expansion of 93' 8 per cent. The third (powder-residue) gave a considerably higher rate
of expansion, above 100 per cent. ; but we have not included the result, as, owing to the
presence of a piece of platinum put in to test the temperature of the furnace, we were
unable to make a very accurate measurement.
Of course the expansions, under the conditions we have just named, cannot be strictly
compared with those which would have place in a close vessel under the high tension
we know to exist ; but they tend to confirm the results arrived at by a perfectly inde-
pendent method. The experiments also show that, at a temperature approaching that
developed by explosion, and under atmospheric pressure, the liquid products are still in
that condition ; and our experiments so far confirm those of Bunsen aud Schischkofe to
which we have alluded.
E. OBSEEVED PEESSUEES IN THE BOEES OF GUNS.
The data which we shall use for the discussion of the phenomena attending the com-
bustion of gunpowder in ordnance are nearly entirely derived from the experiments
carried on by the Committee of Explosives under the presidency of Colonel Young-
husband, F.R.S.
Two methods, of an entirely distinct nature, were employed by the Committee for the
elucidation of the questions they had to consider.
One method consisted in determining the tension of the gas at various points in the
bore, by direct measurement. The other mode consisted in measuring the time at which
the projectile passed certain fixed points in the bore, thence deducing the velocities
from the seat of the shot to the muzzle, and finally obtaining, by calculation, the gaseous
pressure necessary to generate the observed velocities.
The apparatus used for determining the tension by direct measurement was the
crusher-gauge, which we have already described ; that for ascertaining the velocity was
a chronoscope specially designed for measuring very minute intervals of time. As the
p 2
108
CAPTAIN NOBLE AND MR. F. A. ABEL ON FIRED GUNPOWDER.
construction of this instrument has been fully explained elsewhere, we shall only here
give a very general description of it.
Its most recent form is shown in plan and elevation in Plate 18. figs. 1 & 2. The
mechanical part consists of a series of thin disks, A, A, &c., 36 inches in circumference,
keyed on to a shaft, S, and made to rotate at a very high and uniform velocity through
the train of wheels F, by means of a very heavy descending weight at B, arranged, to
avoid an inconvenient length of chain, upon a plan originally proposed by Huyghens.
This weight is continually wound up by means of the fly-wheel and handle at T. The
stop-clock D, which can be connected or disconnected with the shaft E at pleasure,
gives the precise speed of the circumference of the disks, which is usually arranged at
about 1250 inches a second.
The recording arrangement is as follows : — Each disk is furnished with an induction-
coil, G, the primary wire from which is conveyed to any point, K, in the gun where we
may wish to record the instant at which the shot passes. There is at each such point a
special contrivance by which the shot in passing severs the primary wire, thereby causing
a discharge from the secondary, which is connected with the discharger, Y. The spark
records itself on the disk by means of paper specially prepared to receive it. The
instrument is capable of recording the millionth part of a second, and, when in good
working order, the probable error of a single observation should not exceed 4 or 5 one
millionths of a second.
The guns were arranged for the experiments as shown in fig. 3 in the same Plate.
Holes were drilled in the powder-chamber in the positions marked A, B, C, and in the
bore in the positions marked 1 to 18.
In A, B, and C crusher-gauges were always placed ; the holes numbered 1 to 18 were
fitted with crusher-gauges or the chronoscope-plugs at option.
It would be beside our object in this paper to enter into a discussion of the special
experiments undertaken by the Committee of Explosives. The chief object of their
investigations was to determine the nature of powder most suitable for use with heavy
guns — that is to say, the powder which will allow of the highest effect being realized
without unduly straining the structure within which the explosion is confined. A number
of experiments were therefore made with powders of abnormal types, interesting and
instructive only to artillerists ; and these experiments will doubtless be fully reported on
at a later date, by the proper authorities.
In our present paper we shall confine our attention chiefly, if not entirely, to the
results obtained with the well-defined and well-known powders which have been admitted
into the service for use with rifled guns, and which are known under the names of “Rifled
Large Grain” and “ Pebble.” These powders are, moreover, the same as were used by
us in our experiments in closed vessels, and therefore allow of a strict comparison with
the tensions so obtained. But before giving the details, we cannot pass without notice
certain differences in the results obtained by means of the two modes of experimenting
to which we have alluded.
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GUNPOWDEE.
109
With pebble and other powders, where a slow and tolerably regular combustion takes
place, the maximum tension of the gas, obtained both by direct measurement and by the
chronoscope, agrees remarkably closely. There is generally a very slight difference
indeed between the indicated pressures ; but the case is greatly different where the
powder is of a highly explosive or quickly burning description. In such a case, not
only are the pressures indicated by the crusher-gauge generally much above those
indicated by the chronoscope, but they differ widely in various parts of the powder-
chamber, in the same experiment, and even in different parts of the same section of the
bore. They are also locally affected by the form of the powder-chamber, and frequently
indicate pressures considerably above the normal tensions that would be attained were
the powder confined in a close vessel.
It is not difficult to explain these anomalies. When the powder is ignited compara-
tively slowly and tolerably uniformly, the pressure in the powder-chamber is also uniform,
and approximates to that due to the density of the products of combustion.
The crusher-gauges, then, give similar results throughout the powder-chamber, and
they accord closely with the results deduced from the chronoscope observations. But
when a rapidly lighting or “ brisante ” powder is used, the products of combustion of
the portion first ignited are projected with a very high velocity through the interstices
of the charge, or between the charge and the bore ; and on meeting with any resistance
their vis viva is reconverted into pressure, producing the anomalous local pressures to
which we have drawn attention.
We have pretty clear proof that, when this intense local action is set up, the gases
are in a state of violent disturbance, and that waves of pressure pass backwards and
forwards from one end of the charge to the other, the action occasionally lasting the
whole time that the shot is in the bore. In fact, with the rapidly burning, and in a
less degree even with the slower burning powders, motion is communicated to the pro-
jectile not by a steady, gradually decreasing pressure like the expansive action of steam
in a cylinder, but by a series of impulses more or less violent.
The time during which these intense local pressures act is of course very minute ; but
still the existence of the pressures is registered by the crusher-gauges. The chrono-
scopic records, on the other hand, which are, so to speak, an integration of the infini-
tesimal impulses communicated to the shot, afford little or no indication of the intensity
of the local pressures, but give reliable information as to the mean gaseous pressure on
the base of the shot.
The two modes of observation are, as we have elsewhere pointed out, complementary
one to the other. The chronoscope gives no clue to the existence of the local pressures
which the crusher-gauge shows to exist ; while, on the other hand, where wave- or
oscillatory action exists, the results of the crusher-gauge cannot be at all relied on as
indicating the mean pressure in the powder-chamber.
An interesting illustration of this distinction was afforded by two consecutive rounds
fired from a 10-inch gun, in one of which wave-action was set up, in the other not. In
110
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GUNPOWDER.
both cases the projectile quitted the gun with the same velocity, and the mean pressure
throughout the bore should of course have been the same. The chronoscopic records
were, as they ought to be, nearly identical for the two rounds ; but the pressures indi-
cated by the crusher-gauge were in the one round at the points A, B, C, 1, 4 (tig. 3,
Plate 18), respectively 63*4, 41-6, 37*0, 41-9, and 25'8 tons on the square inch ; in the
other, at the same points, respectively 28-0, 29*8, 3T0, 29-8, and 19-8 tons on the
square inch.
Where no wave-action exists, the chronoscopic pressures are generally somewhat
higher than those of the crusher-gauge. The difference is not generally greater than
about 5 to 7 per cent., although, in the case of some exceptionally heavy shot, this
variation was considerably exceeded. Among the causes tending to produce this differ-
ence may be cited : — 1. Friction in the parts of the crusher-gauge. 2. Slight diminu-
tion of pressure due to windage *. 3. Vis viva of particles of the charge and products
of combustion, a portion of which would be communicated to the shot, but would not
take effect on the crusher-gauge. On the whole, however, the accordance of results
derived from methods so essentially different was quite as close as could reasonably be
expected, and entirely satisfactory.
We now pass to the consideration of the tensions actually found to exist in the bores
of guns. Two series of experiments were made by the Committee on Explosives with
the 10-inch 18-ton gun. The one series was with charges of 70 lb. (31-75 kilos.) of
pebble powder. The weights of the shot were made to vary, the first rounds being fired
with projectiles of 300 lb. (136‘05 kilos.), and the weights being successively increased
to 350 lb., 400 lb., 450 lb., 500 lb., 600 lb., 800 lb., 1000 lb., and concludingVith pro-
jectiles of the weight of 1200 lb. (544-20 kilos.).
In the other series charges of 60 lb. (27*21 kilos.) R. L. G. were used. The projectiles
were of increasing weights as above; but the experiments were not carried so far, the
heaviest projectile in this series being of 600 lb. (272 kilos.) weight.
As we shall have occasion more than once to refer to these experiments, and as the
powder used was carefully selected to represent as nearly as possible the normal service-
powder of each description, it appears to us convenient, in order to illustrate the methods
followed in determining the powder-pressures, to take an example from each series.
This plan will further enable us to compare the difference of behaviour of pebble and
R. L. G. powder in the bore of a gun.
Commencing, then, with the charge of 70 lb. (31-75 kilos.) pebble powder and the
projectile of 300 lb. (136-05 kilos.), the results given by the chronoscope, to which we
shall turn our attention in the first instance, are given in Table IX.
* In the experiments with, the 38-ton gun an opportunity occurred of determining the differences in pressure
due to the escape of the gases by the windage, and it was found that a reduction of windage of -07 inch (1-75
millim.), i. e. the difference between -01 inch and -08 inch windage, reduced the maximum pressure indicated
by the crusher-gauge by about 1 ton per square inch. Of course the mean pressure on the base of the projectile
was not reduced in any thing like the same proportion.
CAPTAIN NOBLE AND MR. E. A. ABEL ON EIRED GUNPOWDER.
Ill
In this Table column- 1 gives the distances of the various plugs from the seat of the
shot in feet, see fig. 3, Plate 18 (the distance from the seat of the shot to the bottom
of the bore being 2 feet=-610 metre). Column 2 gives the same distances in metres.
Column 3 gives the observed time of passing each plug. Column 4 gives the corrected
time from the commencement of motion, the time from the commencement of motion
to the first plug being interpolated. Column 5 gives the differences of time — that is,
the time taken by the projectile to traverse the distance between the plugs. Column 6
gives the mean velocity of the projectile over the space between the plugs, in feet; and
column 7 gives the same velocities in metres.
Table IX. — Giving data obtained with chronoscope for calculating velocity and pressure
in the bore of a 10-inch 18-ton gun. Charge 70 lb. (31-75 kilos.) pebble powder.
Weight of projectile 300 lb. (136-05 kilos.). Muzzle-velocity 1527 ft. (465-4 metres).
1.
2.
3.
4.
5.
6.
7i
Distance from seat
of shot.
Time observed
at plugs.
Total time from
seat of shot.
Time taken by
shot to traverse
distance
between plugs. .
Mean velocity over
spaces between plugs.
feet.
0-00
0-06
0-26
0- 46
0-66
0*86
1- 06
1- 46
1-86
2- 26
2-66
3- 46
4- 26
5- 06
6- 66
8-26
metres.
0-000
0-018
0-079
0-140
0-201
0-262
0-323
0-445
0- 567
0-689
0-811
1- 055
1-298
1- 542
2- 030
2-518
seconds.
•000000
•001096
•001611
•001967
•002272
•002548
•003036
•003469
•003869
•004244
•004947
•005605
•006234
•007426
•008554
seconds.
•000000
•002683
•003779
•004294
•004650
•004955
•005231
•005719
•006152
•006552
•006927
•007630
•008288
•008917
•010109
•011237
seconds.
•002683
•001096
•000515
•000356
•000305
•000276
•000488
•000433
•000400
•000375
•000703
•000658
•000629
•001192
■001128
feet per
second.
22
183
388
562
656
725
820
924
1000
1065
1138
1215
1273
1342
1418
metres per
second.
6-7
55-8
118-3
171-3
199*9
221-0
249-9
281-6
304-8
324-6
346-9
370-3
388-0
409*0
432-2
From these data are deduced, by correction and interpolation, the times given in
Table X. From the differences of the times are calculated the velocities, and from the
velocities the pressures necessary to produce them are obtained.
Table X. — Giving the total time from commencement of motion, velocity, and tension
of products of explosion, in bore of a 10-inch 18-ton gun, deduced from Table IX.
Travel.
Time.
Velocity.
Pressure.
Total.
Over intervals.
feet.
0-00
0-02
0*04
0-06
0-08
0-10
0-12
0-14
0-16
0-18
0-20
0*22
0-24
0-26
0-28
0-30
0-32
0-34
0-36
0-38
0-40
0-42
0-44
0-46
0-48
0-50
0*52
0-54
0- 56
0-66
076
0-86
0-96
1- 06
1-16
1-26
1-36
1*46
1- 56
1-66
176
1-86
1-96
2- 06
2-1 6
2-26
2-36
2-46
2-56
2-66
276
2-86
2- 96
3- 06
3- 46
3*86
4- 26
4- 66
5- 06
5-46
5- 86
6- 26
6-66
7-06
7- 46
7-86
8- 26
metres.
•000
•006
•012
•018
•024
•030
•037
•043
•049
•055
•061
•067
•073
•079
•085
•091
•098
•104
•110
•116
•122
•128
•134
•140
•146
•152
•158
•165
•171
•201
•232
•262
•293
•323
•353
•384
•414
•445
•475
•506
•536
•567
•597
•628
•658
•689
719
750
•780
•811
•841
•871
•902
•932
1-054
1-176
1-298
1-420
1-542
1-664
1786
1- 907
2- 029
2-151
2-273.
2-395
2-517
seconds.
•ooooooo
•0018182
•0023772
•0026330
•0028950
•0C30576
•0031908
•0033044
•0034042
•0034936
•0035748
•0036496
•0037190
•0037840
•0038452
•0039030
•0039580
•0040106
•0040610
•0041094
•0041560
•0042010
•0042446
•0042868
•0043278
•0043676
•0044064
•0044442
•0044810
•0046544
•0048132
•0049614
•0051013
•0052347
-0053625
•0054856
•0056047
•0057202
•0058325
•0059420
•0060490
•0061537
•0062562
•0063570
•0064560
•0065534
•0066493
•0067438
•0068371
•0069292
•0070201
•0071100
•0071989
•0072869
•0076337
•0079685
•0082933
•0086097
•0089185
•0092209
•0095177
•0098093
•0100965
•0103797
•0106593
•0109357
•0112089
seconds.
•0018182
*0005590
•0003058
•0002120
•0001626
•0001332
•0001136
•0000998
•0000894
•0000812
•0000748
•0000694
•0000650
•0000612
•0000578
•0000550
•0000526
•0000504
•0000484
•0000466
•0000450
•0000436
•0000422
•0000410
•0000398
•0000388
•0000378
•0000368
•0001734
•0001588
•0001482
•0001399
•0001334
•0001278
•0001231
•0001191
•0001155
•0001123
•0001095
•0001070
•0001047
•0001026
•0001007
•0000990
•0000974
•0000959
•0000945
•0000933
•0000921
•0000909
•0000899
•0000889
•0000880
•0003468
•0003348
•0003248
•0003164
•0003088
•0003024
•0002968
•0002916
•0002872
•0002832
•0002796
•0002764
•0002732
feet per
second.
11-0
35-8
65-4
94-3
123-0
150-0
176-1
200-6
223-9
246*2
267*6
288-2
308-0
327-1
345-5
363*3
380-5
397'2
413-4
429-1
444-5
459-4
473-9
488-0
501-7
515-1
528-1
540-8
576-7
629-6
674-8
714-7
750-0
782-3
812-1
839-9
865-9
890-2
913-1
934-7
955-1
974-4
992-8
1010
1027
1043
1058
1072
1086
1100
1112
1125
1137
1154
1195
1232
1265
1295
1322
1347
1371
1392
1412
1431
1448
1465
metres per
second.
3-35
10-91
19-93
28-74
37-49
45-72
53-68
61-14
68-24
75-04
81-56
87-84
9388
99-70
105-3
110-7
116-0
121-1
126-0
130-8
1355
140-0
144-4
148-7
152 9
157-0
161-0
164-8
175-78
191-90
205-68
217-84
228-60
238-45
247-53
256-00
263 93
27133
278-31
284-90
29111
297 00
302 6l
307 85
313-03
317 91
322-48
326-75
331 01
335-28
338-94
342-90
346-56
351-74
364-24
375-51
385-57
394 72
402-95
410-57
417-88
424 28
430-38
436-17
441-35
446-53
tons per
square inch.
1-723
3- 843
6-096
8-270
9-873
1 1 198
12-192
13- 120
13915
14- 578
15- 174
15- 638
16 036
16- 407
16-698
16- 963
17*228
17*414
17- 599
17-745
17-864
17-944
17-957
17- 997
18- 023
17-997
17-904
17-800
16-910
15-637
14-710
13-716
13 093
12-590
12-192
11-755
11-331
10 920
10-575
10 231
9-873
9 568
9-250
8-972
8-706
8-442
8-190
7-952
7-739
7-541
7-355
7-183
6-874
6-402
5-911
5-487
5-089
4- 745
4-453
4-175
3-936
3-711
3-526
3-340
3-168
atmo-
spheres.
262
585
928
1259
1503
1705
1857
1998
2119
2220
2311
2381
2442
2498
2543
2583
2623
2652
2680
2702
2720
2733
2734
2741
2745
2741
2726
2711
2575
2381
2240
2089
1994
1917
1857
1790
1725
1663
1610
1558
1503
1457
1409
1366
1326
1286
1247
1211
1178
1148
1120
1094
1047
975
900
836
775
723
678
636
599
565
537
509
482
CAPTAIN NOBLE AND MR. F. A. ABEL ON FIRED GUNPOWDER.
113
We have not space within the limits of our paper to enter upon a discussion of the
methods of calculation and correction necessary to arrive at the results tabulated ; they
are attended with very great labour, and a full consideration of the question would
necessitate a separate paper. As we shall hereafter show, it is not difficult, if we were
to suppose the powder entirely converted into gas on the instant of explosion, to lay
down the law according to which the pressure would vary in the bore of the gun ; but
the case under consideration is a much more complicated one. The charge of powder
is not instantly exploded, but is generally ignited at a single point; the pressure (com-
mencing at zero) goes on increasing at an extremely rapid rate until the maximum
increment is reached. It still goes on increasing, but at a rate becoming gradually
slower, until the maximum tension is reached, when the increase of density of the gas,
aided by the combustion of the powder, is just counterbalanced by the decrease of
density due to the motion of the projectile. After the maximum of tension is reached,
the pressure decreases, at first rapidly, subsequently slower and slower.
If these variations in pressure be represented by a curve, it would commence at the
origin convex to the axis of x, would then become concave, then again convex, and
would finally be asymptotic to the axis of x.
In the same way, the curve representing the velocity would commence by being
convex to the axis of abscissse ; it would then become concave, and, were the bore
long enough, would be finally asymptotic to a line parallel to the axis of x.
The results of Table X. are graphically represented in black lines in Plate 19, the
space described by the shot being taken as the equicrescent or independent variable,
and the two curves giving respectively the velocity and pressure at any point of the
bore.
From the Table (or curves) it will be seen that the maximum pressure attained by
the powder is 18 tons per square inch (2745 atmospheres), and that this pressure is
reached when the projectile has moved '5 feet (T53 metre) and at '00437 second from
the commencement of motion.
The results given in the Table have, as we have said, been arrived at by special
methods of correction and interpolation ; and their general correctness can be tested by
examining whether a material alteration of pressure or velocity at any point can be
made without seriously disturbing the times actually observed. It will be found that
they cannot. But another question here presents itself for consideration. We have, in
the curves on Plate 19, taken s as the independent variable ; but if t were taken as the
independent variable, and the relation between s and t were capable of being expressed
by the explicit function the velocity corresponding to any value of t would be
represented by the first derived function of f(t), and the pressure by the second derived
function. This, then, if a simple relation between s and t could be established, would
be an easy method of treating the problem ; but it has appeared to us practically im-
possible to obtain a single expression which shall represent the relation between s and
t for the whole time occupied by the shot in its passage through the bore.
MDCCCLXXV. Q
114
CAPTAIN NOBLE AND MR. E. A. ABEL ON FIRED GUNPOWDER.
If, for example, we endeavoured to represent the relation between s and t by a linear
equation of the form
s = cut -J- bt2 -f~ ct3 4“ dt^ &c., (8)
we should have to determine the most probable values of the coefficients a, b , c, d, See.
from the eighteen to twenty direct observations connecting s and t. The equation
would further have to be such that the first and second derived functions should repre-
sent curves of the general nature we have described. It is obvious that, setting all
other considerations aside, the labour of such a series of calculations would be insur-
mountable.
But although it is impossible to obtain a single relation between s and^ t for the
whole length of the bore, we have endeavoured, on account of the great importance of
the question, to obtain such a relation for the commencement of motion, where the
question of pressure is of vital importance.
To do this we have taken only the observed values of s and t so far that we could
be certain the position where the maximum pressure was attained was included, but
have made no assumption whatever as to the actual position of maximum pressure.
We then assumed that the relation between s and t was capable of being expressed
by an equation of the form
s=ata+pt+yt2 ; (9)
and from the observed values of s and t the probable values of a, a, (3, y were com-
puted by the method of least squares.
Treating in this manner the experiment under discussion, and taking from Table IX.
the first six values of s and t *, we have obtained for the most probable values of
o= 3-31076,
«= 1-37851,
(3= -76600,
y= — -06932,
and for the relation between s and t the equation
5=3-31076 1-37851 + V6600i- -06932*2 (IQ)
By differentiation we obtain for the velocity
ds s
^=V=-{(a + /3^ + ^2).(l + log^)-(«-yf).log^}; (11)
and by a second differentiation,
rp W d2S
pressure T=-.^
+ r^X1 +l°ge t) — (aL— yf)loget - 1 }
-f.^{/3-fO-4y^).(1 + loge^} (12)
* For the convenience of calculation, the unit of time used is not a second hut the thousandth part of a
second. The unit of space is altered in like proportion.
CAPTAIN NOBLE AND MR. F. A. ABEL ON PIRED GUNPOWDER.
115
Table XI. gives the results of the calculations necessary for obtaining the values of
s, v, and T from equations (10), (11), and (12).
To avoid repetition, we have introduced in this Table the following abbreviations : —
M=te+f 3t+ytf, )
N ~K — ryt 2,
[ (13)
P = M(1 -f loge £) — N loge t, |
F=/3+(/3-4y0.(l+log.i);J
and the values furnished in Table XI. can be compared with those given in Table X.
But the comparison, both as to velocity and pressure, can be more readily seen by a
graphical representation ; and we have accordingly laid down in Plate 20, in full black
lines, the curves of velocity and pressure taken from Table X.
The results of Table X. have already been graphically represented in Plate 19 ; but
in Plate 20, t instead of s is taken as the independent variable, with the view of
enabling the accordance of the methods to be more easily compared. The curves in
dotted lines indicate the velocity and pressure shown in Table XI., and deduced from
formulae (10), (11), and (12).
It will be observed that the two curves of velocity approximate exceedingly closely.
The difference between the pressure-curves also is not greater than might be expected ;
and the difference, such as it it, is due to our not having succeeded in obtaining an
equation which represents the corresponding observed values of s and t so closely as do
the values given in Table X.
The pressures given by the crusher-gauges (which can be compared with those given
in either of the Tables X. or XI.) at the points A, B, C, 1, 4, are respectively 17’2,
15'6, 15-6, 12‘8, and 11T tons per square inch, or in atmospheres, 2169, 2376, 2376,
1949, and 1690.
We now pass to the consideration of the results furnished by E. L. G. powder.
Taking, as in the case of pebble powder, the particular set of experiments where shot
of 300 lb. (136'05 kilos.) were used, the data furnished by the chronoscope are given
in Table XII. (p. 117).
116
CAPTAIN NOBLE AND MB. E. A. ABEL ON EIEED GUNPOWDER.
cr*
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01 CO
CAPTAIN NOBLE AND MR. E. A. ABEL ON EIRED GUNPOWDER.
117
Table XII. — Giving data obtained with chronoscope for calculating the velocity and
pressure in the bore of a 10-inch 18-ton gun. Charge 60 lb. (27*2 kilos.) E. L. G.
Weight of projectile 300 lb. (136*05 kilos.).
Distance from base of
shot.
Time observed
at plugs.
Total time from
seat of shot.
Time taken by
shot to traverse
distance between
plugs.
Mean velocity over spaces
between plugs.
feet.
0-00
0-06
0-26
0- 46
0-66
0-86
1- 06
1-46
1-86
metres.
0-000
0-018
0-079
0-140
0-201
0-262
0-323
0-445
0-567
seconds.
•000000
•000596
•001007
•001323
•001601
•001856
•002325
■002755
seconds.
•000000
•000767
•001363
•001774
•002090
•002368
•002623
•003092
•003522
seconds.
•000767
•000596
•000411
•000316
•000278
•000255
•000469
•000430
feet per
second.
78-2
336
488
633
719
781
855
935
metres per
second.
23-8
102-4
148-7
192-9
219-1
238-0
260-6
285-0
From these data, in the same manner as in the case of pebble powder, are calculated
the velocities and pressures exhibited in Table XIII. (p. 118).
The velocity and pressure obtained with the E. L. G. powder are graphically repre-
sented by the dotted curves in Plate 19 ; and by comparing these with the similar curves
furnished by pebble powder, the advantages obtained by the use of the slow-burning
pebble powder are clearly seen.
Thus it will be observed that the muzzle-velocity obtained with the pebble powder
is 1530 feet (466*3 metres), while the maximum pressure in the bore is 18 tons per
square inch (2745 atmospheres). The velocity given by the E. L. G. powder is, on the
other hand, only 1480 feet (451*1 metres), while the maximum pressure is 22*07 tons
per square inch (3360 atmospheres).
If, as in the case of pebble powder, we express for the first instants of motion the
relation between s and t by an equation of the form of that given in (9), we obtain
$ 57837f42802- ■°2336<+‘ ooirnof2 (i4)«
and the values of s, v, T corresponding to those of t are given in the scheme shown in
Table XIV.
* In this equation and Table XIY. the unit of time is, for convenience, the one ten-thousandth part of a
second.
120
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIRED GUNPOWDER.
The results of Table XIV., in comparison with those of the other mode of calcula-
tion (Table XIII.), are graphically compared in Plate 21. It will be observed that, as
in the case of pebble powder, the two methods give values closely accordant ; and if
Plate 21 be compared with Plate 20, the differences in velocity and pressure at the
commencement of motion between the two natures of powder are very strikingly shown.
Thus it will be observed that with pebble powder the maximum pressure, 2745 atmo-
spheres, is reached when the projectile has moved -5 foot (T52 metre), and at about
•00437 second after the commencement of motion. With R. L. G. powder the
maximum pressure, 3365 atmospheres, is reached when the projectile has moved only
*05 foot ('015 metre), and at about ’00070 second from the commencement of motion.
The first foot of motion is, with the one powder, traversed in about ’0025 second, with
the other in about 'OOfil second.
The pressure given by the crusher-gauges in the experiments with R. L. G. under
discussion (and these pressures should be compared both with those given in Table XIII.
and with the crusher-gauge pressures furnished at the same points by pebble powder)
were, at A, B, C, 1, and 4 respectively, 44-2, 30-3, 22-5, 13‘5, 12 tons per square inch,
or, in atmospheres, 6731, 4614, 3426, 2056, and 1827.
In deducing the pressure from the velocity, we of course assumed that the gaseous
products of combustion acted on the projectile in the manner in which gases are
generally assumed to act.
With the slower-burning powders this hypothesis appears to be not far from the
truth ; but with the more explosive powders the crusher-gauges show that the powder
acts on the shot, as we have already observed, by a succession of impulses ; and in this
case the curve of pressures derived from the chronoscopic observations must be taken to
represent the mean pressures acting on the projectile throughout the bore.
With the various powders experimented on by the Committee on Explosives, there
have of course been very great variations in the pressures indicated.
The highest mean pressure indicated by the chronoscope was 30-6 tons, 4660 atmo-
spheres ; and this pressure was attained with a charge of 60 lb. R. L. G., and a projectile
weighing 400 lb. In the same series, the highest local or wave-pressure exhibited by
the crusher-gauges was 57-8 tons, 8802 atmospheres; but this excessive pressure was
exhibited only in the crusher marked A in Plate 18. fig. 3, and was probably confined
to that particular point. The pressures exhibited by the same powder in the same
round, at the points B and C in the powder-chamber, were respectively 37 tons, 5634
atmospheres, and 29-6 tons, 4507 atmospheres.
But although, in the various guns and with the various charges and special powders
experimented with, the pressures at different points of the bore exhibit, as might be
expected, marked differences, these differences almost altogether disappeared when
powders of normal types and uniform make were experimented with, and Avhen the
pressure was referred, not to fixed positions in the bore of the gun, but to the density
of the products of combustion.
CAPTAIN NOBLE AND MR. E. A. ABEL ON EIRED GUNPOWDER.
121
We have already referred to the experiments made with cylinders gradually in-
creasing in weight in the 10-inch gun. A similar series was made in the 11-inch gun
with charges of powder of 85 lb. (38*56 kilos.); and as the series in both guns were
made with great care and under as nearly as possible the same conditions, we selected,
in the first instance, the experiments with pebble powder, in these guns to test the
accordance or otherwise of the tensions, under the varied conditions of experiment, when
taken simply as functions of the density.
The results of these calculations are graphically represented in curves 1 and 2,
Plate 22 ; and it will be observed that with these different calibres and charges the
tensions developed are as nearly as possible identical.
Curves 3 and 4 on the same Plate exhibit the results of similar calculations for 60 lb.
R. L. G. fired in the 10-inch gun, and 30 lb. R. L. G. fired in the 8-inch gun. In this
case also, although there are differences between the curves representing the pebble and
R. L. G. powders, to which we shall allude further on, the accordance between the same
description of powder fired from the different guns is almost perfect.
S. EEFECT OE INCREMENTS IN THE WEIGHT OE THE SHOT ON THE COMBUSTION AND
TENSION OE POWDER IN THE BORE OF A GUN.
In our preliminary sketch of the labours of previous investigators, we alluded to the
views held by Robins and Rumford upon the rapidity of combustion within the bore.
The latter, relying chiefly upon the fact that powder, especially when in very large
grains, was frequently blown unburned from the muzzle, concluded that the combustion
was very slow. Robins, on the other hand, considered that, with the powder he employed,
combus’tion was practically completed before the shot was materially displaced ; and
it is not easy to see why the unanswerable (if correct) and easily verified fact of which
he makes use has received so little attention from artillerists.
Robins, it will be remembered, argues that if, as some assert, a considerable time is
consumed in the combustion of the charge, a much greater effect would be realized from
the powder where heavier projectiles were used, but that such is not the case.
The Committee on Explosives have completely verified the correctness of Robins’s
views.
In the 10-inch gun, with a charge of 60 lb. (27*2 kilos.) R. L. G. powder, the work
realized from the powder is only increased by about 5 per cent, when the weight of
shot is doubled.
In the slower-burning pebble powder, with a charge of 70 lb. (31*75 kilos.), with a
similar increase in the shot, the greater effect realized was about 8^ per cent. ; but
when the weight was again doubled (that is, increased to four times the original weight),
the additional effect was barely 1 per cent.
Piobert’s views, moreover, that the pressure exercises but a trifling influence upon
the rate of combustion, appears to us entirely untenable. With a particular sample of
service pebble powder, we found the time required for burning a single pebble in the
MDCCCLXXV. R
120
CAPTAIN NOBLE AND MR. F. A. ABEL ON FIRED GUNPOWDER.
The results of Table XIV., in comparison with those of the other mode of calcula-
tion (Table XIII.), are graphically compared in Plate 21. It will be observed that, as
in the case of pebble powder, the two methods give values closely accordant ; and if
Plate 21 be compared with Plate 20, the differences in velocity and pressure at the
commencement of motion between the two natures of powder are very strikingly shown.
Thus it will be observed that with pebble powder the maximum pressure, 2745 atmo-
spheres, is reached when the projectile has moved ’5 foot (T52 metre), and at about
•00437 second after the commencement of motion. With R. L. G. powder the
maximum pressure, 3365 atmospheres, is reached when the projectile has moved only
•05 foot (*015 metre), and at about -00070 second from the commencement of motion.
The first foot of motion is, with the one powder, traversed in about '0025 second, with
the other in about '0051 second.
The pressure given by the crusher-gauges in the experiments with It. L. G. under
discussion (and these pressures should be compared both with those given in Table XIII.
and with the crusher-gauge pressures furnished at the same points by pebble powder)
were, at A, B, C, 1, and 4 respectively, 44-2, 30-3, 22-5, 13-5, 12 tons per square inch,
or, in atmospheres, 6731, 4614, 3426, 2056, and 1827.
In deducing the pressure from the velocity, we of course assumed that the gaseous
products of combustion acted on the projectile in the manner in which gases are
generally assumed to act.
With the slower-burning powders this hypothesis appears to be not far from the
truth ; but with the more explosive powders the crusher-gauges show that the powder
acts on the shot, as we have already observed, by a succession of impulses ; and in this
case the curve of pressures derived from the chronoscopic observations must be taken to
represent the mean pressures acting on the projectile throughout the bore.
With the various powders experimented on by the Committee on Explosives, there
have of course been very great variations in the pressures indicated.
The highest mean pressure indicated by the chronoscope was 3(16 tons, 4660 atmo-
spheres ; and this pressure was attained with a charge of 60 lb. II. L. G., and a projectile
weighing 400 lb. In the same series, the highest local or wave-pressure exhibited by
the crusher-gauges was 57*8 tons, 8802 atmospheres ; but this excessive pressure was
exhibited only in the crusher marked A in Plate 18. fig. 3, and was probably confined
to that particular point. The pressures exhibited by the same powder in the same
round, at the points B and C in the powder-chamber, were respectively 37 tons, 5634
atmospheres, and 29-6 tons, 4507 atmospheres.
But although, in the various guns and with the various charges and special powders
experimented with, the pressures at different points of the bore exhibit, as might be
expected, marked differences, these differences almost altogether disappeared when
powders of normal types and uniform make were experimented with, and when the
pressure was referred, not to fixed positions in the bore of the gun, but to the density
of the products of combustion.
CAPTAIN NOBLE AND MR. F. A. ABEL ON FIRED GUNPOWDER.
121
We have already referred to the experiments made with cylinders gradually in-
creasing in weight in the 10-inch gun. A similar series was made in the 11-inch gun
with charges of powder of 85 lb. (38 -56 kilos.); and as the series in both guns were
made with great care and under as nearly as possible the same conditions, we selected,
in the first instance, the experiments with pebble powder, in these guns to test the
accordance or otherwise of the tensions, under the varied conditions of experiment, when
taken simply as functions of the density.
The results of these calculations are graphically represented in curves 1 and 2,
Plate 22 ; and it will be observed that with these different calibres and charges the
tensions developed are as nearly as possible identical.
Curves 3 and 4 on the same Plate exhibit the results of similar calculations for 60 lb.
R. L. G. fired in the 10-inch gun, and 30 lb. It. L. G. fired in the 8-inch gun. In this
case also, although there are differences between the curves representing the pebble and
It. L. G. powders, to which we shall allude further on, the accordance between the same
description of powder fired from the different guns is almost perfect.
S. EFFECT OF INCREMENTS IN THE WEIGHT OF THE SHOT ON THE COMBUSTION AND
TENSION OF POWDER IN THE BORE OF A GUN.
In our preliminary sketch of the labours of previous investigators, we alluded to the
views held by Robins and Rumford upon the rapidity of combustion within the bore.
The latter, relying chiefly upon the fact that powder, especially when in very large
grains, was frequently blown unburned from the muzzle, concluded that the combustion
was very slow. Robins, on the other hand, considered that, with the powder he employed,
combus’tion was practically completed before the shot was materially displaced ; and
it is not easy to see why the unanswerable (if correct) and easily verified fact of which
he makes use has received so little attention from artillerists.
Robins, it will be remembered, argues that if, as some assert, a considerable time is
consumed in the combustion of the charge, a much greater effect would be realized from
the powder where heavier projectiles were used, but that such is not the case.
The Committee on Explosives have completely verified the correctness of Robins’s
views.
In the 10-inch gun, with a charge of 60 lb. (27-2 kilos.) R. L. G. powder, the work
realized from the powder is only increased by about 5 per cent, when the weight of
shot is doubled.
In the slower-burning pebble powder, with a charge of 70 lb. (31-75 kilos.), with a
similar increase in the shot, the greater effect realized was about 8-| per cent. ; but
when the weight was again doubled (that is, increased to four times the original weight),
the additional effect was barely 1 per cent.
Piobert’s views, moreover, that the pressure exercises but a trifling influence upon
the rate of combustion, appears to us entirely untenable. With a particular sample of
service pebble powder, we found the time required for burning a single pebble in the
MDCCCLXXV. r
122 CAPTAIN NOBLE AND MR. E. A. ABEL ON EIRED GUNPOWDER.
open air to be about 2 seconds. The same sample was entirely consumed in the bore
of a 10-inch gun, and must therefore have been burned, in less than '009 second.
T. EEPECT OP MOISTURE UPON THE COMBUSTION AND TENSION OF POWDER.
It is perhaps unnecessary to say that we do not share the views of those who
consider that the presence of water in powder may increase the tension of the products
of explosion. We have made no experiments upon this head in closed vessels ; but the
following Table exhibits the effect of moisture in gunpowder upon the velocity of the
projectile and the tension of the gas when the powder is fired in a gun, the proportions
of moisture varying from 0-7 to T55 per cent. The powder from which these results
were obtained, was pebble, carefully prepared by Colonel Younghusband, and was the
same in all respects, except as regards the quantity of moisture.
Table XV. — Showing the effect of moisture in the powder upon the velocity of the
projectile and pressure of the gas.
Percentage
of
moisture.
Velocity.
Maximum Pressures.
feet.
metres.
tons per
square inch.
atmospheres.
070
1545
470*92
22-02
3353
075
1541
774-50
21-70
3304
0-80
1537
468-47
21-38
3256
0‘85
1533 5
467-41
21-07
3208
0-90
1530
466-34
20-77
3163
0-95
1526 5
465-30
20-47
3117
1-00
1523-5
464-40
20-18
3073
1-05
1520 5
463 44
19-90
3030
1-10
15175
462 53
19-63
2989
1*15
15145
461-61
19-37
2949
1-20
1512
460-85
19-12
2911
1-25
1509-5
460-10
18-87
2873
1-30
1507
459-33
18-63
2837
1-35
1504-5
458-60
18-40
2802
1-40
1502
457-80
18-18
2768
1-45
1499-5
457-04
17*97
2736
1-50
1497-5
456-43
1776
2704
1-55
1495-5
455-82
17-55
2672
From this Table it will be seen that by the addition of considerably less than 1 per
cent, of moisture, the muzzle-velocity is reduced by about 60 feet, and the maximum
pressure by about 20 per cent., pointing obviously to a much more rapid combustion
in the case of the drier powder.
U. LOSS OF HEAT BY COMMUNICATION TO THE ENVELOPE IN WHICH THE CHARGE
IS EXPLODED.
We have now given a hasty sketch of the means that have been adopted to determine
the pressures actually existing in the bores of guns, and of the general results we have
CAPTAIN NOBLE AND MR. E. A. ABEL ON FIRED GUNPOWDER,
123
arrived at ; and before proceeding to the theoreticalc onsideration of the relation which
should then exist between the tension and the density of the gases, we must direct
attention to an important point — and that is, “ what loss of heat do the gases suffer 1 or,
in other words, what proportion of energy in the powder is wasted by communication
to the envelope in which the powder is fired, that is, to the barrel of the gunl”
Every one is aware that if a common rifled musket be very rapidly fired, as may
easily now be done by the use of breech-loading arms, the barrel becomes so hot that
it cannot be touched with the naked hand with impunity, and, even with a field-gun,
the increment of heat due to a few rounds is very considerable.
As far as we know, the Count de Saint-Robert* made the first attempt to deter-
mine the amount of heat actually communicated to a small arm.
De Saint-Robert made three series of experiments with service rifled muskets, firing
the ordinary charge of 4-5 grms. In the first series the muskets were loaded in the
usual manner, in the second series the ball was placed near the muzzle, in the third
the muskets were loaded with powder alone. The results at which De Saint-Robert
arrived, and which are not difficult to explain, were, that the greatest quantity of heat
was communicated to the musket when the ball wras placed near the muzzle, that the
quantity communicated, when no projectile at all was used, stood next in order, and
that least heat was communicated when the musket was loaded in the usual manner.
He further found that the quantity of heat communicated in this last case, with the
powder and arm used, was about 250 gramme-units per gramme of powder fired.
We found ourselves unable, however, to adopt Count de Saint-Robert’s important
results for the guns and charges we have been considering, because conclusions derived
from small arms could hardly be applied to large ordnance without modification.
We therefore instituted the experiments described under Nos. 72 and 73. The gun,
used was a 12-pr. B. L., and in the first experiment (No. 72) nine rounds were fired
with If lb. (794 grms.) and a projectile weighing nearly 12 lb. (5330 grms.).
Prior to the rounds being fired, arrangements were made for placing the gun, when-
ever the series should be concluded, in a vessel containing a given weight of water ; and
before the experiment was commenced the gun and water were brought to the same
temperature, and that temperature carefully determined.
After the firing the gun was placed in the water, and the rise of temperature due
to the nine rounds determined. This rise was found to be equivalent to 236,834 grms.
of water raised through 2°‘305 C., or the heat communicated to the gun by the com-
bustion of 1 gramme of the charge was equal to 76 ‘4 gramme-units.
Of course an addition has to be made to this number on account both of some loss of
heat in the determination and of the unavoidable loss of heat between the rounds.
The second experiment (No. 73) was made with 5 rounds of 1^- lb. (680-4 grms.) of
the same powder with the same weight of projectile. The heat communicated to the
gun by the five rounds was, when expressed in water, sufficient to raise 112,867 grms.
* Traite de Thermodynamique (Turin, 1865), p 120.
R 2
124
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GUNPOWDER.
through 20-694 C., or 1 gramme of the charge, in burning, communicated to the gun
89-4 gramme-units of heat.
Considering the difficulty, in an experiment of this nature, of avoiding a considerable
loss from radiation, conduction, and other causes, we do not think we shall be far wrong
in assuming that in the case of the 12 pr.-B. L. gun, fired under the conditions named,
the heat communicated to the gun is about 100 gramme-units for each gramme of powder
exploded.
To arrive at the amount of heat communicated to the gun wThen still larger guns are
employed, there are two principal points to be considered — 1st, the ratio which the
amount of the surface bears to the weight of the charge exploded ; and 2nd, the time
during which the cooling effect of the bore operates upon the products of explosion.
The first of these data is of course exactly known, and from our experiments the
second is also known with very considerable exactness. Computing, therefore, from
the data given by the 12-pr., the loss of heat suffered by the gases in the 10-inch gun,
we find that loss to be represented by about 25 gramme-units ; and hence we find that the
quantity of work in the form of heat communicated to the gun varies approximately from
250 gramme-units per gramme of powder in the case of a rifled musket, to 25 gramme-
units in the case of a 10-inch gun.
Similar considerations lead us to the conclusion that in a close vessel such as we
employed for explosion, when filled with powder , the loss of pressure due to the com-
munication of heat to the envelope would not amount to 1 per cent, of the total pressure
developed.
Y. PRESSURE IN THE BORES OF GUNS, DERIYED FROM THEORETICAL CONSIDERATIONS.
We now pass to the theoretical consideration of the question. Suppose the powder
to be fired, as is the case in the chamber of a gun, and suppose, further, that the products
of combustion are allowed to expand, what will be the relation between the tension of
the gases and the volume they occupy throughout the bore \
For the sake of simplicity, we shall, in the first instance, assume that the gravimetric
density of the powder is unity, that the powder fills completely the space in which it
is placed, that the whole charge is exploded before the projectile is sensibly moved
from its initial position, and that the expansion takes place in a vessel impervious to heat.
In our preliminary sketch we alluded to the results of Hutton’s investigations as to
the relations existing between the density and tension of the gases and the velocity of
the projectile at any point of the bore. Hutton, however, assumed that the tension of
the inflamed gases was directly proportional to their density, and inversely as the space
occupied by them. In other words, he supposed that the expansion of the gases, while
doing work both on the projectile and on the products themselves, was effected without
loss of heat.
Eecent research, which has demonstrated that no work can be effected by the expan-
sion of gases without a corresponding expenditure of heat, has enabled modern artillerists
CAPTAIN NOBLE AND MR. F. A. ABEL ON FIRED GUNPOWDER.
125
to correct Hutton’s assumption ; and the question of the pressure exercised and work
performed by gunpowder in the bore of a gun has been examined both by Bunsen and
Schischkoff, and by the Count de Saint-Robert *.
De Saint-Robert, like Hutton, supposed that the whole of the products of explosion
were, on ignition, in a gaseous state, and that hence the relation between the pressure
and the volume of the products followed from the well-known law connecting the tension
and volume of permanent gases.
Bunsen and Schischkoff, on the other hand, who, like ourselves, have arrived at the
conclusion that at the moment of explosion a large part of the products is not in the
gaseous state, have deduced the total work which gunpowder is capable of performing,
on the assumption that the work on the projectile is effected by the expansion of the
permanent gases alone, without addition or subtraction of heat, and that, in fact, the
non-gaseous products play no part in the expansion.
Sufficient data were not at the command of either of the authorities we have named
to enable them adequately to test their theories ; and we propose in the first place, with
the data at our disposal, to compare their hypotheses with actual facts, by computing
the tensions for different volumes and comparing the calculated results both with the
tensions in a close vessel and with those derived from actual experiments in the bores
of guns.
Assuming, in the first place, with De Saint-Robert, that the whole of the products
are in the gaseous form, —
Let^? be the value of the elastic pressure of the permanent gases generated by the
combustion of the powder corresponding to any volume v, and letp0, v0 be the known
initial values of and v. Let also Cp be the specific heat of these gases at constant
pressure, and C„ be the specific heat at constant volume. Then, from the well-known
relation existing between ]) and v, where a permanent gas is permitted to expand in a
vessel impervious to heat, we have
and this equation, upon De Saint-Robert’s hypothesis, expresses the relation between
the tension of the gases and the volume occupied by them in the bore of a gun.
Taking^ from Table VIII. at 41 ‘477 tons per square inch, and assuming at unity
the space v0 occupied by the charge when at a gravimetric density of 1, taking, further,
0
the value of 0£=1,41 as computed by De Saint-Robert, equation (15) becomes
^ = 41-477 Q1'41 (16)
If we now take Bunsen and Schischkoff’s view, that a portion only of the products
is in the form of permanent gases, and that they expand without addition or subtraction
* Traite de Thermodynamique, p. 154.
126 CAPTAIN NOBLE AND ME. E. A. ABEL ON FIEED GUNPOWDER.
of heat, we are able, from equation (15), to deduce the law connecting the tension and
the pressure. For if we call v' and v'0 the volume at any instant and the initial volume
of the permanent gases, we have from (15)
P=l>o(^) Cv> (17)
but if a he the ratio which the volume of the non-gaseous products at the moment
of explosion bears to that of the unexploded powder, we have
v'0=v0(l — cc), v'=v—ctv0, (18)
and equation (17) becomes
and this is the relation between and v on Bunsen and Schischkoff’s hypothesis.
Taking, as before, j90=4T477, w0=l, and remembering that we have found the value
of a to be '6, we have
J»=«-477(^)^ (20)
Q
The value of the exponent ^ can be deduced from the data given in Table XYI.
Table XYI. — Showing the percentage weights, specific heats at constant volume, and
the specific heats at constant pressure of the permanent gases produced by the
explosion of powder.
Nature of gas.
Percentage weight
of gas.
Specific heat at
constant pressure.
Specific heat at
constant volume.
Sulphuretted hydrogen
•0262
•2432
•1840
Carbonic oxide
•1036
•2450
•1736
Carbonic anhydride
•6089
•2169 .
•1720
Marsh-gas
•0012
•5929
•4680
Hydrogen
•0023
3-4090
2*4110
Nitrogen
•2579
•2438
•1727
From the data in this Table the value of Cp is found to be=,23528, of C0=T782,
and that of the fraction ^=T3203; and equation (20) becomes
(•A \ 1-3203
^=i) (21)
The results of (16) and (21) are given in Table XVII. ; and in the same Table are
given the values of j?, both as deduced from actual experiment in the bore of the 10-inch
and 11-inch guns (see Plate 22), and also as deduced from our experiments in a close
vessel. The results of the experiments upon the tension of different densities in a close
vessel represent of course the elastic force which would exist were the gas allowed to
expand in a vessel impervious to heat, without production of work.
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GUNPOWDEE.
127
Table XVII. — Showing in terms of the density (1) the tension actually found to exist
in the bores of guns, (2) the tension which would exist were the gases suffered to
expand without production of work, (3) the tension calculated upon De Saint-
Robert’s hypothesis, (4) the tension calculated on Bunsen and Schischkoff’s
hypothesis.
Mean, density
of products of
combustion.
Tension observed in
bore of 18-ton gun
(pebble powder).
Tension observed
where the gases
expand without
production of work.
Tension calculated
upon
Count De St.-Robert’s
hypothesis.
Tension calculated
upon Bunsen and
Schischkoff’s
hypothesis.
Tons per
sq. inch.
Atmo-
spheres.
Tons per
sq. inch.
Atmo-
spheres.
Tons per
sq. inch.
Atmo-
spheres.
Tons per
sq. inch.
Atmo-
spheres.
1-00
41-48
6320
41-48
6320
41-48
6320
•90
20-35
3101
32*46
4946
35*75
5448
30-00
4572
•80
17-01
2590
25-52
3889
30-14
4593
21-85
3330
•70
14-03
2133
20-02
3051
25-08
3822
15-85
2416
•60
11-33
1722
15-55
2370
20-18
3076
11-62
1771
•50
8-87
1352
11-85
1806
15-61
2378
7-93
1209
•40
6-65
1019
8-73
1330
11-40
1736
5-30
808
•30
4-67
722
6-07
925
7-60
1157
3-28
500
•20
2-93
459
3-77
574
4-29
653
1-75
267
•10
1-77
270
1-61
246
•64
98
The graphical representation of this Table is given in Plate 23 ; and by examination
either of the Table or of the Curves, it is obvious that neither formula (16) nor (21)
gives results which can be taken as at all representing the truth. The values of the
elastic force, calculated on the assumption that the whole of the products of combustion
are in the gaseous state, and that the effect on the projectile is produced by such expan-
sion, are largely in excess of the pressures observed in the gun, and very greatly in
excess even of the pressures observed when the gases were expanded without production
of work. On the other hand, the pressures calculated on the assumption that the work
is caused by the expansion of the permanent gases alone , without addition or subtraction
of heat, are considerably in defect of those actually observed, and this too, although, no
allowance is made for the absorption of heat by the gun.
At an early stage in our researches, when we found, contrary to our expectation, that
the elastic pressures deduced from experiments in close vessels did not differ greatly
(where the powder might be considered entirely consumed, or nearly so) from those
deduced from experiments in the bores of guns themselves, we came to the conclusion
that this departure from our expectation was probably due to the heat stored up in the
liquid residue. In fact, instead of the expansion of the permanent gases taking place
without addition of heat, the residue, in the finely divided state in which it must be on
the ignition of the charge, may be considered a source of heat of the most perfect
character, and available for compensating the cooling effect due to the expansion of the
gases on production of work.
The question, then, that we now have to consider is — What will be the conditions
of expansion of the permanent gases when dilating in the bore of a gun and drawing
128
CAPTAIN NOBLE AND MR. E. A. ABEL ON EIRED GUNPOWDER.
heat, during their expansion, from the non-gaseous portions in a very finely divided
state ?
To solve this question we must have recourse to certain well-known principles of
thermodynamics.
Let <7H be the quantity of heat added to, or drawn from, the non-gaseous portion of
the charge by the permanent gases, while the latter pass from the volume v' and tempe-
rature t to the volume v'-\- dd and temperature we then have*
dH=t . d<p, (22)
<p being Rankine’s thermodynamic function.
But if X be the specific heat of the non-gaseous portion of the charge, and if /3 be the
ratio between the weights of the gaseous and non-gaseous portions of the charge, and if
we assume further, as we can do without material error, that X is constant, we shall have
dH=-f3xdt; (23)
.-.d<p=-t&j, (24)
and by integration
<P— <P.=log (25)
But the value of <p—(p0 for permanent gases is well known, being readily deduced from
the general expression for the thermodynamic function.
This expression being f
?=Clog.i+lJ|.*' (26)
(J being Joule's equivalent), and ^ being readily obtained from the equation of elasti-
city and dilatability of perfect gases,
_pv'=Ut,
we deduce from (26), by integration,
?-?0=log.({)C'. (£)'
since J j=Cp—Cv.
Hence, equating (25) and (27),
* Rankine, ‘ Steam-Engine,’ p. 310. De Saint-Robeet, loe. tit. p. 68.
t Raneine, loc. tit. p. 311. De Saint-Robert, loc. tit. p. 72.
J Raekine, loc. tit. p. 318. Claesitjs, loc. tit. p. 39. De Saint-Robert, loc. tit. p. 93.
CAPTAIN NOBLE AND MR. F. A. ABEL ON FIRED GUNPOWDER.
129
Therefore
and
Lp~Lu
1_(V0\CV+PK
t0 VJ ’
Cp+fi A.
»o \W
or, since v'0=v0(l — a), v'=v — ctv0,
P.
Po
Cp+j3A
C„+/3,V
(28)
(29)
(30)
and equation (30) gives the true relation connecting^ and v when the gaseous products
expand in the bore of a gun with production of work.
The values of the constants in this equation we have already determined ; they are
as follow :—C„= -1782, Cp= -2353, ^=41-477, X=-4090, /3=1-3148.
The results of equation (30) are given in Table XVIII.; and, as before, for comparison
we give similar values of p both as derived from experiments with heavy ordnance and
on the supposition of expansion without performance of work.
Table XVIII.— Giving, in terms of the density, the tensions actually found to exist in
the bores of guns with pebble and E. L. G. powders ; giving, further, (1) the tensions
calculated from equation (30), (2) the tensions which would exist were the gases
suffered to expand without production of work.
Mean density
of products of
combustion.
Tension observed
in bores of guns.
Pebble powder.
Tension observed
in bores of guns.
B. L. Gr. powder.
Tension calculated
from formula (30).
Tension observed
when the gases
expand without
production of work.
Tons per
sq. inch.
Atmo-
spheres.
Tons per
sq. inch.
Atmo-
spheres.
Tons per
sq. inch.
Atmo-
spheres.
Tons per
sq. inch.
Atmo-
spheres.
1-00
41-48
6316
41-48
6316
•95
36-30
5528
36-65
5581
•90
20*35
3099
27-33
4162
31-84
4848
32-46
4943
•85
18-63
2837
24-63
3751
27*95
4256
28-78
4383
•80
17-01
2590
22-01
3352
24-56
3740
25-53
3888
•75
15-48
2357
19-50
2969
21-56
3283
22-63
3446
•70
14-03
2136
17*16
2613
18-89
2877
•20-02
3049
•65
12-65
1926
15-05
2292
16-51
2514
17-68
2692
•60
11-33
1725
13-21
2011
14-38
2190
15-55
2368
•55
10-07
1533
11-61
1768
12-46
1897
13-62
2074
•50
8-87
1351
10-18
1550
10-72
1632
11-85
1804
•45
7-73 ,|
1177
8-87
1351
9-15
1393
10-23
1558 I
•40
6-65
1013
7-65
1165
7-71
1174
8-73
1329
•35
5-63
857
6-49
988
6-40
975
7-35
1119
•30
4-67
711
5-39
821
5-21
793
6-07
924
•25
3-77
574
4-34
661
4-11
626
4-88
743
•20
2-93
446
3-33
507
3-11
474
3-77
574
•15
2-15
327
2-35
358
2-20
335
2-73
416
•10
1-37
209
1-76
268
s
MDCCCLXXV.
130
CAPTAIN NOBLE AND MB. E. A. ABEL ON EIEED GTJNPOWDEB.
The results of Table XVIII. are graphically represented in Plate 24 ; and on the
axis of abscissae are figured, for convenience, both the density of the products and the
volume they occupy.
The curve marked A represents the tensions deduced (with a slight correction for loss
of heat) from actual observation in a close vessel, and may, as we have already said, be
taken to represent the pressures that would exist were the products of combustion
allowed to expand in a vessel impervious to heat and without production of work.
The curve marked B, derived from equation (30), denotes the tensions that would exist
in the bore of a gun, if we suppose the powder, of a gravimetric density =1 and filling
entirely the chamber, to be completely consumed before the projectile is moved from
its place, and to expand in a gun impervious to heat. By comparison with the Curve A
will be seen the difference in tension arising from the loss of heat due to the work
expended. The great importance of the heat contained in the non-gaseous portion
of the charge is rendered apparent by comparison of Curve B with Curve 4, Plate 23,
or Table XVII., where, on Bunsen- and Schischkoff’s hypothesis, the permanent gases
are supposed to expand without deriving any heat from the non-gaseous portion of the
charge.
The area comprised between Curve B and the axis of abscissae represents the maxi-
mum work that it is possible to obtain from powder.
Curve C represents the mean results obtained with It. L. G. powder from the 8-inch
and 10-inch guns, and Curve D represents the mean results obtained with pebble powder
from the 10-inch and 11-inch guns.
It is interesting to study the differences exhibited by these curves B, C, and D. The
Curve C, representing the pressures obtained with It. L. G., denotes tensions not far
removed from the theoretic curve, while the densities are still very high ; before the
volume is much increased, the two curves slide into one another and become almost
coincident.
The Curve D, on the other hand, is at first very considerably below both the E. L. G.
and the theoretic curve. It is still considerably lower even when the E. L. G. curve is
practically coincident with the theoretic curve, and it retains a measurable though slight
inferiority of pressure even up to the muzzle of the gun.
These differences are without doubt due to the fact that with the E. L. G. powder,
at least under ordinary circumstances, the whole or a large proportion of the charge
is consumed before the projectile is greatly removed from the seat of the shot. With
the slower-burning pebble powder, on the other hand, a considerable quantity of powder
remains unconsumed until the projectile approaches the muzzle; and the curve indicates
in a very striking way the gradual consumption of the powder, and the portion of the
bore in which the slow-burning powder may be considered practically burned.
It might perhaps be expected that the difference between the theoretic Curve B and
the observed Curves C and D near the muzzle would be greater than is shown, since the
Curve B has been obtained on the supposition that the expansion has taken place in a
vessel impervious to heat.
CAPTAIN NOBLE AND ME. E A. ABEL ON FIEED GUNPOWDER,
131
We have pointed out, however, that although in muskets and small arms the loss of
heat arising from communication to the bore is very considerable, it is comparatively
unimportant in very large guns. In our calculations also we have taken X, the specific
heat of the non-gaseous portion of the charge, at its mean value. It should, however,
be taken at a higher value, since the specific heat must increase rapidly with the
temperature ; and this difference no doubt more than compensates for the loss of heat to
which we have referred as not being taken into account.
Our hypothesis as to a portion of the charge remaining unconsumed until the pro-
jectile approaches the muzzle, is confirmed by the well-known fact that in short guns, or
where powder of high density or very large size is employed, considerable quantities
sometimes escape combustion altogether.
The appearance of pellet or pebble powder which has been ignited and afterwards
extinguished in passing through the atmosphere is well known to artillerists.
The general appearance (and in this appearance there is wonderful uniformity) is
represented in Plate 15. fig. 5, and gives the idea of the combustion having proceeded
from centres of ignition.
If we imagine a grain, or rather (taking into account the size of the grains of
the present day) a pebble, of powder arriving unconsumed at a point a little in advance
of that of maximum pressure, it is not difficult to conceive that such pebble will
traverse the rest of the bore without being entirely consumed, when the great influence
of diminished pressure, combined with the shortness of time due to the increasing
velocity of the projectile, is considered.
Thus by reference to Table X. it will be found that the time taken by the projectile to
describe the firstfoot (’305 metre) of motion is about ‘005 second, while the time taken
to describe the remaining length of the bore, 7'25 feet (2’21 metres), is only about
•Oil second.
The mean powder-pressure over the first foot, again, is about 15 tons per inch
(2300 atmospheres), and over the remainder of the bore is only 5’25 tons (800 atmo-
spheres).
W. TEMPEEATURE OF PRODUCTS OF COMBUSTION IN BORES OF GUNS.
The temperature in the bore of the gun during the expansion of the products is
given by equation (28), or, restoring the values of v' and v'0,
t—
Cp-Cy
\V0{l—Ci))cc+f3.\
M V-XV0 /
(31)
The temperatures calculated from this formula are given in Table XIX. It is hardly
necessary to point out that the values given in this Table are only strictly accurate
when the charge is ignited before the projectile is sensibly moved; but in practice the
correction due to this cause will not be great.
s 2
132
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GUNPOWDEE.
Table XIX. — Giving the temperature, in degrees Centigrade, and in terms of the density,
of the products when expanded, with production of work, in the bore of a gun
supposed impervious to heat.
Mean density
of products of
combustion.
Number of
volumes of
expansion.
Temperature.
Degrees
Centigrade.
Mean density
of products
of combustion.
Number of
volumes of
expansion.
Temperature.
Degrees
Centigrade.
1-00
1-0000
2231°
•50
2 0000
2019
•95
1-0526
2209
•45
2-2222
1996
•90
1-1111
2188
•40
2-5000
1971
•85
1-1765
2167
•35
2-8571
1943
•80
1-2500
2146
•30
3-3333
1914
•75
1-3333
2126
•25
4-0000
1881
•70
1-4286
2105
•20
5 0000
1843
•65
1-5385
2084
•15
6-6667
1796
•60
1-6667
2063
•10
10-0000
1734
•55
1-8182
2041
•05
20-0000
1637
X. WOEK EPPECTED BY GUNPOWDEE.
The theoretic work which a charge of gunpowder is capable of effecting during the
expansion to any volume v is, as we have said, represented by the area between the
curve B, Plate 24, the ordinates corresponding to v and v0, and the axis of abscissae.
In mathematical language it is expressed by the definite integral
j ' . dv. (32)
Replacing in this equation the value of jp derived from equation (30), we have for the
work done by the powder in expanding from v0 to v,
The values of all the constants in this equation have already been given ; but for our
present purpose it is convenient to determine the work which 1 gramme of powder is
capable of performing for different degrees of expansion. Assuming, then, that a
gramme of powdei is of the gravimetric density of unity (that is, that it occupies a
volume of 1 cub. centim.), we have v0=l i and expressing the initial pressures 4T5 tons
(6320 atmospheres) in grammes per square centimetre, we have ^0=6,532,450 grammes
per square centimetre.
We have calculated W from (34) for various values of v up to and inclusive of v=20.
The results are embodied in the following Table, and are expressed both in kilogramme-
metres per kilogramme and foot-tons per lb. of powder.
CAPTAIN NOBLE AND MR. F. A. ABEL ON EIRED GUNPOWDER.
133
Table XX. — Giving the total work that gunpowder is capable of performing in the
bore of a gun, in kilogrammetres per kilogramme and foot-tons per lb. of powder
burned, in terms of the density of the products of explosion.
Total work that the gunpowder
is capable of realizing.
Density of
products of
combustion.
Number of
volumes of
expansion.
Per kilogramme
burned in kilo-
grammetres.
Per lb. burned
in foot-tons.
•95
1-0526
3210-8
4-70
•90
1-1111
6339-6
9-29
•85
11768
9412-8
13-79
•80
1-2500
12443-3
18-23
•75
1-3333
15460-8
22-65
•70
1-4286
18488-1
27-08
*65
1-5385
21544-9
3156
•60
1-6667
24650-8
3611
•55
1-8182
27841-9
40-78
•50
2-0000
31153-7
45-62
•45
2-2222
34614-0
50-70
•40
2-5000
38290-0
56-08
•35
2-8571
42234-7
61-86
•30
3 3333
46565-9
68-21
•25
4 0000
51414-8
75-31
•20
5-0000
57031-7
83-53
•17
5-8824
60952-1
89-35
•16
6-2500
62368-1
91-45
•15
6*6667
63884-4
93-64
•14
7-1429
65470-1
95-94
•13
7-6923
67138-4
98-39
•12
8-3333
68940-1
101-00
•11
9*0909
70855-4
103-82
•10
10-0000
72903-7
106-87
•9
11-1111
75214-5
11018
•8
12-5000
77679 9
113-81
•7
14-2857
80462 1
117-85
•6
16-6667
83582-1
122-42
•5
20-0000
87244-4
127-79
The results embodied in this Table are of very considerable importance. They
enable us to say by simple inspection what is the maximum work that can be obtained
from powder such as is employed by the British Government in any given length of gun.
To make use of the Table, we have only to find the volume occupied by the charge (gravi-
metric density = 1) and the number of times this volume is contained in the bore of the
gun. The maximum work* per kilogramme or pound which the powder is capable of
* It is hardly necessary to point out that the velocity of the projectile at any point of the bore is directly,
deducible from equation (134). For the velocity being connected with the work by the equation
velocity =. . W,
V w
w being the weight of the shot, we have only to take out from equation (34) or Table XX. the value of W for
any given expansion, multiply it by the ‘‘factor of effect ” (see p. 134) for the particular gun, charge, &c., and
use in the above equation the value of W so found.-7
As an illustration, if it be required to determine the velocity at the muzzle of the 10-inch gun under the
134
CAPTAIN NOBLE AND ME. F. A. ABEL ON FIEED GUNPOWDER,
performing during the given expansion is then taken out from the Table ; and this work
being multiplied by the number of kilogrammes or pounds in the charge gives the total
maximum work. Thus, for example, in an 18-ton 10-inch gun, a charge of 70 lb.
(31-75 kilos.) pebble powder is fired, and we wish to know what is the maximum work
that the charge is capable of performing. We readily find that the length of the gun
is such that ^ = 5*867 vols. ; and from the Table we find that 89-4 foot-tons or 61,000 kilo-
grammetres is the maximum work per lb. or per kilog. ; multiplying by the number of
pounds or kilos., we find that 6258 foot-tons or 1,936,750 kilogrammetres is the maxi-
mum work which the whole charge is capable of performing.
As a matter of course, this maximum effect is only approximated to, not attained ;
and for actual use it would be necessary to multiply the work so calculated by a factor
dependent upon the nature of the powder, the mode of firing it, the weight of the shot,
■&c. ; but in service-powders fired under the same circumstances the factor will not
vary much. In the experimental powders used by the Committee on Explosives there
were, it is true, very considerable differences, the work realized in the same gun varying
from 56 foot-tons to 86 foot-tons per lb. of powder ; but with service-powders fired
under like conditions this great difference does not exist.
We have prepared at once, in illustration of the principles we have just laid down,
as a test of the general correctness of our views and as likely to prove of considerable
utility, a Table in which we have calculated, from the data given, first, the total
work realized per lb. of powder burned for every gun, charge, and description of
powder in the English service ; second, the maximum theoretic work per lb. of powder
it would be possible to realize with each gun and charge ; and third, the factor of effect
with each gun and charge — that is, the percentage of the maximum effect actually
realized.
If the factors of effect be examined, it will be observed how, in spite of the use of
slow-burning and therefore uneconomical powders in the large guns, the percentages
realized gradually increase as we pass from the smallest to the largest gun in our Table
— the highest factor being 93 per cent, in the case of the 38-ton gun, the lowest being
50‘5 per cent, in the case of the little Abyssinian gun.
This difference in effect is of course in great measure due to the communication of
heat to the bore of the gun, to which we have so frequently referred.
Y. DETERMINATION OF TOTAL THEORETIC WORK OF POWDER WHEN INDEFINITELY
EXPANDED.
To determine the total work which powder is capable of performing if allowed to
expand indefinitely, the integral in equation (33) must be taken between co and v0. If
circumstances discussed at p. Ill, the total work, as shown in the text, which the charge is capable of effecting,
is 6258 foot-tons; multiplying this by the factor for the gunpowder and weight of shot, we have W=4880
foot-tons; substituting this value of W in the above equation, we obtain i;=1532 feet, or nearly identical with
the observed velocity. — February 1875.
CAPTAIN NOBLE AND ME. E. A. ABEL ON FIEED OUNPOWDEE.
135
Table XXI. — Giving, with the data necessary for calculation, the work per lb. of
powder realized, the total maximum theoretic work, and the factor of effect for
every gun and charge in the British Service.
Nature of gun.
Bore.
Charge.
Projectile.
Gas.
Energy of powder.
Dia-
meter.
Length.
Nature.
Weight.
Weight.
Velocity.
Total
volumes
in bore.
Final
density.
Total.
Realized
per lb. of
powder.
Calcu-
lated
maxi-
mum.
Per-
centage
realized.
inches.
calibres.
lb.
oz.
lb.
ft. per sec.
foot-tons.
foot-tons.
foot-tons.
3S t ons
12
16-5
P.
110
0
700
1430
7-342
•1362
9932
903
970
931
35 tons
12
135
P.
110
0
700
1300
6-007
•1665
8209
74 6
90-2
82-7
25 tons
12
120
P.
85
0
600
1300
6-910
•1447
7036
82-8
94-9
87-3
P.
85
0
495
1358
6-910
•1447
6334
74-5
94-9
78-6
P.
55
0
495
1142
10679
•0936
4479
81-4
108-9
74-8
R. L. G.
67
0
600
1180
8-765
•1141
5797
86-4
102-8
841
R. L. G.
67
0
495
1271
8-765
•1141
5549
82 8
102-8
80-6
R. L. G.
50
0
495
1140
11-750
•0851
4464
89-3
111-8
800
25 tons
11
132
P.
85
0
535
1315
5-585
•1708
6419
75-5
89-2
84-7
P.
85
0
535
1315
5-855
•1700
6419
75-5
892
84-7
R, L. G.
70
0
535
1217
7-109
•1407
5498
78-6
95-8
82 1
R. L. G.
70
0
535
1217
7-109
•1407
5498
78-6
95 8
82-1
18 tons
10
14-5
P.
70
0
400
1364
5-867
1704
5164
73-8
89-4
82-6
P.
70
0
400
1340
5-867
•1704
4984
71-2
89-4
79-7
P.
44
0
400
1125
9-334
1071
3513
79-8
104-7
76-3
R. L. G.
60
0
400
1298
6-844
•1461
4676
77-9
94 5
82-4
R. L. G.
40
0
400
1117
10-269
■0974
3463
86-6
107 9
80-3
I2J tons
9
13-9
P.
50
0
250
1420
5-742
•1742
3498
70-0
88-6
79-1
P.
50
0
250
1420
5-742
•1742
3498
70-0
88 6
791
R. L. G.
43
0
250
1336
6683
■1496
3096
72-0
93-6
77-1
R. L. G.
43
0
250
1336
6-683
•1496
3096
72-0
93-6
77-1
R. L. G.
30
0
250
1192
9-566
1045
2465
82-2
105-2
78-2
9 tons
8
14-8
P.
35
0
180
1413
6-136
. -1630
2493
71-3
90-9
78-4
P.
35
0
180
1413
6-136
•1630
2493
71-3
90-9 .
78-4
R. L. G.
30
0
180
1330
7-154
•1398
2209
73-7
96-0
76'8
R. L. G.
30
0
180
1330
7154
•1398
2209
73-7
96-0
76-8
R. L. G.
20
0
180
1163
10-724
•0932
1689
84-5
109-1
77-6
1 7 tons
7
18-0
P.
30
0
115
1561
5-827
1716
1945
64-8
89-0
72-9
P.
30
0
115
1561
5-827
•1716
1945
64-8
890
72-9
R. L. G.
22
0
115
1458
7-948
1258
1696
77-1
99-4
77 -6
R. L. G.
22
0
115
1458
7-948
■1258
1696
711
94-4
77-6
R. L. G.
14
0
115
1258
12-495
■0800
1263
90-2
113-3
75-7
[ 6} tons
7
15-9
P.
30
0
115
1525
5-148
•1943
1856
61-9
84-6
732
P.
30
0
115
1525
5-148
1943
1856
61-9
84-6
73-2
R. L. G.
22
0
115
1430
7021
•1424
1632
74-2
95-5
777
R. L. G.
22
0
115
1430
7-021
•1424
1632
74-2
95-5
77-7
R. L. G.
14
0
115
1230
11-039
•0906
1207
862
110-0
78-4
i 80-pr. of 101 cwt
6-3
180
L. G.
10
0
80
1240
12-748
•0784
835-5
85-4
1141
74-9
64-pr. of 64 cwt. wrt. iron
63
15-5
R. L. G.
8
0
64
1252
13-715
•0729
696-1
870
1160
751
L. G.
8
0
64
1229
13-715
■0729
670-8
83-8
1160
72-3
64-pr. of 58 cwt
63
17-2
R. L. G.
8
0
64
1245
15-234
•0656
688-3
86-0
118-7
725
64-pr. of 71 cwt
63
16-4
R. L. G.
8
0
64
1230
14-518
■0689
671-9
84 0
117-3
71-6
40-pr. of 35 cwt
475
18-0
R. L. G.
8
0
40
1357
6-830
1464
511-1
63-9
94-6
67"6
R. L. G.
7
0
40
1336
7-805
•1281
495-4
70-8
991
71-5
R. L. G.
6
0
40
1305
9-105
•1098
472-7
78-8
103-8
760
25-pr. of 21 cwt
40
180
R. L. G.
5
0
25
1355
6-518
1534
3185
63-7
92-8
687
R. L. G.
4
8
25
1320
7-244
•1380
302-3
67-2
96-4
69 8
R. L. G.
4
0
25
1278
8-151
1227
283-3
70-8
100-4
705
16-pr. of 12 cwt
3-6
190
R. L. G.
3
0
16
1352
8-365
•1195
202-9
67-6
1010
67-9
R. L. G.
2
8
16
1273
10-043
•0996
179-9
72-0
106-8
67'5
R. L. G.
2
0
16
1167
12541
•0797
151-2
75 -6
1134
66-6
9-pr. of 8 cwt
30
213
R. L. G.
1
12
9
1381
9-320
•1073
1191
680
104-6
651
R. L. G.
1
8
9
1325
10-865
0920
1096
73-1
109-5
66 9
R. L. G.
1
4
9
1203
13-026
•0768
90-38
72-3
114-5
63-2
9-pr. of 6 cwt
30
17 5
R. L. G.
1
12
9
1262
7-649
•1307
99-46
56-8
981
579
R. L. G.
1
8
9
1234
8-918
•1121
9510
63-4
103-5
61-3
i 7-pr. of 220 lb. (bronze) ...
30
11-3
F. G.
0
12
725
955
11-538
•0867
45-88
61-2
111-0
55-2
F. G.
0
10
725
854
13 873
•0721
36-69
58 -7
116-0
50-6
7-pr. of 150 lb. (steel)
30
80
F. G.
0
6
7-25
673
16 346
•0612
22-79
60-8
121-0
50-5
7-inch B.L. of 82 cwt
70
14-2
R.L. G.
10
0
110
1013
13-794
•0725
783-2
78-3
116-0
67'5
R. L. G.
11
0
90
1165
12-541
0797
847-6
77-1
113-0
68-0
64-pr. B.L. of 61 cwt
6-4
10.9
R. L. G.
9
0
64
1200
8-982
•1113
639-5
71 1
103-5
68-8
40-pr. B.L. of 35 cwt
4-75
22-4
|R. L. G.
5
0
41
1180
13-590
•0736
396 1
79-2
115-6
68-6
20-pr. B.L. of 16 cwt. L. S.
3-75
22-4
R-. L. G.
2
8
21
1130
13-377
•0748
186-1
74-4
115-3
64-5
20-pr. B.L. of 13 cwt. S. S.
375
14-5
R. L. G.
2
8
21
1000
8-672
•1153
145-7
583
102 4
57'0
12-pr. B.L. of 8 cwt
30
205
R. L. G.
1
8
11-75
1150
10-457
■0956
107-8
71-9
108-0
67-9
9-pr. B.L. of 6 cwt
30
1 77
R. L. G.
1
9-25
1057
120)9
•0832
71-71
63-7
112-1
55 9
6-pr. B.L. of 3 cwt
25
21-2
R. L. G.
0
12
6'6
1046
12-500
1
•8000
5011
66-8
113-4
59 0
136
CAPTAIN NOBLE AND ME. F. A. ABEL ON FIEED GUNPOWDER.
so taken, we have
Total work=w(1~-^M (35)
= 332,128 gramme-metres per gramme of powder
(486 foot-tons per lb. of powder).
Bunsen and Schischkoff’s estimate of the work which powder is capable of performing-
on a projectile, if indefinitely expanded, we have already given ; but their estimate (being
only the fifth part of that at which we have arrived) is altogether erroneous, as these
eminent chemists appear to have overlooked the important part which the non-gaseous
portion of the charge plays in expansion.
It is interesting to compare the above work of gunpowder with the total theoretic
work of 1 gramme of coal, which is about 3,400,000 gramme-units. The work stored
up in one gramme of coal is therefore more than ten times as great as that stored up
in 1 gramme of powder.
The powder, it is true, contains all the oxygen necessary for its own combustion, while
the coal draws nearly 3 grammes of oxygen from the air. Even allowing, however,
for this, there is a considerable inferiority in the work done by gunpowder, which is
doubtless in part due to the fact that the coal finds its oxygen already in the form of
gas, while a considerable amount of work is expended by the gunpowder in placing its
oxygen in a similar condition.
In an economic point of view also the oxygen stored up in the gunpowder is of no im-
portance, as that consumed by coal costs nothing, while the oxygen in the powder is in a
most expensive form. The fact is perhaps worth noting as demonstrating the impracticabi-
lity of making economic engines deriving their motive power from the force of gunpowder.
Z. SUMMARY OF RESULTS.
It only now remains to summarize the principal results at which we have arrived in
the course of our researches (a) when gunpowder is fired in a space entirely confined ;
( b ) when it is suffered to expand in the bore of a gun.
(a) The results when powder is fired in a close space are as follow, and for convenience
are computed upon 1 gramme of powder occupying a volume of 1 cub. centim. : —
1. On explosion, the products of combustion consist of about 57 per cent, by weight
of matter, which ultimately assumes the solid form, and 43 per cent, by weight of perma-
nent gases.
2. At the moment of explosion, the fluid products of combustion, doubtless in a very
finely divided state, occupy a volume of about -6 cub. centim.
3. At the same instant the permanent gases occupy a volume of *4 cub. centim., so
that both the fluid and gaseous matter are of approximately the same specific gravity.
4. The permanent gases generated by the explosion of a gramme of powder are such
that, at 0°C. and 760 millims. barometric pressure, they occupy about 280 cub. centims.,
and therefore about 280 times the volume of the original powder.
5. The chemical constituents of the solid products are exhibited in Tables III. & VI.
6. The composition of the permanent gases is shown in the same Tables.
CAPTAIN NOBLE AND ME. P. A. ABEL ON FIEED GUNPOWDEE.
137
7. The tension of the products of combustion, when the powder fills entirely the
space in which it is fired, is about 6400 atmospheres, or about 42 tons per square inch.
8. The tension varies with the mean density of the products of combustion accord-
ing to the law given in equation (3).
9. About 705 gramme-units of heat are developed by the decomposition of 1 gramme
of powder such as we have used in our experiments.
10. The temperature of explosion is about 2200° C. (about 4000° F.).
(5) When powder is fired in the bore of a gun, the results at which we have arrived
are as follow : —
1. The products of explosion, at all events as far as regards the proportions of the
solid and gaseous products, are the same as in the case of powder fired in a close vessel.
2. The work on the projectile is effected by the elastic force due to the permanent gases.
3. The reduction of temperature due to the expansion of the permanent gases is in a
great measure compensated by the heat stored up in the liquid residue.
4. The law connecting the tension of the products of explosion with the volume
they occupy is stated in equation (30).
5. The work that gunpowder is capable of performing in expanding in a vessel im-
pervious to heat is given by equation (34), and the temperature during expansion is
given by equation (31).
6. The total theoretic work of gunpowder when indefinitely expanded is about
332,000 gramme-metres per gramme of powder, or 486 foot-tons per lb. of powder.
With regard to one or two other points to which we specially directed our attention
in these investigations, we consider that our results warrant us in stating that : —
1. Very small-grain powder, such as F. G. and It. F. G., furnish decidedly smaller
proportions of gaseous products than a large-grain powder (R. L. G.), while the latter
again furnishes somewhat smaller proportions than a still larger powder (pebble), though
the difference between the gaseous products of these two powders is comparatively
inconsiderable.
2. The variations in the composition of the products of explosion furnished in close
chambers by one and the same powder under different conditions as regards pressure, and
by two powders of similar composition under the same conditions as regards pressure, are
so considerable that no value whatever can be attached to any attempt to give a general
chemical expression to the metamorphosis of a gunpowder of normal composition.
3. The proportions in which the several constituents of solid powder-residue are
formed are quite as much affected by slight accidental variations in the conditions which
attend the explosion of one and the same powder in different experiments as by decided
differences in the composition as well as in the size of grain of different powders.
4. In all but very exceptional results the solid residue furnished by the explosion of
gunpowder contains, as important constituents, potassium carbonate, sulphate, hypo-
sulphite, and sulphide, the proportion of carbonate being very much higher, and that
of sulphate very much lower than stated by recent investigators.
MDCCCLXXV. T
138
CAPTAIN NOBLE AND MB. E. A. ABEL ON FIBED OUNPOWDEB.
ABSTBACT OF EXPERIMENTS.
In this abstract the following abbreviations are used : —
l to represent the mean density of the products of explosion ; A the area of the
piston of the crusher-gauge ; a, the sectional area of the crushing-cylinder.
Experiment 1, April 20, 1871. — The cylinder (fig. 2, Plate 14) having been prepared
for the experiments, was calibrated and found to contain 14,000 grs. (907-2Q grms).
A charge of 1400 grs. (90-72 grms.) It. L. G. powder was then placed in the cylinder
and fired.
The gaseous products of combustion were collected in tubes and sealed.
On opening the cylinder the solid products of combustion were found adhering to
the sides pretty uniformly, but thicker at the bottom ; they had to be scraped off for
collection.
_ . Crush, copper Pressure per
cylinder. square inch.
•0940 -1667 -0417 -009 1-6 ton.
Experiment 2, April 4, 1871. — Fired 3500 grs. (226-80 grms.) It. L. G. powder as
above, in a similar cylinder, the powder exactly filling the space in which it was
confined.
The gas was retained in the cylinder for about a second, and then, owing to a want
of accurate fit in the collecting-screw, made its escape with a considerable explosion,
completely, so to speak, washing away every trace both of the male and female screw
along the channel it cut out for itself.
On opening the cylinder but little solid residue was found, and that uniformly
distributed over the surface, and about -07 inch thick.
Its colour was of a very bright vermilion red, rapidly changing to black on the
surface, and was similar in all respects to the deposit so often seen in the powder-
chambers of heavy guns.
Residue collected and sealed up in a test-tube.
- . Crush, copper Pressure per
cylinder. square inch.
•915 -1667 -0833 -293 34-5 tons.
Experiment 3, April 29, 1871. — Cylinder No. 6 calibrated and found to contain
14,702 grs. (952-68 grms.). 2940 grs. R. L. G. (190-54 grms.) were fired and the gases
collected within fifteen minutes after firing.
On opening the cylinder the solid products were found to be collected at the bottom,
only a very thin light-coloured deposit being on the sides.
The appearance of the deposit was very different from any yet obtained, being grey
on the smooth surface and very bright yellow in fracture. It was exceedingly hard
and very deliquescent.
The interior surface of the cylinder appeared quite bright when the deposit was
removed.
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GUNPOWDER,
139
A portion of the deposit, whitish on the surface, dark grey next the cylinder, was
collected and sealed in separate test-tubes.
A tin cylinder was substituted for copper, to measure the crush in this experiment.
a.
•1973
A.
■1667
a.
•0833
Crush, tin
cylinder.
•165
Pressure per
square inch.
2-67 tons.
Experiment 4, May 10, 1871. — 4411 grs. (285’5 grms.) of R. L. G. powder were fired
in cylinder No. 7. Gases were collected, commencing seven minutes after explosion.
On opening the cylinder the solid products were found in a mass at the bottom ;
and the sides of the cylinder were also as noted in the last experiment.
The residue, however, was of intense hardness, and the difficulty of removing it was
very great. Hardly any could be got off in lumps, but it flew off like sand before the
chisel.
Copper firing-wire fused off and dropped in the form of a button.
•2963
A.
•1677
•0833
Crush, copper
cylinder.
•033
Pressure per
square inch.
6-4 tons.
Experiment 5, June 22, 1871. — Cylinder No. 6 calibrated and found to contain
15,859 grs. P. powder. Fired 1586 grs. (102-77 grms.) P; but, owing to the low pressure,
the cylinder did not become closed up very tightly and most of the gas slowly escaped.
Solid products at the bottom and easily removed. Colour light grey on surface, dark
grey next steel, shading into light grey near the surface.
a.
•1064
A.
•1667
•0833
Crush, tin
cylinder.
•042
Pressure per
square inch.
T39 ton.
Experiment 6, June 28, 1871. — Fired 1586 grs. (102-77 grms.) pebble in same
cylinder (No. 6) as that used in the last experiment. Nearly all the gas escaped from
the same cause (defect of pressure). Products of combustion not collected.
•1064
A.
•1667
•0833
Crush, tin
cylinder.
•032
Pressure
in tons.
1-26
Experiment 7, June 28, 1871. — Fired 3150 grs. (204T2 grms.) pebble powder in
cylinder No. 6. Gas collected immediately. Solid products at bottom as usual, and
tolerably easily detached. Colour whitish grey on the smooth surface, almost black
next steel. Fracture yellowish green with splotches of grey. .
1.
•2114
A.
•1667
•0833
Crush, tin
cylinder.
•188
Pressure
in tons.
2-93
140
CAPTAIN NOBLE AND ME. F. A. ABEL ON FIEED GUNPOWDER.
Experiment 8, June 29, 1871. — Fired 1586 grs. (102-77 grms.) pebble powder in
cylinder No. 6. There was a slight escape of gas at first, but the plug soon tightened.
Gas collected and sealed immediately.
On opening the cylinder the deposit was found principally at the bottom. It
adhered very firmly, and was removed with great difficulty.
The colour of the smooth surface was light grey and green, buff in one or two places.
Fracture yellowish green.
The portions of the residue that could not be removed with a chisel were dissolved
out.
The firing copper wires -07 in diameter were melted and had formed a button, having,
however, rather long stumps.
c. A. a. Crush, tin. Pressure in tons.
•1064 -1667 -0833 -033 1-28
Experiment 9, June 29, 1871. — Fired 4725 grs. (306-18 grms.) pebble in cylinder
No. 4.
On firing there was a slight escape of gas past the crusher-gauge.
The gases were collected within five minutes of the explosion ; and after the tubes
were sealed a rough measurement was made of the remaining quantity of gas, which
amounted to 59,000 cub. centims.
The residue was very easily detached from the cylinder. It was darker grey on the
surface than in the last experiment. The fracture
was a deep olive-green with a stratum of light
grey in the middle, thus (see figure).
The deposit was all on the bottom, excepting a
very thin coating on the sides. Firing-wires fused
level with the plug.
g a Crush, copper Pressure
cylinder. in tons.
•3171 -1667 -0833 -018 4-90
Experiment 10, July 5, 1871. — Fired 6344 grs. (411-09 grms.) P. powder in cylinder
No. 6. Most of the gas escaped before enough could be collected.
Residue was found, when the cylinder was opened, at the bottom, not in the usual
hard compact mass, but much looser in texture.
On the surface there were three large spongy
projections, presenting an appearance as if the
surface had been broken by the escape of oc.
eluded gas, thus (see figure).
Colour of surface grey in parts, also light
CAPTAIN NOBLE AND ME, E. A. ABEL ON FIEED GUNPOWDER.
141
yellow shading into dark yellow. Colour of fracture grey, shading off into dirty yellow
and occasionally into gamboge. Powerful odour of sulphuretted hydrogen.
Crush, copper Pressure
’ a‘ cylinder. in tons.
•4258 -1667 -0833 -054 8-4
Experiment 11, July 5, 1871. — Fired 5881 grs. (381-09 grms.) R. L. G. in cylinder
No. 4. Some little escape of gas past crusher-plug. Residue very hard and adhering
strongly to the side ; a portion obtained in solid lumps. Colour grey on surface, black
next steel. Fracture olive-green.
A good deal of the deposit was chiselled off in the form of fine dust, and this, when
it had lain for a minute or two, heated very much, say to about 80° or 90° C., agglo-
merating into loose lumps and changing from a light greenish-grey colour to a bright
yellow. A portion of this last deposit was collected in a separate bottle.
When the crusher-gauge was taken out, the plug at the end was found to be broken
right through transversely.
The fracture was perfectly clean and bright ; it was therefore concluded that it must
have broken after the great heat had subsided.
. Crush, copper Pressure
cylinder. in tons.
•3947 -1667 -0833 -051 8T0
Experiment 12, July 8, 1871. — Fired 6344 grs. (411-09 grms.) P. powder in cylinder
No. 6. A good deal of leakage past the crusher-plug. Gas collected. Residue very
hard, but it split off tolerably easily. The colour was grey throughout ; fracture much
the colour and appearance of slate. The difference in physical appearance between
this residue and that in the last experiment was very great, the colour of the fine dust
being grey, while in the last experiment it was a light yellow.
s . Crush, copper Pressure
cylinder. in tons.
•4258 -1667 -0833 -063 9-1
Experiment 13, July 12, 1871. — Fired 7351 grs. (476*34 grms.) R. L. G. in cylinder
No. 6. The products cut away the screw of the pressure-gauge and escaped.
g ^ a Crush, copper Pressure
cylinder. in tons.
•4934 -1667 -0833 -091 11-5
Experiment 14, July 12, 1871. — Fired 7930 grs. (513’86 grms.) P. in cylinder No. 4.
Gas and residue collected as usual. Cylinder tight.
2. A.
■5322 -1667
Crush, copper Pressure
cylinder. in tons.
‘•100 12-2
•0833
142
CAPTAIN NOBLE AND ME. F. A. ABEL ON FIEED GUNPOWDER.
Experiment 15, July 22, 1872. — Fired, in cylinder No. 6, 1586 grs. (102-77 grins.) of
F. G. Cylinder perfectly tight. Gas and residue collected.
* . Crush, copper Pressure
d • A‘ a‘ cylinder. in tons.
•1064 *1667 -0467 -003 1-66
Experiment 16, July 22, 1872. — Experiment 15 repeated with tin cylinder.
^ Crush, Pressure
A- a' tin. in tons.
•1064 1667 -0467 '148 1-25
Experiment 17, July 24, 1872. — Fired, in cylinder No. 6, 3172 grs. (205-55 grms.)
F. G. Collected gas and residue. Residue very hard, but not so dark in colour as that
in experiment No. 16. Surface dark grey, but of a lighter colour when fractured.
A very thin coating on the sides of the cylinder.
Small bright yellow crystals pretty uniformly distributed through the residue.
2.
A.
et.
Crush, copper
Pressure
cylinder.
in tons.
•2129
•1667
•0417
•0475
3-70
Second experiment.
•2129
•1667
•0417
•0435
3-58
Experiment 18. — Fired 4758 grs. (308-32 grms.) F. G. in cylinder No. 6. Cylinder
perfectly tight. Collected gas and residue.
On opening the cylinder the residue was found all collected at the bottom ; and it had
evidently run down the sides in a very fluid state, the deposit on the side being very
thin. Colour on surface dark grey. Fracture more uniform than usual, there being
no patches of yellow and but few of a lighter colour.
„ . Crush, copper Pressure
o. A. a. , rr . ,
cylinder. m tons.
•3193 -1667 -0467 -132 6-75
Experiment 19, August 26, 1872. — Fired, in cylinder No. 6, 6344 grs. (411-09 grms.)
F. G. Cylinder perfectly tight. Colour and fracture dark grey, nearly black ; but in
places both surface and fracture light grey. No appearance of yellow anywhere in this
deposit. All the residues, so far, of F. G. differ very considerably in appearance both
from pebble and R. L. G.
The deposit on the sides was exceedingly thin, not more than ‘01 inch in thickness.
2.
•4258
(This pressure rejected.)
A. a.
•1667
Crush, copper Pressure
cylinder. in tons.
•222 9-98
•0417
CAPTAIN NOBLE AND ME, F. A. ABEL ON FIEED GTJNPOWDEE.
143
Experiment 20, August 28, 1872. — Fired, in cylinder No. 6, 7930 grs. (513-86 grms.)
F. G. Cylinder was absolutely tight. Gas collected in the usual manner. On opening
the cylinder and removing the firing-plug, observed that the little button of residue
adhering to the firing-plug, "when cut into, had a large well-defined crystalline structure,
the crystals being transparent although the surface of the button was dark grey. Sealed
a portion in a tube for examination.
Kesidue in mass at bottom of cylinder as usual ; next to nothing on sides. Colour
and fracture much the same as in the last experiment, but the centre much lighter grey.
Crush, copper Pressure
cylinder. in tons.
■0834 '-145 15-8
Experiments 21 to 24. — These experiments discarded.
N.B. From Experiment 16 inclusive, the crusher-gauge was put loose in the charge
of powder to be fired ; but it having been found that the crusher-gauge was heated to
such an extent as to soften the copper cylinder and thereby affect the observations, these
experiments were repeated, as far as regards the pressure determinations, in experiments
25 to 32.
2. A.
•5322 T667
(This pressure rejected.)
Experiment 25, October 1, 1872. — Fired 2974 grs. (192-72 grms.) F. G. in cylinder
No. 7.
s A Crush, copper Pressure
cylinder. in tons.
•3860 -0834 -0417 -051 7-68
Experiment 26, October 17, 1872. — Fired 1586 grs. (102-77 grms.) F. G. in cylinder
No. 6.
. Crush, tin Pressure in
cylinder. tons.
•1064 -0834 -0417 -016 0-96
Experiment 27, October 18, 1872. — Fired 3172 grs. (205-55 grms.) F. G. in cylinder
No. 6.
2.
•2129
A.
•0834
a Crush, copper
cylinder.
•0417 -008
Pressure
in tons.
3-0
Experiment 28, October 18, 1872. — Fired 4758 grs. (308-32 grms.) F. G. in cylinder
No. 6.
s A rush, copper Pressure
o. A. a. v -i r • ,
cylinder. in tons.
•3193 -0834 -0417 -032 6-32
144
CAPTAIN NOBLE AND MR. F. A. ABEL ON FIRED GUNPOWDER.
Experiment 29, October 19, 1872. — Fired 6344 grs. (411-09 grms.) F. G. in cylinder
No. 6.
x . Crush, copper Pressure
A" a' cylinder. in tons.
•4258 -0834 -0417 -074 9-34
Experiment 30, October 21, 1872. — Fired 7930 grs. (513-86 grms.) F. G. in cylinder
No. 6.
5 . Crush, copper Pressure
cylinder. in tons.
•5322 -0834 -0417 -104 11-48
Experiment 31, October 29, 1872. — Fired 3507-5 grs. (227‘286 grms.) F. G. in cylinder
No. 7.
^ . Crush, copper Pressure
cylinder. in tons.
•4615 -0833 -0417 -065 8-68
Experiment 32, October 31, 1872. — Fired 3719 grs. (240-991 grms.) F. G. in cylinder
No. 7.
^ ^ Crush, copper Pressure
cylinder. in tons.
■4893 -0833 -0417 -085 10-14
Experiment 33 (repetition). — Fired 2980 grs. (193-104 grms.) P. in cylinder No. 6.
» . Crush, copper Pressure
cylinder. in tons.
•200 -0833 -0417 -006 2-70
Experiment 34 (repetition). — Fired 4470 grs. (289-656 grms.) P. in cylinder No. 6.
^ . Crush, copper Pressure
S. A. a. t a LL ■ i.
cylinder. m tons.
•300 -0833 -0417 -020 5-40
Experiment 35. — Fired 4560 grs. (295-488 grms.) P. in cylinder No. 7.
g a Crush, copper Pressure
cylinder. in tons.
•600 -0833 -0417 -136 13-78
Experiment 36. — Fired 4560 grs. (295-488 grms.) P. in cylinder No. 7. Gas escaped.
g A Crush, copper Pressure
cylinder. in tons.
•600 -0833 -0417 -132 13-50
Experiment 37, November 26, 1872. — Fired 4560 grs. (295"488 grms.) P. in cylinder
No. 7.
CAPTAIN NOBLE AND ME. P. A. ABEL ON PIEED GUNPOWDEE.
145
On firing, a slight quantity of gas escaped with a puff. Gas collected. Surface of
the deposit was rough and dark-looking. Fracture grey, with greenish-yellow patches
in places ; hardly any deposit on sides.
s . Crush, copper Pressure
' a' cylinder. in tons.
•600 *0833 -0417 -150 14-80
Experiment 38, November 28, 1872. — Fired 5320 grs. (344-736 grms.) P. in cylinder
No. 7.
A good deal of gas escaped through the gas-hole. Gas collected as usual. On open-
ing, all the residue was found at the bottom ; but in cooling the residue had contracted
very much, separating on one side from the cylinder and leaving a considerable crack.
The surface had a frothy appearance, as if occluded gas had been given off while still
fluid. Colour dark grey on surface. Texture much more open than usual. Very
much less yellow than in last experiment, and darker in colour than in experiment 36,
from which the gas escaped. Examined the colour carefully next day, and found it
had become more yellow, although not so yellow as the residue in experiment 37.
^ ^ a Crush, copper Pressure
cylinder. in tons.
•7000 -0833 -0417 -203 18-60
Experiment 39, November 29, 1872. — Fired 4560 grs. (295-488 grms.) It. L. G. in
cylinder No 7. Cylinder was perfectly tight. Residue all at bottom and firmly
attached to sides. Surface level, but little dark roughnesses all over it. Colour and
fracture much the same as in last experiment, but a little more grey.
^ ^ a Crush, copper Pressure
cylinder. in tons.
•6000 -0833 -0417 -144 14-36.
Experiment 40, December 2, 1872. — Fired 4560 grs. (295-488 grms.) F. G. in
cylinder No. 7.
Cylinder tight, but a slight smell of sulphuretted hydrogen perceptible. Thirty
seconds after explosion the cylinder was placed at an angle of 45°, and retained there
for two minutes. When cylinder was opened the deposit was found lying at this
angle, the surface being smooth and the edges sharply defined. Hence the deposit
must have been perfectly fluid half a minute after explosion, and perfectly set two
minutes later. Surface of deposit dark greenish grey ; fracture much the same colour,
and considerably darker either than that of R. L. G. or P. The bottled deposit had a
powerful smell of ammonia.
g ^ a Crush, copper Pressure
cylinder. in tons.
•6000 -0833 -0417 T41 14-14
Experiment 41, December 3, 1872. — Fired 5320 grs. (344-736 grms.) R. L. G. in
cylinder No. 7.
mdccclxxv. u
146
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GUNPOWDER.
One minute after firing, the cylinder was placed at an angle of 45°. Forty-five
seconds later the position of the cylinder was reversed. Cylinder quite tight. On
opening, it was found that one minute after explosion the
deposit had just commenced to congeal on the top, a thin
crust having been formed, which was broken through
when the cylinder was returned to its original position ;
but a considerable portion of the crust was left. The
sharpness with which the cylinder had struck its rest had
made the deposit run up the side, as at a. Hence, a minute
after explosion, the deposit was in a very fluid state, but
had just begun to set. It could not, as evidenced by the
mark at a, have been viscid. Forty-five seconds later the
deposit was perfectly set. Colour dark grey with a dark
olive-green hue. A few cavities in the deposit.
% A a Crush, copper Pressure
cylinder. in tons.
•7000 -0833 -0417 -216 19-54
Experiment 42, December 4, 1872. — Fired 5320 grs. (344-736 grms.) F. G. in cylinder
No. 7.
Cylinder tight, but slight smell of SH2. On opening the cylinder, the nose of the
crusher-plug was found to have broken off, and it lay loose on the top of the deposit,
showing that it must have fallen off after the deposit was solid. Crusher covered with
slight deposit and numerous small crystals, apparently sulphide of iron. Deposit
more like that of P. and R. L. G. than formerly. The bottled residue smelt most
powerfully of ammonia, too powerfully to hold to the nose.
^ A a Crush, copper Pressure
cylinder. in tons.
•7000 -0833 -0417 -197 18-2
Experiment 43, December 5, 1872. — Fired 6080 grs. (393-984 grms.) pebble powder
in No. 7 cylinder.
Cylinder perfectly tight.
j. Crush, copper Pressure
cylinder. in tons.
•8000 -0833 0833 T26 28-6
Experiment 44, December 6, 1872. — Fired 6080 grs. (393-984 grms.) R. L. G. in
cylinder No. 7.
A small quantity of gas leaked shortly after explosion. Deposit had a great many
bright crystals (sulphide of iron) diffused through it.
A. a.
d.
•8000
•0833
•0833
Crush, copper
cylinder.
TOO
Pressure
in Ions.
24-4
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GUNPOWDEE.
147
Experiment 45, December 17, 1872. — Fired 6080 grs. (393-984 grms.) F. G. in
cylinder No. 7.
Gas escaped past cone.
* a Crush, copper Pressure
d- ' ’ cylinder. in tons.
•8000 . '0833 *0833 -092 23-2
Experiment 46, December 24, 1872. — Fired 3800 grs. (246-286 grms.) R. L. G. in
cylinder No. 7. •
The weight of the mild steel cylinder was 72,688 grms. After firing, the cylinder
being perfectly tight, 9,912 grms. water were added.
The temperature of the cylinder before firing was . 54°T5 F. (12°*28 C.).
The temperature of the water before firing was . 55°-75 F. (13o,20 C.).
After firing, the following observations of temperature were made, that of the room
in which the observations were made being 56° F. (130-35 C.) : —
Temperature of water before
explosion .
55-75 F. (13-20 C.)
„ „ 5 minutes after explosion
67-0
(19-4 C.)
„ „ io
55
55
70-8
(21-5 C.)
„ „ 15
55
55
71T
(21-66 C.)
„ „ 20
55
55
71-2
(21-71 C.)
» v 25
55
55
71-0
(21-6 C.)
„ » 30
55
55
70-8
(21-5 C.)
„ » 35
55
55
70-5
(21-35 C.)
„ „ 40
„
55
70-5
(21-35 C.)
» 5? 45
55
55
70-4
(21-30 C.)
„ n 50
55
„
70-3
(21-25 C.)
Since in twenty minutes the mass cooled by 0o,7, this amount should be added to
the maximum temperature of the water.
At fifty-five minutes after the explosion the gases were suffered to escape, and water
taken from the calorimeter was placed in the cylinder. The temperature of the water
was found to be 690,4 F. (20o,72 C.). N.B. Volume of deposit=1180 grs. (76-464 cub.
centims.).
* . Crush, copper Pressure
cylinder. m tons.
•5000 -0833 -0417 -090 10-48
Experiment 47, December 28, 1872. — Fired 6080 grs. (393-978 grms.) F. G. in same
cylinder as was used in last experiment. After firing, the cylinder was at once placed
in a vessel prepared for it filled with water. There was a slight crackling sound, but
no escape of gas, except a few minute bubbles, which, however, soon ceased.
u 2
148
CAPTAIN NOBLE AND MB. F. A. ABEL ON FIEED GTJNPOWDEK.
Weight of cylinder
„ water
Temperature of cylinder before experiment
„ water „
15,340-0
57°-5 F.
60°-45 F.
and the heat generated by the explosion raised the common temperature of the cylinder
and water to 80o,45 F. (26°-87 C.). Hence the steel was raised through 22°-95 F.=
12°-75 C.; water through 20°-00 F.=ll°-ll C.
Residue and gas collected from this experiment.
S.
•8000
A.
•0833
•083!
Crush, copper
cylinder.
•117
Pressure
in tons.
27T
Experiment 48. — Fired 3800 grs. (246-286 grms.) F. G. in same cylinder as before,
and with the same arrangements. On placing the cylinder in the water a few very
small bubbles escaped from the firing-plug, and this slight escape continued during
the experiment.
Weight of cylinder 72,688'0 grms.
„ water 14,158 „
Temperature of cylinder before experiment . 560,5 F.
„ water „ . 59°T5 F. ;
and the heat generated by the explosion raised the common temperature to 71°"9 F.
(22°T5 C.). Hence the steel was raised through 150,4 F. = 80,5 55 C. ; water through
12°-75 F. = 7°-083 C.
Amount of deposit=1038 grs. (67'262 cub. centims.). The deposit seemed to have
contracted, since solidification, from -2 to *25 inch.
■5000
A.
•0833
•0417
Crush, copper
cylinder.
•090
Pressure
in tons.
10-48
Experiment 49.— Fired 6080 grs. ( 3 9 3 • 9 7 8 grms.) R. L. G. in same cylinder Cylinder
perfectly tight, but before placing in water crackling sound noticed.
Cylinder weighed 72,688 grms.
Water „ 14,845 „
Temperature of cylinder before explosion . . 460-2 F.
„ water „ . . 51°-85 F.
„ room ■ . 61° F. ;
and the heat generated raised the common temperature of cylinder and water to
710-32 F. Hence steel raised through 259T2 F.=130,95 C. ; water through 19°-47 F.
=10°-82 C.
CAPTAIN NOBLE AND ME. P. A. ABEL ON PIEED GUNPOWDER.
149
Amount of deposit = 1900 grs. (123,120 cub. centims.).
a. a.
■8000 -0833
a.
•0417
Crush, copper
cylinder.
•265
Pressure
in tons.
23-2
Experiments 50 to 52. — These experiments were undertaken to measure the volume
of gas produced by the explosion of a given weight of powder. The gas was allowed
to escape into a gasometer charged with a saturated saline solution ; but as it was found
that a considerable quantity of gas was absorbed by the water, this apparatus was
replaced by the more perfect one described in the body of the paper.
Experiment 53, February 6, 1873. — Fired 5960 grs. (386-2 grins.) P. powder in
cylinder No. 6 ; measured the quantity of gas produced.
Quantity of gas produced 112,455’5 cub. centims.
Temperature of gas when measured . . . . 180,3 C.
Barometric pressure 767 millims.
Experiment 54, February 7, 1873. — Fired
same arrangements as in last experiment.
Quantity of gas measured . . .
Temperature of gas when measured
Barometric pressure
5960 grs. (386*2 grms.) P. powder with
. . . . 110,633-4 cub. centims.
. . . . 17°-2 C.
. . . . 770 millims.
Experiment 55, February 8, 1873. — Fired 5960 grs. (386-2 grms.) R. L. G. with
same arrangements.
Quantity of gas measured . . . .
Temperature of gas when measured
Barometric pressure . . .
110,26 9 '6 cub. centims.
16°-0 C.
774 millims.
Experiment 56, February 10, 1873. — Fired 5960 grs. (386'2 grms.) F. G. under
same conditions.
Quantity of gas measured 104,875‘3 cub. centims.
Temperature of gas 15o,0 C.
Barometric pressure 775 millims.
Experiment 57, February 11, 1873.— Fired 5960 grs. (386*2 grms.) F. G. under
same arrangements.
Quantity of gas measured
Temperature of gas .
Barometric pressure
103,345’2 cub. centims.
13°-3 C.
768 millims.
150
CAPTAIN NOBLE AND ME. E. A. ABEL ON EIEED GUNPOWDER.
Amount of deposit measured, and found to occupy a space of 115-34 cub. centims,.
The deposit appeared not to have contracted much after solidification ; but it had
parted from the side, leaving a crack about 0-04 in. (1 millim.) wide.
Experiment 58, February 12, 1873. — Fired 5960 grs. (386-2 grms.) R. L. G. Same
arrangements.
Quantity of gas measured 107,354-5 cub. centims.
Temperature of gas 14°-5 C.
Barometric pressure 772 millims.
Deposit occupied a space of. . . . 110 ‘8 cub. centims.
Experiment 59. — Experiment on mode of closing firing-plug.
Experiment 60, March 5, 1873. — Fired 5960 grs. (386-2 grms.) P.
Quantity of gas 114,059-7 cub. centims.
Temperature of gas 19° C.
Barometric pressure 765 millims.
Deposit occupied a space of. . . . 111-78 cub. centims.
Experiment 61, March 6, 1873. — Fired 5960 grs. (386*2 grms.) R. L. G.
Quantity of gas 111,367-5 cub. centims.
Temperature of gas 150-94 C.
Barometric pressure 755-6 millims.
Deposit occupied a space of. . . . 105-30 cub. centims.
Experiment 62. — Fired 5960 grs. (386‘2 grms.) F. G.
Quantity of gas 108,881-8 cub. centims.
Temperature of gas 19°-61 C.
Barometric pressure 739 -4 millims.
Deposit occupied a space of. . . . 108-5 cub. centims.
Experiment 63. — Fired 3800 grs. (246-286 grms.) R. L. G. to determine heat.
Cylinder quite tight.
Cylinder weighed 72,688 grms.
Water „ 15,655-4 „
Temperature of cylinder before explosion . . 51°-4 F. (10o,72 C.)
„ water „ „ . . . 51-65 F.
„ room 52-5 F.
The heat generated raised the temperature of water and cylinder to 64°-25 F. 1
Hence steel raised through 12°-25 F.=7°T39 C. ; water through 12°-6 F. = 7°-0 C.
CAPTAIN NOBLE AND ME. E. A. ABEL ON PIEED GUNPOWDEE.
151
Experiment 64. — Fired 5960 grs. (386-2 grms.).
Quantity of gas . 106,625-0 cub. centims.
Temperature of gas 160,55 C.
Barometric pressure . 758-2 millims.
Experiment 65. — Fired 6840 grs. (443-23 grms.) P. in cylinder No. 7. This charge
filled the cylinder nearly quite full. Cylinder, on firing, cracked between the firing- and
crusher-plugs. Crack about -5 millim. wide. Report very loud.
^ a Crush, copper Pressure
cylinder. in tons.
•900 -0833 -1833 -156 33-4
Experiment 66. — Fired 6840 grs. (443-23 grms.) P. In about a second after firing
the gas made a fizzing sound, and in about another second escaped by blowing out the
gauge-plug with a loud report. Lower threads of the screw on the crusher-plug washed
away by the escape of the gas.
£ ^ a Crush, copper Pressure
cylinder. in tons.
•900 -0833 -0833 -145 31-6
Experiment 67. — Experiment on mode of detonating a charge.
Experiment 68. — Fired 6840 grs. (443-23 grms.) R. L. G. Cylinder and all parts
perfectly tight. Residue and gas collected. Observed that the deposit had apparently
not contracted much.
On the firing-plug were several congealed drops of deposit like icicles, and on the
surface below spots, which had apparently dropped from above, were visible.
Surface of deposit dark grey, almost black.
Fracture olive-green, with frequent spots of brilliant yellow of the size of a pin’s
head.
Top part of deposit put in separate bottle from bottom part, each sample being
ground and mixed carefully in an atmosphere of dry nitrogen.
§ a Crush, copper Pressure
cylinder. in tons.
•900 -0833 -0833 -168 35-6
Experiment 69, May 29, 1873. — Fired 6840 grs. (443-23 grms.) F. G. Cylinder &c.
perfectly tight. On opening the cylinder, found white crystals deposited on firing-plug.
Deposit very dark and more greasy than usual.
Fracture dark grey, with only few spots of yellow.
Deposit first taken did not heat ; but there was great difficulty in getting it to grind
in an atmosphere of dry nitrogen.
The portion we succeeded in grinding was sealed in test-tube marked experiment 69a.
Unground portion sealed in test-tube marked B. Bottom portions of the deposit,
when exposed to the air, changed with great rapidity to a bright yellow on the surface,
152 CAPTAIN NOBLE AND MR. F. A. ABEL ON FIRED GUNPOWDER,
with development of heat. It was got as rapidly as possible into the mill and was easily
ground in dry nitrogen. This was sealed in bottle marked C, while some unground
lumps were marked D.
A mixture of the top and bottom was ground in nitrogen and was marked E.
Transparent crystals (on firing-plug) also preserved in small tube.
Crush, copper Pressure
a" cylinder. in tons.
•900 -0833 *0833 T18 27-2
Experiment 70, October 20, 1873. — Fired 3800 grs. (246-286 grms.) E. L. G. by
means of a detonator containing 2 grms. of fulminate of mercury. Cylinder perfectly
tight. Eesidue full of lustrous scales, otherwise of usual appearance ; considerable
lump of metal found in bottom (firing-wire and detonator-case).
Crush, copper Pressure
A- a‘ cylinder. in tons.
•500 -1667 *0833 -081 10-7
Experiment 71, October 22, 1873. — Last experiment repeated with similar results.
j. . Crush, copper Pressure
a' cylinder. in tons.
•500 -1667 -0833 -086 11-10
Experiment 72, October 24, 1873. — Fired, with a view to determine the amount of
heat absorbed by a gun when fired, nine rounds of 1 lb. 12 oz. (793-788 grms.) E. L. G.
in a 12-pr. B. L. gun; weight of shot 11 lbs. 12 oz. (5,329-72 grms.). Temperature of
air 46°-2 F.
Time of firing six minutes. After firing, the gun was at once placed in a vessel of
water and the changes of temperature observed. The following are the data : —
Weight of gun 387,141-6 grms.
Weight of water . . . . . . 192,777-0 „
Temperature of gun and water before firing 47o,0 F. ; the heat communicated to
the gun by nine rounds raised the common temperature of the gun and water to
51°-15 F.
Hence the heat raised the water and gun through 4°T5 F. = 2°-305 C.
Experiment 73. — Fired five rounds 1-5 lb. (680-39 grms.) E. L. G. in a 12-pr. B. L. gun.
Weight of shot . , 532-75 grms.
Temperature of air 46°*5 F.
Time of firing 2|- minutes.
Weight of gun 387,141-6 grms.
Weight of water 68,810-1 grms.
Temperature of gun and water before firing . . . 45°-7 F.
„ „ „ after „ ... 50o,55 F.
CAPTAIN NOBLE AND MR. F. A. ABEL ON FIRED GUNPOWDER.
153
Hence the heat communicated to the gun raised gun and)
water through /
4°-85 F.=2°-694C.
Experiment 74. — Exposed four crucibles filled with deposit from experiment 36 to
most intense heat of one of Siemens’s gas-furnaces ; one crucible uncovered, the rest
covered. Temperature estimated at 1700° C. A portion of the residue spirted imme-
diately and then became quiet. On removal from the furnace half an hour afterwards,
a little vapour was observed coming from the crucibles. Their contents were perfectly
liquid, setting at about 700° or 800° C.
The colour of the contents when cool was a bright sealing-wax red, similar to the
deposit found in the chambers of guns, turning black on the surface on exposure to
the air : sealed for examination.
Experiment 75, November 1, 1873. — Experiment 20 repeated, 3800 grs. (246'286
grms.) F. G., analysis of 20 being unsatisfactory. When exploded, cylinder perfectly
tight ; had to put a drop of water in gas-hole before gas would come away, the hole
being sealed by the deposit.
Residue when got out very dark in colour ; no yellow or green apparent when put in
bottle ; after grinding in nitrogen, a little heat appeared to be developed and a tinge of
yellow appeared.
s. . Crush, copper Pressure
o. A. a. n- j • ,
cylinder. m tons.
•5000 -1667 ' '0833 -076 10-2
Experiment 76, November 3, 1873. — Experiment 43 repeated, results of analysis
of previous experiment being irreconcilable; 6080 grs. (393‘986 grms.) P.
On opening the cylinder observed that the contraction was greater than usual ; nothing
else remarkable.
£ . Crush, copper Pressure
cylinder. in tons.
•8000 -0833 -0833 -098 24-2
Experiment 77, November 13, 1873. — Fired 6840 grs. (417*312 grms.) P. After
firing, the cylinder was allowed to stand for 60 seconds, then tilted over to an angle of
45° and replaced. At 75 seconds after firing it was again tilted on a different place, and
so on up to 2 minutes.
On opening the cylinder it was found that
at 60 and 75 seconds after explosion the
deposit was perfectly fluid; at 90 seconds it
was rather thick, and at 105 seconds it hardly
moved.
The development of the interior surface of
the cylinder appeared thus (see figure).
mdccclxxv. x
154
CAPTAIN NOBLE AND ME. F. A. ABEL ON FIEED GUNPOWDER.
a . Crush, copper Pressure
' ‘ a‘ cylinder. in tons.
•9000 -0833 -0833 1-44 31-4
Experiment 78, January 12, 1874. — Fired 5320 grs. (344*74 grms.) in same cylinder.
On opening, the colour of the deposit was a lighter grey than usual. The contraction
after setting appeared to be considerable, apparently *2 inch.
In this experiment, before firing, a piece of the finest platinum wire *, also a piece of
sheet platinum about 1 inch (26 millims.), square and *03 inch (’76 millim.) thick were
placed among the powder. After the explosion the thin platinum wire had disappeared,
but small globules of the metal were found in many places welded to the surface of the
cylinder.
The sheet platinum was not melted, but was doubled up ; there were appearances,
however, of fusion on its surface, and in places the platinum wire had been welded to
the sheet. The weight of the sheet platinum was about 0*25 oz. (about 6 grms.).
S. A. a. Crush. Pressure in tons.
•7 *0833 -0833 -067 18-9
Experiment 79, January 14, 1874. — Fired 5320 grs. (344-74 grms.) Spanish pebble
powder; put in a coil of platinum wire *06 inch (1'52 millim.) in diameter, weighing
about 15 grms.
The platinum after the explosion was found in a lump at the bottom of the deposit
thoroughly fused, with the exception of a small portion. Colour and appearance of
residue rather different from the ordinary. There were a good many light-coloured
splotches. The surface of the deposit was broken and rough, as if by the escape of gas.
S. - A. a. Crush. Pressure in tons.
•700 -0833 -0833 *056 17
Experiment 80, January 16, 1874. — Fired 5960 grs. (386-21 grms.) R. F. G.
Quantity of gas measured . . . . 109*540 cub. centims.
Temperature of gas 180,33 C.
Barometric pressure 729 millims.
Experiment 81. — Fired 5960 grs. (386‘21 grms.) pebble (Spanish).
Quantity of gas measured .... 98,607-7 cub. centims.
Temperature of gas 160,67 C.
Barometric pressure 735 millims.
Experiment 8 2. —Placed in a Siemens furnace, at a temperature of about 1700° C.,
two crucibles, one containing powder-residue, the other equal weights of potassium
carbonate and liver of sulphur. On first placing them in the furnace a little ebullition
took place, apparently in both crucibles, but with some violence in the crucible with
powder-residue. This ebullition, however, soon subsided and a slow volatilization
* Wound round the sheet platinum.
CAPTAIN NOBLE AND MR. E. A. ABEL ON FIRED GUNPOWDER.
155
appeared to proceed. On taking the crucibles from the furnace, the height of the con-
tents (which left marks on the crucibles) was noted, and the volume of the deposit and
the amount of contraction were measured by means of mercury, with the following
results : —
Powder-residue.
Volume at 1700° C. =17-859 cub. centims.
Volume at 0°C. =10-044 „
Expansion between 0° and 1700°=7’815 cub. centims., =77*8 per cent.
Potassium carbonate and liver of sulphur.
Volume at 1700° C. =28-188 cub. centims.
Volume at 0°C. =14-580 „
13-608 „
.-. expansion between 0°C. and 1700° C. =13-608, =93-3 per cent.
With the above two crucibles there was also a third, containing powder-residue, and
in this crucible a piece of platinum was placed. The expansion measured was over 100
per cent., but could not be depended on, on account of the platinum. The metal was
not appreciably altered by the heat.
Experiment 83.— Experiment 79 repeated.
Experiment 84. — Fired 5320 grs. (344-74 grms.) F. G. in small cylinder. Put a piece
of platinum wire 4 inches long (100 millims.), 16 W. G. (1-5 millim. in diameter), with
the powder. This wire showed signs of fusion on the surface, but was not at all melted.
Experiment 85, February 18, 1874. — Fired 5320 grs. (344-736 grms.) E. L. G. in
cylinder. Placed in cylinder a piece of platinum wire 4 inches (100 millims.) long and
0-04 inch (1 millim.) in diameter. The wire was superficially fused, but otherwise little
altered. No crusher used, the gauge having been destroyed in experiment 83.
Experiment 86, February 19, 1874.— Fired 5320 grs. (344-736 grms.) E. L. G. in
same cylinder. Placed in the cylinder a piece of platinum wire of same dimensions as
in last experiment, also the same length of copper wire, 0-13 inch(3-2 millims.)in diameter.
The copper was completely fused and firmly attached to the cylinder, it being found
necessary to remove it with a chisel. The platinum wire was superficially fused, as in
the last experiment.
[ 157 ]
III. On the Atmospheric Lines of the Solar Spectrum , illustrated by a Map drawn on
the same scale as that adopted by Kirchhoff. By J. B. N. Hennessey, F.R.A.S.
Communicated by Professor Stokes, Sec. B.S.
Received January 11,-^Read January 28, 1875.
The spectroscopic observations hereafter discussed were made with instruments belong-
ing to the Royal Society, and in accordance with certain suggestions which a Com-
mittee were good enough to make in connexion with my letter to Sir Edward Sabine,
President, dated 13th February, 1866. In view of my residence at a considerable
height, and the exceedingly clear atmosphere prevailing at some periods of the year, it
was suggested that the locality was peculiarly favourable for comparing the solar
spectrum when the sun was high with the corresponding spectrum at sunset; any
differences between these aspects which might appear were to be noted on Kirchhoff’s
well-known maps. Accordingly I set to work with the spectroscope first supplied to
me (hereafter distinguished by the prefix old), and during the autumns of 1868 and
1869 I mapped the differences in question from the extreme red to D: these results
appeared in the ‘Proceedings of the Royal Society,’ No. 123, 1870, the Map being
marked vol. xix. pi. 1 ; it is unnecessary, therefore, to dwell on this portion of my
labours, excepting to add that the definitions and general procedure there adopted
have been retained in the remarks which follow.
2. The observations hereafter noticed were always taken in the autumn, when, the
rainy season having passed away, the atmosphere on these mountains is exceedingly
clear, so that the sun, the object of inquiry, is bright even to his setting, and a spec-
trum may therefore be then obtained through a long stretch of terrestrial atmosphere
corresponding to the height of the station of observation ; on the other hand, with the
sun about the meridian, the height of station places the observer above a relative amount
of atmosphere, so that the spectrum obtainable at this time and about sunset are highly
eligible for the comparison in view. Accordingly the two spectra are given in the accompa-
nying map (Plate 25) ; and for easy comparison they are placed in juxtaposition. By “ sun
high” is to be understood any position for the sun within a couple of hours of the meridian;
by “ sun low ” that the sun was within 3 or 4 diameters of his setting and yet quite bright.
Indeed it is only when very near sunset that the marked alterations in the lines appear ;
so that the spectrum required is not only rarely obtainable, but it hardly lasts beyond
10 minutes of an evening. In this short period (when, moreover, the observer is fatigued
with previous watching) changes from the sun-high spectrum must first be detected ;
then their position must be identified, and, failing this, found by measurement ; next,
MDCCCLXXV. Y
158
MR. J. B. N. HENNESSEY ON THE ATMOSPHERIC
the appearance should be drawn, and finally the drawing should be compared with the
original : under these conditions a week may be easily absorbed by a single group. It
is also to be borne in mind that no human eye will endure, without at least temporary
injury, protracted watching of the bright solar spectrum for more than four or five
weeks at a time ; indeed, though I habitually used both eyes as a relief to one another,
they both invariably suffered, and continued to do so for several weeks after every
autumn. The following facts may be here mentioned : —
In 1870, commencing October 17, I observed 17 sunsets.
„ 1871, „ „ 5, „ 20 „
„ 1872, „ „ 10 (about), „ 20 „
„ 1873, „ „ 6, „ 35 „
3. In the autumns of 1870 and 1871 1 continued to work with the old spectroscope,
mapping from D to E, in extension of the Map already published ; but all desire for
publication of these results was naturally suppressed when Professor Stokes gratified
me by announcing that the Royal Society had ordered a new spectroscope for my use.
This instrument reached my residence at Dehra, together with two actinometers,
when I was absent with the eclipse expedition in December 1871 ; and I need hardly
add that after my return I lost no time in examining the contents of the package. It
appears inevitable that instruments should suffer in travelling ; this one did, and the
injuries took weeks to repair; but once the spectroscope was fit for use and I was
able to judge of its capabilities, the idea of not superseding the map already published,
based on my work of 1868 and 1869, or of not suppressing the map in hand from obser-
vations 1870 and 1871, was at once relinquished; thus the map now submitted was
obtained entirely with the new spectroscope. However, I had my old maps as skeletons
to begin with ; and adopting Professor Stokes’s suggestion to compare, in the first
instance, the spectra by the two instruments, I set to work de novo from the extreme
red in the autumn of 1872, and finished the work in November 1873 ; it was not, how-
ever, until the following summer that I was able to forward the map appended, nor
have I had it in my power until now to attempt this explanatory paper.
4. As regards my station of observation, it is best known locally by Vincent’s Hill *,
being a knoll on some property once owned by the late General Vincent: the site is in
N. lat. 30° 27', E. long. 78° 3' ; height above sea 7100 feet ; and it commands a complete
view of the horizon from S.E. to S.W. by W. The site in question was made available
for my purposes through the courtesy of Surgeon-Major R. Whittall. Next, of the
new spectroscope by Grubb of Dublin : it mounts three (compound) prisms, which are
moved with the telescope by an automatical contrivance for maintaining minimum de-
viation ; the eye-end of the telescope is fitted with a micrometer, and the highest power
eyepiece which may be generally employed gives an image of the dispersion about
3-g- fifths of that delineated in Kirchhoff’s maps at the usual distance of reading:
* On the Himalaya Mountains, N. AV. Provinces, India.
LINES OF THE SOLAE SPECTEUM.
159
the prisms are beauties: an object-glass, about 1 inch in diameter, is fitted at the end of
a rod, and can be adjusted so as to throw an image of the object on the slit ; this pro-
vision was exceedingly useful to me. Further description of the instrument appears
unnecessary, excepting to state generally that I am much pleased with its good qualities.
5. I now proceed to add a few words as to my reasons for ascribing the differences in
certain parts of the solar spectrum, sun high and sun set, in all cases to the influence
of the earth's atmosphere, believing that I can definitely show the relation between this
effect and this cause. I will premise that I now have access to the Philosophical
Transactions for 1860, in which the paper by Sir David Brewster and Dr. Gladstone
on the lines of the solar spectrum is given, together with an illustrating map ; and I here
make allusion to these documents, because, though the Committee were good enough to
call my attention to them, I was unable when writing in 1870 to get possession of a
copy. I have also access to other volumes of the Philosophical Transactions, including
Professor Stores’s drawings in the volume for 1852, besides various documents on the
subject of air-lines, as Report on a Mission in Italy by M. Janssen, &c. All these
papers contain descriptions or allusions to experiments showing the effect of reflections
from various surfaces, and of the passage of light through strata of variable lengths, &c.
And in turn I also (in keeping with suggestions by Professor Stores, for which I am very
much obliged) tried certain experiments which I will now briefly allude to. Selecting a
bright clear day, I first turned the collimator to the sun about the meridian, and set
the slit for good definition of the lines ; after this, with the slit as before, I admitted
the sun’s light reflected from blue or white glass backed with velvet, from ink of various
degrees of blackness, from coloured solutions, &c. ; and finally I got a reflection from a
distant muddy river; but none of these, or other experiments which need not be
detailed, produced the smallest approach to the variable lines which were the especial
aim of these experiments, nor yet, as a matter of fact, to those seen only at sunset that
are plainly air-lines. Some of the belts are specially deserving of attention — for instance
the huge shadow 1073 to 1155 of Kirchhofe’s scale on my Map; this shadow or belt
stands out like a wall at sunset, and then not only comes into existence itself, but
with it come 1108, 1114, and 1121, which I could not see sun high, nor has Kirch-
hoff shown.
6. I now turn to another fact. When the autumn has well advanced here, there springs
up from the plain country, stretching away S.E. and S.W. by W., a kind of haze which
becomes visible at sunset, and which grows day by day in height until it attains to
perhaps 3° or more above the horizon ; this haze, moreover, grows denser daily, until at
last it is sufficiently opaque to obscure the sun’s rays. I need not in this place enter
into the causes which produce this haze ; it is sufficient to remark here that I have
noticed it year after year, and from its opacity and its formation occurring just before
winter, I always call it “ the winter bank ;” indeed I remember talking about it one
evening with the late Archdeacon Pratt, who also had noticed it, in connexion with
some other fact. N ow this haze bank practically compelled the sun to set whenever
160
ON THE ATMOSPHERIC LINES OE THE SOLAR SPECTRUM.
the latter sank behind the former ; so that in the first autumn of my observations the
appearance of the haze obliged me to close work for the season. Subsequently it
occurred to me that the gradual growth in height of this haze gave me exactly the very
test I required, viz. sunset varying one day with another from a depression of 1^° to an
altitude of some 3^°. Accordingly I watched the corresponding effect on the air-lines,
and found beyond all question that as the bank rose and the corresponding sunset
occurred higher, the variable and air-lines all disappeared, each in its turn. This test
is of course most effectually applied to lines which require the lowest of sunsets to be
developed, and the behaviour of all lines is by no means the same. For instance, 813 is
almost as good as a clock to me, commencing to change so early as 2 or 3 p.m. ; whereas
712 (which is, in fact, the more prominent line eventually , and is, I believe, noticed here
for the first time) hardly presents the smallest change until the sun is under 1° of
altitude or thereabout. Similarly, my air-wall (above noticed) requires a low sunset,
but not so low as 712. The test just explained gave a visible connexion between the
atmospheric lines and the terrestrial atmosphere ; i. e. the higher the sunset, the more
the air-lines were absent. I state the fact thus briefly, notwithstanding that I tested
it day after day, and that I possess abundance of notes on the subject; these notes,
however, are in the main repetitions, which have no interest once the fact has been
announced, and I therefore refrain from transcribing them.
7. It will be seen that in the portion extreme red to D there are some slight discre-
pancies between my map of 1870 and my present map; these are solely due to the far
greater powers of the new spectroscope, and not to any want of care in preparing the
earlier map : the additions are chiefly due to the same cause, and to some extent are the
results of greater skill, which experience may have brought me. Amongst the new
lines or bands are group 315-352, the additions about A, 460, 730, 950, and else-
where, not forgetting 712 (which, I repeat, is a very prominent air-line, but only so at a
very low sunset). For further discussion of the map now submitted to the Royal
Society, and for comparison with other maps which have preceded it, I must await a
more favourable opportunity — merely remarking at present, that while looking for air-
lines I happened to detect a few other lines which do not vary, but which are not given
in Kirchhoff’s map; of this class are 1006, the pair 1310, and some others. I may
repeat my conviction, already stated in my paper dated 25th April, 1870, that besides
other changes in the light, as the sun approaches the horizon, there is this peculiarity,
that rays of less refrangibility become visible, so that the spectrum appears to be extended
towards the red end. My search, as will be seen from the map, has not as yet extended
rigorously beyond F ; indeed examination of the spectrum beyond this line is hardly
practicable for the detection of air-lines without some additional provision for collecting
light, which, however, I think I could contrive ; with my present means, but little light
reaches beyond F when the earth’s atmosphere intervenes to a depth which may be
expected to produce an effect, the brightest part of the spectrum being the portion that
is last visible at sunset.
[ 161 ]
IV. Contributions to Terrestrial Magnetism . — No. XIV.
By General Sir Edward Sabine, B.A., K.C.B., F.B.S.
Received June 18, — Read June 18, 1874.
In this paper ( i.e . the XlV.th Number of the “Contributions to Terrestrial Magnetism”)
I have the pleasure of presenting to the Royal Society the second half of the Magnetic
Survey of the Northern Hemisphere, of which the first half was presented by me last
year and is printed as No. XIII. of my “ Contributions to Terrestrial Magnetism.” These
two papers, taken together with No. XI. (appertaining to the Southern Hemisphere),
embrace fully three quarters of the entire globe.
The form in which the observations are collected in the two latest papers (No. XIII.
and the present, No. XIV.) is the same, viz. arranged in zones of latitude, each zone
beginning with the meridian of Greenwich, and passing eastward round the globe until
the same meridian is again reached. In No. XIII. these zones were eight in number,
being each 5° of latitude in breadth (excepting the last, which comprised also the few
observations north of the 80th parallel). In the present paper the zones are four in
number, each being 10° in breadth.
Zone 1, comprehending from the equator to 10° N.
Zone 2, „ „ lat. 10° N. „ 20° N.
Zone 3, „ „ „ 20° N. „ 30° N.
Zone 4, „ „ „ 30° N. „ 40° N.
The statements in the introduction to No. XIII. regarding the different Magnetic
Elements apply equally to the present paper ; it may, however, be remarked in addition,
that while the observations of Force are fewer, a larger proportion of them were made
by the observers in absolute measure, and have therefore not needed conversion ; the
remainder have been converted by the same method of proceeding as that described in
No. XIII.
In the present paper corrections for “ secular change.” have been much more
sparingly introduced. For this three reasons may be assigned : — the first being the very
satisfactory one that a larger proportion of the observations are at dates differing by so
few years from the Mean Epoch (1840-45) that any corrections on this account may
well be dispensed with ; another being, that in this part of the globe more of the earth’s
surface is covered by the ocean, and it has not been thought advisable in either paper
to correct “ Sea Observations ” for differences of epoch (regarding these generally as
less influential than differences of “ Ship’s Attraction ”) ; the third reason being of a
MDCCCLXXV. Z
162
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
less satisfactory character, viz. that there are generally fewer available grounds for
assigning “ secular change ” on tolerably sufficient and accordant evidence.
I have now to offer again, and in increased measure, my most grateful acknowledg-
ments to Captain Frederick John Evans, R.N., the present Hydrographer of the
Admiralty, for his most valuable assistance in many ways, but preeminently in the
superintendence of the formation and execution of the Maps (Plates 26-28) embodying
the results.
ZONE I.— LATITUDES, EQUATOR TO 10° N.
Authorities.
Denham MSS. in the Magnetic Office, received from the Hydrographic Office.
Sabine Pendulum and other Experiments (1825).
Allen MSS. in the Magnetic Office, received from the Author.
Owen L. S. Kamtz ; MSS. in the Magnetic Office, Kew Observatory.
De Clerval L. S. Kamtz ; MSS. in the Magnetic Office.
Baikie MSS. in the Magnetic Office, received from the Observer.
Yidal Sabine in Philosophical Transactions, 1849.
Basevi Reports of the Great Trigonometrical Survey of India.
Laplace L. S. Kamtz • MSS. in the Magnetic Office.
Taylor & Caldecott . . Schlagintweit ; Scientific Mission to India and High Asia (Leipzig and London, 1861).
Powell Schlagintweit ; Scientific Mission to India and High Asia.
Franklin Schlagintweit ; Scientific Mission to India and High Asia.
Ludlow MSS. in the Magnetic Office.
Novara (Austrian Frigate) Reise um die Erde (Wien, 1862-65).
Blosseville Schlagintweit ; Scientific Mission to India and High Asia (Leipzig, 1861).
Belcher MSS. in the Magnetic Office, received from Admiral Sir Edward Belcher.
Schlagintweit Scientific Mission to India and High Asia (Leipzig and London, 1861).
Elliot Magnetic Survey of the Indian Archipelago, Philosophical Transactions, 1851.
Bonite Yoyage de la Bonite (Paris, 1842).
Bougainville L. S. Kamtz ; MSS. in the Magnetic Office, Kew.
Stanley Contributions to Terrestrial Magnetism, Sabine in Philosophical Transactions, 1849.
Prussian Ships .L. S. Kamtz; MSS. in the Magnetic Office, Kew.
..^ f Mem. by Lenz in the Sci. Mem. of the Acad, of St. Petersburg ; and L. S. Kamtz, MSS
l in the Magnetic Office, Kew.
D’Urville L. S. Kamtz ; MSS. in the Magnetic Office, Kew.
Duperrey L. S. Kamtz ; MSS. in the Magnetic Office, Kew.
Erman Reise um die Erde (Berlin, 1841).
FitzRoy Yoyage of the ‘ Beagle,’ 1849.
Barnett L. S. Kamtz ; MSS. ; and MSS. received from the Observer (Capt. Barnett).
Austin L. S. Kamtz ; MSS. in the Magnetic Office, Kew.
Horne L. S. Kamtz ; MSS. in the Magnetic Office, Kew.
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
163
Emory TJ. S. Coast-Survey Reports ; and Memoirs of American Academy, vols, v. & vi. 1857.
Kellett MSS. in the Magnetic Office, received from Admiral Kellett.
Foster Kamtz ; MSS. in the Magnetic Office, Kew.
Haig Phil. Trans. 1862.
Friesach . Memoirs of the Imperial Academy of Sciences, Vienna, vols. 29-44.
Harkness Smithsonian Contributions, vol. xviii.
Boussingault L. S. Kamtz ; MSS.
Schomburgk MSS. received from the Observer.
Hudson L. S. Kamtz ; MSS.
Sulivan Sabine in Phil. Trans. 1840.
Rumker )
Young ( L. S. Kamtz ; MSS. in the Magnetic Office, Kew.
Smith j
Du Petit Thouars . . Sabine in Philosophical Transactions, 1849.
James Ross MSS. in the Magnetic Office, received from Admiral Sir James Ross.
Collinson MSS. received from the Hydrographic Office.
Berard MSS. in the Magnetic Office, received from Admiral Duperrey.
Stanley Sabine in Philosophical Transactions, 1849.
Dunlop L. S. Kamtz, MSS. ; and Sabine in Phil. Trans. 1840.
MSS. in the Magnetic Office, Kew.
Lefroy
Dayman
H.M.S. ‘Fly’ ..
The ‘John Fleming ’J
Z 2
164
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
NORTH EQUATORIAL ZONE I.— Lat. Equator to 10° N.
Declination.
Inclination.
Stations.
Lat. N
Long. E.
Date.
Ob-
served.
Correction
to Epoch
1842-5.
Corrected.
Ob-
served.
Cor. to
Epoch
1842-5.
-Corrected.
Force in
British units.
Observers. 1 ■
° /
o ,
o /
o /
0
0 ,
° /
o
5 55
1 00
1846
19 55 w
19-9 w.
Denham.
At sea (5 observations)
5 50
1 29
1846
20 39 w
20-7 w.
Denham.
6 13
1 36
1846
20 21 w
20-4 w.
Denham. .
Whydah
6 19
2 05
1846
20 08 w
201 w
Denham.
At sea (6 observations)
6 12
2 05
1846
19 19 w
19-3 w.
Denham.
6 24
2 53
1846
20 30 w
20-5 w.
19-9 w.
Denham.
At sea (3 observations)
6 21
2 53
1846
19 51 w
Denham.
6 24
3 27
1846
19 36 w
19-6 w
Denham.
At sea (2 observations)
5 39
4 09
1846
20 47 w
20-8 w.
Denham.
At sea (4 observations)
5 19
5 03
1846
19 55 w
19-9 w.
Denham.
At sea (5 observations)
4 56
5 23
1846
20 25 w
20-4 w.
Denham.
At sea (5 observations)
4 48
5 32
1846
19 21 w
19-4 w.
Denham.
Middleton River
4 32
5 41
1846
19 50 w
19-8 w.
Denham.
At sea (6 observations)
4 06
5 55
1846
19 39 w
19-7 w.
Denham.
At sea (2 observations)
4 10
6 00
1846
19 23 w
19 4 w.
Denham.
0 25
6 45 |
1822
22 47 w.
22-8 w.
0 04 s.
01 s.
7-19
Sabine.
Owen.
1826
Opposite Kende, on 1
the Tsbadda /
8 01
7 16
1854
6 07 n.
61 N.
Baikie.
1 41
7 27 |
1827
18 56 w.
18-8 w.
3 33 s.
3-6 s.
De Clerval.
Allen.
1842
7 07
7 49
1835
19 51 w.
19-9 w.
Allen.
7 45
8 29
1854
4 38 n.
4-6 n.
Baikie.
1826
22 00 w.
Owen.
/
1836
19 50 w.
19*8 w. I
1 °
Vidal.
Fernando Po
3 45
8 45 j
1842
1 19-5 w.
2 13 s.
2-2 s.
Allen.
1846
19 04 w.
191 w..
Denham.
Rabba
6 27
9 13
1835
20 36 w.
20-6 w.
Allen.
Corisco Bay
0 55
9 20
1836
20 04 w.
201 w.
Vidal.
Cameroon’s Eiver
3 55
9 30
1836
19 46 w.
19 8 w.
Vidal.
Magadoxa
2 02
43 20
1825
9 00 w.
9-0 w.
Owen.
Bhava
1 07
43 58
1825
10 00 w.
1 00 w
Owen.
Minicoy
8 17
73 02
1870
0 16 b.
0 28 e.
0-7 E.
0 3 w.
3 48 s.
0 28 n.
3-3 s.
7-97
Basevi.
Andomnatis Island . . .
1 26
73 26
1830
0 15 w.
Laplace.
Balghatty
9 59
76 14
1838
0 19 n.
0 04 s.
0-3 n.
Taylor and Cal'bott.
Basevi.
Aleppy
9 30
76 20
1870
0 36 e.
0 28 e.
M E.
1 41 s.
0 28 n.
1-2 s.
799
Quilon
8 54
76 40
1838
2 22 s.
0 04 s.
2-4 s.
Taylor and Caljeott.
Taylor and Cabcott.
1838
1
3 15 s.
0 04 s.
3-3 s.
Trevandrum
8 29
76 56 |
1841
0 40 e.
0-7 e.
| 0-7 e.
Caldecott.
1855
0 27 e.
0 13 e.
0-7 e. J
Broun.
Nagraeoil
8 11
77 25
1838
3 53 s.
0 04 s.
3-9 s.
Taylor and Ca|cott.
Powell.
Near Cape Comorin . . .
8 03
77 35
1843
1 10 E.
1-2 e.
Punnae
8 10
77 41
1869
0 45 e.
0 27 e.
1-2 v.
3 21 s.
0 27 n.
2-9 s.
807
R
Basevi.
Kudankolam
8 11
77 45
1869
0 44 e.
0 27 e.
1-2 E.
3 34 s.
0 27 n.
3T s.
8-08
Basevi.
Palameottah
8 44
77 45
1838
2 46 s.
0 04 s.
2-8 s.
Taylor and Ca&cott
Franklin.
Tinnevelly Coast
8 00
77 50
1846
0 10 E.
0-2 e.
Powani
8 49
77 54
1838
2 46 s.
0 04 s.
2 8 s.
Taylor and Cajecott.
Basevi.
Mallapatti
9 29
78 04
1869
0 52 e.
0 27 e.
1-3 E.
0 37 s.
0 27 n.
0-2 s.
8-03
Yadinatrum
8 57
78 07
1838
1 34 s.
1-6 s.
Taylor and Caecott. ,
Franklin.
Trichendor
8 30
78 08
1842
1 58 e.
2-0 e.
Tutocorin
8 48
78 10 |
1838
2 38 s.
2-6 s.
Taylor and Ca lecott.
1842
0 51 e.
u*y e.
Franklin.
Carrysbandy
9 11
78 24
1838
1 52 s.
1-9 s.
Taylor and Cdecott.
Franklin.
Tinnevelly Coast
8 25
78 25
1846
1 58 e.
2-0 e.
Tinnevelly Coast
8 40
78 30
1846
0 51 e.
0 9 e.
Franklin.
Palk Strait
9 03
78 35
1838
0 51 e.
0-9 e.
Powell.
Eamnad
9 22
78 51
1838
1 25 s.
1-4 s.
Taylor and Cdecott.
Taylor and Caecott.
Xalehennary
9 40
78 57
1838
0 06 n.
01 N.
Devaputnum
9 29
78 58
1844
0 35 s.
0 6 s.
Ludlow.
Tonday
9 45
79 05
r
1844
0 08 n.
0-1 N.
Ludlow.
1837
0 35 w.
0-6 w.
1 °
Powell.
Paumben
9 17
79 161
1838
1 36 s.
1-6 s. 1 1-2 s.
Taylor and Cjdecott.
Ludlow.
1844
0 45 s.
0-8 s. J
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
165
NORTH EQUATORIAL ZONE I.— Lat. Equator to 10° N. (continued).
Declination.
Inclination.
Lat. N
Long. E.
Date.
Ob-
served.
Correction
to Epoch
1842-5.
Corrected.
Ob-
served.
Cor. tc
Epoch
1842-5.
1
Corrected.
Eoree in
British units.
Observers.
0 /
o ,
■o /
o
° '
o
9 30
79 18
1838
0 30 e.
0-5 e.
Powell.
9 17
79 36
1844
0 45 s.
0-8 s.
Ludlow.
9 28
9 32
79 38
1844
0 12 s.
0-2 s.
Ludlow.
79 42 |
1838
1 40 e.
1-7 E.
Powell.
1844
0 31 s.
0-5 s.
Ludlow.
7 41
79 44
1844
0 13 e.
0-2 e.
Powell.
5 24
79 47
1858
0 37 e.
0'6 e.
Novara.
9 46
79 49
1844
0 20 n.
0-3 n.
Ludlow.
8 32
79 50
1845
1 15 E.
1-3 E.
Franklin. 1
8 59
79 54 |
1844
1845
1 04 e.
Me.
1 16 s.
1-3 s.
Ludlow.
Franklin.
9 47
79 56
1828
1 16 E.
1-3 E.
0 37 s.
0-6 s.
Blosseville.
8 27
80 01
1833
2 18 s.
2-3 s.
Blosseville.
9 40
80 01 |
1833
1844
1 16 E.
1-3 E.
0 40 s.
0 02 s.
s- 1 o-3 s
0-0 s.)Uds-
Blosseville.
Ludlow.
9 06
80 09
1844
1 13 s.
1-2 s.
Ludlow.
6 15
80 10
1839
1 15 E.
1-3 E.
Powell.
6 03
80 11 1
1842
1856
0 41 e.
0 41 e.
......
8 07 s.
7 41 s.
8'1 S. \ *.Q
7-7 s.j79s-
8-02 1 8-05
8 08 ) 8 05
Belcher.
Schlagintweit.
9 40
80 12
1844
0 04 s.
0-1 s.
Ludlow.
9 50
80 15
1844
0 42 n.
0-7 n.
Ludlow.
8 34
81 18 |
1833
1 08 e.
ri e.
Blosseville.
1837
2 37 s.
2-6 s.
Anon. (Hydr. Office).
0 42
82 02
1858
0 32 e.
0-5 e.
Novara.
8 22
82 42
1858
0 44 e.
0-7 e.
Novara.
6 44
84 08
1858
0 56 e.
0-9 e.
Novara.
4 02
85 48
1858
0 55 e.
0-9 e.
Novara.
9 10
92 15
1858
1 46 e.
1-8 E.
Novara.
9 14
92 45
1858
2 00 e.
2-0 e.
1 19 N.
1-3 N.
8-19
Novara.
9 10
92 48
1848
1 53 e.
1-9 E.
1 15 N.
1-3 N.
8-16
Elliot.
8 14
93 19
1848
0 23 s.
0-4 s.
Elliot.
8 02
93 35 |
1848
0 54 s.
0-9 s.
Elliot.
1858
2 00 e.
20 e.
Novara.
7 12
93 40
1857
3 00 s.
3 0 s.
Novara.
6 48
93 50
1858
1 55 e.
1-9 E.
Novara.
9 05
94 05
1837
2 35 e.
2-6 e.
Bonite.
7 17
94 30
1858
2 09 e.
2-2 e.
Novara.
5 41
95 24
1842
2 22 e.
2-4 e.
5 29 s.
5 5 s.
8-07
Belcher.
5 36
95 25
1842
2 22 e.
2-4 e.
5 58 s.
6-0 s.
8-06
Belcher.
7 18
96 40
1837
2 27 e!
2-5 e.
Bonite.
6 48
97 20
1858
1 53 e.
1-9 E.
Novara.,
1 18
97 41
1848
1 44 e.
1-7 E.
14 06 s.
14-1 s.
Elliot.
2 17
97 52
1848
1 34 e.
1-6 E.
12 24 s.
12-4 s.
Elliot.
7 18
97 56
1837
2 34 e.
2-6 e.
Bonite.
2 01
98 32
1848
1 17 E.
1-3 E.
12 58 s.
13 0 s.
Elliot.
1 45
98 56
1848
1 41 E.
1-7 E.
13 03 s.
13-1 s.
Elliot.
0 34
99 20
1848
1 28 E.
1-5 E.
15 32 s.
15-5 s.
Elliot.
1 23
99 23
1848
13 47 s.
13-8 s.
Elliot.
0 44
99 31
1848
15 03 s.
15-1 s.
Elliot.,
0 51
99 32
1848
1 44 e.
1-7 E.
14 48 s.
14-8 s.
Elliot.
0 42
99 43
1848
1 35 e.
1-6 E.
15 20 s.
15-3 s.
Elliot.,
0 39
99 47
1848
15 42 s.
15-7 s.
Elliot.
0 36
99 52
1848
1 39 e.
1-7 E.
15 50 s.
15-8 s.
Elliot.
0 33
99 57
1848
1 37 e.
1-6 E.
15 37 s.
15-6 s.
Elliot.
0 24
100 04
1848
15 35 s.
15-6 s.
Elliot.
f
1837
1 34 e.
1-6 E. 1
4 25 s.
4-4 s. 1
1
Bonite.
5 26
100 25 \
1841
1 30 e.
1-5 E. 1 16 E.
4 40 s.
4-7 s. 1 4-7 s.
8-20 l 8-20
Belcher.
\
1848
1 49 e.
1-8 E.J
4 53 s.
4-9 s. J
8-19 J
Elliot. ...
4 13
100 33
1848
1 49 e.
1-8 E.
7 31 s.
7-5 s.
8-19
Elliot.
4 20
100 40
1824
2 26 e.
2-4 E.
Bougainville.
2 50
101 20
1824
1 30 e.
1-5 E.
Bougainville.
ipi Strait
Pa rayan Eattoo
Pairyn
M kbandi
mg.iddaway
W Dast of Ceylon .
Gli ichemy
Pd Pedro
Tii omalee
A* i (2 observations)
(2 observations)
Ail i (2 observations)
All a (6 observations)
Al i (3 observations)
Sa Carnicobar .
H par
B >oko
S' jvri Harbour
C| ul Islar.il
■In i!i ^ a (2 observations)
, ... m ra I:
■torf
i Island
a (3 observations)
a (2 observations)
Ai a (2 observations)
11 s
:ha ;;;;;;;
i
ng Sidompang
■ Batoo
Elout
nopan
ghay
Penang .
Dinding ...
ing Point ...
it Parcellus
166
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
NORTH EQUATORIAL ZONE I.— Lat. Equator to 10° N. (continued).
Malacca .
Mount Ophir.
Pulo Peesang.
Singapore ....
Palo Booaya .
At sea
Anambas Island
Victory Island . .
At sea. ,
At sea. ,
At sea (2 obser1
Pigeon Island
Permanket
Tanjong Api . .
At sea...
Sambas
Santubon
Kuching..
Sarawak
At sea (2 observations)
Moarroo Island,
At sea
Palo Labuan ....
Pulo Teega
Amboong
Mantanini
Batemande Eock
At sea
Balambangan
At sea
G-unung Tabor
Cagayan (Sooloo)
Legeetan Islands
Unsang
Samarang Island
Koolassian Island :
Islet off C. Elvers')
(Celebes) J
At sea
Solo Bay (Sooloo).
Cagayan Island....
Salliolookit Eock .
Samboangan
Samboanga
At sea
Tondano . .
Manado Bay .
Keemah
Lat. N.
Long. E.
Date.
Declination.
Inclination.
Force in
British units.
Observers. |
Ob-
served.
Correction
to Epoch
1842-5.
Corrected.
Ob-
served.
Cor. to
Epoch
1842-5.
Corrected.
0 /
0 /
0 /
0
o /
°
1
r
1837
1 °
10 48 s.
10-8 s. ) °
Bonite.
2 10
1841
1 36 e.
1-6 e. Li-7e.
11 02 s.
.. 11*0 s. 1 11-1 s.
8-28 1 8-28
Belcher.
102 19 j
1848
1 50 e.
1-8 E.J
11 25 s.
11-4 s.
8-28 J
Elliot.
2 22
102 38
1848
9 55 s.
9-9 s.
8-26
Elliot.
1 28
103 19
1846
1 31 E.
Elliot.
0 59
103 27
1846
1 23 e.
Elliot.
1837
1
12 29 s.
12-5 s. 1
1
Bonite.
1 19
103 57 j
1843
1 43 e.
1-7 E. 1 1-7 E.
12 27 s.
12-5 s. i 12-6 s.
1 8-32
Belcher.
1846
1 36 e.
1-6 E.J
12 55 s.
12-9 s.J
8-32 J
Elliot.
0 09
104 21
1846
1 29 e
Elliot.
4 40
104 50
1837
2 21 e.
2-4 e.
Bonite.
0 38
105 14
1858
1 21 E.
1-4 e.
Novara.
0 22
106 06
1843
13 08 s.
13-1 s.
Belcher.
3 10
106 19
1825
1 07 e.
11 E.
Bougainville.
1 19
106 32
1825
1 12 E.
1-2 E.
Bougainville. I
1 48
106 40
2 00 e.
2-0 e.
Novara.
1 31
107 10
1843
10 29 s.
10-5 s.
Belcher.
8 33
107 29
1837
2 10 e.
2-2 e.
Bonite.
5 30
107 35
1858
2 06 e.
21 E.
Novara.
4 39
107 51
1831
1 30 e.
1-5 E.
Laplace.
8 40
108 02
1828
0 37 e.
0-6 e.
Prussian ships.
1 06
108 05
1829
0 10 e.
0-2 e.
Liitke.
2 37
108 12
1846
1 32 e.
1-5 E.
19 40 s.
19 7 s.
Belcher.
1 10
109 04
1848
1 10 E.
1-2 E.
12 36 s.
12 6 s.
8-38
Elliot.
1 56
109 20
1844
0 09 e.
0-2 E.
11 05 s.
11-1 s.
Belcher.
1 51
109 25
1843
9 22 s.
9-4 s.
Belcher.
1 22
109 28
1848
1 16 E.
1-3 E.
11 31 s.
11-5 s.
8-33
Elliot.
1 42
109 51
1843
1 29 e.
1-5 E.
10 27 s.
10-5 s.
Belcher.
1 43
110 20
1843
1 30 e.
1-5 E.
10 36 s.
10-6 s.
Belcher.
1 33
110 22
1843
1 28 e.
1-5 E.
10 46 s.
10-8 s.
Belcher.
1 34
110 29
1848
1 10 E.
1-2 E.
11 15 s.
11-3 s.
8-35
Elliot.
9 23
111 12
1858
2 00 e.
2-0 e.
Novara.
5 00
115 08
1843
1 17 e.
1-3 E.
3 10 s.
3-2 s.
Belcher.
7 22
115 08
1843
2 15 n.
2-3 n.
Belcher.
5 17
115 18
1848
1 36 e.
1-6 E.
2 52 s.
2-9 s.
8-25
Elliot.
5 43
115 35
1845
1 16 E.
1-3 E.
1 48 s.
1-8 s.
Belcher.
6 18
116 19
1844
1 20 e.
1-3 E.
0 35 s.
0-6 s.
Belcher.
6 40
116 22
1844
1 38 e.
1-6 E.
0 16 s.
0-3 s.
Belcher.
6 50
116 32
1845
0 46 e.
1-8 E.
0 41 s.
0-7 s.
Belcher.
8 24
116 35
1844
3 32 n.
3-5 n.
Belcher.
7 12
116 49
1845
0 50 e.
0-8 e.
1 20 s.
1*8 s.
Belcher.
9 56
117 09
1844
7 20 n.
7-3 n.
Belcher.
2 10
117 30
1845
0 30 e.
0-5 e.
9 04 s.
9-1 s.
Belcher.
6 58
118 24
1845
0 12 e.
0-2 e.
0 56 n.
0-9 n.
Belcher.
4 19
118 31
1845
0 45 e.
0-8 e.
4 49 s.
4-8 s.
Belcher.
5 17
119 16
1845
1 02 e.
10 E.
2 34 s.
2-6 s.
Belcher.
5 28
120 15
1845
0 40 e.
0-7 e.
1 53 n.
1-9 N.
Belcher.
6 25
120 25
1845
0 46 e.
0-8 e.
Belcher.
1 20
120 45
1844
1 01 E.
l'O E.
10 40 s.
10-7 s.
Belcher.
1 34
120 57
1844
9 48 s.
9-8 s.
Belcher.
6 03
121 00
1844
0 34 e.
0-6 e.
1 44 n.
1-7 N.
Belcher.
9 36
121 15
1844
0 12 e.
0-2 e.
7 38 n.
7-6 n.
Belcher.
6 49
121 24
1844
0 17 e.
0-3 e.
0 20 n.
0-3 n.
Belcher.
6 55
122 05
1844
1 12 E.
1-2 E.
1 29 n.
15 N.
Belcher.
6 54
122 14
1848
1 15 E.
1-3 E.
1 18 N.
1-3 N.
8-16
Elliot.
1 11
122 21
1844
11 00 s.
11-0 s.
Belcher.
1 18
124 50
1848
1 08 e.
Mb.
10 54 s.
10-9 s.
Elliot.
r
1828
1 06 e.
1-1 E.l
1
D’Urville.
1 30
124 50 |
1845
1 37 e.
1-6 E. t 1-4 E.
10 22 s.
10-4 s. 1 10-5 s.
Belcher.
[
1848
1 26 e.
1'4 E. J
10 44 s.
10-7 s.J
Elliot.
1 22
125 08
1848 !
1 40 e.
1-7 E.
11 01 s.
|
11-0 s.
8-41
Elliot.
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
167
NORTH EQUATORIAL ZONE I. — Lat. Equator to 10° N. (continued).
Declination.
Inclination.
Long. E.
Date.
Ob-
served.
Correction
to Epoch
1842-5.
Corrected.
Ob-
served.
Cor. to
Epoch
1842-5.
Corrected.
Force in
British units.
Observers.
o /
° /
o
o ,
c
127 15
1845
0 40 e.
0'7 e.
11 37 s.
11-6 s.
Belcher.
129 50
1823
0 21 e.
0-4 e.
Duperrey.
134 47
1823
1 55 e.
1-9 E.
13 05 s.
13-1 s.
Duperrey.
136 10
1828
1 37 e.
1-6 E.
D’Urville.
143 56
1824
0 53 e.
0-9 e.
12 14 s.
12 2 s.
Duperrey.
143 57
1828
3 07 e.
31 E.
0 39 n.
0-7 n.
7-81
Liitke.
145 47
1828
3 20 e.
3-3 e.
Liitke.
147 03
1824
3 20 e.
3-3 e.
6 ’ 33 s.
0-6 s.
Duperrey.
151 33
1824
5 42 e.
5-7 e.
1 11 N.
1-2 N.
Duperrey.
152 00
1828
5 40 e.
5-7 e.
D’Urville.
152 38
1824
4 03 e.
4-1 E.
Duperrey.
153 58
1828
6 29 e.
6-5 e.
0 46 s.
6-8 s.
7-76
Liitke.
155 25
1824
6 34 e.
6-6 e.
4 36 k.
4-6 n.
Duperrey.
156 20
1828
7 26 e.
7-4 E.
Liitke.
157 05
1828
7 00 e.
7-0 e.
1 38 s,
1-6 N.
7*72
Liitke.
157 45
1858
7 38 e.
7-6 e.
Novara.
158 02
1827
8 00 e.
8-0 e.
5 16 n.
5-3 n.
7-70
Liitke.
159 41
1858
8 33 e.
8-6 e.
Novara.
161 06
1858
8 29 e.
8-5 e.
Novara.
161 26
1858
8 34 e.
8-6 e.
Novara.
162 03
1828
8 47 e.
8-8 e.
Liitke.
162 26
1827
8 45 e.
8-8 e.
Liitke.
162 50
1827
8 58 e.
9-0 e.
1 39 s.
1-7 s.
7-92
Liitke.
162 54
1827
9 00 e.
9-0 e.
0 37 n.
0 6 n.
7-78
Liitke.
162 59
1827
0 30 s.
0-5 s.
7-85
Liitke.
163 23 j
1824
1828
9 20 e.
8 51 e.
9-3e’19-1e
8-9 e.)91e-
3 11 N.
2 55 k.
2-9 ;:}*° n-
Duperrey.
Liitke.
167 32
1824
9 07 e.
9-1 E.
4 48 k.
4-8 k.
Duperrey.
172 23
1824
9 08 e.
9-1 E.
2 58 n.
3 0 n.
Duperrey.
173 11
1824
8 21 e.
84 e.
1 25 n.
1-4 N.
Duperrey.
229 32
1834
4 13 e.
4-2 e.
Prussian ships.
229 54
1830
4 04 e.
41 E.
Erman.
229 55
1830
4 06 n.
4-1 N.
7-34
Erman.
230 44
1830
3 34 n.
3-6 k.
7-53
Erman.
231 33
1827
5 00 e.
5-0 e.
Liitke.
231 33
1827
5 05 e.
5-1 E.
Liitke.
232 08
1827
4 42 e.
4-7 e.
8 46 n.
8-8 n.
Liitke.
232 15
1830
3 28 n.
3*5 n.
Erman.
232 26
1830
4 17 e.
4-3 e.
Erman.
232 43
1830
5 14 k.
5*2 n.
7-37
Erman.
233 17
1830
7 21 n.
7*4 n.
7-56
Erman.
233 26
1829
5 19 e.
5-3 e.
Prussian ships.
233 40
1830
4 07 e.
4-1 E.
Erman.
234 06
1830
9 19 n.
9-3 k.
7-61
Erman.
234 45
1831
4 43 e.
4-7 e.
Prussian ships.
235 37
1830
13 03 k.
13-1 N.
7-72
Erman.
235 45
1830
4 31 e.
4-5 e.
Erman.
235 49
1830
23 06 n.
[231 n.
8-23
Erman.
235 51
1830
20 15 k.
20-3 n.
7-99
Erman.
235 56
1827
4 46 e.
4-8 e.
5 43 k.
5-7 n.
Liitke.
236 14
1830
5 12 e.
5-2 e.
.
Erman.
236 25
1830
17 29 n.
1 7‘5 k.
7-85
Erman.
236 28
1830
15 32 n.
... 155 k.
7-83
Erman. .
236 30
1830
4 06 e.
4-1 E.
Erman.
254 31
1836
8 19 e.
8-3 e.
Bonite.
256 22
1836
6 43 e.
6-7 e.
Bonite.
256 54
1836
1 7 10 e.
7-2 e.
Bonite.
258 31
1836
7 28 e.
7-5 e.
Bonite.
262 33
1834
| 8 43 e.
8-7 e.
FitzRoy.
263 06
1836
7 32 e.
7-5 e.
Bonite.
265 31
1836
8 21 e.
8-4 e..
Bonite.
268 55
1834
9 35 e.
9-6 e.
FitzRoy.
Stations.
ng Island
sea (2 observations)
sea (2 observations)
sea(28 observations)
sea (3 observations)
sea (4 observations)
;unor
sea (2 observations)
ea(22 observations)
Valientes
sea (5 observations)
sea (4 observations)
sea (7 observations)
sea (5 observations)
sea (8 observations)
sea (2 observations)
sea (2 observations)
| sea (2 observations)
sea (2 observations)
ea (2 observations)
ea (2 observations)
ea (4 observations)
■ea (2 observations)
sea (4 observations)
■ea (3 observations)
ea (2 observations)
1 ea
ea (3 observations)
■ea (2 observations)
ea(12 observations)
ea (4 observations)
ea
ea (2 observations)
ea (2 observations)
■A ea (2 observations)
4 ea
a (2 observations)
(5 observations)
0 44
0 18
0 03
8 03
0 41
7 22
8 10
6 40
7 13
7 02
7 29
5 29
8 28
6 17
5 46
8 14
6 55
5 23
3 25
0 58
6 35
3 31
2 56
4 17
3 47
5 50
2 46
0 32
7 20
0 05
0 10
0 04
3 33
6 24
2 24
0 09
0 26
0 46
1 33
7 51
2 15
2 42
2 15
4 35
4 49
9 43
8 33
0 35
7 53
6 51
5 49
6 12
9 33
7 46
6 57
0 22
0 10
4 55
4 05
0 51
168 GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
NORTH EQUATORIAL ZONE I. — Lat. Equator to 10° N. (continued).
Declination.
Inclination.
Stations.
Lat. N.
Long. E.
Date.
Ob-
served.
Correction
Ob-
served.
Cor. to
Force in
British units.
Observers. !
to Epoch
1842-5.
Corrected.
Epoch
1842-5.
Corrected.
5 34
272 58
1838
8 24 b.
23 14 n.
23 2 n.
8-81
Belcher.
9 00
278 05
f
1839
7 28 e
7-5 e.
6-5 e. 1
31 11 N.
31-2 n.
1
Barnett.
1831
6 28 b.
1 0
I
Austin.
9 20
280 00 |
1834
6 46 e.
6-8 e.
i 6-7 e.
32 30 n.
32-5 n. |
32-3 n.
1 8-75
Horne.
Barnett.
1840
i
l
1849
6 55 b.
6-9 e.
I
32 11 n.
32-2 n.J
1
8-75 J
Emory.
0 52
280 06
1846
8 49 e.
Kellett.
9 32
280 22
1830
32 42 n.
327 n.
Foster.
8 48
280 28 |
1846
6 34 e.
6-6 e. ]
> 6 6 e.
9-08
Kellett.
Haig.
1858
J
f
1837
7 02 e.
7-0 e. )
31 52 n.
31-9 n.'
1
9-03 )
Belcher.
1849
6 55 e.
6-9 e.
32 00 n.
320 n. 1
8-75 |
Emory.
8 57
280 29 j
1858
1
► 6-5 e.
32 21 n.
32-4 n. 1
j.31-9 n.
1
9 07 18-96
Haig.
Friesach.
1858
6 17 e.
6-3 e. j
31 12 n.
31 -2 n.
1
1866
5 36 e.
5-6 e. )
31 56 n.
31-9 n. j
I
8-97 j
Harkness.
0 30
281 45
J831
18 25 n.
18-4 n.
Boussingault. j
Kellett.
3 00
281 50 |
1846
7 24 e.
7-4 e. ]
■ 7-4 e.
| 31 "8 n.
8-72
1849
J
31 47 n.
31 -8 n.
Emory.
0 48
282 22
1857
7 08 e.
7 09 e.
7 08 e.
71 E.
7- 2 e.
7-1 E.
Friesach.
1 12
282 38
1857
1846
Friesach.
3 49
282 44
Kellett.
6 06
283 09
1825
28 10 n.
28-2 n.
Boussingault. I ■ j,
Boussingault.
Friesach.
2 38
283 20 (
1831
6 58 e.
7 0 e.
20 47 n.
20-8 n. '
[ 20-9 n.
■ ■ 1 8-05
1 857
21 00 n.
21-0 n.J
8-05 j
Carthago
4 45
283 54
1830
25 52 n.
25-9 n.
Boussingault. i
Boussingault. J
Boussingault. , i
Boussingault. ,
Bio Suno
5 26
284 29
1825
27 20 s.
27-3 n.
Bio Negro
6 18
284 30
1825
28 12 n.
28-2 n.
Vega de Sapia
5 28
284 33 1
1825
27 14 n.
27-2 n. 1
1 27-5 n.
1830
27 40 n.
277 n. J
Boussingault. ; g.
Paraneo
5 24
284 46
1829
26 37 n.
26-6 n.
Boussingault. j u
Boussingault. j i ;>1
Boussingault. j ,;t
Mariquita
5 13
284 58
r
1825
26 50 n.
26-8 n.
1825
25 51 n.
25-9 n. 1
1
Santa Fe de Bogota . . .
4 36
285 46 J
1829
25 59 n.
26-0 n.
\ 25-6 n.
18-28
Boussingault. , gj
1857
6 10 e.
6-2 e.
24 54 n.
24-9 n. J
8-28 J
Friesach.
Serinza
5 46
286 32
1829
28 30 n.
28-5 n.
Boussingault. 1
Boussingault. p r/
Kellett.
Socorro
6 41
286 44
1829
29 54 n.
29-9 n.
Esmeralda...
3 11
289 17
1846
7 59 e.
8-0 e.
Junction of Wenamu 1
and Cuyuni J
6 44
298 45
1843
3 53 e.
3-9 e.
33 33 n.
33-6 n.
8-73
Schomburgk. j
Mean of Boraima 1
and “OurYillage” J
5 03
299 01
1842
4 07 e.
4-1 E.
31 00 n.
31-0 n.
8-40
Schomburgk. j
Torong Yauwise
4 17
299 42
1842
3 56 e.
3-9 e.
30 06 n.
30-1 n.
8-46
Schomburgk. ;
Mouth of Cotinga
3 22
299 48
1842
4 32 e.
4-5 e.
28 25 n.
28-4 n.
8-52
Schomburgk. J ,
Tenette
2 50
300 12
1842
4 03 e.
4*1 E.
T?. .
Schomburgk. |)
Schomburgk.- n
Schomburgk. j
Schomburgk. i
G-uainia Biver
8 25
300 24
1841
2 47 e.
Pirara
3 39
300 40
1842
4 00 e.
4-0 e.
28 46 n.
28-8 n.
8-48
Penal Settlement
6 24
301 18
1843
3 58 e.
4-0 e.
George Town Obser- 1
vatory J
6 49
301 49
1841
2 41 e.
2-7 e.
34 07 n.
341 n.
8-68
Schomburgk.
Maspityan Village
1 25
301 54
1843
3 50 e.
3-8 e.
Schomburgk. |
Demerara
6 50
302 00
1837
33 57 n.
340n.
Home.
Pianoghotto
2 02
303 32
1843
3 33 e.
3-6 e.
n i ™
Schomburgk. >
Harkness.
Salute Islands
5 17
307 27
1865
0 04 w.
34 35 n.
34-6n.
8-19
At sea (4 observations)
9 39
313 30
1849
0 48 w.
0-8 w!
Hudson.
At sea
7 22
320 53
1839
39 32 n.
39-5 n.
878
Sulivan.
At sea (3 observations)
7 28
322 32
1829
4 18 w.
4-3 w.
Bumker.
At sea
5 10
322 53
1839
36 22 n.
36-4 n.
8-36
Sulivan. j -b
At sea
2 07
324 19
1839
32 02 n.
32-0 n.
7-87
Sulivan.
At sea
1 10
324 39
1839
30 32 n.
30-5 n.
7-87
Sulivan.
At sea (3 observations)
2 13
326 31
1829
6 38 w.
6 -6 w.
Bumker.
At sea(12 observations)
3 44
326 35
1849
8 23 w.
8-4 w.
Hudson.
At sea (2 observations)
7 35
327 58
1846
13 22 w.
13-4 w.
Sulivan.
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM. 169
NORTH EQUATORIAL ZONE I. — Lat. Equator to 10° N. (continued).
1
Declination.
II
Inclination.
Lat. N
Long. E.
Date.
Ob-
served.
Correction
to Epoch
1842-5.
Corrected.
Ob-
served.
Cor. tc
Epoch
1842-5
)
i Corrected.
Force in
British units.
Observers.
2 30
329 21
1830
o /
°
30 47 n.
30-8 n.
7-81
Erman.
1 40
329 24
1830
10 28 w
10-5 w.
Erman.
9 49
329 30
1830
10 00 w
10 0 w.
Young.
0 26
329 35
1830
27 16 n.
27-3 n.
7-55
Erman.
4 01
329 42
1830
11 08 w
11-1 w.
Erman.
4 26
329 45
1830
34 30 n.
34-5 n.
7- 87
Erman.
5 30
329 48
1846
13 57 w
14-0 vv.
Sulivan.
2 48
329 49
1830
j 9 57 vv
10 0 vv.
Erman.
0 41
329 56
1852
13 23 w
13-4 w.
Denham.
3 25
330 10
1846
12 49 w.
12-8 w.
Sulivan.
8 23
330 14
1851
9 30 w.
9-5 w.
Smith.
0 24
330 19
1840
7- 32
Boss.
0 51
330 35
1832
7 20 w
7-3 w.
FitzRoy.
3 22
330 36
1846
12 55 w.
12-9 w.
Sulivan.
1 00
330 37
1832
9 23 w.
9-4 w.
FitzRoy.
0 56
330 40
1840
11 50 w.
11-8 w.
27 08 n.
27-1 n.
7-46
Ross.
3 39
330 49
1836
10 27 w.
10-5 vv.
FitzRoy.
2 32
330 53
1836
10 23 w.
10-4 w.
FitzRoy.
1 20
330 55
1832
10 39 w.
10-7 w.
FitzRoy.
5 18
331 03
1852
13 43 w.
13-7 w.
Denham.
2 49
331 06
1846
12 58 w.
13 0 w.
Sulivan.
5 45
331 10
1830
35 25 n.
35-4 n.
7-68
Erman.
1 12
331 16
1838
26 27 n.
26-5 n.
7-48
Sulivan.
2 06
331 25
1839
7-47
Ross.
3 02
331 33
1852
14 11 w.
14-2 w. .
Denham.
1 57
331 38
1839
13 16 w.
13-3 w.
Ross.
2 10
332 10
1832
11 08 w.
Il l w.
FitzRoy.
7 26
332 36
1830
36 51 n.
36-8 n.
8-19
Erman.
3 18
332 46
1839
12 18 w.
12 -3 w.
29 52 n.
29-9 n.
7-52
Ross.
5 12
332 48
1852
14 44 w.
14-7 w.
Denham.
8 50
332 58
1832
12 44 w.
12-7 w.
FitzRoy.
8 33
333 16
1830
11 42 w.
11-7 w.
Erman.
9 39
333 24
1830
13 00 vv.
13 0 w.
39 12 n.
39-2 n.
8-19
Erman.
6 36
333 26
1836
14 43 w.
14-7 w.
Du Petit Thouars.
5 13
333 35
1839
7 73
Ross.
7 58
333 41
1852
15 51 w.
15-9 w.
Denham.
3 33
333 49
1842
8-02
Lefroy.
6 46
333 54
1839
14 58 w.
15 0 w.
7-83
Ross.
4 45
333 59
1839
14 21 w.
14-4 vv.
Du Petit Thouars.
2 10
333 59
1843
13 15 w.
13-3 w.
26 1 1 n.
26-2 n.
Ross.
6 42
334 04
1846
14 45 w.
14-8 w.
H.M.S. ‘ Fly.’
8 39
7 58
334 25
334 31
1850
1852
15 50 w.
15 51 w.
15-8 w.
15 -9 w.
Collinson.
Denham.
8 48
334 32
1838
37 07 n.
37-1 n.
8-19
Sulivan.
2 51
334 38
1839
14 10 w.
14-2 w.
Ross.
9 48
334 41
1839
39 12 n.
39-2 n.
8-15
Ross.
1 30
335 07
1839
14 31 w.
14 5 w.
Du Petit Thouars.
5 53
335 15
1843
14 44 w.
14-7 w.
31 21 n.
31-4 n.
Ross.
5 25
335 15
1850
16 17 w.
16-3 w.
Collinson.
6 32
335 19
1832
14 23 w.
14-4 vv.
Prussian ships.
2 38
335 27
1850
16 07 w.
161 vv.
Collinson.
4 12
335 30
1838
30 35 n.
30-6 n.
7-41
Sulivan.
8 58
335 34
1842
15 15 w.
15*3 w.
Berard.
0 09
335 35
1839
14 53 vv.
14-9 vv.
Du Petit Thouars.
2 40
335 47
1842
7-67
Lefroy.
4 10
335 49
1850
18 16 w.
18 3 w.
Collinson.
0 50
335 50
1841
19 05 n.
19-1 N.
In the ‘ J ohn Fleming.’
7 58
335 51
1852
16 40 w.
16-7 w.
Denham.
1 43
336 07
1842
7 71
Lefroy.
8 16
336 07
1843
14 23 vv.
14-4 w.
34 14 n.
34-2 n.
Ross.
2 31
336 20
1829
14 08 w.
14-1 w.
Liitke.
0 44
3t)b 22
1850
15 51 w.
15-9 w.
Dayman.
A ea (2 observations)
A 3a (2 observations)
4 sa
A] 3a
A 3a
Al ;a (4 observations)
m
St 'aul’s roots
Alta
A a
A| a
A a (2 observations)
A a
a| a :::::::::::::::::::: :
A a (2 observations)
At a
Al a
At a
Al a
Alj a (4 observations)
Al
At]
Atl a (2 observations)
At i (4 observations)
At
Ati i (4 observations)
At i
Atl i
At i (3 observations)
(2 observations)
'
ieM
At
At
loits At
. (4 observations)
i (4 observations)
(2 observations)
(2 observations)
At| l (9 observations)
(2 observations)
(3 observations)
(2 observations)
(3 observations)
(2 observations)
2 A
MDCCCLXXV.
170
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
NORTH EQUATORIAL ZONE I. — Lat. Equator to 10° N. (continued).
Declination.
Inclination.
Stations.
Lat. N.
Long. E.
Date.
Ob-
served,.
Correction
Ob-
Cor. to
Force in
British units.
Observers.
to Epoch
1842-5.
Corrected.
served.
Epoch
1842-5.
Corrected.
At sea (3 observations)
6 32
336 23
1838
0 /
0
33 45 n.
33-8 n.
7-67
Sulivan.
3 37
336 24
1850
17 10 w.
17-2 w.
Collinson.
At sea (2 observations)
1 50
336 34
1850
23 50 n.
23-8 n.
Dayman.
At sea (2 observations)
6 59
336 50
1842
14 45 w.
14-8 w.
Berard.
At sea (10 observations]
2 56
337 00
1830
13 51 w.
13-9 w.
Prussian ships.
At sea (2 observations)
6 47
337 13
1841
29 36 n.
29-6 n.
In the ‘ John Fiend),’
1 18
337 18
1822
12 57 w.
13 0 w.
23 49 n.
23-8 n.
Duperrey.
In the ‘John Flerag.’
At sea (2 observations)
3 41
337 19
1841
25 09 n.
25-2 n.
At sea (8 observations)
9 24
337 21
1847
15 07 w.
151 w.
Stanley.
At sea (8 observations]
6 40
337 22
1847
15 54 \v.
15-9 w.
Stanley.
5 50
337 24
1 846
15 11 w
w
Berard.
Stanley.
At sea(13 observations)
5 25
337 34
1847
15 54 w.
15 9 w.
At sea (6 observations)
1 11
337 36
1847
14 51 w.
14-9 w.
Stanley.
5 39
337 38
1850
13 57 w
14-0 w.
Dayman.
Liitke.
At sea (11 observations]
6 52
337 56
1828
16 02 w.
16-0 w.
At sea (2 observations)
5 38
338 00
1842
15 00 w.
15 0 w.
Berard.
At sea (2 observations)
9 25
338 01
1850
34 29 n.
34-5 n.
Dayman.
At sea(16 observations)
4 28
338 07
1847
15 42 w.
15-7 w.
Stanley.
At sea (9 observations)
2 08
338 09
1847
14 49 w.
14-8 w.
26 37 n.
Stanley.
At sea ..
2 50
338 19
1822
12 51 w.
12 9 w.
26-6 n.
Duperrey.
Berard.
At sea (3 observations)
4 57
338 38
1842
14 47 w.
14-8 w.
At sea (3 observations)
6 44
338 43
1852
17 42 w.
17-7 w.
Denham.
At sea (2 observations)
7 33
339 06
1836
16 56 w.
‘ 16-9 w.
Bonite.
At sea (3 observations)
2 28
339 17
1842
15 50 w.
15-8 w.
Berard.
At sea (3 observations)
9 03
339 21
1837
16 41 w.
16-f w.
Bonite.
At sea
7 00
339 37
1822
12 00 w.
12 0 w.
33 11 n.
33-2 if.
Duperrey.
Berard.
At sea (2 observations)
0 03
339 47
1842
17 01 w.
17 0 w.
At sea (2 observations)
1 47
340 13
1836
17 30 w.
17-5 w.
Bonite.
At sea (3 observations)
6 42
340 55
1852
17 45 w.
17-8 w.
Denham.
At sea (2 observations)
8 21
340 55
1837
17 22 w.
17-4 w.
Bonite.
At sea ....
9 43
341 00
1843
35 1 1 n.
35-2 n.
Belcher.
5 37
341 03
1831
28 57 n.
29-0 n.
7'56
Dunlop.
Liitke.
At sea (3 observations)
4 34
341 17
1826
16 47 w.
16-8 w.
At sea
5 24
341 57
342 00
1837
1843
16 30 w.
16-5 w.
Bonite.
At sea
8 27
31 44 n.
31-7 n.
Belcher.
At sea (2 observations)
4 30
342 06
1837
16 42 w.
16-7 w.
Bonite.
At sea (2 observations)
6 05
342 11
1852
18 42 w.
18-7 w.
Denham.
At spq
5 23
342 35
1831
26 13 n.
26-2 n.
7-56
Dunlop.
Belcher.
At sea.. .
7 10
342 49
1843
1837
1829
1843
1826
29 24 n.
29-4 n.
At sea. . ...
0 34
343 21
17 15 w.
1 7-3 w.
Bonite.
At sea
3 16
343 30
16 10 w.
16 2 w.
D’Urville.
At sea
5 50
343 39
25 45 n.
25-8 n.
Belcher.
Isles de Bos
9 27
346 12 |
18 00 w.
18-0 w. 1
► 17-8 w.
Owen.
1836
17 43 w.
17-7 w. I
Vidal.
At sea -.
1 53
346 20
1831
18 35 n.
18-6 n.
Dunlop.
Belcher.
At sea
3 27
346 28
r
1843
19 29 n.
19-5 n.
1826
18 48 w.
18-8 w.l
Owen.
Sierra Leone
8 30
346 44 -
1836
19 23 w.
19-4 w. |
L 19-3 w.
Vidal.
1836
19 36 vv.
19-6 w. 1
Denham.
l
1842
J
1
27 18 n.
27-3 n.
Allen.
At sea
2 15
346 48
1843
15 53 n.
15-9 n.
Belcher.
Moot Tsla,nrl ...
7 39
346 56
1836
19 17 w.
19-3 w.
Vidal.
At sea
2 37
347 40
1831
19 44 n.
19-7 n.
7-20
Dunlop.
Dunlop.
Vidal.
At sea
3 36
347 53
1831
20 05 n.
20-1 n.
7-20
G-all inas
7 00
348 21
1837
18 53 w.
18-9 w.
At sea
0 28
349 09
1843
11 28 n.
11-5 N.
Belcher.
Monrovia
6 09
349 11
1837
1837
20 07 w.
20- 1 w.
Vidal.
Cape Mesurada
6 19
349 11
19 29 w.
19-5 w.
Vidal.
3 18
349 16
f
1839
19 37 n.
19-6 n.
7-20
Dunlop.
Richardson. |
1831
19 00 w.
19-0 w. 1
•
Cape Palmas
4 22
352 16 |
1836
20 00 w.
20 0 w. 1
L 19-4 w.
Vidal.
1
1845
19 05 w.
191 w. |
Denham.
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
171
NORTH EQUATORIAL ZONE I.— Eat. Equator to 10° N. (continued).
Stations.
Lat. N.
Long. E.
Date.
Declination.
Inclination.
Force in
British units.
Observers.
#
Ob-
served.
Correction
to Epoch
1842-5.
Corrected.
Ob-
served.
Cor. to
Epoch
1842-5.
Corrected.
,pe Three Points . . .
4 45
4 48
5 06
5 10
5 32
O /
357 54
358 03
358 46 |
358 54
359 49 |
1837
1838
1838
1841
1838
1838
1846
20 03 w.
20 37 w.
20 11 w.
20 13 w.
20 18 w.
20 39 w.
20-1 w.
20-6 w.
20-2 w.
20-2 w.
20-3 w. 1 20 -5 w
20-7w.;^05 w-
■
Vidal.
Vidal.
Vidal.
Allen.
Vidal.
Vidal.
Denham.
pe Coast Castle
11 32 n.
11-5 N.
.......
NORTH EQUATORIAL ZONE II.— LATITUDE 10° TO 20° N.
Authorities.
(■ Royal Geographical Society’s Journal, vol. xxv. ; and MSS. of the Observer in the Mag-
°^6 1 netic Office.
D’Hericourt ■>
Lefebore I L. S. Kamtz, MSS.
Haines J
Moyes MSS. in the Magnetic Office.
Schlagintweit Scientific Mission to India and High Asia.
Jflsted 1 L. S. Kamtz, MSS.
Orlebar J
Montrion Schlagintweit’s Scientific Mission to India and High Asia.
Chambers Reports of the Colaba Observatory,
Basevi Reports of the Great Trigonometrical Survey of India.
Caldecott & Taylor . . Schlagintweit’s Scientific Mission to India and High Asia.
Koppe Mem. by Erman in the Astr. Nachrichten.
Ludlow. MSS. in the Magnetic Office,
Powell Schlagintweit’s Scientific Mission to India and High Asia.
Bonite (La) Yoyage (Paris, 1842).
Blosseville L. S. Kamtz, MSS. ; and Schlagintweit’s Scientific Mission to India and High Asia.
Elliot Phil. Trans. (1851) Art. XII.
Novara (Austrian Frigate) Reise um die Erde (Wien, 1862-65).
Laplace L. S. Kamtz, MSS.
Fell Schlagintweit’s Scientific Mission to India and High Asia.
Crawford I L. S. Kamtz, MSS.
Bougainville J
j..^r j Mem. by Lenz in the Sci. Memoirs of the Acad, of St. Petersburg; and L. S. Kamtz,
U 6 t MSS.
Belcher MSS. in the Magnetic Office, received from the Author.
Prussian Ships L. S. Kamtz, MSS.
Collinson MSS. in the Hydrographic Office.
2 A 2
172 GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
Dumont D’Urville ->
Ereycinet I
Beechey >L. S. Kamtz, MSS.
Kotzebue I
Byron J
Douglas (David) . . . .Report on the Variations of the Earth’s Magnetic Force (Brit. Assoc. Report, 1838).
Erman Reise um die Erde (Berlin, 1841).
Venus (La) Voyage (Paris, 1841).
Harkness . . Smithsonian Contributions, vol. xviii.
Muller and Sonntag . . Smithsonian Contributions, vol. xi.
Behard MSS. in the Magnetic Office, received from Admiral Duperrey.
Home . . . i Kamtz, MSS.
Barnett MSS. in the Magnetic Office; and L. S. Kamtz, MSS.
Sabine Report on Pendulum Experiments, 1825.
Owen, Milne . . . . i
Austin } KSmtz- MSS'
Eriesach Mem. Imp. Acad, of Sciences, Vienna, vol. xxix. (et seq.) to xliv.
Zahrtmann Kamtz, MSS.
Norwegian Officers . . Hansteen, Mag. Beob. (Christiania, 1863).
Schomburgk MSS. in the Magnetic Office, received from the Observer.
Berard MSS. received from Admiral Duperrey.
Foster MSS. in the Hydrographic Office.
Du Petit Thouars .... Sabine, Mag. Contrib. in Phil. Trans.
Hudson and Rumker .L. S. Kamtz, MSS.
Lefroy MSS. in the Magnetic Office, received from the Observer.
Young Kamtz, MSS.
Sulivan . „ .Sabine, Mag. Contrib. in Phil. Trans. ; and L. S. Kamtz, MSS.
Denham ->
Trollope J ^SS. the Magnetic Office.
FitzRoy Voyage of the ‘ Beagle.’
Ross (James) and j jy-gg. receive(j from the Observers.
Crozier J
Duperrey L. S. Kamtz, MSS.
Pasley MSS. in the Magnetic Office.
Stanley MSS. in the Magnetic Office.
King Kamtz, MSS.
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MANGETISM.
173
NORTH EQUATORIAL ZONE II.— Lat. 10° N. to 20° N.
Declination.
Inclination.
Force in British units.
Stations.
Lat. N.
Long. E.
Date.
Ob-
served.
Correction
to Epoch
18425.
Corrected.
Ob-
served.
Cor. to
Epoch
1842-5.
Corrected.
Ob-
served.
Cor. to
Epoch
1842-5.
Corrected.
Observers.
o ,
o ,
o ,
0 ,
o
o /
,
o
Yi oa (Bautchi)
10 10
10 52
9 36
13 17
1855
16 13 w.
16-2 w.
13-8 w.
13 - 8 w.
141 w.
Yogel.
Yogel.
V ogel.
Yogel.
D’Hericourt.
13 17
1854
26 03
26-1 n.
k].....
12 55
13 20
1854
14 03 w.
13 09
13-2 n.
12 36
37 31
1848
5 46
5-8 n.
14 18
39 00 |
1839
8 50
*2} s-s ».
|S|}n-5».
Lefebore.
15 36
39 32 |
1849
1839
9 01
10 43
D’Hericourt.
Lefebore.
1849
12 19
D’Hericourt.
r
1834
5 02 w.
]
Haines.
A(l
12 46
45 lot
1850
4 34
4-6 l 5-1 n.
Moyes.
Schlagintweit.
Wells ted.
So] ra
13 16
1
52 55
1857
1835
4 15 w.
4 30 w.
4-3 w. J
4-5 w.
5 38
5-6 J
18 56
72 54 |
73 38
1845
1847
0 13 w.
0 14 e.
0 03 w.
0 05 w.
0-3 w.A
°'2 w. I 0.0
01 E.
0-3 E. J
17 59
18 18
-03
-05
17- 9 A
18- 2 1Q .
18-9 [18'4lf-
18-6 J
16-2 n.
8-20
8-37
| 8-40
Orlebar.
Montrion.
17 55
J856
1867
0 19 e.
0 42 e.
0 14 w.
0 25 w.
19 06
19 02
16 26
-14
-25
-14
8-48
8-53
Schlagintweit.
Chambers.
Schlagintweit.
Pel 1
18 30
73 52
1856
19 02
7 24
14 27
2 43
-14
-28
-14
+04
18-8 n.
6-9 n.
14-2 n.
2-8 n.
Schlagintweit.
Basevi.
Schlagintweit.
Caldecott.
12 52
74 49
75 30
75 45 |
1870
1856
1838
1 06 e.
0 30 e.
0 28 w.
0 14 w.
0 6 e.
0-3 e.
813
813
16 13
11 15
1846
0 25 e.
0 04 w.
0 4 e.
Montrion.
Pe ig
10 47
75 55
1838
1 11
1 13
4 27
14 14
15 29
+04
+04
-14
1-3 N.
1-3 N.
4-2 n.
Caldecott.
Caldecott.
Schlagintweit.
Koppe.
Koppe.
Cl ?aye
10 32
76 01
1838
TJt imand
11 24
76 43
76 45
76 47
1856
0 57 e.
1 05 e.
1 52 e.
0 14 w.
0 26 w.
0 26 w.
0-7 e.
8-86
Mi Tar
16 35
1868
1868
O OO
Be pore .
16 50
1-4e.
-26
15-1 N.
Be -i
15 09
76 54
77 04
77 36
77 40
1856
1838
1868
0 21 e.
0 14 w.
12 00
0 00
11 41
7 17
14
11
8*83
8-83
Schlagintweit.
f Caldecott and
Sfe n
10 02
15 06
01
E.
N.
Na habad
1 11 E.
0 58 e.
0 26 w.
0 26 w.
0*0
ll.q„
8-28
8-28
8-17
1 Taylor.
Basevi.
Ba ilore Base
13 03
1868
o'fl B
_ or
J I O N.
6"9 N-
Basevi.
U'O E.
8-17
Ba dore
Pa polliam 1
Kc ngul
So ma
Da rgidda i
12 59
11 00
17 08
19 05
18 03
77 41
77 41
77 41
77 42
77 43
1869
1868
1868
1868
1868
1 12 E.
1 04 E.
1 29 e.
0 28 e.
1 29 e.
0 27 w.
0 26 w.
0 26 w.
0 26 w.
0 26 w.
0-8 E.
0-6 E.
11 E.
00
11 E.
7 12
2 48
16 37
23 43
19 33
-27
-26
-26
-26
-26
6-8 n.
2-4 n.
16 2 n.
23-3 n.
19-1 N.
8-19
8-05
8- 41
9- 16
8-48
8-19
8-05
8-41
916
848
Basevi.
Basevi.
Basevi.
Basevi.
Basevi.
Ki jol. ..........
15 50
17 27
10 48
11 05
78 06
1868
1 Ol
0 26 w.
0- 9 E.
1- 8 E.
IQ /IQ
-26
-26
13-3 n.
16-9 n.
2-5 n.
2-6 n.
8-31
8-51
8-31
8 51
Basevi.
S& derabad
78 32
78 43
yc <19
1868
1844
1856
J Zl E.
1 34 e.
I o 4o
17
Tr inopoly
0 26 w.
1/ 1 /
2 28
O CA
Basevi.
-14
Ludlow.
Schlagintweit.
/ O
J DU
Bo looottah
10 23
10 53
f
78 52 1
79 09
1838
1843
1844
0 55
0 57
1 03
0-9 'j
10 l 1-0 N.
ii;
20 n.
T Taylor and
\ Caldecott.
Ludlow. ■
Ludlow.
Ludlow.
Tr dy.
1844
2 01
Mi namelegoody ...
Ta re
10 03
10 46
79 12
1838
1 QA A
0 11
0-2 n.
f Taylor and
[ Caldecott.
Au learputtaaum ...
Ad apatam
10 01
10 17
79 18
79 22
1844
1 OQQ
1 20 e.
0 04 e.
1-4 E.
2 01
0 39
2-0 n.
0-7 n.
Ludlow.
Ludlow.
Powell.
J OOO
Co: aconum
10 58
10.40
10 05
79 27
79 29
1814
2 20
0 52
2 3 n.
0-9 n.
Ludlow.
f Taylor and
[ Caldecott.
Powell.
Mb rgoody
Ba. Strait ...
1838
1 20 e.
0 04 e.
1-4 E.
/ 03
1838
She y
1 1 16
2 28
2-5 n.
f Taylor and
{ Caldecott.
Bo: Ifovo .
11 29
10 16
/9 4 7
7Q
1838
Boi Calymere
/ t7 ttO
79 49
1 844
1 C/l A
3 41
3-7 n.
Ludlow.
lo44
1 13
1-2 N.
Ludlow.
-
1
174 GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
NORTH EQUATORIAL ZONE II.— Lat. 10° N. to 20° N. (continued).
Declination.
Inclination.
Force in British units.
H
Stations.
Lat. N
Long. E.
Date.
Ob-
served.
Correction
Ob-
served
Cor. tc
>
Ob-
Cor. tc
)
Observe'
to Epoch
1842-5.
Corrected.
Epoch
' 1842-5
Corrected.
served
Epoch
' 1842-5
Corrected.
o /
o /
o ,
o . /
o
o /
/
o
1837
0 52 e.
0 05 e.
1-0 E.
4 31
4-51 o
Bonite. J 1
11 54
79 50 1
1838
4 27
5 05
4- 5 l 4-7 n.
5- 1 J
( Taylor ail
1 Caldecv.
Ludlow. !
1844
10 47
79 51 |
1838
1 42
^U-On.
/ Taylor ai
1 Caldect. 1
1844
2 20
2-3 J
Ludlow.
I
10 55
79 53 |
1828
1 14 E.
0 14 e.
1 -5 E.
O
j 1-3 E.
1 51
+ 14
21 N.
Blosseville 1
1833
1 02 E.
0 09 e.
1-2 E.
Blossevillei
11 01
79 55 |
1838
2 05
f Taylor at 1
1 Caldedt.
Ludlow.
1843
2 40
2-7 J
14 09
79 55
79 58 1
1843
9 36
9-6 n.
Ludlow, j
14 00
1838
8 49
8>8 l 9-1 N.
/ Taylor ai
1 Caldejtt. ;
1843
9 23
9-4 J
Ludlow.
12 14
79 59
1838
4 50
4-8 n.
(Taylor id
1 Caldejtt. i .
Nellur
14 28
79 59
80 00
1838
9 41
9-7 n.
( Taylor i d
13 52
1843
9 07
91 N.
1 Caldett.
Ludlow. '
13 41
80 02 1
1838
8 11
8 ^ 1 8-5 n.
(Taylor d
1 CaldAtt.
1843
8 40
8-7 J
Ludlow.
Ongole
15 30
80 02
80 03
80 04
80 08
1838
11 37
11-6 N.
( Taylor Id
\ CaldJptt,
(Taylor lid
Eampata.ii
15 03
14 41
13 21
1838
10 44
10-7 n.
10-3 n.
Allur
1838
1838
10 19
\ Caldjbtt.
( Taylorp
[ Caldlott.
( Taylorfid
1 Caldott.
Poodway
7 17
7-3 n.
Goomerapoondy
13 24
80 11
1843
8 09
8-2 n.
Ludlow.
Sadras
12 32
80 12 T
1838
5 31
5'515-8n.
( Taylorpd
[ Calc’iott.
Ludlow,
1843
6 08
6-1 1
Red Hills
13 10
80 15
80 16
(
1843
7 59
8*0 n.
Ludlow,
Poonairy
13 20
1843
1838
7 54
7 9 n.
Ludlow.'
6 50
6-8 1
( Tayloind
[ Calffiott.
|
1843
7 30
7-5 |
Ludlow
Madras ....
13 05
80 17 -j
1846
1848
0 56 b.
0 04 w.
0-9 e.
■0-9 e.
... }-7-4n.
7-5
.8-16
Elliot, .
T 34
-6
815
Elliot. (
1856
0 59 e.
0 14 w.
0-8 e.
7 52
-14
7-7
8-10
Schlagiiveit,
. 1
1870
1 20 e.
0 28 w.
0-9 e.J
7 48
-28
7-3j
8-22
j
Basevi.
At sea (3 observations)
12 56
80 29
1858
0 52 e.
0-9 e.
Novara;
At sea (2 observations)
10 48
81 25
1858
0 58 e.
1-0 E.
Novara i
At sea (2 observations)
13 44
81 29
1858
0 51 e.
09 e.
Novara!
Rajahmandri
17 11
81 47
82 15
1-856
1 25 e.
0 14 w.
1-2 E.
16 24
-14
1 6-2 n.
9-20
9-20
Schlagijweit.
Fell. j
Eoringa Bay
16 45
1848
0 50 e.
0 06 w.
0-7 e.
Coconada
16 56
82 18
1870
1 51 E.
0 28 w.
1-4 E.
BaseviJ
At sea (3 observations)
13 51
82 44
1858
1 14 e!
1-2 E.
Novara!
At sea (2 observations)
13 28
83 52
1858
1 16 E.
1-3 E.
Novaraj
At sea
12 12
85 57
86 27
1858
1 12 E.
2 58 e.
1*2 E.
Novaraj
At sea (4 observations)
14 32
1837
3-0 E.
Bonite,
At sea (2 observations)
17 45
86 32
1837
2 03 e.
2-1 E.
Bonite
At sea (2 observations)
15 32
87 00
1837
2 07 e.
21 E.
Bonite!
At sea (3 observations)
17 06
87 39
1837
2 41 e.
2-7 E.
Bonite
At sea (2 observations)
14 28
88 05
1837
2 36 e.
2-6 e.
Bonitej
At sea (2 observations)
10 36
88 13
1858
1 40 e.
1-7 E.
Now
At sea (2 observations)
13 03
88 33
1837
2 36 e.
2-6 e.
Bonite|
At sea (3 observations)
19 10
89 03
1837
2 23 e.
2-4 e.
Bonite
Port Owen
13 05
90 20
1830
2 25 e.
1
2-4 e.
Laws.
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM. 175
NOETH EQUATOEIAL ZONE II.— Lat. 10° N. to 20° N. (continued).
Declination.
Inclination.
Force in British units.
Stations.
Lat. N
Long. E.
Date.
Ob-
served.
Correction
Ob-
served.
Cor. to
Ob-
served.
Cor. to
Observers.
1
to Epoch
I 1842-5.
Corrected.
Epoch
1842-5.
Corrected.
Epoch
1842-5.
Corrected.
O /
, o ,
O / 1
o
O /
O
At)
Ch
: Kt
Ch
10 05
92 31
1837
1 54 e. .......
1-9 E
Bonite.
ba Island
19 00
93 00
1830
1 2 30 e.
2-5 e.
Laws.
19 29
93 29
1830
2 06 v.
Laws.
ba Straits
18 30
93 45
1830
2 45 e.
2-8 e.
Laws.
Dii
nd Island
15 51
94 18
1826
3 00 e.
3-0 e.
Crawford.
■ 1
r
1833
0 50 e.
0-8 e.
°
17 52
17 9 | °
Blosseville.
■*>
16 46
96 17
1837
. 0-8 e.
17 53
17 57
17-9 L 17 9 n.
18 0 J
Taylor.
1837
Felly.
To>
12 00
97 00
1835
3 00 e.
Laws.
Ml
97 46
1846
2 20 e.
2-3 e
17 46
17-8 n.
8-52
8-52
Elliot.
■Rpi
15 33
97 51
1830
Laws.
gs Island
10 07
98 21
1846
2 13 e.
2-2 e.
4 19
4-3 n.
8-20
8-20
Elliot.
To;
16 07
108 17
1837
1 54 e.
1-9 is
19 01
19-0 n.
Bonite.
: S
(2 observations]
16 45
109 04
1837
0 38 e.
0-6 e.
Bonite.
At
14 26
109 16
1837
0 30 w.
0-5 w
Bonite.
d
14 20
109 20
1825
1 00 E.
1-0 E
Bougainville.
Novara.
(2 observations)
10 50
112 54
1858
1 58 e.
2-0 e.
T At
(4 observations)
12 30
114 10
1829
0 04 e.
0-1 E.
Liitke.
At
19 42
114 14
1843
22 30
22-5 n.
Belcher.
At;
12 26
115 13
1858
1-5 E
Novara.
(8 observations)
17 36
115 53
1830
0 17b.
0-3 e.
Prussian ships.
‘At
(2 observations)
19 25
116 09
1858
0 53 e.
0-9 e.
Novara.
At
16 12
116 35
1843
19 13
19-2 n.
Belcher.
7 At
(3 observations)
17 06
116 48
1858
1 03 e.
M E.
Novara.
A
, (2 observations)
13 45
117 02
1829
1 47 e.
1-8 e.
Prussian ships.
■ At:
;(2 observations)
13 14
117 33
1858
0 42 e.
0-7 e.
Novara.
At:
15 23
118 05
1858
1 16 E.
1-3 E.
Novara.
, At;
13 49
118 21
1843
14 18
14-3 n.
Belcher.
‘At;
(2 observations)
19 22
119 04
1851
0 03 w.
01 w.
Collinson.
-At:
11 28
119 06
1843
10 10
10-2 n.
Belcher.
!
At s
(2 observations)
14 27
119 25
1858
0 33 e.
0-6 e.
Novara.
1 ^
(3 observations)
15 41
119 34
1837
0 00
00
Bonite.
(3 observations)
16 58
119 47
1837
0 16 e.
0-3 e.
Bonite.
Island
13 52
119 53
1843
15 11
15*2 n.
Belcher.
;;DaI
an Island
10 59
119 56
1843
8 05
81 N.
Belcher.
‘•In
(2 observations)
[2 observations)
17 20
120 02
1833
1 00 E.
LO e.
Prussian ships.
18 24
120 07
1837
0 26 w.
0-4 w.
Bonite.
. At s
13 11
120 16
1844
0 56 e.
0-9 e.
0-2 e.
13 21
12 30
12 08
13 21
16 05
16 16
13-4 n.
12-5 n.
12- 1 N.
13- 4 n.
16 1 N.
16-3 I
Belcher.
•Ape
land
12 40
120 24
1846
0 09 e.
Belcher.
Cah
ane
12 13
120 25
1844
0 38 e.
0-6 e.
Belcher.
I i
©At!
12 38
120 42
1844
Belcher.
©Cav
14 27
120 55
f
1846
0 48 e.
0 10 E.
0 8 e.
0-2 e. I
Belcher.
Liitke.
©
"to,
It
1829
I
14 36
120 58
1830
1 00 E.
1-0e.
- 0-5 e.
|
L 8-40
Laplace.
Bonite.
1836
0 30 e.
0-5 e.
16 30
16-5 [ 16 4 N‘
S'
l
1844
0 18 e.
0-3 e. J
16 26
16-4 J
8-40
J
Belcher.
: Gai
‘‘ sland
12 13
121 09
1846
0 38 e.
0-6
0-3
0-8
11 30
10 58
10 27
11-5 N.
1 10 N.
10-5 n.
Belcher.
Belcher.
Belcher.
©Par
it tan
11 51
121 19
1844
1846
0 15 e!
0 45 e.
'Hat
f rin Island ....
11 36
121 37
At;
Si At!
Sft
* 8 observations)
18 56
123 13
1828
0 44 w.
0-7 w.
Liitke.
* 2 observations)
18 45
129 50
1837
0 12 w.
0-2 w.
Bonite.
At!
u if .
* 3 observations)
18 28
134 50
1837
0 21 e.
0-4 e.
Bonite.
-it :
LaS'I ,
K 3 observations)
17 25
135 25
1828
0 03 e.
0-1 E.
Liitke.
At i
At!
©At s
3 observations)
18 08
135 54
1833
0 36 e.
0-6 e.
Prussian ships.
ie 2 observations)
12 48
137 24
1831
1 12 E.
1 2 E.
Prussian ships.
® 3 observations)
12 09
137 45
1828
1 34 e.
1-6 E.
Liitke.
c
j;At f
|Ats
-it s
® l observations)
19 36
140 28
1851
1 10 w.
1-2 w
Collinson.
® ! observations)
18 32
16 05
12 18
140 35
l irt *;q
1837
1 QKQ
0 57 e.
1- 0 E.
2- 3 e.
2-3 e.
Bonite.
Novara.
Prussian ships.
;,At s
T s
® 1 observations)
141/ OO
140 58
J ooo
1831
2 16 e.
2 15 e.
L.U s
:ei : observations)
12 25
143 20
1828
2 35 e.
2 6 e.
Liitke.
e£ observations)
18 18
144 25
1830
3 27 e.
3-5 e.
1
Prussian ships.
176 GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
NORTH EQUATORIAL ZONE II.— Lat. 10° N. to 20° N. (continued).
Lafc. N.
Declination.
Inclination.
1 Force in British units.
'. Long. E.
Date.
Ob-
served.
Correction
to Epoch
1842-5.
Corrected.
Ob-
served.
Cor. tc
Epoch
1842-5,
►
Corrected.
Ob-
served,
Cor. to
Epoch
1842-5.
Corrected.
Observe)1
144 44 |
1828
1 36 e.
1-6 s.l».
3 0 e.)23 E‘
o ,
o .
Dumont dT/illei
1829
2 57 e.
12 52
12 9 n.
Liitke.
144 46
1858
3 51 e.
3-9 e.
Novara.
144 50
1819
4 39 e.
12 47
12 8 k.
Freycinet. 1
2 145 09
1851
0 35 w
0-6 w.
Collinson. 1
145 24
1827
5 42 e.
5-7 e.
Beechey. j L
145 54
1819
3 30 e.
Freycinet. ; •
146 10
1837
3 34 e.
3-6 e.
Bonite. j
146 15
1819
3 50 e.
21 43
21 7 n.
Freycinet. j
147 11
1819
3 50 e.
24 47
24 8 n.
Freycinet. 1
149 03
1858
5 28 e.
5-5 e.
Novara. , -
149 58
1858
2 16 e.
2-3 e.
Novara. 1
151 23
1837
5 34 e.
5-6 e.
Bonite. j
152 54
1831
6 45 e.
6-8 e.
Prussian sh's.
153 23
1858
6 09 e.
6-2 e.
Novara. !
154 42
1858
6 40 e.
6-7 e.
Novara, j
155 13
1830
6 55 e.
6 9 e.
Prussian sis.
157 07
1836
7 15 e.
7-3 e.
Bonite. j , , (j
157 40
1851
4 52 e.
4-9 e.
Collinson. j
157 58
1828
7 46 e.
7-8 e.
Liitke.
161 43
1836
9 24 e.
9-4 e.
Bonite. j l
161 52
1828
8 24 e.
8-4 e.
14 17
14 3 n.
7-54
754
Liitke.
162 30
1828
8 45 e.
8-8 e.
Liitke.
163 42
1851
6 19 e.
6-3 e.
Collinson. ,; [
t 1 63 55
1827
8 45 e.
8-8 e.
27 55
27 9 n.
7-69
7-69
Liitke. j
) 165 30
1825
10 52 e.
10-9 e.
Kotzebue. :
- 166 22
1830
10 08 e.
101 E.
Prussian slis.
166 30
I 169 51
1836
1825
9 28 e.
11 18 e.
9-5 e.
11-3 E.
Bonite.
Kotzebue.
; 170 oo
1825
10 54 e.
10-9 e.
Kotzebue. 1
: 171 11
1851
8 50 e.
'8-8 e.
Collinson. iij j
i 172 02
1836
11 23 e.
11-4 E.
Bonite. ■ ,jq 1
174 40
1830
11 19 E.
1 1-3 E.
Prussian sips.
1 77 57
1836
10 21 e.
10-4 e.
Bonite. ; a 1
180 38
1851
7 25 e.
7-4 e.
Collinson. |
184 55
1831 !
11 03 e.
Il l E.
Prussian sips. * l
191 06
1851
6 40 e.
6-7 e.
Collinson; f ..a 1
191 09
1836
12 04 e.
12-1 E.
Bonite.. m |
193 47
1831
9 40 e.
9-7 e.
Prussian slbs. f.
203 50 I
1819
1824
9 50 e.
10 14 e.
9-8 e. I
10-2 e. !■ 10-0 e.
Freycinet. - 1
Byron. j
203 59
1830
1836
7 43 e.
J
7-7 e.
37 58
39 18
38 On.
39 3 n.
8 21
8-21
Douglas, j
Bonite. i
204 45
1836
8 33 e.
8 6 e.
Bonite. til
209 43
1836
8 03 e.
8-1 E.
Bonite. , it
214 25
1836
7 31 e.
7-5 e.
Bonite. j mi |i
215 52
1831
6 44 e.
6-7 e.
Prussian sps. :
218 33
1836 !
7 09 e.
7-2 e.
Bonite. i (4 :
221 27
1828
6 53 e.
6-9 e.
Prussian slbs. ■ 1
222 44
1827
7 18 e.
7-3 e.
Liitke.
223 21
1853
33 40
33 7 n.
Trollope.
224 24
1836
5 50 e.
5-8 e.
Bonite.
227 00
1827
5 49 e.
5-8 e.
30 05
30 1 n.
8-65
8-65
Liitke.
228 34
1827
6 04 e.
6-1 E.
Liitke.
228 50
1831
5 53 e.
5-9 e.
Prussian sps. 1
232 19
1836 1
7 17 e.
7-3 e.
Bonite. j id i
236 06
1830
5 08 e.
51 E
Erman. . aj '■
236 14
1830
25 45
25 8 n.
8-42
8-42
Erman. ;
236 20
1830
27 15
27 3 n.
8-35
8-35
Erman.
236 28
1830
5 30 e.
5 5 e.
29 45
29 8 n.
8-55
8-55
Erman. I
236 47
1830
5 30 e.
5-5 e.
32 28
32 5 n.
8-77
8-77
Erman. I
Guahan Island
At sea (2 observations)
Agagna or Guahan
At sea (2 observations)
Assumption Island
Gugnan Island ....
At sea (2 observations)
At sea
At sea
At sea (3 observations
At sea
At sea (2 observations)
At sea (2 observations)
At sea (4 observations)
At sea (5 observations)
At sea (8 observations)
At sea (2 observations)
At sea (2 observations)
At sea (3 observations)
At sea
At sea
At sea (4 observations)
At sea (2 observations)
At sea
Escholtz Island
At sea(12 observations)
At sea (2 observations)
Button Island
Ailu Island
At sea (2 observations)
At sea (2 observations)
At sea (11 observations)
At sea
At sea (3 observations)
Atsea(ll observations)
At sea (3 observations)
At sea
At sea(lOobservations)
Owyhee ...
Kowroa
At sea (3 observations)
At sea (2 observations)
At sea (2 observations)
At sea(lOobservations)
At sea (2 observations)
At sea
At sea (4 observations)
At sea(12observations)
At sea (2 observations)
At sea
At sea (3 observations)
At sea (12 observations)
At sea (2 observations)
19 13
18 59
17 35
18 49
18 00
12 05
17 02 1
11 28
11 18
12 18
At sea 13 37
At sea 15 15
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MANGETISM. 177
NORTH EQUATORIAL ZONE II.— Lat. 10° N. to 20° N. (continued).
Declination.
Inclination.
1 For
■ce in British units.
Stations.
Lat. N.
Long. E.
Date.
Ob-
served.
Correction
Ob-
Cor. to
Ob-
Cor. to
Observers.
to Epoch
1842-5.
Corrected.
served.
Epocli
1842-5.
Corrected.
served.
Epoch
1842-5.
Corrected.
O ,
O /
O
o /
o
At
At
At
At
Atl
16 5S
237 04
1836
6 21 e.
6-4 e.
Bonite.
237 06
1830
35 34
35 6 n.
8-86
8-86
Erman.
55
237 27
1830
39 03
391 m
9-06
9 06
Erman.
19 40
237 38
1830
40 15
40-3 m
9-22
9-22
Erman.
I
(2 observations)
16 53
241 33
1836
6 26 e.
6-4 e.
Bonite.
At
(3 observations)
16 17
244 45
1836
5 50 e.
5*8 e.
Bonite.
ti:
Cla
U
18 21
245 19
1839
8 05 e.
8-1 E.
37 03
37-1 n
9-52
9-52
Belcher.
(2 observations)
12 35
246 41
1836
5 49 e.
5-8 e.
Bonite.
;
it
(2 observations)
11 19
248 45
1836
6 40 e.
6-7 e.
Bonite.
....
At
18 43
249 06
1839
40 44
40-7 n.
9-87
987
Belcher.
:r_
::
(2 observations)
10 38
253 42
1836
7 22 e.
7-4 e.
Bonite.
f
1828
9 07 e.
9-1 E.i
1
0
1
Beechey.
IB
Acr
lm
16 50
260 10
1838
1838
8 13 e.
8 2 e.
o
8 5 e.
37 57
38-0 |
39 On.
10-03
L .10-06
Belcher.
8 17®.
8 3 e.
39 05
39-1
|
La Venus.
i:
l
1866
8 22 f.
8 4 e.
39 54
39-9 J
1009
J
Harkness.
Me
Ch;
J
19 26
260 55
41 26
41 -4 n
10-11
1011
Miiller & Sonntag.
7
m
19 18
261 09
1856
9 03 e.
91 E.
43 12
43-2 n
10-35
10-35
Muller & Sonntag.
k
Ha
ias
19 03
261 21
1856
8 28 e.
8-5 e.
42 34
42 6 n
10-28
10-28
Muller & Sonntag.
Muller & Sonntag.
Muller & Sonntag.
Muller & Sonntag.
Sai
Nei
Pot
Mi
18 59
262 45
8 13 ®.
8-2 e.
42 38
42-6 n
10-31
10-31
18 53
1856
8 28 e.
42 51
42-9 n
10-34
10-34
m
18 56
263 12
1856
8 39 e.
87 e.
42 51
42-9 n
10-33
10-33
b:
1:5
19 13
263 23
1856
8 02 e.
43 50
43-8 n.
10-43
10-43
1045
Miiller & Sonntag.
Behard.
Miiller & Sonntag.
Llk
Cth
Tei
19 12
263 51 |
1839
1856
8 22 e.
8-4 e.
8-3 e.
43 58
44 U N.
10-45
Li'
M
At
: (2 observations')
19 33
266 20
1838
9 32 e.
9-5 e.
Behard.
At
■ (4 observations)
19 57
266 46
1839
9 39 e.
97 e.
Behard.
Pita
Lei
19 49
269 26
1847
1839
8 02 e.
8 0 e.
Barnett.
M
Cai
3che
19 51
269 29
9 27 e.
9-5 e.
Behard.
U
Kei
12 28
272 52
1838
7 53 e.
7-9 e.
34 37
Belcher.
Soi
Key
16 08
273 01
1844
7 45 e.
7-8 e.
1
Lawrence.
w
Colfe
Mi
'LP13,
10 56
276 18 |
1834
1 7-0 e.
34 05
34- i |
■ 34-4 n.
Home.
1839
7 00 e.
7-0 e. j
34 43
34-7 j
Barnett.
Pros
C:l]
Iracias a Dios...
15 00
276 42
1833
41 04
41 1 N.
Barnett.
!i
Th.l
Eobbies
16 04
276 49
1833
6 00 e.
6-0 e.
Barnett.
Ca’
an Island
19 14
278 55
1822
48 48
48-8 n
10-90
10-90
Sabine.
Col
At]
(3 observations)
19 40
279 03
1838
4 37 e.
4-6 e.
.
Behard.
Pus
Bel
a Key
15 48
280 09
1844
6 00 e.
6-0 e.
Lawrence.
Col
Boil
Y
1822
1
46 55
46-9 )
10*90
)
Sabine.
Pros
1
1822 i
4 54 e.
0 20 w.
4 6 e.
Owen.
1832 !
5 13 e.
0 lOw.
51 E.
Foster.
Fieji
Bw
Po,
Eoyal and 1
gston J " ’
17 56
283 09 i
1834
1834
► 4-3 e.
47 19
47 04
47-3
471 j
j-470 n.
}■ 10-67
Barnett.
Horae.
'
1837
4 18 e.
0 05 w.
4-2 e.
I
Milne.
W
1847
3 40 e.
0 05 e.
3-8 e.
Barnett.
Bait
■
1857
3 43 e.
0 15 e.
4-0 ev
46 32
46-5 J
1044
J
Friesach.
Mi Poi
Morant
17 55
283 44
1831
5 13 e.
0 11 w.
5 0 e.
Austin.
Ed Car
;ena
10 25
284 25
1837
5 41 e.
0 05 vv.
5*6 e.
Milne.
Pits Cui
arland Harbour .
19 55
284 45
1837
3 31 e.
0 05 vv.
3-4 e.
Milne.
U- Bai
iguilla
10 59
284 54
1857
5 24 e.
0 15 e.
5-7 e.
5-4 e.
Friesach.
Pits
' Sar
Marta
11 15
285 45 |
1837 1
5 29 e.
0 05 vv.
| 5-4 e.
j. 36-6 n.
| 9-52
Milne.
Li
1857 i
5 04 e.
0 15 e.
5 3 e.
36 34
36-6 j
9-52
Friesach.
rf
.Alt
ela
17 28
288 21
1835
47 39
47-7 i
r.
Home.
IP:-.: At
(2 observations)
19 43
290 50
1838
0 2i w.
0 04 w.
0-4 w.
Behard.
Li Cm
la
12 06
291 04
1833 i
38 39
37 16
50 15
38-7 n.
37-3 n.
sn.a
Zahrtmann.
Lull Cai
is .M.
10 31
293 03
1836
Poi
Rico
18 29
293 46
.1852
Norwegian Offi-
cers.
Behard.
Fits
t 1 At.
(2 observations)
i 19 39
294 06
1838
1 09 w.
0 04 w.
1 -2 vv.
Em
|
1834
49 29
49-5
i
1
Zahrtmann.
i-
, at.
omas
. 18 20
295 04 ]
1846
49 40
49-7
1 49-6 n.
| 10-43
Sehomburgk.
Harkness.
Eid
1
1865
0 40 e.
49 38
49-6.
10-43
Erd'Sai
Croix
17 45
295 16
1853
1 32 e.
1*5 E.
1*3 E.
Lang.
Zahrtmann.
Eid Do:
liea
. 15 18
295 27
1826
1 15 E.
2 b
MDCCCLXXV.
178
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
NORTH EQUATORIAL ZONE II.— Eat. 10° N. to 20° N. (continued).
Declination.
Inclination.
Force in British units.
Stations.
Lat. N.
Long. E.
Date.
Ob-
served.
Correction
Ob-
served.
|Cor. to
Ob-
served.
Cor. to
j
Observe)
to Epoch
1842-5.
Corrected.
Epoch
1842-5.
Corrected.
Epoch
1842-5.
Corrected.
o ,
o /
o ,
°
0 /
°
I
At sea
19 39
295 51
1838
0 01 E.
00
Berard.
18 14
296 51
1846
0 56 E.
0-9 e.
50 15
50-3 n.
Barnett.
Behard.
At sea (2 observations}
19 53
297 17
1838
0 39 e.
0-7 e.
17 08
298 08 |
1840
1848
0 42 e.
0-7 e. )
08 e.
49 11
Vn o 1 49-2 N.
Milne. (
0 46 e.
0-8 e. j
49-2 J
Barnett. ^
r
1822
39 02
39 0 I
8-98
1
Sabine.
Trinidad (Port Spain)
10 39
298 25 \
1822
4 00 e.
4-0 e.
v39-0n.
l 8-98
Owen.
l
1830
39 00
39-0 J
J
Foster.
19 48
299 17
f
1838
2 30 e
2-5 e.
Behard. 1
Phillips. ,|<
1833
1 29 e.
1-5 E.
1
13 05
300 23 |
[
1839
1 13 E.
1-2 E.
Jl-4E.
1 44*0 n.
Milne.
1846
1 27 e.
43 57
44*0 J
Schomburg rlf
At sea (3 observations'
11 47
311 23
1849
2 00 w
2 0 w.
Hudson.
At sea
1 18 28
317 07
1839
52 57
53 On. \
9-84
9-84
Sulivan. 1;
At sea
15 40
317 36
1839
50 07
501 n.
9-73
9-73
Sulivan. I ,
At sea
12 50
318 28
1839
47 05
47-1 N.
9-35
9-35
Sulivan. 1
At sea (5 observations)
17 35
318 38
1829
3 47 w
3-8 tv.
Rumker. 1
At sea (3 observations)
14 08
318 45
1829
4 09 w
4-2 w.
Rumker. i 1
At sea
10 07
319 51
1839
42 27
42-5 n.
909
9-09
Sulivan. 1 ij
At sea
18 18
321 24
1846
11 24 w.
11-4 w.
Sulivan. j j | n
17 02
321 51
1846
9 38 w.
Sulivan. | I
At sea
19 19
321 51
1839
1 1 -9 TV.
Du Petit T] iiars,
At sea
15 21
322 28
1846
10 49 w.
10-8 w.
Sulivan.
323 27
1839
11 13 w.
11 34 w.
11-2 TV.
Du Petit TJ uars.
At, sea
13 55
325 01
1839
1 1-6 TV.
Du Petit T uars.
At sea. . . .
17 40
325 36
1829
12 29 vv.
12-5 w.
Liitke. «
At sea
10 20
325 50
1842
902
9 02
Lefroy. j
At sea
19 05
326 25
1830
52 42
52-7 n.
9-58
9-58
Erman. j tJ l,--
At sea (3 observations)
17 36
326 36
1829
12 39 w.
12 7 w.
Prussian alls.
At sea
11 58
327 30
1839
11 42 w.
11-7 w.
Du Petit T uars.
At sea
14 32
327 40
1850
11 15 vv.
1 1 -3 TV.
Young, j j) L
At sea (2 observations)
16 18
328 52
1830
12 36 w.
12-6 tv.
49 03
4S-1 n.
9-17*
9-17
Erman. ■
At sea (3 observations)
19 22
329 33
1846
16 22 w.
16-4 tv.
Berard. j ;
At sea
18 47
329 36
1830
13 02 w.
13-0 w.
Erman. ij ; ■
At sea (3 observations)
18 05
329 58
1850
17 12 w.
17-2 w.
Dayman, i
At sea (3 observations)
! 18 11
330 00
1843
13 52 \v.
13-9 w.
49 35
496 n.
Ross.
At sea (2 observations)
| 14 53
330 21
1830
12 58 tv.
13-0 tv.
Erman.
At sea
14 03
330 30
1838
45 26
45 4 n.
Sulivan. | '< |
At sea
14 36
330 43
1830
46 31
46-5 n.
9-58
9-58
Erman.
At sea (2 observations)
11 32
330 43
1858
16 04 tv.
16-1 TV.
Novara.
At sea
12 36
331 29
1830
12 23 tv.
12-4 w.
44 03
44-1 n.
Erman. 3
At sea (2 observations)
17 35
331 32
1837
14 12 w.
14-2 w.
Bonite. 1
At sea (2 observations)
13 18
331 34
1830
13 01 w.
13 0 w.
Erman.
At sea (2 observations)
16 47
331 34
1850
47 28
. 47*5 n.
Dayman. I
At sea (3 observations)
11 15
332 17
1830
13 39 w.
13-7 w.
Erman. \
At sea (2 observations)
1 14 55
332 19
1843
13 49 w.
13-8 tv.
4 5 i ’2
45-2 n.
Ross.
At sea (2 observations)
14 38
332 22
1850
16 34 w.
16-6 w.
Collinson.
At sea
11 03
332 25
1830
41 54
41-9 n.
8-64
8-64
Erman.
At sea (3 observations)
15 36
332 48
1850
17 17 w.
17 3 w.
Dayman. ;
At sea (2 observations)!
18 13
333 16
1833
16 38 w.
16-6 w.
Prussian |p9u| r
At sea (2 observations)
10 20
333 25
1830
13 06 tv.
131 TV.
4 0 *49
40-8 n.
8-10
810
Erman. i
At sea
14 03
333 30
1838
45 26
45-4 n.
8-65
8-65
Sulivan. i
At sea
10 08
333 32
1830
13 10 tv.
13-2 w.
Erman. |
At sea (2 observations)
11 34
333 35
1 850
16 36 w.
16-6 tv.
Collinsonj
At sea
12 17
333 35
1832 .
13 43 w.
13-7 w.
FitzRoy. :
At sea (3 observations)
12 50
333 38
1852
16 38 w.
1 6-6 tv.
Denham. .
At sea (7 observations)
11 48
333 38
1829
14 23 w.
14 4 w.
Prussian ;ips-
At sea
12 05
333 40
1838
42 45
42-8 N.
8-46
8-46
Sulivan.
At sea
10 24
333 47
1852
16 49 w.
16-8 w.
Denham.
At sea (2 observations)
14 22
334 10
1837
14 49 w.
14-8 w.
Bonite.
At sea (2 observations)
12 53
334 16
1843 !
14 19 w.
14-3 w.
42 02
42 0 N.
Ross.
-ilia
fe)l2S
;
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM,
179
NORTH EQUATORIAL ZONE II.— Lat. 10° N. to 20° N. (continued).
Stations.
Declination.
Inclination.
1 For
■ce in British units.
Lat. N
Long. E.
Date.
Ob-
served.
Correction
Ob-
served.
Cor. to
Ob-
Cor. to
Observers.
to Epoch
1842-5.
Corrected.
Epoch
1842 5.
Corrected.
served.
Epoch
18425.
Corrected.
o ,
o /
° /
o
o ,
0
13 20
334 17
1842
13 25 w
13-4 w.
Berard.
1 14 57
334 18
1843
16 00 w
16-0 w.
Pasley.
11 53
334 29
1843
13 41 w
13-7 tv.
40 41
40-7 i
Boss.
15 44
334 30
1852
17 50 w
1 7*8 w.
Denham.
14 18
334 30
1850
17 07 w
171 TV.
Dayman.
13 45
334 34
1822
15 1 5 w
15 -3 w.
45 06
451 i
L
Duperrey.
15 49
334 35
1822
15 15 w
15-3 tv.
47 21
47 4 i
Duperrey.
11 13 334 35
1842
15 00 \v
15-0 w.
Berard.
15 10
334 39
1853
43 20
43-3 n.
Trollope.
13 20
334 40
1832
14 49 w.
14 8 vv.
FitzBoy.
16 35
334 42
1842
1 7 00 w.
17-0 tv.
Berard.
10 00
334 44
1840
15 47 w
15-8 w.
Boss.
16 42
334 46
1852
18 23 w.
18-4 w.
Denham.
14 16
334 50
1853
42 20
42-3 n.
Trollope.
17 32
334 55
1841
45 42
457 n.
The J ohn Fleming.
17 10
334 57
1822
15 03 w
15-1 TV.
Duperrey.
r
1841
48 44
48-71
Fishbourne.
16 53
334 57 \
1841
1842
48 56
45 35
48-9
45-6 |
o
47 9 n.
Trollope.
Allen.
[
1853
48 33
48 6 J
Trollope.
11 58
335 02
1828
13 51 w.
13-9 w.
Liitke.
11 19
335 07
1840
41 01
41 0 i
8-35
8-35
Boss.
13 14
335 20
1843
15 15 w.
15-3 w.
Pasley.
18 20
335 30
1838
50 45
50-8 n.
8-84
8-84
Sulivan.
12 12
335 30
1840
16 26 w.
16-4 tv.
Boss.
18 38
335 30
1853
45 13
45-2 i
j.
Trollope.
Dayman.
13 04
335 31
1850
17 55 w.
17-9 tv.
12 39
335 35
1840
43 17
43-3 i
854
854
Boss.
12 22
335 50
1837
16 02 w.
16 0 w.
Bonite.
11 42
336 00
1838
39 14
39-2 n.
Stanley.
10 42
336 02
1843
12 49 \v.
12-8 tv.
38 02
38-0 n.
Boss.
13 00
336 12
1850
41 10
41-2 n.
Dayman.
15 13
336 21
1832
15 43 w.
15-7 tv.
FitzBoy.
14 43
336 21
1836
17 02 w.
17 0 w.
FitzBoy.
10 13
336 28
1837
16 59 w.
17-0 w.
Du Petit Thouars.
14 56
336 28
1840
16 26 w.
16-4 w.
Boss.
(
1822
15 00 w.
15 0 w.'
Owen.
1822
45 26
45-4
8-93
Sabine.
1
1826
18 30 w.
185 tv.
45 45
45-8
Dumont d’Urville.
14 54
336 30 j
1826
1836
16 30 w.
16 5 w.
■ 16-9 w.
45 46
45-8
- 45*4 n.
8-82
8-66
> 8-76
King.
FitzBoy.
1840
16 26 w.
16-4 w.
45 25
45-4
8-65
Boss.
{
1840
45 19
45-3
Crozier.
1843
18 12 tv.
18-2 tv. J
44 52
44-9 j
i
J
Belcher.
13 36
336 36
1846
17 04 w.
17-1 TV.
B6rard.
17 45
336 47
1847
18 16 w.
18-3 w.
Stanley.
12 17
336 48
1847
14 58 w.
15-0 w.
Stanley.
17 50
336 50
1832
17 06 w.
17-1 TV.
FitzBoy.
17 10
336 55
1840
47 52
479 n.
8-72
872
Boss.
19 50
336 56
1826
18 30 tv.
18 5 w.
Liitke.
11 44
336 58
1837
17 16 w.
17 3 w.
Du Petit Thouars.
12 37
337 11
1826
14 15 w.
14-3 w.
D’Urville.
12 42
337 13
1846
17 07 w.
17-1 TV.
Berard.
16 01
337 26
1838
44 33
44-6 n.
Stanley.
19 06
337 43
1832
17 39 w.
17 7 tv.
FitzBoy.
12 38
337 44
1850
18 08 w.
181 TV.
Dayman.
18 42
337 50
1839
17 58 tv.
18-0 tv.
Boss.
19 31
338 03
1832
18 06 w.
18-1 TV.
FitzBoy.
10 24
338 06
1850
16 03 w.
16-1 TV.
Dayman.
19 08
338 07
1840
49 47
49-8 n.
8-77
877
Boss.
13 43
338 18
1843
41 51
41-9 n
Belcher.
1 10 41 |
338 32
1837
16 15 w.
16-3 w.
Bonite.
1H«
It;
p Por prande
it S;.
‘ - At s .
At s ,
K At
l ' At
At
IcUt
feAts
At
Us
t- At
At s
tits
Er- At s
At s
M
E,.
fc
L Port
l
A At
Atse
(■- At se
(S At
Cii At
K,
,1 At
' Atse
Iti Ats
h\
pi ^ £
j>Atse,
A
At
;|p;At se£
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3 observations)
raya ,
-0 observations)
8 observations)
l observations)
i observations)
180
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
NORTH EQUATORIAL ZONE II.— Lat. 10° N. to 20° N. (continued).
Declination.
Inclination.
Force in British units.
Ob-^
Correction
Ob-
Cor. to
Ob-
Cor. to
Observer
to Epoch
Corrected.
Epoch
Corrected.
Epoch
Corrected.
1842-5.
served.
1842-5.
served.
18425.
o /
o
o /
o
16 54 w.
16-9 xv.
39 27
39-5 n.
Bonite.
Belcher.
19 48 w.
19-8 xv.
Bonite.
15 35 w.
15-6 xv.
Belcher.
35 23
35*4 n.
Belcher. j
19 04 w.
19-1 xv. 0
o
Denham.
17 54 w.
17-9w.}17'9w-
40 23
40-4 j 40-4 n.
8-55
| 8-55
Sabine.
Owen.
19 12 w.
19-2 xv.
Denham. |
19 10 xv.
19-2 xv.
Denham.
18 11 xv.
ISIw:}*92-
Owen.
20 13 xv.
Denham, j
Stations.
Long. E.
At sea (2 observations) 12 23 339 10
At sea 11 53 339 37
At sea (2 observations) 18 16 339 54
At sea 10 35 340 26
At sea 10 55 340 28
At sea 12 52 340 50
Gambia Eiver 13 08 343 27
Guancho.
Bulama .
11 40
11 33
344 15
344 21
11 52 344 23
1836
1813
1836
1843
1845
1846
1822
1826
1846
1846
1826
1846
Vogel
A
MSS. in Magnetic Office, received from L. S. Kamtz.
NORTH EQUATORIAL ZONE III.— LATITUDE 20° TO 30° N.
Authorities.
J Royal Geographical Society’s Journal, vol. xxv. ; and MSS. of the Observer in the Mag-
1 netic Office.
D’Hericourt ,
Laplace . . .
Becquerel. . .
Haines
Brown
Blosseville J
Schlagintweit Scientific Mission to India and High Asia (Leipzig and London, 1861).
Eenner ^
Grieve ....
Campbell . .
Eisher ....
Boileau ^Schlagintweit’s Scientific Mission as above cited.
Broun ....
Hodgson . .
Gerard ....
Blosseville J
Basevi x
Montgomerie I ®el>or^s Great Trigonometrical Survey of India (Dehra Doon).
Bonite ]
Darondeau j Vo»e de la Bonite <P‘ris’ 1842)'
-Rfilchfir I Magnetic Office; and Contributions to Terrestrial Magnetism (Sabine in Phi-
1 losophical Transactions).
GENERAL SIE EDWARD SABINE ON TEREESTE1AL MAGNETISM.
181
Novara (Austrian
Erigate)
Collinson ■
Blackwood
Richards
Lawrence
Crane
American Expedit" -
Eeise um die Erde (Wien, 1862-65).
>MSS. in British Hydrographic Office.
Liitke Mem. by Lenz in the Sci. Mem. Acad. St. Petersburg ; and L. S. Kamtz, MSS.
Duperrey ^
D’Urville
Du Petit Thouars. .
Jehenne, Ereycinet
Beechey
Barnett
Berghaus
Milne
Austin >L. S. Kamtz, MSS.
Smith
Eoster
Byron
Hudson
Young
Eumker
Sulivan
Prussian ships . ... J
Douglas Report on the Variations of the Earth’s Magnetic Eorce (Brit. Assoc. Reports, 1837).
Eriesach Memoirs of the Imperial Academy of Sciences, Vienna, vols. xxix. to xliv.
La Venus Voyage de la Venus (Paris, 1841).
Harkness Smithsonian Contributions, vol. xviii.
United States Coast")
Survey |
Emory ^United States Coast-Survey Reports.
Graham I
Nicollet J
MSS. in the Magnetic Office, received from Admiral Duperrey.
EitzRoy Surveying Voyage of the ‘ Beagle ’ (London, 1839).
Ross
Crozier I
[Contributions to Terrestrial Magnetism (Sabine in Phil. Trans.) and MSS. in the Mag-
Bethune j netic Office.
Sulivan
Stanley J
Sabine Pendulum and other Experiments (London, 1825).
Berard
Behard
Dumoulin
Deville J
182
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
NORTH EQUATORIAL ZONE III.— Eat. 20° N. to 30° N.
Stations.
Lat.N
Long. E.
Date.
25 52
24 19
24 53
29 15
28 33
27 43
14 12
14 52
15 10
15 30
34 10
34 22
1853
. 1854
1854
1853
1847
1832
Kassance Island
24
58
37 12
1832
Grane.
29
23
47 58
1825
Telodji Island
29
27
48 16
1824
Manamak
29
58
48 25
1827
Karnak
29
10
50 15
1824
Jask Bay
25
48
57 45
1829
Gutter Bay
25
10
62 02
1829
Karrachee
24
46
67 01 |
1848
1856
Yari Creek
23
52
67 49
1848
Sevan
26
25
67 57
1856
Mouth of the Til- River
23
38
68 05
1848
Hear Moinda Point . . .
23
36
68 22
1848
Nerani Creek
23
23
68 25
1848
Lalekatta Tomb
28
47
68 36
1848
Yaku Swamp
23
07
68 37
1848
Skikarpur
27
55
68 52
1856
Abdullah Shah
22
25
69 00
1848
EH
23
17
69 40
1856
Tomb
22
58
70 01
1848
Rajkot
22
13
71 07
1856
Surat
21
06
72 57
1848
Mean of 8 stations 1
in Rajvara J
27
00
75 00
1835
Chickuldah
21
24
75 56
1867
Kurnal
29
38
76 46
1828
Bhopal
23
16
77 22
1828
Sironi
24
09
77 39
1828
Badgaon
20
44
77 39
1868
Kalianpur
24
07
77 42
1867
Ehmadpur
23
36
77 43
1867
Meerut
29
00
77 44 |
1856
1867
Pahargurk
24
56
77 44 L
1867
Dholpur
26
45
77 55
1823
(
1823
Agra
27
09
78 02
1823
1856
l
1867
Aligarh
27
54
78 04
1856
Sag6r
23
50
78 43
1856
Hagri
20
25
78 53
1856
Ramnugger
29
24
79 10
1869
.Hynee Tal
29
23
79 30 |
1856
1869
Nauagau
25
56
79 32
1823
Bheem Tal
29
21
79 35
1869
Bagesir
29
50
79 48
1869
Jablpur
23
10
79 56
1856
Lukhnow
26
51
80 56
1856
Benttres
25
18
83 00
1856
Sigauli
26
47
84 44
1856
Patna
25
37
85 08
1856
Kathm4ndu
27
42
85 12
1856
Kissengani
26
06
87 56
1856
Falut
27
06
87 59
1856
Declination.
served. Epoch
1842-5.
Corrected.
Inclination.
Force in British units.
Ob-
Cor. tc
1
Ob-
served
Cor. tc
)
Observers
Epoch
Corrected.
Epoch
Corrected.
served..
' 1842-5
■ 1842-5,
38 38
38-6 n.
Vogel.
Vogel.
Vogel.
43 22
43-4 n.
Vogel.
36 41
36-7 n.
D’Hericourt.1
Becquerel.
Becquerel.
Haines.
Haines.
Haines.
Haines;
Haines.
Haines. I ;
Fenner.
Scklagintweil :
Grieve.
Schlagintweifj
Grieve.
Grieve. !
Grieve.
Grieve. > j
Grieve. 1 jj
36 02
360 n.
9-89
9-89
Scklagintwei
Campbell, j
28 25
28-4 n.
9 1 1
9-i’f
Scklagintweil ,
Campbell, j
Schlagintweil f;
Grieve.
Boileau. \
25 42
25-7 n.
8-86'
8-86
Basevi. J
Broun.
Hodgson. 1 ).
Hodgson. fc
22 41
22-7 n.
8-64
8-64
Basevi.
30 18
30-3 n.
909
9-09
Basevi. i
29 54
29-9 n.
8-95
8-95
Basevi. 1 i
Schlagintwe;;1 ,
39 07
-0 25
38-7 n.
9-55
9-55
Basevi. j
31 59
32-0 n.
9-09
9-09
Basevi. ; i
Hodgson.
1 O
Gerard. 1 ij
i 36-0 n.
[ 9-34
Hodgson.
Schlagintwe
Basevi. 1 J 1
36 01
36-0 J
9-34
J
36 59
370 n.
Schlagintwe : &
29 59
300 n.
Schlagintwa < £
22 50
22-8 n.
9-37
9-37
Schlagintwd jj.
1 40 06
-0 27
39 -7 n.
9-60
9-60
Montgomer! j ©,
38 34
-0 14
383 1 nn Q
9-86
| 9-72
Schlagintwfl , J
39 50
-0 27
39-4 J 38 8 N‘
9-58
Montgomer n
Hodgson, j 1 1
40 08
-0 27
39-7 n.
Montgomer . 1 )!
40 53
-0 27
40-4 n.
9-72
9-72
Montgomer. II
28 31
28-5 n.
986
9-86
Schlagintwil. 1 jj
35 19
35-3 n.
1002
1002
Schlagintwd |jj
32 41
32-7 n.
9-29
9-29
ScklagintW'|. j
35 40
35-7 n.
Scklagintws. 1
33 33
33-6 n.
9-22
9-22
Schlagintwi. I‘.j
37 34
376 n.
8-73
8-73
SchlagintwS.
35 12
35-2 n.
8-19
8-19
Scklagintwj;. 1 j
36 55
369 n.
8-32
8 32
Schlagintwi. I |
13 05 w.
13 09 w.
13 13 w.
9 48 w
7 51 w
6 00 w
5 22 w
4 50 w
4 35 w
3 20 w
1 20 w
0 17e.
0 06 e.
0 12 e.
0 35 e.
0 24 e.
0 51 e.
0 18 e.
1 12 E.
0 29 e.
0 43 e.
0 12 e.
1 27 e.
0 13 e.
1 00 E.
1 54 E.
1 31 E.
0 39 e.
0 57 e.
0 55 e.
1 49 e.
2 06 e.
1 48 e.
2 46 e.
2 10 e.
I 25 e.
1 25 e.
1 23 e.
1 20 e.
2 46 e.
1 37 e.
1 11 E.
2 37 e.
1 50 e.
1 54 e.
2 36 e.
2 20 e.
2 25 e.
0 14 w.
0 25 w.
0 25 w.
0 19 e.
0 19 e.
0 19 e.
0 14 w.
0 25 w.
0 14 w.
0 1 4 w.
0 14 w.
0 14 w.
0 14 w.
13-1 w.
13-2 w.
13-2 w.
9-8 w
7-9 w
60 w
5-4 w
4-8 \v
4-6 w
3-3 w
1-3 w
0-3 e.
01 E.
0-2 e.
0-6 e,
0-4 e.
0-9 e.
0-3 e.
1-2 E.
0 5 e.
0-7 E.
0-2 e.
1-5 E.
0-2 e.
l’O E.
1’9 E.
I ’5 E.
0-7 e.
I'O E.
0-9 e.
1-8 E.
21 E.
1- 6 E.
2- 4 e.
1-8 E.
1*7 E.
1- 7 E.
]-7 E.
M E.
2- 4 E.
1-4 E.
1 0 E.
2-4 e.
1-6 E.
1- 7 E.
2- 4 E.
2-3 E.
2-4 e.
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
183
NORTH EQUATORIAL ZONE III.— Lat. 20° N. to 30° N. (continued).
Declination.
Inclination.
Eorce in British units.
Lat. N
Long. E.
Date.
Ob-
served.
Correction
Ob-
served.
Cor. to
Ob-
served.
Cor. tc
Observers.
to Epoch
1842-5.
Corrected.
Epoch
1842-5.
Corrected.
Epoch
1842-5.
Corrected.
° /
o ,
o ,
0 /
0
o /
/
o
27 02
88 04
1856
2 31 e.
2-5 e.
36 25
36-4 n.
8-54
8-54
Schlagintweit.
Schlagintweit.
27 03
88 15
1856
2 48 e.
2-8 e.
36 33
36*6 n.
815
8-15
. 22 11
88 11
1837
3 06 e.
31 E.
26 38
26-6 n.
Bonite.
(
1827
2 38 e.
2-6 e.
'I
Blosseville.
1828
2 41 e.
2-7 e.
o
o
1
Hodgson.
22 33
88 20 }
1829
1829
2 24 e.
2 32 e.
2-4 e.
2-5 e.
■ 2-5 e.
j-27‘4 n.
U-ii
Hodgson.
Hodgson.
1833
j 2 38 e.
2-6 e.
26 33
26-6 j
Blosseville.
l
1856
2 25 e.
2-4 e.
28 15
28-3 ;
9-11
J
Schlagintweit.
22 50
88 23
1833
2 40 e.
2-7 e.
26 47
26-8 n.
Blosseville.
24 22
88 34
32 01
32-0 n.
7-90
7-90
Schlagintweit.
Schlagintweit.
Schlagintweit.
Schlagintweit.
22 46
89 37
2 30 e.
2 5 e.
29 20
29-3 n.
24 23
89 43
32 04
32-1 n.
23 43
90 20
1856
2 21 e.
2-4 e.
31 01
31 On.
25 14
91 41
1856
2 20 e
2 -3 e.
33 37
35 19
33-6 n.
35 3 n.
9-45
9-45
Schlagintweit.
Schlagintweit.
26 06
91 44
1856
2 00 e.
20 e.
9 54
9-54
24 53
91 47
2 29 e.
2-5 e.
Eisher.
26 46
91 57
1856
2 36 e.
2-6 e.
36 28
36-5 n.
9-62
9-62
Schlagintweit.
26 54
92 06
1856
4 43 e.
4-7 e.
37 08
37-1 n.
911
911
Schlagintweit.
26 35
92 47
1856
0 23 e.
37 15
37-3 n.
975
975
Schlagintweit.
S clilagintweit.
Beechey.
27 32
94 58
1856
0 46 e.
0-8 e.
38 30
38-5 n.
9-88
9-88
r
1827
1 58 e.
0 15 w.
1-7 E.l
29 57
30-0 4
22 11
113 30
1830
1837
1 30 e.
1 00 E.
0 12 w.
0 05 w.
1-3 E.
0-9 e.
l’l E.
30 32
30 *5 [30'2tr-
18-98
Laplace.
Darondeau.
l
1843
0 35 e.
0-6 e.
30 01
30-0 J
8-98
J
Belcher.
22 43
113 40
1841
0 22 e.
0-4 e.
30 26
30-4 n.
9-03
9-03
Belcher.
21 57
114 08
1836
1 04 e.
M E.
Bonite.
f
1813
0 37 e.
0-6 e. 1
30 03
30-1 ]
8-95
1
Belcher.
22 16
114 10
1851
1
► 0-6 e.
29 40
29-7 1 30-3 n.
l 8-95
Collinson.
l
1858
J
31 08
31-1 J
8-95
J
Novara.
22 17
114 10
1855
0 30 e.
0-6 e.
Richards.
20 14
114 46
1843
26 38
26-6 ur.
Belcher.
22 34
114 52
1845
0 25 e.
0-4 e.
Collinson.
22 50
1 15 45
1845
1 32 e.
1-5 E.
Collinson.
22 50
116 04
1844
0 36 e.
0-6 e.
Collinson.
23 00
116 31
1844
0 01 E.
00
Collinson.
23 26
116 54
1844
0 47 e.
0 8 e.
Collinson.
23 43
117 22
1844
0 38 e.
0-6 e.
Collinson.
24 02
117 54
1844
0 31 e.
0-5 e.
Collinson.
24 27
118 03
1841
0 45 e.
0-8 e.
Collinson.
24 32
118 32
1844
1 30 e.
1-5 E.
Collinson.
24 49
118 41
1844
0 25 e.
0 4 e.
Collinson.
24 07
118 51
1858
0 1 2 w.
0 16 e.
01 E.
N ovara.
23 30
119 30
1843
0 29 e.
0-5 E.
Collinson.
24 11
119 37
1828
1 18 e.
0 14 w.
1-1 E.
Liitke.
, 26 08
119 38
1855
1 08 w.
0 13 e.
0-9 w.
Richards.
26 09
119 40
1843
0 30 w.
0-5 w.
Collinson.
25 22
119 45
1843
0 16 e.
0-3 e.
Collinson.
26 26
119 55
1844
1 10 E.
1-2 E.
Collinson.
25 58
119 57
1843
0 58 e.
10 E.
Collinson.
23 06
120 05
1855
0 34 w.
0 13 e.
0-4 w.
Richards.
22 36
120 17
1855
0 34 w.
0 13 e.
0-4 w.
Richards.
26 42
120 23
1843
2 01 e.
20 e.
Collinson.
27 10
120 32
1844
1 03 e.
M E.
Collinson.
26 59
120 44
1842
2 26 e.
2-4 e.
Collinson.
27 26
121 06
1842
0 55 e.
0-9 e.
Collinson.
27 48
121 07
1842
1 54 e.
19 E.
Collinson.
22 38
121 26
1845
0 19 e.
0 3 e.
30 45
30-8 w.
Belcher.
29 53
121 33
1842
2 55 e.
2-9 e.
Collinson.
25 09
121 47
1845
0 40 w.
07 w.
Collinson.
29 06
121 54
1842
1 00 E.
10 E.
Collinson.
28 26
121 54
1842
1 24 e.
1-4 E.
Collinson.
sling
jnd Harbour
lernagore .
ur Bolea .
Hoi Kong
ban
184
GENERAL SIR EDWARD SABINE ON TEEEESTEIAL MAGNETISM.
NORTH EQUATORIAL ZONE III.— Lat. 20° N. to 30° N. (continued).
Declination.
Inclination.
Force in British units.
Stations.
Lat. N.
Long. E.
Date.
Ob-
served.
Correction
Ob-
served.
Cor. to
Ob-
served.
Cor. to
to Epoch
1842-5.
Corrected.
Epoch
1842-5.
Corrected.
Epoch
1842-5.
Corrected.
0 ■/
o ,
o ,
o
o /
o
San Miguel, Batan . . .
20 28
121 56
1844
0 30 w.
0-5 w.
27 23
27-4 n.
29 13
121 57
1842
1 17 b.
1-3 E
29 42
122 01
1840
1 40 b.
1-7 E.
29 57
122 11
1840
1 56 b.
1-9 E
29 52
122 14
1840
1 21 E.
1-4 m
28 51
122 14
1842
1843
1858
1843
1 52 e.
1-9 B.
11 w.
1-7 w.
1-4 w.
124 02
124 09
1 03 w.
1 40 w.
33 40
337 n.
29 34
24 21
124 12
1 25 w.
33 43
337 n.
At sea (5 observations)
22 15
124 24
1851
2 20 w.
2-3 w.
24 44
125 15
1844
1 23 w.
1-4 w.
34 04
34-1 n.
1827
0 41 b.
0-7 b. ]
1 °
Loo Choo Islands
26 13
127 39 \
1845
1 35 w.
1-6 vv. 1
l 0-6 w.
36 13
36 -2n.
{
1853
1 00 w.
1-0 w. ,
1
29 52
129 48
1845
1851
0 36 w
44 52
44-9 n.
At sea (5 observations)
22 23
132 25
3 24 w.
34 w.
20 47
133 25
1858
1851
01 w.
2 0 w.
At sea (6 observations)
At sea (3 observations)
26 29
22 08
27 05
138 52
139 16
139 54
2 00 w.
0 25 e.
1 09 b.
1828
1827
0-4 e.
1*2 E.
At sea (3 observations)
27 04
141 22
1828
0 01 w.
00
27 43
142 08
1827
1828
2 37 b.
2-fi e
27 07
142 24 1
0 06 w.
0-1 W.)
. 0-2 w.
36 48
36' l ] 37-2 n.
8-64
| 8-64
1851
0 15 w.
0-3 w. 1
37 35
37-6 j
At sea (3 observations)
22 00
161 06
1827
8 40 e.
87 e.
At sea (7 observations)
27 37
161 29
1827
7 06 b.
71 E.
At sea
20 10
173 19
1836
11 42 e.
117 E.
At sea
29 54
183 06
1851
47 04
47-1 n.
At sea (4 observations)
28 35
187 41
1851
13 42 e.
137 e.
At sea
29 40
191 49
1848
52 28
52-5 n.
At sea
27 44
193 41
1848
51 45
51-8 n.
At sea
26 17
195 12
1848
50 43
507 n.
At sea (2 observations)
24 42
195 41
1851
11 55 e.
11-9 E.
At sea (5 observations)
24 25
197 34
1848
48 46
48-8 n.
At sea (2 observations)
27 58
198 09
1853
10 25 e.
10-4 e.
At sea
27 36
198 20
1852
1 1 09 b.
11-2 B.
At sea (2 observations)
25 48
199 10
1853
9 44 e.
9-7 e.
At sea (2 observations)
22 23
199 19
1851
6 20 e.
6-3 e.
At sea (2 observations)
24 21
200 12
1852
10 11 E.
10-2 e.
At sea (3 observations)
23 58
200 23
1853
41 16
4 1 *3 n.
At sea (2 observations)
23 36
200 25
1853
9 24 b.
9-4 e.
(
1
1824
9 52 e.
9-9 e. 1
I
1827
10 26 e.
10-4 e.
Oahu
21 17
202 00 j
1830
^10-4 e.
41 39
41-7 >41-5 n.
[ 8-66
1
1837
10 39 e.
107 e. 1
41 35
41-6
(
1838
10 39 e.
107 e. J
41 17
41-3 J
8-66
J
(
1836
10 11b.
10 2 e. "I
1
42 04
42-1 )
1837
10 00 E.
10 0 E.
Honolulu
21 19
202 18 <(
1
1840
9 17 e.
9-3 e.
^97 e.
{-42-1 n.
1852
9 10 e.
9-2 e.
1
l
1859
9 42 e.
9-7 e. ^
1
J
Mowi
20 52
203 19
1817
8 49 e.
8-8 e.
41 39
41 -6 n.
At sea (3 observations)
21 06
203 39
1838
8 46 e.
8-8 e.
At anchor at sea
21 20
203 49
1848
. ...
42 36
42-6 h.
At sea (3 observations)
20 48
205 42
1831
8 28 e.
8-5 e.
At sea
20 21
.211 34
1828 '
7 50 e.
7-8 e.
At sea
25 21
213 56
1827
13 00 e.
130 e.
47 38
47-6 n.
1070
1070
At sea (2 observations)
26 58
216 42
1827
11 47 e.
11-8 E.
At sea
23 26
218 02
1827
11 06 e.
11-1 E.
46 03
46-1 n.
9-43
9-43
At sea (2 observations)
22 33
218 20
1827
11 06 e.
1M E.
At sea
21 19
218 57
1827
10 00 E.
10-0 E.
43 08
43-1 n.
At sea (2 observations)
21 10
237 50
1830
7 34 e.
7-6 e.
42 15
42-3 n.
9-42
9-42
Belcher.
Collinson.
Collinson. j
Collinson.
Collinson.
Belcher.
Belcher.
American Ejedi-
Belcher. ' ; ;
L 3 l(i
Beechey
Belcher.
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM,
185
NORTH EQUATORIAL ZONE III.— Lat. 20° N. to 30° N. (continued).
~
Declination.
Inclination.
Fo)
:ce in British units.
Stations.
Lat. N
Long. E.
Date.
Ob-
served.
Correction
Ob-
served.
(Cor. to
Ob-
served.
Cor. tc
)
Observers.
to Epoch
1842-5.
Corrected.
Epoch
■1842-5.
Corrected.
Epoch
1842-5,
Corrected.
Vt
23 06
238 07
1S30
8 10 e.
8 2 e.
44 48
44-8 n.
9-62
9-62
Erman.
'3 observations)
2 observations'
28 53
238 32
1830
9 00 e.
9 0 e.
53 14
53-2 n.
10-50
10-50
Erman.
25 40
238 40
1830
48 50
48-8 n.
1007
1007
Erman.
26 36
239 02
1830
50 14
50-2 n.
10-23
10-23
Erman.
At
3 observations)
27 24
239 02
1830
11 50 e.
11-8 E.
Erman.
At
3 observations)
tholomew
28 09
239 04
1830
10 04 e.
101 E.
52 09
52-2 n.
10-37
10-37
Erman.
27 40
245 07
1S39
10 46 e.
10-8 e.
51 41
51 7 n.
11-20
11-20
Belcher.
.
f
1837
8 17 e.
8 3 e.
°
50 43
50-7 1 0
1
Venus. .
24 38
247 53 |
1839
9 15 e.
9-3 e.
• 9-4 e.
46 34
46 6 1 48-6 n.
10-66
| 10-75
Belcher.
‘
1866
10 41 e.
10-7 e.
48 32
16-5 J
10 84
Harkness.
St,
•
22 52
250 07
f
1839
8 38 e.
45 39
45-7 n.
1
10-63
10-63
1
Belcher.
7
1828
9 48 e.
9-8 e.
Beechey.
Mai
m
23 11
253 36 |
1837
8-6 e.
9 3 e.
47 45
47-7 l 47-2 n.
[ 10-75
Venus.
1839
9 24 e.
9-4 e.
46 39
46-7 J
10-/5
Belcher.
San|
21 32
254 44 |
1837
1838
9 09 e.
8 47 e.
9-2 e.
8-8 e.J
9-0 e.
46 09
44 36
46-21 ,
44-6 j 4o*4 N‘
j 10-66
Venus.
Belcher.
10-66
29 34
255 35
1852
10 16e.
10-3 e.
55 41
55-7 n.
Emory.
Eag
28 42
259 30
1852
10 01 E.
55 31
55*5 n.
Emory.
Emory.
Emory &U.S.C.S.
27 30
259 55
1852
10 00 e.
54 07
54-1 n.
r.
Kin
26 23
261 17
1853
9 15 e.
9-3 e.
52 27
52-5 n.
Kioj
ande ..
25 57
262 52
1853
9 01 e.
90 e.
52 24
52-4 n.
TJ. S. Coast Survey.
T
28 55
264 40
1853
9 09 e.
57 12
57-2 n.
12-15
1215
U. S. Coast Survey.
U. S. Coast Survey.
East
ise
29 13
265 05
1853 I
9 05 e.
9-1 E.
57 42
57-7 n.
12-15
1215
Doll
29 26
265 07
1848
9 0 e.
57 55
57-9 n.
12-31
12-31
U. S. Coast Survey.
Behard.
At s
)2 observations)
21 08
265 13
1839
11 11e.
11*2 E.
Mou
of Sabine River
29 44
266 08
1840
8 40 e.
87 e.
58 33
586 n.
Graham.
]n
Sabi.
R,;™.
29 44
266 08
1840
8 40 e.
87 e.
U. S. Coast Survey.
U. S. Coast Survey.
Barnett.
Cl
C-'te
fl.TlpVlP
29 44
268 18
1860
8 22 e.
8*4 e.
59 09
59-2 n.
12-42
1242
r
Arer
22 07
268 36
49 32
49-5 n.
i -
Isle
'•nip.'Pft
29 02
269 04
r
1853
8 19 e.
8-3 e.
1
U. S. Coast Survey.
Nicollet.
|
1834
60 15
60-3)
1
it
New1
leans
29 57
269 56 |
1857
8 00 e.
80 e.
► 7-9 e.
59 30
59-5 L 59-9 n.
12-52
l 12-50
Friesach.
i
1858
7 52 e.
7-9 e.J
59 47
59-8 J
12-49
j
U. S. Coast Survey.
-
Fort
vingstone
29 17
270 11
1853
7 38 e.
7-6 e.
U. S. CoastSurvey.
Ligh
louse .
28 59
270 39
1840
58 46
58-8 n.
Graham.
F
Cubi
29 10
270 46
1859
7 32 e.
7-5 e.
58 54
58-9 n.
12-35
12-35
TT.S. CoastSurvey.
U. S. CoastSurvey.
U.S. CoastSurvey.
Barr
ley ..
29 54
270 53
1858
59 48
59-8 n.
12 37
12 37
1'
S.E.
29 05
270 58
1859
58 45
58-8 n.
12-35
12-35
(V
Passi
l’outre
29 11
270 59
1860
7 30 e.
7-5 e.
58 47
58-8 n.
12-33
12-33
U. S. Coast Survey.
: At si
: 1 observations)
21 42
271 26
1839
9 52 e.
9-9 e.
Behard.
At s<
: i observations)
21 50
271 30
1838
9 19 e.
9-3 e.
Behard.
J Cont
* Island
21 32
273 11
1838
49 48
49-8
Barnett.
: Woe
tp-L
c s Islands
21 12
273 20 |
1831 .
1844
6 10 e.
6 40 e.
6-2 e. 1 a r
6-7 e. r5E-
Lawrence.
Lawrence.
;
St. J
oh
29 52
274 37 L
1843
6 24 e.
6-4 e.
U. S. Coast Survey.
U. S. Coast Survey.
U. S. CoastSurvey.
■
Cape
i a Bias
29 40
274 38
1854
6 07 e.
61 E.
St, c-
1 ge’s Island . . .
29 37
274 57
1853 :
6 02 e.
6-0 e.
Anal
pc. a
i >la
29 43
275 01
1860
6 12 e!
6*2 e.
60 i 9
60-3 n.
12-45
12-45
U. S. CoastSurvey.
Barnett.
i intonio
21 52
275 02
1847
6 00 e.
6 0 e.
; Dog
I nd
29 47
275 24
1853
5 51 e.
5-9 e.
U.S. CoastSurvey.
U. S. Coast Survey.
U. S. CoastSurvey.
U. S. Coast Survey.
Behard.
I
Depi
it ey
29 07
276 57
1852
5 20 e.
5-3 e.
59 55
59-9 n.
12-25
12-25
Tort
Egm
24 28
277 07-
1843
6 15 e.
63 e.
f
10 Key
27 36
277 15
1843
5 25 e.
5*4 e.
At si
1
3£ | observations)
23 47
277 30
1839
7 38 e.
7*6 e.
,
1822
1
51 55
51-9 1
11-25
y
Sabine.
ilav
Mb.. .
23 09
277 38 j
1857
5 15 e.
5-3 e.
5-3 e.
L 5.3 B.
1,520n.
L 11-25
U. S. CoastSurvey.
Friesach.
: Sane
1857 ;
5 18 e.
52 00
52*0 J
li-25
I
i: 7
24 27
278 07
1849
5 29 e.
5-5 e. ‘
4-8 e. "
54 26
54-4 n.
11-62
J 11-62
U. S. Coast Survey.
U.S. CoastSurvey.
; Key
n
24 33
278 12 |
1850
4 46 e.
[ 5‘1 E.
I' At Si
1860
4 51 e.
4-9 e. j
54 39
54-7 n.
11-66
11-66
U. S. Coast Survey.
&a ...
28 22
279 35 ^
1841
4 57 e.
5-0 e.
Barnett.
i Cap<
3 1 rida
25 40
279 51
1850
4 25 e.
4-4 e.
56 13
56-2 n.
11-90
11-90
U. S. Coast Survey.
_
MDCCCLXXV.
2 C
186
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
NORTH EQUATORIAL ZONE III.— Lat. 20° N. to 30° N. (continued).
Stations.
Lat. N.
Long. E
At sea
29
17
280
24
Nassau
25
05
282
39
St. Jago (Cuba)
20
00
283
57
San Domingo
21
33
284
15
At sea . . . .
27
55
285
24
Barracon, Cuba
20
22
285
26
Watlingo Island
23
57
285
35
Crooked Island
22
07
285
36
Crooked Island
22
47
285
39
Cape Maize
20
14
285
48
At sea (3 observations)
28
06
307
46
At sea (2 observations)
22
16
309
10
At sea (2 observations)
21
27
310
50
At sea (2 observations)
21
26
316
20
At sea (3 observations)
28
26
316
26
At sea (5 observations)
27
19
316
32
At sea
23
49
316
40
At sea
21
32
316
43
At sea
24
43
3i6
55
At sea
25
48
317
19
At sea
28
36
317
30
At sea
27
10
317
49
At sea
27
51
318
27
At sea (2 observations)
26
05
318
39
At sea (2 observations)
29
56
318
45
At sea (4 observations)
27
43
319
02
At sea
26
32
319
46
At sea
29
27
319
50
At sea
24
00
320
08
At sea
29
34
320
11
At sea (2 observations)
20
57
34
320
320
31
56
At sea (2 observations)
28
07
321
13
At sea (6 observations)
27
46
321
26
At sea
24
32
321
40
At sea
22
52
321
51
At sea
26
25
321
51
At sea (2 observations)
29
42
322
12
At sea (3 observations)
22
25
322
22
At sea (2 observations)
24
15
322
44
At sea (4 observations)
27
00
323
05
At sea (4 observations)
27
25
323
21
At sea
23
00
323
23
At sea
21
04
323
25
At sea
25
34
323
29
At sea
29
15
323
40
At sea
22
48
323
54
At sea
28
07
324
00
At sea |
22
06
324
20
At sea (4 observations)
At sea (2 observations)!
24
27
324
30
29
02
324
37
At sea (2 observations)
24
10
324
40
At sea (2 observations)
21
08
324
47
At sea
29
53
324
52
At sea
26
19
325
00
At sea
28
12
325
11
24
53
325
27
At sea (2 observations)
29
17
325 ,
31
At sea I
25
00
325
41
Declination.
Inclination.
Eorce in British units.
Date.
Ob-
served.
Correction
to Epoch
1842-5.
Corrected.
Ob-
served.
Cor. to
Epoch
1842-5.
Corrected.
Ob-
served.
Cor. tc
Epoch
1842-5
Corrected.
Observei
o /
o
o /
0
1841
4 52 e.
4-9 e.
Barnett, i £
1839
3 07 e.
3-1 E.
1 °
Milne.
1841
56 13
56-2 1 56-3 n.
Barnett. | e
1843
56 23
56-4 J
Barnett. |
1837
3 39 e.
3-7 e.
Milne.
1837
4 02 e.
4-0 e.
Milne.
1842
2 07 e.
2-1 E.
Jehenne. » n r
1831
3 17 e.
3-3 e.
50 07
501 n.
Austin and ster.
1831
2 31 e.
2-5 e.
Smith.
1831
4 27 e.
4- 5 e. 1 9 n
5- 2e.}4'9e-
Austin. | i
1835
5 13 e.
Foster. A
1837
2 34 e.
v.
Milne.
1831
2 27 e.
2-5 e.
Austin. ;tl ■'
1849
8 00 w
8 0 vv.
Hudson. |
1849
9 30 w
9 5 vv.
Hudson. | |
1838
5 45 w
5-8 w.
Behard. | .I
1838
8 20 vv
8-3 vv.
Behard. t T ■
1839
13 44 w
13-7 w.
Du Petit Tiuai-s.
1829
8 49 w
8 8 w.
Rumker.
1839
58 47
5 8 Bn.
1051
10-51
Sulivan. i
1839
56 50
56-8 n.
10-23
10-23
Sulivan.
1839
59 47
59-8 n.
10-56
10-56
Sulivan. '(. f-
1839
60 50
60-8 n.
10 70
10-70
Sulivan. j \--
1839
62 52
62-9 n.
10-89
10-89
Sulivan.
1839
62 02
62 0 n.
10 75
10-75
Sulivan. j ,'j
1839
62 27
62 5 n.
10-85
10-85
Sulivan. i •
1839
12 34 w.
12-6 vv.
Du Petit lluars.!
1858
17 06 vv.
1 7 1 vv.
Novara. >
1851
15 16 vv.
15-3 w.
Smith. i
1846
j 13 17 w.
13-3 w.
Sulivan. I
1846
14 24 vv.
14-4 vv.
Sulivan. i
1839
11 30 w.
11-5 w.
Du Petit Tmars.
1830
63 11
63-2 n.
10-61
10-61
Erman. \
1846
11 56 vv.
1 1*9 vv.
Sulivan.
1839
11 20 vv.
11-3 w.
Du Petit I.'uars.
1830
14 36 vv.
14-6 w.
ei 52
61-9n.
10 45
10-45
Erman.
1829
14 03 vv.
14-1 vv.
Prussian sjps. !
1859
14 59 vv.
15-0 w.
Novara, f
1830
12 12 vv.
12-2 w.
Erman. i i.
1830
13 05 vv.
13 1 w.
60 49
60-8 n.
10-58
10-58
Erman. j A
1850
15 40 vv.
15-7 vv.
62 24
62-4 n.
Dayman.
1834
12 08 w.
12-1 vv.
Prussian Ips;
1830
11 26 w.
1 1 -4 vv.
58 22
58-4 n.
1013
10-13
Erman. 1
1850
1 6 50 vv.
16 8 w.
Dayman.
1829
15 40 vv.
15-7 w.
Liitke.
1850
12 56 vv.
12-9 vv.
Smith. |
1829
12 50 w.
1 2-8 w.
Liitke.
1850
11 00 vv.
11-0 w.
Young, i
1836
17 10 w.
17-2 vv.
FitzRoy, j
1838
9 40 w.
9-7 w.
Behard.
1836
17 06 w.
171 vv.
FitzRoy.
1830
11 30 w.
11-5 w.
Erman. i
1850
16 1 1 vv.
16-2 w.
Dayman.!
1846
17 43 w.
17-7 vv.
Berard. !
1850
57 33
57-6 n.
Dayman.
1830
12 25 w.
12-4 w.
54 44
54-7 n.
968
9-68
Erman. |
1843
16 12 w.
16-2vv.
62 04
62-1 n.
Ross.
1843
14 01 w.
14-0 w.
59 10
59-2 n.
Ross i
1843
16 30 vv.
16-5 w.
60 45
60-8 n.
Ross. j
1843
15 17 w.
15-3 vv.
57 43
57-7 n.
Ross. |
1837
17 30 vv.
1 7-5 vv.
Bonite. !
1836
16 05 w.
161 w.
j FitzRoy.
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
187
NORTH EQUATORIAL ZONE III.— Lat. 20° to 30° N. (continued).
Stations.
Lat. N.
Long. E.
Date.
Declination.
Inclination.
Force in British units.
Observers.
Ob-
served.
Correction
to Epoch
1842-5.
Corrected.
Ob-
served.
Cor. to
Epoch
1842-5.
Corrected.
Ob-
served.
Cor. tc
Epoch
1842-5.
I Corrected.
O /
o ,
o ,
O
O /
o
At !
(2 observations)
22 55
325 42
1838
10 05 w.
10-1 w.
Behard.
At -
(3 observations)
28 27
325 53
1846
17 47 w.
17-8w.
Berard.
21 49
326 00
1850
Young.
23 41
326 11
1836
15 20 w.
FitzBoy.
-
25 23
326 35
1846
17-1 w.
Berard.
It J
23 36
326 37
1843
13 46 w.
13-8 w.
56 15
56-3 n.
Boss.
At ;
(2 observations)
25 57
327 11
1837
1 6 36 w.
16-6 w.
**
Bonite.
It •
22 10
327 24
1843
14 53 w.
14-9 w.
54 26
54-4 n.
Boss.
At -
20 40
327 29
1850
16 11 w.
16 2 w.
Dayman.
At d
23 02
327 30
1838
10 30 w.
10 5 w.
Berard.
20 50
327 51
1843
14 37 w.
Boss.
1:
At si
At s
21 32
329 31
1837
14 38 w.
U-6 w.
Bonite.
(2 observations)
25 39
331 58
1838
17 02 w.
17 0 w.
Berard.
At s
(2 observations)
22 51
334 00
1851
19 08 w.
19-1 w.
Colli nson.
At s
(5 observations)
22 35
334 38
1830
19 06 w.
191 w.
Prussian ships.
28 34
336 24
1851
21 25 w.
21-4 w.
Collinson.
At i
(2 observations)
21 29
336 28
47 49
47-8 n.
Trollope.
6.:
29 54
336 46
1850
59 44
597 n.
Collinson.
¥■
At s|
(2 observations)
21 33
337-20
1841
49 41
49-7 n.
The John Fleming.
At j
(7 observations)
27 42
337 22
1830
20 16 w.
20-3 w.
Prussian ships.
At s
(2 observations)
23 42
337 44
1841
51 47
51-8 n.
The John Flemi ng.
b
At s
(3 observations)
21 58
337 46
1826
17 52 w.
17 9 w.
Dumont d’Urville.
}
At s
(3 observations)
21 41
337 48
1826
19 52 w.
19 9 w.
Liitke.
t
Ats
(2 observations)
21 24
337 52
1842
19 45 w.
19-8 w.
Berard.
At ;
24 41
337 52
51 02
51-0 n.
Trollope.
Ats
22 24
338 29
1842
20 00 w.
200 w.
Berard.
!:
Ats
20 22
338 29
1846
19 40 w.
19-7 w.
Denham.
jh
Ats
!(2 observations)
20 30
338 35
1832
18 22 w.
18-4 w.
.FitzBoy.
>
Ats
f(2 observations)
22 23
338 36
1846
18 58 w.
19 Ow.
Stanley.
At s]
26 31
338 56
52 07
52-1 n.
Trollope.
Ats
23 10
339 15
1838
53 26
53*4 n.
901
9-01
Sulivan.
y
At J
20 54
339 18
1840
8 91
8-91
Boss.
Ats1
21 41
339 20
1832
1 8 30 w.
18-5 w.
FitzBoy.
-
At si
:
21 10
339 35
1837
1 8 42 w.
18-7 w.
Du Petit Thouars.
ii
Ats
(2 observations)
22 20
339 40
1832
18 28 w.
18-5 w.
FitzBoy.
Ats
24 26
339 52
1822
16 33 w.
16-6 w.
55 22
55-4 n.
Duperrey.
Ats
22 20
340 04
1840
19 25 w.
1 9-4 w.
8-98
8-98
Boss.
Ik
[r,
Ats
23 09
340 13
1832
18 47 w.
18-8 w.
FitzBoy.
Ats
21 50
340 28
1837
20 03 w.
201 w.
Du Petit Thouars.
' fos
At s
23 38
340 43
1840
19 30 w.
19-5 w.
Boss.
n
Ats
23 40
340 45
1840
52 54
52*9 n.
9-08
9-08
Boss.
Ats
23 50
340 51
1840
19 12 w.
19-2 w.
Boss.
\h
Ats
(2 observations)
26 58
340 52
1846
20 28 w.
20-5 w.
Denham.
l
Ats
(2 observations)
22 49
340 52
1836
! 20 35 w.
20 6 w.
Bonite.
At s
29 12
340 56
1846
20 26 w.
204 vv.
Denham.
-
Ats
24 57
340 57
1838
55 00
55 0 n.
9-09
909
Sulivan.
Ats
23 31
341 10
1837
19 55 w.
19 9 w.
Du Petit Thouars.
m
Ats
24 31
341 17
1840
20 15 w.
20-3 w.
Boss.
E
At s
24 40
341 18
1832
19 53 w.
19-9 w.
FitzBoy.
At s
24 51
341 18
1840
53 43
53-7 n.
9 1 1
9 11
Boss and Crozier.
i:
At s
5 (5 observations)
I 26 3S
341 23
1826
21 19 w.
213 w.
Liitke.
(n
Ats
i
25 33
341 55
1840
21 33 w.
21-6 w.
Boss.
At s
i
25 26
341 58
1832
19 59 w.
20 0 w.
FitzBoy.
is
i (2 observations'
1 27 08
341 59
1842
21 00 w.
21-0 w.
Berard.
At :
26 01
342 25
1840
54 03
54-1 n.
9-30
9-30
Boss.
E
At:
* '2 observations]
) 27 39
342 36
1822
I 18 45 w.
18-8 w.
Duperrey.
At:
27 59
343 00
1842
21 00 w
21 -0 w.
Berard.
Pa
At i
31
26 48
343 04
1837
21 54 w
21 "9 w.
Dumoulin.
i-
At:
26 59
343 12
1832
20 04 w
20-1 w.
FitzBoy.
P
At:
3<
27 30
343 14
1826
22 04 w
Liitke.
jS
»*
1 ? Teneriffe * . .
. 28 16
343 21
1842
23 40 w
23-7 w!
Deville.
p
At:
51 (2 observations]
I 25 36
343 30
1836
21 25 w
21-4 w.
.....
| |
Bonite.
Not used in the Map.
188 GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
NORTH EQUATORIAL ZONE III.— Lat. 20 N. to 30° N. (continued).
Stations.
Lat. N.
Long. E.
Date.
Declination.
Inclination.
Force in British units.
Observers
Ob-
served.
Correction
to Epoch
1842-5.
Corrected.
Ob-
served
Cor. to
[Epoch
1842-5.
Corr
ected.
Ob-
served.
Cor. to
Epoch
1842-5.
Corrected.
° /
o /
o /
o
o ,
o
At sea (2 observations)
29 31
343 39
1832
20 44 w.
20-7 w.
FitzEoy.
At sea (2 observations)
28 16
343 42
1832
20 22 w.
20-4 w.
FitzEoy.
1822
21 00 w.
21 0 w.)
57 06
57-1)
9-46
Duperrey.
1826
22 37 w.
22-6 w.
Dumont d’ L r
1<\
1836
57 28
57-5
Bethune.
1837
22 50 w.
22-8 w.
o
°
Vidal.
Santa Cruz. . #
28 28
343 45 \
1837
21*7 w.
57 47
57-8
► 57*4 n.
9-56
- 9-45
Wickham.
1838
57 21
57-4
Stanley.
1838
57 40
57-7
939
Sulivan. '
1840
20 31 w.
20-5 w.
57 05
571
9-41
Eoss.
1842
)
57 17
57’3 j
Blackwood, j
At sea
28 43
344 38
1837
1 20 38 v.
20-6 w.
Dumoulin.
At sea
29 15
345 15
1842
! 22 00 w.
22 0 w.
Berard.
At sea (2 observations)
28 17
345 20
1836
21 53 w.
21-9 w.
Bonite.
At sea
345 30
1822
| 21 00 w.
1 ■ i i
21-0 w.
.
57 40
j
577 n. '
Duperrey. j
NORTH EQUATORIAL ZONE IV.— LATITUDE 30° TO 40° N.
Authorities .
^ ^ J MSS. in the Magnetic Office, communicated by Admiral Duperrey ; and for a few
\ land stations, MSS. in the Magnetic Office, communicated by Professor L. S. Kamtz.
Airne Exploration Seientifique de l’Algerie (Paris, 1845).
Norwegian Officers Hansteen, Mag. Beob. (Christiania, 1863).
Novara (Austrian Frigate) Reise um die Erde (Wien, 1862—65).
Beechey, Fisher, Smith, l _ _ _ , '
I L. S. Kamtz, MSS.
and Caiigny J
Shadwell . MSS. in the British Hydrographic Office.
Schaub Mag. Beob. von Dr. F. Schaub (Triest, 1858).
D’Abbadie, D’Hericourt, -i
Estconrt, Rawlinson, v L. S. Kamtz, MSS.
Parrot, and Freycinet . J
Ivatinsk
Lenz
Schlagintweit
Cunningham
Walker and Basevi
Fuss, G. von Kowanko, 1
and Schatskoff J
Basil Hall
Collinson, Richards, )
Crane, and Kellett . . j
Erman
Survey of the Caspian Sea, St. Petersburg, 1870 (in the Russian Language).
Petermann, Mittheilungen, 1870 (Gotha).
. Scientific Mission to India and High Asia (Leipzig and London).
In Sehlagintweit’s Scientific Mission.
Reports of the Great Trigonometrical Survey of India.
Mem. by Fritsche in Wild’s Repertorium for 1870, Band I. Heft 2.
, In Kamtz MSS., above cited.
MSS. in the British Hydrographic Office.
. Reise um die Erde (Berlin, 1841).
GENEEAL SIE EDWABD SABINE ON TEEEESTEIAL MAGNETISM.
189
Douglas (David) Eeport on the Variations of the Earth’s Magnetic Eoree (Brit. Assoc. Eeport, 1837).
Belcher (Sir Edward) . . . .MSS. in the Magnetic Office.
American Expedition . . . .MSS. in the British Hydrographic Office.
Liitke Mem. by Lenz in the Sci. Mem. of the Acad of St. Petersburg, 1838 ; and L. S.
Kamtz, MSS.
Moore (Sea observations) MSS. in the Magnetic Office, received from Admiral Moore.
United States Coast Sur- ) , 1Q , 1Q
} Annual Eeports, 18o6 to 1863.
vey J
Harkness Smithsonian Contributions, vol. xviii.
La Venus Voy. autour du Monde (Paris 1841).
Perry, Emory, and other 1 United States Coast Survey Eeports ; Smithsonian Contributions ; and Memoirs of
United States Officers J the American Academy, vol. vi. part 1.
Graham Xicollet, Loon*, | Mtea States Coast s
Schott, and Locke . . J J
Friesach Memoirs of the Imperial Academy of Sciences, Vienna, vols. xxix. to xliv.
Barnett MSS. in the Magnetic Office, and L. S. Kamtz, MSS.
f Contribution to Terrestrial Magnetism, No. VII. Philosophical Transactions, 1846,
^ ( and in U. S. Coast Survey.
Behard MS. in the Magnetic Office, received from Admiral Duperrey.
Hudson, Austen, Foster, ^
Milne, Gaint, Jehenne,
Lunt, Young, Eumker,
Smith, Prussian Ships,
Sulivan, and Du Petit
Thouars
Bonite Voyage (Paris, 1842).
FitzEoy Surveying Voyage (London, 1839).
Vidal Contribution to Terrestrial Magnetism, No. IX., Philosophical Transactions, 1849,
Art. XII.
Eattlesnake H.M.S. ‘ Battlesnake,’ MSS. in the Hydrographic Office.
Lamont Erdmag. S.W. Europa’s (Miinchen, 1858).
Boss (James) MSS. in the Magnetic Office.
Sabine Pendulum and other Experiments (London, 1825).
190
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
NORTH EQUATORIAL ZONE IV.— Lat. 30° N. to 40° N.
At sea
At sea (3 observations)
At sea (2 observations)
Algiers
Port Mahon
Bougia
At sea (3 observations
Djegelli
Cap de Fer
Bona
Cali t a Island ....
At sea (2 observations)
Tripoli
At sea (2 observations)
Valetta
Catania
Cape Mesurata
Messina
At sea
Corfu
Bengazi
Zante
Marza Suza ...
Cape Matapan
Cerigo .
Bombah .
Athens .
Tenedos .
Milo ....
Candia ,
Smyrna
Rhodes .
Adalia
Cairo ..
Tineh .
Suez .
Limassol
Jaffa
Beyrout
Latakia
Port William
Babylon
Ararat
Bassora
Sara Island
Kuriskchi Raman .
Enzili
Lefil-rud
Tchaabi-djet
38 58
37 04
38 49
39 52
36 50
38 09
36 50
37 05
36 54
37 31
38 20
32 54
38 25
35 54
37 30
32 23
38 11
39 38
39 38
32 07
37 48
32 55
36 21
36 07
32 23
37 58
39 51
36 43
35 25
38 26
36 26
31 11
36 52
30 03
31 04
30 00
34 40
32 03
33 52
35 31
37 00
32 30
39 42
30 30
38 53
39 01
37 29
37 24
37 11
Long. E.
0 58
1 03
1 05
7 46
8 56
11 32
15 05
15 17
15 34
18 31
19 55
20 03
20 55
21 20
22 25
23 02
23 12
23 46
23 45
24 27
27 07
28 17
30 45
31 15
32 32
32 36
33 06
34 48
35 33
35 50
38 00
44 15
44 15
47 53
49 00
49 23
49 36
50 20
50 25
Date.
Declination.
Inclination.
served.
Correction
to Epoch
1842-5.
Corrected.
Ob-
served.
Cor. to
Epoch
1842-5.
Cor
O
r
o r
o
o »
O
0
1846
19
48 w.
19-8 w.
1842
17
40 w.
17 7 w.
1842
1 7 30 w.
17-5 w.
f 1842
18 35 w.
18-6 w.
57 21
57-41
1843
57 08
+
3
57-2/
1842
59 59
60 0 n
1832
18
24 w
0 50 e.
1 7 6 w.
1859
16
17 w
1 25 w.
17 7 w.
1832
18
16 w
0 50 e.
17-4 w.
1832
17
33 w
0 50 e.
16 7 w.
1832
17
39 w
0 50 e.
16-8 w.
1833
17
07 w
0 45 e.
16-4 w.
1859
! 14
21 w
1 25 w.
15-8 w.
f 1821
16
35 w
1 45 e.
14-8 w.l 0
1828
17
08 w
1 10 E.
16-0 w. 1 15-4 w.
[ 1853
14
20 w
0 55 w.
15 3 w.J
49 21
+
38
50 0 n
1859
L3
16 w.
1 25 w.
14 7 w.
| 1829
15
15 w.
1 05 e.
14-2 w.l
54 18
—
45
53-51
1839
15
25 w.
0 15 e.
15-2 w. 1 ]47w
1
1843
53 28
+
3
53-5
l 1862
J
52 17
+ 1
10
53-5 J
1830
16 28 w.
1 00 E.
15 5 w.
1828
17
05 w.
1 10 E.
15-9 w.
r 1830
17
12 w.
1 00 E.
16 2 w.
56 29
_
36
55-91
1 1841
55 49
—
3
55 -8;
1859
10
46 w.
1 25 w.
12 2 w.
1857
10
48 w.
1 15 w.
12-1 w.
55 42
+
45
56-5 n
1828
15
00 w.
1 10 E.
13-8 w.
1857
10
23 w.
1 15 w.
1 1-6 w.
53 30
+ ’
45
54-3 s
1828
1 14
29 w.
1 10 E.
13-3 w.
1839
12
00 w.
0 15 e.
11-8 w.
1857
9
32 w.
1 15 w.
10-8 w.
51 14
+
37
51-9 n
1857
9
29 w.
1 15 w.
10-7 w.
46 04
+
37
46-7 n
1843
53 53
+
3
53-9 n
1839
11
36 w.
0 17 e.
1 1-3 w.
18430
52 13
+ ’
”3
52-3 n
f 1823
12
00 w.
1 37 e.
10'4 w. 1 J0.o w
l 1857
8
44 w.
1 15 w.
10 0 w. J J0“
49 54
+
"37
50-5 n
r 1830
10 36 w.
1 02 e.
9-6 w.
54 34
—
30
54 1 1
1 1843
53 48
+
3
53-9/
1857
7
30 w.
1 15 w.
8-8 w.
50 50
+
30
51-3 n
f 1839
43 48
_
6
43-71
1847
43 47
+
10
44-0 l
{ 1857
7
10 w.
1 15 w.
8 4 w.
43 19
+
30
43-8 J
1857
6
20 w.
1 15 w.
7-6 w.
51 32
+
30
52-0 n
1857
7
08 w.
1 15 w.
8-4 w.
41 24
+
30
49-1 n
1848
43 19
+
9
43-5 n
[ 1848
41 37
+
12
41-81
1 1856
5
23 w.
1 10 w.
6 6 w.
41 11
+
28
41-7 j
1857
6
03 w.
1 15 w.
7-3 w.
47 59
+
21
48-3 n
1857
5
18 w.
1 15 w.
6-6 w.
44 15
+
15
44-5 n
1857
5
19 w.
1 15 w.
6-6 w.
46 42
+
15
47 0 u
1857
4
59 w.
1 15 w.
6-2 w.
48 43
+
15
49-0 n
1836
50 35
4 50-5 n
1853
4
00 w.
0 44 w.
4-7 w.
1
1829
4
29 w.
0 52 e.
3-6 w.
53 07
-
"6
53 0 n
1836
4
05 w.
0 24 e.
3-7 w.
40 25
_
2
40*4 n
1862
0
03 e.
1 20 w.
1 -3 w.
52 15
52-3 n
1862
0
25 e.
1 20 w.
0-9 w.
52 19
52-3 n
. 1862
0
15 E.
1 20 w.
I T w.
1862
0
34 e.
1 20 w.
0-8 w.
50 24
50:4 n
1862
0
25 e.
1 20 w.
0-9 w.
50 06
50-1 n
Force in
British units.
9:54 1
9-60 |
940
925
914
884
9-31
9-38
915
904
8-84
901
912
8-77
8-60
9-71
9-70
9-63
9-59
Observers.
Berard.
Berard.
Berard.
Aime.
Norwegian Officers.
Norwegian
Berard.
Novara.
Berard.
Berard.
Berard.
Berard.
Novara.
Smith.
Beechey.
Yogel.
Novara.
Fisher.
Caligny.
Norwegian Officers.
Shad well.
Fisher.
Beechey.
Fisher.
Norwegian Officers.
Novara.
Schaub.
Beechey.
Schaub.
Beechey.
Caligny.
Schaub.
Schaub.
Norwegian Officers.
Caligny.
Norwegian Officers.
Smith.
Schaub.
Fisher.
Norwegian Officers.
Schaub.
D’Abbadie.
D’Hericourt.
Schaub.
Schaub.
Schlagintweit.
D’Hericourt.
D’Hericourt.
Schlagintweit.
Schaub.
Schaub.
Schaub.
Schaxib.
Estcourt.
Rawlinson.
Parrot.
Estcourt.
Ivatinsk.
Ivatinsk.
Ivatinsk.
Ivatinsk.
Ivatinsk.
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
191
NORTH EQUATORIAL ZONE IV.— Eat. 30° N. to 40° N. (continued).
Declination.
Inclination.
Force in
British units.
Stations.
Lat.N
Long. E.
Date.
Ob-
served.
Correction
Ob-
Cor. to
Observers.
to Epoch
1842-5.
Corrected.
served.
Epoch
1842-5,
Corrected.
O /
o /
O /
O' /
-a
o /
/
o
33 57
51 15
1859
0 08 w.
1 06 vv.
1-2 w.
45 59
44 0 n.
9-40
Lenz.
35 48
51 30
1859
0 10 W.
1 06 w.
1-3 w.
48 03
48-1 n.
Lenz.
36 41
51 34
1862
0 27 E.
1 20 w.
0-9 w.
49 33
49-6 n.
9-59
Ivatinsk.
32 40
51 45
1859
0 00
1 20 w.
1-3 w.
44 15
44-3 n.
9-35
Lenz.
36 43
52 47
1862
0 49 e.
1 20 w.
0-5 w.
49 35
49-6 n.
9-61
Ivatinsk.
39 05
53 11
1862
2 07 e.
1 20 w.
0-8 e.
52 30
52-5 n.
9-88
Ivatinsk.
39 33
53 13
1862
1 55 e.
1 20 w.
0-6 e.
52 57
53 0 n.
9-96
Ivatinsk.
36 54
54 04
1862
1 12 E.
1 20 w.
01 w.
49 51
49 9 n.
9-66
Ivatinsk.
31 54
54 30
1859
0 01 E.
1 06 w.
11 w.
42 42
42-7 n.
931
Lenz.
54 30
1 04 e.
1 06 w.
0-0
49 53
49-9 n.
9-48
Lenz.
36 42
54 30
1859
49 51
49 9 sr.
Lenz.
36 25
55 00
1859
0 52 e.
1 06 w.
0-2 w.
48 38
48-6 n.
9-58
Lenz.
33 36
56 52
1859
0 58 e.
1 06 w.
0-1 w.
45 32
45 5 sr.
9-49
Lenz.
30 18
57 15
1859
0 21 e.
1 06 w.
0-8 w.
41 02
41 0 n.
974
Lenz.
30 25
57 45
1859
0 35 e.
1 06 w.
0-5 w.
40 56
40-9 sr.
9-38
Lenz.
36 12
57 45
1859
49 31
49-5 n.
Lenz.
34 00
58 07
1859
1 15 E.
1 06 w.
0-2 e.
45 57
46 0 sr.
9-66
Lenz.
36 28
58 22
1859
1 26 E.
1 06 w.
0 3 e.
48 59
49 0 n.
9-94
Lenz.
34 21
58 37
1859
I 26 e.
1 06 w.
0-3 e.
46 36
46-6 n.
9-69
Lenz.
32 16
58 46
1859
1 11 E.
1 06 w.
0-1 E.
Lenz.
31 57
59 00
1859
1 20 E.
1 06 w.
0-2 e.
43 46
43-8 sr.
9-45
Lenz.
32 53
59 15
1859
41 34
416 n.
Lenz.
36 18
59 37
1859
2 00 e.
1 06 w.
0-9 e.
49 16
49-3 n.
9-95
Lenz.
INJVoh
31 32
60 00
1859
1 13 E.
1 06 w.
01 E.
43 00
43-0 n.
Lenz.
Turbet
35 15
60 37
1859
1 58 E.
1 06 w.
0-9 e.
48 20
48-3 n.
9-90
Lenz.
31 43
61 30
1859
43 16
43-3 sr.
Lenz.
G-urian
34 21
61 30
1859
1 58 e.
1 06 w.
0-9 e.
47 25
47-4 n.
9-95
Lenz.
32 46
61 37
1859
44 42
44-7 sr.
970
Lenz.
S b
62 00
1859
45 21
45 '4 n.
976
Lenz.
Herat
34 21
62 07
1859
1 55 e.
1 06 w.
0-8 e.
46 38
46-6 n.
9-87
Lenz.
Dera Ismael Khan . . .
31 40
70 56
1856
0 58 e.
0 40 w.
0-3 e.
44 23
-14
44-2 n.
1070
Schlagintweit.
Peshawur
34 03
71 33
1856
2 28 e.
0 40 w.
1-8 E.
46 26
-14
46 2 sr.
10-89
Schlagintweit.
Mmilt, ATI
30 10
71 35
1856
0 54 e.
0 40 w.
0-2 e.
Schlagintweit.
Schlagintweit.
Sp&Hpur
32 14
72 33
1856
1 20 e.
0 40 w.
0-7 e.
Baulpmdi
33 37
73 00
1856
3 06 e.
0 40 w.
2-4 e.
45 56
— 14
457 n.
9-90
Schlagintweit.
1 Marri
33 51
73 23
1856
3 21 e.
0 40 w.
2-7 e.
46 03
— 14
45-S n.
9-63
Schlagintweit.
1 Mozaferabad
34 22
73 31
1856
3 24 e.
0 40 w.
2-7 e.
47 20
-14
47 1 n.
9-83
Schlagintweit.
Lahore
31 34
74 15
1856
2 02 e.
0 40 w.
1-4 E.
43 17
-14
431 sr.
9-86
Schlagintweit.
i T&shing
35 16
74 41
1856
4 18 e.
0 40 w.
3-6 e.
48 24
-14
48-2 sr.
1075
Schlagintweit.
T)4vftr
34 34
74 46
1856
47 42
— 14
47'5 sr.
Schlagintweit.
Cunningham.
Schlagintweit.
Srinagger
34 05
74 49 (
1847
1856
2 45 e.
3 00 e.
0 10 w.
0 28 w.
| ? B‘ ) 2-6 e.
46 40
46 58
- 5
46 6 sr. 1 „
467 N.j 46-6 N‘
l
2-5 e. J
— 14
9-99
Dras
34 28
75 43
1856
46 51
-14
46 6 n.
1012
Schlagintweit.
Schlagintweit.
Schlagintweit.
Schlagintweit. j
Schlagintweit.
Skardo
35 20
75 44
1856
4 05 e.
0 28 w.
3-6 e.
48 21
-14
48-1 N.
10-94
Chorkonfla,
35 33
75 56
1856
2 53 e.
0 28 w.
2-4 e.
48 43
- 14
485 sr.
1 Iso-Ka
35 58
76 03
1856
49 19
47 57
-14
— 14
491 w.
477 N.
Kargil
76 04
1856
3 10 e.
0 28 w.
2-7 e.
10 20
Mulbe
34 20
76 07
1847
2 44 e.
0 10 w.
2-6 e.
46 56
- 5
46-9 sr.
Cunningham.
Schlagintweit.
Schlagintweit.
Schlagintweit.
1 AmMla
30 21
76 49
1856
2 26 e.
0 28 w.
2-0 e.
40 48
-14
40-6 sr.
Padum
33 28
76 54
1856
3 41 e.
0 28 w.
3-2 e.
45 52
-14
45-6 n.
Slrdong
32 34
77 01
1856
3 23 e.
0 28 w.
2-9 b.
44 28
-14
44 2 n.
10-96
Bultanpur
31 58
77 06
1856
3 03 e.
0 28 w.
2 6 e.
43 52
— 14
43-6 si.
Schlagintweit.
Schlagintweit. ;
Simla
31 06
77 08
1856
2 56 e.
0 28 w.
2 5 e.
42 30
-14
42-3 n.
971
Mi
34 08
77 15 |
1847
1856
2 47 e.
3 23 e.
0 10 w.
0 28 w.
2’6 E. | ,
2-9 e.)27e-
46 43
- 5
nT 46-6 n.
10-11
Cunningham.
Schlagintweit.
46 53
— 14
467 n.J
Sasser Pass . .
35 06
77 28
1856
3 32 e.
0 28 w.
31 E.
48 18
— 14
48- 1 n.
Schlagintweit.
Schlagintweit.
larakorum Pass
35 47
77 30
1856
3 34 e.
0 28 w.
3-1 E.
49 14
-14
49 0 n.
10-93
lampur
31 31
77 37
1856
42 46
— 14
42 5 n.
Schlagintweit.
Schlagintweit.
Schlagintweit.
iiiget
36 10
77 50
1856
4 22 e.
0 28 w.
3-9 e.
50 12
-14
50 0 n.
iangtu Bridge
31 37
77 54
1856
43 23
- 14
43-2 sr.
lassuri
30 29
78 00
1856
41 15
-14
41-0 n.
10-81
Schlagintweit.
192
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
NORTH EQUATORIAL ZONE IV.— Lat. 30° N. to 40° N. (continued).
Stations.
Lat. N.
Long. E.
Date.
Declination.
Inclination.
Force in
British units.
Observers.
Ob-
served.
Correction
to Epoch
1842-5.
Corrected.
Ob-
served.
Cor. to
Epoch
1842*5.
Corrected.
o /
o /
o -
o /
O
o* >
7
o *
Mud ...
31 56
78 01
1856
3 44 e
35 E
44 18
-14
44*1 n.
Schlagintweit.
36 08
78 05
1856
50 05
-14
49*9 n.
10*88
Schlagintweit.
Debra Doon
30 20
78 06
1869
3 06 e.
0 27 w.
' 2-7 e.
41 31
-27
41*1 N.
9*74
Walker.
Massoori
30 27
78 10
1867
2 37 e.
0 25 w.
2-2 e.
41 41
-25
41 *3 n.
9*75
Walker and Basevi.
32 45
78 17
1856
45 20
-14
45*1 n.
Schlagintweit.
31 08
78 18
1856
42 13
-14
42*0 n.
10*96
Schlagintweit.
2 Stations in Rukchu..
33 13
78 26
1847
45 01
— 5
44*9 n.
Cunningham.
Tsomognalari
33 40
78 39
1856
3 22 e.
0 14 w.
3-1 E.
46 34
-14
46 3 n.
9*97
Schlagintweit.
32 48
1847
44 23
- 5
44*3 n.
Cunningham.
32 09
79 09
1847
43 37
43*5 n.
Cunningham.
Mana
30 47
79 21
1856
2 45 e.
0 14 w.
2A e.
41 25
-14
41*2 n.
10*53
Schlagintweit.
Milum
30 35
79 55
1856
2 40 b.
0 14 w.
2 4 e.
40 32
-14
40*3 n.
10*49
Schlagintweit.
(
1831
1 48 w.
0 11 w.
2-0 w. )
54 50
+38
55*5 n. )
11*01)
Fuss.
1835
2 10 w.
0 7 w.
2-3 w. |
O
1
o
1
Kowanko.
39 57
116 28
1842
^ 2 1 w.
55 42
55*7 n. ]
^•55*5 n.
11*13 ;
[■11*18
Repertorium, Bd. VII.
1852
::::::
56 02
-35
55*5 n.
......
Schatskoff.
{
1868
2 25 w.
0 26 e.
2-0 w.J
57 00
-94
55*4 n. j
i
11 42 J
Fritsche.
38 57
117 50
1816
2 16 w
9
Basil Hall.
38 00
120 00
1816
9
Basil Hall.
31 15
121 29
1-7 w
45 21
-32
44*8 n.
Novara.
31 24
121 30
1841
1 37 w.
1-6 w.
Collinson.
At sea (2 observations)
31 25
121 32
1858
1 1 24 w.
1 4 \v.
Novara.
37 36
121 34
1816
2 16 w
?
Basil Hall.
30 14
121 36
1842
Collinson.
J ust in the Way
30 00
121 54
1840
0 10 w.
0-2 w.
Collinson.
Stewart
30 00
121 56
1840
0 08 w.
0*2 w.
Collinson.
Fishers Peak ....
30 12
122 03
1841
2 22 \v.
2-4 w.
Collinson.
Chusan ....
30 03
122 07
1840
2 18 w.
2 3 w.
Collinson.
At sea (3 observations)
31 15
122 09
1858
1 47 w.
1*8 w.
Novara.
Skeppey Island
30 10
122 10
1841
2 31 w.
2*5 w.
Collinson.
Grutzlaff Island
31 10
122 11
1842
1 25 w.
1*4 w.
Collinson.
Shaweishan
31 25
122 14
1840
0 30 w.
0-5 w.
Collinson.
At sea (4 observations)
30 51
122 36
1858
1 37 w.
1*6 w.
Novara.
At sea (4 observations)
31 10
122 47
1858
1 30 w.
1*5 w.
Novara.
Saddle Group
30 42
122 47
1841
0 20 w.
0*3 w.
Collinson.
At sea (2 observations)
31 15
122 47
1858
1 30 w.
1*5 w.
Novara.
Alceste Island
34 00
124 45
1816
2 03 w.
9
Basil Hall.
At sea
30 44
1 25 46
1855
2 17 w.
2*3 w.
Richards.
Amherst Island
34 22
126 05
1816
2 30 w.
?
Basil Hall.
At sea
31 14
126 34
1855
1 56 w.
1-9 w.
Richards.
Quelpart Island
33 30
126 53
1845
2 30 w.
2-5 w.
46 54
46*9 n.
Belcher.
Black Island
34 16
127 13
1845
2 24 w. '
2*4 w.
48 23
48*4 n.
Belcher.
Nangasaki Bay
32 43
129 44
1845
2 35 w. |
2*6 w.
45 00
45*0 n.
Belcher.
At sea (3 observations)
35 45
132 10
1855
3 02 w.
3*0 w.
Richards. ‘
At sea (2 observations)
37 24
134 51
1855
3 56 w.
3*9 w.
Richards.
At sea
39 28
137 39
1855
3 32 w.
3*5 w.
Richards.
Simoda Harb. (Japan)
34 39
138 58
1854
0 52 w.
0*9 w.
American Expedition.
S. r1' 'll in
35 27
139 40
1854
0 25 w.
0-4 w.
American Expedition.
At sea (2 observations)
32 30
141 20
1854
43 30
43*5 n.
Collinson.
At sea (2 observations)
33 16
144 55
1854
44 44
44*7 n.
Collinson,
At sea (2 observations)
31 16
145 23
1854
42 25
42*4 n.
Collinson.
At sea
33 41
146 00
1828
1 14 E.
1*2 E.
Liitke.
At sea (2 observations)
36 36
148 11
1854
48 06
48*1 n.
Collinson.
At sea (4 observations)
37 44
149 21
1828
1 42 e.
1*7 E.
Liitke.
At sea (3 observations)
37 40
152 51
1853
48 57
49 0 n.
Collinson.
At sea
39 07
159 03
1827
4 38 e.
4*6 e.
51 32
5 1 -5 tj
8*87
Liitke.
At sea
32 59
161 49
1827
5 21 e.
5*4 e.
40 40
40-7 n.
8*65
Liitke.
At sea (4 observations)
32 02
162 52
1819
7 37 e.
7-6 e.
Freycinet.
At sea (2 observations)
38 35
171 20
1850
52 57
53*0 n.
Collinson.
At sea
35 54
173 50
1850
51 04
51*1 N.
Collinson.
At sea (2 observations)
33 16
177 05
1850
49 26
49*4 n.
Collinson.
At sea
39 19
179 03
1848
55 33
55*6 n.
Moore.
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
193
NORTH EQUATORIAL ZONE IV.— Lat. 30° N. to 40° N. (continued).
Declination.
Inclination.
Force in
British units.
Stations.
Lat. N
Long. E.
Date.
Ob-
served.
Correction
Ob-
served.
|Cor. to
Observers.
to Epoch
1842-5.
Corrected.
Epoch.
1842-5.
Corrected.
o /
o /
° 7
0 /
O
0 /
0
,
30 19
181 20
1850
47 46
47-8 if.
Collinson.
39 56
184 43
1848
58 30
58-5 n.
Moore.
38 50
185 43
1848
57 27
57-5 N.
Moore.
38 22
186 34
1848
54 44
54-7 n.
Moore.
37 13
188 14
1848
57 25
57 4 x.
Moore.
Ia
35 03
188 54
1848
56 40
56-7 if.
Moore.
33 27
1S9 21
1848
55 06
551 n.
Moore.
31 43
190 00
1848
54 05
53 8 n.
Moore.
A ‘a (3 observations)
37 27
193 26
1852
15 15 e.
15-3 e.
Crane.
A ia (2 observations)
35 19
194 03
1852
12 50 e.
12-8 e.
Crane.
A a, (2 observations)
33 16
194 37
1852
13 04 e.
13-1 E.
Crane.
A| 'a (2 observations)
31 30
195 24
1852
12 51 e.
12-9 e.
I
Crane.
Al a (3 observations)
30 51
197 21
1852
13 09 e.
13-2 e.
Crane.
A a
38 21
213 30
1827
17 18 e.
17-3 e.
Liitke.
7 l
30 19
215 30
1827
13 28 e.
13-5 e.
39 47
219 12
1846
17 07 e.
171 E.
Kellett.
Al a
38 15
226 00
1846
15 52 e.
15-9 e.
Kellett.
37 50
230 00
1846
Kellett.
37 23
232 10
1846
15 34 e.
15-6 e.
Kellett.
35 31
233 12
1830
1 1-9 E.
1
34 50
233 28
1830
12 10 e.
12-2 e.
Erman.
Atl i
31 51
234 15
1830
11 40 e.
11-7 E.
56 15
5 6 :3 n.
10-83
Erman.
At i
31 25
234 31
1830
11 53 e.
11 9 E.
Atl a
39 12
235 09
1830
63 47
63-8 n.
11-61
Erman
At] i
30 31
235 38
1830
10 26 e.
10-4 e.
55 03
55-1 if.
10-52
Erman.
At L .
35 25
235 42
1846
15 40 e.
15-7 e.
Kellett.
At i
38 16
235 47
1830
13 08 e.
13-1 E.
M(h.ofiino Tta.y
39 18
236 13
1857
16 35 e.
0 15 w.
16-3 e.
I
( jsj. Coast Survey.
Ati
37 05
236 15
1830
14 53 e.
14-9 e.
EiOj Mountain
38 30
236 54
1860
16 23 e.
0 18 w.
16-1 E.
U. S. Coast Survey.
Po Bodega
38 18
236 58 |
1839
1842
15 20 e.
16 00 e.
0 03 e.
15- 4 e. 1
16- 0 e.
■ 15‘7 E.
62 53
62-9 n.
1 12-22
Belcher.
Duflot de Mofras.
Pu , de los Keyes . . .
38 00
237 00
1857
15 45 e.
0 15 w.
15-5 e.
U. S. Coast Survey.
Bo a Camp
38 18
237 00
1860
16 19 e.
0 18 w.
16 0 e.
TJ. S. Coast Survey.
U. S. Coast Survey.
Soi Earallone Light
37 42
237 01
1857
15 40 e.
0 15 w.
15-4 e.
At
37 42
237 15
1830
14 49 e.
14-8 e.
Erman.
TJ. S. Coast Survey.
Po: Boneta
■37 49
237 29
1852
15 27 e.
0 10 w.
15-3 e.
(
1827
15 27 e.
0 25 e.
15-9 e. )
62 35
62-6 n. )
j 1
Beechey.
1830
14 51 e.
0 12 e.
15-1 E. 1
62 38
62-6 n. | o
12-01 j
Erman.
Sai rancisco
37 46
237 33 -1
1831
1838
15 20 e.
0 04 e.
15-4 e.
1 5 -5 e.
62 58
63-0 n. [ co -
V62-5n.
11-95 1
12 08 U203
Douglas.
62 00
62-0 if. [
Belcher.
I
1852
15 30 e.
0 10 w.
15-3 e. |
62 32
62-5 if. |
Emory and U. S. C. S.
t
1866
16 26 e.
0 24 w.
16-0 e. )
62 22
62-4 nJ
12-17 J
Harkness.
Sar rancisco Soleno..
38 17
237 36
1831
| 63 24
63-4 if.
12-07
Douglas.
San >se
37 32
238 00
1831
62 52
|
62 9 n.
1202
Douglas.
Beechey.
(
1827
15 38 e.
0 23 e.
16-0 e. T
)
1 1 -95 )
|
1831
62 08
62-1 n. j
11-90 |
Douglas.
Mo: rey
36 38
238 06 -j
1837
1839
14 30 e.
0 08 e.
14-6 e. |
^ 14-9 e.
61 15
6L3n. 1 R
61 1 n. f61H
i 1*1)8 h11'94
La Yenus.
j 14 13 e.
0 05 e.
14-3 e. j
61 04
Belcher.
1843
61 59
62-0 n. |
] 1
Perry.
l
1851
14 58 e.
0 10 w.
14-8 E. )
...... )
J
U. S. Coast Survey.
La 1 edad
36 24
238 36
1831
62 04
621 if.
11 94
Douglas.
Douglas.
Emory.
Douglas.
Douglas.
TJ. S. Coast Survey.
San itonio
36 01
238 42
1831
61 46
61-8 n.
11-85
Saci lento
38 34
238 43
1852
|
64 03
64 "1 n.
San iguel
35 45
239 00
1831
61 40
+ 11
619 n.
59-5 *:} 60-5 N
San iis Obispo
35 11
239 16 |
1831
1854
14' 17 e.
0 12 w.
14-Ye.
61 17
59 42
La 1 issima
34 40
239 33
1831
60 53
+n
61T n.
11-75
Douglas.
U. S. Coast Survey.
Douglas.
Douglas.
Pon Conception
34 27
239 33
1850
13 50 e.
0 08 w.
13-7 e.
Sant jiez
34 36
239 49
f
1831
60 53
+11
+11
61-1 N.
1 1-81
Sanl Barbara ....
1831
]
60 48
610 n. ]
11-87 )
34 24
240 18 {
1839
13 28 e.
0 03 e.
13-5 e.
- 13 6 e.
58 54
+ 3
59 0 n. UO-On.1
11-74 1 1181
Belcher.
—
[
1854
13 30 e.
0 08 e.
13 6 e. J
J
J
U. S. Coast Survey.
MDCCCLXXY. 2 D
194
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
NORTH EQUATORIAL ZONE IV.— Lat. 30° N. to 40° N. (continued).
Declination.
Inclination.
-
Station.
Lat. N
Long. E.
Date.
Ob-
served.
1 Correction
Ob-
served.
Cor. tc
,
Force in
British units.
Observers.
to Epoch
1842-5.
Corrected.
Epoch
1842-5.
Corrected.
o /
o r
O 1
o r
o
O 1
o
33 43
241 45 |
f
1839
1853
13 08 e.
13 30 e.
0 03 w.
0 08 w.
13-1 E. 1
[ 13-2 E.
58 21
59 32
+ 6
-24
58- 5 x. 1
59- 1 n.
|.5S-8x
11*54]
12 12 j
I- 11*83
Belcher.
D. S. Coast Survey. !
13*4 e.
I
1839
12 21 e.
0 03 e.
12-4 e.
57 06
+ 6
57-2 k. |
11*58 |
Belcher.
3 40
242 50 j
1851
12 29 e.
0 08 w.
12-4 e.
| 12-4 e.
57 35
-16
57-3 x.
j- 57*3 x.
11*65
B. S. Coast Survey.
B. S. Coast Survey.
l
1853
12 32 e.
0 11 w.
12-4 e.
57 39
— 22
573 x. J
11-72 J
Mean of Santa Maria '/
and Santa Isabel.. J
33 05
243 14
1849
12 55 e.
0 07 w.
12-8 e.
58 45
-14
58-5 x.
Emory.
30 22
244 01
1839
12 06 e.
121 E.
54 30
+ 6
-24
54*6 x.
11*41
Belcher.
Soda Lake
35 03
244 01
1854
13 51 e.
0 06 w.
13-8 e.
61 07
60-7 x.
12 25
B. S. Officers.
35 06
244 14
1854
.60 49
-24
60-4 x.
12*24
B. S. Officers.
Marl Spring
35 11
244 27
1854
13 59 e.
0 06 w.
13-9 e.
60 56
-24
60-5 if.
12-20
B. S. Officers.
JNew Kirer
32 42
244 35
1849
58 19
-14
58-1 x.
B. S. Officers.
Paiute Creek
35 06
245 06
1854
14 17 e.
0 06 w.
14-2 e.
61 10
-24
60-8 x.
12-26
B. S. Officers.
Gila Junction
32 43
245 07
1851
12 50 e.
0 05 w.
12-8 e.
58 30
-18
58-2 x.
Emory.
Colorado R., 3 Stations
34 45
245 36
1854
13 48 e.
0 06 w.
13-7 e.
60 45
-24
60-4 x.
12-22
B. S. ‘Officers.
Colorado R., 2 Statious
34 23
245 54
1854
14 08 e.
0 06 w.
14 0 e.
60 34
-24
60-2 if.
12-26
B. S. Officers. A
3 Stations (Mean)
32 45
246 11
1851
58 33
-18
58-3 x.
B. S. Officers.
-Big Horn Springs
35 01
246 24
1854
14 18 e.
0 06 w.
14-2 e.
61 02
-24
61-6 n.
12*23
B. S. Officers.
Williams R.., 6 Stations
34 21
246 25
1854
60 20
—24
59-9 n.
1219
B. S. Officers.
White Cliff Creek
35 08
246 29
1854
14 42 e.
0 06 w.
14-6 e.
60 48
-24
60-4 n.
1236
B. S. Officers.
Williams R., 4 Stations
34 25
246 31
1854
13 46 e.
0 06 w.
13-7 e.
B. S. Officers.
White Cliff Creek
35 12
246 39
1854
61 14
— 24
60 -8 x.
12*42
B. S. Officers.
7 Stations
246 43
1851
58 50
-18
58-5 x.
B. S. Officers.
Williams River
35 07
246 47
1854
13 40 e.
0 06 w.
13-6 e.
61 17
-24
60-9 x.
12*14
B. S. Officers. ...
Pueblo Creek
34 57
247 14
1854
13 59 e.
0 06 w.
13-9 e.
61 13
-24
60-8 if.
12-39
B. S. Officers.
Cedar Creek
35 21
247 40
1854
13 49 e.
0 06 w.
13 7 T3
62 06
— 24
6L7 x.
12*55
B. S. Officers.
Le Roux Spring
35 17
248 20
1854
13 52 e.
0 06 w.
13-8 e.
61 33
— 24
61-2 x.
12*44
B. S. Officers.
B. S. Officers.
7 Stations
33 08
248 26
1851
59 18
-18
59-0 x.
10 Stations (Mean) . . .
33 06
249 19
1851
59 16
-18
59-0 x.
B. S. Officers.,
Nogales and Santa 1
Cruz R. (Mean)... j
31 -20
249 19
1855
11 59 e.
0 07 w.
11-9 E.
57 20
-26
56-9 x.
11*51
B. S. Officers.
San Pedro
32 59
249 20
1851
12 25 e.
0 04 w.
12-4 e.
B. S. Officers.
Colorado, Chiquito 1
R., 6 Stations ...J
35 09
249 21
1854
61 50
-24
61-4 x.
12*50
B. S. Officers. .
Colorado, Chiquito 1
R., 4 Stations ... j
35 08
249 24
1854
13 35 e.
0 06 w.
13-5 e.
B. S. Officers.
Colorado, Chiquito ...
34 53
219 56
1851
13 42 e.
0 04 w.
13-6 e.
62 15
-18
62 0 x.
12*53
B. S. Officers.
10 Stations
33 03
250 03
1851
59 29
-18
59-2 x.
B. S. Officers.
Rio Puerco
34 58
250 08
1851
14 00 e.
0 04 w.
13 9 e.
61 46
-18
61-5 n.
12*51
B. S. Officers.
Lithodendron Creek...
35 02
250 19
1851
13 33 e.
0 04 w.
13-5 e.
61 57
-18
61 *7 x.
12*50
B.’S. Officers.
Carriso Creek
35 07
250 28
1854
13 54 e.
0 06 w.
13-8 e.
62 05
-24
61-7 x.
1254
B. S. Officers.
Navajo Spring
35 06
250 40
1854
13 23 e.
0 06 w.
13-3 e.
61 58
—24
61-6 x.
12-56
B. S. Officers.
Jacobs Well
35 04
250 46
1854
13 44 e.
0 06 w.
13-6 e.
62 00
—24
61-6 x.
12-55
B. S. Officers.
San Bernardino
31 20
250 46
1855
11 45 e.
0 07 w.
11-6 E.
57 19
-26
56-9 n.
11*58
B. S. Officers.
Cedar Pores t
35 01
251 05
1854
13 01 e.
0 06 w.
12-9 e.
61 40
—24
61*3 x.
12-59
B. S. Officers.
Arch Spring
35 05
251 12
1854
61 55
-24
61*5 k.
12-62
B. S. Officers.
San Luis Springs
31 20
251 12
1855
11 45 e.
0 06 w.
11-7 E.
57 37
-26
57*2 if.
11*70
B. S. Officers.
Zuni River
35 06
251 21
1854
13 24 e.
0 06 w.
13-3 e.
62 02
-24
61*6 x.
12-63
B. S. Officers.
Aqua del Perro
31 21
251 40
1855
11 59 e.
0 06 w.
11-9 E.
57 28
-26
57*0 x.
11-45
B. S. Officers. Aj
Ojr> de Inez
32 45
251 46
1851
59 18
-18
59*0 x.
B. S. Officers.
Inscription Rock
35 03
251 46
1854
12 57 e.
0 06 w.
12-9 e.
62 03
-24 i
61*7 x.
1259
B. S. Officers.
Copper Mines
32 47
251 56
1851
11 22 e.
0 04 w.
11-3 E.
59 17
-18 .
59 0 x.
B. S. Officers.
Agua Fria
35 02
252 02
1854
13 26 e.
0 06 w.
13-3 e.
62 05
-24 i
61*7 x.
12-66
B. S. Officers. ■ - i
Carrizallilo
31 51
252 04
1855
12 02 e.
0 06 w.
11-9 E.
58 31
-26 ,
58*1 x.
11*73
B. S. Officers. ; v
Espia
31 21
252 04
1855
12 05 e.
0 06 w.
12-0 e.
57 59
-26 .
57*6 x.
11-77
B. S. Officers.. J
Covera
35 05
252 34
1854 1
13 49 e.
0 06 w.
13-7 e.
62 26
-24 i
62 0 x.
12-67
U. S. Officers. j .5
Rio San Jose
35 01
252 46
1854
13 46 e.
0 06 vv.
13-7 e.
63 18
-24 i
52*9 x.
12-67
B. S. Officers. j
Dona Ana
32 22
253 13
1851
12 07 e.
0 04 iv.
12-1 E.
59 06
-18 l
58*8 x.
B. S. Officers. j I
Tslfifa.
34 54
253 20
1854 !
13 13 e.
0 06 w.
13-1 e.
13-3 e.
62 24
62 28
— 12 i
62*2 x.
12-65
12*67
B. S. Officers.
Albuquerque
35 06
253 22
1854
13 25 e.
0 06 w.
-12
62*3 x.
B. S. Officers. i
Frontera
31 48
253 27
1852
12 24 b.
0 05 w.
12-3 e.
59 05
-io ;
58*9 x.
B. S. Officers.
Emory’s Initial Point,.
31 47
253 32
1855 |
11 55 e.
0 06 w.
11-8 E.
58 39
-13 I
58*4 x.
11*92
B. S. Officers.
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
195
NORTH EQUATORIAL ZONE IV.— Lat. 30° N. to 40° N. (continued).
Stations.
i i Elcearis
; uth of Canon
] -t of Brazos River...
( Trinity Waters, \
■ Stations J
] ir Sabine River . . .
I .nes Berry
i ehitoches
] eliez
] vport
] nticello
Louis
4™
1 jer Alton
] vardsville
l| iker’s Hill
(I Island
1 sissippi City
I t Pascagoula
I )ile
I i; Morgan
II' Harmony ....
l int Vernon ....
ij ;aloosa
I er Peach Tree.
I iceton
1 ;ennes
I dy Pensacola
j® lville
I i
1 itgomery
I ricane Island
I isville
Ida
B unond
P ifcfort
0 >rd
T diassee
B lilton
C. innati
V amstinvn
L Qgton
Ci ’s Perry
D on
m >n
St [ark’s Light
Ci )lton
Lf non
E ville
Sp igfleld
M; n
Lat. N.
Long. E.
Date.
Declination.
Inclination.
Force in'
British units.
Observers.
Ob-
served.
.
Correction
to Epoch
1842-5.
Corrected.
Ob-
served.
Cor. to
Epoch
1842-5.
Corrected.
O
r
O /
. o /
o
o /
/
o
31 35
253
44
1852
58 57
-10
58-8 n.
II. S. Officers.
31 02
254
23
1852
12 01 e.
0 05 w.
11-9 E.
57 38
-10
57-5 n.
1 1-28
Emory.
33 00
260
43
1854
11 12 E.
11-2 e.
U, S. Officers.
33 34
261
45
1854
10 27 e.
10-5 e.
U. S. Officers.
32 01
266
00
1840
61 37
61-6 n.
Graham.
31 28
266
15
1840
8 41 e.
8-7 e.
60 57
61 0 n.
Graham.
31 44
266
55
1834
62 11
62-2 n.
Nicollet.
31 34
268
35
1834 1
62 11
62-2 n.
Nicollet.
38 34
268
54
1S39
9 21 e.
9-4 e.
Goebel.
38 57
269
55
1841
69 39
69-7 n.
Loomis.
(
1835
8 49 e.
8 8 e.
^
1
1839
69 31
69-5 n. | 0
1345
Locke.
38 38
269
56 -(
1841
69 24
69*4 w. J- 69-5 n.
Loomis.
1841
69 27
69-5 n. |
Nicollet.
l
1857
J
1315
Eriesach.
38 54
269
56
1841
69 25
69-4 n.
Loomis.
38 55
269
57
1841
69 46
69-8 n.
Loomis.
38 50
270
07
1841
69 58
70-0 n.
Loomis.
39 04
270
07
1841
69 49
69-8 n.
Loomis.
30 15
270
54
1847
7 12 e.
0 05 e.
7*3 e.
Barnett.
30 23
270
59
1855
7 22 e.
0 13 e.
7’6 e. . o
IT. S. Coast Survey. •
98 (
1847
7 13 e.
0 05 e.
60 27
-oi
60-4 isr.
12-61
IT. S. Coast Survey.
l
1855
7 09 e.
0 13 e.
7-4 e. j ' 8 E*
U. S. Coast Survey. ■
f
1835
7 12 e.
0 07 w.
7-1 e.1
61 38
61:6 ir. ]
U. S. Coast Survey.
30 42
271
58
1847
7 04 e.
0 05 e.
7-2 e. 1 7-1 e.
j 61-2 n.
IT. S. Coast Survey.
l
1857
6 52 e.
0 15 e.
7-1 E..J
60 51
’-03
60-8 n. J
12-61
IT. S. Coast Survey.
, 30 14
272
00
1847
7 04 e.
0 05 e.
7-2 e.
IT. S. Coast Survey.
. 38 11
272
12
1840
69 04
69 In.
13-46
Locke.
. 37 59
272
13
1840
68 56
68-9 n.
13-47
Locke.
. 33 12
272
18
1835
64 22
64-4 n.
IT. S. Coast Survey.
. 31 50
272
27
1857-
6 02 e.
0 15 e.
6-3 e.
62 17
-03
62-2 n.
12-83
IT. S. Coast Siu-vey.
. 38 23
2 72
30
1840
69 23
69-4 n.
13-48
Locke.
38 43
272
35 |
1840
69 51
69-9 n. 1 g9.9
13-56
Locke.
1841
69 53
69 9 n. jbJ9N-
Loomis.
30 25
272
48 (
1858
6 47 e.
0 16 e.
7’} 1 ?-o e
61 06
-03
6I‘l N‘ 1 60-8 w
12'68h309
IT. S. Coast Survey.
1
1861
6 42 e.
0 19 e.
7-0 e. j ' u E-
60^39
-04
60-6N./bO8N-
13-50 J 16
IT. S. Coast Survey.
273
11
1834
6 51 e.
0 08 w.
6-7 e.
67 05
67-1 n.
Nicollet
, 38 35
273
25:
1840
69 34
69-6 n.
13-44
. 32 22
273
42
1855
5 18 e.
0 13 e.
5-5 e.
63 05
-02
63-1 n.
12-93
IT. S. Coast Survey.
. 30 04
274
21
1854
6 12 e.
0 12 e.
6-4 e.
IT. S. Coast Survey.
. 38 03
274
30
1840
69 54
69 9 n.
13-53
Locke
, 31 54
274
52
1860
5 12 e.
0 18 e.
5-5 e.
63 06
-03
63-1 n.
IT. S. Coast Survey.
39 49
275
13
1845
4 52 e!
0 03 e.
4-9 e.
71 20
7 1-3 n.
13-61
Locke.
38 14
275
20
1840
69 55
69-9 n.
13-43
39 30
275
22
1845
4 50 e.
0 03 e.
4-9 e.
71 10
71-2 n.
13-66
Locke.
30 28
275
24
1835
61 23
61-4 n.
IT. 8. Coast Survey.
39 23
275
28
1840
70 58
71 0 n.
T .
r
1840
70 27
70-5 n.’’|
It) VO
13-59
-LocRe.
Locke.
. 39 00
275
35 \
1841
70 28
70-5 n. 1 70-5 n.
Loomis.
l
1845
4 04 e.
0 03 e.
4-1 E.
70 29
70-5 sr. J
Locke.
. 38 36
275
38
1840
70 04
70-1 u.
1350
Locke.
, 38 06
275
42
1840
69 55
69-9 n.
. 37 54
275
42
1840
69 49
69" 8 n.
io oo
juocKe.
Locke.
. 39 44
275
43
1840
71 22
71*4 N.
IO ‘i o
1360
Locke
. 39 22
275
47
1840
1
70 54
70-9 n.
13-57
. 30 04
275
48
• 1852
5 29 e.
0 10 E.
5-7 e.
U. S. Coast Surrey.
. 39 38
275
51
1845
4 45 e.
0 03 e.
4-8 e.
71 10
71-2 n.
13-62
Locke.
, 39 26
275
54
1840
71 03
71-1 N.
13-60
35 59
276
06
1833
1 "A!
67 06
67-1 n.
juocice.
Nicollet.
39 54
276
09
1840
j 4 30 e.
0 02 w.
4-5 e.
71 27
71-5 n.‘
13*55
. 32 50
276
22
1855
4 37 e.
0 13 e.
4-8 e.
63 51
T03
63-8 n.
12-79
IT. S. Coast Survey.
D
O
2
196
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
NORTH EQUATORIAL ZONE IV.— Eat. 30° N. to 40° N. (continued).
Date.
Declination.
Inclination.
Force in
British units.
Ob-
served.
Correction
to Epoch
1842-5.
Corrected.
Ob-
served.
Cor. to
Epoch
1842-5.
Corrected.
O , t
o r
O
o t
0
1834
65 40
65-7 k.
1840
71 05
711 N.
13-53
1841
71 04
71-lw.
1845
j 2 29 e.
0 03 e.
2-5 e.
71 04
71 In.
1833
67 39
67-7 n.
1833
67 25
67-4 n.
1841
71 10
71-2 n.
1845
2 25 e.
0 09 e.
2-6 e.
71 22
71-4 n.
13-62
1857
4 02 e.
4-0 e. o
62 07
-03
62-1 n. 0
12-59
1852
3 40 e.
0 30 e.
4-2 b. "1 j.q r
63 40
-02
63 6 n. I
12-62
1857
3 28 e.
0 45 e.
4-2 e. |42k
63 44
-03
63-7n. j637N-
1854
3 02 e.
0 36 e.
3-6 e.
66 08
-02
661 n.
13 04
1852
3 32 e.
0 30 e.
4-0 e.
63 38
-04
63 6 n.
12-57
1859
3 04 e.
0 51 e.
3-9 e.
64 08
-03
641 n.
1850
2 54 e.
0 24 e.
3-3 e.
64 04
-01
64-1 n.
12-65
1841
2 24 e.
2-4 e.
64 37
646 n.
1849
2 17 e.
0 21 e.
2 6 e.
64 32
-01
64-5 n.
12 69
1841
3 04 e.
31 E.
1841
2 33 e.
2-6 e.
1853
2 07 e.
0 33 e.
2-7 e.
65 30
—02
65-5 n.
1303
1840
71 31
71-5 n.
1844
71 36
7T6 n.
1854
0 45 e.
0 36 e.
1-4 E.
68 12
-02
682 n.
13-31
1841
2 26 e.
2-4 e.
1859
0 38 e.
0 51 e.
1-5 E.
66 i7
—03
66-2 n.
1301
1840
0 58 w.
10 w.
71 47
71 8 n.
1842
—
1340
1854
1 14 E.
0 36 b.
1*8 E.
66 47
-02
66-8 n.
1313
1842
71 57
72 0 N.
1353
1856
( 1 02 w.
0 42 e.
0-3 w.
70 38
-03
70 6 n.
1342
1856
0 15 w.
0 52 e.
0-6 e.
69 48
-03
69-8 n.
13-35
1852
0 27 w.
0 30 e.
01 w.
69 17
-02
69-3 n.
1304
1842
71 46
71-8 n.
1355
1844
70 56
70-9 n.
13-49
1842
1 37 w.
1-6 w.
71 18
71-3 n.
1351
1839
0 15 e.
0-3 e.
1850
2 07 w.
0 24 e.
1-7 w.
71 57
-02
71 9 n.
13-37
1850
2 19 w.
0 24 e.
1-9 w.
71 12
-02
71 2 n.
13 39
1839
1 05 e.
11 E.
1845
2 11 w.
0 09 e.
2 0 w.
72 07
72Tn.
13-20
1850
2 08 w.
0 24 e.
1-7 w.
71 24
-02
71-4 N.
13-42
1842
2 03 w.
21 w.
71 41
71 7 n.
13-49
1846
2 09 w.
0 16 e.
1-9 w.
71 11
71-2 n.
1317
1845
2 14 w.
0 12 e.
2 0 w.
1847
2 19 w.
0 15 e.
2’1Mt.Qw
1856
2 29 w.
0 42 e.
1-8w.)I9w-
71 46
-03
71 7 n.
13-43
1846
2 17 w.
0 12 e.
2-1 w.
71 49
71-Sn.
1318
1846
2 16 w.
0 12 e.
2-1 w.
71 30
71-5 n.
1332
1846
1 37 w.
0 12 e.
1-4 w.
71 30
715 n.
1318
1847
2 02 w.
0 15 e.
1-8 w.
71 43
-01
71-7 n.
1 3"35
1845
2 24 w.
0 09 e.
2-3 w.
71 37
7T6 n.
1334
1849
2 30 w.
0 21 e.
2*2 w.
71 17
-01
71 3 n.
1311
1856
1 15 w.
0 42 e.
0-6 w.
69 32
-03
69 5 n.
13 32
1856
1 36 w.
0 42 e.
0-9 w.
69 29
-03
69-4 n.
13-31
1865.
2 38 w.
1 15 e.
1-4 w.
69 38
-06
69-5 n.
13-54
1845
2 32 w.
0 09 e.
2-4 w.
71 48
71-8 h.
13-26
1847
2 29 w.
0 15 e.
2-2 w.
71 50
71-8 n.
13-21
1847
1 40 w.
0 15 e.
2-4 w.
68 55
68-9 n.
1295
1856
2 41 w.
0 42 e.
2 0 w.
70 58
-03
70-9 n.
1344
1847
2 14 w.
0 15 e.
2-0 w.
71 52
71-9 n.
1313
1841
0 52 e.
Athens . . .
Columbus
Warm Spring
Ashville
Hebron
Marietta Island.
Fernandina ....
Savannah
Columbia
Tybee Island .
Port Eoyal . ,
Edisto Island
Charlestown .
Breach Inlet ,
At sea
At sea
Allston
Frostburg ....
Cumberland
Raleigh
At sea (3 observations)
Smithville
Irwin’s Mill 1
MercersburgJ
Wilmington
Chambersburg
Brown’s Island
Mayo Isl., Richmond.
Roslyn
Mount Saint Mary’:
Mount Vernon
Washington
At sea
Soper’s Hill
Hill’s Hill ...
At sea
Rosanne
Webb’s Hill
Baltimore
Marriott
Annapolis
Fort McHenry
Finlay
Taylor
North Point
Bodkin Light
South Base Point .
Kent Island
Old Point Comfort
Norfolk
Gosport
Osborne’s Ruin
Pool’s Island
Stevenson’s Point . . .
Oxford
Susquehanna Light
At sea
Lat. N.
33 57
39 57
35 50
35 36
39 59
39 25
30 41
34 00
32 02
32 18
32 33
32 41
32 46
30 54
31 54
33 22
39 41
39 56
35 47
32 14
33 55
39 47
34 14
39 55
38 18
37 32
37 14
39 41
38 41
38 53
32 55
39 05
38 54
34 20
39 18
39 05
39 18
38 52
38 56
39 16
39 24
39 00
39 12
39 08
38 54
39 02
37 00
36 51
36 49
39 28
276 35
276 58-
n 12
277 30
277 31
278 32
278 32
32 05 278 55
39 17
36 06
38 41
39 32
33 55
278 58
279 09
279 22
279 50
280 07
280 11
280 15
280 29
280 48
281 04
281 13
281 22
281 34
281 59
282 04
282 04
282 20
282 33
282 34
282 36
282 42
282 53
283 03
2S3 03
283 07
283 10
283 17
283 20
283 22
283 24
283 25
283 25
283 29
283 32
283 34
283 35
283 38
283 41
283 42
283 43
283 43
283 43
283 44
283 49
283 50
283 55
283 57
Observers.
U. S. Coast Survey.
Locke.
Loomis.
Locke.
Nicollet.
Nicollet.
Loomis.
Locke.
U. S. Coast Surrey.
TJ. -S. Coast Survey.
U. S. Coast Survey.
U. S. Coast Survey.
TJ. S. Coast Survey.
U. S. Coast Survey.
TJ. S. Coast Survey.
Barnett.
U. S. Coast Survey.
Barnett.
Barnett.
U. S. Coast Survey.
Bache.
A
Locke.
U. S. Coast Survey.
Barnett.
U. S. Coast Survey.
Bache.
Bache.
TJ. S. Coast Surrey.!
Locke.
Schott.
Schott.
IT. S. Coast Survey.
Locke.
Locke.
f Gillis, TJ. S. C.
\ and Lefroy. •
Berard.
U. S. Coast Survey!
U. S. Coast Survey!
Berard.
U. S. Coast Surveyij
U. S. Coast Survey
U. S. C. S. and Lefri.
U. S. Coast Survey
TJ. S. Coast Survey!
U. S. Coast Survey)
U. S. Coast Survey
TJ. S. Coast Survey
U. S. Coast Survey
U. S. Coast Survey!
TJ. S. Coast Survey
TJ. S. Coast Survey
U. S. Coast Survey
U. S. Coast Survey!
TJ. S. Coast Survel
Harkness.
TJ. S. Coast Survey!
TJ. S. Coast Survey
U. S. Coast Survel
TJ. S. Coast Surveyl
U. S. Coast Surve
Barnett.
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
197
NORTH EQUATORIAL ZONE IV.— Lat. 30° N. to 40° N. (continued).
Stations.
ipe Henry ...
,pe Charles . . .
ott
•enchtown ...
ellbank
ynes
illmington . . .
wyer
rt Delaware
die’s Island
mbay Hook
ead
laware City
le Mount . . .
son’s Landing .
Igsborough
res's Landing ,
ecurn Light
sea (2 observations)
kerton
sea
ker’s Island.,
ig Beach
negat Light .
<ea (2 observations)
iea (2 observations)
nuda
Declination.
Lat. N.
Long. E.
Date.
Ob-
served.
Correction
Ob-
served.
to Epoch
1842-5.
Corrected.
O /
o ,
o /
o /
o
o /
36 56
284 00 |
1841
1856
0 45 w.
1 28 w.
0 03 w.
0 42 e.
0-8 w. ) n a
0-8 w. °'8 w'
69 39
37 07
284 02
1856
1 35 w.
0 42 e.
0-9 w.
69 43
37 21
284 06
1856
1 38 tv.
0 42 e.
0-9 tv.
70 02
39 35
284 09
1840
71 40
36 03
284 16
1847
1 45 tv.
0 15 e.
1-5 tv.
68 38
37 42
284 23
1856
2 03 w.
0 42 e.
1-4 TV.
70 21
39 45
284 26
1846
2 31 w.
0 12 e.
2-3 w.
71 25
39 43
284 26
1846
2 48 w.
0 12 e.
2-6 w.
71 58
39 35
284 26
1846
3 17 tv.
0 12 e.
31 TV.
71 35
35 48
284 28
1847
1 13 w.
0 15 e.
10 TV.
68 18
39 22
284 30
1846
3 18 tv.
0 12 e.
31 TV.
71 38
37 58
284 34
1856
2 18 vv.
0 42 e.
1-6 TV.
70 31
39 35
284 39
1842
3 30 w.
3-5 w.
71 46
89 25
284 40
1846
3 14 tv.
0 12 e.
3 0 w.
71 41
39 26
284 42
1846
2 56 w.
0 12 e.
2-7 w.
71 44
38 14
284 45
1856
2 23 w.
0 42 e.
1-7 w.
70 45
38 36
284 45
1856
2 41 tv.
0 42 e.
2 0 tv.
71 03
38 49
284 48
1846
2 45 w.
0 12 e.
2-6 w.
39 48
284 50 |
1846
1846
3 20 w.
3 45 w.
0 12 e.
0 12 e.
3-1 w. \ o.4 _
3-6 w.j34w’
72 15
72 14
39 58
284 50
1842
3 30 w.
3-5 tv.
71 59
284 50
1846
2 43 w.
0 12 e.
2-5 w.
71 19
39 11
284 52
1846
3 03 w.
0 12 e.
2-9 w.
71 45
38 20
284 54
1853
2 33 vv.
0 33 e.
2 0 w.
70 58
38 47
284 55
1856
3 04 w.
0 42 e.
2-4 w.
71 22
39 15
284 59
1846
3 04 vv.
0 12 e.
2-9 w.
71 40
34 33
285 00
1841
0 34 w.
0-6 w.
38 56
285 01 {
1846
1855
3 05 w.
3 45 w.
<M C5
r“i CO
o o
2-9 w. 1 „ n
31 w.)30w-
71 26
71 34
38 59
•285 03
1846
3 00 w.
0 12 e.
2-8 tv.
71 24
35 08
285 28
1841
1 57 vv.
2 0 w.
34 20
285 30
1839
1 05 f.
11 E.
39 22
285 35
1860
4 54 w.
0 54 e.
4 0 tv.
71 47
37 35
285 36
1841
0 23 w.
0-4 w.
39 36
285 40
1846
72 12
35 29
285 40
1841
2 29 w.
2 5 w.
39 31
285 44
1846
4 28 w.
0 12 e.
4-3 w.
39 30
285 45
1860
5 1 9 tv.
0 54 e.
4-4 w.
71 59
39 46
285 54
1860
5 24 vv.
0 54 e.
4-5 w.
72 05
35 59
286 14
1841
2 00 w.
2-0 w.
39 55
288 50
1839
2 14 w.
2-2 w.
38 45
289 09
1841
6 44 w.
6 7 tv.
39 28
290 25
1841
6 06 w.
6-1 w.
38 46
291 00
1839
8 15 tv.
8-3 w.
39 52
291 20
1841
6 37 w.
6-6 tv.
37 06
291 28
1849
6 45 tv.
6-8 w.
f
1831
6 59 tv.
7-0 tv. )
65 18
32 23
295 13 \
1837
6 40 w.
6-7 w. 1 6-9 w.
1
1846
6 53 w.
6-9 w. J
65 24
37 10
300 23
1850
11 16 TV.
11-3 TV.
I 38 48
300 25
1839
9 33 w.
9-6 w.
) 33 10
300 27
1849
8 15 tv.
8-3 tv.
, 32 18
300 42
1842
8 46 tv.
8-8 w.
, 39 50
301 20
1839
10 11 TV.
10-2 tv.
. 37 42
. 34 59
306 12
1850
13 15 tv.
13 3 tv.
310 59
1850
9 40 tv.
9-7 tv.
. 32 02
. 31 24
314 50
315 04
1829
1851
12 53 tv.
14 02 tv.
12 9 tv.
14-0 w.
Cor. to
Epoch
1842-5.
Corrected.
-03 69-6 n.
-03 69-7 n.
-03 70-0 n.
.... 71-7 n.
(38 (3 n.
70- 3 n.
1-4 N.
2 0 n.
71- 6 n.
68 3 n.
16 N.
70-5 n.
718 n.
717 n.
717 n.
07 n.
7 10 n.
2:3 n. ’
72- 2 N<J
2 0 n.
13 N.
1-8 N.
70-9 n.
71 3 n.
71-7 n.
Force in
British units.
ass}™*
71 4 n.
1 7n.
72-2 n.
19 N.
72 0 n.
65-3 k. ]
<
65-4 n. J
13-29
13-34
1338
12- 94
13- 35
13-38
13-49
13-38
12-86
13 36
1334
13-45
1336
13 39
13-45
13-50
13-40
1343
13-28
13-41
13-39
13-36 )
13-23 J
13-39
13-45
13-29
13-43
13-36
Observers.
Nicollet.
U. S. Coast Survey.
U. S. Coast Survey.
U. S. Coast Survey.
Bache.
U. S. Coast Survey.
U. S. Coast Survey.
Locke.
Locke.
Locke.
U. S. Coast Survey.
Locke.
U. S. Coast Survey.
Barnett.
Locke.
Locke.
U. S. Coast Survey.
U. S. Coast Survey. '
U. S. Coast Survey.
Locke.
U. S. Coast Survey.
Observatory.
U. S. C. S. and Locke.
U. S. C. S. and Locke.
TJ. S. Coast Survey.
TJ. S. Coast Survey.
U. S. C. S. and Locke.
Barnett.
Locke.
Schott.
Locke.
Barnett,
Berard.
U. S. Coast Survey.
Barnett.
U. S. Coast Survey.
Barnett.
U. S. Coast Survey.
U. S. Coast Survey.
IJ. S. Coast Survey.
Barnett.
Berard.
Barnett.
Barnett.
Berard.
Barnett.
Hudson.
Austin and Foster.
Milne.
Barnett.
Graint.
Berard.
Hudson.
Jehenne.
Berard.
Lunt.
Young.
Bumker.
Smith.
198
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
NORTH EQUATORIAL ZONE IV.— Lat. 30° N. to 40° N. (continued).
Declination.
Inclination.
Force in
British units.
Stations.
Lat. N.
Long. E.
Date.
Correction
Ob-
Cor. to
Observers.
served.
to Epoch
1842-5.
Corrected.
served.
Epoch
1842-5.
Corrected.
o /
o /
O f
O
o /
O
At sea (4 observations)
32 21
317 17
1830
14 52 tv.
14-9 vv.
Prussian ships.
30 00
318 05
1839
64 05
64-1 u.
Sulivan.
At sea (2 observations)
34 30
318 12
1830
16 47 tv.
16-8 vv.
67 27
67-5 n.
11-16
Erman.
At sea (2 observations)
34 58
318 20
1830
17 16 w.
17 3 w.
67 30
67-5 n.
11-07
Erman.
At sea (2 observations)
33 39
318 32
1830
17 02 w.
17 0 w.
66 06
66-1 n.
11-12
Erman.
At sea (2 observations)
32 51
318 57
1830
16 54 w.
16 9 w.
65 21
65-4 n.
10-94
Erman.
31 57
319 00
1839
64 55
64-9 n.
11-01
Sulivan.
At sea (2 observations)
32 45
319 01
1830
15 46 w.
15-8 w.
Erman.
At sea (2 observations)
31 46
319 09
1839
15 56 w.
15 9 vv.
Du Petit Thouars.
At sea (2 observations)
30 25
319 28
1830
14 59 w.
15 0 w.
64 16
64 3 n.
11-01
Erman.
At sea (2 observations)
32 13
319 39
1859
19 48 w.
19 8 w.
Novara.
At sea (3 observations)
33 52
319 46
1850
17 37 iv.
17 6 w.
Lunt.
At sea (2 observations)
36 16
319 52
1830
18 35 vv.
18-6 w.
68 iV
68-3 n.
11-23
Erman.
At sea
30 44
319 58
1830
15 14 w.
15 -2 vv.
Erman,
At sea (2 observations)
31 08
320 07
1830
15 54 w.
15 9 w.
64 30
64-5 n.
1087 •
Erman.
34 04
320 12
1839
17 22 w.
1 7-4 w.
Du Petit Thouars.
30 48
320 16
1846
17 47 w.
17-8 w.
Sulivan.
34 27
320 54
1839
67 50
67-8 n.
11-16
Sulivan.
At sea (ship’s head on 1
16 points) J
37 55
320 58
1859
23 52 w.
23-9 w.
Novara.
At sea (3 observations)
36 21
321 02
1859
22 37 w.
22-6 w.
Novara.
At sea (2 observations)
32 12
321 07
1840
18 21 w.
18-4 w.
Sulivan.
At sea (2 observations)
37 19
321 10
1830
18 30 vv.
18-5 w.
68 24
68-4 n.
11-40
Erman.
At sea (2 observations)
36 47
321 20
1829
17 10 w.
17-2 w.
Runxker.
At sea (5 observations)
32 52
321 33
1830
16 10 w.
16 2 w.
Prussian ships.
At sea.....
37 05
321 35
1842
21 02 w.
210 w.
Jehenne.
37 39
321 45
1830
19 43 w.
19-7 w.
Erman.
At sea
35 09
321 58
1839
67 35
67*6 n.
11-23
Sulivan.
At sea
33 46
322 10
1846
19 15 vv.
19-3 w.
Sulivan.
At sea (2 observations)
35 48
322 30
1837
18 05 w.
18-1 w.
Bonite.
At sea
36 53
322 30
1839
68 15
68-3 n.
11-22
Sulivan.
At sea
38 25
322 50
1830
21 25 w.
21-4 w.
69 08
69-1 if.
11-21
Erman.
At sea (7 observations)
37 39
322 51
1830
21 50 w.
21-8 w.
Prussian ships.
At sea
37 48
323 07
1839
19 57 w.
20 0 w.
Du Petit Thouars.
At sea (6 observations)
32 34
323 10
1829
18 28 vv.
18 5 w. _
Liitke.
At sea
33 54
323 13
1837
18 02 w.
18 0 w.
Bonite.
At sea (3 observations)
32 15
323 13
1846
18 43 w.
18-7 w.
Berard.
At sea (4 observations)
39 17
323 32
1859
27 47 w.
27 8 w.
Novara.
At sea (2 observations)
34 15
323 32
1846
1 S 32 w.
18-5 vv.
-Berard.
At sea (2 observations)
31 28
323 33
1843
18 08 vv.
18-1 w.
63 27
63-5 n.
Boss.
A+ KAT
38 21
323 40
1839
69 42
69 7 h.
11-16
Sulivan.
39 07
323 41
1830
22 06 w.
22 1 w.
At sea
31 04
324 03
1836
18 28 vv.
18-5 w.
FitzRoy.
Ross.
At sea (2 observations)
33 40
324 05
1843
20 45 v.
20 8 w.
65 01
65-0 n.
At sea
39 15
324 36
1830
23 11 w.
23-2 vv.
Erman.
At sea
37 09
324 36
1846
23 37 w.
23-6 vv.
Sulivan.
At sea,
324 55
1836
18 22 vv.
18-4 w.
FitzRoy.
Ross.
At sea (3 observations)
36 01
325 07
1843
20 28 vv.
20-5 w.
66 57
67 0 n.
At sea (2 observations)
30 31
325 09
1837
18 25 vv.
18-4 w.
Bonite.
At sea (2 observations)
36 37
325 14
1850
67 16
67 3 n.
Rattlesnake.
At sea (3 observations)
37 36
325 16
1843
23 39 w.
23 -7 w.
68 43
68-7 n.
Ross.
At sea (2 observations)
38 51
325 25
1843
25 23 w.
25-4 tv.
69 12
69-2 n.
Ross.
I At sea
37 55
325 35
1846
23 35 yf.
23-6 tv.
Sulivan.
39 32
325 54
1839
20 55 vv.
20-9 tv.
Du Petit Thouars
| At sea (3 observations]
34 50
325 56
1846
19 03 w.
19 1 w.
Berard.
| At sea (2 observations'
39 51
326 50
1843
26 55 w.
26-9 tv.
69 34
69-6 n.
Ross.
I At sea (3 observations]
36 38
328 14
1846
20 53 w.
20-9 tv.
Berard.
a At qpq
35 38
328 28
1836
21 34 w.
21-6 w.
Fitz Roy.
Yidal.
| Mores
328 48
1844
27 30 w.
27 30 w.
27-5 w.
I Corvo
39 41
328 53
1842
27-5 tv.
Vidal.
GENERAL SIE EDWARD SABINE ON TERRESTRIAL MAGNETISM.
199
NORTH EQUATORIAL ZONE IV.— Lat. 30° N. to 40° N. (continued).
Declination.
Inclination.
Stations. .
Lat. N.
Long. E.
Date.
Ob-
served.
Correction
Ob-
Cor. to
Force in
Observers,
to Epoch
1842-5.
Corrected.
served.
Epoch
1842-5.
Corrected.
o ,
o ,
o /
o /
o
o /
O /
38 32
331 22 |
1829
1850
25 55 w.
25-9 w.
65 53
65 ■9 it..
Liitke.
Rattlesnake.
A 3a (2 observations)
37 32
331 33
1836
23 05 w.
231 w.
FitzRoy.
38 28
331 36
1842
27 00 w.
Vidal.
39 05
331 56
1844
26 46 w.
Vidal.
T'| eira
38 39
332 47
1836
24 19 w.
24-3 w.
68 06
68-1 n.
FitzRoy.
L
38 45
332 52
r
1836
24 21 w.
FitzRoy.
Austin and Foster.
1831
24 31 w.
24-5 w. 1 °
67 34
67-6 sr.
37 46
334 19 j
1S36
24 15 w.
24-3 w. 124-8 w.
FitzRoy.
Vidal.
1844
25 45 w.
25-7 w. J
36 57
334 55
1844
25 17 w.
Vidal.
All :a (2 observations)
38 39
334 58
1859
26 42 w.
26-7 w.
Novara.
AJ a (2 observations)
36 34
337 01
1846
20 49 w.
20-8 w.
Berard.
Al a (2 observations)
38 11
338 09
1859
26 15 w.
26-3 w.
Novara.
All a (7 observations)
38 10
341 22
1830
25 31 w.
25 5 w.
Prussian ships.
37 05
341 35
1842
21 02 w
Jehenne.
At sa (mean of 2 1
36 06
342 20
1846
21 00 w.
21-0 w.
Berard.
iervations J
1822
62 12
-2 20
59-9)
9 81 )
Sabine.
(
|
1826
62 00
-1 52
60-1 | °
Xing.
Fijbal
32 38
343 05 -j
|
1839
60 16
-0 21
-0 14
59- 9 J-G00 n.
60- 2
59-7 )
9-88 )■ 9 80
Norwegian Officers.
Ross.
1840
60 23
9-71 |
1841
59 50
-0 07
)
Fishbourne.
At i
30 47
343 10
1840
9-56
Ross.
At i
33 00
343 50
1832
23 00 w.
23 -Off,
FitzRoy.
Liitke.
At i (2 observations)
36 34
344 08
1826
22 00 w.
22 0 w.
At i (2 observations)
31 24
344 13
1826
23 45 w.
23-8 w.
Liitke.
At [i
37 20
344 30
1836
23 54 w.
23-9 w.
FitzRoy.
Sulivan.
At i
34 35
344 48
1838 .
61 07
61-In.
9-47
At h
38 41
345 00
1836
23 35 w.
23-6 w.
FitzRoy.
Sulivan.
At i
37 28
346 04
1838
63 02
63-0 n.
9-56
Ati i
35 07
346 10
1843
23 34 w.
23 6 w.
Pasley.
Bonite.
At i
30 02
346 18
1836
22 24 w.
22-4 w.
At i (2 observations)
36 42
347 05
1859
23 10 w.
23-2 w.
Novara.
At l (2 observations)
30 59
347 08
1842
22 30 w.
22-5 w.
Berard.
At i
39 30
347 51
1840
10-46
Ross.
At i
33 16
348 08
1838
20 01 w.
20 0 w.
Berard.
At i (2 observations)
33 34
349 05
1836
24 32 w.
24-5
Bonite.
At i (2 observations)
32 40
349 24
1842
22 22 w.
22-4
B6rard.
At i (2 observations)
35 53
350 20
1859
21 32 w.
21-5
Novara.
Lis a
38 43
350 51
1842
23 33 w.
23-6 w.
22-3 w.
21-1 w.
61 19
61-3 n.
9-79
Lamont.
At s
36 00
352 13
1836
22 20 w.
Bonite.
At ;
35 25
352 15
1846
21 05 w.
Berard.
At , (2 observations)
34 49
352 17
1842
22 00 w.
22-0 w.
Berard.
At (2 observations)
35 11
352 30
1838
21 09 w.
21-2 w.
Berard.
At (3 observations)
35 57
353 37
1846
20 29 w.
20-5 w.
Berard.
At i (mean of 2)
c srvations) j
35 43
353 45
1846
20 27 w.
20-5 w.
Berard.
Cac
36 28
353 48 |
1842
22 05 w.
22-1 w.
58 44
58 -7 n.
9-55
Lamont.
Sev ! ..
1845
59 27
59-5 n.
Norwegian Officers.
37 23
353 59'
1842
1845
22 10 w.
22-2 w.
59 33
58 47
59 15
59-6 n.
58-8 n.
5S}»«*
9- 59
9-55
9-72
Lamont.
Norwegian Officers.
Norwegian Officers.
Tai jrs
35 47
354 12
Gib tar*
36 10
354 40 {
1844
1857
19 13 w.
1 53 w.
211 w.
57 39
+0 40
Novara,
At i ...
36 03
355 20
1854
19 51 w.
19-9 w.
Novara.
Mai
At s , . . .
36 43
36 26
355 32
356 02
1842
1846
21 36 w.
19 15 w.
21-6 w‘.
19 3 w.
58 29
58-5
9-93
Lamont.
Berard.
1
_ „
* r
andl
corre
empl
3 ‘Novara’ entries in this portion of the Zone are those moBt distant from the Mean Epoch. The only land station of the ‘Novara ’ is Gibraltar. The latitude
;itude of Gibraltar are so near to those of Malaga that it seems quite justifiable to apply to the ‘ Novara’ result, at the first-named station, the secular change
>ns employed at the last-named station by so high an authority as Lamont, viz. 7,-5 Declination and 2'm7 Inclination annually. These rates have been
;d by Dr. Lamont’s own directions, in reducing his observations to the epoch of 1842, in the preceding and present Papers (Nos. XIII. and XIV.).
200
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
NORTH EQUATORIAL ZONE IV.— Lat. 30° N. to 40° N. (continued).
Stations.
Lat. N.
Long. E.
Date.
Declination.
Inclination.
Force in
British units.
Observers.
Ob-
served.
Correction
to Epoch
1842-5.
Corrected.
Ob-
served
Cor. to
Epoch
1842-5.
Corrected.
o ,
o '
o
O f
o
Tembleque
1 39 42
356 30
1842
21 46 w.
21-8 w.
61 01
610 N.
9 67
Lamont.
G-ranada
37 10
356 33
1842
21 26 w.
21-4 w.
58 40
58-7 n.
9-50
Lamont.
At sea
35 48
357 00
1842
18 30 w.
18-5 w.
Berard.
Almeria
36 52
357 29
1842
20 57 w.
2 10 w.
58 07
58-1 n.
9-46
Lamont.
At sea
36 15
357 34
1858
19 23 w.
19-4 w.
Novara.
At sea (2 observations)
35 52
357 41
1842
18 40 w.
18 7 w.
Berard.
At sea (2 observations)
37 43
358 06
1846
19 41 w.
19-7 w.
Berard.
At sea
i 36 46
358 52
1838
19 47 w.
19 8 w.
Berard.
Cartagena
37 36
358 58
1842
20 29 w.
20-5 w.
58 22
58-4 n.
9-44
Lamont.
At sea (3 observations)
36 21
359 06
1846
18 58 w.
19-0 w.
Berard.
Valencia
39 29
359 35
1842
20 32 w.
20-5 w.
60 08
60-1 n.
9-60
Lamont.
At sea (2 observations)
36 10
359 42
1846
19 18 w.
19-3 w.
Berard.
A few observations are subjoined which should have been included in Zone I.
Stations.
Lat. N.
Long. E.
Date.
Declination.
Inclination.
Force in
British units.
Observers.
Ob-
served.
Correction
to Epoch
1842-5.
Corrected.
Ob-
served.
Cor. to
Epoch
1842-5.'
Corrected.
o /
o )
o /
o
r
1841
2 33 n.
2-6 n.1 °
Fishbourne.
Mean Point;
4 18
6 05 •
1841
2 29 n.
2-5 n. L 2-5 n.
Fishbourne.
1841
2 30 n.
2-5 n. J
Fishbourne.
Eboe ....
5 40
6 27
1841
4 46 n.
4-8 n.
Fishbourne.
Cliff of Idda . . .
7 04
7 00
1841
7 45 n.
7'8 n.
Fishbourne.
Fernando Po
3 45
8 45
1841
2 14 s.
2-2 s.
Fishbourne.
Stioura, Peono
8 30
346 44
1841
26 30 n.
26 5 n.
Fishbourne.
Liberia
6 25
349 30
1841
22 57 n.
230 n.
Fishbourne.
Grunyille ....
1841
19 02 n.
19 0 n.
Fishbourne.
5 00
351 00
1841
18 58 n.
19-0 n.
Fishbourne.
Cape Coast Castle
5 06
358 46
1841
11 26 n.
11-4 N.
Fishbourne.
Accra
5 32
359 49
1841
11 24 n.
11-4 N.'
Fishbourne.
In the following Tables I have placed in comparison with each other, the values of
the magnetic Elements at every fifth degree of latitude between 40° N. and the Equator,
and at every tenth degree of longitude between 0° and 360°, as shown (1) in the Table
published by MM. Gauss and Weber, in the ‘Atlas des Erdmagnetismus ’ (Leipsic,
1840), and (2) in the Tables and Maps of the present paper. For the values of the
Magnetic Force, which in the Atlas of MM. Gauss and Weber are expressed in the
Arbitrary Scale, of which the fundamental value is T372, or (as written by M. Gauss)
1372 = the Force in London in 1836, I have substituted the Absolute Values corre-
sponding to 10-28 as the Absolute Force in London at the same Epoch, in the scale
which was originally adopted in conformity with the Report of the Committee of
Physics of the Royal Society, 1840, page 21. In all the three Elements there are some
blanks in the columns derived from the data in the present paper, owing to observations
being either wanting or insufficient in those localities.
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
201
Declination.
Lati-
Gauss.
| Sabine.
Gauss.
1 Sabine.
Gauss.
Sabine.
Gauss.
| Sabine.
Gauss.
j Sabine.
Gauss.
Sabine.
Lati-
tudes.
Long
. 0° E.
Long. 10° E.
Long. 20° E.
Long. 30° E.
Long. 40° E.
Long. 50° E.
0
o /
l ° /
o /
1 ° '
o /
1 ° '
o /
o /
0 /
0 /
0 /
0 /
0
40 n.
24 20 vv
20 35 w
20 48 w
16 54 w
16 13 vv
12 41 w
. 11 03 vv
.[ 8 58 vv.
5 49 vv,
. 4 23 vv
. 1 04 w.
. 0 55 w.
40 n.
1 35 n.
23 48 vv
20 57 vv
[ 16 37 vv
16 49 vv
12 39 vv.
. 11 52 vv
. 8 38 vv.
6 40 w.
5 06 vv
. 1 50 w.
. 1 53 vv.
35 n.
I 30 n.
23 17
21 06 w
17 25 vv
1 12 40 w.
. 12 43 vv
. 9 06 w.
7 32 w.
. 5 49 vv.
. 2 36 w.
2 57 vv.
30 n.
I 25 n.
22 50 vv
21 16 vv
18 03 vv
12 53 vv.
13 35 vv
. 9 37 vv.
8 26 vv.
6 26 vv.
, 3 02 vv.
3 42 w.
25 n.
20 n.
22 25 w
21 29 w
18 44 vv
! 13 13 vv.
14 30 vv,
. 10 15 vv.
9 22 vv.
7 09 vv.
. 4 11 vv.
4 19 w.
20 n.
15 N.
22 10 vv
21 46 vv
19 28 vv
1 13 40 w.
15 30 w.
. 10 54 w.
1 10 25 w.
7 52 vv.
5 04 w.
4 50 vv.
15 N.
10 N.
! 21 58 vv
22 08 w
20 18 vv
14 17 vv.
16 36 vv.
11 36 vv.
11 34 vv.
8 45 vv.
6 01 w.
5 38 vv.
10s.
! 05 n.
21 51 vv
22 34 w
18 20 vv
21 13 vv
115 20 vv.
17 50 vv.
12 27 vv.
12 53 vv.
9 43 vv.
7 17 w.
6 35 vv.
05 n.
00 N.
21 49 w
23 04 w
i 19 32 vv
22 14 w
16 31 vv.
19 14 vv.
13 39 w.
1 14 26 vv.
10 54 vv.
8 45 vv.
7 50 vv.
00 N.
Long
60° E.
Long. 70° E.
Long. 80° E.
Long.
90° E.
Long. 100° E.
Long.
110° E.
40 n.
2 42 e.
1 18 E.
4 56 e.
3 05 e.
5 47 e.
4 55 e.
2 52 e.
0 24 e.
I 0 22 vv.
40 n.
35 X.
2 03 e.
0 34 e.
4 33 e.
1 55 e.
5 25 e.
3 07 e.
4 41 e.
2 48 e.
0 30 e.
0 00
35 n.
30 n.
1 27 e.
0 08 w
4 06 e.
1 05 e.
5 07 e.
2 12 e.
4 32 e.
2 48 e.
0 40 e.
30 n.
25 n.
0 52 e.
1 19 w
3 41 e.
0 23 e.
4 49 e.
1 18 E.
4 23 e.
2 49 e.
0 53 e.
25 n.
20 n.
0 14 e.
2 08 vv
3 14 e.
0 01 E.
4 31 e.
0 58 e.
4 13 e.
1 54' E.
2 49 e.
1 05 e.
1 08 e.
20 n.
15 N.
0 27 w
2 38 w.
2 44 e.
0 25 vv
4 10 e.
0 47 e.
4 00 e.
1 44 e.
2 47 e.
1 15 e.
1 22 e.
15 N.
10 N.
1 15 w
3 04 w.
2 07 e.
0 40 vv
3 42 e.
0 40 e.
3 41 e.
1 35 e.
2 39 e.
1 22 e.
1 11 E.
10 N.
05 n.
2 14 w
3 42 w.
1 20 e.
1 06 vv
3 04 e.
0 28 e.
3 12 e.
1 17 E.
2 22 e.
2 00 e.
1 21 e.
1 23 b.
05 n.
00 N.
3 29 w
4 42 w.
0 17 e.
2 01 w.
2 11 E.
2 30 e.
1 54 e.
1 12 E.
00 N.
. Long. 120° E.
Long.
130° E.
Long. 140° E.
Long.
150° E.
Long. !
160° E.
Long. :
170° E.
40 n.
1 34 w
1 54 w.
2 21 w.
1 39 vv.
2 00 vv.
0 27 e.
1 04 e.
3 35 e.
4 24 e.
7 15 e.
9 02 e.
40 n.
35 n.
1 20 w
1 28 w.
2 02 w.
1 18 w.
1 13 w.
0 47 e.
1 37 e.
3 51 e.
4 51 e.
7 20 e.
9 23 e.
35 n.
30 n.
1 00 w.
1 03 w.
1 35 w.
1 53 w.
0 47 w.
0 34 w.
1 18 E.
2 17 e.
4 17 e.
5 33 e.
7 33 e.
9 43 e.
30 n.
25 n.
0 37 w.
0 34 w.
1 03 vv.
1 12 w.
0 09 w.
0 00
1 57 e.
2 58 e.
4 50 e.
6 02 e.
7 53 e.
10 02 e.
25 n.
20 n.
0 12 w.
0 06 w.
0 27 vv.
0 31 vv.
0 34 e.
1 07 e.
2 43 e.
3 44 e.
5 30 e.
6 48 e.
8 16e.
10 18 e.
20 n.
15 N.
0 12 e.
0 18 e.
0 10 E.
0 10 E.
1 21 e.
1 48 e.
3 32 e.
4 12 e.
6 12 e.
7 17 e.
8 42 e.
10 32 e.
15 N.
10 N.
0 34 e.
0 41 e.
0 47 e.
2 13 e.
2 27 e.
4 23 e.
4 40 e.
6 56 e.
7 35 e.
9 07 e.
11 00 E.
10 N.
05 n.
0 52 e.
0 53 e.
1 22 e.
2 55 e.
5 13 e.
5 08 e.
7 38 e.
9 30 e.
05 n.
00 N.
1 04 e.
1 09 e.
1 51 E.
3 37 e.
5 58 e.
8 16 e.
9 49 e.
00 N.
Long. 180° E.
Long. 190° E.
Long. 200° E.
Long. 210° E.
Long. 220° E.
Long. 230° E.
j 40 w.
10 55 e.
14 05 e.
16 28 e.
17 56 e.
18 28 e.
18 08 e.
40 n.
35 n.
10 41 e.
13 25 e.
15 17 e.
14 21 e.
16 16 e.
15 23 e.
16 27 E.
15 24 e.
15 59 e.
14 40 e.
35 n.
30 n.
10 33 e.
12 49 e.
14 10 e.
12 32 e.
14 42 e.
12 56 e.
14 37 e.
12 56 e.
14 05 e.
12 26 e.
30 n.
25 n.
10 29 e.
12 15 e.
13 06 e.
10 47 e.
13 14 e.
10 35 e.
12 55 e.
10 35 e.
12 25 e.
10 16 e.
25 n.
20 n.
10 27 e.
11 42 e.
12 03 e.
11 49 e.
8 57 E.
11 22 e.
8 20 e.
10 56 e.
8 05 e.
20 n.
15 N. I
10 26 e.
11 09 e.
11 02 e.
10 29 e.
9 56 e.
9 36 e.
6 37 e.
15 N.
10 N. 1
10 23 e.
10 36 e.
10 03 e.
9 14 e.
8 38 e.
8 31 e.
5 11e.
10 N.
05 n.
10 20 e.
10 05 e.
9 09 e.
8 07 e.
7 29 e.
7 27 e.
05 n.
00 N.
10 15 e.
9 36 e.
8 22 e.
7 10 e.
6 32 e.
6 39 e.
00 N.
Long. 240° E.
Long. 250° E.
Long. 260° E.
Long. 270° E.
Long. 280° E.
Long. 290° E.
40 n.
16 57 e.
14 52 e.
14 45 e.
11 45 e.
11 56 e.
7 29 e.
7 37 e.
2 03 e.
0 00
4 20 w.
8 00 vv.
40 n.
35 n.
14 56 e.
13 51 e.
13 16 e.
12 44 e.
10 52 e.
11 18 E.
7 36 e.
7 40 e.
3 21 e.
2 14 b.
1 47 w.
4 12 w.
35 n.
30 n.
13 13 e.
11 51 e.
11 58 e.
11 17 e.
10 10 E.
10 18 e.
7 40 e.
7 33 e.
4 18 e.
3 32 e.
0 04 e.
1 28 w.
30 n.
25 n.
11 47 e.
9 56 e.
10 55 e.
9 41 e.
9 39 e.
9 29 e.
7 45 e.
7 27 E.
5 03 e.
4 31 e.
1 31 E.
0 37 e.
25 n.
20 n.
10 32 e.
8 14 e.
10 03 e.
8 35 e.
9 14 E.
8 49 e.
7 51 e.
7 23 e.
5 41 e.
5 12 e.
2 39 e.
2 04 e.
20 n.
15 N.
9 29 e.
6 48 e.
9 22 e.
7 25 e.
8 58 e.
8 10 e.
8 00 e.
7 18 e.
6 15 e.
5 38 e.
3 38 e.
3 15 e.
15 N.
10 N.
8 36 e.
5 23 e.
8 50 e.
6 26 e.
8 49 e.
7 24 e.
8 12 e.
7 39 e.
6 49 e.
6 25 e.
4 30 e.
4 30 e.
10 N.
05 n.
7 53 e.
8 28 e.
6 07 e.
8 47 e.
7 25 e.
8 30 e.
7 23 e.
7 14 e.
5 19 e.
5 29 e.
05 n.
00 N.
7 21 E.
8 14 e.
8 52 e.
8 53 e.
8 00 e.
6 08 e.
6 19 e.
00 N.
Long. 300° E.
Long. 310° E.
Long. 320° E.
Long. 330° E.
Long. 340° E.
Long. 350° E.
40 n.
11 03 w.
14 08 vv.
17 17 w.
19 15 w.
22 17 vv.
25 34 vv.
26 57 w.
26 29 w.
40 n.
35 n.
7 31 w.
9 16 w.
13 17 w.
14 00 w.
18 24 w.
18 13 vv.
22 18 vv.
24 35 vv.
25 04 w.
35 n.
30 n.
4 52 \v.
6 31 w.
10 09 vv.
1 0 52 vv.
15 13 vv.
15 24 vv.
19 30 vv.
19 04 vv.
22 27 vv.
23 42 w.
30 n.
25 n.
2 49 vv.
4 01 w.
7 40 vv.!
8 28 vv.
12 37 vv.
12 51 vv.
17 07 vv.
16 36 vv.
20 36 vv.
19 42 vv.
22 35 w.
25 n.
20 n.
1 12 w
1 34 w.
5 42 w.
6 10 w.
10 31 vv.
10 48 vv.
15 08 w.
15 13 vv.
19 00 w.
18 01 vv.
21 34 w.
20 n.
15 N.
0 08 e.
0 31 e.
4 06 vv.
3 52 w.
8 47 vv.
8 55 vv.
13 29 vv.
13 31 vv.
17 38 vv.
20 41 w.
15 N.
10 N.
1 16 E.
1 44 e.
2 46 vv.
1 59 w.
7 16 w.
7 17 vv.
12 06 vv.
12 16 vv.
16 30 vv.
19 58 w.
10 N.
05 n.
2 17 e.
2 48 e.
1 36 vv.
0 22 vv.
6 08 vv.
6 00 w.
10 56 vv.
1 1 23 vv.
15 32 w.
19 22 vv.
05 n.
00 N.
3 14 e.
3 44 e.
0 33 vv.
0 34 e.
5 02 vv.
4 53 vv.
9 54 vv.
10 43 w.
14 42 vv.
15 39 w.
18 52 vv.
19 26 w.
00 iv.
MDCCGLXXV. 2 E
202
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
Inclination.
Sabine.
Gauss.
Sabine.
Gauss.
Sabine.
Gauss.
Sabine.
Gauss, f |
Sabine.
Lati-
1
1
1
Lati-
tudes.
Long.
0° E.
Long. 10’ E.
Long. 20° E.
Long. 30° E.
Long. 40’ E.
Long. 50° E.
tudes.
O
o ,
o ,
o /
° /
o /
o /
o /
0 .
o /
o ,
o r
0 ,
o
40 n.
60 44 n.
61 00 n.
57 04 n.
58 55 n.
53 38 n.
57 25 n.
50 53 if.
55 40 n.
49 12 n.
54 55 if.
48 47 n.
54 10 n.
40 n.
35 n.
56 22 n.
51 56 n.
54 07 n.
47 37 n.
51 25 n.
44 03 n.
49 11 N.
41 47 n.
47 41 if.
41 07 n.
47 16 n.
35 n.
30 n.
51 25 n.
50 05 n.
46 05 n.
46 30 n.
40 47 n.
43 06 n.
36 17 if.
40 56 n.
33 20 n.
40 15 n.
32 21 n.
40 00 n.
30 n.
25 n.
45 49 n.
44 18 n.
39 31 n.
39 25 n.
33 17 n.
34 06 n.
27 34 n.
31 21 n.
23 52 n.
30 20 n.
22 31 n.
30 00 n.
25 n.
20 n.
39 31 n.
37 53 n.
32 12 n.
29 42 n.
24 38 n.
23 53 n.
18 01 n.
21 05 if.
13 32 n.
20 00 n.
11 48 n.
19 38 n.
20 n.
15 N.
32 28 n.
27 56 n.
24 09 n'
19 31 n.
15 29 n.
13 58 n.
7 53 n.
11 29 n.
2 42 n.
10 00 n.
0 36 n.
9 08 n.
15 N.
10 N.
24 44 n.
18 37 n.
15 30 n.
9 04 n.
5 54 n.
4 52 n.
2 26 s.
2 23 n.
8 08 s.
0 25 n.
10 32 s.
1 04 s.
10 N.
05 n.
16 22 n.
9 31 n.
6 28 n.
1 34 n.
3 46 s.
3 22 s.
12 27 s.
18 24 s.
20 58 s.
05 if.
00 N.
7 36 n.
2 38 s.
12 58 s.
21 44 s.
27 42 s.
30 24 s.
00 N.
Long. 60° B.
Long. 70° E.
Long. 80° E.
Long. 90° E.
Long. 100° E.
Long. 110° E.
40 n.
49 32 n.
51 08 n.
53 02 n.
54 45 n.
55 50 n.
56 06 n.
40 n.
35 n.
41 56 n.
47 15 n.
43 49 n.
47 35 n.
46 06 n.
48 24 n.
48 10 n.
49 40 n.
49 32 n.
50 41 n.
49 55 n.
51 06 n.
35 n.
30 n.
33 14 n.
40 00 if.
35 26 n.
40 08 n.
38 10 n.
40 34 n.
40 39 n.
41 17 n.
42 18 n.
42 22 if.
42 51 n.
42 40 n.
30 n.
25 n.
23 27 n.
30 15 n.
25 59 n.
30 56 n.
29 08 n.
31 52 n.
32 06 n.
32 51 n.
34 06 n.
34 02 n.
34 49 n.
34 42 n.
25 N.
20 n.
12 44 n.
20 00 n.
15 33 n.
20 50 n.
19 11 If.
21 53 n.
22 32 if.
23 10 n.
24 51 n.
24 47 n.
25 47 n.
25 54 n.
20 N.
15 N.
1 28 n.
9 1 7 n.
4 28 n.
9 27 n.
8 24 n.
10 59 n.
1 2 06 n.
13 13 if.
14 42 n.
15 00 if.
15 49 n.
16 03 n.
15 N.
10 N.
9 48 s.
1 28 s.
6 47 s.
0 51s.
2 43 s.
0 22 n.
1 09 n.
2 32 n.
3 56 n.
4 46 n.
5 12 n.
6 00 n.
in w
05 n.
20 27 s.
17 36 s.
11 41 s.
13 37 s.
10 19 s.
9 47 s.
7 49 s.
6 58 s.
5 34 s.
5 33 s.
4 00 s.
117 N.
00 N.
30 04 s.
27 29 s.
23 47 s.
20 09 s.
17 27 s.
16 03 s.
00 N.
Long.
120° E.
Long. 130° E.
Long. 140° E.
Long. 150° E.
Long. 160° E.
Long. 170’E.
40 n.
55 33 n.
54 28 n.
53 15 n.
52 21 n.
52 05 n.
53 40 n.
52 38 if.
54 20 n.
40 n.
35 n.
49 23 n.
50 54 n.
48 15 n.
49 29 n.
46 59 n.
47 30 n.
46 06 n.
46 12 n.
46 00 n.
46 28 n.
46 48 n.
48 38 n.
35 n.
30 n.
42 22 n.
42 38 n.
41 12 n.
42 01 n.
39 56 n.
40 32 n.
39 09 n.
40 00 n.
39 16 n.
40 45 n.
40 27 n.
42 58 sr.
30 n.
25 n.
34 24 n.
34 56 n.
33 16 n.
34 37 n.
32 03 n.
33 41 n.
31 27 n.
33 23 n.
31 55 n.
34 15 n.
33 32 n.
37 00 if.
25 n.
20 n.
25 27 n.
26 09 sr.
24 24 n.
25 44 n.
23 20 n.
25 17 n.
23 00 n.
25 22 n.
23 52 n.
27 00 n.
26 02 n.
30 00 n.
20 n.
15 N.
15 38 n.
16 09 n.
14 43 n.
15 55 n.
13 54 n.
15 33 n.
13 55 n.
15 50 n.
15 18 n.
18 24 n.
18 01 n.
22 09 n.
15 N.
10 N.
5 1 1 N.
6 23 n.
4 31 n.
6 13 n.
4 01 if.
5 40 n.
4 29 n.
6 23 n.
6 22 n.
9 38 n.
9 35 n.
14 08 N.
10 N.
05 n.
5 25 s.
3 05 s.
5 49 s.
3 16 s.
5 55 s.
3 52 s.
4 59 s.
3 00 s.
2 38 s.
0 31 n.
0 58 sr.
5 37 n.
05 n.
00 N.
15 41 s.
13 34 s.
15 45 s.
13 15 s.
15 27 s.
13 25 s.
14 07 s.
11 25 s.
7 35 s.
00 N.
Long. 180° E.
Long. 190° E.
Long. 200° E.
,Long. 210° E.
Long. 220° E.
Long. 230° E.
40 n.
53 55 n.
55 00 n.
55 47 n.
56 00 n.
57 59 n.
57 35 n.
60 16 if.
59 40 n.
62 32 n.
61 45 n.
64 42 n.
40 n.
35 n.
48 27 n.
52 00 n.
50 39 n.
53 05 n.
55 30 n.
55 41 n.
57 47 sr.
57 14 n.
59 55 n.
58 55 n.
35 n.
30 n.
42 31 n.
46 08 n.
45 04 n.
49 23 n.
47 43 n.
51 35 n.
50 13 n.
51 38 n.
52 28 n.
52 28 n.
54 31 n.
53 15 n.
30 n.
' 25 n.
36 04 n.
40 42 n.
38 59 n.
43 21 n.
41 50 n.
45 18 n.
44 20 if.
46 28 n.
46 29 if.
47 1 1 n.
48 25 n.
47 30 n.
25 n.
20 n.
29 04 n.
33 17 n.
32 21 n.
37 16 n.
35 20 n.
38 53 n.
37 46 n.
40 11 n.
39 44 n.
40 35 n.
41 30 n.
40 37 n.
20 n.
15 N.
21 32 n.
26 09 n.
25 07 n.
28 10 n.
31 39 sr.
30 27 n.
32 24 n.
32 09 n.
32 41 n.
33 40 n.
32 38 n.
15 N.
10n.
13 31 n.
19 03 n.
17 18 n.
20 1 8 n.
22 21 n.
23 43 n.
23 37 n.
24 55 n.
23 16 if.
10 N.
05 n.
5 09 n.
11 20 n.
9 00 n.
11 50 n.
13 32 n.
14 30 n.
14 33 n.
15 19 n.
13 55 n.
05 if.
00 N.
3 21 s.
0 22 n.
2 55 n.
4 14 n.
4 45 n.
5 12 n.
00 N.
Long. 240° B.
Long. 250° E.
Long. 260° E.
Long. 270° E.
Long. 280° E.
Long. 290° E.
1
40 n.
66 44 n.
65 00 n.
68 39 n.
67 10 n.
70 24 n.
69 10 n.
71 54 n.
70 37 n.
73 02 n.
72 00 n.
73 40 n.
40 n.
35 n.
61 56 n.
60 35 n.
63 52 n.
62 01 n.
65 42 n.
63 41 n.
67 22 N.
65 20 n.
68 44 n.
66 53 if.
69 40 n.
68 07 n.
35 n.
30 n.
56 30 n.
54 22 k.
58 27 n.
55 54 n.
60 24 n.
57 46 n.
62 15 n.
59 46 n.
63 53 n.
61 21 n.
65 07 if.
62 53 n.
30 n.
25 n.
50 19 n.
48 05 n.
52 19 n.
49 28 n.
54 24 n.
51 14 n.
56 29 n.
53 11 n.
58 24 n.
55 1 7 n.
59 58 n.
57 19 sr.
25 n.
20 n.
43 18 n.
41 02 n.
45 20 n.
42 14 n.
47 35 n.
44 03 n.
49 57 n.
46 16n.
52 13 n.
48 37 n.
54 08 n.
57 53 n.
20 n.
15 N.
35 22 n.
32 59 n.
37 25 n.
34 20 n.
39 53 n.
36 21 n.
42 35 n.
38 48 n.
45 15 n.
41 30 n.
47 35 n.
43 59 n.
15 N.
10 N.
26 27 n.
23 36 n.
28 32 n.
25 08 n.
31 13 n.
27 41 n.
34 17 if.
30 44 n.
37 23 n.
33 29 n.
40 07 n.
36 32 n.
10 N.
05 n.
16 38 n.
14 03 n.
18 43 n.
15 15 n.
21 36 n.
17 56 n.
25 02 n.
20 47 if.
28 37 n.
24 35 if.
31 54 n.
28 17 n.
05 n.
00 If.
6 15 n.
8 15 n.
11 15 N.
14 59 if.
19 00 n.
22 46 n.
00 N.
Long. 300° E.
Long. 310° E.
Long. 320’ E.
Long. 330° E.
Long. 340° E.
Long. ,
350° E.
40 n.
73 43 n.
73 07 n.
71 50 n.
70 55 n.
69 54 n.
68 20 n.
67 21 n.
65 30 if.
64 14 n.
63 00 n.
40 if.
35 if.
70 01 if.
68 27 n.
69 42 n.
68 12 n.
68 37 n.
66 57 n.
66 43 n.
64 39 n.
63 59 n.
62 06 n.
60 30 n.
59 25 if.
35 ».
30 n.
65 47 n.
63 50 n.
65 44 n.
64 08 n.
64 50 n.
63 07 n.
62 58 n.
61 07 if.
60 06 n.
58 12 n.
56 13 n.
54 25 if.
30 n.
25 n.
60 57 n.
59 19 n.
61 10n.
60 21 n.
60 28 n.
59 28 n.
58 39 n.
56 51 n.
55 37 n.
53 41 n.
51 19 n.
50 00 n.
25 n.
20 N.
55 28 n.
52 43 n.
55 59 n.
54 02 n.
55 28 n.
53 50 n.
53 42 if.
52 03 n.
50 29 n.
48 47 n.
45 44 n.
44 09 n.
20 n.
15 If.
49 17 n.
46 01 n.
50 06 n.
47 36 n.
49 46 n.
48 13 n.
48 02 n.
46 26 n.
44 39 n.
42 53 n.
39 27 if.
37 36 n.
15 N.
10 N.
42 19 n.
39 10 n.
43 28 n.
41 08 n.
43 20 n.
41 42 n.
41 38 if.
40 13 n.
38 04 n.
36 01 n.
32 25 n.
28 10 n.
10 N.
05 n.
34 29 n.
31 02 n.
35 59 n.
33 32 n.
36 08 if.
35 04 n.
34 26 n.
33 13 n.
30 42 n.
27 49 n.
24 40 n.
18 48 n.
05 n.
00 N.
25 49 n.
27 41 n.
28 00 if.
26 25 n.
22 35 if.
16 16 n.
9 47 n.
00 N,
GENERAL SIR EDWARD SABINE ON TERRESTRIAL MAGNETISM.
203
Force in British Units.
Sabine.
Gauss.
Sabine.
Gauss.
Sabine.
Gauss.
Sabine..
Gauss. I
Sabine.
Lati-
1
1
Lati-
1 tudes.
Long. 0°E.
Long.
10’ E.
Long.
20’ E.
Long. 30° E.
Long. 40° E
Long. 50° E.
tudes.
40 x.
9-S5
953
9-33
9-28
9-36
9-57
40 n.
j 35 n.
9-49
9-12
8-88
8-77
91
8-82
9-4
9-01
35 x.
30 x.
9-08
8 9
8-67
8-39
8-26
8-4
8-29
8-6
8-45
90
30 x.
i 25 n.
8-61
8-6
8-21
7-92
7-78
77
7-81
7-9
7-96
8-3
25 x.
20 x.
8-16
8-3
7-76
7-49
7-38
7-42
7-57
20 x.
j 15 N.
770
81
7-33
712
7-07
716
7-32
15 x.
j 10 X.
7-26
7-6
6-97
6-84
6-88
7-02
7-20
10 x.
05 x.
(>•87
70
6-68
6-66
679
701
7-23
05 x.
00 x.
655
6-47
656
679
707
7-32
00 x.
Long. 60° E.
Long.
70° E.
Long. 80° E.
Long.
90° E.
Long. 100° E.
Long. 110° E.
1 40 x.
9-88
10-23
10-56
10-80
11-3
1094
1093
40 x.
35 x.
9-30
97
9-64
100
9-97
10-4
10-23
107
10-36
107
10-36
10-6
35 x.
30 x.
872
9-3
904
9-5
935
9-8
9-60
9-9
973
9-9
972
9-9
30 x.
25 n.
819
8-8
8-48
91
S-75
9-3
8-98
9-4
9 11
94
9 11
94
25 x.
1 20 x.
778
8-1
801
8*6
8-25
8-8
8-45
8-9
8-56
fc8-9
8-57
8-9
20 x.
15 x.
7-50
7-69
8-1
7-87
8 03
8-4
814
8-6
815
8-6
15 x.
; 10 X.
7-37
7"53
7-66
7-78
7-87
8-2
7-90
8-4
10 x.
05 x.
7 39
7 51
7 61
771
7-79
7-83
05 x.
| 00 x.
751
7-62
7-72
7-80
7- 89
7-96
00 x.
Long.
120’ E.
Long. 130° E.
Long. 140° E.
Long. 150° E.
Long. 1 60° E.
Long. 170° E.
40 x.
1078
1053
1025
9-98
9-82
979
40 x.
35 x.
1019
105
9-93
964
937
91
920
8-9
917
8-9
35 n.
30 x.
9-57
9-8
931
9 02
8-9
876
87
8-59
8-5
8-56
8-5
30 x.
25 n.
8-97
9 2
873
8-9
8-46
87
821
8-4
8 05
8-2
801
81
25 x.
20 n.
845
8-8
824
8-5
7-99
8-4
776
8 1
7-60
7-9
756
7-8
20 x.
15 x.
8 06
8-5
7-89
8-2
7-67
81
7-45
7-8
7-29
7"22
15 x.
10 x.
7-84
§■2
770
751
7-30
713
703
10 x.
04 x.
7-81
7-67
753
734
7 14
701
05 x.
00 x.
797
7-90
776
7"55
7-33
7 15
00 N.
Long.
180° E.
Long. 190° E.
Long. 200° E.
Long. 210° E.
Long. 220° E.
Long. 230° E.
40 x.
9 89
10-14
1050
10 93
11-39
11-82
12-0
40 x.
35 x.
9-29
955
9-93
10-39
10-87
11-33
11-1
35 n.
30 x.
8-68
8-95
9-34
979
10-27
10-74
10-4
30 x.
25 x.
8 13
8-39
8-75
8-8
9-19
9-2
9-65
10-10
9-8
25 x.
20 x.
7-65
7 89
8 22
8-3
8-62
8-6
9-05
8-9
9-46
9-2
20 x.
15 x.
7-29
7-48
7- 76
7-8
8 1 1
8-1
8-49
8-4
8-86
87
15 N.
10 x.
7 05
719
7-42
7-69
8-03
7-9
8-35
8-2
10x.
05 x.
6-97
7-04
7-20
7-43
7-69
7-97
05 x.
00 x.
7-04
70.5
715
7-32
7-53
7-74
00 x.
Long. 240° E.
Long. 250° E.
Long. 260° E.
Long. 270° E.
Long. 280° E.
Long. 290° E.
40 x.
12-20
12 50
12 68
12-75
1270
13-6
12-53
40 x.
35 x.
1174
117
1206
12-4
12-28
12-8
12-39
131
12-37
13 1
12-24
127
35 x.
30 x.
11-16
10-9
11-50
115
1175
12 0
11-89
12-4
1191
12-4
11-81
122
30 x.
25 x.
1051
10-2
10-86
107
11-12
11-2
11-29
11-6
11-34
117
11-28
1 1-5
25 x.
20 x.
9-85
9-6
1018
10 1
1044
10-5
10-62
10-8
10 69
10-9
10-67
10-8
20 x.
15 x.
9-21
90
9-5 1
9-4
975
9-8
9-92
100
10-01
10-1
10-00
10-0
15 x.
10 N.
8-64
8-5
8-90
8-8
9 11
9-0
9-25
9-2
9-33
9 2
9 34
9-2
10 x.
05 x.
8-20
8-0
8-40
8-2
8-56
8-4
8-66
8-5
870
8-5
8-69
8-5
05 x.
00 x.
7-92
807
815
7-8
8-19
7-8
8-19
7-8
8 13
7-8
00 x.
Long. 300° E.
Long. 310° E.
Long. 320° E.
Long. 330° E.
Long. 340° E.
Long. 350° E.
40 n.
12-27
1 1-93
11-54
11-11
10-67
10-23
100
40 x.
35 x.
1200
11-68
11-8
11-30
10-86
10-7
1040
10-2
993
9-5
35 x.
30 x.
11-61
11-8
11-32
11-3
10-95
10-8
1052
10-3
1004
97
955
9-1
30 x.
| 25 x.
11-12
112
1085
10-8
1051
10-4
1009
9-8
9-62
92
9-12
8-8
25 x.
20 x.
10-54
10-6
10-31
102
9-99
9-8
9-60
93
9-14
8-8
8-64
8-5
20 x. j
15 x.
9-90
9-8
970
9-6
9-42
9-2
9 05
8-8
8*61
8-4
814
8-2
15 x.
10 x.
9 24
9-1
9-07
8-9
8 81
87
8-47
8-3
8-07
80
7-65
7-8
10 x.
05 x.
8-60
8-4
8 45
8-3
8-20
8-1
7-89
7-8
7-55
7 18
7-3
05 x.
I 00 x.
8-03
7-8
7-87
7-7
7 65
7-38
7-07
6-77
6-9
00 x.
[ 205 ]
V. Addition to the Paper on “ Volcanic Energy : an attempt to develop its true Origin
and Cosmical Relations”*. By Robert Mallet, A.M., C.E., F.R.S., M.B.I.A.
Received April 3, — Head May 7, 1874.
In the paper whose title is given above (Philosophical Transactions, part i. 1873) the
author has shown upon experimental data, and upon the acknowledged basis that the
amount of heat annually dissipated from our globe equals that evolved by 777 cubic
miles of ice at 32° melted to water at the same temperature, what is the amount of heat
that can be annually produced by the transformation of the mechanical work of mean
rock when crushed by the descent of the external shell upon the nucleus contracting
beneath it; he has also estimated the annual supply of heat necessary for the main-
tenance of the volcanic activity at present existing upon our globe ; has shown that its
total amount cannot exceed a small fraction of the entire heat dissipated annually, being
only Y5t 9 thereof, or, in terms of crushed mean rock, equal 0-5579 of a cubic mile (para-
graphs 179 and 197); he has also given, in Table II. (page 201) and succeeding para-
graphs, his experimental results as to the contraction by diminution of temperature of
melted matter that may be presumed similar to the rocky material of our globe from
which natural lavas are derived. This contraction in volume, in relation to temperature
between that of the blast-furnace and of the atmosphere, is shown graphically by the
curve Plate X. of the above paper, the upper and lower portions of the curve being
derived from experiment. The preceding elements afford some of the data necessary
for any calculation as to the actual contraction of our globe now taking place annually
by its secular refrigeration ; but the author refrained from attempting any such calcula-
tion on the grounds that other data indispensable to any certain result are yet wanting.
If we knew the thickness of the earth’s solid shell and the true increment of hypogeal
temperature from the surface to the centre, or even the mean temperature of the nucleus
and the nature of the whole of the matter composing the latter, we might with some
assurance approximate to the amount of annual contraction of the globe due to refri-
geration. But of the deep interior of our planet we really Jcnow but two things, viz.
that the interior is hotter than the exterior, and what is the mean density of the whole.
By making certain suppositions, however, as to some of the chief data wanted, we may
approximate to some probable measures of the present annual contraction, and be
enabled to see how far the results tend to sustain or overthrow the views enunciated by
the author as to the nature and origin of volcanic heat and energy, and may also find
* Bead June 20, 1872 ; Philosophical Transactions for 1873, p. 147.
2 F
MDCCCLXXV.
206
ME. EOBEET MALLET ON VOLCANIC ENEEGrY.
that they throw some additional light upon the conjectured thicknesses that have been
assigned to the earth’s solid crust, as well as upon the question left undecided by
Laplace as to how far the effects of contraction due to refrigeration would be astrono-
mically observable during the period of scientific history. In the author’s paper above
referred to he has only dealt with the total contraction of the slag experimented upon
between the temperature of its issue from the blast-furnace (viz. 3680°) and that of the
atmosphere (53°), or by volume from 1000 to 933 for 3617° Fahr., from which the
Eev. O. Fisher has calculated a mean coefficient of contraction =0-0000217 for 1° Fahr.
(Geol. Mag., February 1874). This, though sufficient for that able writer’s immediate
object, is not quite correct, as it treats the curve of contraction (Plate x. Philosophical
Transactions, 1873) as a straight line. And in order to make use for our present
purpose of these experimental contractions, it is necessary to obtain partial mean coeffi-
cients for different portions of the entire curve. This the author has done for ranges
of about 500° between the temperatures of the blast-furnace and that of the atmosphere.
The diagram fig. 1 (reduced from Plate x. Philosophical Transactions, 1873) shows the
Pig. 1. — Curve of Total Contraction of Slags.
Volume.
1014
Coefficient.
00001061
1000
0-0000477
9877
00000257
976-9
0-0000186
967-6
0-0000167
959-35
0-0000147
0-0000144
944-8
0-0000136
938
933
0-0000100
Temperature.
ME. ROBERT MALLET ON VOLCANIC ENERGY.
207
intervals of temperature within which the mean coefficients for contraction in volume
have been calculated ; the results are probably sufficiently clear on inspection, but may
be tabulated thus : —
Table I. — Coefficient of Contraction of Slags experimented upon at Barrow.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Higher
tempe-
rature
Fahr.
Bower
tempe-
rature
Fahr.
Range
of tempe-
rature.
Volume
at higher
tempe-
rature
taken as
Volume
at lower
tempe-
rature
then
equals
Volume at
3680° Fahr.
taken as 1000,
then volume
at other
temperatures
is as
Total con-
traction from
volume at
3680° to
volume at each
following
temperature.
Amount of
contraction
between
each two
temperatures.
Coefficients
of
contraction
per degree
Fahr.
Mean coefficient.
3810
3680
130
1014
1000
1014
14
1014
14
1014
0-0001061
36S0
3419
261
1000
9877
987-7
123
1000
12-3
1000
0-00004 77
1
3419
3000
419
1000
989
976-9
23 1
1000
10-8
1000
0-0000257
3000
2500
500
1000
991
967-6
32-4
1000
9-3
1000
0-0000186
2500
2000
500
1000
992
959-35
40-65
1000
8-35
looo
0-0000167
48
1000
7"5
■ 0000020087
2000
1500
500
1000
993
952-00
1000
0-0000147
1500
1000
500
1000
993
944-80
55-2
1000
7-2
1000
0-0000144
1000
500
500
1000
993
93800
62
1000
6-8
1000
00000136
500
53
447
1000
995
933-00
67
1000
5
1000
00000100
From inspection of the diagram fig. 1 and Table I., the upper and lower portions of
both of which (between 3680° and 53°) are reliable as being experimentally obtained,
we may observe that the mean coefficient of contraction in volume for the total range of
temperature shown in the diagram is =0-00002972 for one degree of Fahr. reduction
in temperature, or to 0-000020087, or very nearly 0-0000201 for the limits of tempe-
rature actually embraced by experiment, being those employed by the Rev. O. Fisher.
We also observe that the rate of dilatation or of contraction in volume for the two
uppermost segments of the curve, viz. between the temperatures 3419° and 3810°, or a
range of 391°, is 6-4 times greater than that for the two lowermost segments of the
curve, viz. from 53° to 1000°, or a range of 947° Fahr. If, therefore, the mean tempe-
rature of the nucleus of our globe be assumed within the limits of the former, and that
of the shell within those of the latter, and the capacity for heat of both the same, the
contraction in volume of the former will be 6-4 times that of the latter for an equal
decrement of temperature in both.
It is immaterial as to what follows whether we regard the nucleus of our globe as
solid or liquid, or in what way or through what intermediate state of viscosity the solid
2 f 2
208
ME. EOBEET MALLET ON VOLCANIC ENEEGY.
shell may pass into the nucleus if the latter be liquid ; it is only necessary for the author
to postulate a higher temperature, and therefore a larger coefficient of contraction, for
the interior of the globe than for the colder shell which surrounds it, and to suppose
as was done by the late Mr. Hopkins in his researches as to the thickness of the shell
4n relation to precession, that, whatever thickness may he assigned to the shell, it passes
jper saltum into the nucleus — all that is here meant being, that all below this imaginary
couche contracts more than does all above it for a given decrement of temperature of
both. We have no certain knowledge of the rate at which temperature increases either
in the shell or the nucleus in descending from the surface, nor what may be the highest
temperature of the nucleus itself ; but as the mean temperature of the shell may he
presumed greatly inferior to that of the nucleus, it may be allowable to regard the
whole of the heat dissipated from our globe in a unit of time (a year) as derived from
the nucleus only, and transmitted merely through the shell, the thickness of the latter
being taken as not too large in relation to the earth’s radius. The total heat dissipated
from our globe in a year, or, on the above suppositions, from the nucleus only, being, as
above stated, equal to that evolved by the melting of 777 cubic miles of ice at 32° to
water at 32°, may be considered for any moderate secular period, such as 5000 years, as
constant. The refrigerative power of the unit of volume of a cubic foot of such ice is
C=gX$,
g being the specific gravity and s the latent heat of ice. Therefore
C=57-8xl43=8265°-4 Fahr.,
or units of heat, assuming the capacity for heat of water to be the same at all tempe-
ratures ; and the refrigerative effect of this upon an equal volume of the mass of the
nucleus is
s' and §' being the specific heat and specific gravity or weight per unit of volume,
respectively, of the matter of the nucleus. We in reality know nothing as to what may
be the chemical or physical nature of the matter composing the nucleus ; we therefore
have no basis for assigning its specific heat in whole or in part ; nor do we know any thing
as to its specific gravity beyond this, that the mean density of our globe being 5-5, that
of the nucleus alone must be somewhat greater. We are therefore obliged to adopt
the most probable suppositions we can for the values of s' and g'. It is highly probable,
as appears to be generally conjectured by geologists, that a large proportion at least of the
entire mass of our globe, and therefore of the nucleus as here defined, consists of rocky
material not very dissimilar from that known to us by observation or inference in the
superficial crust of the earth. Now as none of the materials of the crust, excluding
those of metallic veins or beds relatively small in quantity, at all approach the average
density of 5’5, we may reasonably conclude that towards the centre of our planet there
exist masses of metals, the only bodies we are acquainted with whose high specific
ME. EOBEBT MALLET ON VOLCANIC ENEEGY.
209
gravities would bring the mean density of the whole to 5 -5. The exterior portions of
the sphere, constituting by far the largest portion of its entire volume, have a density of
little more than 2-0. But we cannot deal with the absolutely unknown, nor assign
either specific heat or specific gravity to the extremely dense material, whether metallic
or not, which we must suppose to exist about the centre of figure of our planet. The
most reasonable supposition, therefore, that we can make in reference to our present
object is to neglect the nature of this extremely dense matter, and to assume the whole
nucleus as composed of material not greatly different from the hardest and densest rocks
with which we are acquainted, and, with some allowance for their further increase in
density by compression, to adopt fof the whole nucleus a value for a density of 2 -75
(or one half the mean density of our entire globe), and for its specific heat s'=0’200,
being a little above the mean experimentally ascertained by the author for the five
hardest and densest rocks in Table I. column 27 of his paper in Philosophical Trans-
actions, 1873. The equation
C
s' X §'
therefore becomes
8265-4
0-2x2-75 x 62-425
=24°-74 Fahr.,
which is the amount of refrigeration produced by a unit in volume (1 cubic foot) of
melted ice upon an equal volume of the nucleus. Having for the constant refrigerative
power the 777 cubic miles of melted ice, and having the volume of the nucleus for any
assigned thickness of shell, we at once obtain the amount of refrigeration of the nucleus ;
and applying to that the partial mean coefficient of contraction for 1° Fahr. found at
the upper portions of our curve, we are enabled to calculate the reduction in volume,
and hence the diminution in radius, due to the amount of heat abstracted in the unit of
time, viz. one year. The author has assumed four successive thicknesses for the shell,
viz.
1001
200 i miles,
400 f
800 j
and proceeding on the above principles has calculated the total annual contraction of
the nucleus for each case. The partial mean coefficient of contraction adopted for that
of the nucleus has been the mean between the two highest partial means shown in the
curve and Table I. above given, viz. 0-0000769 for 1° Fahr.
The final results obtained are comprised in Table II., before referring to which,
however, some explanation and reference to diagram fig. 2 are necessary.
E being the radius of our globe=3957-5 English miles,
r=the radius assumed for the nucleus, whose thickness =11— r.
Let the nucleus be assumed to contract by loss of its heat transmitted through the
210
ME. KOBEET MALLET ON VOLCANIC ENEEGY.
shell until its radius =r', the shell then, in following down after the contracted nucleus,
must descend everywhere through a vertical height equal r—r'.
The spherical shell having the original external and internal radii R and r must
Eig. 2.
accommodate itself to this descent so as to remain in contact with the diminished
nucleus : it may do this in either of two ways ; it may increase in thickness, or R'— r' be
greater than R—r; or the thickness R—r may remain constant, in which case, as the
volume of the shell after descent is less than before, a certain portion of its volume must
be extruded or got rid of in some way. In the earlier stages of our globe’s refrigeration,
as explained in the author’s paper of 1873, the thickness of the descending shell did
not remain constant, but was increased by external corrugations and wrinklings, and
other like changes due to tangential pressure in that epoch of mountain-raising. But
the epoch of mountain-building has practically ceased, the shell being too thick and
rigid to admit of it. The thickness of the shell now must therefore be viewed as constant,
and the accommodation of its volume to enable it to remain in contact with the con-
tracting nucleus is produced by extrusion of some of its mass blown out to the surface
by volcanic action. The difference in volume thus to be got rid of is the difference
between
w{(2R)3— (2r)3} and w{(2R')3-(2r')3}5
the constant n=^ beings ’5236,
and as stated, the thickness of the shell remaining constant, the thickness of the ima-
ginary spherical shell which measures the reduction in volume of the nucleus, or r—rr,
must be = to the vertical descent of the external surface of the original or uncontracted
shell, or
r-r'=R-R' .
and as the absolute thickness of both these imaginary spherical shells is small, the
ME. ROBERT MALLET ON VOLCANIC ENERGY.
211
quantity of matter to be extruded is proportionate to the difference between their
internal or external surfaces respectively, or as
(2r7 : (2R/)2.
In dealing with these enormous volumes, this relation affords a convenient method of
determining the volume of matter that must be extruded from the shell.
Table II.
1.
2.
3.
4.
5.
6.
7.
8.
Thick-
ness
of
shell.
Diameter
of
nucleus.
Volume of
nucleus.
Volume of
contracted nucleus.
Reduction
in yolume
due to heat
lost.
Radial con-
traction in miles.
Volume of
extruded
matter.
Radial
contraction
in inches.
miles.
miles.
100
7715
240440392958- 15
240440392956-6793
0000000007806
0-07663643
00004945
200
7515
22221176499215
222211764990-67939
0-00000000836
0-15374
00005296
1-470602
400
7115
188592463139 15
18859246313767939
0-00000000928
0-34636
0-00058995
800
6315
131882013356-15
131882013354-67939
00000000106
0-758199
0-0006716
The results arrived at are seen at one view in Table II. On examining the Table,
it will be seen that the diminution in volume of the nucleus is constant whatever be the
thickness of the shell, for the obvious reason that the absolute reduction in temperature,
and therefore the absolute contraction in volume, are inversely as the mass of the nucleus
acted upon by the constant refrigeration, 777 cubic miles of melted ice; but the radial
contraction is greater as the volume of the nucleus is smaller. Recalling from the
author’s paper of 1873 the result that (15579 of a cubic mile of crushed mean rock is the
amount annually necessary for the maintenance of the volcanic activity of our globe at
present (an amount which the author believes to exceed the actual truth), and viewing
such crushed rock as the same thing with the extruded matter of the shell, it will be
seen that, on the suppositions we have made, the thickness of the solid shell of our globe
necessary for the support of its volcanic activity must exceed 400 miles, and that with
a thickness of shell of 800 miles the annual volume of the extruded or crushed rock
exceeds by about one half the quantity required to support volcanic activity. As the
rigid shell is and has been for ages in a state of elastic compression by tangential thrusts,
it is easily perceived that any increase, however slowly taking place, in these compressive
strains must be promptly responded to by disturbances in the mechanical equilibrium
of the shell itself. Some minute portion of these may perhaps still be disposed of in
small partial thickenings of the shell itself, giving rise to slight secular variations in level,
such as have been observed in Scandinavia and Greenland ; but these expiring remains of
ancient mountain-building are relatively so minute that they may be disregarded here.
The reliability of the conclusions here arrived at is of course only proportionate to the
admissibility of the suppositions made upon which they depend. In so far, however
they tend to support the author’s views as to the nature and origin of volcanic heat and
212
ME. EOBEET MALLET ON VOLCANIC ENEEGY.
energy, and also to support the views of those who regard the solid crust of our globe as
necessarily much thicker than geologists generally have been in the habit of admitting
it. It is probable that the contractions here determined for our planet are below the
truth; for
1st. Some contraction must always take place through cooling of the solid shell itself,
and especially of its lowermost and hottest portions, which has been here neglected.
2nd. It is probable that the coefficient of contraction employed is below the truth
for the material of the nucleus such as we have supposed it.
If the central parts of the nucleus be metallic, it is probable that their coefficient of con-
traction may largely exceed that here employed, while their specific heat is considerably
less than that adopted for the entire nucleus. On the other hand, it must be remembered
that a wave of heat from the central parts of the nucleus may take ages to travel con-
ductively outwards to the lower surface of the shell, even when the latter is assumed
800 miles in thickness, which is one of the reasons why in what precedes these central
parts have been supposed of a nature similar to the nucleus. It follows that, on the
supposition of a shell of 800 miles in thickness, the annual diminution in diameter of
our globe, due to its secular refrigeration, may somewhat exceed, but cannot be less than,
1493 3 96 9 9 64 1 4 diameter, a mere film wholly incapable of being recognized by the
senses ; or taking the diminution of diameter from the unit of a British inch instead of
a mile, it would amount in a period of 5000 years to a diminution of the diameter of our
globe of 6*71616 inches, or less than 7 inches, a quantity so small that it must have
escaped the most refined observation of the astronomer during the last 2000 years, even
were we to suppose that during the whole of that period the instrumental resources of
the astronomer were as perfect as at the present day. When we add to this the consi-
deration that the matter composing the imaginary spherical shell of less than 3^ inches
in thickness, which measures the contraction in volume of our globe during 5000 years,
has by its refrigeration increased in density in the ratio at least of 1000 to 933, we readily
discern the reasons for the negative results arrived at by Laplace in considering this
question from the point of view of an observable diminution in the length of the day.
Yet insignificant when thus measured as is the amount of annual contraction of our
globe by its secular refrigeration, we see how important and mighty are its effects in
preserving through the volcano the cosmical regimen of our world ; it is another added
to the many instances already known in the range of natural philosophy, in which causes
so minute a§ for long to remain occult to us are yet, though unseen and unnoticed,
essential parts of the mighty machine.
Three quantities related to each other indeed, but yet entirely different, have been
treated of in the author’s present paper or in that of 1873.
1st. The volume of mean rock which must be crushed annually in the earth’s shell
in order to supply the heat necessary for existing annual vulcanicity, viz. (K5579 of a cubic
mile, the heat due to which is fsV 9 of the total annually dissipated from our globe.
MR. ROBERT MALLET ON VOLCANIC ENERGY.
21
2ndly. The volume of matter that must be annually crushed and extruded from the
shell of 800 miles in thickness in order to admit of its following down after the con-
tracting nucleus, being 0-758199 of a cubic mile, which, if measured in terms of mean
crushed rock, amounts to xrr6 °f the heat annually dissipated. The former of these
quantities is comprised within the second as its source of supply, which, as we observe,
exceeds the annual demand necessary for existing volcanic energy by about one half.
Srdly. The volume of material heated or molten annually blown out of all the volcanic
vents of our globe, as based upon the estimates made in the author’s original paper
(paragraphs 195 to 197), which amounts to 0-1486 of a cubic mile, a quantity probably in
excess of the truth. The first of these quantities, upon the data assumed in this paper,
would be produced by a thickness of the solid shell of our earth of more than 400 but
less than 800 miles. The third of those quantities might be accounted for by a shell
of more than 200, but less than 400 miles in thickness. If the shell be actually less than
the smallest of these thicknesses, it follows either that the annual dissipation of heat
from our globe greatly exceeds that due to 777 cubic miles of melted ice, or that the
coefficient of contraction for the nucleus here employed and based on experiment is
below the truth, neither of which suppositions is improbable. It will be remarked that
the results in this paper have been obtained by an independent and different method of
investigation from that employed in the author’s original paper (Philosophical Trans-
actions of 1873), and that they coordinate to such an extent as to support the proba-
bility of the truth of the views enunciated in both papers.
In conclusion I wish to acknowledge the efficient aid I have received from my assistant
Mr. W. Worby Beaumont, Assoc. Inst. C.E., in completing the laborious calculations
involving a mass of figures of which the results only are here seen.
MDCCCLXX V.
G
[ 215 ]
VI. Research on the Smallpox of Sheep. By E. Klein, M.D., Assistant Professor at the
Laboratory of the Brown Institution , London. Communicated by John Simon,
F.R.S., D.C.L., Medical Officer of the Privy Council and of the Local Government
Board.
Received June 11, — Read June 18, 1874.
Description or Narrative of Experiments 215
Anatomical Method 219
Investigation of the Organisms contained in fresh Lymph by cultivation 220
Anatomical Investigation of the Eruption ' 226
A. Summary of previous Investigations 226
B. Anatomical Peculiarities of the Skin of the Sheep 228
C. Early Stage of the Development of the Primary Pustules 230
D. Pustular Stage of the Development of the Primary Pustules 239
E. Anatomical Investigation of Secondary Pustules 243
Section I.— DESCRIPTION OR NARRATIVE OF EXPERIMENTS.
Experiments with fresh Lymph. ■
Experiment 1. — Lymph sent by Professor Chauveau was used for the inoculation of a
sheep on the 8th of December, 1878, in the following manner : — With the aid of a subcu-
taneous Pravaz syringe an extremely small quantity was introduced into each of four
punctures in the true skin of the groin on the right side and of five on the left side. On
the morning of the 13th of December, two of the punctures in the groin on the right side
and four of those on the left were discernible as surrounded by a small circumscribed
areola, which projected somewhat above the general surface ; the puncture itself occu-
pied the summit, and was marked as a brownish speck.
On the morning of the 14th of December there appeared a new pock on the right, and
in the evening of the same day one on the left side. They increased rapidly in size, the '
red hypertemic areolae becoming larger in breadth and in thickness. After the first two
days of their appearance (that is, after the evening of the 15th December) they only
became more elevated, i. e. thicker.
As long as they increased in breadth they nearly all showed the central part most
elevated ; but as soon as they ceased to increase in breadth, or shortly before that, they
became depressed and at the same time pale in the centre, whereas the peripheral part
seemed now to be very much elevated and red ; hence the line of demarcation between
healthy and diseased skin was more marked than before.
In this stage they presented themselves as large patches above the general surface,
2 g 2
216
DR. E. KLEIN ON THE SMALLPOX OF SHEEP.
the peripheral part only being red. One puncture failed and one pock disappeared four
or five days after its appearance ; the others were excised, thus —
No. 1 on the 13th December.
„ 2 „ 14th „ in the morning.
„ 3 „ 14th „ in the evening.
„ 4 „ 15th
„ 5 „ 16th „
„ 6 „ 16th „
„ 7 „ 21st „
Only No. 7 showed commencing pustulation.
Tlie relation of the temperature of the animal was as follows : —
Decembei
• 8 (before inoculation) .
. 39*3
55
9
. 39
55
10
. 39
'55
11
. 39-1
„
12
. 39-3
55
13
. 39*5
55
14
. 40-2
55
15
. 41
16
. 40-4
55
17
. 40
„
18
. 39-8
55
19
. 39-2
55
20
From this it appears that before the eruption of the variola; the temperature rose
only gradually ; whereas it rapidly increased during the eruption and the increase of the
pocks in size, and it became lower again as soon as they ceased to make any marked
progress.
Experiment 2. — A second quantity of lymph from the same source as that used in
experiment 1 was used in a similar manner. On the evening of January 15th, 1874,
extremely small quantities of lymph were injected into the true skin of the groin of a
sheep with the aid of a subcutaneous Pravaz syringe, four punctures being made on the
right side and three on the left. On the evening of January 19th all the seven punc-
tures were recognizable as circumscribed red elevations, the centre of which (the punc-
ture) was marked as a brownish speck. All of these increased in size until January
24th, and while doing so they changed in the same manner as those in experiment 1 :
they became pale and depressed in the centre ; whereas the periphery remained very much
elevated above the general surface, and at the same time much reddened.
DK. E. KLEIN ON THE SMALLPOX OE SHEEP.
217
They were excised as
follows : —
No. 1.
January
20
o
5?
55
22
„ 3.
55
26
„ 4.
,5
29
„ 5.
February
1
„ 6.
55
1.
One had disappeared.
Only Nos. 4, 5, and 6 showed traces of the formation of pustules.
The relation of the temperature of the animal was as follows : —
O O
January 15 . .
. 39-2 C.
January 22
. 41 C.
„ 16 . .
. 39-2
„ 23
. 40-7
„ 17 . .
. 39-3
„ 24
. 41-1
„ 18 . .
. 39-5
„ 25
. 40-8
„ 19 . .
. 40-3
„ 26
. 40-5
„ 20 . .
. 40-8
„ 27
. 41
„ 21 . .
. 41-2
„ 28
. 40-8
The temperature remained over 40° C. until the 1st of February, when the animal
died. It had very extensive suppuration of the part from which the pocks had been
cut out, and these extensive suppurations may easily have caused the abnormally high
temperature after January 24. On a post-mortem examination being made, the lungs,
liver, and peritoneum were found to contain numerous nodules of a parasitic nature,
which of course stand in no relation to the inoculated disease.
Experiment 3. — On the 10th of March, 1874, lymph sent by Professor Cohn, of
Breslau, diluted with ten times its bulk of thoroughly boiled ^ per cent, saline solution,
was used for inoculating a healthy sheep ; four punctures were made in the skin of the
right and five in that of the left ear-lobe. On the 16th of March most of the pocks
had made their appearance ; they were in all respects similar to those described in
experiments 1 and 2. They enlarged in size until March 20, and most of them became
pale and depressed in the centre, thickened and red in the periphery. Commencing
from the 24th they all showed suppuration and sloughing.
The course of temperature was as under : —
March 11 . .
. 39-2 C.
March 18
. . . 40-5 C.
55
12 . .
. 39-3
„ 19
. . . 40-4
55
13 . .
. 39-2
„ 20
... 40
55
14 . . .
, 39-3
„ 21
. . . 39-8
55
15 . . ,
. 39-5
„ 22
. . . 39-8
55
16 . . ,
. 40-5
„ 23
. . . 39-6
55
17 . . ,
. 40-9
„ 24
. . . 39-5
218
DK. E. KLEIN ON THE SMALLPOX OE SHEEP.
Experiment 4. — On the 1st of April, 1874, lymph diluted with 15 to 20 times its
volume of saline solution was used for infecting a healthy sheep ; thus
(a) Several punctures (three) were made in each ear-lobe.
(b) Four punctures in each mammary gland.
(c) Three in the right groin.
(d) About \ to 1 division of a Pravaz syringe was injected into the subcutaneous
vein which runs between the mammary gland and the median line.
The pocks on the mammary glands, groin, and ear-lobes were discernible on the
evening of the 4th of April as small red circumscribed swellings. On the 6th of April
they were very much enlarged. On the 7th of April, while still increasing in size, they
already showed a differentiation between a central somewhat pale depressed part and a
peripheral portion still red and thickened.
On the evening of the same day (April 7) there appeared several small red swellings
round the lips as the first indication of a general eruption.
The number of secondary pocks increased rapidly until the Xlth of April, especially
on the lips and nostrils ; there were several in the axillae, and a great number in the
skin of the chest and hypochondrium.
During the appearance of the later secondary pocks those (secondary pocks) which
had made their appearance first (on the lips) had already commenced to form pustules
and to dry up.
It is important to state that the primary pocks, in this as in the former cases, were of
a very much larger size than the secondary ones — many of the former reaching a diameter
of ^ to 1 or l^r inch, whereas the diameter of most of the secondary ones did not reach
a quarter of an inch. There were, however, amongst the secondary pocks, especially
those that came out very late, e. g. on the chest and hypochondrium, some which
had a diameter of J to inch, or even a little larger.
Another point worth noticing is this: the primary pocks showed in nearly all
instances, while increasing in diameter, a differentation between a central depressed and
a peripheral thickened part ; whereas the secondary ones, except those that were of a
large diameter, remained thickest in the centre, or at least did not become depressed.
It will be seen subsequently that this difference is chiefly due to the differences in the
changes of the epidermis.
The course of the animal’s temperature was the following : —
o o
March 31 . ,
. . 39-1 C.
April 7
. . . 41-8 C.
April 1 . ,
. . 39
„ 8
. . . 41-5
„ 2 . ,
, . 39-1
„ 9
... 41
„ 3 . .
, . 39-3
„ 10
. . . 40-2
„ 4 . .
, . 39-8
„ 11
... 39
„ 5. , ,
, . 40-8
„ 12
. . . 39-3
„ 6 ,. ,
. . 41-8
„ 13
. . . 39-7
DB. E. KLEIN ON THE SMALLPOX OE SHEEP.
219
From the 14th of April the temperature was over 40° C. ; this may be easily accounted
for by the fact that, from this date for the next four or five days, a number of secondary
pocks had been cut out from different parts, whereby extensive suppuration was pro-
duced in different places.
Besides the characters of the primary and secondary pocks above mentioned, they
had all the common character, that when excised, no matter whether it was twenty-four
hours after their appearance, or whether they were in the stage of increase of size, or
of the formation of the pustules, or in the stage of drying up, the subcutaneous loose
tissue by which the skin is connected with the subjacent adipose or muscular tissue
was always found in a state of oedema. This oedema was greatest in the stage of their
increase in size and for a short time after.
I have to tender my thanks to Mr. W. Duguid, Veterinary Surgeon at the Brown
Institution, for assisting me in the experiments, and particularly for making and
recording the observations on temperature.
Section II.— ANATOMICAL METHOD.
The pocks that were excised were all used for anatomical examination. The skin
was invariably cleaned before the operation, and the pock was cut out with a surrounding
small zone of healthy skin.
Immediately after the pock was cut out, clean instruments always being used, it was
pinned out on a cork like a tent, the pins being fixed in the surrounding healthy skin,
and the object was then placed, cork upwards, either in J to ^ per cent, chromic acid
solution or in methylated spirit.
In some instances the pock was divided into two halves, and one half placed in each
of the above-named reagents. After twenty-four hours the object was removed from
the cork and returned to the hardening fluid.
Four or five days are usually quite enough to bring the object to such a consistence
that it can easily, when imbedded in a mixture of wax and oil, be cut into micro-
scopical sections.
Those pocks that were hardened in chromic acid were placed in spirit for several
hours before they were imbedded.
It was found that chromic acid was preferable to spirit for hardening the pocks ; for
in those hardened in chromic acid the topography of the elements and their relation to
each other was found to be unaltered and very clear and distinct ; whereas when
hardened at once in spirit it was found that these relations became considerably altered,
the reagent producing too much shrinking.
As I shall afterwards mention, in all the pocks the corium was more or less cedema-
tous; the hardening in spirit was found especially damaging in those pocks where there
was only slight oedema of the corium.
The contrast between the microscopical preparations of that half of a pock hardened
220
DR. E. KLEIN ON THE SMALLPOX OE SHEEP.
in chromic acid and those of the other half hardened in spirit was very striking. In the
latter case the oedema of the tissue of the corium could not be detected at all, whereas
in the former the distribution of it and the changes of the elements of the tissue were
very well preserved.
Section III.— INVESTIGATION OP THE ORGANISMS CONTAINED IN FRESH LYMPH
BY CULTIVATION.
Previous Investigations. — In a paper by Professor Coiin, of Breslau, published in the
55th volume of Viechow’s ‘ Archiv,’ I find quoted the statements of the more important
observers who have studied organisms in the fresh lymph of cow-pox and human
smallpox.
Kebee (Viechow’s ‘Archiv,’ vol. xlii.) found in fresh lymph peculiar granular corpuscles
which were perfectly different from pus-corpuscles ; they are about 3-^0 to x5~o °f a line
in diameter, and contain 3 to 20 spherical elongated or hourglass-shaped particles, -g-^o
to 3^5-0 of a line in diameter.
After the solution of the cell-wall, those particles having become free, they are distri-
buted through the lymph in enormous numbers, forming chiefly aggregates of 2 to 4
and 6 individuals, which are connected by a very delicate intervening substance. They
divide rapidly into smaller and smaller particles. In old lymph (vaccine tubes) there are
always present flakes and coagula, which consist of groups of the above-mentioned
granular corpuscles, free particles and molecules held together by an intervening sub-
stance. These bodies represent the carriers of the virus. Kebee could not, however,
determine whether these particles are simply changed nuclei of the cells of the rete
Malpighii of the epidermis, or whether they are living organisms.
Halliee and Zuen (Viechow’s ‘ Archiv,’ vols. xli. & xlii.) found in the lymph of cow-
pox, sheep-pox, and human smallpox a swarming caudate Micrococcus of a conical
shape endowed with a rotatory movement sometimes in the act of division.
Besides this they found delicate Leptothrix- filaments ( Micothrix , Itzigsohn), in each
small chain of which there was a distinct Micrococcus- swarm.
By cultivation Halliee thought to be able to transform the Micrococcus of the lymph
into sporidia — further, into Cladosp orium, Sporidesmium , Tilletia , Monilia , Pleospora
herb arum, Oidium, Eurotium , Aspergillus, Stemphylium, Ustilago, Torula, and other
forms, all of which he regarded as different stages of development of the Micrococcus
of variola.
As the sporids originating from Micrococcus of sheep-pox develop,, according to
Halliee, in the air to a Cladosporium, which is identical with one of the forms of Pleo-
spora recognized by Tulasne as the conidium-bearing form, and as this latter, a parasi-
tical fungus living on Lolium perenne, is contained in spoiled hay, the inference which
may be drawn from this is obvious according to Halliee, viz. that spoiled hay is the
source of infection of sheep-pox.
Chauveau deduced the presence of organic particles being the carriers of the contagion
DR. E. KLEIN ON THE SMALLPOX OF SHEEP.
221
in the lymph, of vaccine, as well as in that of sheep-pox, in a very ingenious manner from
very numerous experiments (Comptes Rendus, vols. xlvii. & xlviii., February, October,
and November 1868).
Burdon Sanderson, confirming the accuracy of the experiments of Chauveau, examined
those particles microscopically, and found them to be identical with the Torula form of
the Micrococcus , viz. small spheroids joining so as to form necklace-like chains. According
to Sanderson, these spheroids (microzymes) tend to elongate into rod-like bodies endowed
with a peculiar progressive or oscillatory movement, generally regarded as belonging to
Bacteria (Twelfth Report of the Medical Officer of the Privy Council, 1869, p. 229).
Cohn found that when lymph is collected from a pustule with the utmost care, it can
be kept free from Bacteria or spores of fungi for an indefinite period. Cohn’s method
is as follows: — A perfectly clean lancet is used for the opening of the pustule ; the drop
of lymph which escapes from the aperture is drawn into a capillary tube, and then
brought on a glass slide previously cleaned with ammonia, and covered with a covering-
glass cleaned in the same manner, care being taken that there are no air-bubbles either
in the middle or at the edges of the preparation. The edges of the covering-glass are
then fixed by means of asphalt varnish, and the preparation can now be examined either
fresh or after exposing it in an incubator to a constant temperature of 35° C.
In this way Cohn found that the lymph remains barren of Bacteria and any other
germs of mould. Such clear lymph could also be used for inoculating, after Dr. Sander-
son’s method, boiled Pasteur’s fluid without producing Bacteria or other vegetable
fungi, even when it was kept exposed to a temperature of 30 to 40° C., whereas after
the least contamination the fluid soon became turbid and decomposed. In the perfectly
fresh lymph, Cohn describes, in accordance with Dr. Sanderson, pale spheroids of an
extremely small size, below 01 001 of a millim. ; they have no peculiar movement; they
are, immediately after the preparation is made, generally isolated, occasionally in couples,
like a dumb-bell.
In a very short time, however, the dumb-bells increase in number, and form curved
or zigzag chains of four members. After one to two hours there are already numerous
necklaces of eight members, or the members arrange themselves like Sarcina, or they
form, by simple juxtaposition, groups or colonies.
The spheres proliferate very quickly by transverse division ; so that after six or eight
hours there are, besides chains of two to four and eight members, also very numerous
colonies of sixteen to thirty-two or more members to be found all over the preparation.
The proliferation continues during several days ; the colonies enlarge and reach even
the size of ten micromillimetres.
A colony or zoogloea represents a group of spheres held together by an intervening
gelatinous transparent substance. Cohn calls these organisms Micros'phaera vaccince , and
places them amongst the family of Schizomycetes in the group of Bacteriaceas (Virchow’s
‘ Archiv,’ vol. lv. p. 234). In the second volume of 4 Beitrage zur Biologie der Pflanzen,’
in his well known “ Untersuchungen fiber Bacterien,” p. 161, Cohn calls them Micrococci
MDCCCLXXV. 2 H
222
DR. E. KLEIN ON THE SMALLPOX OE SHEEP.
vacdnce ; this Micrococcus, as well as any other Micrococcus, i. e. Sjphcer obacterium,
differs completely from Hallier’s Micrococcus, as the former stand in no genetical rela-
tion whatever either to other kinds of Bacteria or to the spores of other fungi with a
mycelium.
I come now to describe the results of my own observations of the lymph of variola of
sheep. Clear lymph, which had been kept for several days in a sealed capillary tube,
was diluted with thoroughly boiled half per cent, saline solution and was used thus :
one portion of the diluted liquid having been reserved for further experiments, the
remainder, which was intended for microscopical examination, was sealed, immediately
after it was prepared, with dammar varnish and examined. It contained structures as
represented in Plate 29. fig. 1. First there were to be found minute highly refractive
spheres isolated, or in couples or in small groups ; they correspond to the solid granules
(Micrococci) in Cohn’s figure in the above-mentioned paper. They did not show any
other than Brownian movement. Then there were present a great number of circular
pale bodies, which, from their circular shape and size, could be easily recognized as decolo-
rized blood-corpuscles. They were generally to be met with in small groups, between
the members of which the same spheres, i. e. dark granules as before mentioned, were
seen in couples or in necklace-like chains; these Micrococci followed exactly the inter-
stices between the blood-corpuscles. Besides these structures there were to be seen a
few rod-like Bacteria belonging to those types which are designated by Cohn as Bacte-
rium termo and Bacillus subtilis.
They were either isolated or in couples, and exhibited only slight oscillatory move-
ment. The most characteristic features, however, were the following : —
(a) Lumps of a pale transparent substance containing very irregularly distributed
smaller and larger granules, the smaller granules being pale and indefinite, the larger
ones very bright and highly refractive.
" (b) Spheres generally considerably larger than the spheres above mentioned, at least
twice as large. They were arranged in small groups, chiefly composed of couples or of
necklace-like chains.
These spheres were different from the above-mentioned ones, not only in their being
larger, but chiefly by the fact that they were bordered by a sharp line as if by a mem-
brane, whereas their contents appeared perfectly transparent. They correspond to the
spheres figured by Sanderson, and to the spheres (transparent) in Cohn’s figure, only
that they are generally larger than the dark solid granules, and not of equal size as
represented in Cohn’s figure.
(c) Groups consisting of the highly refractive small spheres above named and the
granules mentioned under (a). They are also represented in Cohn’s figure in Virchow’s
4 Archiv,’ with the difference that the transparent spheres are always larger than the
solid highly refractive ones. On careful examination of these groups of mixed spheres,
it is found that there are all transitional forms between the two kinds of spheres which
DE. E. KLEIN ON THE SMALLPOX OE SHEEP.
223
form the groups, viz. small spheres not markedly larger than the highly refractive ones,
the centre of which is different from the peripheral part, the former being transparent,
the latter a highly refractive substance : then there are others whose central transparent
part is greater, the highly refractive substance representing only an envelope, generally
possessing at one spot a thickening ; these spheres are markedly larger than the solid
granules, and smaller than the perfectly transparent spheres above mentioned : further,
there are others that are still larger, and whose highly refractive substance is reduced to
a very thin envelope, possessing at the same time at one point a minute granule. It is
quite evident that these are transitional stages.
If the preparation is kept for twenty-four hours in the incubator at a temperature of
about 38° C., the number of transitional spheres is immense ; they are either isolated or
form couples with each other or with one solid or one perfectly transparent sphere.
( d ) Very bright shining highly refractive spheres, which are not only of a character-
istic brightness and somewhat greenish in colour, but which appear at least of twice
the size of the first-mentioned dark granules. They are found to form small groups,
chiefly composed of couples, which resemble rod-like structures with terminal swellings,
the more so as there is a more or less distinct connecting substance between the two
joints. Some of these couples appear to be surrounded by a narrow clear zone limited
by a thin membrane. There are also isolated bodies of this kind to be seen, which
appear to be in the act of division, viz. a somewhat elongated sphere of the same bright
substance showing a slight constriction in the centre.
If the preparation has been kept for twenty-four hours in the incubator, the above-
mentioned pale transparent masses containing irregularly distributed granules are seen
to undergo some remarkable changes. They become more or less distinctly fibrillar, in
such a manner that they appear to consist of a feltwork of very delicate branched fila-
ments, in or on which the granules are now found. Plate 29. fig. 2 gives a very accu-
rate representation of them. Under a very high power (such as an immersion-lens) we
see that these masses consist of spherical bodies, granules of different sizes arranged in
rows : the members of each row are imbedded in, or, rather, connected by, a pale trans-
parent substance ; hence the appearance of minute granular fibrils. In some places the
granules seem to lie only alongside the fibrils. Still later (forty-eight hours) the net-
work of fibrils is very distinct, especially because the large masses, after having enlarged
considerably, are seen to break up into smaller masses, in which it is easier to trace the
individual fibrils.
The granules have increased considerably in size ; and now it is very easy to recognize
that they correspond completely to the spheres above mentioned as (l) and (c) ; that is
to say, that the highly refractive spheres (the granules) become gradually transformed
into transparent spheres bordered by a delicate membrane, and that all these spheres
bud on, and become separated from, the filamentous matrix.
The longer a period the preparation is subjected to the constant temperature, the
more numerous highly refractive and transparent spheres originate from that matrix.
2 h 2
224
DE. E. KLEIN ON THE SMALLPOX OE SHEEP.
Spheres in the act of transverse division are very often met with.
It is worth noticing that the few rod-like Bacteria mentioned above as being present
in the fresh preparation disappeared completely after the preparation had been kept in
the incubator twenty-four to forty-eight hours.
A drop of lymph was obtained on March 24 from a pustule of an animal which had
been infected March 10 (see experiment 3), and was used for a microscopic preparation
as in the former case, without, however, being diluted with saline solution. When
examined fresh, it showed, besides large numbers of granular pus-corpuscles and
coloured blood-corpuscles, numerous small highly refractive granules, isolated and in
couples, exhibiting molecular movement. . The preparation was placed in the incubator
and kept at a constant temperature of 32° C. for twenty-seven hours, after which time
when examined it showed the following structures : —
(a) Besides intact granular pus-corpuscles there were numerous pus-corpuscles the
substance of which had become swollen and transparent ; these contained two to six
spherical homogeneous, not very highly refractive, bodies, about half the size of a coloured
blood-corpuscle, or even less. Some pus-corpuscles containing these bodies were seen
to be in the state of becoming disintegrated, and thus those spherical bodies becoming
freed. That they are not nuclei of the pus-corpuscles is shown by the fact that they
become the more distinct the more the matrix of the pus-corpuscle becomes swollen
and disintegrated. They are most distinct when they have become freed from a cor-
puscle. Besides they have a slightly greenish colour and are homogeneous ; whereas it is
well known that when pus-corpuscles swell, also their nuclei become swollen, and have
then the appearance of vesicles bordered by a thin membrane. Similar spherical bodies
are found in the surrounding medium in great numbers ; they are either isolated or in
couples ; they are generally spherical ; occasionally they are oblong, and possess a more
or less deep constriction in the middle part.
(b) From these forms one can trace others, which possess one or two small dark
granules ; in the latter instance the corpuscle is generally somewhat elongated, and the
grannules are situated at its pole.
From these, again, we come to other forms, which consist of two granules (dumb-bell)
surrounded by a very thin pale envelope, and, finally, dumb-bells in which there is just
a trace of the envelope to he seen under a very high power. I refer the reader to l in
fig. 3, Plate 29, in which most of the forms just mentioned are represented.
From this we are justified in saying that there exist spherical bodies, either enclosed
in pus-corpuscles or freely suspended in the medium, which are not nuclei; they are
isolated or in couples (transverse division), of a slightly greenish colour, homogeneous,
and pretty nearly of the same size.
It may be further stated that these spheres become transparent, while in them gra-
nules, i. e. highly refractive minute spheroids ( Micrococci ), make their appearance ; these
multiply by the act of transverse division (dumb-bells), and the matrix now represents
a transparent more or less distinct envelope or connecting substance of the dumb-bells.
DE. E. KLEIN ON THE SMALLPOX OF SHEEP.
225
( c ) That there is going on in these dumb-bells an immensely rapid proliferation by
transverse division is proved by the really astounding number of Torula-Wke chains
(necklaces), most of them consisting of 4, many of 6, 8, 12, and 16 members (see 2 in
fig. 3). All the Micrococci of these necklaces are distinctly held togther by a transparent
connecting substance. The larger the necklaces grow, the more they become curved
and convoluted (see 3 in fig. 3).
It is worth noticing that in some instances the necklaces possess at one end or laterally
at one point a comparatively large pear-shaped body, which consists of a greenish
matrix, in which there is occasionally a highly refractive Micrococcus to be seen.
The necklaces, which have grown to an immense length, and which have become con-
voluted in a very complicated manner, are very liable to break up into a number of
shorter chains ; in this case we have a convolution of necklaces from which several free
ends stick out.
( d ) If in such a convolution, consisting of a single chain or of several of them, the
Micrococci become more and more closely packed together, and the connecting sub-
stance of the individual chains becomes more and more coalescing, then we have a colony
of Halliee or a zoogloea of Cohn.
These changes of chains into colonies can be traced with great ease.
( e ) There are many colonies which can be still recognized as being composed of
necklaces closely packed together, and from which project shorter or longer filaments —
in some places showing distinct divisions into rod-like joints, in others apparently smooth
and homogeneous. I have tried to reproduce these features in fig. 3, 4, as accurately as
possible.
If the preparation is left a further twenty-four hours in the incubator and then
examined, it is found that the isolated necklaces and colonies increase in number and
size, whereas at the same time some of the Micrococci of the latter appear to become
not only larger, but of a very great brightness and somewhat greenish. At the edges
of the colonies, where the latter happen to project freely in small groups, we find them
to possess a striking resemblance to those bodies represented in Plate 29. fig. 1, 7.
At the same time we find a great number of perfectly transparent spheres, exactly
similar to those described in the first preparation, and represented in fig. 1, 2, and fig. 2, ] ,
as far as size and aspect is concerned.
They can be easily traced as being transformations of the spheres described on page 224
and represented in fig. 3, 1 . The preparation having been kept in the incubator until
March 28, i. e. during four days, was examined again, and it was found that the number
of colonies was very great, that many of the Micrococci had become enlarged and of
great brightness and of a greenish aspect. Besides, the filaments represented in fig. 3, 4,
appear now to be very distinctly composed of rod-like joints, many of which have a more
or less distinctly granular aspect.
I have until now deliberately abstained from introducing any terms excepting “ Micro-
cocci''1 and “ colony,” and I have tried to limit myself to a simple description of what
226
DE. E. KLEIN ON THE SMALLPOX OE SHEEP.
I found and what I think I am justified in connecting with each other ; and if I com-
pare these observations with those of other authors, I am inclined to believe : —
(1) That the spheres figured by Sanderson, and some of those figured by Cohn,
being identical with those figured by me, fig. 1, 2, and fig. 2, l, do not represent the
true Micrococcus of the lymph of variola in its active condition, but represent rather a
dropsical condition of the true active Micrococcus , which is a highly refractive spheroid,
and appears solid and uniform under the microscope.
(2) That the filaments stand in a genetical connexion with the development of Micro-
coccus is shown by the observation of the lymph described on page 223, and repre-
sented in fig. 2, i, 2, & 3.
Section IV.— ANATOMICAL INVESTIGATION OE THE ERUPTION.
A. Summary of previous Investigations.
According to Luginbuhl* the pathological process in human smallpox consists in the
penetration of the Micrococcus-yaxiolte into the skin, partly through the epidermis,
partly through the hair-follicles and sweat-glands. By this means the inflammatory pro-
cess known as smallpox, characterized by the following anatomical changes, originates : —
1. In the epidermis an opaque swelling (Virchow) takes place, due to the cells of the
rete Malpighii containing Micrococci. The nuclei of some of the epithelial cells, as
well as some of the latter, become dropsical. The cells of the rete Malpighii, which are
filled with Micrococci , show active proliferation ; they enlarge and their nuclei divide
rapidly. Thus multinuclear giant cells are formed which are crammed full of Micrococci.
In the deeper strata of the rete Malpighii, where the cells have only a very delicate cell-
wall, the giant cells never become very large ; their membrane soon bursts and their
nuclei become free : in the more superficial strata, however, the cells possess thicker and
more resistant walls, and therefore the proliferation of their nuclei may go on for a much
longer time.
By the giant cells and those groups of nuclei just mentioned, as well as by the
dropsical epithelial cells, spaces are formed in the rete Malpighii which represent the
pustules. Certain conical giant cells in the deeper- strata of the rete Malpighii, while
growing towards the corium, cause the communication of the latter with the spaces in
the epidermis ; in this way cellular elements penetrate from the epidermis into the
corium, whereas their previous place is occupied by a pale coagulable fluid. If the com-
munication between epidermis and corium is once established, then the formation of the
pustules makes rapid progress ; all around them appear new giant cells, which, however,
do not reach a large size, but soon lose their former contents {Micrococci), and in its place
contain- fibrinous coagula ; the neighbouring cells become compressed and dragged in
manifold ways, so that finally a system of spaces is found, separated and penetrated by
lumps (giant cells) and tracts (compressed epithelial elements).
* “Der Micrococcus der Variola,” Arb. aus dem Berner path. Institut, 1871-72, p. 159.
DE. E. KLEIN ON THE SMALLPOX OE SHEEP.
227
In the sweat-glands and hair-follicles the epithelial cells show also the opaque swelling
due to their containing Micrococci.
Between epidermis and corium of those places where there is the least microscopical
change there are constantly semilunar spaces of different diameters to be seen, the convex
surface of which corresponds to the elevation of the papillae. These spaces contain
Micrococci imbedded in a transparent fluid. In those pocks in which the formation of
pustules is going on, the corium becomes gradually penetrated by the elements which
have been previously in the epidermis, viz. Micrococci and nuclei ; thus the boundary
between epidermis and corium gradually loses its sharpness. The papillae show sometimes
in their longitudinal axis an infiltration of fine granules.
In the deeper parts of the corium larger or smaller tracts present themselves, formed
partly by larger spherical cells and partly (seldom though) by a finely granular sub-
stance. Luginbuhl therefore makes the whole process start in the epidermis, and hence
gradually to extend into the corium. These statements are, according to my obser-
vations of variola of sheep, wholly inconsistent with the facts occurring in this latter
disease, which, as is well known, is in clinical and anatomical respects very similar if
not analogous to smallpox of Man.
The results of the examination of smallpox of Man obtained by Auspitz and Basch are
described by Neumann*, who confirms fully the observations of these authors, in this
way : — In papules, on the second day of their appearance, the epidermis is elevated,
apparently from the increased thickness of the rete Malpighii, the individual cells of
which are larger than those of the neighbouring normal parts; their nuclei are
enlarged. The vessels in the corium, those in the papillary region as well as those
beneath it, are distended ; on their walls are numerous small roundish cells, and similar
cells are .found in the stroma of the papillae. The papillae and glands are unchanged.
The structure of the vesicles and the pustules is thus described : — Under the stratum
corneum of the epidermis there is a layer of longitudinal cells, which merge uninter-
ruptedly into the roundish or flattened and distinctly swollen cells of the rete Malpighii ;
beneath this a mesh work is seen, which is nearer to the stratum corneum than to the
corium, and occupies a great part of the breadth of the vesicles, but does not extend
deeply. This mesh-like structure consists of transverse septa of fine fibrous tissue, which
are evidently formed of the compressed spindle-shaped cells of the hypertrophied rete
Malpighii ; in its interstices pus-cells are imbedded, some of the large vesicles containing
ten or more small cells. Under this mesh-like structure and extending between the
papillae there are found roundish cells, which either resemble those of the meshw'ork
or the swollen Malpighian cells. The underlying papillae appear broader, and those in
the immediate vicinity of the vesicles lengthened. Proliferation of cells is observed
around the vessels.
The meshwork extends gradually towards the corium, and increases in width from the
centre to the periphery ; in the interstices there are round cells.
* See ‘Textbook of Skin Diseases/ by Dr. Neumans, translated by Dr. Pullab, London, 1871, p. 74.
228
DR. E. KLEIN ON THE SMALLPOX OF SHEEP.
The pustular contents are enclosed, as if by a capsule, by two layers of unnucleated
epidermic cells. Besides the pus-cells there are also unnucleated elements (insoluble in
acetic acid) with fine granular contents.
Auspitz and Basch are of opinion that the so-called umbilicus of the pock, the cen-
tral depression, is due to the pustule gradually extending towards the periphery, whereby
the pressure in the centre diminishes and the central part becomes depressed.
According to Rindfleisch and others, on the other hand, the central umbilicus is pro
duced by there being a sweat-duct or a hair-follicle in the centre of the pock, which,
when the pustule is formed in the epidermis, keeps the latter fixed to the corium like a
retinaculum*.
B. Anatomical Peculiarities of the Skin of the Sheep.
Before I describe the pathological changes of the skin, I will draw the attention of
the reader to several anatomical points, as regards the structure of the skin of the sheep,
which have not been properly described yet.
(a) In the skin of most parts of the body (e. g. groin, wall of abdomen and chest,
axilla, and so on) the epidermis (stratum corneum plus rete Malpighii) is in hardened
preparations thin and rather opaque — only the deepest, or at most this latter and the
next stratum, appear to be composed of cells elongated vertical to the surface ; the other
layers of the rete Malpighii are composed of more or less polyhedral cells, which are
the more flattened the nearer to the surface. In general the outlines of the cells are
very indistinct ; the whole rete Malpighii looks more like an opaque granular substance,
in which nuclei are imbedded in more or less definite intervals.
( b ) The papillae of the corium are very scarce, short, and small ; in many places the
rete Malpighii rests on a corium, the surface of which is only slightly wavy, i. e. the
papillae are only just indicated.
(c) The corium may be divided into a superficial stratum, which includes the papilla
and the tissue directly underneath it, and a deep stratum beneath the former, containing
the sebaceous glands, sweat-glands, and the roots of the hair-follicles.
The superficial stratum is a dense connective-tissue feltwork with numerous elastic
fibres ; it contains the ultimate ramifications of the blood-vessels and lymphatic vessels.
The deep stratum is somewhat looser in its structure than the former, but is still
similar to it, as the connective-tissue bundles of its matrix are very small, run in all
* If the central depression I have mentioned in the primary and some secondary pocks of sheep in Section I.
correspond to what is described as the umbilicus of variola of man (and to all appearance they do correspond
to each other), then I must anticipate so far as to say that this central depression has no connexion whatever
either with the formation of the pustule or with the hair-follicles or sweat-ducts, hut, as we shall see hereafter,
is due, to a great extent, to certain morphological changes of the epidermis in the centre of the pock. In
Luginbuhe’s paper, quoted above, I find, on p. 160, a reference to Auspitz and Basch, Neumann, and Cornie
having found Micrococci in the meshes of the fully developed pustule and also in the corium ; and, finally,
C. Weigert describes (Centralblatt der medicin. "Wissensch. 1871, No. 39) sinuous tubes in the corium of
smallpox, which tubes (lymphatic vessels) are filled with Micrococci.
DE. E. KLEIN ON THE SMALLPOX OE SHEEP.
229
directions, and cross and join each other very closely. This stratum contains, in that
layer which is nearest to the surface, the sebaceous glands, a little deeper the roots of
the hair -follicles, and in the deepest layer the sweat-glands.
( d ) The subcutaneous tissue between the corium and the panniculus adiposus may
also be divided into two strata, a superficial and a deep one. This superficial stratum
is very markedly different from the deep stratum of the corium ; for it consists of large
broad bundles of connective tissue, which run in two, or generally in three, directions ;
they are by no means so close as in the latter, and the interfascicular spaces are there-
fore more distinct and much larger. The amount of elastic tissue is not great.
This stratum contains the minor trunks of the blood-vessels and the lymphatics, which
run to or from the corium ; they are not very numerous.
The deep stratum of the subcutaneous tissue is similar in its structure to the former ;
it is still looser, and contains the main trunks of the blood-vessels and lymphatic vessels,
and also a greater or smaller amount of fat-tissue, either in the act of development or
already fully developed.
(e) The sebaceous glands are characteristic for being enormously large in respect to
the hair-follicles into which they lead ; they are short, slightly branched tubes, swollen
at their end, and lead into a large duct, which is identical with the mouth of the hair
follicle. The sebaceous glands of the groin and the axilla are the largest. The hair-
follicles are possessed of arrectores pili, which, relatively to the size of the hair-follicles,
are of very great strength. When, after an oblique course around the sebaceous gland,
they enter the superficial stratum of the corium, they split in two, three, or more minor
bundles, which can always be traced very close to the papillary layer, into which they do
not, however, enter, but generally bend before that into a horizontal direction.
Each sweat-gland consists in its secreting part of a tube, which is generally convoluted
in a direction parallel to the surface. The tube consists of an apparently homogeneous
thick membrane, on the inner surface of which lies one or even two continuous layers of
longitudinal unstriped muscles. Close to these, without the intervention of a membrane,
is attached a single layer of nucleated columnar epithelial cells, which line the lumen
of the gland.
The duct of each gland becomes narrower the more it approaches the surface, and
pursues always an almost vertical course ; it leads generally into an epithelial prolon-
gation of the mouth of the hair-follicle, or, as one might say with equal truth, into the
mouth of the duct of a sebaceous gland. The duct of the sweat-gland does not possess
a muscular coat, at least not in some distance from the proper gland, and is lined by
polyhedral epithelial cells, which become the more laminated (stratified) the nearer to
its mouth. The lumen of the sweat-duct is much narrower than that of the proper
gland, and is reduced at its mouth to its smallest diameter *.
* The sebaceous glands of the lips of the mouth are different from the sebaceous glands above described, the
former (glands of the lips) being very much longer; they consist generally of a number of narrow ducts leading
into a common hair-follicle. They are of a relatively great length, and terminate in a number of wavy, pear-
shaped, somewhat branched sacs.
MDCCCLXXV. 2 I
230
DK. E. KLEIN ON THE SMALLPOX OE SHEEP.
(/) The large lymphatic trunks, situated, as mentioned above, in the deep stratum of
the subcutaneous tissue, are provided with valves ; they form rich anastomoses, and
stand in direct connexion with the intercommunicating system of the interfascicular
spaces, i. e. lymphatic spaces of the deep and superficial stratum of the subcutaneous
tissue. The interfascicular spaces contain the connective-tissue corpuscles ; that is to say,
the latter are so fixed upon the connective-tissue bundles that the interfascicular spaces
appear to be lined by the connective-tissue corpuscles. The deep stratum of the
corium -contains the greatest number of lymphatic vessels ; they have chiefly a course
parallel to the surface ; they are provided with valves, and stand everywhere in direct
connexion with interfascicular spaces lined by the connective-tissue corpuscles. The
lining membrane of the lymphatic vessels, composed of a continuous layer of endothe-
lium, is therefore in direct continuation with the latter. The interfascicular spaces
of this and of the superficial stratum of the subcutaneous tissue are in many places
very much enlarged, and resemble lymphatic sinuses or lymphatic sacs, through which,
in many instances, the smaller branches of blood-vessels are seen to penetrate — perivas-
cular lymphatics. These lymphatic sinuses are especially well developed around the
sebaceous glands at the bases of the arrectores pili, and also around the proper sweat-
glands. Into the plexus of lymphatic vessels which lie in the deep stratum of the
corium lead lymphatic vessels which come from the superficial stratum of the corium ;
they are also provided with valves, and can be traced up to the papillary layer. Many
of the lymphatic vessels of the superficial and deep stratum of the corium are seen to
be in close relation to the blood-vessels, especially the veins, as they always seem to
run with each other.
C. Early Stage of the Development of the Primary Pustules.
As has been already stated, the pocks designated as primary were excised in their
different stages of development up to the period of pustulation, for anatomical exami-
nation. The latest stage ( stadium exsiccationis) has not been particularly investigated,
as it does not differ from any other restitutory process of the skin. In examining pocks
in the earlier stages, I have usually cut up the whole into microscopic sections. Of the
more advanced pocks I have examined sections of only one half.
Sections through the primary pocks which had appeared only several hours (six to
twelve) show as the most characteristic features the following: — The epidermis has
markedly increased in thickness, chiefly due to an increase of the thickness of the rete
Malpighii. The cells of the latter are more transparent and larger, their outlines more
distinct than in the normal condition ; the cell-substance is finely granular ; the nuclei
are enlarged, each possessing one or, more generally, two distinct nucleoli. The differ-
ence in size, distinctness, and transparency of the rete Malpighii is very striking at the
point where the skin of the pock is in contact with healthy skin. The cells of the three
deeper strata of the rete Malpighii are elongated in a direction vertical to the surface.
The papillae are much more distinct in the corium of the pock than in that of the
neighbouring healthy tissue ; they appear broader and longer. The blood-vessels of
DR. E. KLEIN ON THE SMALLPOX OE SHEEP.
231
the corium are somewhat distended ; in the small veins and capillaries the endothelium
is seen with much greater distinctness than in those of the healthy tissue. Especially
in transverse sections through small veins and capillary blood-vessels it is found that the
endothelial cells are swollen, distinctly granular, and their nuclei enlarged. Accordingly
the wall of these blood-vessels appears thicker and altered. This is in so far an
interesting fact, as Cohnheim, by the aid of experiments (see his latest researches on
Inflammation, Berlin, 1878), arrived at the conclusion that the walls of the blood-vessels
must necessarily in inflammation undergo some changes to cause the exudation of the
fluid and the formed parts of the blood, which, as is well known, represent very material
morphological symptoms in inflammation.
The tissue of the corium in general is slightly oedematous, the interfascicular spaces,
i. e. lymph-canalicular system, being larger and more clearly visible than in the normal
condition. The connective-tissue corpuscles, situated in the interfascicular system of
spaces, are recognizable at the same time in many places, their nuclei being more distinct
than in the normal parts. In the interfascicular lymph-canalicular system of the
corium, chiefly where the blood-vessels are more numerous, e. g. around the glands,
there are found lymph-corpuscles, which are the more numerous the nearer one
approaches to the blood-vessels ; this fact enables us to say that they are probably all
extravasated colourless blood-corpuscles. Whereas the lymphatic vessels of the corium
are hardly to be found in the corium of healthy skin after simple hardening, they
are in our case easily traced, being distended and more or less filled with a transparent,
homogeneous or finely granular substance, which in all its appearances resembles
coagulated plasma.
The changes of the subcutaneous tissue are similar, only much slighter ; they diminish
more and more towards the depth. We have therefore only such changes as one
might expect in inflammation in the strictest sense of the word, viz. distended blood,
vessels, altered walls of blood-vessels, exudation of plasma, and extravasation of colourless
blood-corpuscles, seen in the distended lymph-canalicular system and distended lymphatic
vessels. The greater distinctness of the connective-tissue corpuscles and the enlarge-
ment and greater transparency of the rete Malpighii are probably due to the increased
irrigation of the tissue with exuded plasma.
If we direct our attention to the pocks that have been cut out twenty-four hours after
they made their appearance, we find the changes above stated much more marked.
The rete Malpighii is still thicker, more transparent, the nuclei of the epithelial cells
of the deeper strata enlarged, many of them in the act of division or already divided ; the
papillae and the corium in general more oedematous than in the former case, the lymph-
canalicular system being not only. very marked and distended, but containing a finely
granular material — coagulated plasma. Further, the infiltration of the corium with
lymph-corpuscles has increased, it being now possible to trace the course of these bodies
from the larger branches of the blood-vessels of the corium into the distended lymph-
canalicular system. The connective-tissue corpuscles of the oedematous corium appear
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232
DE. E. KLEIN ON THE SMALLPOX OE SHEEP.
now swollen, distinctly granular, and their nucleus in the act of division or already
divided. The changes of the walls of the blood-vessels, as stated above, are now to be
traced not only in the blood-vessels of the corium, but also in those of the superficial parts
of the subcutaneous tissue. Although the oedema and infiltration with lymph-corpuscles
is chiefly limited to the corium, still it is noticeable that the subcutaneous tissue has in
some places, especially around larger blood-vessels, become also materially involved in
the morbid process, the interfascicular spaces being in some places very markedly
distended, and containing not only a few lymph-corpuscles, but also a finely granular
material, in which are imbedded peculiar ovoid or spherical sharply outlined structures,
containing in a clear substance one large or two, three, or four small highly refractive
bodies. These structures are of different sizes, the smallest being not smaller than the
nucleus of a connective-tissue corpuscle, the larger ones two or three times as large.
The connective-tissue corpuscles which line the bundles of the connective tissue are at
the same time enlarged ; they appear swollen, granular, and their nucleus single or
divided.
Comparing the sharply outlined structures found in the interfascicular spaces, as
mentioned just now, amongst themselves, one cannot help thinking that the highly
refractive bodies found in their interior are in the state of undergoing proliferation by
division.
I will draw the attention of the reader to Plate 32. fig. 12, which shows these rela-
tions very accurately. The question now arises, What are these sharply outlined struc-
tures with the highly refractive bodies in their interior %
That these bodies are free nuclei must he excluded at once, — first, free nuclei not
being observable anywhere else in the tissue ; and, secondly, the nuclei of connective-
tissue corpuscles and of lymph-corpuscles being altogether different. The issue rests
only between their being lymph-corpuscles (extravasated) or something not belonging
to the skin at all ; I mean, a fungus. In case they should be lymph-corpuscles, the
transparent sharp-outlined matrix would represent the swollen cell-substance, and the
highly refractive bodies in their interior would correspond to the shrunken coagulated
nuclei. It certainly cannot be denied that pus- or lymph-corpuscles, when treated with
dilute acids (i. e. chromic acid, acetic acid), show appearances similar to those just
mentioned ; but in the present instance, although the preparation, in question had
been hardened in chromic acid, no such appearance was to be found either in the lymph-
corpuscles situated in the corium or in the veins and lymphatic vessels of the sub-
cutaneous tissue. In these parts the lymph-corpuscles appeared as they do in general
in hardened preparations, viz. as spherical more or less transparent or finely granular
cells, containing one relatively large nucleus, and seldom two or three small spherical
nuclei which are readily stained with carmine. The structures in question not only
differ from lymph-corpuscles in shape, but they also show a great difference in then-
contents — the contents of the former being highly refractive bodies in the state of
division, which are not stained with carmine at all.
From all this it is probable that they are not lymph-corpuscles ; and therefore it is
DR. E. KLEIN ON THE SMALLPOX OE SHEEP.
233
not impossible that they do not belong to the tissue of the skin itself, but that they
perhaps correspond to what Hallier calls Cryptococcus. This is also supported, to a
certain extent, by the fact that I found them chiefly in those parts of the subcutaneous
tissue which (as I could make out from several circumstances) had been penetrated by
the canula of the injecting-syringe when the inoculation with lymph was performed.
The most important characteristics of this stage of the disease, however, are those
which depend on the changes in the lymphatic vessels in the deeper part of the corium.
The lymphatic vessels (those accompanying blood-vessels and filled more or less with
lymph-corpuscles, as well as the others) are, as stated above, distended, and from this
reason, as well as from the lymph-canalicular system being also distended, are distinctly
seen to be in direct continuity with the latter, viz. with the interfascicular lymph-
canalicular system.
Many of these lymphatics contain a material which, as represented in Plate 31. figs. 9,
7, & 8, is composed of a transparent matrix, in which lie imbedded highly refractive
spheres, in some parts closer than in others.
From the lymphatics this material extends also into the interfascicular lymph-canali-
cular system, or, more correctly speaking, it extends from the latter into the former.
In some lymphatics these highly refractive granules are seen to be arranged in shorter
or longer, branched or unbranched filaments. These filaments are more or less curved,
and resemble either necklaces or smooth filaments according as the individual joints
are more like spheres or like rods. One and the same filament may also be partly
granular, i. e. like a necklace, and partly smooth.
In those places where they are to be found in greater numbers they are seen to cross
each other and decussate, so as to form a close feltwork.
These relations come out very distinctly in a little later stage. Thus in a pock cut
out a little after forty-eight hours (see Plate 31. fig. 9), it is seen that in the lymphatics
of the deeper stratum of the corium the granular mass is not only replaced by filaments
(or, let us say at once, that most of the granules have arranged themselves into filaments),
but, what is also of great importance, the filaments have more or less lost their granular
aspect, and have become smooth, longer, and more branched.
In fig. 10, 1., a lymphatic vessel of the subcutaneous tissue is shown, in which is seen
a network of branched filaments without granular matter, some of which exhibit small
swellings at one or other point of their course, while in other instances the swelling is
at the end of the filaments.
There can, I think, be no doubt whatever that the granular material is not plasma
or serum coagulated by the hardening reagent ; for these granules are not only of a
definite large size (very much larger than the granules one meets with in coagulated
serum), but stand, as the examination proves, in a definite genetical relation to the
filaments. As regards these latter there is only one possible explanation, viz. that they
represent an organism.
In pocks which were cut out between twenty-four and eighty-four hours, all the
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DR. E. KLEIN ON THE SMALLPOX OE SHEEP.
distended, interfascicular lymph-spaces, and especially the distended lymphatic vessels
of the corium (in the lymphatic vessels of course with much greater distinctness), con-
tained these filaments in very great numbers. In the more advanced stage of their
development the individual filaments differ from each other considerably in size ; the
branching is more distinct, so that they form a network. Each filament follows a
course which is alternately curved and straight, so as to form more or less dense convo-
lutions. The filaments are highly refractive, and appear to be of a greenish colour,
which is the more distinct the thicker they are. Generally they appear perfectly smooth,
even under a high power ; in some instances, however, I was able to see not only that
they were composed of elongated joints, but also that it was possible to distinguish a
surrounding delicate membrane and highly refractive greenish contents. The composite
nature of the filaments is especially noticeable at the free ends ; here it can be distinctly
seen that they are composed of joints. Towards the ends of the filaments these joints
are short, elliptical, or spheroidal, becoming more and more elongated as their distance
from the end increases; There are terminal filaments of a relatively great length, which
are distinctly composed of spherical or elliptical joints. Other filaments occur which,
at some point near the free end, possess one or more elliptical or spherical joints larger
than the rest, or give off small lateral branchlets terminating in a similar manner. In
the necklace-like filaments so formed it is sometimes observed that each of the spherical
or elliptical bodies just mentioned appears to be enveloped by a delicate thin membrane
(<?/. Plate 31. fig. 10, II., III., IV., & V., and Plate 32. fig. 11, A & B).
In fig. 11 it will be noticed that the spherical bodies undergo [transverse division,
thus forming dumb-bells and necklaces, and also that, by becoming elongated, they
form the basis of the filaments.
I think from the foregoing it can be stated with safety that we have to deal with the
development of a fungus. It commences as a mass which corresponds in appearance
to a mass of Micrococci (i. e. zooglcea) ; these grow into a mycelium, the constituent
filaments of which differ very considerably from each other in thickness. The mycelium
fructifies, forming conidia like an Oidium. The spherical spores proliferate by trans-
verse division, forming thus smaller groups — dumb-bells and necklaces of smaller and
smaller bodies. The conidia are, just like the filaments of the mycelium, highly
refractive and of a greenish colour.
The deeper stratum of the corium is the part in which the fungus is found chiefly in
the earlier stages of the disease.
Eventually the superficial stratum of the corium, as well as the superficial stratum of
the subcutaneous tissue, is filled with them ; the former to a greater extent than the
latter. As the natural direction of movement of liquid in the tissue is from the inter-
fascicular or lymph-canalicular system into the lymphatics, and as the fungus is found
in the latter as well as in the former, it might be expected a priori that the fungus,
while increasing, would penetrate from the interfascicular channels into the lymphatics.
That this is actually the case may be deduced from microscopic examination ; for it can
DR. E. KLEIN ON THE SMALLPOX OE SHEEP.
235
be seen in many places that the mycelium extends from the lymph-canalicular system
into the neighbouring lymphatic vessels in which their ends are provided with the
conidia.
In fig. 11, in A & B for instance, the mycelium-filaments, from the terminations of
which spring the conidia seen in the lymphatic vessel, can be traced for a long distance
into the 1-ymph-canalicular system, from which the lymphatic vessel receives its supply.
Not only does the fungus extend from the tissue into the lymphatic vessels, but also
into some veins ; for I have seen several instances where one could trace the mycelium
from the interfascicular spaces into the veins, containing filaments in a state of fructifi-
cation similar to that observed in lymphatic vessels (fig. 10, V.). The mycelium and
its conidia-bearing parts are most easily seen, and with the greatest distinctness,
in the distended lymphatics, where they are found in immense numbers, and sometimes
form a very dense thallus. They are, however, seen to extend 'all through the tissue of
the corium — in the earlier stages, as mentioned above, only in the deeper stratum of the
corium ; later also in the superficial stratum of the corium and the subcutaneous
tissue. In the latter the fructification is seen in the later stages to go on with such
rapidity that the distended interfascicular lymph-spaces at some parts become filled with
a zooglcea-like mass, in which here and there the minute spores, the products of division
of the spores previously mentioned, can be still recognized to form necklace-like chains.
In Plate 32. fig. 13 this zooglcea is represented in lymphatic vessels and in the inter-
fascicular spaces of the subcutaneous tissue.
We return now to the structural changes in the skin of the pock. In pocks which
have been cut out two to three days after their appearance, the rete Malpighii is seen
to be many times thicker than in the normal parts, and thickest in the centre. The
cells of the deeper and middle strata are enlarged and sharply outlined. Many of them
are in the condition of multiplication, as may be deduced from the fact that they possess
two nuclei, and that, particularly in the deepest layer, the nuclei are much closer to
each other, i. e. more numerous. In the flattened cells of the more superficial strata there
lie close to the poles of the oblong nucleus highly refractive granules, which are largest
and most numerous in the most superficial cells, and become smaller and scarcer in the
deeper strata ; at the same time the nuclei of many cells of the superficial strata look
as if they were vacuolated, viz. sharply outlined with perfectly clear contents.
At the central parts of the pock the rete Malpighii shows other important changes :
isolated epithelial cells, or, as is oftener the case, small groups of two, four, or a greater
number, are met with, which differ from the rest in containing much coarser granules
and possessing very distinct sharp outlines ; they are at the same time always more or
less rounded : in some of them the nucleus is double or is in the act of division ;
these occur chiefly in the middle strata of the rete Malpighii. Amongst them some
are seen to be darker and more homogeneous than the rest, so that their nuclei are
hardly or not at all visible ; while others appear to have become confluent, so as to give
rise to the appearance of dark more or less homogeneous horny streaks of longer or
236
DR. E. KLEIN ON THE SMALLPOX OE SHEEP.
shorter dimensions in the section. This transformation of the epithelial elements is at
first limited to the central parts of the pock and the middle strata of the rete Malpighii ;
but as the pock increases in size, the horny streaks, at first isolated, increase in number
and length until they become confluent, so as to form one more or less continuous horny
stratum, thus dividing the rete Malpighii of the central part of the pock into a deep
layer below the horny stratum, and a superficial layer between the newly formed horny
stratum and the original stratum corneum. This change goes hand in hand with the
growth of the pock in breadth and with the appearance of the central pale depression
mentioned on several occasions (see Plate 29. fig. 4 and Plate 30. figs. 5 & 6).
Simultaneously with the formation of the horny stratum, the superficial as well as
the deep part of the rete Malpighii (fig. 6, B & C) undergoes remarkable changes. The
cells of the former become more transparent and flatter ; commencing from the centre
of the pock, they gradually assume the characters of horny scales, the nuclei of which
gradually disappear ; in this way the horny stratum (D in fig. 6) increases rapidly in
thickness towards the surface. The cells of the superficial layers of the deep
stratum of the rete Malpighii (viz. the layers directly beneath the horny stratum)
exhibit rows of highly refractive granules, which are seen to be the more deeply stained
by hsematoxylin the further the cells containing them are from the corium, while the
cells themselves are larger the nearer they are to the horny stratum. Many of those
nearest to the horny stratum look as if they possessed a thick membrane enclosing clear
contents, in which there are here and there a few granules besides the nucleus. These
cells are no doubt swollen dropsical epithelial cells.
The deepest stratum of the rete Malpighii is in a state of very active proliferation.
This is evinced by the fact that the interpapillary processes grow to extremely large
dimensions, and that cylindrical processes composed of young epithelial cells penetrate,
?. e. grow, into the papillae of the corium from them, the papillae themselves being
longer and thicker than natural. These epithelial processes penetrate into the papillae
in different depths and in different directions ; so that in sections many of them present
themselves as isolated patches, surrounded by papillary substance, in the neighbourhood
of the Malpighian layer. These, as well as the processes which in the section are not
severed from their natural connexion with the rete Malpighii, are composed of the
same granular substance as the deepest layer of the rete Malpighii, and contain spherical
nuclei at more or less regular intervals, which exactly resemble those of the epithelial
cells of the rete Malpighii.
In most cases these processes show in section a distinct division into “ territories,”
each surrounding an individual nucleus. Sometimes, however, this separation is indi-
stinctly seen, and then the areas in the section which correspond to the tips of processes
cut through resemble, to a certain extent, large multinuclear giant cells. Considering
what has been stated on this subject by certain writers, it is necessary to repeat that the
conical, cylindrical, thin or thick, short or long processes which penetrate into the
papillae are direct outgrowths of the rete Malpighii. And it must be added that the
DE. E. KLEIN ON THE SMALLPOX OF SHEEP.
237
proliferation of the deepest layer of cells of the rete Malpighii can be traced into the
depth at every place with great certainty (see fig. 6). In consequence of the extremely
active proliferation of the deep stratum of the rete Malpighii at the centre of the pock
into the corium, the epidermis as a whole is thicker in the centre than at the periphery,
notwithstanding that a great part of it has been converted into a horny mass, which
occupies less space than it did before its transformation.
It is further necessary to state that the conversion of the middle layers of the original
rete Malpighii into a horny stratum gradually extends outward, i. e. towards the peri-
phery of the pock, and that the proliferation of the deep stratum is the more active the
more rapidly the horny stratum increases in breadth and thickness.
These observations enable us to see how it happens that the central part of the pock
becomes depressed and pale as regards the peripheral portion, — depressed, because a
great number of layers of the original rete Malpighii have become converted into layers
of horny scales, while the deep stratum of the rete Malpighii grows very actively
into the corium ; and pale, because the central portion is covered with a thick horny
dry membrane, i. e. the layers of the rete Malpighii, which have changed in the above-
named manner. Consequently, as has been already hinted, the appearance of the
depressed pale centre of most of the examples of sheep-pox has nothing whatever to do
either with glands or hair-follicles, or with the spreading of the pustules towards the
periphery of the pock, for all those changes take place before there is a trace of the
formation of the pustules. It is to be noted that the formation of the horny stratum
as described above is not constant ; for in some pocks it does not occur until after the
appearance of the pustules, the superficial layers of the rete becoming gradually trans-
formed into a horny substance, spreading from the stratum corneum towards the depth.
The changes of the other parts of the skin are these : — The whole corium and the
whole subcutaneous tissue in the peripheral portion of the pock shows infiltration with
lymph-corpuscles ; this infiltration is especially marked in the corium around the glands
and in the deep subcutaneous tissue. From the peripheral portion the infiltration
extends into the corresponding strata of the central parts, but is here very much slighter.
The older the pock the more intense is the infiltration of the peripheral part; hence,
although the infiltration of the papillary tissue extends a little way in the surrounding
zone of normal skin, there is a sharp line of demarcation corresponding to the edge of
the pock. In the centre the papillary tissue becomes the more infiltrated the older
the pock.
As regards the distribution of the lymph-cells, it is very easy to notice, on those places
where the infiltration is not too intense, that most of the lymph-corpuscles are situated
around the blood-vessels, and extend from here into the interfascicular channels towards
the lymphatic vessels, many of which contain a greater or smaller number of them.
The superficial stratum of the subcutaneous tissue is especially interesting in prepa-
rations stained with heematoxylin. Here it is seen that the interfascicular lymph-spaces
are very much dilated ; and one can follow the lymph-cells from around the blood-
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DR. E. KLEIN ON THE SMALLPOX OE SHEEP.
vessels of the peripheral part of the pocks with great distinctness into the interfascicular
spaces and towards the lymphatic vessels of the central part of the pock; at the
same time the interfascicular spaces of this as well as of the deep stratum in the
centre of the pock are very well marked by the presence of a homogeneous or slightly
granular material, which stains blue in hsematoxylin, and with which those spaces are
more or less filled. This material is in all probability plasma which fills the inter-
fascicular spaces, and which, being alkaline, becomes stained blue by hsematoxylin.
The connective-tissue corpuscles show marked changes, their nuclei being in the act
of division or already divided and the cells themselves swollen and coarsely granular.
Many of the nuclei of the connective-tissue corpuscles appear to be vacuolated.
As regards the glands, we may briefly state that the changes are similar to those of
the epidermis. In the hair-follicles and the sebaceous glands the nuclei of the epithelial
cells of the most external layer, corresponding to the deepest layer of the rete Malpighii,
are in a state of very active proliferation, being smaller and much more numerous than
in the healthy parts. The epithelium of the ducts of the sebaceous glands is very much
thickened, and the more superficial layers of its epithelium, i. e. those nearer to the
lumen of the gland, are also composed of cells which are somewhat dropsical, and which
contain rows of highly refractive granules near the poles of the nucleus.
The horny transformation of the rete Malpighii also extends to the epithelium of the
mouths of the ducts of the sebaceous glands and hair-follicles. The epithelium of the
proper secreting part of the sweat-glands seems to resist longer than that of the sebaceous
glands and hair-follicles, remaining longer unchanged : pocks, however, which are about
six or seven days old and more show the external membrana propria of the sweat-
glands thickened ; the epithelium which lines the lumen is more or less detached from
the muscular coat, and the nuclei of the epithelial cells are in the act of proliferation ;
in general the epithelial cells become more and more loosened, as well from the mus-
cular coat as from each other.
The nearer the pocks approach the stage of formation of the pustule the more intense
becomes the infiltration of the corium, both in the peripheral and central part of the
pock. The subcutaneous tissue does not show an increase of the infiltration in its
superficial stratum.
The very intense infiltration of the peripheral part of the pock next to the surrounding
healthy zone is an additional cause, and perhaps one which weighs materially, why the
peripheral part of the pock appears very much elevated in respect to the centre.
A very peculiar change takes place in the lymph-corpuscles which occupy the inter-
fascicular lymph-spaces of the deep stratum of the corium and of the superficial stratum
of the subcutaneous tissue, viz. the lymph-corpuscles, or rather their nuclei, break up
into a number of small particles, deeply stained by heematoxylin ; these particles are
found of all sizes, from the size of a minute granule up to the size of an intact nucleus
of a lymph-corpuscle.
The connective-tissue bundles of the infiltrated corium lose their distinct fibrillar
DK. E. KLEIN ON THE SMALLPOX OF SHEEP.
239
appearance as the process advances, becoming at the same time much thinner. In
advanced pocks, i. e. shortly before and during the formation of the pustules, they
become homogeneous or finely granular ; this is to be found in the papillse as well as
in the deep stratum of the corium and in the subcutaneous tissue (Plate 30. fig. 5).
In all primary pocks which have depressed centres and peripheral thickening the
infiltration with lymph-corpuscles presents the characters described in the foregoing
pages. In the absence of peripheral thickening the peripheral infiltration was not
much greater than the central.
D. Pustular Stage of the Development of the Primary Pustules.
Pustulation commences by the formation of isolated vesicles in the rete Malpighii,
which, as they gradually increase in number and size, become eventually fused together
so as to form larger cavities and canals. This occurs generally at a time when the rete
Malpighii has increased so much in thickness that it sometimes exceeds 2 millims. and
more in vertical diameter ; the papillae of the corium have reached an extreme length
by the extensive growth of the interpapillary process of the rete Malpighii, and at the
same time the papillary tissue contains more or less numerous lymph-corpuscles. We
have mentioned previously that the infiltration of the papillary tissue is most intense in
the peripheral parts of the pock, and that the epithelial cells of the rete Malpighii in
the middle layers are very transparent and large, the peripheral substance (membrane)
of each cell looking as if it were much thickened. To this it is to be added that the
papillary tissue, and in general the superficial stratum of the corium, contains, in its
dilated interfascicular lymph-spaces and lymphatics, either a distinct mycelium with the
spores as products of its fructification, or those zooglcea-like masses of spherical Micro-
cocci or their necklace-like chains. In Those primary pocks which show a central
depression the formation of the vesicles invariably commences at the periphery and
soon extends towards the centre in a horizontal direction, so that the formation of the
vesicles in the centre of the pock takes place later than that in the periphery.
Notwithstanding this, however, numerous vesicles are seen to make their appearance
in the centre, which stand in no direct connexion with those of the periphery. But
in pocks of which the central portion, instead of being depressed, is elevated (as in
many pocks on the mammary glands), the formation of the vesicles commences centrally
and gradually spreads towards the periphery. Now the question arises, In what way
do the vesicles form 1 That the vesicles in their first stage are filled with a trans-
parent fluid lymph and that they afterwards gradually become filled with lymph or
pus-corpuscles are well-known facts ; but the question of their mode of origin has, I
think, not been investigated with sufficient detail. The assertion of Luginbuhl that
the formation of the pustule is to a great extent due to the appearance of giant cells,
must be at once abandoned so far as relates to variola of sheep, for in no instance have
I been able to see any indication of such giant cells in the rete Malpighii.
Considering that the infiltration of the corium with lymph-cells, fungi, and serum
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DK. E. KLEIN ON THE SMALLPOX OE SHEEP.
(the distension of the interfascicular lymph-system) spreads from the deeper strata
gradually towards the surface of the corium, and that the nearer the stage of the
formation of the pustules is reached the more the epithelial cells of the middle layer
of the rete Malpighii become dropsical and the proliferation of the deeper cells increases
in activity, it appears evident that the excessive irrigation of the corium gradually
extends towards the surface. I am inclined to think that this is probably attributable
to stagnation in the large subcutaneous lymphatics and in the veins ; for I have found
the lymphatics leading from infiltrated parts dilated and plugged up by dense myce-
lium and lymph-corpuscles. I have also observed veins densely packed with lymph-
corpuscles and mycelium.
It can therefore be easily understood that inasmuch as the lymphatics and veins of
the deeper parts of the pocks become prevented from carrying away the morbid products,
and inasmuch as there is a constant addition of them, as shown by the increase of the
infiltration, it must naturally lead to a stagnation in the passages leading to the efferent
vessels, which stagnation may be the cause of the morbid material of these passages
being gradually carried in another direction, i. e. towards the surface. This view,
as we shall see presently, is further supported by the fact that the lymph-corpuscles
of the papillary tissue not only find their way in great numbers into the rete Malpighii,
but also into the epithelium of the sebaceous glands, the hair-follicles, and the sweat-
glands, which structures become surrounded by more and more numerous layers of these
bodies. That the spontaneous movement of the lymph-corpuscles is to a certain extent
of importance in determining their migration, cannot of course be denied ; but it is
improbable that this is the only factor, for it is very difficult to see how that could be
the case, considering how densely they are packed in some places.
The formation of the vesicular cavities invariably depends on the transformation of
individual epithelial cells of the middle layer of the rete (sometimes nearer, sometimes
further from the surface) into spherical or elliptical vesicular structures, which possess
a thick membrane and clear contents. The process of transformation is usually as
follows : — An individual cell expanded by dropsical swelling presses on the surrounding
cells so much that they gradually become flattened and so compressed that they almost
coalesce. In this way a vesicle is formed, the membrane of which is composed of
concentrically arranged scales. These scales when seen in profile appear to be spindle-
shaped. Of the epithelial cell from which the vesicular structure originated, all that
remains is the nucleus surrounded by a thin zone of granular protoplasm (the original
substance of the cell). This remains attached to one side of the vesicle, and finally
disappears.
But there is also another way by which individual epithelial cells become transformed
into vesicles, i. e. by vacuolation. A cell first shows a small vacuole ; by the enlarge-
ment of the vacuole the nucleus becomes pressed at the periphery, while the original
cell-substance expands into a vesicular membrane enclosing the vacuole ; with this
membrane the nucleus, which becomes more flattened the larger the vacuole grows, is
DK. E. KLEIN ON THE SMALLPOX OF SHEEP.
241
incorporated. By the gradual coalescence of groups of vesicles, smaller or larger
spherical, irregular, or elongated sinuses are formed, which may acquire a large size
by the disappearance of the intervening septa composed of compressed epithelial cells.
If the formation of the vesicles extends in a horizontal direction and the vesicles are pretty
close, the epithelial cells subjacent to them form continuous layers of horny scales,
the nuclei of which soon disappear. And this is the case whatever may be the deve-
lopment of the horny stratum, and even when it is not distinguishable. The smaller
vesicles contain clear fluid ; in the larger there are structures, consisting partly of lymph-
corpuscles but principally of mycelium, which may or may not be in fructification. I
have preparations in which spores of exactly the kind described in the former chapter,
and represented in Plate 32. fig. 11 and Plate 31. fig. 10, V., could be very distinctly
traced from the papillae through the deeper strata of the rete Malpighii into the vesicles.
In some cavities the mycelium is dense and composed of filaments so thin that it
looks like a zoogloea, especially where the filaments are beset with very small conidia.
In such cavities the fructification of the mycelium is probably going on with very great
rapidity and intensity (Plate 29. fig. 18 and Plate 30. fig. 19). In those cavities which
lie deepest, that is, most remote from the layer which is the seat of the horny trans-
formation of the rete Malpighii, it can be made out, by the examination of different
cavities lying side by side, that by fructification the mycelium may assume an appear-
ance similar to that of zoogloea of Micrococci. The comparison of the two conditions
can even be made in one and the same cavity, which may contain in one part very
distinct mycelium with conidia, in another material like zoogloea — the transition from
the former to the latter consisting in this, that the filaments of the mycelium gradually
become thinner and their network denser, while the spores diminish in size by division
and are more closely aggregated.
The infiltration of the vesicular cavities with lymph-corpuscles from the papillae takes
place in some cases simultaneously with this formation, sometimes later. It commences
at the periphery of the pock, where the subjacent tissue is most intensely infiltrated,
and spreads from thence towards the centre (cf. Plate 32. figs. 14 & 15). Besides the
lymph-corpuscles migrating through the deep stratum of the rete Malpighii, there are
seen also other small highly refractive bodies which, from their aspect, I am inclined
to take as spores.
Many of the lymph-corpuscles themselves contain a number of spherical bodies which,
from their characters, cannot easily be assumed to be their nuclei, being of a greenish
colour, and being similar to those found free beside the lymph-corpuscles on their way
through the deep stratum of the rete Malpighii and in the papillary tissue; they
correspond probably also to spores.
This is in accordance with what was found in the pus-corpuscles of fresh lymph (see
Plate 31. fig. 10, III., and Plate 29. fig. 3, i). I can easily imagine that lymph-
corpuscles, while migrating from the papillary tissue into the rete Malpighii, take up
the spores lying in the former and carry them with them just as they would take up
242
DR. E. KLEIN ON THE SMALLPOX OF SHEEP.
pigment-granules on a warm stage and creep away with them. As the rete Malpighii
becomes infiltrated with lymph-corpuscles, they appear to be eliminated from the corium ;
for I have preparations of pocks in which, while the very abundant cavities in the
rete Malpighii are crammed with lymph-corpuscles, the papillary tissue has become
almost barren of them.
In one instance I have had opportunity of observing a primary pock in which an
enormous infiltration of the corium with lymph-corpuscles, and the formation of very
numerous pustular cavities containing them, had taken place at a relatively very early
period, the fourth or fifth day after its appearance. In this case the deepest stratum
of the rete Malpighii at the periphery of the pock was actually completely broken
through by the contents of the papillae, whereby a broad direct passage was established
between the latter and the intercommunicating pustular cavities. In primary pocks
of old standing, when the formation of the vesicles and their infiltration with lymph-
corpuscles has reached a very high degree, the layers of the rete Malpighii containing
the vesicles nearest the surface are seen to become very much loosened from the sub-
jacent strata of the rete and to detach themselves easily. In this stage, when the
papillae contain few lymph-corpuscles, there are found, in the matrix of the papillae
(which is now transparent, finely granular, or homogeneous), more or less sinuous large
spaces very close to the rete Malpighii, which contain a clear lymph and occasionally
also masses of Micrococci. These spaces enlarge into the rete, and may even become
continuous with the deepest vesicles.
I have now only to add a few words relating to the other parts of the skin.
Of the glands of the corium the sebaceous glands deserve the most attention. The
epithelium of the glands and their ducts (properly speaking the mouths of the hair-
follicles) become immensely enlarged, chiefly on account of their epithelium proliferating
so enormously that it is composed, like that of the rete Malpighii, of a very great number
of layers. The deepest epithelial cells, the nuclei of which are rapidly dividing and
many of them in a state of vacuolation, become smaller and smaller and at the same
time more loosely connected with one another.
In the ducts the epithelial cells which are nearer to the lumen are, on the other hand,
more swollen, more transparent, and dropsical. The infiltration of the rete Malpighii
with pus-corpuscles extends into the mouth of the sebaceous gland and also into the
proper secretory parts of the glands. The pus-corpuscles of the surrounding tissue
gradually penetrate amongst the epithelium of the former to such an extent that the
centre of the gland in some places becomes completely filled with closely packed pus-
corpuscles.
Although there is a marked infiltration of the sweat-glands with pus-corpuscles from
the surrounding tissue, this infiltration never reaches such an extent as in the sebaceous
glands. The epithelium of the sweat-glands becomes more and more loosened under
the infiltration, and the lining epithelial membrane becomes broken up into a number
of small cells, the nuclei of most of which show vacuolation.
DR. E. KLEIN ON THE SMALLPOX OF SHEEP.
24:
E. Anatomical Investigation of Secondary Pustules.
The examination of the secondary pocks, i. e. those of the general eruption, proves
that the anatomical changes are substantially the same as in the primary. We find also
here, at the outset of the process, thickening of the rete Malpighii and oedema of the
corium, combined with the presence of lymph-corpuscles around the blood-vessels and
extending hence into the distended lymph-canalicular system.
The infiltration of the corium with lymph-corpuscles extends very soon, however,
upwards into the papillary stratum and downwards into the subcutaneous tissue. In
general it may be said that in the secondary pocks the whole process goes on much more
rapidly, i. e. the stage of pustulation is much sooner reached than in the primary pocks.
In most of the secondary pocks on the lip, the pustulation was seen to be going on
as early as from two to four days after their appearance ; in those of the walls of the
chest and abdomen the same thing was seen after from three to seven days.
The infiltration of the subcutaneous tissue and corium was always found to be greater
in the peripheral part than in the central. This was better marked in those pocks which
were of long standing, i. e. which developed slowly, and particularly in those in which
a central depressed and a peripheral thickened part could be distinguished. In the
rete Malpighii the same immense overgrowth of the interpapillary processes occurred as
in the primary pocks, and the cells of the middle layers showed the same tendency to
become soon dropsical. I have not observed the formation of the horny stratum ; but
in the central parts of many of the pocks I have noted the conversion of groups of
epithelial cells into horny masses.
As regards the interfascicular lymph-channels and the lymphatic vessels of the corium
and their contents, I have only to repeat what I have stated as regards the primary
pocks, viz. that one is able to follow the at first zooglcea-like masses of Micrococci into
necklace-like filaments, which gradually become more and more branched, so as to form
a delicate mycelium ; in some places the filaments of the mycelium bear conidia, and
show the same fructification as those mentioned in the former section. The formation
of the vesicles takes place in the same way as in the primary pocks, viz. by dropsical
swelling and vacuolation of individual epithelial cells.
The pustulation commences as a rule in the centre, and spreads rapidly into the
periphery. The vesicles make their appearance in great numbers simultaneously, and
are situated chiefly in the middle layers of the rete Malpighii, but are generally met
with much nearer the corium than in the primary pocks. It is worth noticing that
when the vesicles lie deep in the rete Malpighii, the expansion of the individual vesicles
goes on at the expense of the interpapillary processes ; so that as the vesicles enlarge
the interpapillary processes become shorter, until the line of demarcation between the
rete Malpighii and the corium becomes almost as even as in. the normal state : in the
latter case, therefore, the deepest cells of the rete Malpighii appear very much com-
pressed, as if the rete had been dragged over the surface of the corium. There is
244
DR. E. KLEIN ON THE SMALLPOX OE SHEEP.
another point, as regards the distribution of the vesicles, which I think important, viz.
that even in those pocks in which there was a very marked central depression, the most
numerous and best developed vesicles were found in the centre, and they became smaller
and fewer the nearer to the periphery — thus showing clearly that the depression in the
centre is n'ot caused by the disappearance of previously existing vesicles.
I have now to call the attention of the reader to Plate 29. fig. 16, in which the
formation of the vesicles is shown, as well as the presence of an Oidium- like fungus in
their contents.
In some vesicles the mycelium, which here also is composed of filaments of very
various thickness, is imbedded in a finely granular matrix, which I suppose is only
coagulated plasma ; in others the matrix is almost homogeneous, and is stained slightly
with carmine and hsematoxylin as in D. After some time pus-corpuscles are seen to
penetrate from the papillary tissue through the deeper strata of the rete Malpighii into
the vesicles, just as in the primary pocks. So also the transformation of the mycelium
in the vesicles by rapid fructification into a zooglcea-like mass of Micrococcus occurs in
the manner already described. I have represented the characters of the mycelium and
the spores attached to it in Plate 29. fig. 17, drawn with every possible accuracy
from the contents of a vesicle of a secondary pock.
The mycelium, as well as the spores, possess a greenish colour, and are of a bright
and shining aspect.
As peculiarities which I had not seen in any of the primary pocks, and in only one
secondary pock of the upper and one of the lower lip, may be mentioned the occurrence
of blood in a single vesicular cavity, the rest not containing any. This vesicle was
situated rather deeply in the rete Malpighii. In another instance I observed the
effusion of blood into the sheath of a hair-follicle and into the adventitia of an artery.
In both'cases the blood was contained in a number of large irregular spaces communi-
cating with each other.
I am unable to refer the fungus of which we have spoken in the foregoing and in
this chapter, and which, as we have mentioned and figured, occurs first in the tissue of
the corium and its lymphatics and is gradually carried or penetrates into the vesicles
formed in the rete Malpighii, to any described species, and would propose to call it
provisionally Oidium variolce.
Although nobody could, from the very great distribution of this fungus through the
whole pock, take it to be a mere accidental entophyte, yet it might be objected that we
are wrong in asserting that its development begins and ends in Micrococcus. Against
this objection it must be maintained that, besides our being able to follow the one into
the other as far as place as well as time is concerned, we also find (and this appears to
me to be of still greater importance) at one time only the one organism and at another
time only the other ; we have found first only the Micrococcus , then we have found
only the Oidium form, which we finally see again replaced by Micrococcus. Whether
a form of vegetation corresponding to Oidium variolce in sheep is to be met with in
DE. E. KLEIN ON THE SMALLPOX OF SHEEP.
245
the. cow-pock or in human smallpox, is a very important question, and one which
deserves alike the attention of physicians and anatomists.
Explanation op the Plates.
PLATE 29.
Fig. 1. Lymph from pustules of sheep-pox, kept in a sealed capillary tube. (Examined
March 10, 1874, with Hartnack’s ocular 3, objective 9.)
1 . Transparent masses of various sizes, containing granules, some of which
are small, pale, and indistinct, others large and shining.
2. Transparent spheroid bodies containing necklaces.
3. Highly refractive Micrococci in proliferation, forming dumb-bells,
Sarcina-Wke structures, and small colonies.
4. The same, between decolorized blood-disks.
5. Bacterium.
6. Colonies of Bacterium termo.
7. Shining Micrococci imbedded in a greenish matrix, some being sur-
rounded by a thin membrane.
8. Groups of bodies similar to those in 2 and 3.
Fig. 2. Similar preparation to fig. 1, but which had been kept for 24 hours in the
incubator. (Examined March 11, with Hartnack’s oc. 3, obj. 10, immersion.)
1 . Network of fine filaments beset with Micrococci ; transparent spheroids
like those in fig. 1, 2.
2. Network of filaments more defined, with spheroid bodies budding from it.
3. Part of the same preparation, kept in the incubator till March 17.
Fig. 3. Lymph from pustule of sheep-pox kept for 24 hours at a temperature of 32° C.
(Examined March 25, with Hartnack’s oc. 3, obj. 8.)
1. Homogeneous sporids, some free, others contained in pus-corpuscles.
The same sporids of a paler colour, containing one or two Micrococci.
2. Micrococci forming necklaces.
3. The same in groups.
4. The same in colonies connected by filaments of various lengths.
5. Diagrammatic representation of the relation of 1 to sporids and of 2
to Micrococcus ( Cryptococcus of Hallier).
Fig. 4. Preparation from a vertical section of the thickened epithelium of the peripheral
part of a pock three days after its first appearance. (Hartnack’s oc. 3,
obj. 7.)
A. Horny layer.
B. Superficial layers of the rete Malpighii. Near the poles of the nucleus
2 L
MDCCCLXXV.
246
DE. E. KLEIN ON THE SMALLPOX OE SHEEP.
of some of the cells rows of highly refractive granules may be seen.
These granules become fewer and smaller as they approach the middle
layers, C, of the rete Malpighii, and eventually disappear. Many of
the nuclei of the epithelial cells of the middle layers and of the lower
layers, D, are seen to be divided. In D some of these divided nuclei
are vacuolated or dropsical. In the middle layers epithelial cells may
he seen, both isolated and in groups, which are sharply defined and
opaque. These are being converted into a homogeneous horny
substance.
PLATE 30.
Fig. 5. Vertical section of half of a pock, excised seven days after its appearance,
showing a pale central and a thickened reddish peripheral part. The figure
shows the general distribution of the infiltration. (Oc. 3. obj. 2.)
A. Part of the pustule where the peripheral thickening is in contact with
healthy tissue.
B. Epidermis of healthy skin.
C. Epidermis of central part of pustule, showing the rete Malpighii divided
into three layers — a superficial layer composed of nucleated somewhat
flattened cells, a middle, horny layer, and a lower layer composed of
polyhedral, nucleated, granular epithelial cells, the true rete Malpighii.
(Compare with fig. 6.)
D. Superficial layer of corium, showing infiltration with lymph-cells around
the blood-vessels and in the lymphatics.
E. Deep layer of corium, containing sebaceous and sweat-glands.
F. Superficial layer of subcutaneous tissue, showing the interfascicular
lymph-channels much distended. The smaller branches of the
canalicular system could not be represented, owing to their extreme
minuteness.
G. Deep layer of subcutaneous tissue, showing fat-cells and transverse
sections of blood-vessels and lymphatics.
It will be observed that infiltration with lymph-cells occurs abun-
dantly at the periphery of the pustule, and extends through all the
layers, but chiefly in the corium and deep subcutaneous tissue.
Fig. 6. Vertical section of central depression of a primary pustule seven days old,
showing the changes in the epithelium. (Oc. 3, obj. 7.)
A. Horny layer.
B. Superficial layers of rete Malpighii undergoing conversion into horny
scales.
C. Deep layers of rete, composed of protoplasmic, germinating epithelial
DR. E. KLEIN ON THE SMALLPOX OE SHEEP.
247
cells. In the deepest layer are seen conical or cylindrical processes
composed of young epithelial cells (E), which penetrate into the
papillary tissue of the corium, in which dilated blood-vessels and
cellular elements may also be observed. ,
D. Middle horny stratum connected by pillar-like processes with the inter-
papillary processes of the deep rete Malpighii. The cells below the
middle horny stratum contain series of granules of an arrangement and
distribution similar to those represented in fig. 4. Some cells imme-
diately below D are seen to be enlarged, dropsical, and in a state of
vacuolation. The interpapillary epithelial processes and the papillae
are much enlarged.
PLATE 31.
Fig. 7. Section through a primary pustule 24 hours old, in which are seen transverse
sections of lymphatic vessels (A) of the deep layer of the corium, as well as
the interfascicular lymph-channels (B) containing connective-tissue corpuscles.
The lymphatics are filled with zooglcea. (Oc. 3, obj. 7.)
Fig. 8. Similar preparation. (Oc. 3, obj. 7.)
A. Lymphatic vessels containing granular material (zoogloea) and a fila-
mentous substance (necklaces of Micrococci).
B. Interfascicular lymph-canaliculi, in connexion with the lymphatic
vessels, and containing connective-tissue corpuscles. In I. a blood-
vessel (C) is seen to penetrate a lymphatic vessel (perivascular lym-
phatic) ; in II. a valve D is represented.
Fig. 9. Similar preparation from a pustule about 60 hours old. (Oc. 3, obj. 7.)
A. Lymphatic vessels lined with endothelium, like those in previous figures.
I. contains lymph-corpuscles, zoogloea, and filaments, the last men-
tioned being in II. much more numerous.
Fig. 10. Sections of lymphatic vessels lined with endothelium. Mycelium is seen to
be contained in them. Nos. I. & V. are drawn with Hartnack’s oc. 3, obj. 8 ;
Nos. II., III., and IV. with oc. 3, obj. 7.
I. Part of subcutaneous lymphatic of a pustule about 60 hours old.
II. & III. Lymphatics of corium of a pustule of the same period.
IY. & Y. Preparations from a similar pustule.
PLATE 32.
Fig. 11. Section through lymphatic vessels of the deeper layer of the corium of a primary
pustule 30 hours old. (Oc. 3, obj. 11, immersion.)
In both A & B the conidia of the mycelium represented in fig. 10 and the
proliferation of the spores may be seen.
2 l 2
248
DE. E. KLEIN ON THE SMALLPOX OP SHEEP.
Fig. 12. From a section of the subcutaneous tissue of the same pustule as fig. 11
(oc. 3, obj. 8), showing: —
A. The distended interfascicular lymph-spaces.
B. Connective-tissue corpuscles in an altered condition.
C. Bundles of connective tissue.
Fig. 1 3. Section through subcutaneous tissue of a primary pustule from 3 to 4 days old.
(Oc. 3, obj. 7.)
A. Lymphatic vessels.
B. Interfascicular lymph-spaces.
C. Bundles of connective tissue.
The lymphatic vessel and the interfascicular spaces contain Micrococci
either in the form of zooglcea or of necklaces.
The lymphatic vessel is lined with endothelium. On the surface of
the bundles of connective tissue the corpuscles are seen to extend
into the interfascicular spaces.
Fig. 14. Vertical section through the periphery of a primary pustule 10 days old.
(Oc. 2, obj. 7.)
A. Horny layer.
B. Bete Malpighii. There is a striking difference in the thickness of the
epidermis in the pustule and in the neighbouring healthy skin. In
the former the rete Malpighii is divided into three parts by a middle
horny layer, viz. a superficial layer and a deep layer which is under-
going active proliferation, sending out long thick interpapillary
processes.
C. Superficial layer of corium. It is seen to be very different from that
of healthy skin, being infiltrated with lymph-cells and having large
papillse.
D. A vesicle in the rete Malpighii, the lymph-corpuscle of which can be
traced to have migrated from the papillae into the deep layer of the
rete. To the left of the drawing small cavities containing lymph-
corpuscles may he observed in the deep layer of the rete Malpighii.
These are the first traces of the formation of vesicles.
Fig. 15. Vertical section of the rete Malpighii below the middle horny stratum (see figs.
6 & 14) from a primary pustule 12 days old. The epithelial cells are seen
to be much enlarged, many of them somewhat dropsical and vacuolated and
changed into vesicles of various sizes. They are confluent, and thus form
channels. It may be observed that there is a migration of lymph-corpuscles
from the lower portion (B) towards the surface (A). The highly refractive
bodies contained in the vacuolated epithelial cells originate, probably, partly
from the nuclei of those cells, partly from lymph-corpuscles. Some of them
are of a greenish colour, and are contained in lymph-corpuscles. A granular
DR. E. KLEIN ON THE SMALLPOX OF SHEEP.
249
or filamentous substance may be observed in some of the superficial vacuo-
lated epithelial cells, which is probably connected with the fungus found
in the pustules (see figs. 18 & 19).
PLATE 29.
Fig. 16. Vertical section of rete Malpighiiof a secondary pustule — that is, one forming
part of the general eruption. (Oc. 3, obj. 7.) The rete Malpighii is thickened,
and in the middle layers single epithelial cells are seen being converted into
vesicles.
A. Horny layer.
B. Deep layer of the rete Malpighii. In both layers of the rete many of
the nuclei of the epithelial cells are changed into well-defined vesicles.
C. Vesicles containing the mycelium of the Oidium- like fungus.
D. Vesicle in which the matrix of the mycelium has been stained with
carmine.
Fig. 17. Part of the contents of the pustule represented in fig. 16. (Oc. 3, obj. 10,
immersion.) The OidiumASke, fungus seen in the previous figure is imbedded
in a finely granular substance (coagulated plasma).
Figs. 18 (PI. 29) & 19 (PI. 30) are both preparations from a primary pustule, showing
the identity of the fungus found in primary and secondary pustules. (Oc. 3,
obj. 10, immersion.)
[The research to which the present paper relates has been made as one of the series
of scientific investigations which the Lords of the Council are pleased to authorize me
to have conducted at their expense in aid of Pathology and Medicine.
The paper itself, being of the nature of a Report for the Lords of the Council, may
probably appear entirely or in part as a Parliamentary Publication ; but the immediate
interest of the facts makes me think that the Royal Society will be glad to be at once
possessed of them ; and I therefore avail myself of their Lordships’ permission to com-
municate the paper to the Society. — John Simon.]
..
'
[ 251 ]
VII. Description of the Living and Extinct Daces of Gigantic Land-Tortoises. —
Parts I. & II. Introduction, and the Tortoises of the Galapagos Islands. By Dr.
Albert Gunther, F.B.S., V.P.Z.S., Keeper of the Zoological Department of the
British Museum.
Received June 4, — Read June 18, 1874.
Pakt I.— INTRODUCTION.
In 1865 and following years the Trustees of the British Museum obtained a series of
Tortoise-bones from the Mauritius, chiefly due to transmission by Mr. George Clark,
C.M.Z.S. It consisted of limb-bones and portions of the cranium ; and particular
interest was attached to it, as these remains had been found associated with the bones
of the Dodo, and as the race of these reptiles had shared the fate of that remarkable
bird, having long ago succumbed to the onslaught of the numerous enemies who took
possession of their limited home.
The circumstances under which these bones were found will be readily understood
from the following abstract of Mr. Clark’s “ Statement”*: —
“ On the estate called ‘ Plaisance,’ about three miles from Mahebourg, in the island
of Mauritius, there is a ravine of no great depth or steepness, which, apparently, once
conveyed to the sea the drainings of a considerable extent of circumjacent land, but
which has been stopped to seaward, most likely for ages, by an accumulation of sand
extending all along the shore. The outlet from this ravine having been thus impeded,
a sort of bog has been formed, called ‘ La Mare aux Songes,’ in which is a deposit of
alluvium, varying in depth, on account of the inequalities of the bottom, which is formed
of large masses of basalt, from 3 to 10 or 12 feet. The proprietor of the estate, a few
weeks ago, conceived the idea of employing this alluvium as manure ; and shortly after,
the men began digging in it ; when they had got to a depth of 3 or 4 feet they found
numerous bones of large tortoises, among which were a carapace and a plastron pretty
nearly entire, as also several crania These were found imbedded in a black
vegetable mould, the lighter-coloured specimens being near the springs.”
My attention was directed to these remains in the year 1872, when I received from
my esteemed correspondent, L. Bouton, Esq., a further consignment of Chelonian bones,
consisting : —
1. “Of the carapace of a Tortoise found at Grand Port, a few years ago, in the same
place where the bones of the Dodo were also found — in a marshy place called 4 Mare*
aux Songes.’ ” [This appears to be the carapace mentioned in the above statement
but no plastron was received with it then or afterwards.]
* See Trans. Zool. Soc. vi. p. 51.
252
DE. A. GUN THEE ON GIGANTIC LAND-TOETOISES.
2. “ Of bones from Mauritius, very abundant in the district of Flacq.”
3. “ Of bones from the island of Rodriguez ” *.
Similar bones had been discovered and had reached Europe many years ago. In
the year 1830 M. J. Desjardins, one of the first explorers of the fauna of Mauritius,
had discovered “ three deposits of the remains of Tortoises ”f . The same naturalist sent
a bone of a Tortoise, found, in 1786, in a cave in Rodriguez, with some remains of the
Solitaire to ParisJ, where they were examined by Cuvier and Blainville, who erro-
neously stated them to have been recently found under a bed of lava in Mauritius §.
Another Mauritian naturalist, C. Telfair, in searching, in 1832, for bones of the Solitaire
in Rodriguez, succeeded in obtaining “ numerous bones of the extremities of one or
more large species of Tortoise,” which were presented to the Zoological Society of
London, and exhibited at one of the Meetings [|. These bones were still in the posses-
sion of the Society three or four years before the publication of Strickland and
Melville’s memoir on the Dodo (1848) ; but no further attention being paid to them,
they were lost. Another portion of Telfair’s collection was presented by him to the
Andersonian Museum at Glasgow.
The causes of the indifference with which these remains were treated are twofold : —
First, the all-absorbing interest centred in the bird-remains ; and, secondly, the belief
that the bones were those of a still-existing gigantic species of Tortoise commonly called
Testudo indica. Under this name were comprised all gigantic Land-Tortoises brought
to Europe in ships which, on their return from India, had touched at the Mascarenes.
When, at a later period, zoologists became acquainted with a similar Tortoise from the
Galapagos Islands, some considered the latter specifically distinct, whilst others main-
tained that they were specimens of the same species, “ which had been scattered by man
in different tropical parts of the globe” (Gray, Shield Rept. 1855, p. 7).
However, a closer examination and comparison of the remains at my disposal revealed
important differences unmistakably pointing at a multiplicity of species ; and as the
remains were of a comparatively very recent period, so that I could reasonably expect
to find carapaces, skeletons, or even stuffed examples of the very same species in our
collections, it became imperative, for the proper interpretation of the Mauritian remains,
to include in my researches the forms known or supposed to be still living. The results
of these researches were startling, and may arrest the attention of the zoologist all the
more, as the facts elucidated bring us face to face with the mystery of the birth and
life of an animal type. I may shortly indicate them as follows : —
1. Mauritius and Rodriguez were formerly inhabited by several species of gigantic
Tortoises, the Rodriguez species differing more markedly from those of Mauritius than
* Letter from L. Bolton, Esq., dated Oct. 18, 1872. t Proc. Comm. Zool. Soc. i. p. 45.
X Proc. Comm. Zool. Soc. i. p. Ill ; Strickland and Melville, c The Dodo,’ pp. 51, 53.
§ Edinb. Journ. Nat. Sc. iii. p. 30. || Proc. Zool. Soc. 1833, p. 31.
With a dismay excusable in an ornithologist, Strickland exclaims (l. c. p. 52), “Alas ! the bones of the
Solitaire, apterous as it was, had flown away, and the only hones that remained belonged to Tortoises ! ”
DB. A. GtfNTHEE ON GIGANTIC LAND-TOETOISES.
253
these latter among themselves. All these species appear to have become extinct in
modern times.
2. These extinct Tortoises of the Mascarenes are distinguished by a flat cranium,
truncated beak, and a broad bridge between the obturator foramina.
3. All the recent examples of gigantic Tortoises in our museums said to have been
brought from the Mascarenes, and the single species which is known still to survive in
a wild state in the small island of Aldabra, have a convex cranium, trenchant beak, and
a narrow bridge between the obturator foramina, and are therefore specifically, if not
generically, distinct from the extinct ones.
4. On the other hand there exists the greatest affinity between the extinct Masca-
rene Tortoises and those still inhabiting the Galapagos group. The latter must be
considered to be indigenous to this archipelago.
5. Among the Galapagos Tortoises five species can be distinguished at present ; they
are inhabitants of different islands of the group.
I propose to preface my detailed description of the various species by a general
account of the historical evidence given by travellers who have met with those Tortoises,
whilst the scientific part of the literature will be better referred to in the descriptions
of the several species.
Historical evidence.
Nearly all the voyagers of the 16th and 17th centuries who have left accounts of
their adventures and discoveries in the Indian and Pacific Oceans mention the occur-
rence, in certain isolated islands or groups of islands, of gigantic Land-Tortoises in
countless numbers. The islands on which they met with these animals, although all
between the equator and southern tropic, form two most distant zoological stations,
widely different in their physical characteristics. One of those stations was the
Galapagos Islands, the other comprised Aldabra, Reunion, Mauritius, and Rodriguez.
But they had this in common, that at the time of their discovery they were unin-
habited by man or even some larger terrestrial mammal. Not one of those voyagers
ever mentions having met with those Tortoises in any other island of the tropics or in
any portion of the Indian continent ; and it is not likely that one or the other should
not have mentioned the fact if he had seen them in some novel locality. In fact
the hardy sailors of that period took the greatest interest in these animals, which
were to them a most important article of food. At a time when a voyage now
performed in a few weeks took as many months, when every vessel, for defence’ sake
and from other causes, carried as many people as it was possible to pack into her,
when provisions were rudely cured and but few in kind, those tortoises which could be
captured in any number with the greatest ease within a few days proved to be a most
welcome addition to the stock. The animals could be carried in the hold of the ship
or in any other part, without food, for months, and were slaughtered as occasion
required, each tortoise yielding, according to size, from 80 to 200 pounds of whole-
31DCCCLXXV. 2 M
254
DE. A. GUNTHEE ON GIGANTIC LAND-TOETOISES.
some food. Thus we are informed that ships leaving the Mauritius or the Galapagos
used to take upwards of 400 of these animals on board.
When we consider that these helpless creatures lived in perfect security from all
enemies, and that nature had endowed them with great longevity*, so that the indi-
viduals of many generations lived simultaneously in their island home, we can well
account for the multitudes found by the first visitors to those islands.
Leguat (1691) says that “ there are such plenty of Land-Turtles in this isle (Rodri-
guez) that sometimes you see two or three thousand of them in a flock, so that you
may go above a hundred paces on their backs.” Down to 1740 they continued to be
numerous in Mauritius; for Grant (Hist. Maurit. p. 194) writes in that year, “We
possess a great abundance of fowl as well as both Land- and Sea-Turtle, which are
not only a great resource for the supply of our ordinary wants, but serve to barter with
the crews of ships who put in here for refreshment in their voyage to India ! ” Yet
they appear to have been much more scattered in the larger island than in Rodriguez ;
and, according to Admiral Kempinfelt, who visited the latter island in 1761 (see
Grant’s Maurit. p. 100), small vessels were constantly employed in transporting these
animals by thousands to Mauritius for the service of the hospital. Soon, however,
their numbers appear to have been rapidly diminished ; the old ones were captured by
man, the young ones devoured by pigs. Numbers must have succumbed in consequence
of the numerous conflagrations by which the rank vegetation of the plains was destroyed
to make room for the plantations of the settler. Early in the present century the
work of extermination appears to have been accomplished ; and there is at present
not a single living example either in the Mauritius, in Rodriguez, or Reunion ;
a few isolated individuals are kept in a state of captivity in the Seychelles, imported
from the island of Aldabra, the only spot in the Indian Ocean where this Chelonian
type still lingers in a wild state in small and gradually diminishing 'numbers f. That
this Tortoise from Aldabra is specifically distinct from the extinct ones of the Mauritius
and Rodriguez, we shall see subsequently.
In the second place, I have to refer to the accounts given by the most trustworthy
visitors to the Galapagos Islands. According to the unanimous testimony of geo-
graphers, the first discoverers of this archipelago, the Spaniards, found the islands so
* On this point the testimony is unanimous and not to he doubted : in fact all Tortoises are long-lived.
Mr. E. W. H. Hoedsworth, E.L.S., informs me of an individual carried to Ceylon (Colombo),- and said to have
lived in the island for 150 years. Another example, in Cerf Island, is known to have been kept there for the
last 70 years (unfortunately its present owner asks a price for it commensurate to its age). A very young-
living example from Aldabra, 7 inches long, sent to me by Dr. W. M'Gregor, is now 3 years old.
t I am indebted to His Excellency Sir Aether Gordon, Governor of the Mauritius, for this information.
I may add, from my own experience, that the Aldabra species is but rarely brought to’ London now. In
the years 1857-59 I saw several large living examples brought into the London market, and one which I
bought for £4 was considered to be dear. Since that time I have heard of one adult only, beside the young
sent to me by Dr. M'Gregor. However, they are not readily sold, as hitherto none of them have been kept
alive in England for any length of time, and most zoological museums possess specimens of this species.
DR. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
255
thickly peopled with Tortoises that they applied the Spanish word for tortoise to their
discovery. In Dampier’s time (1680) it was the common practice of vessels to visit
those islands for a supply of water and tortoises. In his ‘ New Voyage round the
W orld’ (Lond. 1697, 8vo), p. 101, he says: — “ The Land-Turtle are here so numerous
that 5 or 600 men might subsist on them alone for several months, without any other
sort of provision. They are extraordinary large and fat, and so sweet that no pullet
eats more pleasantly. One of the largest of these creatures will weigh 150 or 200
weight [pounds], and some of them are 2 foot or 2 foot 6 inches over the callapee
or belly [across the sternum] They have very long small necks and little
heads.”
The condition of this group of islands and of the animals inhabiting them appears
to have been unaltered when they were visited by Amasa Delano and David Porter
the former a captain in the merchant service, the latter in the navy of the United
States.
Delano (‘Narrative of Voyages and Travels,’ Boston, 1817, 8vo) made several visits
to the Galapagos, the first in 1800 (p. 369). He found plenty of Tortoises in Hood’s,
Charles, James, and Albemarle Islands. He gives a good description of them, noticing
particularly the long, serpent-like neck (p. 376): — “I have seen them with necks
between two and three feet long .... They would raise their heads as high as they
could, their necks being nearly vertical, and advance with their mouths wide open ....
They are perfectly harmless. ... I have known them live several months without food ;
but they always in that case grow lighter, and their fat diminishes. ... I carried at one
time from James Island 300 very good terrapins to the island of Massa Fuero;
and there landed more than one half of them, after having them more than 60 days on
board my ship. Half of the number landed died as soon as they took food .... those
that survived the shock which was occasioned by this sudden transition from total
abstinence to that of abundance soon became tranquil, and appeared to be as healthy
and as contented with the climate as when they were at their native place ; and they
would probably have lived as long, had they not been killed for food. ... I have carried
them to Canton at two different times.”
Porter informs us of many interesting particulars in his ‘ Journal of a Cruise made
to the Pacific Ocean’ (New York, 1822, 8vo, in 2 vols.). He found the Tortoises (in
1813) in greater or less abundance in all the larger islands of the group which he visited,
viz. Hood’s, Marlborough, James, Charles, and Porter’s (Indefatigable) Islands. On
Chatham Island, where he made a short stay, a few of their shells and bones were seen,
but they appeared to have been long dead (vol. i. p. 231) ; and on Albemarle Island,
the largest of the group, none were observed by him, evidently because he landed here
only for a few hours on the south-western point. Abingdon, Binloe, Downe, and
Barrington Islands were not visited by him. Some of the Tortoises captured weighed from
oOO to 400 pounds (p. 127). “ Their steps are slow, regular, and heavy ; they carry their
body about a foot from the ground. . . . Their neck is from 18 inches to 2 feet in length,
2 m 2
256
DR. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
and very slender; their head is proportioned to it, and strongly resembles that of a serpent.
.... No animal can possibly afford a more wholesome, luscious, and delicate food than
they do. . . . What seems the most extraordinary in this animal is the length of time
that it can exist without food ; for I have been well assured that they have been piled
away among the casks in the hold of a ship, where they have been kept eighteen months,
and when killed at the expiration of that time were found to have suffered no diminu-
tion in fatness or excellence. They carry with them a constant supply of water in a
bag at the root of the neck, which contains about two gallons ; and on tasting that
found in those we killed on board, it proved perfectly fresh and sweet. ... In the day-
time they appear remarkably quick-sighted and timid, drawing their head into their
shell on the slightest motion of any object; but they are entirely destitute of hearing,
as the loudest noise, even the firing of a gun, does not seem to alarm them in the
slightest degree ; and at night, or in the dark, they appear perfectly blind ” (p. 150).
Near a bay on the north-east part of James Island, Porter took on board as many as
would weigh about 14 tons, the individuals averaging about 60 pounds — that is, about
500 individuals (p. 214) ; and he states that “ among the whole only three were male,
which may be easily known by their great size, and from the length of their tails, which
are much longer than those of the females. As the females were found in low sandy
bottoms, and all without exception were full of eggs, of which generally from ten to
fourteen were hard, it is presumable that they came down from the mountains for the
express purpose of laying. This opinion seems strengthened by the circumstance of
there being no male Tortoises among them, the few we found having been taken
a considerable distance up the mountains The temperature of the air of the
Gallipagos Islands varies from 72° to 75° ; that of the blood of the Tortoise is always
62°. . . . The eggs are perfectly round, white, and of 2^ inches diameter ”
(pp. 215, 216).
Very significant are Porter’s remarks as regards the differences of the Tortoises from
different islands. On Porter’s Island “ they were generally of an enormous size, one of
which measured 5^ feet long, 4|- feet wide, and 3 feet thick ; and others were found by
some of the seamen of a larger size” (p. 164). “ The shells of those of James Island
are sometimes remarkably thin and easily broken, hut more particularly so as they
become advanced in age Those of James Island appear to be a species entirely
distinct from those of .Hood’s and Charles Islands. The form of the shell of the latter
is elongated, turning up forward in the manner of a Spanish saddle, of a brown colour,
and of considerable thickness. They are very disagreeable to the sight, but far superior
to those of J ames Island in point of fatness, and their livers are considered the greatest
delicacy. Those of James Island are round, plump, and black as ebony, some of
them handsome to the eye ; but their liver is black, hard, when cooked,” &c. (pp. 214,
215). The Tortoises of Hood’s Island were small, similar to those of Charles Island
(p. 233).
Before we pass from Porter to his successors we must mention that he proceeded,
DR. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
257
after his cruise round the Galapagos, to the Marquesas Islands, making a prolonged
stay at Madison Island, where he “ distributed from his stock several young Tortoises
among the chiefs, and permitted a great many to escape into the bushes and among the
grass ” (vol. ii. p. 109).
Captain James Colnett’s visit to the Galapagos archipelago deserves to be men-
tioned only because he adds Abingdon Island to the list of those in which Tortoises
occur (‘Voyage to the South Atlantic,’ Lond. 1798, 4to, p. 152). Also Capt. Basil
Hall landed on this island in 1822, where he found plenty of large Tortoises, of which
he laid in a stock which lasted the ship’s company for many weeks (‘ Extracts from a
Journal,’ Edinb. 1824, 8vo, 2nd edit. vol. ii. p. 140).
Twenty-two years had passed since Porter’s cruise, when Darwin visited the Gala-
pagos in the ‘Beagle’ in the year 1835. A change, by which the existence of these
animals was much more threatened than by the casual visits of buccaneers and whalers,
had taken place. The Kepublic of the Equator had taken possession of the archipelago,
and a colony of between two and three hundred people banished by the Government
had been established on Charles Island, who reduced the numbers of Tortoises in this
island so much that they sent parties to other islands (for instance, James) to catch
Tortoises and salt their meat (‘ Journal,’ pp. 375, 376). Pigs had multiplied, and were
roaming about in the woods in a feral state. Darwin adds many interesting observa-
tions on the habits of these Tortoises; but as his ‘Journal’ is in everybody’s hands, I
quote from his account such parts only as have a special bearing on questions with which
we shall have to deal in this treatise. He confirms Porter’s observation as regards
their deafness, also that “ the old males are the largest, the females rarely growing to
so great a size. The male can readily be distinguished from the female by the greater
length of its tail” (p. 382). An egg which he measured was 7f inches in circumfer-
ence, a measure nearly identical with that found by Porter. “ The old ones seem gene-
rally to die from accidents, as from falling down precipices. At least, several of the
inhabitants told me they had never found one dead without some evident cause”
(p. 384). “The Vice-Governor, Mr. Lawson, declared that the Tortoises differed from
the different islands, and that he could with certainty tell from which island any one was
brought. . . . M. Bibron, moreover, informs me that he has seen what he considers two
distinct species of Tortoise from the Galapagos, but he does not know from which
islands. The specimens that I brought from three islands were young ones, and, pro-
bably owing to this cause, neither Mr. Gray nor myself could find in them any specific
differences ” (p. 394).
After an interval of not quite eleven years, H.M.S. ‘ Herald ’ followed the ‘ Beagle ’
on a voyage of discovery and survey. The naturalist of that expedition, which reached
the Galapagos in the year 1846, found that the progress of civilization had been great
(‘Narrative of H.M.S. Herald,’ by B. Seemann, Lond. 1853, 8vo), or, in other words,
that the displacement of the indigenous fauna by man and his companions had pro-
ceeded apace. On Charles Island “ the cattle had increased wonderfully, and were esti-
258
DR, A. GUNTHER ON GIGANTIC LAND-TORTOISES.
mated at 2000 head, beside wild pigs, goats, and dogs. . . . The wild dogs keep the goats
and pigs very much down ” (vol. i. p. 57) ; but “ no turpin, or terrapin, are living on this
island ” (p. 59) ; that is, the Tortoises had been exterminated between the visits of the
‘ Beagle ’ and the ‘ Herald.’ On Chatham Island “ we saw, for the first time, the terrapin
or galapago .... We bought them at the rate of six shillings apiece. They were 2 feet
2 inches in length, 1 foot 10 inches broad, standing 1 foot 2 inches off the ground.” No
specimens were brought home by this expedition.
We have no means of ascertaining from recent accounts the present condition of the
indigenous fauna of these islands. Possibly most of the larger natural-history collec-
tions possess one or several examples of the Galapagos Tortoise; but the majority of
specimens are young, or fragmentary, or without any history ; and there will be found
scarcely one with an indication of the particular island from which it came ! Therefore
the difficulties encountered by the zoologist who undertakes the study of these Tortoises
will be easily understood.
There is no doubt that so singular an animal type as this Land-Tortoise, grown up
within so well-defined an area as the Galapagos, and repeated with almost identical modi-
fications of development at the opposite end of the globe, the Mascarenes, would have
yielded the most valuable material towards solving the question of the genesis of species
if a complete set of examples from every island had been secured for examination. This
is now impossible, the causes of their extermination having been at work for so long a
time. What happened in the Mascarenes has commenced in the Galapagos. From the
account of the voyage of the 4 Herald ’ there cannot be any doubt that of one race at
least, that of Charles Island, we shall never see a complete example again ; and with
regard to the others, it will be most difficult to obtain one of those colossal individuals
which required many scores of years of undisturbed life to attain to the size attested
by Delano, Poetee, and Daewin. Under these circumstances I could not hope that
the scanty material preserved in British collections would be materially increased within
the next years, or that science would be more benefited if this inquiry, already deferred
too long, were put off to a later period ; and, however incomplete the following account
may appear, it will have this effect at least, that these animals, hitherto so much
neglected in our collections, will be carefully preserved, and that advantage will be
taken of every opportunity of contributing towards our better knowledge of them.
In the descriptive portion of this memoir I propose to treat of these Tortoises under
three heads : —
1. The Tortoises of the Galapagos Islands.
2. The recent races of the Tortoises of the Mascarenes.
3. The extinct races of the Mascarenes.
DE. A. GtJNTHEE ON GIGANTIC LAND-TOETOISES.
259
Paet II.— DESCEIPTION OF THE GALAPAGOS TOETOISES.
General Characters.
Tortoises inhabiting the Galapagos archipelago may be recognized and distinguished,
more especially from the living Mascarene Tortoises, by the following characters : —
The nuchal plate is constantly absent.
The posterior margins of the two gular plates are convergent, meeting at a more or
less obtuse angle, never forming a straight, or nearly straight, transverse line.
Neck and legs long.
The shell is black.
One of the scutes on the inner side of the elbow is conspicuous for its size, much
larger than those surrounding it.
In the skull the crown is flat ; the palate moderately concave ; the front part of the
intermaxillary truncated, elevated.
The symphyseal bridge between the foramina obturatoria of the pelvis is flat, broader
than deep.
Osseous carapace very thin. Nuchal vertebrae and limb-bones elongate.
Among the carapaces which have formed a part of the material for this memoir, I
can distinguish five forms; of the first four severally two are more nearly related to
each other than to the other pair, the fifth being intermediate between these two pairs.
In the first pair the shell is of a broader form, with more or less corrugated plates;
in the second it is elongate and perfectly smooth.
a. In one species of the first pair the shell is depressed, with the upper anterior profile
subhorizontal in the male, and with the striae of the plates not deeply sculptured ; the
sternum is truncated behind (Plate 33. fig. A) : Testudo elephant opus,
(3. In the other species the shell is considerably higher, with declivous anterior profile
in the male, and with the striae of the plates much more deeply sculptured ; the sternum
has a triangular excision behind (Plate 33. fig. B, and Plate 35. fig. C.) : Testudo nigrita.
y. In one species of the second pair the shell shows some traces of former concentric
striae, is compressed into the form of a “Spanish saddle” in front in the male; the
sternum is truncated behind (Plate 34 and Plate 35. fig. B) : Testudo ephippium.
In the other species the shell is perfectly smooth, with declivous anterior profile in
the male, and with truncated posterior extremity of the sternum (Plate 36) : Testudo
microphyes.
e. In the last species the shell is depressed, as in the first, with the upper anterior
profile subhorizontal in the male, and with the lateral anterior margins reverted so as
to approach the peculiar shape of T. ephippium ; the striae are distinct and broad ;
sternum of peculiar shape, much constricted and produced in front, and expanded and
excised behind (Plate 35. fig. A) : Testudo vicina.
The degree of distinctness and affinity which obtains in the carapaces is expressed
260
DB. A. GrtjJNTHEE ON GIGANTIC LAND-TOETOISES.
clearly and in exactly the same manner in the skulls. In the skulls of the broad form
of carapace and sternum the palatal region is more concave than in the other ; the outer
pterygoid edge is sharp in its entire length, or for the greater part of its length ; there
is a deep recess at the base of the skull in front of the occipital condyle, and the
anterior wall of the entrance into the tympanic cavity is considerably constricted.
a. The first species (T. elephantopus ) is distinguished by a very short snout, and by
an immensely developed and raised occipital crest (Plate 38. fig. A).
j8. In the second ( T . nigrita) the facial portion is longer and the occipital crest low
(Plate 88. fig. D).
In the skulls of the narrow form, the palatal region is shallow, the outer pterygoid
edge flattened in its whole length ; there is no deep recess at the base of the skull in
front of the occipital condyle, and the anterior wall of the tympanic cavity is bulging-
outwards, not constricted.
y. In T. ephippium the tympanic cavity is much produced backwards, the tympanic
opening elliptic, and the impression in front of the tympanic pedicle is very shallow
(Plates 37 & 38. fig. C).
b. The skull of a perfectly adult T. microphyes is only 83 millims. long, and has the
characteristics of a young skull of one of its more gigantic congeners, neither the occi-
pital crest nor the tympanic case being produced backwards. The impression in front
of the tympanic pedicle is rather deep (Plates 37 and 38. fig. B).
e. Finally, the skull of T. vicina has all the characteristics of that of T. ephippium ,
hut differs from it in having a circular tympanic opening.
These observations fully bear out Porter’s and Darwin’s statements that the various
islands are inhabited by distinct species. Unfortunately we do not possess positive and
exact information as regards the localities whence our examples were obtained ; but
Porter’s accounts are sufficiently detailed to enable us to relegate with more or less
ce tainty some of the species before us to the places of their nativity. James Island
yielded Tortoises of the broad, circular type ; and therefore either T. elephantopus or
T. nigrita came from that island, probably the former. There can be no doubt that we
have in T. ephippium the species inhabiting Charles Island ; and T. microphyes is most
probably the representative from Hood’s Island. We may suppose that other specific
forms exist ; but there is no evidence of them in the material before me.
In young examples, which are rather common in collections, the distinctive characters,
external or osteological, are incompletely developed, so that it is, at present, extremely
difficult and somewat hazardous to refer very young individuals (up to about 15 inches
in length) to the species to which they belong. This resemblance of young examples
cannot be used as an argument against the distinctness of the various species, as gene-
rally, in Vertebrates as well as Invertebrates, specific characters are not developed before
a certain period, which varies exceedingly even in groups nearly related to one another.
DR. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
261
Specific Descriptions.
1. Testudo elephant ojpus.
The Tortoise to which Harlan (Journ. Ac. Nat. Sc. Philacl. v. 1825, p. 284) gave
this name was only 21 inches long over the curvature, or about 17 inches in a straight
line, and therefore a young animal. A reference to the measurements and figure given
by Harlan shows clearly that he had an animal with the broad form of the body and
with a posteriorly truncated sternum, characteristics by which a small series of examples
before me are distinguished, and more especially one individual of nearly the same size
as that described by Harlan.
Dumeril and Bibron (Erpetol. Gener. ii. p. 115) identify Harlan’s example with one
deposited by Quoy and Gaimard in the Paris Museum under the name of Testudo nigra.
This specimen is still smaller than Harlan’s, and of an age at which the specific
characters are not yet developed ; and therefore there is no evidence whatever to show
that this identification by Dumeril and Bibron is correct ; and as long as it is uncertain
to which of the specific forms the young “ T. nigra ” should be referred, the name had
better be disused altogether. Dumeril and Bibron associate with this young specimen
another of large size, distinguished by its broad form, smooth plates, and posteriorly
excised sternum, but without giving any convincing proof that these two examples are
of the same species. I have not seen an example agreeing in all points with that large
example, and it may possibly be another species distinct from those described here.
The materials which I refer to T. elephantopus are the following : —
1. An adult male example : a perfect skeleton with carapace, but without epidermoid
plates. The carapace is 31 inches long. History of the specimen unknown ; property
of the Oxford Museum, and kindly lent to me by Professor Rolleston, F.R.S. (Plate 33.
fig. A).
2. An immature female example: a perfect skeleton with carapace, but without epi-
dermoid plates. The carapace is 28^ inches long. Hal. Galapagos Islands. Property
of the Royal College of Surgeons. Notes on this example by Professor Owen in
Descript. Catal. Osteol. Ser. R. Coll. Surg. i. 1853, p. 194. no. 1011.
3. Carapace, without epidermoid plates, of an immature male example, 23 inches
long. History unknown. Property of the Free Public Museum, Liverpool.
4. Carapace, with epidermoid plates, of a young example, 18 inches long. Sex and
history unknown. Property of the Free Public Museum, Liverpool.
5. A living example, 15^ inches long, obtained by Captain E. M. Leeds (s.s. ‘ Tasma-
nian ’) at Colon, and presented by him to me. This will be deposited in the British
Museum after its death.
Carapace. — In our largest example (specimen No. 1) (Plate 33. fig. A), which has
been prepared into a skeleton, the outlines of the epidermoid plates can be clearly
traced. It is a fully adult male, which, to judge from the condition of the bones, had
ceased to grow a long time before its death ; the dorsal portion of the shell is extremely
MDCCCLXXV. 2 N
262
DR. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
thin, in some parts quite transparent*. There is almost a total absence of anterior
declivity of the first dorsal scute, its front margin being but very little below the level
of the highest point of the carapace. The sides of this fore part of the carapace are
expanded, not contracted as in T. ephipjgium. The caudal plate must have had a dif-
ferent shape from that of T. nigrita, being twice as wide as long (5 inches by 2 f inches) ;
however, these measurements are taken from the osseous base without the horny
covering, which probably would have been somewhat longer. The sternum is 24f inches
long, and 23 inches broad between the lateral margins of the abdominal plates. It is
deeply concave, and when the animal rested on the ground, it touched it with the sides
of the sternum, which are thicker than the remainder of the carapace, and on a trans-
verse terminal callosity produced by the reverted posterior margin of the sternum, which
is straight, truncated, without excision.
Another male example (specimen No. 3) agrees in every respect with the preceding,
except in the sexual characters being much less developed, the specimen being only
23 inches long, and therefore much younger. The first dorsal scute is more declivous
towards the front, the concavity of the sternum less deep, and its terminal callosity
only indicated by the very porous and rough surface of the bone.
In our young example (18 inches long, specimen No. 4) the concentric strise are
numerous, but not deeply cut ; and in this respect the present species is intermediate
between T. nigrita and T. ephippium. The posterior end of the sternum is nearly
truncate, the hind margin of each anal plate being obtusely rounded, and the plates
being separated by so shallow a notch that, evidently, with advancing age, the sternum
would have assumed the same truncate shape which we find in the adult specimens.
It remains to add the principal measurements of the specimens examined: —
Length of carapace. Width of carapace. Sternum. Caudal plate.
In str. line. Over curv. In str. line. Over curv. Length. Width. Length. Width.
Spec. no. inches. inches. inches. inches. inches. inches. inches, inches.
1. e 31 37f 26. 40 24f 23 2ff 5
2. $ 28f 361 23 35 22f 19
3. 6 23 27^ 18 29 18f - 16f Iff 3f
4. $1 ... 18 22 12i 19f 14 12 If 3
5. $1 ... 15i 18i Hi 19 12i 11 If 2f
~ Falconer, in his notes on Colossochelys atlas (Palasontolog. Mem. vol. i. p. 378), states that “ the thickness
of hone in the convexity is almost in an inverse ratio to the size. The physiological reason of this is, that the
smaller the animal, the more liable it is to injury, and it requires a greater arch to sustain it.” This view is
not confirmed by an examination of the living Tortoises ; the Aldabra species is as large as those from the
Galapagos, and even larger than one of these latter, yet it has a much thicker shell. We shall see that the
extinct Mascarene species agree with the Galapagos Tortoises in this respect. Perhaps the cause of this is to
be sought in the small quantity of earthy matter contained in the food on which those animals chiefly subsist,
viz. succulent cacti. A living Galapagos Tortoise in my possession prefers, at present, the petals of a Westeria
to every other plant. Of course, by the thinness of the shell its weight is much reduced, and these Tortoises
are therefore able to walk faster and to carry the shell higher above the ground than the other species of this
genus. The thinness of the shell and the slender osseous framework of the limbs are, in fact, characters correlated
to each other. f Without epidermoid scutes.
DE. A. G-UNTHEE ON GIGANTIC LAND-TOETOISES.
263
Osteology. — In the preceding remarks, as well as in the following notes on the osteo-
logical characters of the various species, it is not my intention to give such a complete
description as would include every detail common to all the species of Testudo ; but I
shall limit myself to those points only by which the various species of gigantic Tortoises
differ from one another in a marked manner.
The skull, then, of our adult example of Testudo elegghantopus (specimen No. 1, fig. A
of Plates 37—39) is distinguished by a very short snout and a singularly raised occipital
crest; it is 4-f inches long, measured from the front margin of the intermaxillary to the
occipital condyle, and 4 inches broad in its widest part, between the zygomatic arches.
1*. The frontal region is perfectly flat, broad, passing into the very short snout, its
greatest width (in front of the postfrontals) being as much as one half of the distance
between the tympanic condyles. 2. The occipital crest is enormously developed; it
rises abruptly above the level of the skull, is strongly compressed and scarcely attenuated
behind, its extremity being broad and rounded. 3. The tympanic case, with the mastoid,
is produced backwards, the hind margin of the paroccipital forming a rather strong
curve (fig. A, a). 4. A deep hollow on the lower surface of the occipital in front of
the condyle (Plate 39. fig. A, b). 5. On the front margin of the temporal fossa, corre-
sponding to the suture between parietal and tympanic, and immediately in front of the
foramen carotidis externae , there is a large, prominent, concave rough tuberosity for the
insertion of a portion of the temporal muscle (Plate 37. fig. A, c); a broad and deep
groove ( d ) separates this tuberosity from the zygomatic arch. 6rj\ Tympanic cavity
large, but constricted by the groove just described; the outer tympanic rim is subcir-
cular, with a broad and deep notch (e) in the posterior part of its circumference for the
passage of the Eustachian tube. 7. The columella is attached to, and rests upon, a long,
straight, sharp ridge, which runs from the notch mentioned to the stapedial foramen.
8. The posterior wall of the inner tympanic cavity, which, in fresh examples, is formed
by cartilage, and an open space in the preserved skull after maceration, is but limited
in extent, about one seventh of the area of the tympanic opening. 9. The front margin
of the intermaxillary projects beyond that of the frontal, but much less than in the
Mascarene Tortoise, so that the nasal opening, although still obliquely sloping down-
wards, is as high as broad. 10. The position of the choanse is advanced forwards ; yet,
on the palatal view of the skull, a portion of them may be seen uncovered by the alve-
olar lamellae of the maxillaries (Plate 39. fig. A). 11. The intermaxillaries are short,
* In this and the following descriptions of the skulls the same points are noticed under the same numbers,
a plan by which the comparison of the several parts (sometimes described many pages apart) is much facilitated.
The significance of certain modifications of structure noticed here will become more apparent when we shall
treat of the skulls of'the Mascarene Tortoises.
i It is very singular that although the osseous parts of the auditory organ are so well developed, nevertheless,
according to the unanimous testimony of the observers, these Tortoises are absolutely deaf. I find this con-
firmed so far in my young living example that it never takes notice of the noisy approach of a person whom it
cannot see, nor is it disturbed by the fall of a stone behind its back. Perhaps the faculty of hearing, although
never acute, is not entirely lost until the individuals have attained to a great age.
2 hr 2
264
DE. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
one half of the length of the maxillaries ; their foremost portion is deeply hollowed out
below, and vertically bent downwards to form the truncated beak. The suture between
the intermaxillary and vomer is immediately behind the inner angle of the alveolar
edges of the maxillaries. 12. The palatal region is much less concave than in the
Aldabra Tortoise, and divided along its middle by a high longitudinal crest. The
triangular space of which the foramina palatina and the anterior extremity of the vomer
form the points is nearly isoscelous in shape, in accordance with the generally short
longitudinal axis of the skull. Outer pterygoid edge (f) rather elevated and sharp.
13. Anterior surface of the tympanic pedicle deeply excavated.
14. Lower jaw with a double alveolar ridge; its symphyseal portion simply vertical,
without a backward expansion of the lower margin of the bone. The parts of the
angular and coronoid which face each other are closely approximate, leaving only a
narrow cleft between them. Upper margin of the angular deeply excised.
The cervical portion of the vertebral column is characterized by its relatively great
length . All observers were struck by the length of the neck, which the animal is in the
habit of erecting so that the head is raised above the level of the shell. A living animal
now before me can turn its head in this position to the right or left, reminding one of
a Cobra rising in a posture of defence. This slenderness of the neck is not due to an
increase in the number of vertebrae (which is constant in Tortoises as in Mammals, and
limited to eight), but to their elongated shape. In T. elephantopus they are not quite
so slender as in T. rodericensis, but much more so than in the species from Aldabra.
Also the spinal canal is narrower than in this latter round-headed form. The crests of
the dorsal as well as visceral surface are well developed, and sometimes accompanied
by low additional crests. All the articulary processes diverge comparatively but little,
and those which in the Aldabra species are nearly perpendicular to the longitudinal
axis of the vertebra, are oblique and much depressed in T. elephant opus.
In the atlas (Plate 40. fig. A) the lateral portion of the neural arch (column) is very
much constricted, not broader than the zygapophysis, which is elongate and considerably
longer than that part of the bone which forms the roof of the arch. The centrum
(odontoid process) (a) is a rhombohedral body.
In the second vertebra the neural arch is remarkably compressed and elevated, also
provided with a high neural crest. The third has a condyle in front, and a glenoid
cavity behind*. The fourth is biconvex. The fifth (Plate 40. fig. C) has a glenoid
cavity in front and a condyle behind ; its median neural crest is low, and accompanied
on each side by two other crests which diverge in the direction of the posterior zyga-
pophyses. The sixth (Plate 40. fig. D) has a glenoid cavity in front and a condyle
behind ; its dorsal surface is flat, without crest, whilst on its visceral surface a low crest
is evenly continued along nearly the whole length of the vertebra. The seventh biconcave
vertebra (Plate 41. fig. B) is distinguished by the high crest on its dorsal and visceral
* We shall see in the following part of this essay that these articulations of the cervical vertebrae are some-
what modified in the Aldabra species.
DR. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
265
surface; in the middle of the vertebra the neural crest is split into two branches,
diverging in the direction of the zygapophyses and leaving a deep triangular recess
between them. The point of divergence forms a kind of summit ( a ) to this vertebra.
The neural arch is deeply hollowed out (5) inwards of and behind each anterior zyga-
pophysis to receive the zygapophysis of the preceding vertebra ; but no perforation of
the bone takes place as in the extinct species of Rodriguez. The eighth vertebra, with
its bipartite anterior and single posterior condyle, and with its expanded hamate poste-
rior zygapophysis, does not differ from that of the Aldabra species.
The measurements of the second to seventh cervical vertebrae are as follows : —
2nd.
3rd.
4th.
5th.
6th.
7th.
millims.
millims.
millims.
millims.
millims.
millims.
Length of centrum
. 55
67
85
83
85
74
Depth of centrum in the middle
co
28
27
27
28
53
Horizontal width of middle of centrum 15
17
18
20
29
27
Width of anterior condyle
. 15
20
19
Width of anterior glenoid cavity
30
34
40
Width of posterior condyle . . .
27
32
37
Width of posterior glenoid cavity .
. 19
20
43
Distance of outer margins of anterior' ]
zygapophyses J
j. 23
CO
35
38
40
38
Distance of outer margins of posterior ,
zygapophyses J
J. 25
26
28
30
29
46
Of the dorsal vertebrae scarcely more than the measurements need to be noticed ; these
are of some importance in comparison with the corresponding vertebrae in other species
and also with the cervical vertebrae. The two heads of the first rib are slender, much
divergent, leaving a wide triangular space between them and the first dorsal vertebra.
The iliac bones abut against the pleurapophyses of the 9th, 10th, 11th, and 12th ver-
tebrae, counting from the first dorsal vertebra. Their distal extremities unite to form
the protuberance for the articulation of the ilium.
Length of centrum of dorsal vertebrae : —
1st. 2nd. 3rd. 4th. 5th. 6th. 7th. 8th. 9th. 10th. 11th. 12th.
mm. mm. mm. mm. mm. mm. mm. mm. mm. mm. mm. mm.
65 80 80 80 78 55 48 48 16 14 16 22
The number of caudal vertebrae I have found to be the same in both our skeletons,
viz. twenty- three.
Iamb-bones. — In the scajgulary (Plate 44. figs. C, C') we notice the very
obtuse angle at which the scapula and acromium meet. The body of the
scapula proper is rather slender, compressed, trihedral in form, with its
anterior side convex, as shown in the annexed figure, which represents a
transverse section through its middle. The coracoid is not anchylosed
to the scapula. The measurements of this bone are the following: —
266
DE. A. QUA THEE ON GIGANTIC LAND-TOETOISES.
millims.
Length of scapula (measured from the suture with the coracoid) . 200
Circumference in its middle 75
Longitudinal diameter of glenoid cavity 50
Length of coracoid 86
Greatest width of coracoid 70
Length of acromium 84
The shaft of the humerus (Plate 42. figs. A, A') is moderately slender, subtrihedral,
with the edges well rounded off. There exists a deep impression on the outer side of
the bone, immediately below the head and ulnar tuberosity (a), and another transverse
impression on the hinder side above the trochlea. The ulnar tuberosity projects high
above the head, which is nearly entirely raised above the level of the summit of the
radial tuberosity. The canal (5) for the blood-vessels on the radial edge of the bone,
close; to the elbow-joint, is perfectly closed, perforating the substance of the bone from
the front to the hinder side.
millims.
Length of the humerus, measured in a straight line from the summit
of the head to the middle of trochlea 216
Circumference of the narrowest part of the shaft 89
Longest diameter of the head 40
Shortest diameter of the head 37
Extreme breadth between the condyles 82
The bones of the forearm do not show any noteworthy peculiarity; but, for the sake
of comparison with some of the following species, I give the measurements : — The ulna
has a length- of 137 millims., and a width of 28 millims. in its narrowest part; the
radius a length of 121 millims., and a circumference of 50 millims., also measured in
its narrowest part.
As in Testudo generally, so here the carpal bones (Plate 44. fig. D) are arranged in
three series, of which the proximal consists of two bones, lunare and cuneiforme, both
articulating with the end of the ulna ( u ) ; the middle of the transversely elongate
scaphoid and “ intermedium ; ” and the distal of five small rounded bones corresponding
to, and articulating with, the five metacarpals. The scaphoid articulates with the end of
the radius (r), the “intermedium” being intercalated between the lunare and third
digit. However, in our old specimen of this species there exists the peculiarity that the
scaphoid and intermedium are coalesced into a single very long bone (a), and that the
two radial ossicles of the distal series are similarly united (b).
Pelvis (Plate 43). — In the first place must be noticed the considerable horizontal
width of the symphyseal bridge ( a ) between the obturator foramina, by which the flat-
headed Tortoises are so signally distinguished from the round-headed ones. But quite
peculiar to this species is, first, that also the vertical diameter of this bridge is consi-
DE. A. GGNTHEE ON GIGANTIC LAND-TOETOISES.
267
derable, and scarcely less than the horizontal ; and, secondly, that, although all other
sutures in this aged specimen have disappeared, the transverse , suture between the pubic
and ischiadic halves of the bridge is still persistent. The iliac bones are comparatively
slender, the longitudinal diameter of the pelvis much exceeding the horizontal one.
The lower part {b) of the pubic bones is gently inclined downwards and slightly concave
above ; it emits laterally a very long, strong, nearly styliform process (c), which is
obliquely directed outwards. The posterior part (d) of the ossa ischii is of considerable
width, very slightly concave above, and provided with a trenchant symphyseal crest
below, which, expanding towards behind, forms a large triangular tuberosity. Lateral
margin of the ossa ischii excised in the shape of a C. Obturator foramina of moderate
width, considerably wider than the bridge between them, which is not provided above
with a median longitudinal crest.
millims.
Longest inner vertical diameter of pelvis (from summit of ilium to
symphysis) 170
Longest inner horizontal diameter of pelvis 132
Shortest inner horizontal diameter of pelvis (between ilio-pubic pro-
minences) 112
Longest diameter of foramen obturatorium 42
Width of symphyseal bridge 26
Depth of symphyseal bridge 26
Least breadth of posterior portion of ossa ischii 61
Length of os ilii 140
Least breadth of os ilii 30
The shaft of the femur (Plate 44. figs. A, A', A") is rather stout, nearly straight, irre-
gularly subtetrahedral, narrower in front than behind. The head has an elliptical form,
and does not rise above the level of the summit of the larger trochanter, from which it
is separated by a deep and broad cavity. The larger (a) and lesser ( b ) trochanters are
confluent into one broad ridge, and not separated from each other by a smooth groove,
as we shall find to be the case in some of the following species. The length of the
femur in this example is 169 millims., with a least circumference of 80 millims. ; the
width of the condyles is 66 millims.
Of the lower leg no part deserves to be mentioned particularly. The tibia is 136
millims. long, and the fibula 123 millims.
Also the bones of the foot may be passed over, with the exception of one point, viz.
that, like some bones of the carpus, the astragalus and calcaneum are entirely coalesced,
so that no trace of their former separation remains.
2. Testudo nigrita.
No doubt can possibly be entertained as regards the correct application of this name
to the species which I am about to describe. It had been given by Dumeril and
268
DR. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
Bibron (‘ Erpetol. Gener.’ ii. p. 80) to two examples, of which the smaller, very young
one, is in the Paris Museum, whilst the larger, but also of young age*, is the property
of the Royal College of Surgeons. Bibron’s description is almost entirely drawn up
from the latter specimen, which, therefore, must be regarded as the type. However, I
suspect that the very young example which Dumeril and Bibron have associated with
this specimen should not be referred to this species, but possibly belongs to one of the
Mascarene Tortoises. Bibron, in his description of its legs, omits all mention of the
large scute in front of the elbow — a character which, as far as we know at present, is
common to all Galapagos Tortoises, but is absent in the Mascarene species. Further, I
am almost certain that the large skull described by Dr. Gray (Shield Kept. p. 6, pi. 34)
under the name of Testudo planiceps belongs to the present species, for the following
reasons: — 1. There is that circumstantial evidence, that we are acquainted with the
adult skulls of T. elephant opus ^ T. ephippium , and T. microphyes , hut not with that of
T. nigrita. The skulls of the three former species have been preserved, together with
their carapaces, but the skull belonging to the shell of our single adult individual of T.
nigrita is lost. As the skull named T. planiceps differs in a marked manner from all
the others, we may reasonably suppose that it is that of the last-named species. 2. The
British Museum possesses a skeleton of a young T. nigrita ; and although the skull of
this individual has the specific characters not well developed on account of its young-
age, it shows a greater resemblance, especially in its narrower snout, to the skull named
T. planiceps than to any of the three others.
The materials available for the description of this species are the following : —
1. A carapace without sternum of a very large example, 41 inches in a straight line;
it was purchased by the Trustees of the British Museum of the Manager of the former
Surrey Zoological Gardens, who could not give any information as regards its history
(Plate 33. fig. B).
2. A carapace 22 inches longf ; type of Testudo nigrita (D. & B.) ; property of the
Royal College of Surgeons ; history and sex unknown. I am indebted to Prof. Flower,
F.R.S., for the loan of this specimen (Plate 35. fig. C).
3. The perfect skeleton with epidermoid plates of a young example, the carapace
being 15^ inches long. History and sex unknown. In the British Museum.
4. A very young example, stuffed, in the British Museum ; carapace 8^ inches long.
This specimen was purchased of a collector coming from Chile, and therefore without
doubt came originally from the Galapagos Islands. A figure of it, somewhat reduced
in size, has been given by Dr. Gray, under the name of T. elephantopus , in Proc. Zool.
Soc. 1870, p. 706, pi. 41 +
* Bibrox considered it to be an adult example ; and its relation to the Galapagos Tortoises appears to have
escaped his notice entirely.
t Bibrox gives 365 millims. as the length of this example, which is evidently a misprint for 565.
+ An example of about the same age is rather indifferently figured in Sowerby and Lear’s ‘ Tortoises, Turtles,
and Terrapins,’ where it is named Testudo indica.
DR. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
269
5. A skull of a very large example, described and figured by Dr. Gkay as T. pla-
niceps (1. c.).
The. carapace of this species is well characterized by its broad, circular shape, great
depth, and more especially by the numerous, deeply cut concentric striae, by which the
areolae are much reduced in size in immature examples, and which are persistent in
considerable number even in specimens of the largest size. Our largest example
(specimen No. 1, Plate 33. fig. B) is a carapace 41 inches long, unfortunately without
the sternum. Nevertheless we can safely affirm that this individual was a male, all
observers agreeing in that the females do not attain to so large a size. It is only
8 inches longer than broad, and when measured over the curvature its transverse
circumference even exceeds the longitudinal. The areolar portions of the dorsal and
marginal plates are perfectly smooth and raised above the general outline of the shell,
especially those of the former ; but each plate has a broad margin deeply sculptured
with concentric and parallel striae, the outer striated margin of the marginal plates being
even broader than the smooth areolar portion. The first dorsal scute and the anterior
half of the second are declivous, the declivity of the former being still steeper than that
of the latter.
A deep notch, nearly as deep as that between the two foremost marginal plates, exists
between the first and second marginals ; and also the posterior margin of the shell is
scalloped. The length of the caudal plate is to its width as 11 : 14 (5-| inches long and
7 inches wide) ; its surface is plane, that is, its posterior margin is not bent either
inwards or outwards. The general colour is a deep black, with a brownish tinge about
the margins of the majority of the plates.
As in the preceding species, the shell is thin and light ; in this specimen it is only
4 millims. thick in the middle of a costal plate. Specimens of the common Testudo
grceca only about 8 inches long have a carapace almost as thick as these gigantic
Tortoises.
The second specimen (Plate 35. fig. C), which is 22 inches long and the type of T.
nigrita, is young, and probably a male, inasmuch as the sternum shows a slight con-
cavity, and the passage between the hind margins of the caudal and sternal plates is
of inconsiderable width. As in specimen No. 3 (15^- inches long), the carapace is
deeply sculptured all over, the smooth areolae being very small. Its transverse circum-
ference equals the longitudinal. The front margin, as well as the hind margin, is
deeply notched, each notch corresponding to the suture between two marginal plates.
The outer surface of the caudal plate is convex, the hind margin being curved inwards ;
its length is to its width as 3 : 4. The sternum terminates anteriorly in a thickened,
rounded, double-headed transverse knob, with a slightly concave surface below; and
posteriorly in a deep rectangular notch. The colour is the same as in the adult example.
Our very young example, which is only 8^ inches long, and figured in Proc. Zool.
Soc. 1. c., agrees in every respect with those of more advanced age, differing from young
mdccclxxv. 2 o
270
DE. A. GUNTHEE ON GIGANTIC LAND-TOETOISES.
examples of the same size of T. ephippium by the greater relative width of the carapace.
The principal measurements of the specimens, described, are as follows : —
Length of carapace. Width of carapace. Sternum. Caudal plate. .
In str. Line.
Over curv.
In str. line.
Over curv.
Length.
Width.
Length.
Width.
Spec. no.
inches.
inches.
inches.
inches.
inches.
inches.
inches.
inches.
1. (J
. . . 41
52
33
53
51
7
2. 6
. . '. 22
27
16
27
181
15f
3
4
3. .
. . . 151
191
11
19
12
91
21
If
4. .
00
101
6
101
61
6
11
1
The skull (Plates 37-39. fig. D) is distinguished by its comparatively longer facial
portion, and by the much produced mastoid processes ; it is (see also Geay, Catal.
Tort. 1855, 4to, tab. 34) 51 inches long, measured from the intermaxillary to the occi-
pital condyle, and 41 inches broad at its widest part, viz. between the tympanic pro-
cesses. 1. Its frontal region is flat, narrow, its greatest width being two sevenths of
the distance of the tympanic condyles. 2. Only the foremost part of the parietals
forms a flat surface, the remainder being compressed into an almost trenchant crest,
passing into the long narrow occipital spine, which is scarcely raised above the level of
the skull (Plate 38. fig. D). 3. The tympanic case with the mastoid is produced far
backwards, so that the paroccipital margin appears as a deep semicircular excision
(Plates 38 & 39. fig. D, a). 4. A very deep hollow on the lower surface of the
occipital, in front of the condyle ( b )*. 5. On the front margin of the temporal fossa,
corresponding to the suture between parietal and tympanic, immediately in front of the
foramen carotidis extern®, there is a large, prominent, flat, rough tuberosity (c) for the
insertion of a portion of the temporal muscle ; a broad, not very deep groove (d) sepa-
rates this tuberosity from the zygomatic arch. 6. Tympanic cavity exceedingly large,
especially its posterior portion, the entrance being somewhat narrowed by the groove
just mentioned; the outer tympanic rim is a regular circle, with a shallow notch in its
hinder circumference for the passage of the Eustachian tube. 7. This notch is very
remote from the columellar foramen, and a sharp ridge runs the whole distance from
the notch to the foramen, serving as a rest for the auditory ossicle. 8. The posterior
wall of the inner tympanic cavity, which in fresh examples is formed by cartilage and
an open space in the preserved skull, is of but small extent, only about one eighth of
the tympanic opening. 9. The front margin of the intermaxillaries projects beyond
that of the frontals, but much less so than in the Mascarene Tortoises, so that the nasal
opening, although still obliquely sloping downwards, is scarcely higher than broad.
10. The inner nostrils are advanced, not very distant from the end of the snout, and on
the palatal view of the skull are nearly entirely hidden below the alveolar lamella of
the maxillaries. 11. The intermaxillaries are short, not quite one half of the length
of the maxillaries, and their foremost portion is deeply hollowed out below, and verti-
* In the figure given by Dr. Gray the artist has entirely omitted to express the depth of this hollow by
shading.
DR. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
271
cally bent downwards to form the truncated beak. The suture between the intermax-
illary and vomer is immediately behind the inner angle of the alveolar edges of the
maxillaries. 12. Palatal region much less concave than in the Mascarene Tortoises,
and provided with a rather high median longitudinal crest ; posteriorly it is bordered
on each side by the raised pterygoid edge, which is obtuse in its anterior, and trenchant
in its posterior half. The distance between the foramina palatina is much less than
their distance from the anterior extremity of the vomer. 13. Anterior surface of the
tympanic pedicle deeply excavated. 14. Lower jaw with a double alveolar ridge, the
symphyseal portion being simply vertical, without a backward dilatation of the lower
margin of the bone. The opposite surfaces of the angular and coronoid are closely
approximate, leaving only a narrow cleft between them. Upper margin of the angular
moderately excised.
The skull of our young example is o'nly 2^- inches long ; it shows some of the charac-
teristics described in the adult skull, viz. the greater depth and the less width of the
palatal region, the deep hollow in front of the tympanic pedicle, and the conformation
of the anterior half of the tympanic cavity. The groove between the temporal tubercle
and zygomatic arch, as well as the hollow in front of the occipital condyle, are clearly
indicated. On the other hand, the tympanic pedicles are less distant from each other
than in the adult, the mastoido-tympanic process is only slightly produced backwards,
and the occipital crest is short and much less prominent — points of difference which can
be accounted for by the young age of the individual.
The description of the skeleton of so young an individual could hardly be accom-
panied by important results as regards the object of this paper, and is therefore
omitted.
Caudal vertebras 24.
3. Testudo ephippium.
I propose this name for a species equally well characterized by the peculiar form of
its carapace and of its skull. Porter’s remarks on the Tortoises of Charles Island
(see ante, p. 256) apply so well to this species that I have no doubt that the specimen
from which the following description is taken came from that island. If this is really
the case, this species is extinct. The specimen is an adult male, 33 inches long, stuffed,
and belongs to the Museum of Science and Arts, Edinburgh. It was lent to me by
T. C. Archer, Esq., Director of the Museum of Science and Art, Edinburgh, who most
kindly allowed the skull and limb-bones to be extracted, which could be effected with-
out the least injury to the outward appearance of the specimen. Nothing is known of
its history.
A very young stuffed example, 7 inches long, in the British Museum is referred to
this species on account of its oblong shape and large smooth areolse.
The carapace (Plates 34 Sc 35. fig. B) is narrow, oblong, and deep ; from the middle
of the central dorsal plate to the front margin of the shell the upper profile is nearly
2 o 2
272
DR. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
horizontal, the fore part of the shell being strongly compressed, concave on each side,
with the anterior margin strongly reverted — this part of the shell having an appearance
which has been so aptly compared by Porter with a “ Spanish saddle.” The hind part
of the shell is rounded, with a steep posterior profile, but more gently declivous on the
sides, the marginal plates above the hind legs being arched outwards with the edge
somewhat reverted, but less so than on the anterior marginal plates. The anterior as
well as the posterior margins are irregularly scalloped. The plates are nearly smooth,
the areolar portions passing gradually into the striated portions ; but the striae them-
selves are inconspicuous, and in many places nearly obliterated. The sternum* is
deeply concave, truncated in front and behind, the substance of the caudal plates and
of the lateral portion of the abdominals being much thickened.
I need not mention the scutellation of the head and legs, none of the Galapagos
Tortoises showing any peculiarity in this respect. The tail is very short, and without
terminal “ claw.”
On comparing the carapace of the young example with that of equally small speci-
mens of other species, we find the areolar spaces larger, the concentric strise deeply
sculptured, but less numerous and further apart. Especially the sternal plates are
smooth, with the striae partly obliterated. Posteriorly the sternum terminates in a
notch (and this appears to be uniformly the case in very young specimens of all the
species) ; but this notch is much shallower than in T. nigrita, obtuse-angular.
The measurements of these two specimens are the following : —
Length of carapace. Width of carapace. Depth of Sternum. Caudal plate.
In str. line. Over eurv. In str. line. Over curv. carapace. Length. Width. Length. Width.
Spec. inches. inches. inches. inches. inches. inches. inches. inches, inches.
Adult . 33 40 23^ 40 17 24 21£ • 3£ 6
Young .7 9f 5 8| 3| 4f 6f 1 1\
Skull. — The skull (Plates 37-39. fig. C) is comparatively smaller than that of T.
elejpliantopus \ it is 4-f inches long, measured from the front margin of the intermaxillary
to the occipital condyle, and 3f inches broad in its widest part between the zygomatic
arches. The sutures between the various bones can be clearly traced ; and growth
evidently had not ceased entirely, an observation confirmed by the examination of other
bones extracted from the specimen. 1. The frontal region is flat, broad, passing into
the very short snout, its greatest width (in front of the postfrontals) being about
one half of the distance between the tympanic condyles. 2. The occipital crest is mode-
rately developed, pointed behind, and rising but little above the level of the upper
surface of the skull. 3. The tympanic case with the mastoid is produced backwards,
the hind margin of the paroccipital forming a rather strong curve (Plate 37. fig. A, a).
4. There is no hollow in front of the occipital condyle ; the space between the condyle
* A large portion in tlie middle of the sternum has been cut out by the person who preserved the animal,
in order to extract the contents of the shell.
DR. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
273
and basisphenoid simply shelving downwards towards the latter (b). 5. On the front
margin of the temporal fossa, in front of the foramen caroticlis externae , there is a large
not very prominent tuberosity ( c ) for the insertion of a portion of the temporal muscle ;
no groove separates this tuberosity from the zygomatic arch ; or, in other words, the
tympanic cavity is not constricted in front. 6. Tympanic cavity very large : the outer
tympanic rim ovate, resembling the outline of the human concha, with the convex side
in front, and the pointed part above ; the notch for the passage of the Eustachian tube
is very broad, but shallow ( e ). 7. The ridge which runs from this notch to the stapedial
foramen, and to which the columella is attached, is rather low and obtuse. 8-11. The
points noticed under these figures in the description of the skull of T. elephant op us
(see page 263) are exactly the same in the present species. 12. The palatal region is
very shallow and broad, in consequence of the outer pterygoid edge being flattened
down and expanded in its whole length (Plate 39. fig. C ,f). The triangular space, of
which the foramina palatina and the anterior extremity of the vomer form the points, is
isoscelous in shape, in accordance with the generally short longitudinal axis of the skull.
13. Anterior surface of the tympanic pedicle with a shallow impression. 14. Lower
jaw with a double alveolar ridge ; its symphyseal portion simply vertical, without a
backward expansion of the lower margin of the bone. The parts of the angular and
coronoid which face each other leave a rather wide cleft between them. Upper
margin of the angular not excised.
Limb-bones. — The following bones have been preserved in our large stuffed example,
and were extracted from it : — The humerus (Plate 42. figs. B, B'), distinguished by its
great length and slenderness ; its shaft is trihedral in the middle, and not much bent.
The two hollows which we noticed in T. elephantopus below the head and above the
trochlea are here absent. The ulnar tuberosity ( a ) projects high above the head, which
is nearly entirely raised above the level of the summit of the radial tuberosity. The
canal ( b ) for the blood-vessels on the radial edge, close to the elbow-joint, is deep and
partly open, cutting off, as it were, a splint from the radial extremity of the bone.
T. elephantopus ,
790 mUlims. long.
miUims.
Length of the humerus, measured in a straight line)
from the summit of the head to the middle of l 216
trochlea J
Circumference of the narrowest part of the shaft . 89
Longest diameter of the head 40
Shortest diameter of the head 37
Extreme breadth between the condyles .... 82
T. epliippium ,
840 millims. long,
millims.
235
91
40
35
82
The bones of the forearm (Plate 45. fig. B) are, like the humerus, comparatively
slender ; they are remarkably smooth, without prominent ridges or tuberosities. The
ulna has its radial edge but slightly emarginate, and is twisted round its longitudinal
274
DR. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
axis, so that the transverse diameters of its proximal and distal dilatations would inter-
sect each other at an angle of about 50°. The olecranon is not much developed. The
articulary facet of the radius for the articulation with the humerus is a rectangular
triangle, with the point directed backwards, and the shortest side in front.
Length of ulna .
Least width of ulna
T. elephantopus ,
790 millims. long.
•millima.
. 137
28
T. ephippium,
840 millims. long,
millims.
155
26
Length of radius 121 149
Least circumference of radius 50 51
Only a few of the carpal bones have been extracted from the specimen, among them
the scaphoid and “ intermedium,” which have remained perfectly separate.
In the pelvis (Plate 45. fig. A) we notice, in the first place, that all the sutures are
present, and that growth was still proceeding in their vicinity. However, on the whole,
the pelvis does not differ in a marked manner from that of T. elephantopus , except that
the symphyseal bridge is broader (the obturator foramina, consequently, narrower) and
not so deep. The posterior part of the ossa ilii also is broader than in the other species.
Other slight differences of form may be seen from the accompanying comparative mea-
surements : —
T. elephantopus, T. ephippium,
790 millims. long. 840 millims. long,
millims. millims.
Longest inner vertical diameter of pelvis (from)
summit of ilium to symphysis) j
Longest inner horizontal diameter of pelvis . . 132 118
Shortest inner horizontal diameter of pelvis) ^
(between ilio-pubic prominences) . . . ./
Longest diameter of foramen obturatorium . . 42 42
Width of symphyseal bridge 26 35
Depth of symphyseal bridge 26 23
Least breadth of posterior portion of- ossa ischii 61 80
Length of os ilii 140 130
Least breadth of os ilii ........ 30 27
The femur is very similar to that of T. elephantopus (p. 267), with the exception of its
proximal portion (Plate 44. fig. B) : the head has an elliptical form, and does not rise
above the level of the summit of the larger trochanter, as in T. elephantopus, but is con-
siderably smaller ; on the other hand, the cavity separating the head from the trochanters
is much larger, as broad as long, and the two trochanters ( a and b) are widely separated
from each other by a smooth groove.
The bones of the lower leg and carpus do not show any noteworthy peculiarity : as in
DR. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
275
T. elephant opus, the astragalus and calcaneum are coalesced, but, owing to the less
advanced age, the line of separation is still visible.
Length of the femur
T. elephcmtopus,
790 millims. long,
millims.
. . 169
T. ephippium,
840 millims. long,
millims.
186
Least circumference of the femur . .
. . 80
90
Longest diameter of head of femur . .
. . 55
43
Width of the condyles
. . 66
67
Length of the tibia
. . 136
150
Least circumference of the tibia ....
. . 60
72
Length of. the fibula
. . 123
138
Least circumference of the fibula . . .
. . 45
45
4. Testudo microphyes.
This is the smallest of the Galapagos Tortoises, a fully adult male being only 22%
inches long. As Porter states that “ the Tortoises of Hood’s Island were small, similar
to those of Charles Island,” I suppose that the specimen which I propose to describe
under the above name has come from Hood’s Island. It is a fully adult male, stuffed,
with a carapace 22% inches long, and belongs to the Royal Institution of Liverpool.
I am indebted to the Museum-Committee of the Institution not only for having sent to
me the specimen on loan, but also for having permitted the skull to be extracted for
comparison with the other species.
The carapace (Plate 36) is very regularly shaped, its outline being a regular oval,
with scarcely a trace of notches between the marginal plates ; it is depressed. There
is no, or only a very slight, nuchal excision, and the fore part of the shell is declivous
from the centre of the second dorsal plate. The caudal and the two adjoining marginals
are slightly concave, this part of the shell being somewhat arched outwards. The plates
of the back, as well as sternum, are perfectly smooth, without a trace of concentric
striae*; the sternum is deeply concave, truncated in front and behind. As an (probably)
individual peculiarity, must be noticed the confluence of the two anterior marginals into
one plate on each side. The tail, as in the other Galapagos Tortoises, is short, without
terminal claw. Although it is impossible in these stuffed specimens to state in precise
terms the length of the neck, yet, from the manner in which the skin had been stretched
by the taxidermist in our specimen, it is evident that the neck must have been con-
spicuously shorter in this species than in the others.
The measurements are as follows : —
Length of
carapace.
"Width of carapace.
Depth
Sternum.
Caudal plate.
In str. line.
Oyer curv.
In str. line. Over curv.
of carap.
Length.
Width.
Length.
Width.
inches.
inches.
inches.
inches.
inches.
inches.
inches.
inches.
inches.
. . 221
26
15i
29
10
18
14
2
03
°8
* Also Dum£bil and Bebrox (l. c. p. 117) describe an entirely smooth specimen, which they refer to T. nigra
(Q. & G.) ; hut they mention that the sternum of that specimen had a triangular excision behind.
276
DR. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
Skull. — The skull of the adult male (Plates 37-39. fig. B) is 3^ inches long, measured
from the intermaxillary to the occipital condyle, and 2^ inches broad in its widest
part, viz. between the zygomatic arches. In general appearance it has a great resem-
blance to the skulls of young examples of the larger species ; yet nearly all the sutures
have disappeared, so that the example is evidently a fully adult individual. It is thus
another instance of a wrell-known fact, viz. that often small species retain through life
the juvenile characters of their larger and more fully developed congeners. The skull
is conspicuously more similar to that of T. ei^lii'p'pium than to those of the first two
species, as will be seen from the following notes : — 1. The frontal region is flat, very
broad, passing into the very short snout, its greatest width (in front of the postfrontals)
being rather more than one half of the distance between the tympanic condyles. 2. The
occipital crest is comparatively short, pointed behind, and scarcely rising above the level
of the surface of the skull. 3. The tympanic case, with the mastoid, is but little pro-
duced backwards, the hind margin of the paroccipital (a) being nearly straight.
4. There is no hollow in front of the occipital condyle, the space (b) between the con-
dyle and basisphenoid gently shelving downwards towards the latter. 5. On the front
margin of the temporal fossa, in front of the foramen carotidis external, there is a broad
concave prominence ( c ) for the insertion of a portion of the temporal muscle ; no groove
separates this prominence from the zygomatic arch ; or, in other words, the tympanic
cavity is not constricted in front. 6. Tympanic cavity of moderate size, the posterior
portion being particularly small : the outer tympanic ring is subcircular ; the notch (e)
for the passage of the Eustachian tube rather narrow, but deep. 7. The ridge which
runs from this notch to the stapedial foramen, and to which the columella is attached,
is rather low and trenchant. 8-11. The points noticed under these numbers in the
descriptions of the skulls of T. elejohantojpus (p. 263) and T. ephippium (p. 273) are exactly
the same in the present species. 12. The palatal region is moderately shallow and not
very broad, but the outer pterygoid edge is expanded as in T. ephippium. The distance
between the foramina palatina is conspicuously less than that between one of these
foramina and the anterior extremity of the vomer. 13. Anterior surface of the tym-
panic pedicle with a deep impression. 14. Lower jaw with a double alveolar ridge ; its
symphyseal portion is simply vertical, without a backward expansion of the lower margin
of the bone. The parts of the angular and coronoid which face each other are closely
approximate. Upper margin of the angular not excised*.
* With regard to the skull of a very young example in the British Museum, I still hesitate to refer it to this
species. There cannot be any doubt that it belongs either to T. ephippium or to T. microphyes , having the
pterygoid edge expanded in the manner by which those two species are so well characterized. But the occi-
pital spine is more produced backwards than I should have expected to find it in the young of T. microphyes ,
the adult of which has this process comparatively short. However, the outer tympanic rim has exactly the
suhsemicircular shape of that species, and not the ovate outline of T. ephippium.
DB. A. GUNTHEE ON GIGANTIC LAND-TOBTOISES.
277
5. Testudo vicina.
A few days after the preceding notes had been delivered to the Royal Society (see
Proc. Roy. Soc. 1874, June 18th) I received, through the kindness of Professor Huxley,
Sec. R.S., the carapace and skeleton of another adult male example, which on closer
inspection proved to be a highly interesting addition to our knowledge of these Tortoises.
Unfortunately no record of its history has been preserved ; but the condition of the
bones, which have retained a large quantity of fat, clearly shows that the animal had
been living within a very recent period, and therefore came from the Galapagos, and
not from one of the Mascarene islands *.
The form of the carapace (Plate 85. fig. A) reminds us of that of T. elepliantojpus , but
it is still more depressed, the greater part of the two middle costal plates participating
in the formation of the plane surface of the back. The first dorsal scute is but very
slightly declivous towards the front, and the edge of the shell along the three anterior
marginals is reverted and scalloped ; thus the fore part of the shell has in a slight
degree the form of a saddle, but it is much less compressed than in T. ephippiwm.
The striae of the plates are very distinct, but shallow, and distant from one another
(broad), occupying the greater part of the surface of each plate. The striated portions
of the plates are not of the same intense black as the smooth ones, but more or less
tinged with brown. The shape of the sternum differs from that of the preceding species,
its gular portion being singularly constricted and having the lateral margins excised.
The gular plates are truncated in front. The opposite end of the sternum is dilated,
the caudal plates being expanded like wings ; their hind margins meet at an obtuse
angle. All the plates of the sternum, with the exception of the pectorals and abdo-
minals, are striated like the dorsal plates. The surface of the sternum is deeply concave.
There is in the British Museum a young stuffed example, with a carapace 12iy inches
long (without particular indication of its origin), which I am inclined to refer to this
species. It has the same depressed shell as the adult, with a similar striation of the
plates, and with the anterior margins distinctly reverted ; but the sternum is not con-
stricted anteriorly, nor are the caudals expanded like wings. At present we have not
the means of judging whether this difference could be accounted for by age or sex;
however, as the skull of this young individual agrees singularly well with that of the
adult, there is good reason for believing it to be a second example of the same species.
* My endeavours to trace in the various Collections the specimens which are known to have reached England
alive within the last forty years have been hitherto singularly unsuccessful ; and the present example is the
only one which might he supposed to be possibly identical with the individual reported to have been sent to the
Zoological Society in 1834, by the Hon. Byrox Caky, from the Galapagos (Proc. Zool. Soc. 1834, p. 113).
That specimen is said to have weighed 187 lbs., and measured in length, over the curve of the dorsal shell, 44|
inches (I find in our specimen 41| inches), and along the sternum 25§ inches (as in ours) ; its girth round the
middle was 75J inches (69 inches according to my measurement). It is added that “ the lateral compression
of the anterior part of the dorsal shell, and the elevation of its front margin .... are in this specimen strongly
marked.”
2 p
MDCCCLXXV.
278
DR. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
The measurements of the two specimens are as follows : —
Length of carapace. Width of carapace. Depth Sternum. Caudal plate.
In str. line. Over cnrv. In str. line. Over curv. of carap. Length. Width. Length. Width.
Spec. inches. inches. inches. inches. inches. inches, inches, inches, inches.
Ad. <5 38 41£ 25 42 16 25£ 24 4£ 6|
Young ... 121 i4i 9 141 51 1Q1 8£ 1£ 2}
Skull. — The skull * is 4-| inches long, measured from the front margin of the inter-
maxillary to the occipital condyle, and 4 inches broad in its widest part, between the
zygomatic arches ; therefore it is comparatively larger than that of T. ephippium. The
sutures between the various bones can still be traced ; and from the condition of the rest
of the skeleton it is evident that growth had not entirely ceased in this specimen. The
skull is extremely similar to that of T. ephippium ; so that the skulls alone, without the
evidence gained from other parts of the skeleton, would hardly afford sufficient grounds
for specific separation. The points in which the two skulls differ are the following
only: — (6) The outer tympanic rim of T. vicina (Plate 41. fig. A) has a subcircular
outline, and (7) the ridge which runs from the Eustachian notch ( e ) to the stapedial
foramen, and to which the columella is attached, is high and rather sharp. (13) The
impression in front of the tympanic pedicle is much deeper than in T. ephippium.
The skull of our young example is only 2 inches long, and agrees in every respect
with the adult, except that the parietal crest is less compressed and the tympanic case
less produced backwards, as in all skulls of the young of these Tortoises.
Cervical vertebras. — On comparing the neck-vertebrae of T. vicina with those of T.
elephant opus, we find them generally to be somewhat less slender, and with the crests
and ridges less developed ; otherwise they are formed according to the same type, and
the first, seventh, and eighth are the only vertebrae which exhibit peculiarities indi-
cative of specific distinctness. In the atlas (Plate 40. fig. B) the lateral portion of the
neural arch is but little constricted, at least as wide as the broad zygapophysis, which
is longer than that part of the bone which forms the roof of the neural arch. In the
seventh vertebra (Plate 41 . fig. C) the summit (a) of the neural crest is not single as
in the other species, but split into two prominences, separated from each other by a
deep notch. In the eighth vertebra the haemal crest is produced forward to the level
of the anterior articulary surface, and almost hamate in form, whilst it does not extend
beyond the middle third of the length of the centrum in T. elephantopus.
* A reduced figure of this skull is given iu Huxley’s ‘ Elementary Atlas of Comparative Osteology,’ pi. 3,
but, owing to the elementary object of that work, the details of the specific characters to which attention is
drawn in this paper are not sufficiently well expressed ; indeed it would be impossible to render some of them
conspicuous in a figure reduced in size.
DR. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
279
Measurements of cervical vertebrae : —
2nd.
3rd.
4th.
5th.
6th.
7th.
millims.
millims.
millims.
millims.
millims.
millims
Length of centrum
. 47
65
88
80
82
72
Depth of middle of centrum .
. 34
26
25
26
25
49
Horizontal width of middle of centrum 14
18
17
20
25
27
Width of anterior condyle . . .
. 15
18
20
Width of anterior articular cavity .
36
42
41
Width of posterior condyle . . .
25
28
39
Width of posterior articular cavity .
. 19
23
50
Distance of outer margins of anterior
zygapophyses J
j- 20
33
38
37
42
33
Distance of outer margins of posteriory
zygapophyses J
l 28
31
31
35
28
55
Dorsal vertebrae. — The last of the three vertebrae which emit pleurapophyses to form
the protuberance for the articulation of the ilium is the eleventh, so that only eleven
vertebrae can be assigned to this part of the vertebral column. Of the two heads into
which the first rib bifurcates the posterior is more slender than the anterior ; the
triangular space enclosed by them is wide, but less so than in T. elephant opus. For
comparison with the latter species I give the length of the centra of the several dorsal
vertebrae : —
Dorsal vertebrae
1st.
2nd.
3rd.
4th.
5th.
6th.
7th.
8th.
9th.
10th.
llth.
12th.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
mm.
Test, elephantopus
. 65
80
80
80
78
55
48
48
16
14
16
22
Test, vicina . .
. 56
80
87
87
79
61
43
32
17
15
18
(21)
Caudal vertebrae twenty in number, but it is possible that the last rudimentary ossicle
has been lost.
Limb-bones. — Singularly enough the resemblance which we notice between the skulls
of this species and T. ephippiurn does not uniformly extend to the other parts of the
skeleton, the limb-bones of T. vicina being much shorter and stouter than in that
species, approaching more T. elephantopus. The scapulary (Plate 45. figs. C, C') espe-
cially is stout and massive. The angle at which the scapula and acromium meet is
much less obtuse than in T. elephantopus (about 100°) ; the body of the scapula is com-
pressed, elliptical, with both its anterior and posterior sides equally convex ; a trans-
verse section through its middle would be represented by the figure of a greatly elon-
gate O. The shaft of the acromium is trihedral, with the edges rounded, and with
the extremity compressed and slightly dilated. The coracoid is not anchylosed to the
scapula, and its proximal part (neck) is singularly dilated, and very much broader than
the corresponding part in T. elephantopus. In fact the differences in the scapularies of
2 p 2
280
DR. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
these two species are so great, that they alone would clearly prove
their specific
distinctness.
T. elephantopus,
T. vicina,
790 millims. long. 840 millims. long.
millims.
millims.
Length of scapula (measured from the coracoid")
suture)
•J
200
188
Circumference in the middle of the shaft
75
75
Longitudinal diameter of glenoid cavity .
50
55
Length of coracoid
86
83
Greatest width of coracoid
70
74
Least width of neck of coracoid ....
20
33
Length of acromium
84
78
The humerus is so similar to that of T. elephantopus (and consequently very dis-
similar to that of T. ephippium) that no detailed description is needed;
but, as in the
latter species, the canal for the blood-vessels on
the radial edge, close
to the elbow-
joint, is deep and partly open.
T. elephantopus. T. ephippium.
T. vicina.
millims.
millims.
millims.
Length of humerus
216
235
225
Circumference of the narrowest part of the)
1 L
shaft )
89
91
95
Longest diameter of the head ....
40
40
40
Shortest diameter of the head ....
37
35
38
Extreme breadth between the condyles
82
82
81
The bones of th e forearm (Plate 45. fig. D) are also shorter than those of T. ephippium.
more similar to those of T. elephantopus , particularly with regard to the deeply emar-
ginate radial edge of the ulna. Both bones are smooth, without prominent ridges or
tuberosities. The ulna is twisted round its longitudinal axis, so that the transverse
diameters of its proximal and distal dilatations would intersect each other at an angle of
about 45°. The olecranon is not much developed. The articulary facet of the radius
for the articulation with the humerus is a rectangular triangle, with the point directed
backwards, and the shortest side in front.
Length of ulna
T. elephantopus ,
790 millims. long,
millims.
. . . 137
T. ephippium ,
840 millims. long,
millims.
155
T. vicina ,
840 millims. long,
miliims.
137
Least width of ulna
. . . 28
26
26
Length of radius ....
. . . 121
149
122
Least circumference of radius
. . . 50
51
49
DR. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
281
Carpus. — The coalescence of the scaphoid and intermedium, and of the two radial
ossicles of the third series, which we have found complete in T. elephantopus, has
commenced in the present individual, but the lines of separation are still clearly
visible.
The pelvis differs from that of T. elephantopus in the same manner as does that of T.
ephippium, but its horizontal diameter is comparatively greater than in either of those
two species. All the sutures are present.
T. elephantopus,
T. ephippium,
T. vicina.
790 millims. long.
840 millims. long.
840 millims. long.
millims.
millims.
millims.
Longest inner vertical diameter of pelvis .
170
160
157
Longest inner horizontal diameter of pelvis .
132
118
144
Shortest inner horizontal diameter of pelvis .
112
97
97
Longest diameter of foramen obturatorium .
42
42
38
Width of symphyseal bridge
26
35
41
Depth of symphyseal bridge
26
23
26
Least breadth of posterior portion of ossa)
ischii j
61
80
76
Length of os ilii
140
130
134
Least breadth of os ilii
30
27
29
The femur agrees nearly entirely with that of T. elephantopus, thus differing from that
of T. ephippium in the same points which have been indicated in the description of the
latter species. The bones of the lower leg and carpus do not show any noteworthy
peculiarity, the state of coalescence of the astragalus and calcaneum being the same as
in some of the carpal bones mentioned above.
Length of the femur
T. elephantopus,
790 millims. long,
millims.
. . . 169
T. ephippium,
840 millims. long,
millims.
186
T. vicina,
840 millims. long,
millims.
165
Least circumference of the femur .
. . . 80
90
79
Width of the condyles . . . . ,
. . . 66
67
73
Length of the tibia
150
129
Least circumference of the tibia . .
. . 60
72
57
Length of the fibula .
. . 123
138
123
Least circumference of the fibula . .
. . 45
45
43
282
DE. A. G OTHER OX GIGANTIC LAND-TORTOISES.
Explanation op the Plates.
PLATE 33.
Pig. A. Three views of carapace of Testudo elephantopus ; specimen in the Oxford
Museum ; jr the natural size.
Fig. B. Three views of carapace of Testudo nigrita ; specimen in the British Museum ;
-g- the natural size.
PLATE 34.
Testudo ephippium, from the typical specimen in the Museum of Science and Arts,
Edinburgh ; -g- the natural size.
PLATE 35.
Fig. A. Three news of Testudo vicina , from the typical specimen in the British
Museum.
Fig. B. Lower view of the carapace of Testudo ephippium.
Fig. C. Three views of Testudo nigrita juv., from the typical specimen in the Collection
of the Royal College of Surgeons.
All these figures are ^ of the natural size.
PLATE 36.
Testudo microphyes , from the Museum of the Philosophical Institution of Liverpool ;
the natural size.
PLATE 37.
Upper views of the natural size of the skulls of : —
Fig. A. Testudo elephantopus.
Fig. B. Testudo microphyes.
Fig. C. Testudo ephippium.
Fig. D. Testudo nigrita.
a. Posterior margin of paroccipitaL.
c. Tuberosity for the insertion of a portion of the temporal muscle.
d. Groove separating the tuberosity Rom the zygomatic arch.
PLATE 38.
Lateral views of the natural size of the skulls of : —
Fig. A. Testudo elephantopus.
Fig. B. Testudo microphyes.
Fig. C. Testudo ephippium.
Fig. D. Testudo nigrita.
e. Notch for the passage of the Eustachian tube.
DE, A. GUXTHEE OX GIGAXTIC LAXD-TOETOISES.
283
PLATE 39.
Lower views of the natural size of the skulls of : —
Fig. A. Testudo elephantopus.
Fig. B. Testudo microphyes.
Fig. C. Testudo ephippium.
Fig. D. Testudo nigrita.
а, c, d , e as in Plates 37 & 38.
б. Hollow in front of occipital condyle.
f. Outer pterygoid edge.
PLATE 40.
Fig. A. Upper and lateral views of the atlas of Testudo elephantopus.
a. Centrum.
Fig. B. Upper and lateral views of the atlas of Testudo vicina (centrum lost).
Fig. C. Three views of the fifth cervical vertebra of Testudo elephantopus.
Fig. D. Three views of the sixth cervical vertebra of Testudo elephantopus.
All the figures are of the natural size.
PLATE 41.
Fig. A. Tympanic region of Testudo vicina.
e. Xotch for the passage of the Eustachian tube.
Fig. B. Three views of the seventh cervical vertebra of Testudo elephant opus,
a. Summit of neural crest.
h. Hollow behind the anterior zygapophysis.
Fig. C. Three views of the seventh cervical vertebra of Testudo vicina.
a. Bifurcate summit of the neural crest.
All these figures are of the natural size.
PLATE 42.
Fig. A. Front view of the humerus of Testudo elephantopus.
Fig. A'. Back view of the same.
Fig. B. Front view of the hwmenis of Testudo ephippium.
Fig. B'. Back view of the same.
a. Ulnar tuberosity.
h. Badial canal for blood-vessels.
These figures are two thirds of the natural size.
284
DE. A. GUNTHER ON GIGANTIC LAND-TORTOISES.
PLATE 43.
Throe views, of two thirds of the natural size, of the pelvis of Testudo elephantopus.
Fig. A. Front view.
Fig. B. Side view.
Fig. C. Top view.
a. Symphyseal bridge between the obturator foramina.
b. Lower portion of the pubic bones.
c. Styliform process of the pubic bones.
d. Posterior part of the ossa ischii.
PLATE 44.
Figs. A, A'. Front and side views of the femur of Testudo elephant opus.
Fig. A". Top view of the same.
a& b. The confluent larger and lesser trochanters.
Fig. B. Top view of the femur of Testudo ephippium.
a. Larger trochanter separated by a wide groove from
b. Lesser trochanter.
Fig. C. Scapulary of Testudo elephantopus.
Fig. C'. Another view of the upper portion, to show the relative position of the coracoid
and acromium.
Fig. D. Carpus of Testudo elephantopus.
u. Ulna.
r. Radius.
a. Coalesced scaphoid and os intermedium.
b. Coalesced two radial ossicles of distal carpal series.
All these figures are two thirds of the natural size.
PLATE 45.
Fig. A. Top view of the pelvis of Testudo ephippium.
Fig. B. Forearm of Testudo ephippium.
u. Ulna. r. Radius.
Fig. C. Scapulary of Testudo vicina.
Fig. C'. Another view of the upper portion, to show the relative positions of the cora-
coid and acromium.
lig. D. Forearm of lestudo vicina.
u. Ulna.
r. Radius.
[ 285 ]
VIII. On the Development of the Teeth of the Newt, Frog, Slowworm, and Green Lizard.
By Charles S. Tomes, M.A. Communicated by John Tomes, F.B.S.
Received July 23, — Read December 10, 1874.
The researches of Goodsir, constituting as they did a very material advance in knowledge,
became so deeply graven upon the minds of scientific men that subsequent investigations,
tending to modify his conclusions in important particulars, have attracted less attention
than is their due.
As long ago as 1853 Professor Huxley (Quart. Journ. Microscop. Science, vol. i.)
published the statement that, in the frog and mackerel at all events, the tooth-germs
are at no time in the condition of free papillae ; and in the same paper correctly described
the connexion existing between the oral epithelium and the enamel-organ in the fully
formed dental sacs. Thus, although Professor Huxley accepted as in most particulars
accurate the account given by Goodsir. of the sequence of events in the formation of
the human tooth-sac, he in some degree anticipated the discovery made by Professor
Kolliker some years later (Zeitschrift f. wiss. Zool. 1863), that in several Mammalia
the tooth-germs never pass through any papillary stage, but are from the first deep
below the surface.
These observations have been confirmed and extended by Waldeyer (see his article
in Stricker’s ‘ Histology,’ Syd. Soc. Translation, p. 481), by Dursy (Entwickelungsge-
schichte des Kopfes, 1869), and by Legros and Magitot (Journal de 1’Anat. et Phys. Ch.
Robin, 1873); and it has been established to full demonstration that in mammals
i. There is never, at any stage, an open groove from the bottom of which papillae
rise up.
ii. That the first recognizable change in the vicinity of a forming tooth-germ is a
dipping down of a process of the oral epithelium, looking, in section transverse to the
jaw, like a deep simple tubular gland, -which descends into the submucous tissue and
ultimately forms the enamel-organ.
iii. That subsequently to the descent of the so-called enamel-germ, the changes in the
subjacent tissue resulting in the formation of the dentine-papilla take place opposite
to its end, and not at the surface.
iv. That the permanent tooth-germs first appear as offshoots from the epithelial process
concerned in the formation of the deciduous tooth-germ (Kolliker) — the first permanent
molar being derived from a primary dipping down (like a deciduous tooth), the second
deriving its enamel-germ from the epithelial neck of the first, and the third from that
of the second (Legros and Magitot).
MDCCCLXXV. 2 Q
286
MR. C. S. TOMES ON THE DEVELOPMENT OE THE TEETH
The error in Goodsir’s observations was not a very radical one, and was probably, at
that date, almost inevitable, inasmuch as the processes by which more modern investi-
gators have the advantage of seeing structures in situ were not then discovered : never-
theless, though the error in fact was not great, the deductions based upon it effect a
wider divergence from the truth ; and the terms “papillary stage,” “follicular stage,” &c.
should be abandoned, as inapplicable to the phenomena observed in any teeth whatever
which have been satisfactorily examined. The development of the simple teeth which
have no enamel, and that of the teeth of Fish, Batrachia, and Beptilia, has been but
little investigated, though the very early appearance of the enamel-germ in other Mam-
malia lends an additional interest to the inquiry.
I was myself fortunate enough to obtain specimens of foetal armadillos, from which
I was able to establish that, although not a particle of enamel was formed, the sequence
of events was identical with that observed in other mammals *, viz. a dipping down of
epithelium to form an enamel-organ, which differed in minor respects only from that
found where enamel is really formed (Quart. Journ. Microsc. Science, Jan. 1874).
The literature relating to the development of the teeth in Batrachia and Reptiles is
somewhat scanty.
Professor Owen, in his ‘Anatomy of Vertebrates ’ (vol. i. p. 389), reiterates the state-
ment contained in his ‘ Odontography,’ where h£ says, “ The teeth of Reptiles are never
completed at the first or papillary stage ; the pulp sinks into a follicle and becomes
enclosed by a capsule ; ” while a more detailed description is given of the process as it
occurs in the frog, to be again referred to. He also states, “ Dentine and cement are
present in the teeth of all Reptiles.”
He also draws comparisons between the condition permanently retained in reptiles
and various transitory stages of human dentition, which are necessarily open to the same
objections which apply to his descriptions of development, inasmuch as they arise out
of these latter descriptions.
Some advances, however, towards a more correct appreciation of the process have
been made. In the paper of Professor Huxley’s already referred to, it is more than once
clearly stated that the teeth of the frog do not pass through any papillary stage, but
from the first are contained in sacs beneath the surface ; and some years later Dr. Lionel
Beale (Archives of Dentistry, 1864) published some observations upon the common
newt, in which he found that the whole process of formation of the tooth-sac took place
beneath the epithelium, which was intimately concerned in its formation. I am unable
to entirely concur in his description of either the mode of origin or the structure of
the tooth-sacs ; but I have less hesitation in expressing a difference of opinion from
* My attention has since been drawn to an observation of Professor Turner’s, who found a structure homo-
logous with the enamel-organ in a narwhal (Journal of Anat. & Phys. Nov. 1872); this, which I had over-
looked, is, I believe, the first notice of a functionless enamel-organ ; but unfortunately sections showing its
structure and relations undisturbed do not appear to have been made, he having other and more important
points under investigation in this same specimen.
OF THE NEWT, FEOGr, SLOWWOEM, AND GrEEEN LIZAED.
287
so careful and skilled an observer, inasmuch as I am convinced that the facts can hardly
be made out without studying hardened sections, a method of manipulation not, I
believe, in this instance practised by him.
A few years subsequently Letdig (who appears to have overlooked Dr. Beale’s paper)
published, in the ‘Archivf. Naturgeschichte’ (1867), an account of the development of the
teeth of the Salamander, in which he arrives at conclusions very similar. He believes
that the tooth develops in a sac which is a purely epithelial formation, and that the tooth-
papilla, and hence the whole tooth, is entirely epithelial. The figures which he gives are,
however, far from being accurate representations of what takes place in the newt ; but I
have been so unfortunate as to fail in procuring a fresh salamander this summer. Santi
Sikena (Centralblatt f. d. med. Wiss. No. 48, 1870) gives a brief account of an examina-
tion of some Batrachians and Reptiles ; but there are no figures, and the descriptions are
too short to be very definite. Grouping the Frogs and Lizards together, he states there
are no marked differences to be noted from the process as known in Mammalia, save that
the teeth become attached to the bone by the ossification of the tooth-sac ; he contrasts
the development of the frog’s tooth, which takes place in a special sac, with that of the
newt, which he states to be developed freely* in the mucous membrane.
The newt ( Triton cristatus ) being in some particulars easier to study than the
other creatures examined, I will commence the description of my own observations
upon it.
The teeth, examined without any prior treatment with acids, are seen to terminate in
two unequal cusps f, sharply pointed, strongly refractive, and of a clear brownish yellow
colour, which recalls that of many rodent incisors (Plate 46. fig. 9). This thin yellowish
cap is so hard and brittle that it is frequently splintered by the pressure of the covering-
glass, and is always lost when the tooth is rubbed down to reduce it in thickness, as it
easily breaks off bodily.
This enamel cap disappears altogether in decalcified sections, in which, therefore, the
bifid character of the tip of the tooth becomes quite inconspicuous.
The teeth are but feebly attached, by anchylosis of the outer side of their bases, to a
parapet of bone (fig. 1), the enamel-tipped apex of the tooth alone projecting above
the level of the epithelium. The inner side of the base of the tooth descends to a much
lower level, and either tapers to a thin edge, or is actually attached to a slight elevation
of the bone (fig. 2).
The epithelium closely embraces the tooth on all sides where it emerges from it,
forming a plane surface ; and there is neither groove nor fissure in which the successional
teeth are developed, as had been generally supposed (figs. 1 & 3).
In the place of the supposed groove there is, immediately to the inner side of the
tooth and its supporting parapet of bone, a region which, to facilitate description, I will
* “ Bei Siredon nnd Triton geht die Entwickelung der Zahne frei in der Schleimhaut vor sich ; beim Frosche
dagegen in einem Zahnsakchen.”
f This bifid termination of the tootb was noted, I believe for the first time, by Leydig.
2 q 2
288
ME. C. S. TOMES ON THE DEVELOPMENT OF THE TEETH
term the “ area of tooth-formation,” inasmuch as it contains nothing but structures con-
cerned in the development of teeth.
Its outer limit has already been mentioned ; on the inner side, toward the median line
of the palate, it has no osseous boundary, but it is nevertheless very sharply defined by
connective tissue (e, figs. 1, 2, 3, & 5).
At the surface, where it is continuous with the epithelium of the mouth, it is narrow ;
but as it becomes deeper it widens, so that the whole area* is roughly triangular in
form, as is seen in figs. 2 & 3.
Along its basal or deepest portion, nearly, though not quite, resting upon the bone,
are ranged, in horizontal series, two, three, or even four tooth-sacs, the youngest lying
nearest to the middle line. A connexion between the apices of the sacs and the epi-
thelium of the surface may be traced with more or less distinctness in every section
through an elongated narrow neck of cells f; to the inner side of the youngest tooth-
sac may also generally be seen a csecal process of epithelial cells (f \ in figs. 2 & 5), and
to the inner side of this again another and shorter epithelial process, which does not
extend so deeply (f in figs. 2 & 5).
The individual tooth-sacs are oval, very slightly flattened at their bases, and sharply
defined ; when it is so viewed that its surface is in focus, this is seen to be made up of
a tesselated epithelium of great regularity, and when it is subjected to pressure it breaks
up into a mass of cells $ and nothing else (fig. 7).
The arrangement of the cells in the tooth-sac appears to have escaped the notice of
previous writers, though it is to some extent analogous with that met with in Mammalia :
there is a dentine-papilla, the cells upon the surface of which are arranged in ah <! odon-
toblast ” layer (figs. 4 & 8) ; and outside this papilla, which is very soon capped with
dentine, comes a layer of columnar epithelial cells, similar to the enamel cells or internal
epithelium of the enamel-organ of mammals. At the base of the dentine-papilla this
layer of columnar cells becomes continuous with a second layer of shorter cells, which
lie externally, and constitute the tesselated epithelium already mentioned as forming
the surface of the sac (figs. 4, 5, 6). The “ enamel-organ” is therefore, like that of the
armadillo, made up wholly of the two layers of cells, without any intermediate tissue.
The continuity of the cells constituting the enamel-organ with the epithelial processes
or necks before alluded to can generally be traced (figs. 1, 2, 3, 5, 6).
The base of the dentine-papilla is sharply defined, and no crescentic processes pass
up from it around the outside of the enamel-organ, to take a share in the formation of
* The upper jaw has been selected for description because the tooth-sacs are less crowded together than
in the lower jaw.
t This was mentioned by Dr. Lionel Beale, who, however, did not trace out its developmental origin ; and
it was observed also by Professor Huxley in the tooth-sac of the mackerel.
j Although there may be some theoretical difficulties in the way of accepting this, I am, after repeated
examination, inclined to concur in the opinion very positively expressed by Dr. Beale, that these sacs have no
limiting membrane whatever.
OF THE NEWT, FEOGr, SLOWWOEM, AND GKREEN LIZAEI).
289
a capsule, as happens in a mammalian tooth-sac ; and although the fibres of the connec-
tive tissue are to some slight extent pushed on one side, so as to be in some measure
concentrically ranged round the growing tooth-sac, yet they do not form any thing like
a definite investment to it. Vessels are abundant in the immediate neighbourhood of
the tooth-sacs ; but they do not appear to enter them, save when the tooth is somewdiat
advanced.
Although I have never been fortunate enough to obtain a specimen in which the
first tooth-sacs were in process of formation*, yet, owing to the very large number of
successional teeth which are formed, it is possible to trace out all the stages of the
process in an adult animal.
The processes of epithelium which are to be found on the inner side of the youngest
tooth-sacs have already been mentioned ; they are very well seen in figs. 2 & 5 (f&fi) '•
thus in fig. 5 we have three stages in the formation of a tooth-sac — namely, the earliest
dipping down of epithelium, as seen at f[, and an epithelial process which has reached
down nearly to the base of the area of tooth-development, while to the right of this is
a fully formed tooth-sac, which, however, still retains its connexion with the epithelial
cells above it.
These epithelial processes, shooting down from the surface into the connective
tissue beldw, which they push out of their way, are clearly homologous with the
“ enamel-germs ” of mammalian teeth ; and just as the enamel-germ of a human per-
manent tooth is given off from the neck of cells which connects the enamel-organ of
the deciduous tooth-sac with the oral epithelium, so in these Batrachian teeth the
enamel-germs of the successional teeth are given off from those of their predecessors f
(see figs. 5 & 7).
AVhen the end of the epithelial process has nearly reached to the base of the area of
tooth-formation, its cells become more distinctly columnar in character, and its end
enlarges, so that it has a spherical form when viewed on its surface ; but seen in section
it presents the appearance shown in fig. 6, in which the extremity of the enamel-germ
has assumed the form of a bell-shaped cap, embracing the dentine-papilla inside it. At
this early period the cells of the enamel-germ next to the dentine-papilla are elongated ;
and the dentine-papilla shows indications of the bicuspidate form of the crown in one
of my sections (fig. 8), though this may perhaps be accidental, as I have not seen it
constantly.
A peculiarity in the appearance of the tooth-sacs of the newt is that they are very
* Professor Huxley informs me that tooth-development in the newt commences at a very much earlier
period than in the frog.
f This reopens the question, are the milk or the permanent teeth of diphyodonts homologous with the single
set of monophyodonts ? — a question which appeared to have been set at rest by Professor Flower’s paper
(Journal of Anatomy and Physiology, 1869). The arguments in that paper appeared to he conclusive in favour
of the view that the milk-dentition was the thing superadded; hut this is difficult -vto reconcile with the deve-
lopmental relation existing between tooth-germs of the two.
290
ME. C. S. TOMES ON THE DEVELOPMENT OP THE TEETH
sharply defined and mapped off from surrounding tissues from the very first. The
dentine-papilla gives rise to no prolongations from its base ; but the whole tooth-sac is
at first nearly spherical (figs, 6, 7, & 8), and I have failed in any section to clearly see
that the dentine-papilla has an origin distinct from the enamel-germ. Nevertheless
the close resemblance borne by the completed tooth-sac of the newt, as well as the
identical relations displayed by its enamel-germ, to that of the Anguis fragilis and
green lizard, in which I have succeeded in tracing the whole process, as well as the
prima facie improbability of such a view, leads me to reject the views advanced by Dr.
Lionel Beale and Leydig, that the whole tooth, including the dentine, is derived from
an epithelial origin'*.
Common Frog. — The general features of the process are closely similar to those
observed in the newt, although there are many differences of detail.
The region designated as the area of tooth-development, which extended far into the
palate in the newt, is very circumscribed in the frog, so that there is not room for
more than one successional tooth-sac at one time (Plate 47. figs. 11, 12, 13).
And instead of the successional tooth-sac attaining to a considerable size without
noteworthy encroachment on neighbouring structures, it obtains space and at the same
time protection by the absorption of a portion of the bony parapet carrying the teeth
or of the tooth itself (see figs. 12 & 13); thus it is not very unusual for the whole
tooth-sac to pass bodily into what corresponds to the pulp-cavity of the tooth already in
place (fig. 12).
This recession of the tooth under some shelter is in a measure a necessary consequence
of the peculiar antagonism of the upper and lower jaws.
The lower jaw has a smooth rounded border and no vestige of a lip; when the
mouth is closed it passes not only within the upper lip, but also within the teeth and
their supporting parapet of bone (see diagrammatic section, fig. 10), and is received into
a groove, which it closely fits, formed between the maxillary parapet and an inward
jutting process which fits beneath the very peculiar tongue (figs. 10 & 11). Of the
* Dr. Lionel Beale says, “ The tooth is not developed from a papilla, consisting of snbbasement tissue, hut
it is formed in the very centre of a collection of cells ; and it is clear that these cells have been formed in the
central part of a preexisting cellular mass, so that the oldest colls, •which seem but to perform the office of a
protecting envelope, are outside, and, as new ones have been produced in the centre, these oldest cells have
become somewhat flattened on the surface, thus giving the appearance of a boundary or imperfect capsule,
which enables us to distinguish these masses from the collection of cells in which they are imbedded.
“ I have seen a single cell, differing from its neighbours in its larger size, dividing to form three or four
separate cells ; and I believe this was the original cell from which all those which constitute the collection in
which the tooth at length appears resulted.”
In this account neither the intimate structure of the sac nor the share taken by the dipping inwards of
the epithelium is mentioned ; nor was Leydig more explicit in his descriptions.
What is meant by Santi Sirena in the statement that the tooth of the newt is developed free in the mucous
membrane, I do not exactly know; but it is clear that he cannot have recognized the very definite structures
which exist, or he would hardly have so expressed himself.
OF THE NEWT, EROG, SLOWWORM, AND GREEN LIZARD.
291
teeth only just the extreme tips project beyond the surface of the epithelium, so that
their functional importance can be but small.
On its inner side the area is, as in the newt, bounded by a connective-tissue frame-
work only (figs. 12, 13, & 14), which is in appearance very different from the tissue
occupying the residual space within the area. The tooth-sacs themselves differ but
little from those of the newt, though the columnar character of the cells composing
the inner layer of the enamel-organ is less strongly marked*.
The connective tissue which is in the neighbourhood of a forming tooth-sac becomes
to some extent arranged round it, though nothing amounting to a definite connective-
tissue capsule is formed ; indeed I have never been able to satisfy myself of the existence
of a membranous investment to these sacs, though I would not go so far as to deny its
existence.
The first step towards the formation of a sac is that inflection of the oral epithelium
(f in figs. 12, 13, 14) which ultimately forms the enamel-organ; but the connexion
between this latter at the apex of the sac with the oral epithelium is not long trace-
able, for the tooth-sac is so close beneath the surface, that it comes to be in contact
with the epithelium along a considerable part of its circumference (figs. 11 & 13).
In close relation with the inner boundary of the tooth-sac is to be found the enamel-
germ for the successional tooth-sac (f, fig. 13); but whether this arises directly from
the epithelium, starting anew, as it were, for the formation of each tooth, or is derived
from the cells going to form its predecessor, is very difficult to determine, as the
migration of the growing sac speedily masks its origin and would destroy any such
connexion. Hence the enamel-germs often stand alone, as in figs. 14 & 12 ; and
appearances lead to the supposition that their origin is quite independent of previous
tooth-germs.
After the tooth has attained to nearly its full size and is displacing its predecessor,
the formative dentine-pulp undergoes change ; the distinct character of the odontoblast
layer is lost, and it becomes metamorphosed into a close-meshed connective-tissue
reticulum, poor in vessels, a single vascular loop being usually all that it presents
(fig. 11). The tooth becomes attached to the bone more securely than that of the
newt, for it is mounted on a more complete pedestal (fig. 11), and not merely soldered
on by its outer edge ; the inner buttress of bone ( d in fig. 11) is not, however, complete,
but is perforated to admit vessels, and also often excavated by the successional tooth-sac.
In the frog, therefore, just as in the newt, there is no such thing as a dental groove,
no such thing as free dental papilla, and no process of encapsulation such as Goodsir
conceivedf.
* If any enamel at all is formed, it is only an exceedingly thin layer. Prof. Owen described an investment
of enamel on the convex surface only, and a layer of cement on the concave surface, a distinction in which I
am unable to follow him. Waldeyeb says that Owen is altogether mistaken in supposing that the frog has
any enamel at all, while Prof. Hxtxeey speaks of the existence of an exceedingly thin layer of enamel,
t Professor Owen (Odontography, p. 185) writes : — “ In the frog the dental germ makes its appearance in
292
ME. C. S. TOMES ON THE DEVELOPMENT OF THE TEETH
Anguis fragilis and Lacerta viridis. — The descriptions of these two forms may be
most conveniently taken together, as no differences of importance have to be recorded
between them. The area of tooth-development exists in them as a sharply defined
region, bounded on its inner side by connective tissue, just as in the newt and the
frog ; but although it is not restricted by extraneous causes, such as the antagonism
of the upper and lower jaws, it nevertheless is not widely extended as in the newt, but
contains only one advanced tooth-sac at one time (Plate 47. figs. 16, 17, 18). The
tooth-sac acquires a more definite connective-tissue investment than was the case in the
frog (fig. 19 and the right-hand lower corner of fig. 22); but this investment, so far as
it can be said to be such, seems to be mainly due to the displacement of a loose connective
tissue in front of the growing tooth-germ, and it plays no active part in the formation
of the tooth. The base of the dentine-papilla also is not so sharply cut off as in the
newt and frog, but it shows an appearance of prolongation from its base upwards
around the end of the enamel-organ (fig. 19).
The enamel-germ appears to be given off from that of the preceding tooth-sac (fig. 19) ;
at least a process is very often discoverable at the side of this latter, although the con-
nexion with the oral epithelium is not lost and appears to be tolerably direct (see figs.
18 & 16) : I am inclined to think that the enamel-germs do not arise from the oral epi-
thelium quite de now for each tooth-sac, but that they may be justly described as succes-
sive branches of a common stem. An early stage of a tooth-sac is represented in fig. 20,
in which the dentine-papilla is seen to be distinct in its origin from the enamel-organ,
but to be a portion of the tissue into which this latter dips down, and to be quite con-
tinuous with the connective tissue which forms an adventitious investment to the whole
sac and to the elongated neck of epithelial cells above it.
The cells which lie upon its surface become elongated to form an odontoblast layer
or membrana eboris, and the whole dentine-papilla speedily becomes differentiated
from the tissue around from which it took its origin.
The enamel-organ presents no special peculiarity ; the inner layer of cells is distinctly
columnar, and the outer more nearly spherical, the enamel-organ consisting exclusively
of these two layers with no intermediate structure (figs. 19, 21).
When a cap of dentine, tipped slightly with enamel, has been formed, the odonto-
the form of a papilla developed from the bottom and toward the outer side of a small fissure in the mucous
membrane or germ that fills up the shallow groove at the inner side of the alveolar parapet and its adherent
teeth ; the papilla is soon enveloped by a capsular process of the surrounding membrane ; there is a small
enamel pulp developed from the capsule opposite to the apex of the tooth ; the deposition of the earthy salts in
this mould is accompanied by ossification of the capsule, which afterwards proceeds pari passu with the calci-
fication of the dental papilla or pulp ; so that, with the exception of its base, the surface of the uncalcified part
of the pulp alone remains normally unadherent to the capsule.” That there is no papillary stage was pointed
out by Prof. Huxley (Joe. cit.), who, however, did not trace out all the details of the process, and makes no
particular mention of the epithelial inflections ; as to the latter part of Prof, Owex’s description, I have never
observed any thing which could be called ossification of the capsule, if, indeed, there he such a structure as
the capsule at all in the sense in which he employs it.
OF THE NEWT, FEOGr, SLOWWOEM, AND G-EEEN LIZAED.
293
blast layer ( o in fig. 22) is very clearly to be seen ; and where it has been accidentally dis-
placed to a slight extent, the dentinal fibrils discovered in the human tooth by my father
may be seen like harp-strings stretching across to the dentine (fig. 22). Beneath the
odontoblast layer comes an areolar tissue framework, much like that which occurs in
mammalian tooth-pulps. Thus in the teeth of the lizards the tooth-pulp attains to a
higher organization, and is less soon converted into a mere connective-tissue reticulum,
than in the newt and frog ; and although we have no actual basis of observation to rest
upon, it is therefore highly probable that the durability of each individual tooth after
it has become attached to the jaw is greater. As the tooth moves up into position the
whole of the structures comprised in the tooth-sac, including the outer loose and ill-
defined investment of connective tissue, go with it.
When its outer border reaches the level of the top of the alveolar parapet (as in figs.
16 & 21) it comes into contact with a tolerably well-defined band of connective tissue,
which runs up from the apex of the bone towards the epithelium of the surface (m in
fig. 21), and, when there is no tooth in place, bounds the area of tooth-formation on its
outer side. This is continuous with the periosteum, and probably plays an active part in
securing the tooth to the bone ; it may be invariably recognized when a tooth is nearly in
place, and was seen by Professor Huxley, who mentions that a membrane may be traced
on to the tooth of the frog from the outer surface of the bone. The precise manner in
which the succession and attachment of the teeth is effected is a matter of much interest,
but is rather beyond the scope of the present communication.
The enamel-organ with its double layer of cells remains distinctly recognizable up to
the time when the tooth comes into position on the bone ; as it does not quite reach
to the base of the dentine-papilla (see fig. 21), it does not intervene between the dentine
and the apex of the bone and its periosteum ; it is lost sight of afterwards*.
On the inner side the characteristic folding over of its cells, where the inner merges
into the outer layer, may be seen after the tooth is in place, closely applied to the surface
of the tooth (see fig. 18).
As this row of cells intervened between the dentine and the capsule, it is quite
certain that the tooth cannot have received any investment from the ossification of the
capsule.
Before any generalizations can advantageously be drawn from these or any other
observations, the subject of the development of the teeth in Fishesf requires further eluci-
dation ; and some investigations which I have commenced in that direction are not as
yet sufficiently extensive to serve as a basis for general statements. The tooth-sacs of the
Anguis fragilis and Lacerta viridis are, however, instructive, inasmuch as they are deve-
* My preparations do not enable me to speak with absolute certainty as to the ultimate disposal of the enamel-
organ ; the point requires further investigation.
t The only reliable description of the tooth -sac of a fish with which I am acquainted, is given by Professor
Huxley in the paper already several times quoted.
MDCCCLXXV. 2 E
294
ME. C. S. TOMES ON THE DEVELOPMENT OE THE TEETH
loped in the midst of mature structures, whereas the tooth-sac of Mammalia arises in
the midst of embryonic tissue.
The substantial identity of the dentine-papilla and of such capsule as exists is well
shown in fig. 20, where the structures going to form the capsule are continuous and
blended with the forming dentine-papilla ; while above this the perfectly distinct origin
of the enamel-organ from an exceedingly elongated process of the oral epithelium is
clearly seen.
A comparison of the tooth-sacs of the newt, frog, and lizard shows many points of
close resemblance, the most noteworthy difference being in the extent to which a
capsule is derived from the base of the dentine-papilla. In the newt the dentine-papilla
ends abruptly, contributing absolutely nothing to the formation of a capsule external to
the enamel-organ, so that the tooth-“ sac” is devoid of a capsule (Plate 46. fig. 6) ; in
the frog it does appear to take some very slight share in the formation of an imperfectly
defined capsule (Plate 47. fig. 15) ; while in the lizard it is distinctly continuous with a
sort of capsule (Plate 47. fig. 19), which is recognizable at all stages of the development
of the tooth.
In this respect, - therefore, as also in the structure of the tooth pulp, the lizard
approximates more closely to the structure of the mammalian tooth-sac than do the
others.
The much vexed general question as to the existence of a “membrana prseformativa ”
can be more profitably discussed when our knowledge of the tooth-sacs of fishes is more
definite ; but nevertheless a few words about it may not be out of place here.
A “ membrana praeformativa,” in the sense in which the older writers used the term,
viz. as a membrane covering the “ dental papilla” in common with the rest of the
surface of the mucous membrane, clearly cannot be said to exist, seeing that the changes
resulting in the formation of a dentine-papilla take place far below the surface, in the
solid substance, so to speak, of the connective tissue. If there is at any time a membrane
proper to the dental papilla, it is a special subsequent formation, having nothing to do
with the basement membrane, and is in its origin quite a different thing from the mem-
brana praeformativa as originally conceived.
It is quite possible, however, that the offshoot from the oral epithelium may carry
down in front of it during its descent into the submucous tissue a pouch of basement
membrane, which would in this case intervene between the enamel-cells and the dentine-
papilla, though it would belong to the former rather than to the latter. Although
there would seem to be an a priori probability in this supposition, the appearances pre-
sented by the epithelial processes in the frog (Plate 47. fig. 14) do not favour the suppo-
sition that they are bounded by a membrane ; they are distorted and destroyed by very
slight pressure or very slight pencilling ; and in the case of the newt, after a tooth-sac
and its surroundings are broken up by pressure, I can discover nothing whatever but
cells.
And, again, the manner in which the connective tissue outside the area of tooth-
OF THE NEWT, FEOGr, SLOWWOEM, AND GEEEN LIZAED.
295
formation in the newt sends up its branching fibres through the epithelium, reaching
almost to its surface (Plate 46. figs. 2, 3, 5), renders it difficult to suppose that a base-
ment membrane intervenes between it and the epithelium. But there is no such diffi-
culty in the case of the frog, in which animal the boundary-line of the epithelium is less
irregular ; and it must be admitted that there is an a priori probability in the enamel-
germ being enclosed within a basement membrane, if this exists between the oral epithe-
lium and the subjacent tissues ; so that I am unable to speak more positively than to say
that I have uniformly failed in demonstrating the existence of such a membrane.
Explanation of the Plates.
PLATE 46.
a. Tooth-bearing process of maxillary bone.
b. Oral epithelium.
c. Neck of epithelial cells connecting the tooth-sac with the oral epithelium.
d. Young tooth-sac.
e. Dense connective tissue, forming the internal limit to the area of tooth-formation.
f. fi- Processes of epithelium (= enamel-germs of Kolliker) which will ultimately
participate in forming tooth-sacs.
h. Formative pulp of the dentine.
k. Cap of dentine.
l. Columnar epithelium of the enamel-organ (enamel cells).
m. Connective-tissue band on the outer side of the area of tooth-formation.
o. Odontoblast layer of dentinal pulp.
t. Completed tooth.
Figs. 1 to 9. From the upper jaw of Triton cristatus.
Fig. 1. From newt half-grown, x 50.
Fig. 2. From newt half-grown (the lip is omitted from this figure), X 50.
Fig. 3. From adult specimen. Teeth in four stages of development are seen within the
area, X 50.
Fig. 4. Young tooth-sac in which the cap of dentine is just formed, X 120.
Fig. 5. Young tooth, showing its relations with the oral epithelium and with the
successional enamel-germ, X 200.
Fig. 6. Termination of epithelial process, commencing to form the enamel-organ of a very
young tooth-sac, x 220.
Fig. 7. Young tooth-sac, viewed on its surface, which is seen to be a tesselated epithe-
lium, x 220.
Fig. 8. Very young tooth-sac, showing odontoblast layer.
2 r 2
296
ON THE DEVELOPMENT OP THE TEETH OP THE NEWT, ETC.
Fig. 9. Apex of tooth, with its enamel cap undisturbed ; the odontoblast layer is also
seen, x 400.
Fig. 11. Lip and margin of upper jaw of full-grown frog, with tooth in place and
to its normal extent, X 50.
Fig. 20. Young tooth-germ of Lacerta viridis, X400, from the same section, as fig. 18.
PLATE 47.
Lettering the same as Plate 46.
Figs. 10 to 15. Common Frog.
Figs. 16 to 22. Anguis fragilis and Lacerta viridis.
Fig. 10. Diagrammatic section of upper and lower jaws of a common frog, X 5.
Fig. 11. See Plate 46.
Fig. 12. Successional tooth-sac beneath the tooth in place; enamel-germ very distinct,
X 120.
Fig. 13. Successional tooth-sac partly buried in the tooth-bearing parapet of bone, X 80.
Fig. 14. Relations of enamel-germ to the area of tooth-formation and to the maxillary
bone, X 220.
Fig. 15. Young tooth-sac prior to the formation of dentine, X 250.
Fig. 16. Upper jaw of Angitis fragilis, showing a tooth ascending into position, a succes-
sional tooth-sac, and the connective tissue to the right of the area of tooth-
formation, X 40.
Fig. 17. Lower jaw of the same, X 40.
Fig. 18. Upper jaw of Lacerta viridis ; to the right of the perfected tooth is a very early
tooth-sac, X 150.
Fig. 19. Young tooth-germ of Anguis fragilis, X 500.
Fig. 20. See Plate 46.
Fig. 21. Relation of tooth-sac to oral epithelium. The band of connective tissue (m) at
the top of the bone, which takes a share in cementing on the teeth, is well
seen (Anguis fragilis). X 150.
Fig. 22. Apex of a forming tooth ; the odontoblast layer of the pulp, with the dentinal
fibrils stretching across to the dentine, is well seen, X 300.
[ 297 ]
IX. On the Structure and Development of the Teeth of Ophidia.
By Charles S. Tomes, M.A. Communicated by John Tomes, F.B.S.
Received October 5, — Read December 10, 1874.
It has been usual to regard the dentine as the most, and the enamel as the least
constant of the dental tissues, the cementum in this respect occupying an intermediate
position* — this relation being held to have been established as a matter of observation,
no less than as a legitimate inference from the process of development. It has, however,
been shown by Kolliker and Waldeyer in the case of mammals, and by Santi Sirena
and myself in the case of Batrachia and Sauria (the present paper extending these
observations to the Ophidia) that the enamel-organ is absolutely the first structure
which can be recognized in the vicinity of a future tooth, and that the dentine-organ or
“ papilla ” can only be recognized at a later stage.
This very early appearance of an enamel-organ would seem to point towards the
enamel being both more important and more widely distributed than would be indicated
by the statement that “ the enamel is the least constant of the dental tissues ”f. I was
not therefore much surprised to find that the teeth of all the Ophidia which I have
examined, amounting to some ten genera, are coated with a thin layer of enamel.
In point of fact the thin layer of transparent tissue upon the outside of the teeth of
Ophidia described by Professor Owen and others as cementum, is not cementum, but is
enamel ; and this conclusion I can support by evidence which appears to me indisputable.
And not only must the generalization that “ dentine and cement are present in the
teeth of all reptiles ” be abandoned, but, so far as my own observations go, the occur-
rence of cementum in the class of reptiles is comparatively rare, and it is in association
with exceptional conditions of attachment when it occurs at all.
I believe that it would be a correct statement, as regards recent reptiles at all events,
to say that the teeth of reptiles consist of dentine, to which is very generally superadded
* Prof. Owen (Odontography, p. 22) says, “ The enamel is the least constant of the dental tissues ; it is
more frequently absent than present in the teeth of fishes ; it is wanting in the entire order of Ophidia among
existing reptiles ; and it forms no part of the teeth of Edentata and many Cetacea among Mammals.”
Of the cement he says (p. 183), “ Dentine and cement are present in the teeth of all reptiles,” this state-
ment being also indorsed by Giebee (Odontographie, p. xvii).
t In Professor Huxley’s paper (Microsc. Journ. 1853) I find the following passage in a footnote : — “ Why
should not it ( i . e. the dense exterior layer upon the teeth of the skate and the mackerel) be called enamel ?
It has at least as much claim to this title as that of the frog.”
Since finding that there is enamel upon Ophidian teeth, I have again examined the teeth of frogs (the bull-
frog, HyJci, common frog), and believe that there is a very thin enamel layer upon all of them.
298
ME. C. S. TOMES ON THE STEUCTUEE AND
an investment of enamel, partial or complete, but that cementum is only present in a
few instances.
The only reptilian teeth which are really coated with cementum, so far as I am aware,
are those which are implanted in more or less complete sockets or in a groove. Thus the
teeth of the Crocodile and of the Ichthyosaurus have cementum upon their basal portions ;
but whether the inference that cementum is in all cases associated with implantation
in sockets will be borne out by a more extended series of observations, I cannot as yet
with certainty say.
In proof of my statement that the thin outer layer upon Ophidian teeth is enamel,
the following facts may be advanced : —
Its refractive index is high, so that it resembles enamel and does not resemble
cementum. It is very brittle*, so that it is often entirely lost in grinding down a thin
section, and is invariably much cracked when it does remain in situ (see Plate 48. fig. 1).
The application of acids to the sections wholly removes it, whereas cementum is even
less affected by acids than is dentine.
But what is more conclusive than all is its development ; it is formed from the
elongated cells of a perfectly characteristic and unmistakable enamel-organ, to be
presently described — a fact which alone would put it beyond all doubt that enamel
is present on the teeth of Ophidia, and that therefore cementum is not.
So far as tlie general plan of formation of individual tooth-germs goes, the teeth
of Ophidia conform pretty closely with those of Mammalia or Sauria ; but whilst the
essential points are adhered to, there is so much difference in matters of detail that at
first sight the sections of the tooth-developing region of a lizard and of a snake are
strikingly dissimilar. And although it is no more than was to be expected from the
other characters of the animal, it may be interesting to note that, in respect of the
development of its teeth, the slowworm is essentially a lizard, and does not show the
smallest tendency towards that arrangement of the successional tooth-germs which is
so eminently characteristic of the Ophidia.
The tooth-germ of a snake consists of a dentine-organ or dentine-papilla (b in
figs. 4 & 5) (which presents no special characters by which it might be distinguished
from that of other animals), an enamel-organ, and a feebly developed connective-tissue
capsule.
The enamel-organ (f in figs. 4, 5, & 8)] embraces the dentine-papillae in its entire
length, and consists almost entirely of the elongated cells which constitute the “ enamel
cells ” or “ internal epithelium of the enamel-organ.” They are nucleated at the
extremity furthest from the dentine, and closely resemble those of other animals. In
* Its brittleness did not escape the notice of Prof. Owev (Odontography, p. 22a), who speaks of it as “more
readily detached from the dentine where it is thickest at the base of the tooth than in other teeth ; portions
of it adhering to the section are shown at fig. 1 aa, plate 65 whilst a few pages further, speaking of poison-
fangs, he says, “ from its transparency it has been regarded as enamel. There is, however, no trace of true
enamel on the teeth of poisonous serpents any more than upon those of the innocuous species.”
DEVELOPMENT OF THE TEETH OF OPHIDIA.
299
young tooth-germs (cf. fig. 4) the outer or reflected layer of cells may he recognized ; but
their identity is soon lost, and nothing but the “ enamel cells ” can be distinctly made
out. They become shorter after the enamel layer has been formed (the thin coat of
enamel has of course disappeared from the specimens figured, which are all decalcified
sections ; had the layer been cementum it would not have done so), but do not wholly
disappear.
Of the. capsule, such as it is, there is little to be said; it is merely a very slight
condensation of the surrounding connective tissue.
As the tooth approaches completion, there is a peculiarity in the form which its
base assumes which I have not noticed in other animals — namely, that the dentine at
the widely open base of the tooth is often abruptly bent inwards, as though the base of
the tooth were about to be closed by a sort of operculum of dentine (see fig. 5).
An early germ is represented in fig. 4, measuring in its total length xxo' °f an inch ;
it differs from a mammalian tooth-germ by its elongated form, and by the fact that the
two layers of cells which necessarily result from the manner of formation of enamel-
organs, namely the outer and inner epithelia of the enamel-organ, are so closely in
contact as to be indistinguishable except at the base, there being no intermediate stellate
tissue ; while from the tooth-germs of Batrachia and Sauria it differs in no respect save
its exceedingly elongated shape. A still earlier stage, when the tooth-germs may be
said to consist solely of a preparation for the formation of an enamel-organ' in the shape
of a csecal process of epithelial cells, is shown at e in fig. 3.
But it is not in the structure nor in the development of individual tooth-germs that
the Ophidia are peculiar ; it is in the relation of these to one another and in their large
number. Including the tooth which is in situ , no less than eight different stages may
often be seen in a single section ; and their large number necessitates a peculiarity in their
arrangement, for, remembering the small size of the tooth-bearing bones and the extreme
dilatability of the snake’s mouth, it would be manifestly impossible that the successional
teeth should be arranged in linear series from without inwards.
Accordingly we find the greater number of the forming teeth to be placed nearly
vertically one above the other, parallel with the jaw-bone and the tooth in place, thus
interfering but little with the mobility of the mucous membrane and the dilatability
of the mouth (figs. 2 & 3).
The tooth next in order of succession, however, has moved inwards in a curvilinear
direction, so that it no longer stands above the younger teeth, but lies in a measure
between the topmost developing tooth and the one already in place. In other words, a
tooth-germ as it progresses from being the youngest of the series to being the oldest,
moves at first upwards, then outwards towards the teeth in use, and then again a little
downwards, so that it describes a curved path. And not only does the growing tooth-
germ thus bodily migrate, but it also undergoes a change in the direction of its long axis.
Starting at the bottom of the area of tooth-development (1 in fig. 2 & e in fig. 3), its
long axis is nearly perpendicular to that of the jaw ; but as it becomes larger it becomes
300
ME. C. S. TOMES ON THE STRUCTURE AND
inclined, and finally (in the oldest teeth which have not as yet become attached to the
jaw) it is nearly horizontal, so that the tooth lies parallel to the jaw, and is seen in the
preparations in transverse section (7 in fig. 2).
A ready clue to these peculiarities of position is furnished by the dilatability of a
snake’s mouth ; it is essential that the successional tooth-germs should be disposed in
the smallest possible space, while the recumbent position of the teeth which have
attained to nearly their full length carries its own explanation upon the face of it.
If the oral epithelium which is immediately to the inner side of the tooth in place
(which, owing to the backward inclination of the teeth, can never be displayed in all
its length in a section exactly transverse to the jaw) be traced downwards, it will be
found to dip in deeply below the surface in the form of a distinctly circumscribed band,
which does not pursue a perfectly straight course, but bends once or twice as it passes
in (see e in figs. 2 & 3).
This epithelial band reaches the region of the developing teeth, and there is more or
less lost sight of; that is to say, although it reappears in the interspaces of the tooth-
germs (see fig. 3), and doubtless is perfectly continuous from the surface to the deepest
extremity of the area of tooth-formation, it cannot be seen in any one section in its
whole course, as it is pushed out of the way and overlaid by the actively growing tooth-
germs. In the interspace between each of these it can, however, always be seen
distinctly ; and at the deepest or youngest end of the area it is seen in direct continuity
with the enamel-organ of the youngest tooth -germ but one (fig. 4); while its blind
extremity forms all that as yet exists of the youngest tooth-germ (see 1 in figs. 2 & 3).
All the germs, with the exception only of the immediate successor to the tooth in
place, are situated within a capsule or investment of connective tissue (fig. 3), forming
an oblong or slightly pear-shaped area (its smaller end being downwards). This
investment, common to a number of tooth-germs, is, so far as I know, peculiar to the
Ophidia ; at least nothing like it is met in any of the Batrachia or Sauria which I have
examined.
When the tooth has attained to a considerable size, it escapes from the apex of this
investment and passes towards the tooth already in place, which is then rapidly under-
mined by absorption. When the tooth has fallen, the upper, and to some extent the
inner, surface of the bone is exceedingly irregular, being everywhere roughened by the
depressions characteristic of absorption (see the upper part of fig. 7). The tooth moves
into position, carrying with it its capsule and all its contents. A very rapid formation of
bone takes place, to which perhaps the capsule may contribute something ; the bulk of
the new bone by which the tooth is attached, however, is formed outside and beneath
the capsule, which in favourable sections may be distinctly seen passing directly across
the base of the dentine, from one thin free edge to the other, even after a considerable
portion of new bone has been formed.
This new bone, formed altogether outside the tooth-capsule, is continued up on the
outside of the dentine for a short distance (see figs. 6 & 7), and in this position has
DEVELOPMENT OF THE TEETH OF OPHIDIA.
301
apparently been mistaken for cementum ; but a study of its development proves it clearly
not to be such. Simultaneously with this active development of bone the base of the
tooth-pulp, which is furnished with a layer of odontoblast cells (fig. 5), calcifies, forming
an irregular sort of dentine, the tubes of which blend with the newly forming bone
beneath it. The resultant conditions can be perfectly well studied in dry sections; for
the bone of attachment differs most markedly from that of the rest of the jaw, being
full of irregular spaces, and being stratified in a different direction (fig. 8). It adheres
more strongly to the tooth than to the rest of the bone, so that it is often broken away
with the former, and it must be regarded as a very rude, imperfect form of osseous
tissue. It is apparently almost entirely absorbed when the tooth to which it belongs is
shed, as but little trace of “ bone of attachment ” is to be seen after the loss of a
particular tooth ; nor does a careful examination of that which serves to cement on a
particular tooth reveal much evidence of the persistence of portions of an older date,
although some is generally to be found by careful search.
The poison-fangs present some peculiarities in their development which I have not
as yet been able to fully make out, owing to the difficulty of getting poisonous snakes
in a perfectly fresh condition. The early tooth-germs are identical with those of the
simple teeth ; but at a later stage there is an appearance of a duct with definite walls
within the tooth, the origin of which I have thus far failed in tracing.
Explanation of the Plate.
PLATE 48.
Fig. 1. Portion of a longitudinal section of the tooth of a python with a thin, cracked
layer of enamel.
Fig. 2. Transverse section of the lower jaw of a common snake : to the left is seen the
jaw-bone, with a portion of the tooth in situ upon its upper surface ; to the
right of this is the area of tooth-development.
a. Oral epithelium.
b. Dentine-organ or “ papilla.”
c. Tooth already in use.
d. Formed dentine.
e. Process of oral epithelium, passing in to form the enamel-organs.
f Inner epithelium or “ enamel cells” of the enamel-organ.
0. Layer of odontoblast cells.
P- Parapet of fibrillated connective tissue bounding the area of tooth-
formation on its inner side.
1. Youngest tooth-germ, as yet only represented by the process of epithe-
lium (e).
2s
MDCCCLXXV.
302 ON THE STRUCTURE AND DEVELOPMENT OE THE TEETH OP OPHIDIA.
2. Tooth-germ which has an enamel-organ and dentine- organ.
3, 4, 5, 6, 7. Older tooth-capsules.
Fig. 3. Four tooth-germs from a transverse section of the lower jaw of a common snake,
showing their relations with the oral epithelium, and their enclosure in a
species of common capsule (lettering same as in other figures), xlOO.
Fig. 4. Early tooth-germ, in which the double layer of cells originally constituting the
enamel-organ can be seen. Common snake. X 150.
Fig. 5. Longitudinal section of a tooth-capsule of a viper. The enamel cells are dimi-
nished in size, and the base of the pulp has already its odontoblast layer, so
that the tooth had evidently attained its full length, x 50.
Fig. 6. Portion of tooth-germ seen in transverse section, embracing the odontoblast
layer of the dentine-pulp (o), a thin layer, of dentine (d), enamel cells (/), and
outside these a slight fibrous capsule, Xl50.
Fig. 7. Tooth in process of attachment to the bone. The roughened surface of the
jaw ( m ) is well seen, while the tooth is as yet attached to it only by the tissue
represented at g, in which calcification is actively going on. The appear-
ances observed at g do not materially differ from those seen at the edge of
a rapidly growing membrane -bone. Common snake.
Fig. 8. Transverse section of lower jaw of a common snake, with tooth cemented on
by the “bone of attachment” ( h ). From a section mounted dry in Canada
balsam.
All the figures, with the exception of No. 8, are taken from sections hardened and
decalcified in chromic acid, and stained with logwood or carmine.
[ 303 ]
X. On Polishing the Specula of Reflecting Telescopes.
By W. Lassell, F.R.S., V.P.R.A.S. , LL.D.
Received November 11, — Read December 17, 1874.
During my sojourn in Malta (1861 to 1864) I made many experiments in repolishing
my four-foot mirrors, with a view to the obtaining, if possible, further excellence in
figure and polish. To obtain perfection in both these qualities, or so near an approach
to it that no fault is discoverable in a four-foot surface, is not easy, at least I have not
found it so.
Errors of figure may be of various kinds. A surface may be so near to the true para-
bolic curve that the central and circumferential rays may come to the same focus ; but
the intermediate rays, those halfway between the centre and circumference, may have a
different focus. If this error be considerable, and the telescope be turned to an object
requiring fine definition, the effect is most annoying. A first glimpse may lead you to
expect you are coming to a very sharp image ; but just as the image ought to be formed
in perfection, the outstanding intermediate rays introduce confusion, and after several
vain attempts to improve the focus you retire in disgust. This irregularity of curve I
consider to be the most vexatious fault a mirror can have. A deviation from the para-
bola at the circumference of the mirror, whether the deviation be within or beyond the
parabola, is far more tolerable, if it be in a regular progress from the centre to the
circumference. Indeed a figure which deviates sensibly, but moderately, towards the
edge, whether within or beyond the parabola, may give very tolerable vision, if the
curve deviate from the parabola only in regular proportion from the centre outwards.
There is another error which is of less consequence, but still desirable to be got rid of,
as it practically reduces the available aperture of the mirror, and consequently the size
of the telescope. The figure may be sensibly parabolic up to near the margin of the
mirror, where it rapidly falls off and becomes grossly hyperbolic. Probably this may
arise from some different action of the polisher upon those parts of the speculum which
in the process of working are alternately covered and exposed, or from the injudicious
application of the rouge and water only near the edge. With a view to obviate this
defect of figure, I have found it advantageous to increase the sweep or stroke of the
polisher, or, in other words (referring to the description of my polishing-machine in the
eighteenth volume of ‘Memoirs of the Eoyal Astronomical Society’), to increase the throw
of the quick-moving crank. While attempting to do this at Malta, using the same
machine which had been originally constructed for the two-foot speculum, and had given
repeated indications of its being too weak for the work, it broke down hopelessly, and
2 s 2
304
ME. W. LASSELL ON POLISHING THE
I was obliged then to use some other arrangement or modification. I was not able to
alter my machine and carry out my experiments fully before my return home, and it is
only of late that I have had leisure again to return to the subject. But I have succeeded
so perfectly and completely, even beyond my hopes, and by processes so simple, so
certain, and so pleasurable, that I am desirous to place on record and before the world
the means by which this has been accomplished.
In the machine I am about to describe, those familiar with the subject will probably
recognize little that is new , for I have not hesitated to adopt parts of other machines
that have been contrived, and rearrange or simplify them as I thought best for the
required result. In describing, however, this new machine, I am desirous not to say
any thing in disparagement of that which I invented many years ago (above referred to) ;
for with that machine, especially since I applied to it the elegant improvement of a
train of wheels for producing uniform axial motion of the polisher (a condition I had
indeed attempted to secure by less efficient means) invented by Mr. De La Hue, I have
produced many surfaces, on various specula up to 12 inches diameter, which I have never
been able to surpass, and which are indeed so perfect that I cannot discover in them
any error whatever. Still I have found it difficult, though not impossible, to use
Mr. De La Bue’s train for specula as large as 24 inches diameter, the strain on the
wheels (being levers of the third kind) endangering the teeth. It was in applying this
arrangement to polishing the four-foot that, although I had purposely had the wheel
and pinion on which is the greatest strain made of cast steel, the machine broke down,
and I was obliged to give up its use.
Description of the more recently constructed Machine.
Throughout the several figures the same letters generally indicate the same parts of
the machine. Those figures which represent that part of the machinery supporting the
speculum are on a scale of 1^ inch to the foot, or one eighth the full size.
Plate 50. fig. 1 represents a firm support of wood or masonry for the cast-iron frame B
of fig. 2, to which all this part of the machinery is fixed ; and it will be seen that there
is provision made for attaching it to a wall ; but that method is not so convenient as
placing it on a firm and independent base. The form of the plate and bracket B will
be understood from the several views of it in figures 1 to 4. On its upper surface
are two Y-shaped planed grooves shown at Bl. On this travels a cast-iron plate, C, with
V-shaped ribs fitting the grooves of the frame B, and, depending from its centre, is cast
a hollow tube accurately bored inside (C2, figs. 1 & 2). There is also a boss cast on its
under surface (C3, fig. 2) to afford a firmer support to the axis of the pinion (or wheel)
of 26 teeth working through it. In the upper and lower plates of frame B are two
wide recesses or grooves shown in plan at B2, fig. 4. These allow the downward pro-
jecting tube of plate C to pass backward and forward within certain limits, as the
plate C travels along the V-shaped grooves. Fig. 5 shows a turned shaft fitting the
bored tube of plate C with two toothed wheels keyed upon it, the upper wheel having
SPECULA OE REFLECTING TELESCOPES.
305
77 teeth and the lower wheel 60 teeth. These are shown in position in figs. 1 & 2.
Frame D, shown in the several figures, carries a tangent-screw (figs. 3 & 4) working into the
upper wheel of the shaft (fig. 5), the shaft of the tangent-screw having three speed-pulleys,
the largest of which is 9 inches diameter, keyed on to it at its end, distant about 20 inches
from the middle of the tangent-screw. The lower wheel of the shaft (fig. 5) engages
with a smaller wheel or pinion of 26 teeth, in the lower end of the shaft of which is cut
a slightly dove-tailed slot (G, fig. 1). Through this slot passes the adjustable crank-arm
(E, fig. 2), with a turned pin and shoulder at its end. The stout bracket F is bolted to the
underside of B, and contains a planed groove, vertically cut, which is fitted by a brass
step bored to the size of the crank-pin, and travelling truly and smoothly in the slot or
groove cut in the bracket. The extreme throw of this crank is, radially, 2’2 inches;
therefore the entire journey of the plate C, with all that it carries, along the V-grooves
in B is thus insured to the extent of 4 ’4 inches extreme thrust to and fro. Cast on to
the upperside of the tangent-wheel H are a central and three circumferential bosses,
seen in plan in fig. 4, and in elevation in figs. 1 & 2. The projecting pin of the central
boss enters a hole of similar size in the centre of the back-plate of the speculum, on
which, on its disks and levers, it reposes. This central boss thus secures the centrality
of the speculum whenever it is placed upon the machine. The steadiness and horizon-
tality of the back-plate is secured by three adjusting-screws affixed to the other three
bosses (of which one is seen in fig. 1), having pins entering corresponding holes in the
back-plate. By a band from a suitable-sized pulley on the main driving-shaft of the
steam-engine, motion is given to the pulley on the tangent- screw shaft (I, fig. 1).
This being engaged with the wheel of 77 teeth, causes the speculum to revolve on its
axis, and at the same time, by means of the wheel of 60 teeth working into the pinion
of 26 teeth, carries the speculum transversely or laterally along the Y-shaped grooves,
according to the setting of the adjustable crank-arm E, fig. 2. The object of this trans-
verse motion (not always used or even necessary) is to wipe out (so to speak) any ring-
like character which might possibly appear in the process of polishing.
Thus far is a description of the apparatus by which the two motions of the speculum
are obtained. I proceed now to describe the method by which the required motions of
the polisher or grinder are secured.
Description of the Apparatus for driving the polisher or grinder of a two foot Speculum.
Fig. 7 of Plate 51 is a plan, and fig. 8 an elevation, of this part of the machine. A
represents the speculum as placed in position on the bosses of the tangent-wheel H,
figs. 1 & 2. B is the principal spindle, with its adjustable crank for driving the long
shaft C, which, seen in its two positions (figs. 7 & 8), needs but little description. D is
the main driving-pulley, which, in connexion with a shaft running along the ceiling,
also driving the speed-pulley I (fig. 1), gives motion to the whole. E is another vertical
spindle attached to the wall of the laboratory, furnished also with a crank of nearly
similar range to that on the spindle B, and connected also, by a radial bar, with the
306
MR. W. LASSELL ON POLISHING THE
long shaft or lever C, as shown in fig. 7. On the spindle E is keyed a pulley 8*3 inches
diameter, connected by a crossed band with another pulley of 9 inches diameter, keyed
on to the main spindle or shaft B. These pulleys, differing but little in diameter, are
intended to be prime to each other, to avoid a repetition of the same strokes in the
crank-arms.
Attached to the long shaft C is an apparatus for securing a regular slow motion of
the polisher on a vertical axis. On the hack of the polisher is a circular rack of 128
teeth, driven by a pinion of 15 teeth, the shaft of which works in a little frame attached
to the long shaft, as shown at F. On this small shaft are two pulleys, either of which,
by means of two direction-pulleys (G) and a round hand, may be driven by any of the
pulleys which are keyed on the upper portion of the driving-pin of the crank-arm H.
The axis of the direction-pulleys G is secured to a separate piece of wood, which can be
fastened to the long shaft, or raised somewhat from it by means of two wooden screws,
as shown in the drawing ; thus the band can be kept at a proper degree of tension. If
the direction-pulleys were to be brought into immediate connexion with any of those
on the shaft H, the speed would be too great, and therefore two supplementary systems
of speed- or cone-pulleys are introduced between G and H. These afford abundant scope
for alteration of speed ; and by crossing any one of the bands the motion of the polisher
on its axis may be either in the direction of that of the sun or the reverse. At J is a
hook, attached by a cord going over a large pulley in the ceiling to a counterpoise-
weight, by which the whole or any portion of the weight of the long shaft C may be
supported. The teeth of the circular rack and of the pinion are made as long as can
be, consistently with their working well together ; and the counterpoise is so regulated
that they remain engaged without the apices of any of the teeth coming into contact
with the opposite bases. Therefore the weight of the polisher, which is of course a
constant quantity, or very nearly so, is the only weight pressing on the surface of the
speculum. The axial motion of the polisher is usually in the opposite direction to that
of the speculum, and its speed is slower. These constitute the ordinary motions of both
the speculum and polisher.
The polisher, equal in diameter to the speculum, is made of two strata of white deal,
such as is generally used for the inside carpentry of dwelling-houses, the grain of the
wood being placed at right angles in the two disks, which are about 1^ inch thick, cut
out of adjacent parts of the same well-seasoned board. One surface of each board is
planed as flat as possible, and then they are united together with the best glue under
strong and equal pressure. While the pressure is still applied and the glue warm, the
disks are further secured in contact by about two dozen countersunk screws, equally
distributed. Calling the disks A and B, half the screws are entered on the side A, and
half on the side B, each disk having been previously bored and countersunk for its own
screws (for expedition’s sake), so that only what boring may be necessary in the other
disk is done after gluing. The two external surfaces of the polisher are now to be
wrought or planed, for symmetry’s sake, to fit approximately the concave gauge of cur- '
SPECULA OE REFLECTING TELESCOPES.
307
vature of the speculum. The polisher is then to be painted with the best thin oil-paint,
the process being continued or renewed until all the pores of the wood are perfectly
saturated with the oil. When perfectly dry it is to be well varnished, and then will be
ready to receive the pitch. For covering the polisher symmetrically with squares of
pitch with due interstices (a most essential condition), I have used a peculiar apparatus,
which really converts this troublesome and very unmanageable process into one not at
all irksome and also cleanly, speedy, and efficient. This, which may be called a pitch-
mould, is represented in Plate 52. fig. 9, half the real size, a b is a square prism of white
deal, on the upper part of every side of which is hinged a piece of deal fitting closely to
the prism, and extending about four tenths of an inch beyond the upper end of the prism.
The outsides of the upper ends of these pieces are a little tapered, so that, when their
sides or surfaces are in contact with the prism, as in the figure, a light zinc hoop ( e )
may be dropped over them to hold them in position. A cell or mould is thus made on
the top of the prism about inch square and four tenths of an inch deep. The lower
part of the prism (c d) is encompassed by a hoop of sheet lead, sufficient to make it sink in
water and keep upright. To have five or six of these moulds saves time in the process
of casting the pitch. Previous to being used, the moulds should be immersed for days,
or at least 24 hours, in order that the pores of the wood may be so saturated with
water that the melted pitch will not attach itself to any part of it. And to bear this
treatment well, the pins, as well as the leaves of the hinges, should be brass, and the
attaching screws also brass. Fig. 10 represents a cylindrical vessel of thin copper,
about 11 inches in diameter and 11 inches deep, with a short copper tube hard-
soldered in its side near the bottom, six tenths of an inch wide. This tube is to be
fitted with a very long and slowly tapering mahogany plug, so as to give plenty of
latitude for' regulating the flow of pitch. I use black pitch, made from Swedish or
Bussian tar, and have obtained it of very good quality from Tolhurst and Sons,
60 Tooley Street, in small kegs. Formerly I used to strain the pitch through muslin
(a most disagreeable operation), but for many years I have forborne to do so, deeming
it quite unnecessary; and some other niceties, such as polishing the speculum in
water of the same temperature as the laboratory, also I have laid aside. The
general tendency of my experience has been to approximate to the utmost simplicity
consistent with accuracy of workmanship. The best way of opening a barrel of pitch
is to saw the staves through in the middle all round, when by a smart blow or two it
will generally break in the middle into two portions. By inverting one of them over a
large sheet of brown paper and slightly tapping the loosened staves, any required
quantity may be readily detached. The pitch is generally so hard that it will bear this
treatment even in hot weather. The pitch-vessel may be conveniently placed on a low
iron tripod, and the pitch melted by a Bunsen burner mounted at the end of a gas-
bracket. The pitch is adjusted to the proper temperament by adding tar if it be too
hard, and resin if too soft. If the latter has to be added, it should be melted in another
vessel and poured in while fluid. The due attempering of the pitch may be secured by
308
ME. W. LASSELL ON POLISHING THE
a trial- an d-error process as follows: — Take a small sample of the melted pitch, and pour
it on a thin copper plate. Immerse it in a vessel of water of the probable temperature
of the apartment in which the polishing-process is to be conducted. When the pitch
has acquired this temperature, place it on a table, and subject it to the weight of a
new sovereign placed on edge for sixty seconds. If it receives three clear impressions
of the milling-strokes in that space of time, it will be about right. It should not
receive less than 2|- nor more than 3|- strokes. A simple frame should be made to
hold the sovereign vertically, without influencing its weight. When of right consis-
tence, the burner should be so regulated that the pitch should not flow too rapidly
when the plug is partially or wholly withdrawn : indeed, the cooler the pitch, without
endangering its regular flow, the better ; it will be less liable to adhere to any of the
moulds when poured into them. The moulds should have been placed, as before
directed, in cold water, the surface of the water being an inch or two above the tops of
the moulds. One of the moulds is to be withdrawn from the water, quickly emptied
by inversion, placed under the side tube of the pitch-vessel, and filled level full of pitch
by partially withdrawing the plug. The filled mould is then to be sunk just under
the surface of the water of another vessel and allowed to remain a few minutes. This
time may be occupied by filling about half a dozen other moulds, when the first will be
ready to be taken out of the water. On lifting off the zinc hoop and letting down the
hinged sides, the symmetrical casting of pitch will have become hard enough to drop
off instantly into the water, leaving the mould quite clean, which should, however, be
returned to the water before being used again. But little experience will, I think, be
required to secure this process being carried on easily and successfully. Should a
single particle of pitch stick to any of the moulds it must he perfectly removed before
being used again ; and if any of the moulds should give any trouble in this respect, a
slight touch of rouge on the Avood will probably defend it from the pitch ; but if the
moulds have been long enough in the water this ought not to be required. The squares
of pitch must not remain long in contact, even under water, as they are apt to adhere.
They are best placed, soon after being formed, on a level deal board, the squares just
covered Avith water, Avhen they Avill take no harm for a considerable time.
I use the following mode of attaching the squares of pitch symmetrically and firmly to
the base of the polisher. Fig. 11, Plate 52, represents a piece of stout sheet iron 3^ inches
broad and about 13 inches long, bent into the form a a, to which is riveted another
piece (b). The lower part of the upper portion of a is curved into a channel, and a
sheet-iron cup ( c ) receives any waste pitch Avhich may overflow. The upper part of a
is heated by a Bunsen burner being placed below it. Three prisms of deal, four tenths
of an inch square, two of them 12 inches long, the other 24 inches, are to be prepared
and well soaked in water : these are to be lightly tacked to the base, as shown in fig. 12
(Plate 50). ' A fourth prism, some 8 or 9 inches long, is also required, and these serve to
aid in placing the squares correctly and to mark out the interstices between them.
The fourth prism is unattached, and kept in the hand to mark the separation as each
SPECULA OF REFLECTING TELESCOPES.
309
square is applied. I begin at the centre, as in the figure ; and after laying down two
rows along the two radii of the first quadrant, I then proceed to the opposite quadrant,
and similarly with the remaining quadrants, with a view of producing uniformity as
much as possible over the whole surface. The squares are now to be successively taken
up by the fingers, drawn rapidly across the heated plate ( a , fig. 11), which completely
melts the under surface of the square without penetrating beyond a mere film, and
prepares it to adhere firmly to the base by a pretty hard but quickly withdrawn pres-
sure. The 24- and 12-inch rods should be removed as soon as they have answered
their purpose, lest any of the squares should adhere to them. If not used immediately,
the polisher should be kept in a strictly horizontal position, either face up with a cover
on, or inverted and suspended by hooks embracing three pins of stout wire, inserted
equidistantly in the circumference of the polisher, as in figure 13.
Before describing the actual process of polishing, I may say a word or two on the
rough-grinding and preparing the speculum for reception of the polisher. The rough-
grinding proper is a very easy process, and may be accomplished in various ways, the
chief requisite being patience. A very good grinder may be constructed exactly as is
the base of the polisher, and then covered with 2-inch or 2^-inch square leaden castings,
four or five tenths of an inch thick, each screwed to the base by a couple of stout
joiner’s screws. A convenient mould for the castings may be very easily constructed of
sheet iron, with pins inserted to leave holes for the screws. The metal is improved if
a little tin be added to the lead. Of course, the process of grinding must be watched,
and the gauge of curvature applied occasionally, correcting any error by lengthening or
shortening the strokes of the machine as the case may require. In this way, by
gradually increasing the fineness of the emery, the surface of the speculum may be
brought up to a condition fit for the polisher ; but, finding the process very tedious
towards the last, and having been frequently much annoyed by the sudden appearance
of a scratch or two, I have resorted to a bed of hones , as an intermediate tool between
the grinder and polisher.
The base of this is a circular disk of Bangor slate, 24 inches in diameter, and about
eight tenths of an inch thick, planed flat on both sides. This is covered with pieces of
German hone (Bohemian blue stone) ; they are to be obtained from F. Alexander,
103 Leadenhall Street. The hones are about 7 inches long, and about eight tenths of
an inch square. They are cemented on to the base with hard pitch, their under
surfaces having been previously ground flat on a facing-plate, as it is necessary that
their contact with the base should be intimate and accurate. The upper surface of
the bed of hones must of course be made to fit the gauge of curvature, which is accom-
plished, without much difficulty, with a coarse file or rasp, correcting it as the coincidence
approaches accuracy by a few strokes upon the speculum itself. Fig. 14 represents
generally the form of the bed, and the direction in which the hones are placed, attention
being paid to balancing, so to speak, the opposite sides of the tool by having the grain
MDCCCLXXV. 2 T
310
ME. W. LASSELL ON POLISHING THE
of the hones in the same direction*. When the coincidence has been rendered nearly
perfect, the tool may be wrought upon the speculum with a little tine-sifted emery,
water being freely applied as the mud forms, and finishing with finely powdered hone-
dust. This process will produce a very fine surface on the speculum, quite fit for the
application of the polisher and for examination of the figure by the image of a bright
star. This tool is very convenient in case of having, in polishing, produced a hyper-
bolic figure, as it may be reverted to and a spherical figure obtained in an hour’s
working. On the back of the bed of hones, as also on the back of the polisher, is
screwed a cast-iron socket, loosely fitted by a stout pin, about half an inch in diameter,
depending from the lever or long arm (C, fig. 8). This pin should be firmly attached,
as it has to bear all the strain of the machine, both in grinding and polishing. The
weight of the bed of hones is about 61 lb., and of the polisher about 35 lb.
Presuming the speculum to have now a sufficiently fine and approximately spherical
surface from the hone-tool, it will be ready for the polisher. The temperament of the
latter should be of course in due relation to the existing temperature of the laboratory.
The surface of the pitch must retain its originally pure texture, or it will not polish
quickly and well ; and it must be slightly warmed and placed upon the clean wetted
face of the speculum before any powder is applied, to insure a nearly even and uniform
contact between the polisher and speculum.
The surface of pitch is conveniently and uniformly warmed by the apparatus repre-
sented in fig. 13. Two pulleys revolve on axles driven horizontally into a beam, a stout
cord (sash-line) running over both. One end of the cord is attached to a counterpoise-
weight, and the other by a swivel and three cords to the polisher, which is thus suspended
face downwards. The three cords terminate in three hooks, respectively receiving the
ends of the three equidistant pins inserted in the circumference of the polisher. At
a is a piece of wood and tightening-screw, which can be made to clip the cord to the
beam, and prevent its motion when the equilibrium is about to be destroyed by removal
of the polisher. When in cequilibrio the polisher can be raised or lowered at pleasure, the
screw being withdrawn during the process of warming. On the floor, under the polisher, is
placed a small chauffer or furnace (Plate 52. fig. 12), made of four fire-bricks or tiles
9 inches long, 4^ broad, and 2^- inches thick. These are put together so as to enclose a space
about 5^ inches square and 4^ inches deep, which forms the receptacle for the charcoal.
The base on which the bricks stand contains a grating of bars ^ inch square, with equal
spaces between. Supported on the bricks, and a few inches above them, is a piece 'of
sheet iron rather larger than the area of the furnace, to prevent the direct heat of the
ignited charcoal from acting on the pitch. The heated air ascends all round the plate,
and by revolution of the polisher with a little swinging motion, its surface is uniformly
warmed. By means of the counterpoise, the polisher can be raised or lowered at pleasure
according to the heat required. Some judgment is necessary in warming the pitch.
* The hones are put on entire in their whole length ; but their upper surfaces are slightly grooved, so as to
give the tool the aspect of a system of squares.
SPECULA OE REFLECTING TELESCOPES.
311
The heat must not penetrate far into it, nor must the heat be so suddenly or powerfully
applied as to r^elt the surface ; it must be merely softened. The surface of the speculum
having been freely wetted by a large sponge and clean cold water, the pitch-surface as
softened must be quickly laid upon the speculum and gently and slowly moved, to faci-
litate contact. It is well not to err on the side of too much warming, as if necessary the
process can be repeated until the contact is complete. On removal of the polisher it will
be instantly seen to what extent the surfaces coincide ; and it is desirable that the contact
should be very uniform, and that some part at least of every square should touch the
speculum ; if that is not the case, another warming should be resorted to. For polishing
I use th q finest plate-powder, or jeweller’s rouge, which may be obtained of excellent
quality from Medway and Co., Owen’s Court, Goswell Eoad. This requires no further
sifting. A quantity of it is put into a flat-bottomed jar and well stirred about with
water equal to seven or eight times its bulk. It is then left to subside until almost all
the water can be poured off quite clear. Of course the finest particles of the powder
will be now upon its upper surface ; and I have ever found these to be capable of pro-
ducing as fine a lustre as the speculum is capable of receiving. Without disturbing
much more than the surface of the powder, the speculum is now, by means of a flat
camel’s-hair pencil, to be covered with the rouge and water of the consistence of cream.
The polisher may be again very slightly warmed, placed upon the speculum and the
machine set to work.
The motive power I have used and found quite adequate is a steam-engine of 4^
inches diameter of cylinder and 8 inches stroke, making 120 revolutions per minute,
with pulleys on the horizontal shaft of such size as to drive the crank H either thirteen
or seven revolutions per minute.
The mode I have employed for converting the spherical curve into a parabolic one
has been by flattening or wearing down the exterior parts of the mirror, not by deepening
the central ones ; and this has been accomplished generally by altering the throw of the
crank H and its rate of motion. In this I have been guided by the following consider-
ation. If the polisher, at a proper temperament, be placed out of the centre upon the
speculum with one part of its edge hanging over the speculum some 3 or 4 inches, and
be allowed to remain a few minutes in that position, it will require a strong effort to
bring it back to a central position over the speculum, the unsupported pitch-surface
having in that interval fallen down slightly by the force of gravity. In forcing the
pitch back to its normal figure, it must necessarily exert an undue pressure upon the
exterior part of the speculum over which it travels, and, if charged with powder, would
certainly abrade that part more than other parts nearer the centre, and, so far as its
operation reached, would tend therefore to produce a parabolic curve. Now if the
throw of the crank H be lengthened, the polisher at each stroke will be carried more
over the edge, and therefore this tendency would be increased ; and if at the same time
the speed be diminished, the duration of the overhanging of the polisher at each stroke
would be longer, and the parabolic effect proportionally increased. The result is still
2 t 2
312
MR. W. LASSELL ON POLISHING THE
further augmented by the slight increase of temperature acquired by the pitch in the
act of polishing.
Acting on this principle, which has been supported by pretty extensive practice, I
usually set the crank H, for polishing a twenty-four-inch speculum with a focus of
ten diameters, to a radius of 3‘0 inches, and the crank E to a radius of 2 -75 inches,
with a speed of motion of H producing about seven revolutions per minute. The
pulley on the main shaft, in connexion with the largest speed-pulley I, of fig. 1, Plate 50,
is about 4T inches diameter, causing the speculum to revolve once in about 3m 45s
against the sun ; and the speed-pulleys on the long arm C of fig. 8 have their bands
so arranged as to cause the polisher to revolve on its axis once with the sun in
about 5m 8s, none of these bands being crossed. The band on the pulley on the
vertical shaft H, connecting it with that on the vertical shaft E, is necessarily crossed
to increase its friction. A slight addition to the counterpoising weight of the long
arm C lifts its end about 2 inches above its ordinary working position, so that there
is now room to place the polisher upon the speculum already charged with rouge.
By restoring the counterpoise the pin may be introduced into its socket on the back
of the polisher and the engine started. Pretty frequent supervision of the operator
will now be necessary through the whole process, which may last three or four hours ;
and perhaps the lustre may not be brought up to its maximum even in that time.
I generally allow the machine to proceed uncontrolled until the powder begins to dis-
appear from the intermittently exposed margin of the speculum. By this time the
powder, as it works slightly over the edge of the speculum or adheres to it, ought, if it
has been working well, to have become considerably darker in hue, so as to tend to
a purplish colour, from the admixture of minute metallic particles. Nothing like
dryness of the edge must be permitted to supervene. The engine should now be stopped
and the polisher withdrawn by sliding it off the speculum. Probably the incipient
polish may be somewhat more advanced towards the exterior of the speculum, which
is what is desired ; but it should not be very strikingly so, and the advance should be
regular, not sudden. It is not well to add powder while the machine is going ; it cannot
then be added uniformly over the whole surface, and it tends therefore to irregularity
of action. The aspect of the polisher should be examined. Some part at least of every
square ought to have been obviously in contact, and an oblique view should reveal no
apparent inequality of texture. As rapidly as convenient, and before the squares can
dry, the powder which may have lodged in the grooves should be distributed evenly
over the whole surface ; and after the speculum has had another pretty free dose of
powder, the polisher should be placed upon the speculum and the process be carried on.
When the powder has apparently been again used up and has nearly disappeared from
the speculum, the polisher may again be removed. And now the lustre ought to be very
considerably advanced, and the little powder adhering to the edge of the speculum be
of at least a deep purple colour. The powder may be lightly and quickly removed
from the grooves in the pitch with the camel5s-hair brush, and distributed over the
SPECULA OF REFLECTING- TELESCOPES.
313
surface as before. A very slight application of only the finest particles of fresh powder
is now to be applied to the speculum and the process renewed. Before this powder
becomes used up, the lustre ought to be sufficient, as may be ascertained by inspecting
the circumferential parts of the speculum as they become successively exposed.
The tendency to dry at the edge is now much increased, and must be prevented by
touching the edge from time to time with the camel’s-hair pencil charged with scarcely
coloured water. This may be continued for some time, the lustre advancing very
rapidly, and the colour of the powder becoming really black. What I have described,
if all has gone on well, may occupy perhaps three hours, speaking roughly ; for the
perfect success of the process depends upon some niceties — such as the exact adjustment
of the temperament of the pitch to the heat of the apartment, and the steadiness of its
heat during the time of working. I may remark that nothing abnormal in the process,
such as any irregularity in the motion of the polisher on its axis, must be permitted to
occur without at once stopping the engine and correcting the error ; perfect smoothness
and evenness of motion must exist throughout, and also perfect uniformity of aspect of
the polisher in its several removals must be apparent, or a good result cannot be hoped
for. But in this machine the motions of the polisher are so perfectly, and yet, so to
speak, so gently controlled, that irregularity is not to be expected ; and if it should
occur, a moment’s reflection will most likely reveal the cause. It is probable that
this first polishing may not have brought the speculum quite up to the parabola, but
I think it desirable to clean it off and prepare it for examination. This is best done
with a large and very soft sponge and plenty of pure water. This cleansing must be
continued until not a vestige of powder remains, nor any trace of smear or impurity
whatever. The sponge having removed all superfluous water, the drying is to be
effected with a couple of old soft linen cloths, good absorbents. The wiping must
be light and quick, and continued until every particle of moisture has disappeared
from the speculum. It is then best left without a cover for half a day, that it may
uniformly acquire the exact temperature of the apartment. The cover may then be
put on, and afterwards the less the surface of the speculum is touched the better.
If there he occasion for it, however, I never hesitate to wash and wipe it in the same
soft and careful manner; nor indeed, if at any time there appear any grease-stains
or spots, to first pour upon the surface a very little soft water in which a bit of soda
has been dissolved, lightly distributing it over the whole surface with the finger, and
immediately afterwards applying the large sponge and pure water.
The polisher also requires immediate attention* as if no great change in the tempe
rature of the air occurs, it may be used for repeated polishings. But the surface
charged with rouge and metallic particles must be completely removed or it will never
polish well. This is best done by first well washing, to remove all that a painter’s brush
will remove, and then tearing up the extreme film of the surface with a piece of “ steel-
card,” such as is used in cotton-mills for carding cotton. As this film is extremely hard
and rapidly destroys the edge of any cutting-tool, it was a relief to me to find that this
314
MR. W. LASSELL ON POLISHING THE
instrument answers the end perfectly, exposing the pure under surface of the pitch
without sensibly diminishing its thickness. The polisher should be placed in an inclined
position and plenty of cold water used. If not immediately required, the polisher may
be kept for an almost indefinite time in a perfectly fit state for use, and amidst con-
siderable changes of temperature, by keeping it suspended horizontally, and occasion-
ally examining its surface to see if it requires to he kept face downward or the reverse.
For examination of the figure of the speculum I have always chosen to remove it from
the machine, place it in the tube and turn it on a bright star, which is doubtless a severe
and even crucial test. And in addition to thus examining the image and penumbrse of
a star with the full aperture, I am accustomed to expose successively different portions
of the mirror to the stellar rays, noticing whether or not any different setting of focus
is required.
For this purpose I have a set of six diaphragms, exposing respectively a central disk
and five concentric rings, all of equal area ; and I do not pronounce any mirror perfect
in which the eye is not satisfied with the same focus for all these. I do not say that
the same precision of image is to be expected from the extreme external annulus when
all the rest of the mirror is blocked out ; but if the focus he set upon it, it ought to be
the same as that required for the central portion. This I consider a severe test ; and
beside revealing the character of the general curve, it affords a means of determining its
regularity , by examination of the images formed by the intermediate annuli. A strict
measure of any differences of foci which may be manifested will point out where the
error lies. In the surface in question there may probably be a slight spherical error,
which may be removed by another hour’s polishing with the same settings of the
machine and a very moderate dose of the finest rouge. If, on the contrary, the
figure should be hyperbolic, I should revert to the hone-tool, and repeat the process of
polishing.
From this description I think it will be seen that there is little that is irksome,
tedious, or even uncertain in polishing by this process and with this machine a two-
foot mirror. With a little experience and some mechanical aptitude, the operation is
easy, and becomes very interesting ; for though to obtain the highest perfection of
figure repeated trials may be necessary, the process is by no means disappointing — the
figure, if reasonable care be taken, being always useful and to a considerable extent
satisfactory. The principal part of the work can be done single-handed, though occa-
sionally an assistant is required, chiefly in removing the speculum to and from the
observatory. The speculum (weight about four hundred pounds) is lifted from the
machine with a small pair of three-sheave blocks, placed upon a low carriage, taken to
the observatory, hoisted with the same blocks on to a platform nearly level with the
lower end of the tube when placed vertically, and finally lifted into its place by an
elevating-screw placed centrally under the hack-plate. The time consumed by this
operation, including fixing the levers of horizontal support and final adjustment, extends
to about two hours.
SPECULA OE REELECTING TELESCOPES.
315
A well-fitting, but not tight, tin cover, which may be removed and replaced when the
speculum is in the tube through a slit in its side, is all the protection' the mirror
requires ; but it is desirable that there should be a light wooden cover hinged so as to
fall over this opening when the telescope is in use, to prevent any drop of moisture
falling from the roof from reaching the speculum. This is all the protection I give my
mirrors, and I have never found them tarnish. I have tried quicklime, but found it to
be quite unnecessary, and, besides, an intolerable nuisance.
I may add, finally, that I shall rejoice if I have succeeded in my endeavour to describe
this' interesting process so that any person of ordinary intelligence, and not quite
unacquainted with mechanics, may succeed in producing, without difficulty, surfaces of
at least a very high degree of perfection.
lanbester.
Phil . Ttculs. 1875. Platt; 1 .
DEVELOPMENT , OF PIS ID IU M PUSILLUM.
Lanfcester:
-3°
%
development of pisidium pusillum
W FtHsat & Erskme, LitH? i'din*
Zankester.
I
PJuZ. Trans. 1875. Plato 3 .
development of pisidium pusillum
Lankester.
PhzZy. Trans. 1875. PlaZe 4.
Rg.46.C^
§ W
' Farlane & ErsTiine,
OF PISIDIUM PUSILLUM
Lankester.
PTiiL. Trans. 1875. Plalo 5
i -f
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Lancaster.
Phil. Trans. 1875. Plata 6.
Phil. 1 rafts. 1875. Plate, 7
development of pleurobran chidium
JffMme & ErsWe , T,i(Ws Edra?
PJul. Trans. 1875. Plate, 8
m. 29,
DEVELOPMENT OF PLEUROB RAN C HID IUM
Lanktsttr
Phil. Treats. 1875. PlMes 9
1 12 TER&IPES. 13-20 NERITIISfA
21-22 L I M AX
MfFariaue ^Erskine, Liih” Edin*
M? Rotate & Erstaie.LltH? Edit!*
1-9 POLYCERA. 10-16 TETHYS.
Lankester
Phil. Trans. 1875. Plate 10.
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I PART OF THE SOLAR SPECTRUM AS SEEN BETWEEN I0AM.&2P.M.*
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Phil. Trans. 1875. Plate 38
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Scale: p inch, to cl foot.
Lass ell Phil. Trans. 1875. Plate 52.
PHILOSOPHICAL
TRANSACTIONS
OP THE
ROYAL SOCIETY
OP
LONDON.
FOR THE YEAR MDCCCLXXV.
VOL. 165 —PART II.
LONDON:
PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET.
MDCCCLXXVI.
CONTENTS.
PAST II.
XI. On the Tides of the Arctic Seas. By the Bev. Samuel Haugiiton, M.J). Buhl., B.C.L.
Oxon., F.B.S., Fellow of Trinity College, Bublin. — Part IV. On the Tides of
Northumberland Sound, at the Northern Outlet of Wellington Channel page 317
XII. On the Tides of the Arctic Seas. By the Bev. Samuel Haugiiton, M.B. Bubl.,
B.C.L. Oxon;, F.B.S., Fellow of Trinity College , Bublin. — Part V. On the Tides
of Befuge Cove, Wellington Channel 331
XIII. On the Tides of the Arctic Seas. By the Bev. Samuel Haugiiton, M.B. Bubl.,
B.C.L. Oxon., F.B.S., Fellow of Trinity College, Bublin. — Part VI. Tides of Port
Kennedy, in Bellot Strait 339
XIV. On the Mathematical Expression of Observations of Complex Periodical Pheno-
mena ; and on Planetary Influence on the Earth's Magnetism. By Charles
Chambers, F.B.S., and F. Chambers . . 361
XV. Beduction of Anemograms taken at the Armagh Observatory in the years 1867-63.
By T. R. Robinson, B.B., F.B.S., F.A.S., Ac 403
XVI. The Croonian Lecture. — Experiments on the Brain of Monkeys (Second Series).
By David Ferrier, M.A., M.B. , Professor of Forensic Medicine, King's College.
Communicated by Br. Sanderson, V.P.B.S 433
XVII. On a Class of Identical Belations in the Theory of Elliptic Functions. By
J. W. L. Glaisher, M.A., Fellow of Trinity College, Cambridge. Communicated
by James Glaisher, F.B.S. .489
XVIII. On Bepulsion resulting from Badiation. — Part II. By William Crookes,
F. B.S. Ac. . . 619
XIX. On the Structure and Bevelopment of Myriothela. By Professor Allman, M.B,,
LL.B., F.B.S., President of the Linnean Society 549
XX. Spectroscopic Observations of the Sun. By J. Norman Lockyer, F.B.S., and
G. M. Seabroke, F.B.A.S. 577
XXI. Tables of Temperatures of the Sea at different Bepths beneath the Surface,
reduced and collated from the various observations made between the years 1749
and 1868, discussed. With Map and Sections. By Joseph Prestwich, M.A.,
F.B.S., F.G.S. 587
XXII. A Memoir on Prepotentials. By Professor Cayley, F.B.S.
Index ...
675
775
LIST OF ILLUSTRATIONS.
Plates 53 & 54. — Messrs. C. and F. Chambers on the Mathematical Expression of
Observations of Complex Periodical Phenomena.
Plates 55 to 58. — Professor Allmajst on the Structure and Development of Myriothela.
Plates 59 to 64. — Messrs. Lockyer and Seabroke on Spectroscopic Observations of the
Sun.
Plates 65 to 68. — Mr. J. Prestwicii on Submarine Temperatures.
Adjudication of the Medals of the Royal Society for the year 1875 by
the President and Council.
The Copley Medal to Professor August Wilhelm Hofmann, F.R.S., for his
numerous contributions to the science of Chemistry, and especially for his Researches
on the Derivatives of Ammonia.
A Royal Medal to Mr. William Crookes, F.R.S., for his various chemical and
physical researches, more especially for his discovery of Thallium, his investigation of
its compounds, and determination of its atomic weight ; and for his discovery of the
repulsion referable to radiation.
A Royal Medal to Dr. Thomas Oldham, F.R.S., for his long and important services
in the Science of Geology, first as Professor of Geology, Trinity College, Dublin, and
Director of the Geological Survey of Ireland, and chiefly for the great work which he
has long conducted as Superintendent of the Geological Survey of India, in which so
much progress has been made that, in a few years, it will be possible to produce a
Geological Map of India comparable to the Geological Map of England executed by
the late Mr. Greenough ; also for the series of volumes of Geological Reports and
Memoirs, including the ‘ Palseontologica Indica,’ published under his direction.
The Bakerian Lecture was delivered by Professor W. G. Adams, F.R.S. : it was
entitled “ On the Forms of Equipotential Curves and Surfaces and Lines of Electric
Force.”
The Croonian Lecture was delivered by Professor David Ferrier, M.D. : it was
entitled “ Experiments on the Brain of Monkeys (Second Series).”
[ 317 ]
XI. On the Tides of the Arctic Seas.
By the Bev. Samuel Haughton, M.B. Buhl., B.C.L. Oxon., F.R.S.,
Fellow of Trinity College, Bublin.
Part IV. On.the Tides of Northumberland Sound, at the Northern Outlet of
Wellington Channel.
Received July 11, — Read November 19, 1874.
These Tidal Observations were made on board H.M.S. ‘ Assistance,’ Captain Sir Edward
Belcher, R.N., K.C.B., from 24th May to 6th July 1853, the exact position of the
ship being 76° 52' N. lat. and 97° 00' W. long. Sir Leopold M‘Clintock kindly
procured for me, from Sir Edward Belcher, a copy of the Observations; and in
forwarding them to me writes thus: — Sir Edward Belcher wishes me to tell you
how his Tidal Observations in 1853 were made. He says they did not depend upon
the guess of any one, but resulted from machinery connected with the bottom, which
moved a ratchet-wheel, each cog or inch of gauge ringing a bell ; and the rise and fall
was not that of the ship, but of the whole floe in which she was fixed. This machinery
is described in his narrative, ‘ The last of the Arctic Voyages,’ vol. i. p. 141. He further
states that this rise was repeatedly verified by Theodolite Observations.”
The following Table contains the Time and Height of High Water and Low Water,
extracted from the original observations (which are forwarded with this paper) ; also
the Diurnal Tide at High Water and Low Water, calculated from the heights by means
of the formula
Diurnal Tide—
Z-J — 4^2 + 6Aj
16
4//4 + 7is
5
(1)*
which gives the fourth difference of the successive heights.
* This expression for the Diurnal Tide is used and explained by Mr. Atry in his paper “ On the Tides of the
Coasts of Ireland ” (Phil. Trans. 1845), and by the author in his paper “ On the Diurnal Tides of the Coasts
of Ireland” (Trans. Royal Irish Academy, 1855).
o
U
MDC'CCLXXV.
318
EEY. S. HATTGHTON ON THE TIDES OF THE
A. Diurnal Tide (Heights).
Northumberland Sound.
Time.
High Water.
Height.
Low Water.
Height.
Diurnal Tide
at
High Water.
Diurnal Tide
at
Low Water.
1853.
May 27.
27.
28.
h m
ft. in.
16 1
ft. in.
ft.
ft.
10 0 „
14 H
4 40 a.m
16 4J
0-187
28.
12 5 P.M
■ 15 4
0-481
28.
4 0 „
15 11
0-193
28.
11 0 ”
14 41
0-443
99
4 30 a.m
16 3
0-201
29.
29.
29.
30.
1 0 P.M
15 3
0-219
0-381
15 10
14 8
0-339
6 40 a.m
16 4
0-224
30.
1 40 P.M
15 5
0-292
30.
1 0 „
15 11
0-208
31.
12 50 a.m
14 11
0-230
31.
8 0 „
16 4
0-198
31.
3 30 p.m
15 3
0-187
31.
9 0„
16 0
0-214
June 1.
1.
14 10
0-146
8 32 „
16 6
0-234
1.
3 30 p.m
15 1
0-062
1,
9 40
16 0
0-229 .
2.
3 30 a.m. ...
15 0J
0-088
2.
9 40 „
16 5
0-209
2.
4 20 p.m
10 30 „
14 10
0-083
16 0
0-172
3.
4 35 a.m. ...
14 11
0-121
3.
10 30 „
16 3f
0-182
3.
3.
5 0 p.m
11 0 „
16 2
14 7
0 062
0-177
4.
5 0 a.m
15 0
0-224
4.
10 48
16 3
0-010
4.
5 30 p.m
14 6
0-255
5.
12 15 a.m
16 3
0-015
5.
5 30 „
15 0
0-313
5.
11 45 „
16 2
0-031
5.
6 0 p.m
14 31
0-370
6.
12 50 a.m
16 3i
0-010
6.
6 30 „
15 2
0-380
6.
12 15 p.m
16 5|
0-021
6.
6 20 „
14 H
0-391
7.
1 10 A.M
16 8
0-088
7.
7 22 „
15 5
0-438
7.
12 25 p.m
16 5
0-117
7.
6 21 „
14 6
0-474
8.
1 0 A.M
16 8
0-117
8.
7 20 „
15 6i
0-475
8.
12 40 p.m
16 6
0-128
8.
8 0
14 8§
0-474
9-
2 0 A.M
16 10J
0-110
9-
8 22 „
15 9
0-477
9-
1 15 P.M
16 8|
0-107
9.
7 43 „
14 10
0-479
10.
2 38 a.m
16 101 .
0112
10.
8 50 „
15 9
0-484
10.
2 0 p.m
1
16 61
0-125
AECTIC SEAS.- — PAET IV. N OETHUMBEEL AND SOUND,
319
Northumberland Sound (continued).
Time.
High Water.
Height.
Low Water.
Height.
Diurnal Tide
at
High Water.
Diurnal Tide
at
Low Water.
1853.
h m
ft.
in.
ft.
in.
ft.
ft.
June 10.
8 30 p.m
14
8
0-428
11.
3 40 a.m
16
8
0-151
11.
9 35 „
15
6J
0-256
11.
2 30 p.m
16
3
0-214
11.
10 7 „
15
5
0-234
12.
4 0 A.M
16
9
0-240
12.
10 30 „
15
8
0-251
12.
3 15 p.m
16
3
0-203
12.
10 0 „
14
9f
0-339
13.
4 53 a.m
16
8
0-068
13,
11 15 „
15
6
0-339
13.
10 30 p.m
14
10
0-328
14.
5 45 a.m
16
8
0-151
14.
12 15 p.m
15
H
0-286
14.
6 0 „
15
1 if
0-307
14.
14
11
0-219
15.
6 45 a.m
16
8
0-354
15.
1 ] 0 P.M
15
H
0-143
8 0 „
llj
0-360
16.
12 50 a.m
15
2
0-005
16.
8 0 „
16
9
0-339
16.
2 15 p.m
15
2f
0-005
16.
8 10 „
16
2
0-307
17.
2 10 A.M
15
3
0-078
17.
8 30 „
16
91
0-271
17.
3 0 p.m
14
ui
0-151
17.
9 30 „
16
4
0-224
18.
3 12 A.M
15
4
0-187
18.
9 15 „
16
10
0-088
18.
4 35 p.m
14
11
0-214
18.
10 45 „
16
9
0-099
19.
4 50 a.m
1 5
3
0-250
19.
10 12 „
17
0
0-078
19.
4 55 p.m
14
8
0-344
19.
Midnieht
16
10j
0-041
20.
5 30 a.m
15
6
0-427
20.
1 1 20V„
17
°!
20.
6 0 p.m
14
7\
21.
Noon
21.
7 o P.M
22.
1 o „
22.
7 20 „
13
2
23.
2 0 A.M
15
7
23.
8 0 P.M
14
1
24.
2 0 „
16
8
24.
8 30 „
25.
3 0 p.m
16
5
25.
9 55 j,
14
8
26.
4 30 a.m
17
0
0-333
26.
11 30 „
15
6
0-407
26.
4 0 p.m
16
H
0*307
26.
10 40 „
14
8J
0-401
27.
5 45 a.m.
16
10
0-266
27.
12 1 6 P.M
15
7§
0-339
27.
6 0
16
5
0-266
27.
11 0
1 5
2
0-250
2 u 2
320
KEY. S. HAUGHTON ON THE TIDES OF THE
Northumberland Sound (continued).
Time. 1
High. Water.
Height.
Low Water.
Height.
Diurnal Tide
at
High Water.
Diurnal Tide
at
Low Water.
1 1853. h m
ft. in.
ft. in.
ft.
ft.
1 June 28. 6 40 a.m
17 01
0-302
28. 1 38 „
15 8
0-052
28. 6 20 p.m.
16 5h
0-453
28. Midnight
15 6
0-240
29. 7 20 a.m
17 3
0-635
29. 2 10 p.m
13 11
0*297
29. 7 40 „
14 9
0-656
30. 1 30 a.m
13 11!
0-125
30. 8 30 „
15 4
0-364
30. 3 45 p.m
13 11
0-057
30. 9 0 „
14 lOf
0-193
July 1. 12 40 a.m
14 1
0-107
1 9 5,,
15 2J
0-135
1. 4 35 p.m
13 10
0-172
1. 9 40 „
15 0
0-088
2. 4 20 a.m
14 3
0-229
2. 9 38 „
15 2
0-115
2. 4 10 p.m
13 8
0-281
2. 10 45 „
15 1
0-000
3. 4 45 a.m
14 2
0-339
3. 10 30 „
14 111
0-026
3. 5 4 p.m
13 4
0-151
3. 11 13 „
15 0
0-026
4. 5 0 a.m
14 2
0-448
4. 10 45 „
14 1 If
0-021
4. 5 30 p.m
13 21
0-490
5. 12 15 a.m
15 1
0-015
5. (> 0
14 2
0500
5. 12 45 P.M
15 1
0-031
5. 6 15 ,,
13 1
0-511
6. 1 0 a.m
15 11
0-073
6. 8 0 „
14 0
0-521
6. 1 0 p.m
14 10
0 028
6. 6 40 ,,
12 9|
0-521
7. 2 0 A.M
15 0
7. 8 0 „
13 8
The general expression for the Diurnal Tide is the following : —
where
D=S sin 2 cos (s— ?5)+ M sin 2 p cos (m — im), .
D=height of tide,
o', [Jj = Solar and Lunar Declinations, corrected for Age of Tide,
s, m= Solar and Lunar Hour-angles,
is, im— Diurnal Solitidal and Luni tidal Intervals,
S, M= Solar and Lunar Coefficients, uncorrected for Parallax, &c.
(2)
It would he impossible to obtain any result as to the Diurnal Tides from so short a
series of observations, only for a lucky chance which simplifies the calculation at this
station, and enables us to obtain the Solar Diurnal Tide, although it is not easy to
AECTIC SEAS.— PAET IY. NOETHUMBEELAND SOUND.
321
determine the Lunar Diurnal Tide *. It so happened, during the observations, that the
time of vanishing of the whole Diurnal Tide at Low Water corresponded very closely
with the time of vanishing of the Moon’s declination.
So that we have, at the same times,
[jj= 0, D=0,
which reduces the general expression at these times to
S sin 2crcos(s— ^)=0. (3)
The times corresponding to
jM,=0, D=0
were
h m
1st June 3 0 a.m.
15th „ 4 30 p.m.
28th „ 9 30 a.m.
If we now take the hours of Low Water of the Tides occurring nearest to the time
of the Moon’s declination vanishing, we find : —
h m
1st June s= 2 40 a.m.
15th „ 1 10 p.m.
28th „ 1 38 a.m.
Mean value of s . 1 49
Now from equation (3) we have
hence
and, finally,
s-i,= 6h or 18h,
lh 49m— «s=6h or 18h;
?,= — 4h 11“
orf +Th 49m.
The Diurnal Tide at High Water, when ^ = 0, is represented by
D=S sin 2<r cos
and had the following values : —
1st June D= +0-234 ft.
16th „ -0-360 „
28th „ +0-302 „
Mean value of D . . 0-299 „
* See Note A, p. 327.
T An examination of the signs of the numerical values of the tide shows that the negative value of is must
he chosen.
322
REV. S. HAUGHTON ON THE TIDES OE THE
The hours of High Water corresponding to these values, and nearest to the time of
the Moon’s declination vanishing, were : —
1st June ....
15th „ . . . .
28th „ . . . .
Mean
h m
8 32
8 00
6 40
7 44
Hence, using the mean value of 2 cr during the observations (45° 50'), we obtain
±0-299=Ssin 45° 50' cos (s-is);
but
h. m
s= 7 44
is=- 4 11
s—is= 11 55
which corresponds to 180°, or the cosine equal to unity. Hence we have
or, finally,
0-299 =S sin 45° 50',
c 0-299 ft.
b — sin 45° 50'
=0-417 ft.=5-00 inches.
B. Semidiurnal Tide (Heights).
If the preceding Table be plotted to scale, it is easy to separate the Semidiurnal Tide
from the Diurnal Tide just discussed ; but it is not possible, from observations made at
the Solstice only, to separate the Solar and Lunar Tide and determine their coefficients.
The general expression for the Semidiurnal Tide is
T=S' cos 2(s— fs)+M' cos 2(to— im), (3*)
where
S', M'= Solar and Lunar Coefficients, not corrected for declination or parallax,
s, m= Hour-angles of Sun and Moon,
is, v=true Soli tidal and Luni tidal Intervals.
This expression may be thrown into the form
T=A cos 2(to— B), (4)
where
A=n/M'2+S'2+2M'S' cos 2(m^Ts—i~^Isj,
tan 2B — ^ s*n sin 2 (m ~s + Q
M'cos 2 im + S' cos 2 (m — s + is)
(5)
AECTIC SEAS.— PAET IY. NOETHUMBEELAND SOUND.
A is the apparent height of the tide, and
B is the apparent Lunitidal Interval at High Water and Low Water.
At Spring-Tides we have
rn-s=im-is , | .... (6)
A=M'+S';f
at Neap-Tides we have
m—s—im—is= 90°, } (7)
A=M'— S'J
The maximum Spring-Tides occurred: —
Sun’s Hour- Angle.
Moon’s Hour-Angle.
h m
h. m
6 th June .
. 12 50 A.M.
+ 1 18
12 15 p.m.
+ 0 21
19th June
. Midnight.
+ 1 6
20th „ . .
. 11 20 A.M.
+0 2
Mean
. 0 6 '
+0~42
minimum Neap-Tides occurred: —
Sun’s Hour- Angle.
Moon’s Hour- Angle.
h m
h. m
30th May . .
. . 6 40 A.M.
-0 15
7 0 p.m.
-0 19
12th June
..40 A.M.
-0 30
3 15 p.m.
-1 40
Mean .
. +5~14
-0~26
From the Spring-Tides we find, by equation (6),
im—is= 36m;
and from the Neap-Tides, by equation (7), we obtain
The mean of these values gives us
im—i= 38m (8)
We have no means of determining im and is separately.
The maximum and minimum ranges of the Tide, corrected for Diurnal Inequality only,
were : —
Springs. Eange.
6th June 19*3 inches.
20th June 23-7 „
Mean . . 21-5
324
REV. S. HATTGHTON ON THE TIDES OF THE
Neaps. Range.
30th May 12-0 inches.
12th June LL-3 „
Mean . . 11*65 „
Substituting these values in (6) and (7), we find
2(M'+S') = 21*5,
2(M'— S') = 11*65,
and, finally,
®=0-297 (9)
It will be observed that the Diurnal Solar Tide Eange, already determined (9-40 in.),
bears a very large proportion to the Semidiurnal Tide Eanges.
C. Diurnal Tide (Times).
The following Table contains the hour in local time of High Water and Low Water,
and also the Lunitidal Intervals at High Water and Low Water elapsed from the
Moon’s passage of the meridian of the place. The Diurnal Tide in time might be cal-
culated from the Lunitidal Intervals by first or second differences, as in the case
of heights ; but it is not worth the trouble to make the calculations, as the results can
be more readily obtained by plotting the Lunitidal Intervals carefully to scale.
When this is done the diagram shows a fairly regular Diurnal Tide, with vanishing
epochs and range well marked.
The maximum accelerations and retardations of the time of High or Low Water
occasioned by the Diurnal Inequality amounted, generally, to from 35 minutes to
40 minutes, and on 1st July, at Low Water, reached 65 minutes.
D. Semidiurnal Tide (Times).
Northumberland Sound. — Lunitidal Intervals.
High. Water.
Low Water.
High Water.
Low Water.
1853.
k m
k
m
li m
1853.
h
m
k
m
k m
May 27-
4 0 p.m.
-0
46
June 1.
2
40
A.M.
6 38
27-
10 0 „
5 14
1.
8
32
„
+o
12
28.
4 40 a.m.
-0
37
1.
3
30
P.M.
7 10
28.
12 5 p.m.
6 48 .
1.
9
40
„
+ 0
56
28.
4 0; „
-1
41
2.
3
30
A.M.
6 46
28.
11 0 „
5 19
2.
9
40
„
+ 0
39
29.
4 30 A.M.
— 1
38
2.
4
20
P.M.
7 31
29.
1 0 P.M.
6 52
2.
10
30
„
+ 1
5
29-
6 0 „
-0
32
3.
4
35
A.M.
7 10
29.
Midnight.
5 28
3.
10
30
„
+0
48
30.
6 40 A.M.
-0
15
3.
5
0
P.M.
GO
30.
1 40 p.m.
6 45
3.
11
0
+
O
54
30.
7 0 „
-0
19
4.
5
0
A.M.
6 54
31.
12 50 a.m.
5 31
4.
10
48
+ 0
24
31.
8 0 „
+0
on
4.
5
30
P M.
7 6
31.
3 30 p.m.
7 52
5.
12
15
A.M.
+ i
27
• 31.
9 0 „
+ 0 58
5.
5
30
”
6 42
AECTIC SEAS. — PAET IY. NOETHUMBEELAND SOUND.
325
Northumberland Sound. — Lunitidal Intervals (continued).
High Water.
Low Water.
High Water.
Low Water.
1853. h m
h m
h m
1853. h. m
h m
h m
+0 37
June 2\ 1
5. 6 0 „
6 52
21
+ 1 18
aa
fi 6 sn „
6 58
€><%
6. 12 15 p.m
+ 0 21
22. 7 20 P.M
5 55
6. 6 20
6 26
23. 2 0 a.m
-0 5
+ 0 52
23
23
7. 12 25 p.m
-0 18
23. 8 0 p.m
5 31
7 (1 21 T.
5 38
24
j
0 7
24
8. 7 20
6 13
24. 2 0 p.m
-1 28
8. 12 40 P.M
-0 53
24. 8 30
5 2
8 8 0,,
6 27
05
+ 0 3
05
9. 8 22 „
6 25
25. 3 0 p.m
-1 23
9. 1 15 p.m
-1 9
25. 9 55 „
5 32
9. 7 43 „
5 19
26. 4 30 a.m
— 0 18
10. 2 38 a.m
-0 10
26. 11 30 „
6 42
10. 8 50 „
6 2
26. 4 0 p.m
-1 12
10. 2 0 p.m
-1 15
26. 10 40 „
5 28
10. 8 30 „
5 15
27. 5 45 a.m
+ 0 11
11. 3 40 a.m
+0 1
27. 12 16 P.M
6 42
11. 9 35 „
5 56
27. 6 0 „
+ 0 2
11. 2 30 p.m
-1 36
27. 11 0 „
5 2
11. 10 7 „
6 1
28. 6 40 a.m
+ 0 23
12. 4 0 a.m
-0 30
28. 1 38 p.m
7 21
12. 10 30
6 0
28. 6 20
-0 21
12. 3 15 p.m
-1 40
28. Midnight
5 19
12. 10 0 „
5 5
29. 7 20 A.M
+ 0 21
13. 4 53 a.m
-0 26
29. 2 10 p.m
7 11
13. 11 15 „
5 56
29- 7 40 „
+ 0 17
13
30. 1 30 a.m.
6 7
13. 10 30 p.m
4 47
30. 8 30 „
+ 0 50
14. 5 45 a.m
-0 22
30. 3 45 p.m
8 5
14. 12 15 p.m
6 8
30. 9 0 „
+ 0 56
14. 6 0 „
-0 30
July 1. 12 40 a.m
4 36
14. Midnight
5 30
1. 9 0 „
+ 0 38
15. 6 45 a.m
-0 9
1. 4 35 p.m
8 13
15. 1 10 p.m
6 16
1. 9 40 „
+ 0 54
1
15. 8 0
+ 0 42
2. 4 20 a.m
7 34
16. 12 50 a.m
5 32
2. 9 38 „
+ 0 33
16. 8 0 „
+ 0 18
2. 4 10 p.m
7 3
16. 2 15 p.m
6 33
2. 10 45 „
+ 1 16
16. 8 10 „
+ 0 3
3. 4 45 a.m
6 0
17. 2 10 A.M
6 3
3. 10 30 „
+ 0 39
17. 8 30 „
-0 1
3. 5 4 P.M
7 13
17. 3 0 p.m
6 29
3. 11 13 „
+ 0 58
17. 9 30 „
+ 0 31
4. 5 0 A.M
C 45
18. 3 12 a.m
6 13
4. 10 45 „
+ 0 6
18. 9 15 „
-0 8
4. 5 30 p.m
6 51
18. 4 35 p.m
7 12
5. 12 15 a.m
+ 1 12
18. 10 45 „
+ 0 51
5. 6 0
6 57
19. 4 50 a.m
6 56
5. 12 45 p.m
+ 1 17
19. 10 12 „
-0 6
5. 6 15
6 47
19. 4 55 p.m
6 36
6. 1 0 A.M
+ 1 8
19. Midnight
+ 1 6
6. 8 0 „
8 8
20. . 5 30 a.m
6 36
6. 1 0 p.m. ......
+ 0 40
20. 11 20 „
+ 0 2
6. 6 40 „
6 20
20. 6 0 p.m
6 42
7. 2 0 A.M
+ 1 16
20.
21.
—
7. 8 0 „
7 16
21.
—
Mean
+ 0 7-05
6 35-35
MDCCCLXXV.
X
326
REV. S. HAUGfHTON ON THE TIDES OE THE
Having corrected the curve of Lunitidal Intervals for the Diurnal Inequality, the
remainder is the acceleration or retardation on the time of the Semidiurnal Tide.
We have, by equation (5),
tan 2B— sin + sf sin 2 (m — s + is)
M/ cos2zm + S' cos 2 (m— s + i])'
Differentiating this expression so as to obtain for B a maximum value, we find, as
the equation of condition,
0=M' cos 2 (m^s — + S' (10)
Substituting in (5) we obtain
tan 2B=
-t/M'2 — S'2 sin 2 im + S' cos 2 i„,
and assuming
VM'2— S'2 cos 2zm — S' sin 2 i„
S'
M'
=sin 25,
we find, after reduction,
and, finally,
and
tan 2B=tan 2 («m+0) ;
2(B-C)=25
~=sin2(B— C).
(11)
(12)
On examining the Lunitidal Curve, corrected for Diurnal Inequality, we find the fol-
lowing ranges from Springs to Neaps : —
High. Water.
Low Water.
h m
h m
+1 0
7 18
-1 6
5 30
2~~6
1 48
or mean maximum range
2B=lh 57m.
Although we have not found the value of im, we may take as an approximation to it
the Moon’s mean Hour- Angle at High Water, already given in the Table,
im= + 0h 7m.
Hence we have
2B-2C=lh 57m— 0h 14m,
or
^=sin (lh 43m)=sin (24° 55')=0-421 (13)
Collecting together the partial results obtained at this most interesting Tidal Station,
we obtain: — -
AECTIC SEAS.— PAET IV. NOETHUMBEELAND SOUND.
327
Diurnal Tide.
1. Solitidal Interval,
i=-4h 11“
2. Solar Coefficient, corrected for Declination,
S=5‘0 inches.
3. Lunitidal Interval,
^=-8*8“
4. Solar Coefficient, corrected for Declination,
M=4’0 inches.
Semidiurnal Tide.
1. Mean Lunitidal Interval,
High Water. Lew Water,
h m h m
4-0 7-05 6 35-35 '
2. Difference between Lunitidal and Solitidal Intervals,
im — ^=38m.
3. Approximate ratios of uncorrected Solar and Lunar Coefficients,
^,=0-297 (Heights)
= 0-421 (Intervals).
Note A.— Added July 1, 1875.
At the time of writing this paper I abandoned the attempt to determine the Lunar
Diurnal Tide, in consequence of the breakdown of the observations which occurred in
the neighbourhood of the 23rd June, which corresponds with one of the maxima of the
Lunar Declination. This Tide may, however, he found from the tides of 8th and 9th
June and 5th and 6th July, which also correspond to maxima of the Declination. The
Lunar Diurnal Tide is the difference between the Total Diurnal Tide and the Solar
Diurnal Tide, which is determined in the paper.
In the following Tables, the Solar Diurnal Tide is calculated from the formula
Solar Tide=3'58 cos(s+4h llm),
founded on the constants
S=5-00 inches,
4=-4hllm.
328
REY. S. H AUGHT ON ON THE TIDES. OF THE
North Declination of Moon a Maximum.
High Water.
Diurnal Tide.
Solar.
Lunar.
h
m
inches.
inches.
inches.
June 7-
12
45 P.M
- 1-40
+ 1-20
-2-60
8.
1
0 A.M
+ 1-40
-0-76
+ 2-16
8.
12
40 P.M
— 1*53
+ 1-06
-2-59
9-
2
0 A.M
+ 1-32
+ 0-17
+ 1-15
9-
1
15 P.M
-1-28
+ 0-53
-1-81
10.
2
38 A.M
+ 1*34
+ 0-78
+ 0-56
Mean ...
±1-812
Low Water.
June 7. 6 21 p.m
8. 7 20 a.m
8. 8 0 p.m
9. 8 22 a.m
9. 7 43 p.m
10. 8 05 a.m
-5-69
+ 5-70
-5-69
+ 5-72
— 5*75
+ 5*81
-3-28
+ 3-51
-3-58
+ 3-52
-3-55
+ 3-58
-2*41
+ 2-19
-2-11
+ 2-20
-2-20
+ 2-23
Mean ...
+ 2-223
High Water.
July 4. 10 45 a.m
5. 12 15 a.m
5. 12 45 p.m
6. 1 0 A.M
6. 1 0 p.m
— 0-25
+ 0-18
-0-37
+ 0-87
-0-33
+ 2-25
— 1-42
+ 0-54
-0*76
+ 0-76
—2-50
+ 1-60
-0-91
+ 1-63
— 1-09
Mean ...
+ 1-546
Low Water.
July 4. 5 30 p.m
5. 6 0 a.m
5. 6 15 p.m
6. 8 00 a.m
6. 6 40 p.m
-5-88
+ 6-00
— 6-13
+ 6-25
-6-25
-2-91
+ 3-18
— 3-25
+ 3-58
-3-38
-2-97
+ 2-82
— 2-88
+ 2-67
— 2-87
Mean ...
+ 2-842
If m denote the Moon's Hour-Angle at High Water, we have at High Water,
Lunar Tide=M sin 2^ cos m—im, (a)
and at Low Water,
Lunar Tide = — M sin 2/* sin m — im (b)
Hence we find (observing that the Lunar Tide has the same sign at High Water and
Low Water)
June 7, 8, 9 ... . 2^=49° 30' N.
2223
tan m—im— —
m-4= — 50° 49' or +129° IV
= — 3h 23m or -\-Sh 37m.
AECTIC SEAS. — PAET IV. NOETHUMBEELAND SOUND.
329
The value of m, as found from all the observations, is given in the paper,
Hence we find
m=0h 7m.
?m= + 3h 30m or — 8h 30m.
The signs of the Lunar Tide show that the negative value of im is the proper one ;
hence
?;-_8h30m (c)
We have also, from (a) and (b),
M sin2^=>/(2-223)2H-(l-812)2=:2-861,
and, finally,
M = 3-77 inches (d)
July 4, 5, 6 . . . . 2/a=49° 30' N.
— 2842
tan
m-im=~ 61° 27' or +118° 33'
=— 4h 6m or +7h 54m,
?,n= + 4h 13m or — 7h 47m, ........ (e)
of which the latter value must be used.
We have also
M sin 2/4=v/(L546)2+(2-842)2=3-235,
and, finally,
M=4‘26 inches (f)
The mean values of im and M, deduced from the preceding equations, are
;.=-8-8” (g)
M = 4‘00 inches (h)
The Lunar Diurnal Tide is therefore expressed by the equation
Lunar Tide = 4 sin 2/4 cos(m+8h 8ra) (i)
[ 331 ]
XII. On the Tides of the Arctic Seas.
By the Bev. Samuel Haughton, M.I). Bubl., B.C.L. Own., F.B.S.,
Fellow of Trinity College , Bullin.
Part V. On the Tides of Befuge Cove, Wellington Channel.
Received July 11, — Read November 19, 1874.
The following observations, like those at Northumberland Sound, were made on board
H.M.S. ‘Assistance,’ under the command of Sir Edwakd Belcher, R.N., K.C.B.
They were made from 16th September to 11th October 1853. Although the period of
observation is so short, yet, owing to the fact that it was the time of Equinox, some
useful information has been obtained as to the Lunar Diurnal Tide at this Station.
The position of Refuge Cove is
Lat. 75° 31' N.
Long. 92° 10' W.
The following Table contains the Height of each High and Low Water, and the Height
of the Diurnal Tide, calculated by the second difference of the heights.
Table I. — Refuge Cove.
Time.
High. Water.
Height.
Low Water.
Height.
Diurnal Tide
at
High Water.
Diurnal Tide
at
Low Water.
1 1853.
h
m
ft.
in.
ft.
in.
ft.
ft.
Sept. 17-
6
30
A.M.
6
0
17-
12
30
P.M.
10
17.
6
25
„
5
3
0-313
18.
1
0
A.M.
11
H
0-573
18.
7
30
„
5
9
0-271
18.
12
50
P.M.
10
7
0-477
18.
7
0
„
5
2
0-224
19.
l
30
A.M.
11
4
0-393
19.
7
40
„
5
6
0-193 ,
19.
l
45
P.M.
10
6
0-271
19.
7
55
„
5
2
0-167
20.
2
0
A.M.
10
11
0-135
20.
8
20
„
5
8
0-094
20.
2
10
P.M.
10
11
0-057
20.
8
0
„
5
10
0-005
21.
2
5
A.M.
11
0
0-055
21.
8
30
„
6
0
0-083
21.
2
25
P.M.
10
9
0-026
21.
8
40
„
6
5
0-203
22.
2
54
A.M.
10
71
0-046
22.
8
45
„
6
0
0-323
22.
3
30
P.M.
10
8
0-120
22.
9
45
”
6
11
0-234
REV. S. HAUGHTON ON THE TIDES OE THE
Table I. (continued).
Time.
High Water.
Height.
Low Water.
Height.
Diurnal Tide
at
High Water.
Diurnal Tide
at
Low Water.
1853. li m
ft. in.
ft. in.
ft.
ft.
Sept. 23. 3 30 a.m
10 2
0-112
23. 9 50 „
6 2
0-439
23. 3 55 p.m
10 4
0-005
23. 10 30 ,,
7 6
0-516
10 7
0-041
24. 10 30 „
6 9
0-594
24. 5 0 p.m
10 3
0-125
24. 11 10 „
8 0
0-604
25. 5 10 a.m
9 4
0-266
25. 10 20 „
6 10
0-687
25. 5 30 p.m
9 10
0-234
26. 12 30 a.m
8 6
0-698
9 6
0-240
26. 12 30 p.m
7 3
0-661
26. 6 30 „
9 10
0-401
27. 1 15 A.M
8 6
0-651 1
27. 7 0 „
8 6
0-531
27. 1 30 p.m
7 1
0-635
27. 7 30 „
9 7
0-594
28. 3 0 a.m
8 3
0-578
28. 8 0 „
8 8
0-740
28. 3 30 p.m
7 1
0-516
28. 10 5 „
10 10
0-849
29 4 0 A.,\r.
7 ll
0-455
29. 10 25 „
9 4
0-799
29. 4 0 p.m
6 10
0-375
29. 10 40 „
1 1 0
0-740
30. 5 0 a.m
7 21
0-328
30. 10 45 „
9 10jf
0-734
30. 4 45 p.m
6 5
0-344
30. 11 45 „
11 10
0-672
Oct. 1. 6 0 A.M
7""i
0-331
]. 11 0
11 0
0-565
1. 5 15 p.m
6 4
0-208
1. 11 45
12 3
0-490
2. 5 0 a.m
6 7
0-182
2. 12 30 p.m
11 5
0-354
2. 6 15 „
6 3
0-115
3. 12 20 a.m
12 2
0-224
3. 6 0 „
6 8
0-110
3. 1 0 p.m
12 6
0-078
3. 6 45 „
7 4
0-099
3. Midnight
13 0
0-088
4. 7 15 A.M
7 4
0-188
4. Noon
13 0
0-094
4. 8 0 p.m
7 10
0-297
5. 10 A.M
13 3
0-094
5. 8 30
7 0
0-380
5, 1 28 p.m
13 0
0-094
5. 8 20 „
7 9
0-386
6. 1 40 A.M
13 0
0-135
6. 8 30 „
6 11
0-380
6. 1 0 p.m
12 6
0-182
6. 9 30 „
7 8
0-386
7. 4 0 A.M
12 11
0-125
7. 9 0 „
7 l
0-484
7. 3 0 p.m
12 9
0-026
7- 9 45 „
I 8 5
0-615
ARCTIC SEAS —PART V. REFUGE COVE.
333
Table I. (continued).
Time.
High Water.
Height.
Low Water.
Height.
Diurnal Tide
at
High Water.
Diurnal Tide
at
Low Water.
1853. h m
ft. in.
ft. in.
ft.
ft.
Oct. 8. 4 0 a.m
12 6
0*031
8. 10 0 „
7 2
0-688
8. 5 0 p.m
12 3
0-172
8. 10 50 „
8 8
0-755
9. 4 15 a.m
11 5
0-370
9. 10 50 „
7 3
0-823
9. 4 40 p.m
12 2
0-547
10. 12 10 A.M
9 4
0-823
10. 4 30 „
10 9
0-651
10. 12 30 p.m
8 0
0-709
10. 6 45
11. 2 0 A.M
12 2
9 6
0-646
11. 6 40 „
11 0
A. Diurnal Tide.
The general expression for the Diurnal Tide is
D=M sin 2(a cos(m— 4)+S sin 2<r cos(s— is), (1)
which at the Equinoxes reduces simply to the Lunar Tide, viz.
D=M sin 2^ cos(m— im) (2)
If the Tides be plotted carefully to scale, it appears that the Diurnal Tides in height
vanish together at High Water and Low Water, when [a=0, or nearly so.
The mean interval from the time of the Moon’s declination vanishing to the dis-
appearance of the Diurnal Inequality is about 36 hours, which may be regarded as the
age of the Lunar Diurnal Tide. It is evident from equation (2) that if h and l repre-
sent the range of Tide at Lligh Water and Low Water respectively, since the phase
changes by 903 from High Water to Low Water, we have the following equations to
determine the unknown constants im and M: —
2M sin 2(max. value of [a)=s/Ii2-{-12. . (4)
The mean maximum values of h and l were found to be
hence we find
Ar=0'849 foot,
Z=0-761 foot;
cot(m— ?'m) =
±
849
76T
m-4=4 1°52' or -138° 8'
=2h 53m or — 9h 7m .
2 T
MDCCCLXXV.
(5)
334
KEY. S. HAUGHTON ON THE TIDES OE THE
The mean values of in at High Water and Low Water, as appears from the following
Table, are : —
h. m
High Water m— — 0 27
Low Water 6 1
or, reducing both to High-Water Standard,
m= — 0 27
-0 11
Mean . . . . —0 19
Hence, by equation (5),
— 0h19m— im= 2b 53m,
im= — 3h 12m,
or
• — 0h19m— ?m= — 9h 7m,
im= + 8h48m.
An examination of the signs of the Diurnal Tide shows that we must select the value
im= + 8h48m 5 (bis)
From equation (4) we find
V(0-849)2+(0’761)2
iVi~ 2 sin 49°
=076 foot=9-06 inches (6)
If we plot the Luni tidal Intervals at High Water and Low Water to scale, from the
following Table we obtain the Diurnal Inequality in time. It produces a maximum
acceleration or retardation in the time of Tide, amounting to 39 minutes.
The following Table gives the Lunitidal Intervals at High Water and Low Water.
Table II. — Refuge Cove. Lunitidal Intervals.
High Water.
Low Water.
High Water.
Low Water.
1853.
h
m
h
m
h
m
1853.
h
m
h
m
h m
! Sept. 17-
6
30 A.M.
6
35
Sept. 21.
8
30 A.M
6 19
17-
12
30 p.m.
+ 0
11
21.
2
25 p.m
— 0
48
17.
6
25 „
5
54
21.
8
40 „
6 33
18.
1
0 A.M.
+ 0
20
22.
2
54 A.M
-0
39
18.
7
30 „
5
10
22.
8
45 „
6 48
18.
12
50 p.m.
-0
14
22.
3
30 p.m
-0
27
18.
7
0 „
6
4
22.
9
45 „
6 12
19-
1
30 A.M.
+0
7
23.
3
30 A.M
-0
49
19.
7
40 „
5
43
23.
9
50 „
6 29
19-
1
45 p.m.
-0
2
23.
3
55 p.m
-0
48
19.
7
55 „
5
52
23.
10
30 „
6 13
20.
2
0 A.M.
-0
6
24.
4
0 A.M
-1
6
20.
8
20 „
5
46
24.
10
40 „
6 26
20.
2
1 0 P.M.
-0
20
24.
5
0 P.M
-0
30
20.
8
0 „
6
30
24.
11
10 „
G 20
21.
2
5 A.M.
-0
44
25.
5
10 A.M
-0
45
AECTIC SEAS. — PAET V. EEFUGE COYE.
835
Table II. (continued).
High Water.
Low Water.
High Water.
Low Water.
1853.
k
m
k m
h
m
1853.
h m
k m
h m
Sept. 25.
10
20 A.M.
7
35
Oct. 3.
6 45 p.m.
5 51
25.
5
30 p.m.
-0 49
3.
Midnight
— 1 0
26.
12
30 A.M.
5
49
4.
7 15 A.M.
5 45
26.
5
45 „
-1 1
4.
Noon
-1 27
26.
12
30 p.m.
6
16
4.
8 0 p.m.
5 27
26.
6
30 „
-0 40
5.
1 0 A.M.
-0 51
27.
1
15 A.M.
5
55
5.
8 30 „
5 21
27.
7
0 „
-0 37
5.
1 28 p.m.
-0 53
27.
l
30 p.m.
6
7
5.
8 20 „
6 1
2.7.
7
30 „
— 0 31
6.
1 40 a.m.
-1 5
28.
3
0 A.M.
5
l
6.
8 30 „
6 15
28.
8
0 „
-0 29
6.
1 0 P.M.
-2 17
28.
3
30 p.m.
4
59
6.
9 30 „
5 47
28.
10
5 „
+ 1 12
7.
4 0 A.M.
+ 0 19
29.
4
0 A.M.
4
53
7.
9 0 „
6 41
29.
10
25 „
+ 1 6
7.
3 0 p.m.
-1 16
29.
4
0 P.M.
5
19
7-
9 45 „
6 31 1
29.
10
40 „
+ 0 57
8.
4 0 A.M.
-0 40
30.
5
0 A.M.
4
43
8.
10 0 „
6 40
30.
10
45 „
+ 0 36
8.
5 0 p.m.
-0 17
30.
4
45 p.m.
5
24
8.
10 50 „
6 27
30.
11
45 „
+ 1 12
9.
4 15 A.M.
-1 26
Oct. 1.
6
0 A.M.
4
33
9.
10 50 „
6 51
1.
11
o »
+ 0 2
9.
4 50 p.m.
00
©I
7
1.
5
15 P.M.
6
17
10.
12 10 a.m.
6 8
1.
11
45 „
+ 0 23
10.
4 30 „
-2 12
2.
5
0 A.M.
6
22
10.
12 30 p.m.
6 12
2.
12
30 p.m.
+ 0 18
10.
6 45 „
— 0 31
2.
6
15 „
5
57
11.
2 0 A.M.
5 16
3.
12
20 A.M.
-0 16
11.
6 40 „
......
-1 0
3.
6
o
6
36
3.
1
0 P.M.
+ 0 24
Mean
-0 26-7
6 1-1
If we compare the mean Lunitidal Intervals here found with the corresponding
intervals at Northumberland Sound, we find : —
Mean Lunitidal Interval.
High Water. Low Water,
h m h m
Eefuge Cove —0 26-7 6 IT
Northumberland Sound . . -{-0 7'05 6 35-35
Difference .... 33-75 34-25
These differences represent the time of the Atlantic Tide-wave passing from Eefuge
Cove to Northumberland Sound (uncorrected for longitude) ; and their agreement is a
proof of the accuracy of the observations at both places.
B. Semidiurnal Tide (Heights).
When Table I. is plotted to scale, it is easy to correct the tide for the Diurnal
Inequality, or to do so by th.e Diurnal Tide at High Water and Low Water given in
2 y 2
336
EEV. S. H AUGHT ON ON THE TIDES OF THE
that Table. When this correction is made we find the following Spring
Ranges : —
ft. in.
Springs. — 19th September, 1.30 a.m. ...... 5 8
5th October, 1.28 p.m . 5 8|
Neaps. — 27th September, 7.0 a.m. 14
and Neap
Using the formula for the Semidiurnal Tide,
we fin'd at Springs
and at Neaps
from which we obtain
T=M' cos 2 (m-iJ+S' cos 2 (s-is),
T=A cos 2 (m— B),
(M'+S')= 34T inches,
(M7 — S') = 8 inches;
2 M'=42T inches,
2 S' =26-1
S^_
M'“
0-621.
(7)
C. Semidiurnal Tide (Intervals).
When Table II. is plotted to scale, and the Tide corrected for the Diurnal Inequality,
we obtain the following results, making use of the formulae given in discussing the
Tide at Northumberland Sound : —
Maximum Value of 2 B.
Range of Lunitidal Interval at High Water.
h m
29th September, 10.25 a.m +16
9th October, 4.50 p.m —1 24
2 B=2 30
Range of Lunitidal Interval at Low Water.
h m
25th September, 10.20 a.m +6 48
28th September, 3.30 p.m +4 59
2B=1 49
The approximate value of im, taken from the mean of the observations, is,
h m
At High Water —0 27
Low Water •— 0 11
AECTIC SEAS.— PAET Y. EEFUGE COVE.
Hence we have
2(B-y.
h m. o /
High Water 3 24 49 30
Low Water 2 3 30 0
Hence we obtain
' = sin 2 (B— 4)=0-76 High Water
= 0-50 Low Water.
Mean .... 0-63
Collecting the several constants, we obtain: —
Diurnal Tide.
im = + 8h 48m,
M'= 9 ‘06 inches.
Semidiurnal Tide.
^=0-62 (Heights),
^-,=0-63 (Intervals).
High Water. Low Water,
Mean Lunitidal Interval = —0h 26m,7 6h lm,l.
C 339 ]
XIII. On the Tides of the Arctic Seas.
By the Bev. Samuel Haughton, M.JD. Buhl ., D.C.L. Own., F.B.S.,
Fellow of Trinity College, Dublin.
Part VI. Tides of Port Kennedy, in Bellot Strait.
Received January 20, — Read March 4, 1875.
The following observations were made by Admiral Sir Leopold M‘Clintock (then
Captain) in the month of July 1859, at Port Kennedy, in Bellot Strait, on board the
yacht ‘ Fox,’ in eleven fathoms depth, lat. 72° OP N., long. 94° 15' W. The observa-
tions were made hourly, and, judging from the consistent and highly interesting results
obtained from them, they must have been made and recorded with unusual care.
In Table I. the first column contains the Solar Hour, the second contains the
Height of Tide, the third contains the Diurnal Tide, and the fourth the Semidiurnal
Tide.
The Diurnal Tide was calculated as follows : — Let hx, h2, h3 be the heights of the
water at three periods, separated by intervals of twelve hours each, then the Diurnal
Tide corresponding to the height h2 is
D
Aj— 2A2rf-A3
~ 4
(1)
The third column was calculated from the second by this formula, and the fourth
column, containing the Semidiurnal Tide only, is the algebraical sum of the second and
third columns.
4!
REV. S. HATTG-HTON ON THE TIDES OE THE
Table I. — Hourly Values of the Diurnal and Semidiurnal Tide at Port Kennedy
in July 1859.
5th July.
7th July.
Time.
Height.
Diurnal
Tide.
Semidiurnal
Tide.
Time.
Height.
Diurnal
Tide.
Semidiurnal
Tide.
ft. in.
ft.
in.
ft.
in.
ft. in.
ft.
in
ft. in.
Noon.
Noon.
3 10
+ 0
94
4
74
1.
5 2
1.
4 0
+0
114
4
114
2.
5 11
2. 1
4 94
+ 1
Of
5
104
3.
6 2|
3.
5 8
+ 1
If
6
91
4.
6 3
4.
6 5|
+ 1
1
7
64
5.
6 OJ
5.
6 11
+ 1
24
8
14
6.
5 7
6.
7 l
+1
01
8
11
7-
4 9 h
7-
7 01
+ 0
8f
7
94
8.
4 2|
8.
6 9
+ 0
5
7
9.
3 94
9.
6 2
+0
2
6
4
10.
3 7
10.
5 10
-0
5
81
11.
4 01
11.
5 8
-0
5
5
3
Midnight.
5 2
Midnight.
5 101
-0
9 \
5
1
13.
6 10
-0
8
6
2
13.
6 0'
-0
104
5
If
14.
8 1
— 1
2
6
11
14.
6 10
—1
0
5
10
j 15.
9 3
-1
Si
7
94
15.
7 9
-1
Of
6
84
16.
10 0
—1
n
8
34
16.
8 5
-0
ni
7
54
17.
10 01
-1
9 1
8
3
17.
8 11
-0
11
8
0
18.
9 31
-1
H
7
8|
18.
9 24
-0
104
8
44
19.
7 ll J
-1
3
6
8
19-
8 101
-0
74
8
3
20.
6 8
-0
10|
5
94
20.
8 2i
-0
44
7
104
21.
5 5
— 0
6i
4
101
21.
7 21
+ 0
1
7
34
22.
4 8
-0
H
4
4£
°>2
6 2
+ 0
34
6
54
23.
4 1
1 +0
1
4
2
23.
5 6
+0
64
6
°4
Mean ...
6
8£
Mean ...
1 6
7f
6th July.
8 th July.
Noon.
4 2
+ 0
5
4
7
Noon.
4 91
+ 0
94
5
H
1.
4 9|
+ 0
6
5
3|
1.
4 7
+ 0
104
5
54
2.
5 8J
+ 0
11
6
74
2.
4 11
+ 1
04
5
114
3.
6 4|
+ 1
O
7
64
3.
5 7
+ 1
04
6
74
4.
6 10
+ 1
34
8
14
4.
6 6
+0
10
7
4
5.
6 11
+ 1
51
8
44
5.
7 24
+ 0
9
7
114
6.
6 9
+1
21
7
114
6.
7 10|
+0
6f
8
54
7.
6 2
+0
n|
7
14
7.
8 24
+ 0
3f
8
64
8.
5 6|
+0
7f
6
24
8.
8 3
+ 0
1
8
4
9-
4 ll'
+0
4
5
3
9.
7 ll
-0
24
7
8f
10.
4 8
+0
1
4
9
10.
7 7
-0
5g
7
14
11.
4 51
— 0
2
4
31
11.
7 2
— 0
g
6
6
Midnight.
4 101
-0
54
4
54
Midnight.
6 11
-0
104
6
04
13.
5 9
-0
74
5
14
13.
6 8
-0
114
5
8f
14.
7 0
— 0
104
6
14
14.
7 14
— 1
1
6
04
15.
8 ll
-1
0|
7
Of
15.
7 6“
— 1
0
6
6
16.
8 10~
-1
1
7
9
16.
7 114
— 0
91
7
2
17.
9 8
— 1
44
8
34
17.
8 6
-0
8
7
10
18.
9 1
-1
4'
7
9
18.
8 94
-0
41
8
5
19.
8 ll
-0
9
7
41
19.
8 94
-0
If
8
7f
20.
7 0
-0
5
6
7
20.
8 7
+ 0
1
8
8
21.
5 9J
-0
14
5
8
21.
7 104
+ 0
5
8
31
5 0
+ 0
n
5
14
22.
7 1
+ 0
84
7
94
23.
4 2
+ 0
54
4
74
23.
6 21
+ 0
11
7
n
1
Mean ...
6
4
Mean ...
7
2#
AECTIC SEAS. — PAET VI. POET KENNEDY.
341
Table I. (continued).
9th July.
11th July.
Time.
Height.
Diurnal
Tide.
Semidiurnal
Tide.
Time.
Height.
I Diurnal
Tide.
Semidiurnal
Tide.
ft.
in.
ft
in.
ft
in.
ft.
in.
ft.
in.
ft.
in.
N n.
5
7
+ 1
i
6
8
Noon.
7
0
+ 1
34
8
54
1.
5
0
+ 0
ii
5
11
1.
7
1
+ 1
1
8
2.
5
°i
+ 0
iof
5
114
2.
7
0|
+0
9
7
9 J
3.
5
5
+ 1
0
6
5
3.
7
0
+ 0
10
7
10
4.
6
0l
+0
nj
7
2
4.
6
114
+0
94
7
8|
5.
7
1
+ 0
84
7
94
5.
6
111
+0
8|
7
84
6.
8
2
+ 0
3|
8
54
6.
7
0
+ 0
84
7
84
7.
8
9b
+ 0
0
8
94
7.
7
1
+ 0
8
7
9
8.
9
2b
-0
3
8
ll 4
8.
8
]
+ 0
2
8
3
9-
9
5b
-0
11
8
64
9-
8
9
-0
4
8
5
10.
9
4
-0
10|
8
54
10.
9
11
-0
11|
8
H4
11.
8
11
-1
1
7
10
11.
10
1
-1
4
8
9
Midnight.
8
7
-1
0 1
7
4f
Midnight.
10
14
—1
64
8
7
13.
7
0
-0
9
6
3
13.
9
8
— 1
6
8
2
14.
6
7
— 0
n
5
ni
14.
9
0
— 1
14
7
104
15.
7
34
-0
I0i
6
54
15.
8
9
-1
5
7
4
16.
8
4
-1
1
7
3
16.
8
6
-1
4|
7
14
17.
8
6
-0
94
7
84
17.
8
6
— 1
44
7
14
18.
8
74
-0
1
8
64
18.
8
6
-0
114
7
6|
19-
8
10
+ 0
1
8
11
19-
8
6
-0
11
7
7
20.
8
9 \
+ 0
H
9
l
20.
8
6
— 0
44
8
14
21.
8
4
+ 0
6
8
10
21.
7
9|
+ 0
0
7
H4
22.
8
0
+ 0
84
8
84
22.
7
10
+ 0
84
8
64
23.
7
3
+ 0 11|
8
23.
7
H
+1
64
8
lOf
Mean ...
7
8
|
Mean ...
| 7 ill
10 th July.
12th July.
Noon.
6
10
+ 1
Of
7
iof
Noon.
6
104
+ 1
84
8
6|
1.
6
0
+0
11
6
11
1.
6
24
+ 1
84
7
114
2.
5
n
+0
104
6
5f
2.
6
54
+ 1
34
7
8f
3.
5
9
+ 1
i
6
10
3.
4
94
+ 1
11
6
84
4.
6
1
+ 1
2
7
3
4.
4
5
+ 1
84
6
14
5.
6
9
+ 0
10
7
7
5.
4
6
+ 1
94
6
34
6.
7
8|
+ 0
44
8
0|
6.
5
01
+ 1
5
6
54
7.
8
94
— 0
Of
8
8f
7.
6
3
+ 0
94
7
04
8.
9
H
-0
6
9
°i
8.
7
5
+ 0
24
7
74
9.
9
2
-0
5
8
9
9-
7
6i
+ 0
04
7
7~
10.
9
5
-0
84
8
8#
10.
8
74
-0
54
8
24
11.
9
6
— 1
0|
8
54
11.
10
9
-1
74
9
14
Midnight.
9
4
— 1
0
8
Midnight.
10
5
— 1
74
8
94
13.'
8
94
—1
n
7
8
13.
9
8
-1
74
8
04
14.
8
14
-0
1 0|
7
2§
14.
9
04
— 1
44
7
8
15.
8
7
—1
U
7
5f
15.
8
54
-1
8
6
94
16.
8
6
-1
0
7
6
16.
8
1
-1
10|
6
24
17.
8
4
-0
9
7
7
17.
7
7
— 1
64
6
Of
18.
8
4
-0
6
7
10
18.
7
3
-1
14
6
14
19.
8
4
-0
2§
8
11
19.
7
11
-0
64
6
7
20.
8
4
+ 0
3
8
7
20.
7
2~
+0
04
7
24
21.
8
4
+ 0
3|
8
7f
21.
7
6
+ 0
94
8
34
22.
8
1
+ 0
94
8
l°4
22.
7
8
+ 0
9
8
23.
7
6
+ 1
If
8
7|
23.
7
8
+ 1
54
9
14
Mean ...
7
114
Mean ...
7
U
mdccclxxv. 2 z
342
BEY. S. HATTGHTON THE TIDES OE THE
Table I. (continued).
13th July.
15 th July.
Time.
Height.
Diurnal
Tide.
Semidiurnal
Tide.
Time.
Height.
Diurnal
Tide.
Semidiurnal
Tide.
ft.
in.
ft.
in.
ft.
in.
ft.
in.
ft.
in.
ft.
in/
Noon.
7
5
+ 1
71
9
04
Noon.
8
1
+ 1
34
9
4|
1.
6
7
+ 2
0
8
7
1.
7
10
+ 1
54
9
34
2.
6
2
+ 1
ni
8
14
2.
7
3
+ 1
9
9
0
3.
5
6
+ 1
7
7
1
3.
6
4
+ 1
Hi
8
34
4.
4
2
+ 2
n
6
44
4.
5
8
+ 1
104
7
64
5.
4
7
+ 1
7
6
2
5.
4
7
+ 1
102
6
53
6.
4
li
+ 1
2f
6
If
6.
4
91
~2
+ 1
71
5
104
7.
5
10
+ 0
8
6
6
7-
4
64
+ 1
34
5
10
8.
7
1
+0
°i
7
li
8.
5
5
+0
94
6
24
9-
8
7
-0
7i
7
H|
9.
6
10
+0
2
7
0
10.
9
6
-0
ni
8
64
10.
8
3
-0
4
7
11
11.
10
4
-1
4
9
0
11.
9
7
— 0
9|
8
9i
Midnight.
11
0
— 1
9
9
3
Midnight.
9
10
-0
11
8
11
13.
11
6*
— 2
34
9
3
13.
9
10
-0
114
. 8
104
14.
11
1
2
4f
8
8i
14.
9
11
-1
3
8
8
15.
10
2
— 2
2#
7
104
15.
9
11
- 1
74
8
34
16.
9
0
-2
24
6
94
16.
9
1
-1
7i
7
si
17-
7
11
- 1
8i
6
2|
17.
8
9
-1
74
6
64
18.
7
6
-1
4f
6
li
18.
7
5
-1
6
5
11
19-
7
2-
-0
Hi
6
3
19.
7
°4
-1
34
5
9
20.
7
i
-0
H
6
9|
20.
7
o|
-0
H4
6
1
21.
7
H
+0
4f
7
8i
21.
7
24
-0
3i
6
Hi
22.
7
7
+ 0
104
8
Si
22.
7
74
+0
22
7
H>i
23.
7
84
+1
24
8
11
23.
7
n|
+0
6i
8
52
Mean ...
7
74
Mean ...
7
63
14th July.
16th July.
Noon.
7
74
+ 1
8|
9
4i
Noon.
7
114
+ 0
104
1 8
10
1.
7
H
+ 2
2
9
54
1.
8
04
+ 1
If
9
24
2.
6
5
+ 2
54
8
104
2.
7
7
+ 1
7
9
2
3.
5
7
+ 2
4f
7
114
3.
7
04
+ 1
104
8
11
4.
5
0
+ 2
*4
7
24
4.
6
r
+ 1
10“
7
11
5.
4
6
+ 1
104
6
44
5.
5
3
+ 1
9|
7
Of
6.
4
5
+ 1
6|
5
Hi
6.
4
7
+ 1
72
6
23
7.
4
9
+ 1
24
5
114
7.
4
5
+ 1
^2
5
101
8.
6
1
+ 0
54
6
64
8.
4
10
+ 1
14
5
114
9.
7
7
-0
24
7
44
9-
6
6
+ 0
3|
6
93
10.
9
l
-0
9
8
4'
10.
7
11
-0
°4
7
101
11.
9
ll
-1
54
8
54
11.
8
5
-0
4
8
1
Midnight.
11
O
-1
5
9
9~
Midnight.
9
7
— 0
94
8
94
13.
11
8
—1
94
9
104
13.
10
10
-1
1
9
9
14.
11
64
2
44
9
24
14.
11
7
— 1
1041
9
84
15.
10
7
— 2
S|
8
34
15.
11
8
-2
24
9
54
16.
9
9
2
24
7
64
16.
10
5
-1
113
8
5i
17.
8
7
— 2
04
6
6|
17.
9
7
-1
114
7
74
18.
7
7
-1
74
5
114
18.
8
4
-1
8i
6
7$
19.
7
2
-1
3
5
11
19.
7
8
-1
34
6
44
20.
7
0
-0
7
6
5
20.
7
2
-1
24
5
in
21.
7
1
+0
Of
7
if
21.
7
0J
-0
6i
6
6i
22.
7
64
+0
64
8
!i
22.'
7
0
+0
2i
7
Ql
23.
7
111
+ 0 lOf
8
104
23.
7
6
+0
4*
7
i»i
Mean ...
8
13
1
Mean ...1
7
9
AKCTIC SEAS.— PAST VI. POET KENNEDY.
Table I. (continued).
17 th July.
19 th July.
Time.
Height.
Diurnal
Tide.
Semidiurnal
Tide.
Time.
Height.
Diurnal
Tide.
Semidiurnal
Tide.
ft.
in.
ft.
in.
ft.
in.
ft.
in.
ft.
in.
ft.
in.
Noon.
8
0
+ 0
84
8
8|
Noon.
7
oi
+ 0
64
7
64
1.
8
3
+ 1
1
9
4
1.
7
6
+0
104
8
44
Om
8
1
+ 1
u
9
8f
2
8
0
+0
114
8
114
3.
7
6
+ 2
°4
9
64
3.
8
1
+1
0
9
1
4.
6
10
+ 1
ni
8
94
4.
7
8
+ 1
24
8
104
5.
6
01
+ 1
io|
7
H4
5.
7
2
+ 1
4
8
6
6.
5
4
+ 1
7?
6
1 1 4
6.
6
2
+ 1
64
7
84
7.
4
9
+ 1
S#
6
2|
7-
5
6
+1
3
6
9
8.
4
81
+ 1
21
5
11
8.
5
3
+0
10
6
1
9-
5
6
+ 0
114
6
54
9.
5
1
+0
74
5
84
10.
6
10
-0
04
6
9i
10.
5
5
+0
fij
5
104
11.
8
0
-0
41
7
7J
11.
6
5
+0
04
6
54
Midnight.
9
3
-0
81
8
61
Midnight.
7
9
-0
6
7
3
13.
10
0
-0
11
9
1
13.
8
11
-0
94
8
14
14.
11
2
-1
5
9
9
14.
9
10
-0
114
8
104
15.
11
5
— 1
10
9
7
15.
10
0
-0
114
9
04
16.
11
1
-1
i n
9
1|
16.
10
1
-1
14
8
114
17.
10
1
-1
104
8
24
17.
10
0
-1
4
8
8
18.
8
9
-1
n
7
1|
18.
9
31
-1
7
11
19.
7
9
-1
4 1
6
41
19.
8
1
— 1
H
6
114
20.
7
1
-1
n
5
Hi
20.
7
2
-0
10
6
4
21.
6
91
-0
8f
6
0|
21.
6
5
-0
7
5
10
22.
6
6
+ 0
0
6
6
22.
6
2
-0
4
5
10
23.
7
0
+0
4f
7
114
23.
6
0
+0
2
6
9
Mean ...
7
10
I Mean ...
7
5 J
18th July.
20th July.
Noon.
7
8
+ 0
104
8
64
Noon.
6
6
+ 0
54
6
114
1.
8
1 i
+ 0
104
8
114
1.
7
1
+0
94
7
104
2.
8
H
+ 1
21
9
5
0
7
9
+ 0
114
8
8J
3.
8
oi
+ 1
31
9
4
3.
8
0
+0
114
8
114
4.
7
6
+ 1
64
9
04
4.
7
11
+ 1
1
9
0
5.
6
8
+ 1
74
8
34
5.
7
6
+1
34
8
9|
6.
5
9
+ 1
74
7
44
6.
6
11
+ 1
34
8
01
7.
5
3
+ 1
H
6
6i
7.
6
2
+ 1
°4
7
2f
8.
5
0
+0
114
5
114
8.
5
9
+0
9
6
6
9-
5
2
+ 0
8
5
10
9.
5
5
+ 0
64
5
Il|
10.
6
2
+0
2
6
4
10.
5
6i
+0
3"
5
94
11.
7
5
-0
24
7
24
11.
6
3
-0
01
6
04
Midnight.
8
5i
-0
61
7
11
Midnight.
7
0
-0
54
6
84
13.
9
8
-0
ll“
8
9
13.
8
5
-0
9|
7
74
14. '
10
1
— 1
0
9
1
14.
9
6
-1
0
8
6
15.
10
2
-1
°i
9
\\
15.
9
11
-1
1
8
10
16.
10
0
-1
21
8
91
16.
10
1
-1
2
8
11
17.
9
8
-1
41
8
31
17.
10
2
-1
34
8
104
18.
9
11
-1
7
7
6i
18.
9
8
-1
34
8
44
19.
7
11
-1
34
6
7 4
19.
8
6
-1
04
7
5!
20.
6
8
-0
94
5
104
20.
7
4
-0
8
6
8
21.
6
3
-0
6f
5
»4 1
21.
6
5
-0
44
6
04
22.
6
6
-0
44
6
!4 !
22.
5
11
-0
1
5
10
23.
7
0|
-0
O
6
10i
23.
5
8
+0
24
5
104
Mean ...
7
|
Mean ...
7
6
343
2 z 2
34-1
KEY. S. HAUGHTON ON THE TIDES OE THE
Table I. (continued).
21st July.
23rd July.
Time.
Height.
Diurnal
Tide.
Semidiurnal
Tide.
Time.
Height.
Diurnal
Tide.
Semidiurnal
Tide.
ft.
in.
ft.
in.
ft.
in.
ft.
in.
ft.
in
ft.
in.
.Noon.
5
ii
+ 0
5
6
4
Noon.
4
11
+ 0
94
5
84
; 1.
6
6
+ 0
84
7
2\
1.
5
1
+0
84
5
94
2.
7
n
+0
94
8
°~
0
5
7
+0
104
6
54
3.
7
6
+0
10#
8
4I
3.
5
8
+ 1
0
6
10
4.
7
7
+1
0£
8
74
4.
5
8
+ 1
34
6
114
5.
7
7
+ 1
1J
8
84
5.
7
7
+0
54
8
04
6.
7
4
+1
0
8
4~
6.
7
74
+ 0
5
8
04
7.
6
9
+ 0
94
7
64
7.
7
9
+0
If
7
ioi
8.
6
Ol
+ 0
64
6
si
8.
7
7
-0
0|
7
64
9.
6
0
+ 0
24
6
24
9-
7
8
-0
64
7
if
10.
5
11
-0
1
5
10
10.
7
0
-0
64
6
54
11.
6
0
-0
3|
5
84
n.
6
8
-0
84
5
ni I
Midnight.
6
44
-0
54
5
114 1
il Midnight.
6
2
-0
7
5
7
13.
7
4i
-0
6
9i
13.
5
10
— 0
5#
5
44
14.
8
i
-0
7
7
6
14.
7
1
-0
101
6
24
15.
8
8
-0
8
8
0
15.
7
10
— 1
6
8|
16.
9
3
-0
104
8
H
16.
8
04
-1
04
7
0
17.
9
6
-1
0
8
6
17-
8
3
-0
54
7
9#
18.
9
0
-0
104
8
li
18.
8
3
-0
3|
7
114
19-
8
1
-0
8
7
5
19.
8
0
-0
1
7
11
20.
7
2
-0
54
6
si
20.
7
6
+0
3
7
9
21.
6
4
-0
li
6
24
21.
6
94
+ 0
8
7
54
00
5
7
+ 0
2%
5
9|
22.
6
0
+ 0
94
6
94
! ss!
5
2
+0
6 ,
5
7
23.
5
5
+ 0
81
6
11
1
Mean...
7
24
Mean...
6
11#
22nd
July.
24th July.
Noon.
5
l
+ 0
9
5
10
Noon.
5
1
+0
7#
5
si
1.
6
0
+ 0
7|
6
7#
1.
4
10
+0
11
5
9
2.
6
8
+ 0
6#
7
2#
2.
5
1
+ 1
44
6
54
3.
7
0
+ 1
li
8
34
3.
5
7
+1
1
6
8
4.
7
44
+ 0
9'
8
li
4.
6
3
+ 0
10
7
1
5.
7
44
+ 0
101
8
3“
5.
7
2
+0
5f
7
n
6.
7
i $
+ 0
10
7
114
6.
7
8
+ 0
3
7
11
7.
6
9
+ 0
8
7
5
7-
7
11
+ 0
04
7
114
8.
6
4
+ 0
5#
6
9#
8.
8
5
-0
4|
8
04
9.
6
2
+ 0
H
6
34
9.
8
3
— 0
74
7
74
10.
6
2
-0
2#
5
114
10.
8
1 1
— 0
H4
7
24
11.
6
4
-0
7
5
9
11.
7
0'
-0
8
6
4
Midnight.
6
9
— 0
101
5
101
Midnight.
6
7
-0
7|
5
114
13.
7
2
-0
9#
6
44
13.
7
6
-1
34
6
I 14.
7
6
— 0
84
6
9#
14.
7
7
-1
4
6
32
15.
8
2
— 0
101
7
31
15.
7
8
— 1
2
6
6
16.
8
6
— 1
0
7
63
16.
7
10
-0
11#
6
104
17.
8
9
— 0
n
8
14
17-
8
0
-0
7
7
5
18.
8
74
-0
u
8
0
18.
8
1
-0
3
7
10
19-
8
1
-0
5
7
8
19.
8
0
+ 0
04
8
04
20.
7
5
-0
2#
7
24
20.
7
9
+ 0
5
8
2
21.
6
5
+ 0
3
6
8
21.
7
2
4-0
84
7
104
oo
5
10
+ 0
44
6
21
22.
6
6
+ 1
0
7
6
23.
5
2
+ 0
8
5
102
23.
5
11
+ 1
Of
6
Hi
\
Mean...
6
11
Mean...
7 1
ARCTIC SEAS. — PART YI. PORT KENNEDY.
345
Table I. (continued).
25th July.
27 th July.
Time.
Height.
Diurnal
Tide.
Semidiurnal
Tide.
Time.
Height.
Diurnal
Tide.
Semidiurnal
Tide.
ft
in.
ft.
in.
ft.
in.
ft.
in.
ft.
in.
ft.
in.
Noon.
5
6
+ 1
1
6
7
Noon.
6
9
+ 2
4
9
1
1.
5
0
+ 1
0
6
0
1.
6
0
+ 2
6f
8
6f
2.
4
9
+ 1
6
6
3
2.
5
0
+ 2
0
7
2
3.
5
1
+ 1
4
6
5
3.
4
9
+ 2
41
7
1J |
4.
5
4
+ 1
2f
6
6f
4.
4
7
+ 2
2b
6
9* !
5.
6
6
+ 0
8$
7
2\
5.
5
2
+ 1
104
7
Of
6.
7
6i
+ 0
2\
7
9
6.
6
0
+ 1
4b
7
4b
7.
8
H
— 0
2b
8
1
7.
7
2
+ 0
10|
8
o|
8.
8
9
-0
6
8
3
8.
8
6
-j-o
2b
8
81
9.
8
10
— 0
8i
8
If
9.
9
10
-0
10
9
0
10.
8
li
— 1
U
7
9f
10.
10
2
-0
10
9
4
11.
9
0
-1
51
7
6|
11.
10
6
-1
n
9
H
Midnight.
8
9
-1
H
7
3i
Midnight.
12
8
0
H
10
01
13.
8
6
-1
8
6
10
13.
12
8
2
10J
9
9f
14.
7
11
-1
6|
6
4f
14.
11
4
— 2
7b
8
8b
15.
7
10
-1
2
6
8
15.
10
4
— 2
5|
7
io§
16.
7
9
-1
3
6
6
16.
9
8
— 2
3f
7
4i
17.
7
9
-0
9
7
0
17.
9
1
-1
10i
7
21
18.
7
10
-0
H
7
8f
18.
9
1
— 1
6j
7
4
19.
7
9
+0
H
7
J Of
19.
9
0
-0
10|
8
3|
20.
7
9
+ 0
n
8
24
20.
9
1
-0
2
8
11
21.
7
9
+ 0
6
8
3
21.
9
3
+ 0
6
9
9
22.
6
11
+ 1
4
8
3
22.
9
3
+ 0
10J
10
lb
23.
6
3
+ 1
n
7
ni
23.
9
H
' ~
.
Mean...
7
3f
Mean...
8
5
26th July.
28th July.
Noon.
6
1
+ 1
8i
7
9i
Noon.
8
8
1.
5
4
+ 1
10i
7
2i
1.
7
11
C)
4
i n
+ 1
3
6
2J
2.
7
0
3.
4
ii
+ 1
8
6
72
3.
6
2
4.
5
2
+ 1
5|
6
7i
4.
5
6
5.
6
0
+ 1
If
7
if
5.
5
6
6.
7
8i
+ 0
7
11
6.
6
1
7-
7
9|
+ 0
li
7
iof
7.
7
8
8.
8
8~
— 0
3i
8
4i
8.
9
0
9.
9
7\
-0
iof
8
8f
9.
10
8
10.
10
21
— 1
5i
8
9i
10.
11
10
11.
10
32
— 1
sl
s
61
1
Midnight.
10
-1
104
8
3i
,13.
9
7
—1
m
7
7\
14.
7
0
-0
Hi
6
01
15.
8
8
— 1
1 1
6
9'
16.
8
4
—1
85
6
7i
17.
8
10
— 1
71
7
2b
18.
8
5
-0
9 1
7
7 J
The mean
level
of all
the Semidiurnal Tide- j
19-
8
5
-0
2b
8
QI
heights.
538 :
in number,
7 It. 5-414 in. 1
20.
8
5
+ 0
]
8
62
21.
7
11
+ 0
10|
8
9f
22.
7
9
+ 1
2l
8
111
23.
7
4
+ 1
4
8
1 o|
- . ' 1
Mean...
7
81
346
EEY. S. HAUGHTON ON THE TIDES OE THE
A. Diurnal Tide.
Having obtained the hourly values of the Diurnal Tide in height, I plotted them to
scale, and readily obtained the following Table, showing the chief phases of the Diurnal
Tide each day.
Table II. — Times of the Principal Phases of the Diurnal Tide at Port Kennedy
in July 1859.
Time.
High
Water.
Half-Ebb.
Low Water.
Half-Blood.
July 5
h
m
h
m
h
16
40
h m
22 46
6
5
0
10
20
17
0
21 30
7
5
0
10
26
15
0
20 48
8
2
30
8
20
14
0
19 40
9
1
30
7
0
12
0
18 30
10
]
30
6
48
13
30
19 25
11
Noon
8
20
14
30
20 20
12
2
40
9
0
14
30
20
0
13
2
30
8
0
15
0
20 30
14.
2
30
8
40
15
30
21
0
15
3
30
9
20
16
0
21 30
16
4
0
9
48
16
0
21 45
17
4
30
10
0
16
30
22
0
18
4
30
9
30
18
0
23 45
19
5
40
11
0
17
30
22 40
20
5
0
10
30
17
0
22 15
21
5
0
9
40
17
0
21 20
3
0
9
15
16
0
20 30
23
3
0
7
40
15
0
19 15
24.
2
0
7
10
14
0
18
8
25
2
0
6
30
13
0
18 30
26
1
0
7
12
13
30
19 40
27
1
0
8
10
14
0
20 15
If we extract from this Table the Maximum and Minimum values of the apparent
Solitidal Interval for each Phase, and reduce all to the Phase of High Water, we find —
Table III. — Maximum apparent Diurnal Solitidal Interval at Port Kennedy
in July 1859.
High Water.
Half-Ebb.
Low Water.
Half-Blood.
Apparent Solitidal
Interval reduced
to High-Water
Phase.
d h m
d h m
d
h
m
d h m
h
m
s
5 22 46
4
46
0
6 5 0
5
00
0
6
17
0
5
00
0
7 10 26
4
26
0
18
18
0
6
00
0
18 23 45
5
45
0
19 5 40
5
40
0
19 11 0
5
00
0
' |
Mean ...
5
12
1\
AECTIC SEAS. — PAET VI. POET KENNEDY.
347
The Diurnal Tide is represented by the formula
D = S' sin 2a cos (s— is) + M7 cos 2^ cos(m — im), (2)
where the letters have the meaning stated in my former papers, viz. —
S', M7 the Solar and Lunar coefficients uncorrected for Parallax ;
o', (jj the declinations of the Sun and Moon at an interval preceding the observation
called the Age of the Tide ;
s, m the Solar and Lunar Hour-angles at the time of observation ;
is, im the true Solitidal and Lunitidal Diurnal Intervals.
The Lunar Tide vanishes when ^=0 ; and this corresponds with Table III., which
contains the Maximum value of the apparent Solitidal Interval not influenced by the
Moon, but representing the full effect of the Sun.
The Moon’s declination vanished twice :
From N. to S. at 5d5hllm, and
From S. to N. at 19d17h14m,
which correspond fairly with the times of Maximum retardation of Solidiurnal Interval.
The age of the Lunidiurnal Tide may be found from the interval between the Moon’s
declination vanishing and the Lunar Tide vanishing, as shown by the Maximum value
of the Solitidal Interval. From the first time of tide vanishing we have
d h m
5 22 46
6 5 0
6 17 0
7 10 26
Mean=6 13 48
^=0 at 5 5 11
Age of Lunar Diurnal Tide . . . .1 6 37
From second time of tide vanishing we have
18 18 0
18 23 45
19 5 40
19 11 0
Mean=19 2 36
^=0 at 19 17 14
Age of Lunar Diurnal Tide . . . 00 14 38
From Table III. it appears that the value of is, the true Diurnal Solitidal Interval, is
?;=5h12m7|s (3)
The Minimum values of the apparent Solitidal Intervals, caused by the Maximum
influence of the Lunar Tide, are contained in Table IV.
348
EEY. S. HATIGHTON ON THE TIDES OF THE
Table IV. — Minimum apparent Diurnal Solitidal Interval at Port Kennedy in July 1859.
1 High Water.
Half-Ebb.
Low Water.
Half-Flood.
Apparent Solitidal
Interval reduced
to High-Water
Phase.
d h m
d h m
d
h
m
d h m
h
m
s
9
12
0
0
0
0
9 18 30
0
30
0
10 6 48
0
48
0
110 0
0
0
0
24 18 8
0
8
0
25 6 30
0
30
0
25
13
0
0
1
0
26 1 0
0
1
o ;
Mean ...
0
29
30
This Table corresponds with the Maximum effect of the Lunar Tide ; and the age of
Lunar Diurnal Tide may be found by comparing the results of this Table with the
times of Maximum of Moon’s Declination.
The Moon’s Declination attained its Maximum value twice, viz.
d h m o , ,i
July 8 10 0 ^=27 43 33 S.
„ 22 23 0 [*,= 27 43 21 N.
From the first time of Minimum Solitidal Interval in Table IV. we have
d h m
9 12 0
9 18 30
10 6 48
11 0 0
Mean= 10 3 19£
^=Max. 8 10 0
Age of Lunar Diurnal Tide ... 1 17 19^
From the second time of Minimum Solitidal Interval we have
24 18 8
25 6 30
25 13 0
26 1 0
Mean= 25 9 39^
Max. 22 23 0
Age of Lunar Diurnal Tide . . . . 2 10 39^
The Mean Age of Lunar Diurnal Tide is therefore
+ 1 6 37
-0 14 38
+ 1 17 19i
+2 10 39-i-
Mean = 1 4 14-J-
ARCTIC SEAS. — PART VI. PORT KENNEDY.
349
or, Age of Lunar Diurnal Tide, d h m
= 1 4 14£ (4)
We now proceed to determine the value of the Solar Coefficient Sf, which may be
readily found as follows : —
We may throw the expression (2) for the Diurnal Tide into the following form,
writing
S"=S' sin 2<r,
M"=M' sin 2j&,
D =A cos (s — B), ........ (5)
where
A=Vs"2 + M,/2 + 2S"M" cos ( (6)
-p, S" sin is + M7' sin (s — m + im) .
S" cos is -f- M" cos (s — m + im) ' '
The Solar Diurnal Tide will occur alone when M"=0 or ^ = 0.
The values of A are given from Table I., and are as follows, in Table V.
Table V. — Heights of High and Low Water of Diurnal Tide at Port Kennedy
in July 1859.
Time.
High Water.
Low Water.
Time.
High
Water.
Low Water.
h
m
ft. in.
ft.
in.
h
m
ft
. in.
ft.
in. 1
July 5.
17
0
1
9 \
July 17.
4
0
2
01
6.
5
0
1 5h
17-
16
0
1
111
6.
17
0
1
\\
IS.
5
0
1
71
2
7.
5
0
1 2J
18.
18
0
1
7 1
7.
15
0
1
os
19.
6
0....
1
6f
8.
2
30
1 oj
19-
17
30
1
41
8.
14
0
1
i
20.
5
0 ..
1
31
9-
1
30
1 1
20.
17
0
1
3f
9.
12
0
1
Ol
21.
5
0
1
1 1
10.
3
0
1 2
21.
17
0
1
<0
10.
13
0
1
2
22.
3
0
1
ji
11.
0
0
] 3 b
22.
16
0....
1
0 j
11.
13
0
2
1
61
23.
3
30... .
1
3J
12.
3
0
l ii
23.
15
30.
1
11
12.
16
0
1
lOf
24.
2
20
1
41
13.
4
0
2 21
24.
14
0
1
4
13.
14
0
2
H
25.
2
30...
1
6
14.
30
2 5l
25.
13
0..
]
g
14.
14
30
2
41
26.
1
0 .
1
1 ft 4
15.
4
0
1 111
26.
15
30
1
1 1 j
15.
16
0
1
7 J
27.
1
0
2
6£
16.
4
0
1 10J
27.
13
0...
2
101 j
16.
15
30
2
si
If we add the age of the Lunar Diurnal Tide to the times of the Moon’s Declination
vanishing, we shall have the times when M"=0 : —
3 a
MDCCCLXXV.
350
EEY. S. HATTG-HTON ON THE TIDES OE THE
^=0
Ase=
d h m
5 5 11
1 4 14
d h m
19 17 14
1 4 14
6 9 '25 20 21 28
If we take the values of A nearest to these times, from Table V. we find
ft. in. d h m
A=S"==1 5 at 6 9 25,
A=S"=1 3 at 20 21 28,
and using the Sun’s declination at noon of the day before, we find
S"
S'=—
sin z <y ’
and
S'=
S'=
17
sin (45 40')
15
t^=23*8 inches,
= 22-6 inches.
'sin (41° 40';
The mean of these values is
S,=23,4 inches • (8)
We can obtain the ratio of M' to S' from Tables III. and IV., and thus calculate M'
as follows. Differentiating (7) so as to make B a Maximum or Minimum, we find the
equation of condition
M"+S"cos (s—m—is — 0=0 (®)
Substituting in (7), we find at the Maximum and Minimum
tan B :
VS"2— M"2 sin is + M" cos is .
(10)
V S"2 — M"2 cos is — M" sin is
when ^=0, M"=0, and the equation reduces to
tanB— tan£s, or B=4,
as we assumed in determining the value of the true Diurnal Solitidal Interval from
Table III.
If we write
M"
S"’
wTe can reduce (10) to the following form,
tan B = tan (is -f 6),
or
B=?,+4. .
(11)
(1-
The Maximum and Minimum values of B are found from Tables III. and IV.
h. m s
B = Maximum = 5 12 7£,
B= Minimum = 0 29 30 ;
when B is a Maximum, M"=0 and 4=0 ; therefore (12) reduces to
h m s
B=is= 5 12 7£;
ABCTIC SEAS. — PAET VI. POET KENNEDY.
351
when B is a Minimum, equation (12) reduces to
h m s h m s"J
0 29 30= 5 12 7£-M,
or
6=- 4 42 371
or
19 17 22|.
^=sin(4h 42m 37|s)=sin(70° 39^') =0*943;
but
Mv M' sin 2[x.
S' sin 2c ’
or
M' M" sin 2c n.Q/)q v sin43°34f
S' . S" sin2;x sin55027,,
or
|r=0*788 (13)
From (8) and (13) we find
M'=18*4 inches (14)
From the values already found for the constants of the Solar Diurnal Tide, it was
easy to calculate its value, for every hour, from the formula
D=S' sin 2<r cos(s— ie).
These values, if subtracted from the Diurnal Tide in Table I., would leave the Lunar
Diurnal Tide, the principal phases of which are given in the following Table.
Table VI. — Times of Half-Flood and Half-Ebb, and Heights of High Water and Low
Water of the Lunar Diurnal Tide at Port Kennedy in July 1859.
Half-Ebb.
Low Water.
Half-Flood.
High Water.
h m
ft. in.
h m
ft. in.
J«iy 7 ...
2 0
0 5g
13 40
0 6J
8
1 50
0 91
14 10
1 0
9
1 30
1 If
13 50
1 24
10
2 20
1 2*
14 0
1 0
11
1 30
1 3
15 40
1 31
12
6 15
1 If
17 25
1 4
13
5 50
1 64
18 25
1 54
14
7 10
1 5£
19 15
0 8
15.
7 30
0 8J
20 10
0 8
16
8 30
0 9
20 45
0 94
17
9 35
0 7i
21 30
0 4~
1 8.
10 0
19.
j
Half-Flood.
High Water.
Half-Ebb.
Low Water.
20.
23 35
0 4
21
11 50
0 6
22
13 10
0 9
0 40
o 54
23.
13 0
1 2
1 30
0 Ilf
24.
14 30
1 4
2 50
1
25.
15 40
1 6
3 30
1 4
26
17 0
1 7J
4 15
1 84
! 27
—
—
6 15
1 7
3 a 2
EEY. S. HATTGHTON ON THE TIDES OF THE
352
I have used the Times of Half-Flood and Half-Ebb in this Table in preference to
the Times of High Water and Low Water, as the vertical motion of the water is a
maximum at Half-Flood and Half-Ebb.
Table YI. contains the Solar Hours of Half-Flood and Half-Ebb. These are reduced
in the following Table to Lunar Hours.
Table VII. — Moon’s Hour- Angle at times of Half-Flood and Half-Ebb of Lunar
Diurnal Tide at Port Kennedy in July 1859.
Day.
Moon’s Hour- Angle
at Half-Flood.
Moon’s Hour- Angle
at Half-Ebb.
li m
h m
July 7
7 15
19 15
8
6 45
18 48
9
5 38
17 43
10
4 59
17 44
11
4 9
16 6
12
6 36
19 50
13
6 43
18 36
14
6 34
19 14
15
6 51
18 34
16
6 42
18 46
17
6 46
19 6
18.
18 51
IQ.
20
Half-Ebb.
Half-Flood.
21
6 10
18 40
22.
6 29
19 17
23
6 29
18 23
24.
6 53
19 3
25 .
6 34
19 17
26
6 15
19 37
27
7 9
Mean ... 6 23 10s
18 44 30s
Hence the mean value of the true Diurnal Lunitidal Interval is at High Water
im= 0h 33ra 50s (15)
The coefficient M', of the Lunar Diurnal Tide, may be found from Heights from
Table VI.
The Lunar Diurnal Tide reached its maximum —
d h m ft. in.
July 13 11 38 1 6£
July 26 10 3 . . . . . 1 8i
The Moon’s Maximum declination occurred —
d h m o - i II
July 8 10 0 . . . fZ=27 43 33 S.
July 22 23 0 ...„ 27 43 21 N.
AECTIC SEAS. — PAET YI. POET KENNEDY.
35a
These values give for the age of the Lunar Tide deduced from Heights,
d h m
Age of Lunidiurnal Tide .
33 33
Mean .
5 1 38
3 11 3
4 6 20£
This result differs considerably from the age deduced from Times, and agrees with what
I have noticed in several tidal observations, viz. that the age of the Tide deduced from
Heights is greater than that deduced from Times.
Taking the mean of the Maximum Heights, we have
M" 19-25
sin 2 1*. sin 55° 27'
M'=23*37 inches; .
= 23*37 inches,
(16)
and finally, from (8) and (16),
M' 23-37
S' ~ 23*4 :
0*994,
(17)
If we collect together all the preceding results, we obtain the following : —
Constants of the Diurnal Tide at Port Kennedy in July 1859.
Solar Diurnal Tide.
Age . Unknown.
True Solitidal Interval is= 5h 12m 7-|3
Coefficient (uncorrected for Parallax) . S' = 23*4 inches.
Lunar Diurnal Tide.
Age . . . . ld 4h 14-|-ra (Times).
„ . . . . 4d 6h 20im (Heights).
True Lunitidal Interval ?‘m=0h 33m 50s.
Coefficient (uncorrected for Parallax) . M' = 18*4 inches (Times).
„ „ „ . . M'=23*37 „ (Heights).
^-=0*788 (Times).
„ =0*994 (Pleights).
B. Semidiurnal Tide.
From the column of Semidiurnal Tides in Table I. it is easy to construct the following
Table : —
854
REV. S. HAUGHTON ON THE TIDES OF THE
Table VIII. — Heights and Lunitidal Intervals of Semidiurnal Tide at Port Kennedy
in July 1859.
Time.
Heights.
Lunitidal Intervals.
High Water. |
Low Water.
High Water.
Low Water.
d li m
ft. in.
ft. in.
h m
h m
5 16 30
8 3 £
11 17
5 23 0
4 2
17 34
6 5 0
8 4|
23 24
6 11 0
4 3i
5 12
6 17 0
8 31
11 0
6 23 30
4 74
17 17
7 5 40
8 1J
23 18
7 12 0
5 1
5 15
7 18 0
8 4J
11 14
8 1 0
5 5|
18 0
8 7 0
8 6£
23 49
8 13 0
5 8f
5 37
8 19 30
8 8
12 7
9 1 30
5 11
17 55
9 8 0
8 11 J
24 0
9 14 0
5 111
5 48
9 20 0
9 1
11 36
10 2 0
6 5|
17 24
10 8 0
9 0£
23 11
10 14 0
7 2|
4 59
10 22 0
8 10J
12 43
11 5 30
7 8£
39 58
11 10 0
8 11£
23 44
11 16 20
7 14
5 51
11 23 0
8 lOf
13 11
12 4 0
6 1£
18 1
12 11 0
9 li
23 35
12 17 0
6' 0|
5 23
12 23 30
9 14
12 28
13 5 30
6 If
18 16
13 12 20
9 3
24 50
13 18 0
6 14
6 19
14 1 0
9 5§
13 5
14 6 30
5 111
18 24
14 12 0
9 101
23 42
14 18 40
5 11
6 9
15 0 0
9 41
11 18
15 6 40
5 10
17 45
15 12 0
8 11
22 57
15 19 0
5 9
5 43
16 1 30
9 24
12 0
16 7 0
5 101
17 19
16 13 0
9 9
23 12
16 20 0
5 ni
5 58
17 2 0
to
OO
-Wco
11 47
17 8 0
5 11
17 35
17 14 0
9 9
23 32
17 20 0
5 111
5 20
18 2 30
9 5
11 36
18 9 0
5 10
17 53
18 14 40
9 li
23 30
18 21 0
5 84
5 37
19 3 0
9 1
11 26
19 9 0
5 8£
17 14
19 15 0
9 04
23 11
ARCTIC SEAS.— PART VI. PORT KENNEDY.
355
Table YIII. (continued).
Time.
d
h
m
19
21
30
20
3
0
20
10
0
20
16
0
20
22
0
21
5
0
21
11
0
21
17
0
21
23
0
22
5
0
22
11
0
22
17
30
23
0
0
23
5
30
23
13
0
23
18
20
24
0
20
24
8
0
24
12
0
24
20
0
25
1
0
25
7
0
25
14
0
25
21
20
26
2
0
26
9
40
26
14
0
26
21
0
27
4
0
27
12
0
27
17
0
Heights.
High Water.
9
0
8
11
8
81
8
6
8
3|
8
1J
8
H
7 ill
8
oi
8
2
8
3
8
3
8
91
9
1
10
21
Low Water.
ft.
in.
5
10
5
9g
5
10
5
81
5
7
5
9
5
81
5
41
5
81
5
111
6
0
6
41
6
*i
6
n
6
91
7
Lunitidal Intervals.
High Water.
Low Water.
h m
h m
5 28
10 47
17 33
23 30
5 18
12 4
17 52
23 47
5 35
11 24
17 12
23 33
5 50
11 9
18 24
23 33
5 21
12 46
16 38
24 17
5 7
10 55
17 41
24 36
5 7
12 31
16 51
24 46
7 32
13 45
18 35
From this Table we find
Mean of Lunitidal Intervals.
43 High Waters 23 48 58^
43 Low Waters reduced to phase of High Water . 23 43 1-|
Mean Lunitidal Interval .... 23 46 0
ft. in.
Lligh Water 8 10-55
Low Water 5 10-98
The Maximum and Minimum Kariges in height were as follows : —
d h m ft. in.
Maximum Eange 6 2 0 4 1^
14 15 20 3 lU
4 0i
35&
EEV. S. HATJGHTON ON THE TIDES OE THE
d h m ft. in.
Minimum Range 11 3 45 1 2|
„ „ 25 17 40 2 2
i~~8*
Hence we have, if M" and S" represent, the Lunar and Solar Semidiurnal Coefficients,
uncorrected for Declination and Parallax,
2(M"+S")=48.
2(M"-S")=20.
M" = 17 inches.
97 = 0-412 (18)
Table IX. contains the Times and Lunitidal Intervals of Half-Flood and Half-Ebb,
determined from Table I., from the moment at which the water-level passed the mean
height of Tide-level, as noted at foot of column 4, for each day.
Table IX. — Times and Lunitidal Intervals of Half- Flood and Half-Ebb of Semidiurnal
Tide at Port Kennedy in July 1859.
Times.
Lunitidal Intervals.
Half-Flood.
Half-Ebb.
Half-Flood.
Half-Ebb.
.Tilly 5
h m
13 45
h m
h m
8 37
h m
5
18 56
13 38
6
1 46
20 16
6
7 51
1 12
6
14 14
8 29
6
20 17
14 11
7
2 50
20 35
7
8 38
2 11
7
14 56
8 17
7
21 45
14 52
8
3 50
20 50
8
9 48
2 37
8
16 7
8 43
8
22 49
14 47
9
4 48
20 54
9
1 1 22
3 15
9
16 54
8 37
10
0 13
15 40
10.
5 47
21 3
10
12 25
3 27
10
18 26
9 8
11
1 22
15 58
11
7 29
21 49
11
13 33
3 41
11
21 3
10 57
12
2 37
16 9
12.
7 4
21 36
ARCTIC SEAS. — PART YI. PORT KENNEDY.
357
Table IX. (continued).
Times.
Lunitidal Intervals.
Half-Flood.
Half-Ebb.
Half-Flood.
Half-Ebb.
li m
h m
14 41
Ii m
h m
3 57
12
19 48
8 53
1 3.
2 28
15 20
13
8 36
21 14
13
15 13
3 37
13
20 56
9 10
1 4
2 47
14 49
14
9 48
21 34
1 4. .
15 12
OO
1 4.
22 2
9 24
3 58
15 8
15. ...
9 37
20 39
1 5.
15 53
2 42
15
21 41
8 19
16.
4 12
14 36
16
9 53
20 13
16. .
16 50
2 55
16
22 50
8 52
17
5 7
14 48
17
11 14
20 50
17. ...
17 21
2 45
17
22 56
8 9
18
5 42
14 41
18
11 36
20 33
18
17 53
2 36
18
23 52
8 24
19 •
6 16
14 35
19
12 15
20 32
ig
18 28
2 32
20
0 25
8 17
20
6 43
14 23
20
12 53
20 29
«0
18 58
2 22
21
0 58
8 10
c>\
7 24
14 24
21
13 37
20 27
2\
19 23
2 5
09
1 28
7 58
QC)
7 59
14 16
22
14 13
20 22
22
20 31
2 28
23
4 1
9 43
23
9 13
14 44
23
15 50
21 8
23
21 43
2 50
24
4 0
8 54
24
10 9
14 51
24
16 24
20 49
24
22 48
3 1
25
5 13
9 13
<?r}
11 50
15 37
25
17 27
19 49
26
0 7
3 17
26
5 44
8 44
26
12 53
16 1
26
18 8
20 29
27
1 6
3 12
27
7 34
9 28
27
14 21
16 1
27
19 11
20 37
' 1
3 B
MDCCCLXXV
358
EEV. S. HAITGHTON ON THE TIDES OF THE
From this Table we find : — •
Mean Lunitidal Interval of 44 Half-Floods
„ „ 43 Half-Ebbs
h m s
20 45 19
2 54 24
Keducing the Lunitjdal Intervals found from Tables V III. and IX. to the phase of
High Water, we have
Mean Lunitidal Interval =im.
From High Waters 23 48 58
„ Low Waters 23 43 1
„ Half-Floods 23 45 19
„ Half-Ebbs 23 54 46
Mean 23 48 1
h m
im = 23 48
or - 0 11
We may calculate the ratio of the Solar and Lunar Semidiurnal Tides from
Tables VIII. and IX. by the following method :■=—
Let M"=M^~ycos>,
S"= S (^)’cosV,
where P, p are the parallax of the Moon and Sun, taken at an interval before the
observation equal to the age of the respective Tides ; and Pm, pm are the mean values
of same.
Then if the Semidiurnal Tide be
T=M"cos2 (m— ^J+S" cos2(s— is), . . . .
we may write (20) thus,
T=Acos2(m— B), . .
where
A=\/M"2-|-S"2+2M" S" cos 2 .
M" sin 2 im + S" sin 2 [m — s + * j
an M" cos2^”^-l-S,, cos 2 (m — s +
(20)
(21)
(22)
(23)
The Maximum and Minimum values of A are M"+S" and M" — S", as used in finding
(18); and the Maximum and Minimum values of B are found by differentiating (23),
which gives, as the equation of condition,
S,,-FM/' cos 2 {m— s— im— it)=Q.
(24)
ARCTIC SEAS. — PART VI. PORT KENNEDY.
359
Combining (23) and (24) we find, after a few reductions,
tan 2B=v/M"2— s"2 sin 2im+ S" cos 2 im /25)
^/M"2— S"2 cos 2im— S" sin 2 im
If we assume
g n
sin 2<p,
the equation (25) will reduce to the following: —
tan 2B=tan 2 (<p+?'m),
or
B =<p+v, (26)
The Maximum and Minimum values of B, or of the Lunitidal Interval, are found
from Tables VIII. and IX., and are as follows : —
Maximum Values of Lunitidal Interval.
h
m
s
d
h
m
High Water
25
5
0
at
14
1
0
55
.24
46
0
„
26
21
0
Low Water
25
58
0
55
11
5
30
24
35
0
55
27
17
0
Half-Flood
25
57
0
55
11
21
o
O
55
24
28
0
55
27
7
34
Half-Ebb .
25
9
0
55
12
2
37
55
25
1
0
55
27
14
21
Mean=25
7
22—
Minimum Values of Lunitidal Interval.
h
m
s
d
h
m
High Water
23
0
0
at
6
17
0
„
22
55
0
25
7
0
Low Water
....... 23
12
0
55
6
11
0
55
22
38
0
55
24
12
0
Half-Flood
23
16
0
55
6
1
46
„
22
58
0
55
22
1
28
Half-Ebb .
22
12
0
55
6
7
51
55 •
23
5
0
55
21
19
23
Mean =22
54
0
From equation (26) we see that the value of B ranges above and below that of im by
360 ON THE TIDES OE THE AECTIC SEAS— PART YI. PORT KENNEDY.
a quantity equal to <p, which, is half the difference between the maximum and minimum
values of B. Hence we find
h m s
Maximum value of B = 25 7 22^
Minimum ,, „ = 22 54 0
2<p = 2 13 221
2<p = 33° 20i'.
^=-.sin2<p = 0-549 (27)
Collecting together the foregoing results, we have the following
Constants of the Semidiurnal Tide at Port Kennedy in July 1859.
Lunar Semidiurnal Tide.
True Lunitidal Interval
23h 48m Is.
Ratio of^r,
tO -412 (Heights).
(0-549 (Times).
(Uncorrected for Declination or Parallax.)
[ 361 ]
XIV. On the Mathematical Expression of Observations of Complex Periodical Pheno-
mena; and on Planetary Influence on the Earth's Magnetism. By Charles
Chambers, F.B.S. , and F. Chambers.
Received May 26, — Read June 19, 1873 *.
The writers purpose in the following pages to determine, by Bessel’s method, a mathe-
matical expression for a periodical phenomenon from observations which are affected
by one or more other periodical phenomena, and to find criteria for judging of the
extent to which the expression is affected by these other phenomena ; also, having
found an expression for a period of known approximation to the truth, to find from it
the expression for the true period. In the course of these inquiries, certain ambiguities
which affect similarly Bessel’s expression for a single periodical phenomenon and the
results here arrived at will be remarked upon ; and, finally, the results will be applied
to determine the nature of periodic planetary magnetic influence in particular cases.
2. In Bessel’s paper “ On the Determination of the Law of a Periodic Pheno-
menon ” (a translation of which has been published by the Meteorological Committee
in the Quarterly Weather Report, part iv. 1870), the author describes, in Section VII.,
how periodical phenomena which depend on two or more angles can be developed
from observations of the same ; and he remarks upon the simplicity of a certain class
of cases in which both angles are exact measures of 2sr, and one is a multiple of the
other. In the description of the process occur the following words : —
“ If we designate the two angles by x, x1, then in the expression
yz=p-\-pl cos^H-gi sin #+p2 cos2#-{-g,2sin2,r-|- See.
the p, px, qx, See. which occur are not constant, but depend on x1; and as they are
periodic functions of x ', each of them has an expression of the form
a-\-ax cosaf+^i sm.od-\-a2 cos 2#' -j -b2 sin 2x’-\- Sec.
It is therefore necessary to deduce this development of p, px, q , &c. from the obser-
vations. If the available series of observations gives the values of y, not only for
values of x (0, 2, 2z, ... . (n—l)z), which are in arithmetical progression and fill
up the period, but also for the combination of each of these values of x with n- values
of 4/(0, z', 2z\ ( n ' — l)sf), fulfilling the same conditions, the development has
no difficulties.” After a perfect elucidation of a type of these cases follow remarks
upon comparatively difficult cases, which require more cumbrous methods for elimi-
nating the several constants.
MDCCCLXXV.
Subsequently revised by the authors.
3 c
362 MESSES. C. AND E. CHAMBEES ON THE MATHEMATICAL EXPEESSION
3. There is a yet simpler case, the importance of which possibly did not press itself on
Bessel’s attention, but which the present writers (having occasion to describe in con
nexion with actual observations) find it convenient thus to introduce. It is that of
two or more combined phenomena, each of which separately recurs after a certain
period, which is of different duration for each phenomenon ; and the object of this
inquiry will be to determine under what circumstances, and with what degree of
accuracy, may the coefficients of the expression, according to Bessel’s form, of each
separate phenomenon be found from a series of observed values of the combined
phenomena.
4. As the result will be equally applicable to any number of combined phenomena,
we will consider the case of only two, whose periods are respectively z and z'.
x f .
Let ~i=gif and g being the least integral numbers that will satisfy this condition*;
and x being the interval in time (supposed to be constant) between every two conse-
cutive observations, let the series of observations extend over the time gz or _/V, of
which x is a measure, then will the number (r) of observations be ^ , and the angles
2^ o^r
corresponding to the time x under the respective periods — x=z (say) and y x—-z;
further, the angles corresponding to the time rx or gz will be 2^or and 2 fir respectively.
If otm represent the observed value of the combined phenomena at the time mx , and
0m and ym be the separate phenomena of which it is composed, 0m recurring after the
period z, and ym after the period z', we shall have
0 m=i>0+p1 cos mz-\-ql svn.mz-\-])2 cos 2 mz-\-q2 sin 2 mz-\- &c., (1)
ym=.Y0-\-¥x cos^-mz + Qj sin^,m2+P2cos2|^;s+Q2sin2^m.s+ &c., . . (2)
• (3)
The observations will furnish r equations of the following form : —
{+Po+ih cosmz-\-ql sin mz-\-])2 cos ‘^mzJrg2 sin 2to2+&c.
f f f f
+ P0 -f cos - mz + Qj sin - mz + P2 cos 2 - mz + Q2 sin 2 - mz + &c.
9 9 9 9
and the most probable values of^0,^„ &c., P0, P„ Qn &c. will be those which give
a minimum value to
V f +p0+Pi c°s mz-\-qx sin mz-{-][)2 cos 2 mz-\-q2 sin 2mz-\- &c.
% —«„,=< f f f f
m=0 l^ + Po+P, cos-m^+Q, sin - mz +P2 cos 2 mz + Q2 sin 2 J-mz+ &c.,
the sum being taken between the limits m=. 0 and m=r—l for integral values of m.
This will have such a value when the differential coefficients of it with respect to
* It will be shown later that it will suffice that / and g very nearly satisfy this condition ; hut it is conve-
nient in what immediately follows to regard them as doing so rigidly.
OF OBSERVATIONS OF COMPLEX PERIODICAL PHENOMENA.
363
each of the quantities px, qx, &c., P0, P„ Q15 &c. vanish*; or, dividing out the
factor 2, when
0=S [— a»+0»+yJ>
w=0
m=r— 1
0=2 [cos mz(— am+0OT+ym)],
0=2 [sin mz(-am+0m+ym)],
m= 0
0=2 [cos 2mz( — a,„ +3™ +7™)],
771 — 0
0=2 [sin 2mz( — a«+3„+y*)],
w=0
&c. See.,
0=2 [cos tmz{ — am + fim -f- ym)] ,
0=2 [sin aro+0m+yj], >
fltsO
°=|o ^C0S f ““»+&» + ?«)]»
°=£o [sin^m2(-am+0m + yj],
0=2_o [cos 2~rnz(—am-i-^m-\-iym)],
0=2 ^ [sin 2 £ mz( - «m+0m + ym)],
&c. &c.,
0=2 [cos — am+/3TO+ym)],
m=0 ^
0=2 [sintf{wz(-am+0m+ym)].
w=o y
(C)
Representing by s the suffix of a p, q, P, or Q in a type term of (0m+ym) in each of
the equations (6) in turn, and by t the integral numerical factor of the angle in a type
of the sine or cosine which multiplies ( — am+0m-j-ym), let us note that
cos s ^ mz cos tmz = £
m\rz\st+tl sinj rz{si-t\ , , ,
L4_|cosi(r+l>|«i+il + LL_|cosJ(»-+1)zM-4
sini5r|s^ + ^j L J sinls’js^— n L J
l rns If
* The second differential coefficients being all squares, and therefore positive, there is no ambiguity as to
whether equations (6) correspond to a maximum or minimum value of (5).
3 c 2
364 MESSRS. C. AND E. CHAMBERS ON THE MATHEMATICAL EXPRESSION
which, since rz=2g‘T, and if be not a multiple of
or ( sf-±tg ) not a multiple of r,
=0.
Similarly, under the same conditions,
m=r-l * -P
% sins-m2sintfm;z=:0; ....
m= 0 9
X sin s-mz cos tmz=0, 1 ....
> invariably.
m=r-l S J
X cos s-mz sin tmz=Q, ....
m=0 9 J
If, now, we define as follows.
j- + {the sum of all the values ofjt?, for which s is 0, or such that sg is a multiple of r}~|
L + {
„
„
pe
„ s is 0, or
„
}J
i*
„
„
Ps
„ s is 1, or
„ (s+\)g
„
>1
^ + {
»
»
ps
„ s is
» (tf+ff)
5
'+{
„
„
9*
„ s is 1, or
» (s-l)ff
„
}"]
_
-{
„
„
9s
„ s is
„ 0+1 )g
„
}
+ {
„
„
Q.
» s n
» (*f-9)
„
}
’
1
»
»
Q.
„ s „
» (sf+s)
-1
"+{
„
„
Ps *
„ s is 2, or
» 0 +*)9
„
!,
- +{
pe
„ s is
» 0/+2.9)
»
r
"+{
„
„
9s
„ s is 2, or
» 0 -9)9
„
-{
„
„
9s
„ s is
» (s + 2)g
„
}
+ {
»
„
Q.
„ s „
„ (sf-2g)
„
}
5
L-{
»
»
Qs
5» s „
„ 0/+%)
}
rc.
&c.
&c.
&e.
1
r+{
„
„
Ps
„ s is t, or
» (s+t)g
„
n
L+{
»»
»
p ,
„ s is
» (sf+tff)
»
5
r+{
„
9s
„ s is t, or
» 0-05-
„
in
-{
„
9s
„ s is
» (s+t)g
„
>
+{
„
Qs
„ s „
» (tf-tff)
,,
>
5
u-{
»
Qs
,, s „
» (tf+tff)
>
>
r+{
„
„
p .
„ s is 1 , or
.. 0+1)/
„
n
L+{
»
»
Ps
» s is
» O^+Z)
,
r + {
»
„
Q.
„ s is 1, or
» 0-1)/
„
>n
-{
«
„
Qs
„ s is
» 0+1)/
„
}
+{
„
9s
» s »
» 0 9-f)
„
>
9
L_-{
»
»
9s
» s j>
» 0 9+f)
„
}
r+{
ps
„ s is 2, or
» 0+2)/
,,
In
1
»
»
Ps
„ s is
» 0 9 + *f)
»
1*
OF OBSERVATIONS OE COMPLEX PERIODICAL PHENOMENA. 365
+ {the sum of all the values of Qs for which 5 is 2, or such that (s~ 2)f is a multiple of r } ~
b2=
— { »
» Q«
s is
» 0+2/)
uiuiupc VJl # |
» }
+ {
» q.
s „
» Ov-2/)
}
&c.
» q*
s „
» 0^+2/)
» }_
&c.
&c.
&c.
At=
r+i -
» p.
s is t, or
» 0+0/
11
1
L+(
» Ps
s is
1+
» }J
r + {
-{
» Qs
s is t, or
» 0-0/
Bt=
» Q.
s is
» 0+0/
}
+{
» q.
s „
» (Sff-tf)
}
» qs
s „
» (sff + tf)
it is easy by means of (a), (b), (c), (d), (e), and other similar formal®, to convert the
equations (6) into
whence
whence
whence
whence
0=i"' ‘[-a»+ft. + yJ = 2""[-«„] +re„
m-0 m=0
0HL [cos mz( - «..+ P.,+7,,)] = / [cosm(— aj]+^a„
[am cos mz\ \
°=|, [sinm<-“=»+ft.+y,)]=_5""[sinm2(-«J]+^„
2 m=r-l
bi—~% [am sin m2] ;
' m= 0
°=L 1[c°S 2m(-“»+/3-+5'.)]=5""'[cos 2mr(-a„)]+^2,
2 m=r— l
«2=- S [am cos 2 m2:] ;
°=i„ [s“2’®(-a-+&+y.)]=2'",[sin2mr(-a.)]+55,
whence
h=~% [am sin 2 m2] ;
&c. &c.
&c. ;
°-'i. [cosl!m(-“.+^+y-)]=r"[costo2(-a„)]+^„
2 m=r— 1
2 [am cos tmz] ;
whence
366
MESSES. C. AND E. CHAMBEBS ON THE MATHEMATICAL EXPEESSION
0 = 5 [sin tmz{ — a»+0„+y»)] = 5 [sin tmz( — a*)] +2 K
whence
whence
whence
whence
whence
2 m=r-l
bt=~% [am sin tmz] ;
0=5 [cos{mz(— «„+&»+ 7*)] =5 [cos^ mz{ — a*)] + ^ A,
m=0 y m=0 y
2 m=r— 1 f
Ai=7£o [am cos -m2] ;
0=5 [sin^m.z(— aro+^ro+yj]=5 [sin^mz(— am)]+^B1;
ro=0 s' m=0 y
c>m=r- 1 ^
B, =- 2 K sin - m2] ;
1 L » <7 J’
0=5 [cos2-m2(— am+j3m-t-yBl)]=S [cos 2^-m2(— am)]+^ A,
m=0 ^ m=0 #
A2=- £ [am cos 2 - m2] ;
2 r rl0 L m £ 1
/,
0=5 * [sin 2~mz(— am + 0ro + ym)] =5 [sin 2-gmz{— a!)]+^B2
B,, = - 5 [a_ sin 2 -m2];
Tm=0 L ^ J
&C.
&c.
&c.
whence
whence
0=5 [cos £ { mz{ — + 0m + ym)] — 5 [cos £ ~a mz{ — am)] + ^ A„
m-;0 y m = 0 j
2 m=r-l ^
A<=- 5) [am cos t - mz\ ;
* rr- L ^ J
0=5 [sin ^ { mz( - am + /3m + ym)] = 5 [sintf{ms(— a*)]+£B„
m=0 ^ m=0 v *
B t—~ 5 [am sin t ~n mz\
1 r . L J
5. In any special inquiry, having found by (8) the numerical values of «0, ax, «2,
#2, &c., A15 B„ A2, B2, & c., we may insert these in the equations (7), which it will now
be desirable to consider the significance of. If our object was simply to find two
periodical phenomena which would jointly satisfy the r observations, then this could
be done with the same degree of closeness in an infinite variety of ways ; for we might
give to the several terms of the right-hand members of (7) any arbitrary values consis-
tently with their sum being equal to the left-hand member, and so long as the same
coefficient is taken of the same value in all the equations (7). But although all the
varieties would agree in giving the same value of the combined phenomena at any one
OF OBSERVATIONS OF COMPLEX PERIODICAL PHENOMENA.
367
of the r times of observation, they would all generally differ as to its value at any time
intermediate between any consecutive two of the r observations. In the first of the
equations (7), if we were to attribute the whole of a0 to p0 or P0, it would imply that
the phenomenon a0 occurred at all times irrespective of any periodicity ; but if we attri-
bute it all to (say) p it would imply that the phenomenon a0 occurred only at the times
of observation, whilst at intermediate times the corresponding phenomenon would be
represented by a0 cos7- mz, which passes through a complete cycle of change during the
interval between every two consecutive observations, or whilst m passes from one integral
value to the next ; and combined with this there may be a phenomenon represented by
q1- sin^ mz of any arbitrary range. Similarly, the distinction between the different
terms of the other equations is that they go through a full cycle of change in different
periods ; and graphically each term would be represented by a complete wave whose
length corresponded to the period of that term.
6. As the mathematical theory of this process affords no criterion for selection, we
ought to find reasons apart from it for preferring particular appropriations of a0, at,
&c. to the several component parts of their equalities ; otherwise it is clear from what
has been said that no useful result will be attained. It may be remarked that an
ambiguity, similar to the one under consideration, attaches to Bessel’s treatment of a
single periodical phenomenon, the values corresponding to our a0, «15 bx, &c. being given
at the foot of page 26,* Section III. of Bessel’s paper. Bessel remarks that if we
compare a mathematical theory of any periodical phenomenon, based on physical prin-
ciples, with the observations, his expression for the values of the phenomenon is more
convenient for the purpose than the observations themselves — the reason of this being
that, as the expression given by the mathematical theory is developed in the form in
which the observations have been expressed, the two expressions may be compared term
by term, or by equal subordinate periods. This is probably the most important use of
the method ; and as the most striking features of a variation will generally be those of
long period, they may be examined apart from the others. The next most important
use of this method is probably that which has for its object the elimination of casual
irregularities from the observations ; but this is served only when the subordinate varia-
tions of short period are rejected ; and after such rejection, it must always be borne in
mind that the remaining expression is incomplete : this does not, however, interfere with
the comparison of the subordinate variations retained with other phenomena of nature
involving variations of the same subordinate periods ; indeed by indicating the periods
followed by the subordinate variations which are of largest amount, it suggests a means
of distinguishing other phenomena that on examination may be found to be related to
the one which is the subject of the observations. The reason assigned by Bessel for
giving preference to the terms of long period, viz. that “the development of the
368 MESSES. C. AND F. CHAMBERS ON THE MATHEMATICAL EXPRESSION
expression which represents the given values of y will in general only be interesting
when it converges so rapidly that only a few of the first terms have appreciable values,”
had reference doubtless to the incompleteness of the partial expression — this being of
no consequence when the rejected part, the absence of which makes the expression
incomplete, is of inconsiderable amount. We may, however, be guided as to the validity
of this reason by noting well whether the values of at , b„ At, B„ &c. do themselves
become inappreciable whilst t is still small.
7. Now in many special inquiries f, g , and r will have such values that (s + t)g,
(sf+tg), (s+t)f, (sg + tf), &c. will first become a multiple of r only when s or t has
ceased to be small ; in which case, following Bessel, we may neglect as inappreciable
all the terms on the right-hand side of equation (7), except and P0 in the first
equation and the first term of each of the others ; we then have
Jp0-t-p0=«0=^i;
q^b—%
rm=0
■p,—a2=~ 2
^K=-rm£
&c. &c.
9 m=r
Jpt=at=-X^
St=bt=~%
pI=AI=!r
QI=B1=^
9 m—r—
P,=A,=- 2
[«J»
[am cos m2], .
[<xm sin m2],
[<zm cos 2 m2],
[ am sin 2 mz],
&c.,
[am cos tmz],
[am sin tmz] ;
cos ^ mz J ,
am sin - mz
9
[«m sin ^ m2],
j ~am cos 2^mz~J ;
Qa=B2=^S_ [am sin 2 ~ m2] .
&c.
&c.
9
&c,
P«=A
[a* cos m2],
Qt= B t=~r \ [a* sin t~gmz\^\
which are the same values as those
that would be found by applying
Bessel’s method to the r observa-
tions, on the supposition that they
are unaffected by the phenomenon
whose period is %! .
which are the same values as those
that would be found by applying
Bessel’s method to the r observa-
tions, on the supposition that they
are unaffected by the phenomenon
whose period is js.
J
(9)
OP OBSERVATIONS OE COMPLEX PERIODICAL PHENOMENA.
369
8. If instead of applying Bessel’s process at once to each individual obser-
vation, we had begun by finding a mean value 2 ^ (as affected by the other pheno-
menon) of the one phenomenon at a particular phase of its period x, and then proceeded
to apply Bessel’s process to the^ mean values of this character, we shoulcl,have arrived
at precisely the same results.
We might also have regarded a hypothetical complex phenomenon of period gx as
being produced solely by the recurrence of the phenomena whose periods are x and x',
and finding by Bessel’s process from the r observations the coefficients of its expression
— from these determining the coefficients of the expressions for the component periodical
phenomena; this, too, would have led to the same results.
9. To conclude this section, we draw from what has preceded the following practical
rule for deducing from a series of observations of the combined effect of several inde-
pendent phenomena (observations taken at equal intervals of time) the coefficients of
Bessel’s series for each separate phenomenon : — Find the least integral numbers f, g, h,
See. which are proportional (or nearly so) to the periods x, x\ x", &c. of the several
phenomena, and let v be the least common multiple of those numbers ; choose then for
treatment observations extending exactly over some multiple of the period^, and note
whether any values of jps or qs, Ps or Qs, &c., for which s is small, other than the first
terms, enter into the equations (7) ; if not, proceed to apply Bessel’s method to deter-
mine from the observations the coefficients of the expression of each phenomenon, just
as would be done if the observations were unaffected by the other phenomena.
II.
10. It will be useful further to estimate in what degree the phenomenon whose
period is x' affects the values of the constants ^>15 qt, &c., in the expression of the phe-
nomenon whose period is x, when the number (K) of observations is greater than and
not a multiple of r. And here, confining our attention to strictly and exclusively
periodical phenomena, we must reject the constant term (^o+Po) in the expression for
the combined phenomena: this is equivalent to substituting for the original obser-
vations a0, «15 a2, am the excesses of them respectively above their mean value
2 p-. Let — =E==^-, c being an integer, and let cx=(d-\-e]f'ic', d being integral and
e a proper fraction. If we represent (3m by the general term
\_p5 cos smz-\-qs sin smz\,
and ym by the general term
£p* cos s ^ mz + Qs sin s - mz\ ,
3d
MDCCCLXXV.
370 MESSES. C. AND E. CHAMBEES ON THE MATHEMATICAL EXPEESSION
the first set of expressions of (6) may be put into the following typical form,
2 [_ps cos smz-\-qs sin smz] cos tmz
. (10)
which, in the case before us, is
2 cos smz-\-qs sin smz ] cos tmz
(11)
and since Uz=2ct, and neglecting, with Bessel, the terms of (5m and ym for which s is
not small, and also dividing through by this becomes
But after each successive period the quantity
passes again, in each of its terms, through the same identical values ; it is therefore a
proper periodical function, and passes at the same phase of each period fx' through
some maximum value, which cannot ever be of magnitude so great as the sum of all
the P’s and Q’s disregarding their signs ; much less can
ever reach that sum ; hence the last term of (12) can never he so great as twice the
sum of all the P’s and Q’s regardless of signs. Suppose this to be its value at some
time during the first period fx', then at no time in the second period fx' can it exceed
the half of this, since B will have been at least doubled, whilst the part under the sign
of summation cannot have increased; similarly, at no time during the nth period fx' can
2
its value be of greater magnitude than -ths of the sum of its P’s and Q’s regardless of
signs. Hence if n be made large enough, i. e. if the observations be sufficiently extended,
this quantity can always be reduced till its effect upon the value of jpt is inappreciable.
11. Now it has been shown in the preceding investigation that, as B increases and
fx! <2fxJ 3 fx! dfx'
passes successively through the values &c., the quantity
OF OBSERVATIONS OE COMPLEX PERIODICAL PHENOMENA.
371
vanishes at each passage ; when, therefore, the series of observations is not sufficiently
extensive to obliterate the effect of the last term of (12), it may be worth while, in the
first place, to calculate approximately the values of P„ Q,, P2, Q2, &c., choosing for the
purpose a number of observations R/ which very nearly completes an integral number
of periods fx!, and thence the value of
% £PS cos s ~mz-\-Qs sin s ^ mz^ cos tmz
for the fractional part of a period fyJ which is in excess of the last completed
period.
Similar reasoning, with a similar result, may be applied to each of the expressions
of (6), of which (10) is a type.
III.
12. The variations in a series of n observations (equidistant in time) are by hypothesis
due to a periodical phenomenon whose true expression is
a™=Po+Pi cosw.s+2'i sinm;z+^2cos2TO2+2'2sin2m2+&c., . . . (13)
2c7t •
in relation to which 2=—, c=a constant integer not small, «=the period of the
phenomenon, #=;s^=the interval of time corresponding to the angle z, £=the time
reckoned from the commencement of the observations, and m=^. Let the interval
between successive observations be (x-\-Ax), so that the n observations will extend over
a period n[x-\- Ax) =c(k-{- An). The angle {z-\-i) which corresponds to the interval of
time (x-\-Ax) will be equal to z^^~=z-\-z~- or i=z^-=z let this be so small
that mi is also a small angle, s being the suffix of a or q. Under these conditions, to
find the coefficients ^>1? See. Let it first be observed that the condition that sni is a
small angle, implies that n has been so chosen that (z-\- Ax) approximates as closely as
possible to the known or assumed value of %. The phenomenon am occurring at the
time mx, let that which occurs at the time m(x-\- Ax) be called am, ; then we shall have
am’ =jPo +i> i cos m(z + i) -j- q1 sin m(z + 7) -\-p2 cos 2 m(z + i) + q2 sin 2m(z + i) + &c . , (14)
the general term of which is cos sm(z -f i) + qs sin sm(z + 7) } , where s represents the
positive integral suffix of a qp or q; and we may, for shortness, write
«m'=[i>icossrn(2!+^)+g'ssin sm(s-H’)]> (15)
the square brackets indicating that the general term within them is to represent the
sum of its series of values when for s is put 0, 1, 2, 3, &c successively, whence
am'=[j?s(cossm2 cossmi— sinsmz sinm^+^sinsms: cossrni+cossmz sinsjm)] ; (16)
372 MESSES. C. AND F. CHAMBEES ON THE MATHEMATICAL EXPEESSION
and smi being a small angle, we may write for its sine smi, and for its cosine (1— |s2mV),
when we obtain
am/= \_(ps cos smz+qa sin smz)-\-si(qs m cos smz—ps m sin smz)
s2i2 -i
-g- (ps m2 cos smz-\-qs m2 sin smz) J .
Multiplying both sides by cos tmz, t being any positive integer,
am, cos tmz—am cos tmz-\- m cos smz cos tmz—ps m sin smz cos tmz )
“i
— -£-(jpsm2 cos smz cos tmz-\-qa m2 sin smz cos tmz) J ;
and taking the sum on both sides from m= 0 to m=(n— 1),
(17)
. (18)
m—n— 1 m=n— 1
% am, cos tmz— 2 am cos tmz
m=0 m= 0
m—n — i r ^ ^
+ 2 j -x { qs{m cos(s -f £)m;S + m cos (s — £)to2) —ps(m sin(s + t)mz + m sin(s — t)mz) }
m= 0 \_Z j
s2i2 . i I
— (ps(m2cos(s -j- t)mz -j- m2 cos(s — t)mz) -f- qs(m2 sin(s -(- t)mz -{- m2 sin (s — t)mz) } J. J
Now observing, from the collected equations at the end of the first set of demon-
strations in the Appendix, that when nv=2cT, and according as v is not or is 0 or a
multiple of
m cos mv= — x.
S m sin ww= — s cotg,
m= 0
or 0,
«j2
“-”-1 nr n 1 nr n* ,
2 m2 cos mv= — 0 + „ , or x — 77- {-*,
2 1 2 . 0 3 2 1 6
m-0 Sin2
> (20)
% m2sin mv=— cot;
or 0.
J
And as in equation (19) nz=2,cir, applying equations (20), equation (19) becomes
s + ^ n s — t \ ) ‘'j
w.2 n 1_
~o"i 2 <?_
( n n'
/ n2 n
)-?.(
1
“2+2 .
sm 2 ~z
Ls + t
n2
Cot —o~Z-
-9- cot
(19)
OF OBSERVATIONS OF COMPLEX PERIODICAL PHENOMENA.
373
p =2 aOTcostfm;s-j-|jj*(&(— \-\r\— 2»,(— \ cot^z+O^J
s2i2f / n 2 ?i 1 n3 ra2 n\
IT 1-^*1 Hi '2 . ~s + t + 3~~'2+6/
1 x sm2— 2 7
+£.(— J cot^*+0^|j,
P =5 o cos tfmz+ cot z) J
s2i2 f (n3 n2 n n2 n 1 \
+ £s(0-|cOt^z)}],
<ma+^{ffXw “ !)} — w3_w2 + l)}]’
> (21)
or = 5) am cos
according as neither (s-\-t)z nor (s— t)z is 0 or a multiple of 2x; as (s+£)z is not, and
(s—t)z is 0 or a multiple of 2t ; as (s + £)z is, and (s— t)z is not 0 or a multiple of 2tt ;
or as both ( s-\-t)z and ( s—t)z are multiples of 2r.
2
And multiplying both sides by -,
2 772 = 71 — 1
cos tmz=-% am cos tmz-\-
n m= 0
[f { “ 2 Zs+Ps (cot S-~z + cot *-£ z) |
1
. 1 \ / ,S+t s—t
+ —&(w cot -g- 3 + 71 cot -jj-
sin2 ‘-z- '
O
or o “m cos tmz + [f { 1s{n - 2) +i>s (cot —z^j |
-x{^(^2_2w+^+~7+t) - ff.(»cot ^)}j,
or=n f=0 cos [||^-2)+^s(cot^^|
Or=^=o amcoste+[||^2(w-l)J-s-^{i?s(|w2_2w+|)}1
374 MESSES. C. AND E. CHAMBERS ON THE MATHEMATICAL EXPRESSION
according as neither (s 4-^)2 nor {s—t)z is 0 or a multiple of 2-r; as (s+£)z is not, but
(s — t)z is 0 or a multiple of 27t ; as ( s-\-t)z is, but (s — t)z is not 0 or a multiple of 27t ;
or as both ( s-\-t)z and (s—t)z are multiples of 27t.
Now by Bessel’s process, and assuming, as we shall, that only a few of the first terms
of the expression for am have considerable coefficients,
Also let
2*=»“i 2m=n~l
~X um cos tmz =pt, and - X am sin tmz — g_t.
™7W = 0 ^ m = 0
Q m—n—\ Q m=n—\
-X am, cos tmz — PA and - X um, sin tmz = Q;.
nm= 0 nm=0
Therefore, writing at and a* respectively for the coefficients of i and i2 in (22), and
transposing,
pt=Vt—ati—SLti2
Proceeding in a similar manner, we find : —
(28)
am, sin tmz=um sin tmz
r . s2i2
+ 1 si(qsm cos smz sin tmz —psm sin smz sin tmz ) — -x- (psm2 cos smz sin tmz
> (24)
I
4- (pn2 sin smz sin tmz) J ;
am, sin tmz =X um sin tmz
m=n— in0«
+s If
1=0 L_
S2*2
4
qs[m sin (s 4- t)mz — m sin (s — t)mzj —J9s{m cos(s — t)mz — m cos(s 4- t)mz) j >■ (25)
| ps(m2 sin(s 4 -t)mz— m2 sin(s — t)mz) 4- qs(m2 cos (s — t)mz — m2 cos(s-{-t)mz) | |
X um' sin tmz = 2 am sin tmz
tVsi( ( n s + t n s—t \ ( n n\) s2i2f / rt2 s + £
4-|l2 p - ^ ' “ 2 COt ~T- Z+ 2 COt ~2~Z) -?• V ~ 2 + 2 j { _ T \P\- 2 COt ~Y Z
. rc2 , s t \ * / w2 , n 1 , n2 n 1 \)~\
4-2 COt 2 Z)+qsl 2 +2 . o® — t 2 2 . 2s + * )f ’
/ \ sin2 — —z sm2^— z/ t -i
m=n- 1
or =X sin tmz
!~si( ( n s + t n\ (r? n w\) s2i2 ( / n2 s + * A
+ 2COt_2_2: + 0j-^V'2_2'+27} 4 {p(-2"Cot"2"^ + 0
fn3 »*.«,»* n 1 \)~]
+ 6+2"-2 . 2s + t j f I’
\ sm^— z' J -J
y (26)
OF OBSERVATIONS OF COMPLEX PERIODICAL PHENOMENA.
375
or =X am sin tmz
r«( /n i n ,® — ^ \ ( n n1 riW s2i2 f /_ n2 s— \
+ \L2[^[0+2COt~2~Z)~^\~2~2+2)\-^\^{0+2COt~2~Z)
, / n2 . n 1 w3 n2
or=£ am sin tmz,
according as neither (s+£);s nor (s — tf)2 is 0 or a multiple of 27t; as (s-\-t)z is not,
but (s— t)z is 0 or a multiple of 2-n- ; as ( s-\-t)z is, but (s— t)z is not 0 or a multiple of
2?r; or as both (s-\-t)z and ( s—t)z are multiples of 2tt.
2m=n—\ 2 m=n-l
- X ocm> sin tmz—-- X am sin tmz
71 7ft = 0 U 771 = 0
+[f {&(cot S~YZ ~ cot | —S~rfes(n cot S~^z—n cot
/ 1
1 \
A • 0® t
• 0 S+t )
vsm2- — z
Sin2 -rr~Z'
2
2
<
or=:
+[l{^(-cot^)-^}-x{^(“wcot^)+^(x +^“777+7)}]’
> (27)
2 m=n— 1
or=- X am sin a sin tmz
-[!{& (cot S-^z)j -~i-\psn cot +&( - 1 w2 - 1 + ) j j,
2 m=n-l
or=^X am sin tmz.
according as neither ( s-{-t)z nor ( s—t)z is 0 or a multiple of 27 r; as ( s-\-t)z is not,
but (s—t)z is 0 or a multiple of 27r; as ( s-\-t)z is, but (s— t)z is not 0 or a multiple of
2? r; or as both (s+#)2 and ( s—t)z are multiples of 27 r.
And writing bt and bf respectively for the coefficients of i and i2 in (27), and
transposing,
q-Qt-b,ti-bfi2 (28)
376 MESSES. 0. AND P. CHAMBEES ON THE MATHEMATICAL EXPEESSION
13. From the general expressions (23) and (28), for the coefficients^, qt we may now
write down the particular values p15 2L fc, §3 for the particular case in which,
whilst neither s nor t is taken above 3, neither (s — t)z nor (s-\-t)z is ever a multiple of
2tt ; and at the same operation we may substitute for the general terms in which at, a„
b„ b, are expressed, the series of terms obtained by giving s the values, 1, 2, 3
successively, observing also that when s= 0 these terms vanish. We have then,
'i = Pi — — 2) +^>, cot 2— 4 j2 + (cot|« + cot |) — 6 j,+ 3/i,(cot 2« + cot z) j
+l{^(l,i2-2)>+5+5i)-2'recotz + 4*(-2,!+_b“ + ^)
\ / \ sin2— z sin2-2
> (29)
^^2 ('
ncot^z+ncot^ ) +9y8( — ) — 9^ cot 2s cot,
(
4
— Qj — cot 2! — ppz + 2#2 ^cot z2 — cot ^s J + 3£3(cots— cot 9
-j)xn cot 2+^ (§«2+| — + 4pa(» cot|— wcot|«^
+%(T^-T^3-)+9i?3(ncot2-wcot22) + %(iI^-slr^2i)}-
'sm2- sin2-*2 ' 22
> (30)
jp* = p2 — — 2^, +ih (cot | s — cot + 2^2(w — s) + 2p2 (cot 2s) — 6#,
+ 3p3 (cot \z + cot|) | +\Ui ( - 2n+—^Y +-7^7) ~ ft (w cotl 2 w cot
+ fjh (3W2 - 2% + ^ + ^2-*) - 4#ara cot 2s + 9p. ( — 2 n+ —7 + — )
— 9^3 (w cot-s+wcot^ |.
#2— Q2— l ( — cot | — cot |s^ — 2^ cot 2s — 2p2w+ 2>qz (cot 3— cot |s^ j
-f \\pi(~n cot^— w cotes') — 4p2w cot 2s
L ' 2 'sin2^ sin2 -z'
(§*’+§— +9p3(w cot|— ncot\z\ +9^3(—
' 2 ' 2 'sin2- sin2 -2 2 J
> (31)
(32)
OF OBSERVATIONS OF COMPLEX PERIODICAL PHENOMENA.
377
j)3= P3 — g | ■ — 2#i H-jp, (cot 2z — cot z) — 4^2 + 2p2 ^cot -g — cot ^ J + 3#3(rc — 2)
+3^3 cot 3z j + ^ ji>, ( — 2ra + ^2^ + — g_i{n cot 2 z-n cot z)
+ 4p2 ( — 2 n+ — + — ^ ) — 4^ ( w cot §s — n cot
' sin2 %s sin2 ' Z>
W33)
+ 9i> 3 (f w2 — 2w + 3+^3^) — cot 3z j .
§'3= Q3 — ijg'iC — cot z — cot 2z) + 2q2 ( — cot ^ — cot |z^ — 3^3cot 3z — 3 p3w j
+ w cot z - cot 2z) + #, (^, — ^2^) + 4p2 ( - n cot | - - n cot \z^j
+ 4«> (t^- tV) “ 9p‘n COt 3z + 9?1 (I ^“riSs) }•
'sin2- sin2-,?7 ' 7 J
> (34)
J
For the values of^, qx, &c. in the last terms of equations (29) to (34), we must now
insert their first approximations, j9l='P1, qt= Q1} p2=P2, £2=Q2, &c. (and in the last
terms but one, second approximations), as follows : —
P, = Pj — 3 |q,(w— 2) + P, cot z — 4 Q2+ 2P2 (cot |z + cot
— 6Q3 + 3P3(cot 2z+ cot z)j ;
= Qi — 1|— Qj cotz— Pi^+2Q2 (cot^— cot|z^ + 3Q3(cotz— cot 2z)j ;
P2=P2 -|{ - 2Q, +P1 (cot §z-cot f) + 2Qa(w— 2) + 2P2 cot 2z- 6Q3
+ 3P3(cot|z-cot|)j; ^ (35)
22=Q2— 2 |q, (— cot|— cot|z^ —2Q2cot2z—2P2w+3Q3(cot|—cot|z^j;
i>3 = P3 — g | — 2Qj + Pj(cot 2z — cot z) — 4Q2 + 2P2 (cot ^z — cot
+ 3Q3(% — 2) -{- 3P3 cot 3zj> ;
Q3 — 2“[Qi( — c°t z — cot 2z) + 2Q2 ( — cot | — cot|z) — 3Q3 cot 3z — 3P3| .
q3=
MDCCCLXXV.
3 E
378
OBSERVATIONS OF COMPLEX PERIODICAL PHENOMENA.
These operations correspond to the rejection of terms involving i3.
We thus obtain, in lieu of equations (29) to (34), which involve the unknown true
coefficients on both sides, others of the form
ih=Pi+A j+Aj?,
£ = Qi + IM + Bti2,
#= P2 + A 2i -f- A2i2,
5'2=Q2+B^-l--52i2,
£3 = P3 + A3? -f- AA
£ = Q3 + + B3i2, j
&c.=&c.,
(36)
in which A1? A19 B1? Bl9 &c. are numerical quantities.
The true period (and therefore i) being known, these expressions give the values of
the coefficients for the true period in terms of those for the approximate period ; and
these values being inserted in equation '(13), it will then express the phenomenon for
the true period in terms of the coefficients for the approximate period. The general
expression for A, and AY &c. would be too lengthy to write in full, although the calcu-
lation of their numerical values in any particular case is not very tedious ; the most
convenient mode of procedure is to work out, by equation (35), the numerical values of
the second approximations to#, £, &c., and insert these in equations (29) to (34).
14. To illustrate the application of the method described, and to show that advantage
is gained by it, we have chosen, arbitrarily, the law of periodical variation
or
■where
am~ — cos(?w;3+600)+cos2mz— cos 3 mz9
am= — -5 cos *86603 sin mz-\- cos 2mz — cos 3 mz,
# = -•50000; £=+*86603; #,=+1-00000; £=-00000; #= + 1-00000;
£=•00000;
and taking z=30, i— 5', and ^=120, we have calculated one hundred and twenty suc-
cessive values of am, corresponding to the successive values of 2—0° O', 30° 5', 60° 10',
&c. .... (3570°+ 9° 55') ; then, treating these numbers as if they corresponded to values
of z — 0°, 30°, 60°, &c 3570°, and applying to them Bessel’s method, the following
values of the approximate coefficients were obtained : —
P,= --42262; <+=+-90398; P2= + -97128,
Q2= — "17383 ; P3= — -96147 ; <+= + -25536.
With these values, and the other data which supplied them, equations (35) and (36)
give as third approximations to the true values of the coefficients,
#=-•50000; ^=+-86604; #=+1-00011;
£= + •00002; #=--99995; £= + -00002;
PLANETARy INFLUENCE ON THE EARTH’S MAGNETISM. 379
and as second approximations, that is excluding terms involving i 2,
_p—_. 50089; &= + -86829; +1*01028 ;
£,= -•00328; p3= -1-02186; &= +’00416;
the degree of approximation is in the second case close, and in the first almost perfect.
IV.
Application of the processes described to determine whether or not there be any
periodical variation of disturbances of Magnetic Declination and Horizontal
Force at Bombay , due to the influence of the planets Mercury , Venus, and the
Earth, in the periods of their respective orbital revolutions* , and of Mercury,
Venus, and Jupiter in their synodic periods.
15. In view of the remarkably definite evidence of periodicity in sun-spots indicative
of planetary influence, brought to light by the investigations of Messrs. De La Rue,
Stewart, and Loewy, and having regard to the common subjection of sun-spots and
terrestrial magnetism to the well-known decennial period, it seemed to the writers very
desirable to examine whether a similar connexion was exhibited by the two phenomena
in respect of the planetary periods. The connexion was first shown to exist, by General
Sir Edward Sabine, between the larger disturbances of terrestrial magnetism and sun-
spots, but it has since been extended to include also the regular magnetic variations.
The present inquiry will, however, be confined to the larger disturbances, and of these
to the disturbances of Magnetic Declination and Horizontal Force at Bombay, of which
a large body, extending over a period of twenty-six years, is available for use in the
discussion.
16. A description of the Declinometer, and of the method adopted for separating dis-
turbances, which is that of General Sabine, appears in the 4 Philosophical Transactions,’
1869, pp. 363 to 368, and, like the Declinometer, the Horizontal-force Magnetometer is
of the kind by Grubb of Dublin, originally supplied to the British Colonial Observa-
tories. Disturbed observations of Declination (Easterly) may be defined as all those
observations which give a value of the easterly declination in excess of the average of
the remaining observations at the same hour during the same month by more than l'-4,
and the easterly disturbance is that excess ; and disturbed observations of Declination
(Westerly) are all those observations which give a value of easterly declination in defect
of that average by more than l'-4, and the westerly disturbance is that defect. In
Table I. the aggregates of such excesses and defects are shown for each month in each
of the twenty-six years from 1847 to 1872. Disturbed observations increasing the Hori-
zontal Force are all those which give a value of the Horizontal Force in excess of the
average of the remaining observations at the same hour during the same month by more
* The mathematical expression for the Earth’s influence being analogous to the expressions for the influence
of Mercury and Yenus, the influences are here classed together indiscriminately, although doubtless they are
not wholly of the same character in each case.
380
MESSES. C. AND E. CHAMBERS— PLANETARY INFLUENCE
than -00334 (metre-gramme-second) units of force, and the increasing disturbance is that
excess; and the disturbed observations decreasing the Horizontal Force are all those
which give a value of Horizontal Force in defect of that average by more than -00334
units, and the decreasing disturbance is that defect. In Table II. the aggregates of the
excesses and defects of Horizontal Force are shown for each month in each of the
twenty-six years from 1847 to 1872. The two Tables contain all the observational
data used in the present inquiry.
Table I. — Showing the Monthly Aggregates of Disturbances of Declination exceeding
l'-4 in amount, from January 1847 to December 1872.
Easterly Disturbance Aggregates.
Jan.
Feb.
March.
April.
May.
June.
July.
August.
Sept.
Oct.
Not.
Dec.
1847.
32-601
9-313
53-343
81-730
52-675
31-843
41-527
69-892
153-729
108-458
67142
210-564
j 1^48.
52-444
82-755
84-714
46-396
25-086
87-569
87-888
44-773
15-669
81-189
233-638
27-256
1849.
66-268
94-313
55-685
30-832
16-206
16-850
18-278
32 054
19-469
53-973
92-298
20-561
18710.
28-997
28-544
34003
15-067
18-623
16-777
42-915
21-585
15-093
8-540
5-443
82-517
1851.
74-813
21 741
13-837
20-075
20-990
22-818
35-098
21-894
90-523
49-580
18-995
72-240
1852.
53-346
129-985
24-127
74-522
126-439
14-392
18-704
34-921
32-894
16-508
28006
36853
1853.
32-650
24-427
42-940
25-270
67160
39-312
27-949
36-882
94-948
19-424
17-374
38-480
1854.
50-902
64-843
56-504
43-466
10-708
22-208
31-258
10283
22-554
44-416
18-769
22-813
1855.
13100
7-185
36-425
19414
8-449
14-416
13078
10-702
16-942
14624
14 734
14 338
1856.
8054
14-978
10-926
13-924
1-665
12-098
5 052
9-554
21379
15-433
0000
6-893
1857.
8118
6-752
20-732
8-924
10-489
13 311
33118
12-057
25-447
20-650
40-744
96-264
1858.
49-958
39-181
64-664
111-087
18-894
25-834
77-967
30-488
43782
44-923
27-337
15034
1859.
57-819
69-377
48-189
97001
52-618
38-394
57-820
114162
169-905
198-777
15-435
49-717
1860.
23-984
70715
103117
37-567
17-695
38-733
140-932
221-409
64-623
63-580
11-436
38-406
1861.
60-495
56-850
37678
33-454
19002
41-033
39174
32-787
47-383
40-953
35-443
69-321
> 1862.
30153
26-618
179-782
84-432
27-592
21-266
51-978
81-257
55-343
163152
13-866
55-289
1863.
62003
39-771
60-408
56068
56-448
19-299
27-583
32-972
27-227
22576
12 177
0000
1864.
17-328
32-728
26-264
27-672
6-541
80-336
57-361
40140
39-891
20-698
5 020
20-390
1865.
52-565
27-247
9-906
39-858
27211
25-372
53-231
70072
30-130
41-462
50-878
13-940
1866.
30-095
81-696
16-635
3-045
17-569
13 226
3-059
27-330
12088
31-926
32-221
8047
1867.
30-424
15-881
4-994
2-875
14-832
11655
16-841
25 108
21 224
40-817
27-571
0000
1868.
6-695
4-370
16-389
110-398
5-117
18-591
13-281
38-992
55-874
85-009
7-087
6-428
1869.
55-697
43-308
60-588
75-824
67-852
52-912
17095
30-644
116-304
50-840
17-692
59-819
1870.
64-717
57199
70-171
101-645
77-381
64-724
33-539
62-790
79-164
153136
51-690
45-709
1871.
8-155
10-946
9078
15-883
3-705
5-598
14-513
11-408
6-347
6087
12137
2-614
1872.
3-818
18-097
8-803
6006
7109
8-368
10140
14-941
10-221
31-311
3-622
6-856
Westerly Disturbance Aggregates.
1847.
22-397
7-678
0000
44-942
27-333
39-353
28176
40-743
60-499
31-620
37967
53-274
1848.
58-531
54-526
11-946
27-527
22-894
33-295
54 331
53-568
6-745
46017
81-873
17-325
1849.
47-932
29114
51-404
50760
21-203
39-349
40-501
49-756
32347
28-293
26-837
11-849
1850.
11-865
62015
13-427
33-615
39415
11-933
41-324
24-019
23114
10-068
4-772
16-425
1851.
25-920
26131
16-060
6148
36-951
48112
40-230
41-939
26-847
23-471
7-637
10-712
1852.
31093
43-683
19-581
42 771
21-890
11 452
39-386
24-997
35-918
24-430
28-512
17105
1853.
71474
2-889
23612
13-683
35-860
27-882
26-281
23-721
24-766
42-571
6-748
8-598
1854.
49-328
6-672
26-553
9-388
12-748
34-806
16006
8.158
8-245
18-580
12-791
4-506
1855.
8-686
14-803
1-447
13-382
6-207
30-243
21-586
23-924
23 347
5-025
3191
5-548
1856.
16100
9-312
0000
7-282
9-634
6-364
27-199
6-584
25-866
3-252
8-740
3-050
1857.
36052
12035
5-744
7974
36-935
12-845
22012
10-628
97-241
28-370
13-757
57011
1858.
48-242
14-885
36-986
12-387
18-998
24157
31-895
35153
61-432
38-204
32-387
21-273
1859.
29-810
31-247
33086
35 032
54-457
34145
41192
49006
81-670
43-294
22-539
45-387
1860.
45-737
24-530
59-494
53-723
46127
39-309
171-465
59-967
31-190
35-831
16-268
23-089
1861.
23-738
12-540
28022
44-486
19-973
36-941
64-533
31-395
20-087
45-476
10-469
10-644
1862.
24-502
11-317
39-491
99-643
20131
35-380
52-467
36-508
32-164
96-376
18-179
19-360
1863.
45-074
29-515
24148
35-883
17075
9-793
28-931
29-248
10-118
29-466
12-512
9-864
1864.
16-426
21-826
13-412
17-374
17-771
19-065
25-817
37-766
20-984
9-253
8-052
6-418
1865.
12-802
19-926
11-832
3-695
48-677
8-625
25-480
44-368
38 070
34-283
3015
3-355
1866.
36-845
38-828
17-246
20-491
205-299
2-929
17-898
41-593
6695
70-411
3-457
2-902
1867.
14021
6-881
5-481
3-156
3-080
1-811
13-432
23159
21-280
11-930
3-073
0-000
1868.
1-523
14-104
25 252
34-643
12-828
20-381
16-917
19-469
56-602
149-506
1-482
0000
1869.
20-950
6-277
13-912
32-983
21-287
21-938
39-260
20195
55 086
19-379
8-246
33-442
1870.
23-818
19-064
32187
41-901
54-201
63-784
90-833
72-874
40-028
30-685
42-759
28-250
1871.
4-967
6-338
6090
4-773
3-473
5-347
6-644
8-570
4-551
5-588
3-172
2443
1872.
2-720
4-309
5-640
6-245
4-697
3-534
2-892
6-209
4-559
2-592
4-422
3-794
ON THE EARTH’S MAGNETISM.
381
Table II. — Showing the Monthly Aggregates of Disturbances of Horizontal Force
exceeding ‘00334 (metre-gramme-second) units of force, from January 1847 to
December 1872.
Years.
Disturbances
increasing
: the Horizontal Force.
January.
Febru-
ary.
March.
April.
May.
June.
July.
August.
Sep-
tember.
October.
No-
vember.
1 De-
cember-
1847.
•00907
■01775
•01674
•02732
•00000
•00000
•00000
■04421
•01062
•08554
•01976
•02142
1848.
•03658
■06152
•02606
•03002
•02851
•00000
•05591
•05134
•00000
•14069
•03931
•00000
1849.
•15325
•01714
•01512
•00709
•01523
•02326
■00745
■01570
•02459
•02833
•00659
•00418
1850.
•01577
•01544
•01105
•00000
•01620
•01951
•02412
•00000
•00727
•04946
•00364
•00796
1851.
•02077
•02365
•04298
■00000
•04550
•05728
■00349
•01577
•04406
•04360
•00000
■00749
1852.
•04536
•24419
•11981
•01501
•03380
•01076
06502
•01202
•00403
•10634
•00832
•02668
. 1853.
•02796
•04004
•03449
•00369
•04307
•06008
•09990
•02997
•04000
■01945
■00431
•04752
| 1854.
■00409
■00756
•02712
■03405
•07026
■00000
■01132
•01723
•01548
•00708
•00000
•00701
1855.
•00000
■01460
•00748
•00000
•01445
■00000
•04876
■00000
•00000
■00339
•00361
•01106
1856.
•19274
•02631
•00000
•00389
•00349
•01745
■00000
•00763
•00348
■00393
•00000
•00768
1857.
•00000
•00000
■00788
•01888
■02353
•01179
•01651
•00000
•07689
•01406
•04776
•01950
j 1858.
•06034
•03265
■10996
•04717
•09666
■06326
•02741
•00000
04577
•07583
•03001
•00974
1859.
•07124
•02244
•06345
•09157
•02721
■03326
■03232
•04560
■13183
■22485
•08819
■02266
1860.
•05302
•03254
•19500
•14087
•05049
■06765
•07483
•12618
•13884
•03510
■01262
•01841
1861.
•08372
•10390
•02560
•03140
•02096
■19531
•03583
•05782
■01107
•03264
■09290
•03801
1862.
■06612
■09045
•00368
•02728
•04650
•03443
■08801
•10445
•10420
•08087
•00769
■05626
| 1863.
•08151
■10808
•10098
•09064
•02881
•12260
•02140
•20006
•05847
•03759
•03886
01101
I 1864.
•00372
■02653
•01799
•06810
•04201
•13497
•08710
•03553
•04273
■06378
•00788
•00000
1S65.
•07666
•07456
■03871
•00721
•00338
■01185
•04881
•23497
•09785
•18215
•27939
•03966
1866.
•03058
•15329
•14081
•00829
■00746
•00000
•05271
•00382
•02139
•15274
•02206
■00685
1867.
•00492
•00768
•03120
•04817
■03156
•00752
•01156
■00730
•02848
•11074
■03429
•03356
1868.
■01109
■01866
•00729
■13932
•00364
•03920
•02604
■07877
•11978
•02688
■00000
•00000
1869.
•04751
•04613
■03694
•16159
•06674
■11497
•06630
•06377
•10358
•02430
•07031
•03387
1870.
•09332
■07691
•08896
•03309
•04273
■03987
■04036
•13553
•18851
•09500
•25815
•09626
1871.
•17428
■01968
•16671
•29371
■02320
■12342
•10727
•08968
•03199
•04688
•14534
-08743
1872.
•08526
•06741
■04145
•06270
•07961
•09175
•06115
■05030
•09116
•15568
•20619
■01625
Disturbances decreasing the Horizontal Force.
1847.
•13291
■07978
•33491
•47664
■41126
•01228
•03791
•24646
1-29535
•83941
-62093
1-32156
1848.
■41396
•73566
•52963
■44082
•25848
•00839
•42689
•04676
■14562
1-03536
1-31195
•14882
1849.
•15361
■34546
07406
•04392
■06023
■11311
■02902
•01472
■09302
•15531
•42311
•04392
1850.
05317
■12276
•06599
■02308
•04435
■07866
•11441
•02045
•04442
■22712
•01508
•08766
1851.
•50339
•21535
•06455
■00000
■18515
•14645
•06707
■08168
1-34014
•60210
•06286
•29423
1 1852.
•35381
1 05696
•11290
•41404
•12053
•19390
•11268
•02830
•28188
•11441
•14018
•08564
1853.
•04322
■20955
•15304
■28258
•44698
•14385
•28554
•00369
•68770
■02894
■16352
■38029
1854.
■20900
•15717
•33748
•42278
•11508
•03705
•08220
01891
•09457
•26276
•06979
•04745
1855.
01555
■05654
•08636
•10479
■08041
•02081
•07373
•02464
•01256
•25156
•00369
•02274
1856.
01195
•05033
•05268
•03507
•04994
•00866
•01681
•09126
•06655
•10662
•00917
•12140
; 1857.
•00749
■02415
•00839
•10126
•47028
•04741
•02716
•00816
•24404
•05347
•35977
1-24577
1 1858.
•42793
•16029
•58995
•99566
■19593
•43089
•07337
•02714
■35608
•20237
•14029
•32211
j 1859.
•13537
•89391
•11752
•62330
■18915
•30410
•44571
•46413
1 12879
1-77052
•46265
•82666
1 1860.
•10656
■38462
1 09309
•38132
•31114
■08680
•94931
1-00879
•43830
•67307
•21485
•33536
' 1861.
•56006
•29277
•31021
•21158
•05457
•05590
•04264
•17087
•25154
•59525
•29297
■63135
1862.
•24050
•23634
■29742
•23392
•10651
■00891
•18965
•56125
•43924
•88875
•25039
•59343
1863.
•25914
07879
•07900
•14163
•11356
■10037
•19459
•13433
•30873
•34188
■11432
•02252
1864.
•00339
•06082
■29916
•22083
•16067
■63418
•30811
•31811
•29252
•20128
•09667
•02541
1865.
•26233
•27368
•14320
•29201
•19018
■12277
•07451
•81050
•09827
•30819
•33401
■02432
1866.
•06729
•90626
•13067
•07426
•07078
•01029
•01222
•20720
•11476
•29021
•13876
•09057
1867.
■04851
•25234
-05092
■07295
•12774
■04279
•04308
•01123
•13665
•17425
•08676
■02294
1868.
•00000
■08876
■50612
•35348
•15057
•09218
•32487
•15639
■34444
•54636
•00000
•01414
1869.
•27997
•44794
•34134
■61314
•77931
•38806
•06795
■46084
•55401
•29192
•21115
•26690
1870.
•73891
•51550
■47810
•48246
•64513
•35981
•21999
•67844
1-28971
109525
•52101
•57811
1S71.
•36799
112210
•51099
•72576
•05740
•27627
•33183
•44565
•31528
•37913
•73249
•04426
1872.
•05184
■96353
•15542
■92697
•21553
■27526
■51272
•94517
•53956
1-63515
•17688
•15274
17. The sidereal .periods of revolution of Mercury, Venus, and the Earth are 87‘97,
224-70, and 365*26 mean solar days respectively. Nine periods of Mercury are so
nearly equal to 2^ years (26 months) that the accumulated difference after ninety-nine
periods is less than four days, or of one period of Mercury ; and the time of thirteen
periods of Venus differs from 8 years so little that after thirty-nine periods the accumu
382
MESSES. C. AND E. CHAMBERS — PLANETARY INFLUENCE
lated difference is less than three days, or of the period of Venus ; we shall there-
fore, in the first place, find (in accordance with what has preceded) the coefficients of
Bessel’s series expressing the variation of aggregate disturbance of Magnetic Declina-
tion, Easterly and Westerly, and the variation of aggregate disturbance of Horizontal
Force (increasing and decreasing) with variation of the position of Mercury in its orbit,
just as if the observations were wholly due to the action of that planet, and so for each
planet in turn; and we shall afterwards examine to what extent the values of the
coefficients thus found are affected by the influence of the other planets.
18. The ninety-nine periods of Mercury extend over 23 years and 10 months, and
the observations treated commence with the aggregates of March 1847, and end with
those of December 1870. The thirty-nine periods of Venus and twenty-four periods of
the Earth extend over 24 years, the observations treated being those for January 1847
to December 1870.
The application of Bessel’s process to these observations, taken from Tables I. and
II., gives the values of the coefficients for the sidereal periods of Mercury, Venus, and
the Earth as shown below*.
Table III. — Values of the coefficients q„ &c. for the sidereal periods of Mercury,
Venus, and the Earth.
Declination.
Coefficients
Easterly Disturbance.
Pv
Si-
Pv
Sv
Pv
Sv
Mercury
Venus
The Earth
-0-523
-4-591
+1146
-1-190
-1-199
-4-054
+3-604
+ 1-428
-4-812
+3-435
+ 1 055
+7-217
+3-781
+3-422
+0558
+2-707
-2-786
-0-700
Coefficients
Westerly Disturbance.
Pi-
Si-
Pv
Sv
Pv
Sv
Mercury
Venus
The Earth
-4-302
-1-516
-7253
-1-802
+ 1-497
-1-168
— 1-314
+ 1-156
+0131
+ 1-796
- 1 -965
+2-584
+4-533
+2-440
+3-274
-2-495
+2-083
+0-684
Horizontal Force.
Coefficients
Increasing Disturbance.
Pv
Si-
Pv
Sv
Pv
Sv
Mercury
Venus
The Earth
- 00702
— 00493
-00112
+•0003 7
+ 00438
- -00524
+ -00080
- 00203
-■00442
+ -00326
+ 00111
+ -00967
+ 00322
- -00190
+ -00056
- -00428
+ 00004
+ -00779
Coefficients
Decreasing Disturbance.
Pi-
Si-
Pv
Sv
Pv
Sv
Mercury
Venus
The Earth
- -00928
- -02002
+•03 189
- -01847
— -00659
- 06212
+ -02370
- 00353
- 07347
+ -03871
- -00730
+ •04314
+ 05141
+■01617
+-02711
+ 00490
- -02442
+ 01362
* An example of the calculations of one of these sets of coefficients is given at the end of the Appendix.
ON THE EARTH’S MAGNETISM.
383
With these coefficients (and neglecting the non-periodic part of the phenomena) have
been calculated the ordinates for the construction of the thick curves (Plate 53. figs. 1-12),
the ordinates of which represent disturbance, and the abscissae time.
19. It may be objected to the procedure thus far, that the application of Bessel’s.
method to any arbitrary series of periodical numbers would yield a smooth-flowing
curve, although the numbers themselves were subject to no corresponding law: this, we-
reply, is a mistake; the law is inherent in the series of numbers. It is another
question to what cause the law must, in a particular case, be attributed ; but this is so
also when a periodical law has been found in a series of observations, by applying the
common method of finding average values at different phases of the period. It may be
interesting to some of our readers to show that, where the circumstances allow of the
application of the latter method, it leads to the same form of curve as Bessel’s process.
We choose for this purpose the variations, with the sidereal period of Mercury, of
disturbances of Declination (Easterly and Westerly) and of disturbances increasing and
decreasing the Horizontal Force. If we take twenty-six equidistant times in the period
of Mercury and twenty-six consecutive months, the several months will correspond to
the twenty-six phases of Mercury’s period, as shown below.
Twenty-sixths of the period of Mercury . . .
0
1
2
3
4
5
6
7
8
9
10
11
12
Months
0
3
6
9
12
15
18
21
24
1
4
7
10
Twenty-sixths of the period of Mercury . . .
13
14
15
16
17
18
19
20
21
22
23
24
J
Months
13
16
19
22
25
2
5
8
11
14
17
20
23
And arranging each successive twenty-six months’ aggregates in this way and in
successive lines, we get, for each phase, eleven observed disturbance-aggregates, of which
averages are calculated. Means are then taken of each consecutive pair of these
averages, forming twenty-six new averages, and this process is repeated six times ; after
this the means are taken of every consecutive three of the last averages, and these
numbers are curved thin in figs. 1-4. It will be seen that they agree with the thick
curves obtained, by Bessel’s process, which are also constructed from twenty-six equi-
distant ordinates ; but the agreement is closer, as it clearly should be, when the twenty-
six calculated ordinates are treated in the same manner (described above) as the twenty-
six average disturbance-aggregates were, to obtain the ordinates of the thin curves. In
this way the ordinates of the dotted curves have been obtained ; and although the thick
curves must be taken as best representing the true law, the dotted ones are more directly
comparable with the thin curves, having been obtained by a similar process. The slight
disagreement that is observable must be attributed mainly to the omission of the fourth
and higher pairs of terms of Bessel’s expression.
384
MESSES. C. AND E. CHAMBEES — PLANETAEY INFLUENCE
Table IV. — The observed and calculated values of Aggregate Disturbance of Decli-
nation are, for the sidereal period of Mercury, as follows : —
No. and kind
Easterly Disturbance Aggregates, diminished by the constant value 43'180.
of corresponding
figure.
Twenty-sixths of 1
the period J
0
1
2
3
4
5
6
7
8
No.
Kind.
+3-588
+6-862
+4-265
+4-259
+7000
+2-297
+2-746
-M97
-4 038
-4-880
-4-474
-3-926
2
Thin.
+8-622
-2-367
-6 326
-7-796
-6-628
-3-816
2
Thick.
Ditto rendered ]
+4-566
+ 1-911
— 1-383
-4104
—5-392
—5 055
—3-557
2
Dotted.
“observed ” J
Twenty-sixths of 1
the period J
9
10
11
12
13
14
15
16
17
No.
Kind.
-2-967
-0-968
+ 1-256
+2-217
+0-780
+1-872
+0-346
+ 1-455
+0-952
+1-759
+2-748
+2-841
+4-948
+4-381
+6-233
2
Thin.
-0-855
+1-004
+ 1-364
2
Thick.
Ditto rendered 1
comparable with l
“ observed” J
— 1-712
-0-242
+0-552
+0-866
+ M75
+ 1-874
+2-976
+4-038
+4-375
2
Dotted.
Twenty-sixths of]
the period J
18
19
20
21
22
23
24
25
No.
Kind.
Observed
+5-054
+5-482
+2-977
+2-440
-1-792
-6194
-6-892
-3-767
+0-236
+2-629
+2-406
2
Thin.
Calculated
-2012
-6136
-8127
-6-954
-2-924
2
Thick.
Ditto rendered 1
comparable with j-
“observed” J
+3-454
+1-249
-1-632
-4-141
-5-235
-4-362
-1-759
+ 1-601
2
Dotted.
No. and kind
Westerly Disturbance Aggregates, diminished by the constant value 28'-55 7.
of corresponding
jure.
Twenty-sixths of]
the period J
0
1
2
3
4
5
6
7
8
No.
Kind.
Observed
-4-218
—4-580
-4-231
-3-894
-3-739
-3182
-1-705
+0-474
+3-516
+2-394
+4-807
1
Thin.
Thick.
Calculated
-1-083
-3195
-5-847
-7.421
-6-780
-3-889
+0124
1
Ditto rendered 1
comparable with >
“observed” )
-2-531
—3-611
-4-S67
-5-460
-4-804
—2-917
-0-442
+1-654
+2-567
1
Dotted.
Twenty-sixths of ]
the period J
9
10
11
12
13
14
15
16
17
No.
Kind.
Observed
+2-972
+3-554
+ 1-923
+0-078
-2-277
-1-252
-0-909
+ 1-793
+6177
+7-311
+ 9-662
+ 9-641
+ 11-070
1
Thin.
Calculated
+0-607
-3-301
-1-545
+2-539
+ 10-669
1
Thick.
Ditto rendered |
comparable with l
“ observed ” J
+2-078
+0-688
-0-614
-0-838
+0-499
+3103
+6041
+ 8-140
+ 8-415
1
Dotted.
Twenty-sixths of 1
the period J
18
19
20
21
22
23
24
25
No.
Kind.
Observed
+6123
+1-553
+3-286
-1-755
-3 086
-2-880
-2164
-2-108
-3072
1
Thin.
Calculated
+8-239
-1-822
-5-221
-5-980
-4-491
-2171
-0-695
1
Thick.
Ditto rendered 1
comparable with l
“ observed” J
+6-573
+3-248
-0-302
-2-887
-3-955
-3-692
-2-828
-2 252
1
Dotted.
ON THE EAETH’S MAGNETISM.
385
And for the sidereal periods of Venus and the Earth, the calculated values are: —
Easterly Disturbance Aggregates, diminished by the constant value 43'026.
Twenty-fourths of the period
0
1
1 2
3
4
5
6
7
Venus
The Earth
+0-259
-3108
-2-523
-0-602
-5-752
+2109
-7-482
+4-271
-6-555
+5160
-3-543
+4-256
+0-159
+ 1-458
+2-681
-2-764
Twenty-fourths of the period
8
9
1 10
1 "
12
13
1 14
15
Venus
+3 049
-7-370
+ 1-846
-10-993
+ 0-408
-12-375
+ 0-445
j — 10-822
+2-597
—6-516
+6061
-0-516
+9-010
+5-579
+ 9-592
+ 10-163
Twenty-fourths of the period
16
17
1 18
19
20
21
22
23
Venus
The Earth
+ 6-957
+ 12-152
+ 2-113
+11-294
-3-015
+8166
-6-219
+3-882
-6-307
-0-318
-3-956
-3-441
-0-810
-4-937
+0-985
-4-728
Westerly Disturbance Aggregates, diminished by the constant value 28'-463.
Twenty-fourths of the period i
0
1
1 2
3
4
5
6
7
Venus
The Earth
+2-080
-3-848
+2-118
-3105
+0-373
-3-878
-2-227
-5-201
-4-220
-5-738
-4-173
-4-627
-1-742
-1-983
+2-117
+ 1-177
Twenty-fourths of the period
8
9
1 10
11
12
13
14
15
Venus
The Earth
+5-640
+3-586
+7-313
+4-517
+6-483
+4-208
+3-638
+3-693
+0-232
+4-110
-2-118
+5-915
-2-653
+8-484
22
- 1-703
+10-369
23
Twenty-fourths of the period
16
| 18
19
20
21 |
Venus
The Earth
- 0 400
+ 10084
+0133
+6-985
-0-570
+1-721
— 2117
-3-987
-3-360
-8-192
-3-383
-9-685
-1-863
-8-554
+0-402
-6051
mdccclxxv.
F
386
MESSES. 0. AND E. CHAMBEES — PLANET AEY INFLUENCE
Table V. — The observed and calculated values of Aggregate Disturbance of Horizontal
Force are, for the sidereal period of Mercury, as follows : —
Aggregates of Disturbances increasing tlie Horizontal Force, diminished by the constant value 0'4634.
No. and kind
of corresponding
figure.
Twenty-sixths of \
the period J
0
1
2
3
4
5
6
7
8
No.
Kind.
Observed
-•00399
- 00525
-•00613
— •00500
-■00228
-•00003
+•00097
+ ■00168
+ 00214
4
Thin.
- 00300
- 00493
- 00677
-•00702
— -00507
-00144
+ •00239
+•00479
+•00492
4
Thick.
Ditto rendered 1
comparable with l
“observed” J
-•00416
-•00481
- 00537
-•00508
- 00361
-•00128
+ 00114
+ ■00278
+ 00320
4
Dotted.
Twenty-sixths of 1
the period J
9
10
11
12
13
14
15
16
17
No.
Kind.
+•00206
+ 00307
+ 00177
+•00068
+ 00240
-•00049
+ •00410
+•00085
+•00627
+•00460
+ •00840
+•00957
+•00890
+■01370
+•00666
+•01061
4
Thin.
+•00939
+ 01303
4
Thick.
Ditto rendered 1
comparable with [-
“ observed” J
+■00261
+•00178
+•00168
+•00292
+•00540
+•00826
+ 01023
+•01024
+•00788
4
Dotted.
Twenty-sixths of 1
the period J
18
19
20
21
22
23
24
25
No.
Kind.
Observed
+•00369
+ •00456
+ 00021
-•00380
- 00725
-•00852
-■00735
-•00523
-•00387
4
Thin.
Calculated
-•00239
-•00791
-•01044
-•00973
— -00696-?
- 00397
-•00247
4
Thick.
Ditto . rendered |
comparable with L
“ observed ” J
+•00369
-•00114
-00520
-•00748
-•00776
-•00664
-•00513
-•00417
4
Dotted.
No. and kind
Aggregates of Disturbances decreasin
g the Horizontal Force, diminished by the constant value •
27647-
of corresponding
*ure.
Twenty-sixths of ]
the period j
0
l
2
3
4
5
6
7
•8
No.
Kind.
Observed
+ ■03273
+•06583
+ ■03976
+•03006
+•03956
+•00077
-•00306
-•03088
— 04195
-•03283
-•02474
-•02833
3
Thin.
Calculated
+•06731
-04144
- 06043
- 05604
-•03582
-•01417
3
Thick.
Ditto rendered 1
comparable with L
“ observed ” J
+ •03822
+•04076
+•02546
-•00006
- 02481
-■03974
-•04158
-•03354
-•02265
3
Dotted.
Twenty-sixths of 1
the period J
9
10
11
12
13
14
15
16
17
No.
Kind.
Observed
-•02996
-•01902
- 00496
-•00039
+•00022
+ 01175
+•03648
+•06147
+ 07153
3
Thin.
Calculated
- 00344
-•00764
-■02008
-•02769
-■01843
+ 01063
+•05108
+ •08568
+•09700
3
Thick.
Ditto rendered I
comparable with 1
-•01541
-•01401
-•01532
-01297
-00155
+•01955
+•04468
+•06395
+•06782
3
Dotted.
“observed” J
Twenty-sixths of \
the period J
18
19
20
21
22
23
24
25
No.
Kind.
Observed
+•05848
+•07625
+•02410
+■02852
—•01900
— 05104
—■05656
-•03673
- 06350
—•00745
+•01676
+•03363
o
Thin,
Calculated
Ditto rendered 1
-•02870
- 07265
— -0S576
-•01672
3
Thick.
comparable with !•
“ observed” J
+•05200
+•02030
-01640
-•04451
— '05359
-•04103
-01315
+•01760
3
Dotted.
ON THE EAETH’S MAGNETISM.
387
And for the sidereal periods of Venus and the Earth, the calculated values are: —
Aggregates of Disturbances increasing the Horizontal Force, diminished by the constant value -0461 1 .
Twenty-fourths of the period
»
1
2 |
3
4
5
6
7,
Venus
-•00886
-•00615
©
©
©
+•00209
+•00520
+•00657
+■00637
+ •00535
The Earth
-•00498
+ ■00447
+■01036
+•01029
+•00492
-•00260
-•00861
-•01088
Twenty-fourths of the period ......
8
9
1 10
11
12
13
14
15
Venus
+ •00440
+ •00417
+
§
S 1
+•00495
+•00480
+•00373
+•00199
+•00013
The Earth
-•00958
-■00667
- -00444
-•00383
-•00386
-•00247
+•00196
+■00905
Twenty-fourths of the period
46
17
18
19
20
21
22
23
Venus
-•00126
-•00195
- 00231
- 00293
- 00430
-•00639
-•00847
-•00957
The fEarth
+•01624
+•01992
+•01745
+•00888
-•00274
-•01267
-•01672
-•01349
Aggregates of Disturbances decreasing the Horizontal Force, diminished by the constant value '27529.
Twenty-fourths of the period
0
1
2
' 3 1
4
1 5
6 1
7
Venus
- 00738
-•03359
-•05313
-•05480
-•03645
-•00632
+ 02136
+•03422
The Earth
-•01447
+■00146
+•01081
+•01223
+•00912
+•00465
-■00227
-•01667
Twenty-fourths of the period
8
9
10
11
| 12
1 13
I 14
15
Venus
+ 02855
+ 01096
— ■00581
-•01047
+ •00032
+■02017
+•03697
+•04020
The Earth
-•04326
-■08081
-•11915
-•14164
-•13247
-•08558
-■00955
1
+•07405
Twenty-fourths of the period
16
1 17
18
19
20
1 21
| 22
1 23
Venus
+ •02733
+ 00514
-•01430
-•02080
-•01239
+ •00364
1+01493
+ 01165
The Earth
+•13906
+•16575
+•14921
+•10079
+•04200
-•00547
— -02903
-•02876
20. Eighty-two synodic periods of Mercury extend over 26 years, and the observations
treated are those for the years 1847 to 1872. Fifteen synodic periods of Venus and
twenty-two of Jupiter extend over 24 years, the years treated being 1847 to 1870.
Table VI. — Values of the coefficients gb &c. for the synodic periods of
Mercury, Venus, and Jupiter.
Declination.
Coefficients
Easterly Disturbance.
Pi-
Si-
j Pa-
Sr
Pa-
Sa-
Mercury
Venus
Jupiter
+0-719
+0-356
-3-334
-4-541
-0-364
-4-883
+0-776
+3-521
+ 1-361
-1-628
-4-112
-0741
-3122
-7-920
+ 1-916
+0443
-3-402
-1-676
Coefficients
Westerly Disturbance.
Pi-
Si-
Pr
Sr
Pa-
Sa-
Mercury
Venus
Jupiter
+M97
-1-604
+0251
-2-889
-1021
+0-212
+ 1-775
+ 1160
+0-189
+0439
+1-287
-1-534
+2-553
+0-278
+0-806
-1-300
-1-630
+2-264
3 f 2
388
MESSES. C. AND E. CHAMBEES— FLANETAEY INFLUENCE
Table VI. (continued).
Horizontal Force.
Coefficients
Increasing Disturbance.
Pv
2i-
Pi-
Sr
Pr
Sr
Mercury
Venus
Jupiter
-•00553
+•00672
+■00150
-•00804
-•00384
-•00065
+•00127
- 00075
-•00556
-•00037
- 00255
+•00522
-00335
+ 00537
-00146
+ 00320
- 00360
- 00272
[Coefficients
Decreasing Disturbance.
Pv
Si-
Pi-
Sr
Pr
S3 ■
Mercury
Venus
Jupiter
-•01019
+ ■02607
—•03509
-•02015
-■02805
- 03944
+•01047
+•05284
-•00751
+ 00771
-•03936
+ 02636
-•02165
-•04866
+ •04341
-•00065
-■02049
+ 01217
With these coefficients have been calculated the ordinates for the construction of
thick curves, Plate 54. figs. 13 to 24.
21. Table VII. — The calculated values of Aggregate Disturbance of Declination for tl
synodic periods of Mercury, Venus, and Jupiter are as follows: —
Easterly Disturbance Aggregates, diminished by the constant value shown in the last column of the Table.
Twenty-fourths of the period. . .
0
1
2
3
4
5
6
7
8
Mercury
Venus
Jupiter
-1-627
-4043
-0 057
-2-517
-6-762
-3-507
-2-226
-5077
-6-966
— 1-810
-0-922
-9-090
-2-250
+2-462
-9134
-3-793
+2-640
-7-300
-5-760
-0-483
-4-568
-6-951
-4-632
-2-122
-6-392
-6-612
- -684
Twenty-fourths of the period. . .
9
10
11
12
13
14
15
16
17
Mercury
Venus
Jupiter
-3-984
-4-402
- -184
-0-652
+ 1-429
+0-092
+2-135
+7862
+ -965
+ 3179
+ 11-085
+ 2-779
+2233
+8-748
+5-125
+0-182
+ 1-475
+7-042
-1-446
-7-302
+ 7-608
- 1-346
-13104
+ 6-490
+ 0-821
-12-850
+ 4-202
Twenty-fourths of the period...
18
19
20
21
22
23
Po-
Mercury
Venus
Jupiter
+4-208
-6-559
+ 1-846
+7-235
+2-646
+0-504
+ 8-436
+ 10-214
+ 0-608
+ 7-240
+ 12-626
+ 1-666
+4-248
+9-213
+2-552
+0-837
+2-348
+2133
40'-472
43'-026
43'-026
Westerly Disturbance Aggregates, diminished by the constant value shown in the last column of the Table.
Twenty-fourths of the period...
0
1
2
3
4
5
6
7
8
■Mercury
Venus
Jupiter
+5-525
—0166
+ 1-246
+3050
-1120
+ 1-865
-0-440
-1-834
+ 1-353
-3-482
-1-918
-0-176
-4-964
-1-429
— 1-919
-4-685
-0-808
-2-832
-3-364
-0-551
-2-241
-2133
-0-870
-0-288
-1-814
-1-499
+2099
Twenty-fourths of the period...
9
10
11
12
13
14
15
•16
17
Mercury
Venus
Jupiter
-2 442
-1-831
+3-678
-3-274
-1-286
+3-575
-3-310
+0-298
-f- 1*775
— 1-975
+2-486
-0-868
+0-462
+4-416
-3071
+2-974
+5-224
-3-821
+4-360
+4-492
-2-892
+3-950
+2-499
-0-925
+2-049
+0084
+0-970
Twenty-fourths of the period...
18
19
20
21
22
23
Po-
Mercurv
Venus
Jupiter
-0-186
-1-769
+ 1-863
-1-379
-2-426
+ 1-494
-0-720
— 1 891
+0-369
+ 1-564
-0-744
-0-610
+4-288
+0-216
-0-731
+5-946
+0-426
+0087
26'-638
28’-463
28'-463
ON THE EARTH’S MAGNETISM.
389
Table VIII. — The calculated values of Aggregate Disturbance of Horizontal Force for
the synodic periods of Mercury, Venus, and Jupiter are as follows : —
Aggregates of Disturbances increasing the Horizontal Force, diminished by the constant value shown in the
last column of the Table.
Twenty-fourths of the period...
0
1
2
3
4
5
6
7
8
Mercury
Venus
Jupiter
-•00761
+ 01134
—•00552
-•00661
+ 00483
-■00387
- 00530
-■00228
■00000
- 00533
-■00686
+•00493
- 00732
- 0071 8
+ •00895
-01037
-•00384
+•01013
-01251
+■00051
+■00763
-•01189
+ •00282
+•00207
- 00786
+ 00126
- 00451
Twenty-fourths of the period...
9
10
11
12
13
14
15
16
17
Mercury
Venus
Jupiter
-•00151
-■00366
- 00969
+ 00492
-•00950
-•01164
+ •00917
-01321
- 00993
+•01015
-01284
- 00560
+ 00845
- 00867
- 00053
+•00592
- 00288
+ ■00348
+ •00459
+ •00176
+ 00551
+ 00542
+■00350
+ •00565
+■00781
+•00260
+•00471
Twenty-fourths of the period...
18
19
20
21
22
23
Pa-
Mercury
Venus..
Jupiter
+ •00997
+ 00099
+ 00349
+ 01005
+ •00102
+ •00233
+•00724
+ ■00390
+ •00103
+•00225
+•00876
-•00075
-•00302
+ 01318
-•00296
- 00661
+•01445
- 00491
•05000
•04611
•04611
Aggregates of Disturbances decreasing the Horizontal Force, diminished by the constant value shown in the
last column of the Table.
Twenty-fourths of the period...
0
1
2
3
4
5
6
7
8
Mercury
Venus
Jupiter
-•02137
+•03025
+•00081
-■01791
-•00489
- 00674
- 00763
-01960
-01886
+ 00111
-•02085
-•04842
+ 00056
- 02311
-•06853
-01155
-•03690
- 06680
-•02997
-•06040
- 04410
- 04459
-•07984
-01360
- 04592
- 07831
+ ■00771
Twenty-fourths of the period...
9
10
11
12
13
14
15
16
17
Mercury
Venus
Jupiter
- 03053
- 04779
+ ■00986
—•00335
+ •00342
- 00374
+ •02469
+ •05291
-•01808
+ 04231
+ 07543
-01583
+ •04375
+•05705
+ 01150
+ 03145
+ 00426
+•05702
+ 01431
- 05787
+ •10114
+ 00234
- 09791
+ •12169
+ 00111
- 09398
+•10616
Twenty-fourths of the period...
18
19
20
21
22
23
Pa-
Mercury
Venus
Jupiter
+•00903
-•04528
+•05912
+•01875
+ 02768
+•00024
+ •02210
+ •09365
-•04587
+ 01511
+•12651
-•06258
+•00045
+ 11760
-•04942
-•01425
+ •07797
-•02128
•29213
•27529
■27529
22. Let us now estimate the errors in the coefficients for the Earth due to the
sidereal period of Venus, and those of the coefficients for the sidereal period of Venus
due to the Earth’s period. The periods have the ratio of 13 to 8, so that in equations
(7) /=13, ^=8, and r=96; that is, in 96 months eight periods of the Earth and
thirteen of Venus have been just completed. The least value of s for which (sipi)y
or (s+1) 8 is a multiple of r or 96 is 11*, and therefore pn or qu is the first coefficient
(after px or qx) that affects the value of ax or bx ; the least value of s for which (s+2) 8
is a multiple of 96 is 10, and therefore or q10 is the first coefficient (after p2 or q2)
that affects the value of a2 or b2 ; and similarly q?7 or q7 is the first coefficient (after p5
or qb) that affects the value of a5 or bb. Hence if we may disregard as small those
terms in the expression for the Earth’s period which repeat themselves six or more
times in a year, or whose period is less than two months, ax, bx, a.2, b2> a3, b3, &c. will
* See second set of demonstrations in the Appendix.
390
MESSES. C. AND E. CHAMBERS — PLANETARY INFLUENCE
each be affected by only one of the Earth’s coefficients, viz. p2, q2, p3, q3, &c.
respectively. Again, the least positive integral value of s for which (sf+tg) or
(13s^F8tf) is a multiple of r or 96 is 8; and therefore, if we may disregard as small
those terms in the expression for the period of Venus which repeat themselves eight or
more times in that period, the quantities au b„ a2, Z>2, a3, b3 &c., being unaffected by the
disturbance due to the planet Venus, will sensibly represent the true coefficients of the
expression for the Earth’s disturbance variation. In a similar manner it may be shown
that A„ Bj, A2, B2, A3, B3 &c. of equations (7) are sensibly equal to the true coefficients
of the expression for the period of Venus ; for the least integral value of s for which
( s^ft)f or 13 (s=p£) is a multiple of 96 is s=96if£, so that only very high terms, in
the expression for Venus, would affect the values of the coefficients of the earlier terms ;
and further, since the least positive integral values of s and t which make (sg^tf) or
8sipl3£ a multiple of 96 are eleven and eight respectively, and the corresponding
terms repeating themselves eleven and eight times respectively in the periods of the
Earth and Venus, they may, as before, be neglected.
23. But we have adopted for thirteen periods of Venus the approximate time 8 years
or 2922-05 days, instead of the true time 2921-11 days, which is less by 0'94 of a day.
Having worked out the question in Section III. for three pairs of coefficients only, we
will confine the examination to that number and to the Easterly disturbance variation
for the sidereal period of the planet ; and it will suffice that we determine the second
approximations to the true coefficients, rejecting terms involving i 2, i. e. that we apply
equation (35).
The first approximations are
P, = — 4-591 ; Q1=— 1-199; Pa= + 1*428; Q2= +1-055 ; P3= + 3*422 ; Q3= -2-786;
the angle
and the angle
2 cn 3x13
Z n 3 x 96
2t=48° 45',
cAx 2 err cAx 2tt 3 X 0*94
cx ’ n x n 224‘7
3x96
= 0'-94;
and the greatest value of sni is 2x(3x96)x0'-94 = 9o2' (cA% being the error in time
in thirty-nine periods of Venus). Consequently sni being a small angle, the case is one
to which the investigation in Section III. applies ; therefore
^P.+A^ — 4-591 +-044= — 4-547,"
q— Q1+B1«=—l-199-T80 = — 1-379,
i>2=P3+Aai= +1-428-' -088= +1-340,
?2=Qa+Ba^= + l-055+-115 =+l-170, >
^3=PS+A3i= + 3-422 + -330= + 3-752,
?8=Q3+B3«=— 2-786+-406= —2-380,.
from which has been constructed the
interrupted curve (Plate 53. fig. 6),
which is seen at a glance to be almost
identical with the thick curve con-
structed from the first approximations
Pi, Q„ &C.
24. We may now examine how the sidereal disturbance period of Mercury affects the
ON THE EARTH’S MAGNETISM.
391
coefficients of that of the Earth or Venus, and vice versd ; for which purpose we must
use equations (12) of Section II., viz. —
2 w=R— i 2 1 r~ • /* *1
[amcosmz]— Ps cos s - mz + Qa sin s ^ mz cos mz,
which we will suppose to give the Earth’s coefficient pl} Ps and Qs being the coefficients
f
of Mercury, and ~ being the ratio of the periods of the Earth and Mercury, which we
108 54
may take as near enough to -^r or 2=30°, and R=288; inserting these values
(12) becomes
J m=287 1 m= 287 p -54 54 “I
_2?j= — % . [«rocos wnz\—Y^i% [JPjcoss jgmx30o+QssinsY§ mx 30°Jcosmx 30°. • (37)
But the time of 314 observations is equal to 26 years, or 108 periods of Mercury,
therefore
m= 313 r XA KA -i
% |JP+oss 30°+Qssiny|mX 30cJcosmx30°=0 ; .... (38)
and adding -jti of this to (37), we have
1 m=287 I m= 313 p KA F.A -i
-^1==144^ [amCosrn30°]+^^ jjPs cos m X 30°-}- Qssins 30°Jcosmx 30°; (39)
and calculating the last term from the approximate coefficients of Mercury given in
paragraph 18, we find its value to be, for Easterly disturbance, + 0-006; therefore
I m=287
[aOTcosm30°] +0-006.
m=0
Similarly we find
1 m=287
^1=144 ^ [amsinrn30°] —0-021,
1 m=287
-^2=144^ [aro cos 2m 30°] + 0-071,
I m=287
^=144- [«» sin 2m 30°] -0-132;
and for Westerly disturbance
I m=287
•^1=i44^ [«mcosm30°] +0-035,
4 m=28 7
Si= J44 ^ \_Km sin m 30 ] +0-061,
4 m=287
-^2=144^ [“» cos 2m 30°] — 0-013,
1 m= 287
^2=144^ [aro sin 2m 30°] — 0-101,
in all of which the last terms are small
enough to be neglected, in comparison
with the absolute range of any of the
component periodical variations, as may
be seen by simple inspection of the
. values of the several coefficients given in
paragraph 18. And as these calcula-
tions are given more in illustration of
the method than for any intrinsic value
of the result, we need carry them no
further.
392
MESSES. C. AND F. CHAMBERS — PLANETARY INFLUENCE
25. Similarly, to find the effects of the Earth’s period upon the coefficients for the
sidereal period of Mercury, we have in lieu of (37),
Vi=^k cos m 30°) ] — ^ [P, cos sm 30°+(+ sin sm 30°] cos ^y| m 30°^
= ^ X 7 [ ' am cos ^ m 30°) ] + ~ % [P# cos sm 30° + Q, sin sm 30°] cos m 30°) ;
calculating which for Easterly disturbance, we obtain
i>,=ihy1'T“"cos (ilm30°)]-0'0i6; '
also
»,=+2 l: [“*» sin (f|» SO*)] +0-004,
P,= + 2 " [«. cos 2 (|| m 30°) ] - 0-022,
2s=+ s "[«. sin 2 (g m 30°)] +0-022,
^=i4ij_0 [«*cos3f||w80°j] -0-031,
^3=li4^ [«TOsin3 30°^ J— 0*014 ;
and for Westerly disturbance
-PI = Ii4 J~7[““C0S (llm300)] -°'084’
^1 = li4 \ f [a>» sin (if ™ 30°)] +0-000,
P* = fii j J7 [«m cos 2 (ffm 30°)] +0*063,
^=iii£‘8/[anisin2 (jfm30°)] -0-032,
1 ”L=287 r /54 \
^=i4ij_0 cos 3 (t^ 3°°)] -°-°25,
J to=287 r- /C 4 N
fh— 144 [a* sin 3 30°jJ +0*046,
26. To make a similar estimate of the reciprocal actions of Venus and Mercury would,
with a month as the interval between successive observations, be extremely trouble-
some, but what has been done shows sufficiently the practicableness of the process, and
we do not consider it necessary to apply it at present to this or any of the other cases
we are dealing with.
in all of which also the last
terms are small enough to be
neglected, in comparison with
J>the range of each component
variation, as may be seen from
the values of the several coeffi-
cients given in paragraph 18.
ON THE EAETH’S MAGNETISM.
393
27. The principal features pointed out by Messrs. De La Rue, Stewart, and Loewy*
of the growth and decadence of sun-spots were of a simple character ; the spots acquired
a minimum magnitude at a heliocentric longitude a little greater than that of the planet,
and a maximum at a heliocentric longitude a little more than 180° greater than that of
the planet ; and there was a gradual progression in the change from minimum to maxi-
mum and vice versa in the intervening periods.
28. It must be admitted that the curves which we have found of magnetic variation
in planetary periods do not possess the same simple character ; but if we confine our
attention to those of them which have been yielded by the largest number of individual
observations of disturbance, viz. to the curves of Easterly disturbance of Declination
and to the curves of disturbances decreasing the Horizontal Force, we shall find in them
definitiveness of character and some remarkable points of correspondence and difference
that would seem to be deserving of attention. We first note that, for the synodic period
of Venus, the curves of Declination and Horizontal Force have their principal inflections
alike, and that this likeness attaches, though in a less degree, to the curves for the
synodic periods of Mercury and Jupiter, in common with those for Venus; secondly,
that whilst the curves of Venus are strikingly bolder and more definite for the synodic
period than for the sidereal period, there is no very marked difference in the case of
the curves of Mercury. Again, we note the close resemblance in the two curves of the
Earth and in the two of Mercury for its sidereal period — in the latter case of so precise
a kind that, keeping in mind that the curves are derived from independent observations
with instruments of different construction, it is difficult to suppose that they do not
indicate a real periodicity in nature.
29. It is not claimed for these investigations that they account for any substantial
part of the so-called decennial variation of magnetic disturbance, but only that there
may be, and probably are, subordinate planetary variations of the kind described, which
are superimposed upon the more strongly marked decennial variation, and that if they
are, they are included with the variations that have been deduced from the observations.
It must be allowed, too, that, until the character of the decennial variation be brought
out more fully than as yet (by a great extension of the period of observation), doubt
must remain as to whether these apparent variations which follow the periods of the
planets may not be due, wholly or in part, to the imperfect elimination of the decennial
variation. The irregularities observed in the duration of the sun-spot period, with
general correspondence in magnetic disturbance, as far as observation permits the
comparison, would seem to indicate that the decennial period itself must be regarded
as subordinate to some more ' extended period, in the recurrence of which the irregu-
larities alluded to would be repeated in the same order. It is for this reason that we
have not attempted, from the twenty-six years of observations available, to determine
the duration and character of the decennial variation, considering that such an under-
taking would, with present data, be to a great extent labour in vain.
* Proceedings of the Eoyal Society, vol. xx. page 210.
3 Gr
MDCCCLXXV.
394 MESSRS. C. AND F. CHAMBERS ON THE MATHEMATICAL EXPRESSION
It is also because the decennial period would greatly affect the apparent variation of
magnetic disturbance following the sidereal period of Jupiter, that no attempt has been
made to apply these observations, extending over less than three such periods, to the
determination of the character of that variation.
Appendix.
Demonstrations . First set.
To find the sum of each of the following series : —
(1) sin 00 + sin 0 + sin 20 -j- + sin(w — 1)0.
(2) cos 00 +cos0 + cos20 + + cos(w— 1)0.
(3) 0 sin 00 -(-sin 0+2 sin 20 + + (w— 1) sin (n— 1) 0.
(4) 0 cosO0 + cos0 + 2 cos 20 + +(w— 1) cos (n— 1) 0.
(5) 0 sin 00 + sin 0+22 sin 20+ + (w— l)2 sin (n— 1) 0.
(6) 0 cos O0+cos0 + 22 cos 20+ +(%— l)2cos (n— 1)0.
If X =1 — 2#cos0+#a
g = -2cos<3+2<r,
^-+2
dx2 ‘ ’ ...
^-=4 (x — cos 0)2.
(a)
(b)
(c)
(d)
If Y =a’sin(a+0)— #”sin(a+%0)++l+1 sin{a + (w— 1)0}— #2sin«, . .
dY
faT = sin (a + 0) — nxn~ 1 sin (a + w0) + (n + 1) xn sin { a + (n — 1 )0 } — 2x sin k,
(PY
d^=~n (n— 1) xn~2 sin («+w0) + (++ 1) nxn~l sin{a+(w— 1)0} — 2 sin a.
And when x=.l and a= 0, these become respectively
X =2 (1 — cos0),
§=2(1-0080),
«_+2
dx*~
^2=4(1— COS 0)2, ....
Y = sin (3 — sin n(6 + sin 02—1) 0,
(e)
(f)
(g)
(h)
(i)
0)
(k)
0)
Or OBSERVATIONS OE COMPLEX PERIODICAL PHENOMENA.
395
^ = sin0— n sin w0 + (?z+ 1) sin (n— 1) 0, .
d*Y
-j~Y = — n (n — 1 ) sin n(B + (n + 1 ) n sin ( n — 1) 0.
(m)
(n)
When x=l and ot=^ (a) to (d) have the same values as in (h) to (k) respective! y,
and (e) to (g) become as follows : —
Y =cos0 — cosw0 + cos(w— 1)0— 1, (o)
cos 0 — n cos %0+(?i+l) cos (n — 1) 0 — 2, (p)
cPY
-^=—n{n—V) cosw0+(w+l)wcos(w— 1)0 — 2 (q)
Let S=,£sin(a+0)+,!r2sin(a+20)+#3sin(a+30) + . . . . xn~l sin{a+(w — 1)0} . (1)
sin («+w0+0)+sin (a+w0— 0)= 2 sin (a+%0) cos 0,
2#,l+1sin (a-| -%0) cos0=^m+I sin{(a+%0)+0} +#"+1 sin{ (a + w0)— 0}.
Hence, by giving n the values 1, 2, 3 .... . (n— 1),
2a’2 sin { a + 0 } cos 0 = #2 sin { a + 20 } + x1 sin a,
2$3sin{a+20}cos 0— x3 sin{a + 30} -\-xz sin{a+0},
2xi sin{a-f- 30}cos 0=#4 sin{a+40} -\-x4 sin{a+20},
&c. = &c. &c.,
2xn sin{ a + (n— 1) 0 }cos 0 =xn sin{ a n(3 [ +#re sin{ a +(%— 2) 0 j- .
Now adding
2#S cos0 = S — x sin (a +0) + #™sin{ a + w0 } +#2S — #w+1 sin { a + (w — 1 ) 0 } -j- #2sin«, (2)
S ( 1 — 2# cos 0 + .ir2) = ,2? sin (a + 0 ) — sin (a + w0) + #n+ 1 sin { a + (« — 1)0}— sin a, (3)
which, when x=l and a=0, becomes
2S(1— cos0)=sin0— sinM0+sin(^— 1)0, (3 a)
which, when w0 = 2<?7t,
=0, whether or not 0 is 0 or a multiple of 2tt ~)
)■ (ob)
= sin 0-f sin 20 + sin 30+ + sin(w— 1)0. J
If in (3) x be made=l and «=-,
2S(1 — cos0)=cos 0— cos%0+cos(w— 1) 0 — 1, (3c)
which, when W0 = 2c7r,
== — 2 (1 — cos 0) (3f7)
S= — l=cos 04-cos 20+cos 30+ +cos ( n — 1)0,
3 g 2
396 MESSES. C. AND E. CHAMBEES ON THE MATHEMATICAL EXPEESSION
to which adding cos 0/3, we have
0=cos 0+cos/3+cos 2/3+cos 3/3+ +cos(w— 1) (3,1
according as /3 is not or is 0 or a multiple of lir ;
or (say) SX=Y,
S=YX"1,
dS
^-=sin (a + /3)+2# sin (a + 2/3) + 3#2 sin (a + 3/3) +
+ (w— l)#"_2sin{a+(w,— l)/3f
-fx--ygx-, j
which, when x—\ and a= 0 (see equations (h), (i), (1), and (m),
=2-1 (1 — cos /3)_1{sin /3— wsin w/3+(w+l) sin (n— l)/3[
— 2-2(l — cos /3)-2 [2(1 — cos /3) -{ sin /3— sin w/3+sin(w— l)/3 }]
=2-1 (1 — cos /3)_1 [— (n— 1) sin w/3+w sin (n— 1)/3],
which, when n(3=2cT, c being an integer,
n sin B n B
=~~~r^=~2cot2 I
4 sin2 ^
= sin /3+2 sin 2/3 + 3 sin 3/3+ +(n— 1) sin (n— 1) (3 ;
and as 0 sin 0/3 = 0,
% m sinm/3= —xcot^, when /3 is not 0 or a multiple of 2x. . .
But when /3 is 0 or a multiple of 27t, each term of the series is 0, and
% msinm/3=0
Now let x=l and a=~, and (6) becomes
^=2_1(1 cos /3)_1-{ — cos /3— n cosm/3+(m + 1) cos (n— 1)(3}
— 2~2(1 — cos|0)_2[2(l — cos0)| — cos j3— cos w$ + cos(w— l)0 + l}]j
(4)
(5)
(6)
(7)
(8)
(9)
(9«)
m
(10)
= 2 ‘(1 — cos/3) 1 [— (n— 1) cosw0+w cos(n— 1)jQ — 1],
which, when w|3=2c7r,
= 2_1 (1 — cos0) 1 [-(n—V)-\-n cos0— 1]=— -
= cos /3+2 cos 2/3 + 3 cos 3/3+ +(w— 1) cos (n— 1)/3 ;
(11)
OF OBSERVATIONS OF COMPLEX PERIODICAL PHENOMENA.
397
and as 0 cos 0/3=0,
?»=> i — 1 yi
2 tocosto3= — x, (11a)
m= 0 "
except when 3 is 0 or a multiple of 27r, in which case
X mcosra3={0+l+2+3 + +(w— 1)}=— —
m = 0 w
Again, multiplying equation (6) by x ,
sin (a+3) + 2.r2 sin (a+23) + 3^3 sin (a+33) +
+ (w— 1) #"-1 sin{a+(w + l)3}
=^X-1-Yfx-2},
(IB)
(12)
d_( dS
dx
x^\ = sin (a + 3) + 4# sin (a + 23) + 9#2 sin (a + 33) +
+ (w— l)2af"2sin{a+(?i— 1)3}
■-Yfxi+*{
=^ix-
dY rfX 2 dY dX
d*2 X “d* ' d* X —dx ' dx A -
■Yfx-H2Yfx-
(13)
=X-'{S+^}-X1(Y + ^g)f+,Y«} + 2X-.y,§a, . . (14)
which, when x=\ and a = 0,
= 2-1 (1 — cos 3)-1 [sin 3— w2 sin w3 + (^+l)2 sin (n— 1)3]
— 2_2(1— cos3)_2[{3 sin3— (2w+l)sin w3 + (2w + 3)sin (n— 1) (3\2 (1 — cos3)
+ 2{sin3 — sinw3 + sin n— 1)3}]
+ 2_3(1 — cos3)-3[8(l — cos3)2{sin3 — sinw3 + sin(w -1)3}]} • • • (15)
which, when n(3=2c7r,
= — 2_1 (1 — cos 3)"1 [{w2+2w}sin 3]
— 2-2 (1 — cos 3)"2 [2(1 — cos 3){ — 2w sin 3 }]
— 2_i n —
(1 — cos 3)-1 %2 sin 3 =
• 3 3
2sm2COS2 , n2 B
^ = — 2" COt 2
4 sin2? ^
=sin 3+4 sin 23+9 sin 33+ + (n— l)2 sin (n— 1) 3 ; • .
and as 02sin 03=0,
X m2 sin m(5= — o cot 5, when 3 is not 0 or a multiple of 27t.
m = n " & . ±
(16)
(17)
(17a)
398
MESSRS. C. AND E. CHAMBERS ON THE MATHEMATICAL EXPRESSION
But when (3 is 0 or a multiple of 27t, each term of the series is 0, and
% m2sinm/3=0 (176)
771 = 0
Now let #=1 and a=^, and (14) becomes
dxif^) (l — cos/3)-1 [cos/3— %2cosw/3+(w+l)2 cos (n— 1) /3— 4]
— 2-2 (1 —cos /3)-2 [{ 3 cos (3— (2w+l) cos w/3+(2w+ 3) cos [n— 1) /3— 5 }■
X 2 (1— cos /3)+2{cos (3 — cos w/3+cos (n— 1) (3—1 }]
+2-3(l — cos/3)-3[8 (1 — cos/3)2{cos/3— cosw/3+cos(w— 1)/3 — 1}-], . (18)
which, when n(3=2c7r,
= 2-1 (1 — cos /3)-1 [(w2+2w+2) cos/3— n2— 4]
— 2-1 (1— cos /3)-1 [(2 w+6) cos /3— (2w+6)— 2]
+ 2-1(l — cos/3)-1 [4cos/3— 4] (19)
=2-1 (l — cos/3)-1 [(w2+2w+2— 2w— 6 + 4) cos/3— w2— 4+2w+6+2 — 4], (20)
=2-1 (1 — cos /3)-1 [— n2 (1 — cos/3)+2w]
ri2 n l
"2+2
= cos /3 + 4 cos 2/3 + 9 cos 3/3+ +(w— l)2cos(w— 1)/3; j
and as 02 cos 0/3 = 0,
“-™-1 n2 n 1
S m2cosm/3=-- 5-+7} 3,
m=o * sin2?
(21)
. (21a)
except when (3 is 0 or a multiple of 2i r, in which case
2=”~ m2 cos m0 = 02 + 12 + 22 + 32 + +(w-l)2~-|+| (216)
Collecting together equations (36), (3d), (9a), (96), (11a), (116), (17a), (176), (21a),
and (216), we have, according as /3 is not or is 0 or a multiple of 2t,
2 sinm/3=0,
771 = 0
771 = 77 — 1
2 cos m/3=0,
or =0,
1 a n B
m sin m/3 =— -cot g,
or =0,
£ mcosm0= — =
OP OBSERVATIONS OP COMPLEX PERIODICAL PHENOMENA.
399
X m2smm$= — \ cotf, or=0,
m=0 Z "
ot=»-] re2 re 1 re3 re2 re
2 m2 cos mb= — w + o a. or=¥— 2_+6-
m=0 sin2 £
Demonstrations.. Second set.
To find when (sijitf)5, ( sa + tb ), (sijitf)tf, and (sb+ta) are multiples of r if «=13#
b=8, r=96, and s and t are positive and integral.
(1) 8(s+ £) = 96c, c being a positive integer, when
s+£=12<?, I
s=12c±:t.
(2) (13s+8tf)=96c, when
13s=8(12c±f)
=8{13c— (c+£)},
s= 8c— (<?+ 1\ which can only be integral when (c+ 1) is a multiple of 1 3.
(3) 13(s+£)=96c
= 8(13 — l)c,
s^t=8{l-^)c,
s= 8 (c— ~^+t, which can only be integral when c is a multiple of 13.
(4) (8s+13£)=96c, when
8s=96c±13£,
s=12c+J^£, which can only be integral when t is a multiple of 8.
400 MESSES. C. AND F. CHAMBERS ON THE MATHEMATICAL EXPRESSION
Specimen Calculation of Bessel’s Coefficients, for variation of Aggregate
Successive "1
months. J
0
1
3
4
5
6
7
8
9
10
11
12
Twenty-sixths
of the sidereal
0
9
18
1
10
19
2
11
20
3
12
21
4
period of Mer-
cury
Cosine
+ 1000
-•567
-■355
+ ■971
-•749
-•120
+ •885
-•885
+•120
+ 749
-•971
+•355
+ ■568
Sine
0000
+■823
-•935
+•239
+•663
-•993
+•465
+■465
-•993
+•663
+ •239
-•935
+•823
Monthly Aggregates
|
1st 9 period*
53-343
81-730
52675
31-843
41-527
69-892
153-729
108-458
67142
210-564
52-444
82-755
84-714
2nd
16-206
16-850
18-278
32 054
19-469
53-973
92-298
20-561
28-997
28-544
34-003
15 067
18-623
3rd
35-098
21-894
90-523
49-580
18-995
72240
53-346
129-985
24127
74-522
126-439
14-392
18-704
4th „
94-948
19-424
17374
38-480
50-902
64-843
56-504
43-466
10-708
22-208
31-258
10-283
22-554
5th „
14-734
14-338
8054
14-978
10 926
13-924
1-665
12-098
5 052
9554
21-379
15-433
0-000
6th
49-958
39181
64-664
111087
18-894
25-834
77-967
30-488
43-782
44-923
27-337
15 034
57-819
7th „
103-117
37-567
17-695
38-733
140-932
221-409
64-623
63-580
11-436
38-406
60-495
56-850-
37678
8th „
27-592
21-266
51-978
81-257
55-343
163-152
13-866
55-289
62-003
39-771
60-408
56-068
56448
9th
57-361
40140
39-891
20-698
5 020
20-390
52-565
27-247
9-906
39-858
27-21 1
25-372
53231
10th „
12-088
31-926
32-221
8047
30-424
15-881
4-994
2-875
14 832
11-655
16-841
25-108
21-224
1 1th
7-087
6-428
55-697
43-308
60-588
75-824
67852
52-912
17095
30-644
116-304
50-840
17692
Sums
471532
330-744
449-050
470065
453020
797-362
639-409
546-959
295 080
550-649
574 119
367-202
388-687
Means
42-867
30-068
40-823
42'733
41-184
72-487
58128
49-724
26-825
50059
52-193
33-382
35-335
Variations
1 -0-313
-13 112
-2-357
-0-447
-1-996
+29307
+ 14-948
+6-544
- 16-355
+6-879
+9-013
-9-798
-7-845
* Commencing with March 1847.
OF OBSERVATIONS OF COMPLEX PERIODICAL PHENOMENA.
401
Easterly Disturbance of Declination in the Sidereal Period of Mercury.
13
14
15
16
17
18
19
20
21
22
23
24
25
/ Successive
t Months.
13
22
5
14
23
6
15
24
7
16
25
8
17
f Twenty-sixths
I of the sidereal
period of Mer-
l cury.
-1-000
+•568
+•355
-•971
+ •749
+ 120
-•885
+•885
-•120
-•749
+•971
-•355
-•568
Cosine.
0000
-•823
+•935
-•239
-•663
+•993
— -465
-•465
+•993
-•663
-•239
+•935
-•823
Sine.
of Disturbance.
46-396
25086
87-569
87-888
44-773
15-669
81-189
233-638
27-256
66-268
94-313
55-685
30-832
1 1st 9 period*.
16-777
42-915
21-585
15-093
8-540
5-443
82-517
74-813
21-741
13-837
20075
20-990
22-818
2nd „
34-921
32-894
16-508
28-006
36-853
32-650
24-427
42-940
25-270
67-160
39-312
27-949
36-882
3rd
44-416
18769
22-813
13100
7-185
36-425
19-414
8-449
14-416
13-078
10-702
16-942
14-624
4 th
6-893
8-118
6-752
20-732
8-924
10-489
13311
33118
12-057
25-447
20-650
40-744
96-264
5th
69-377
48-189
97-001
52-618
38-394
57-820
114-162
169-905
198-777
15-435
49-717
23-984
70-715
6th
33-454
19-002
41033
39174
32-787
47383
40-953
35-443
69-321
30153
26-618
179-782
84-432
7th
19-299
27-583
32-972
27-227
22-576
12-177
0-000
17-328
32-728
26-264
27-672
6-541
80-336
8th
70-072
30130
41-462
50-878
13-940
30095
81-696
16-635
3045
17-569
13-226
3059
27-330
9th
40-817
27-571
0000
6-695
4-370
16-389
110-398
5-117
18-591
13-281
38-992
55-874
85-009
10th „
59-819
64-717
57199
70171
101-645
77-381
64-724
33-539
62-790
79164
153136
51-690
45-709
11th .,
442-241
344-974
424-894
411-582
319-987
341-921
632-791
670-925
485-992
367-656
494-413
483-240
594-951
Sums.
40-204
31-361
38-627
37-417
29-090
31-084
57-526
60-993
44-181
33-423
44-947
43-931
54-086
Means.
-2-976
— 11-819 -4-553
-5-763
-14-090
-12096
+14-346
+ 17-813
+ 1-001
-9-757
1
+ 1-767
+0-751
+ 10-906
Variations.
* Commencing with March 1847.
MDCCCLXXY
d H
Specimen Calculation (continued).
402
OBSERVATIONS OE COMPLEX PERIODICAL PHENOMENA.
mill!
++I M + l
IIISIll
+ 1 +1* + + +
-10-667
+ 0-993
-10-592
+7 + 1 + U
lllpl
+7-1 l +++
PI
+ + +
!!|!flf
i i7+7 i 7-
PI
+ + +
c?
l!i!«!
1 ++ 1 ++4-
<*
mm
1 1 M i + 1
!!!
1115111
(NQ^OCCOK
1 1 + 1 1 1 +
ssisSIS
(No^oeiOH
1 + 1 1 +++
ill
cbo*
1 + 1
PliPI
It+M + I II
mm .
i + 1 1 1 1 + ii
1!! i
If Hill p
If nil! 1 1
i + + + +
ill II
1 + +
+(0 to 6)
+(13 to 7)
-(14 to 19) ...
-(25 to 20) ...
Sums
Factors
Products
Sum of Pro- 1
ducts J
Ditto -j- 13
+(0 to 6)
-(13 to 7)
+ (14 to 19) ...
-(25 to 20) ...
Sums
Factors
Products
Sum of Pro- 1
ducts J
Ditto 4- 13
ll
$1}
j|°-g7-
ill"!
mm
+ i 7 +++ +
filial#
m
+++
IPIII
+1 1 ++ 1 1
13s
S®S
Him!
1 1 + 1 1 1 +
ISlsISI
i+7 1 7 + i
II!
1 + 1
p7
lil-rsls
1 1 ++ 1 + 1
pT
3Sislll
m+tn
Ph"
II
1 4
alssRiS
<NG5+~(N© +
III1SI1
1 1 l + l 1 +
m
+++-
SiSlslS .
2 N ^ 2 m c ^ p7
imp! ^
i M +7 1 + ii
!!! i
I! Mill 1 1
1 + +++ 1 1
11: III II
1 1 "l+l + +
ill!
+++ + +
Symbol of
operation.
III
+(0 to 6)
+ (13 to 7)
+(14 to 19) ...
+ (25 to 20) ..
Sums
Factors
Products
Sum of Pro-1
ducts J
Ditto+13
il
ify
Pi
!
I
i
l
i
.3
1
§
I
J
l
I
I
*
[ 403 ]
XV. Reduction of Anemograms taken at the Armagh Observatory in the Years
1857-63. By T. R. Robinson, D.D., F.R.S., F.A.S., &c.
Received June 11, 1875, — Read June 17, 1875.
In the beginning of the year 1845 I erected a self-recording anemometer at the Armagh
Observatory, and have a series of its records np to the present time, unbroken except by
accidents to the apparatus or occasional illness of the observers. I, however, soon
found it was impossible for me and my single assistant to reduce continuously the mass
of materials which was accumulating, without neglecting the primary objects of the
establishment ; and I was obliged to content myself with preserving them, in hope that
they might be available to future inquirers. It was thought, however, by some distin-
guished members of the Royal Society that it was desirable to ascertain how far such
observations are able to develop any definite laws amid the seeming lawlessness of the
wind ; and a grant was made to me from the Government Grant sufficient to discuss the
anemograms for the seven years from 1857 to 1863. The work has been long delayed
by the death of one of the computers, the migration of another to India, and my own
temporary blindness.
The anemograph is that described by me in the 4 Transactions of the Royal Irish
Academy,’ vol. xxii. It differs in nothing essential from that employed by the Meteo-
rological Committee of the Royal Society : the recording-apparatus is different, and the
direction is observed by a vane whose excursions are controlled by a peculiar contrivance
instead of by a windmill. The space-records were read to 0-25 of a mile (statute), and
the directions to 0o-5. The S. and W. components of the hourly velocity were computed
for each to two places of decimals.
Wind is caused by a difference of pressure in the air over adjacent portions of the
earth’s surface ; but of the agencies which produce this difference we as yet are imper-
fectly informed. Heat is obviously a most important one. We see that the action of
the sun must produce a current from polar towards equatorial regions, and that when
the geographical conditions of districts not too far asunder are such as to make their
temperatures unequal, air-currents between them will result. The changes of solar
action at a given place depending on the hour of the day am) the day of the year, ought
to produce definite periodical modifications of the wind ; and the currents due to the
varying tension of aqueous vapour ought to be similarly periodical. Were these the
only causes of the wind, there seems no reason why its force and direction at a given
time and place might not be predicted as certainly as the sun’s altitude. But there are
evidently disturbing agencies of great power which entirely mask the regular course of
3 h 2
404
DE. T. E. EOBINSON ON THE SEDUCTION OE ANEMOGEAMS.
the phenomena, and of whose nature we can only form vague conjectures. The accu-
mulation of ice in the polar regions forming icebergs may be such an influence ; and
what we have learned recently of the action of the larger planets on the solar spots,
and of the connexion of the development of those spots with the magnetic storms and
auroral discharges of our own planet, may suggest the possibility of extra-terrestrial
forces playing some part in the question before us. But without following in the track
of imagination, this is certain, that however complicated and irregular a phenomenon
may be, if we have a sufficient number of observations, it is possible to determine the
values and periods of those parts of it which are subject to definite laws. Where any
of these periods agree with those of agents whose influence is certain, they may be
referred to them with certainty, and their effect eliminated, making it much easier to
deal with the residual phenomena.
In the present instance the want of self-recording instruments for pressure, tempera-
ture, and vapour-tension compelled me to consider the wind solely in reference to time,
as depending on the hour of the day and on the month ; and even with this simplifica-
tion it is not easy to come to precise results. Were we to seek a velocity and direction
which might be considered normal for each hour of the year, such is the irregularity of
the air-currents, that I think it could scarcely be obtained in less than 100 years. Even
if we confine ourselves to the west and south components, and take for successive hours
the mean of the seven years concerned, it differs so widely from the means of the pre-
ceding and following hours, that any existence of law might seem impossible. But if
the hour-means be taken for 20 or 30 successive days, their means present a very
different aspect. I have taken them for months.
Before dealing with these components, I think it may be instructive to present a
Table giving a synoptic view of the winds, which may show their general character at
Armagh during the seven years concerned. It gives for each month and for each
octant of the horizon (S. to S.W., S.W. to W., &c.) the mean hourly velocity, the mean
direction, and the approximate number of hours during which this wind has blown.
At the end of each month is given the maximum hourly velocity for each year, the
number of hours when the velocity exceeded 25 miles, and the number of hours during
which the anemograph has recorded 0. This does not imply that during this time there
was no wind, but that there was not enough to move the instrument. This requires a
velocity =lm- 74.
The direction-vane is much more sensitive (very much more so than the windmill-
apparatus now used to record the direction), and therefore the records of direction are
more numerous than those of velocity.
DE. T. E. EOBINSON ON THE SEDUCTION OE ANEMOGEAMS.
405
Table I. — January.
1
1857.
1858.
1859.
1 I860.
1861.
1862.
1863.
! s-
Vel
1 6'-46
16-94
18'-17
13-89
l6'-46
1 2*97
17'*67
Mean 1 6'-07
t0
Dir
28°*7
24°
28°
21°
22°
24°
27°
Mean 25°
s.w.
Hours ...
181
211
199
188
249
216
275
Sum 1519
S.W.
Vel
12-7
17-09
14'-66
I 9'-97
1 1-43
14'-35
l6'-20
Mean 1 3'*78
to
Dir
66°-67
58°
60°
63°
60°
63°
60°
Mean 6l°
w.
Hours...
193
168
412
193
88
192
211
Sum 1457
w.
Vel
12'-24
10-57
10'-28
1 0-75
5-30
8'-89
17*49
Mean 10'*79
to
Dir
103°
112°
103°
107°
120°
114°
107°
Mean 109°
N.W.
Hours...
130
53
65
40
27
88
80
Sum 483
N.W.
Vel
10'-65
5-76
5*32
5'-85
6'-00 i
4'-70
5'-73
Mean 6'-29
to
Dir
152°
150°
156°
146°
146°
156°
163°
Mean 153°
N.
Hours...
92
46
26
40
3
57
38
Sum 302
N.
Vel
o-15
0
5'-43
7'*60
6'-63
6-50
8'-56
Mean 5'-70
to
Dir
183°
223°
202°
208°
212°
206°
188°
Mean 203°
N.E.
Hours ...
106
1
8
62
"76
2
45
Sum 300
N.E.
Vel
6'-39
0
1-70
6'-90
14'*89
23'*22
1 1*23
Mean 9'-19
to
Dir
259°
0
242°
242°
247°
265°
247°
Mean 250°
E.
Hours...
31
0
18
40
54
9
30
Sum 200
E.
Vel
2'- 10
13-11
5'*67
1 1'*02
4'-70
17-21
7'-95
Mean 8'-82
to
Dir
294°
©
291°
293°
300°
287°
©
Mean 295°
S.E.
Hours ...
5
37
4
88
77
43
21
Sum 275
S.E.
Vel
15'-04
18'*59
13-67
15-97
13'-62
20'-60
10-15
Mean 15-38
to
Dir
346°
335°
344°
338°
337°
339°
322°
Mean 337°
S. | Hours... |
12
228
12
93
170
135
45
Sum 695
Maximum
44'-2
46’
68'
6(f
37'
48'
4T
Hours >25'
23
92-3
98
68
40
95
146
Sum 562
Hours of 0
0
3
7
21
12
6
15
Sum 64
Table I. — February.
1 s.
Vel
l7'-48
l6'-36
16-19
16-01
4-63
12-30
15-19
Mean 13'-55
to
Dir
19°-0
15°
21°
21°
23°
26°
28°
Mean 22°
I S.W.
Hours ...
177
56
184
no
118
155
183
Suin 1003
s.w.
Vel
11-18
1 1*52
14'-53
13-32
1 2'- 1 7
ll'*85
14'-24
Mean 13-22
to
Dir
57°
60°
66°
60°
65°
66°
61°
Mean 62°
j w.
Hours ...
149
40
159
167
110
112
193
Sum 935
I w.
Vel
7'-59
5'-8 1
8'-60
9'-62
9'-69
_ 7'- 00
1 2-01
Mean 9'-24
to
Dir
100°
118°
95°
108°
112°
93°
99°
Mean 103°
N.W.
Hours ...
61
26
140
156
48
1
72
Sum 504
N.W.
Vel ~
2*31
4'-78
0
6'-99
7'-30
3'- 13
2" 50
Mean 6'-26
to
Dir
149°
162°
0
157°
175°
76°
172°
Mean 165°
N.
Hours ...
8
18
0
129
20
8
11
Sum 194
N.
Vel
5'"50
6-49
2'-50
5'*75
13'-28
7'-48
17-05
Mean 8'-38
to
Dir
215°
201°
215°
188°
200°
201°
205°
Mean 203°
N.E.
Hours ...
11
48
6
77
50
61
19
Sum 272
N.E.
Vel
5'-83
7'-4l
2! ’27
4'-65
8'- 73
8'-63
2-35
Mean 6'-96
to
Dir
247°
248°
233°
237°
233°
265°
247°
Mean 244°
E.
Hours ...
63
1 22
15
51
33
97
4
Sum 385
E.
Vel ~
5'-20
15' -57
6-32
i'-~oo
14*49
10-51
1 6'- 7 8
M?an 13*61
to
Dir
302°
292°
301°
295°
294°
292°
29-°
Mean 295°
S.E.
Hours...
5
45
25
4
68
102
14
Sum 263
S.E.
Vel 7
14'-60
1 7'-66
19'-23
l'-OO
7'-l 7
18'-23
12'-96
Mean 14'-87
to
Dir
348°
338°
342°
337°
313°
358°
340°
Mean 339°
S.
Hours ...
98
111
43
2
104
36
71
Sum 465
Maximum
4 4'- 5
42”
40'
45'
4&~
56'
Hours >25'
43
91
S3
25
36
54
85
Sum 397
Hours of 0
3
1
6
3
5
4
4
Sum 26
1
406
DR. T. R. ROBINSON ON THE REDUCTION OF ANEMOGRAMS.
Table I. — March.
1857.
1858.
1859.
1860.
1861.
1862.
1863.
s.
Vel
l6'*50
11*15
20*35
13*57
17*70
1 1'*85
15*40
Mean 15*19
to
Dir
20°
27°
32°
27 0
27°
30°
21°
Mean 26°
S.W.
Hours...
107
115
98
131
276
92
209
Sum 1028
s.w.
Vel
14*90
9'*3l
15*70
16'*27
14'*25
13*18
13*00
Mean 13*80
to
Dir
73°
68°
62°
67°
67°
69°
65°
Mean 67°
w.
Hours ...
173
199
368
193
292 ;
61
209
Sum 1495
w.
Vel
9'* 7 7
9*59
10'*90
10*67
13*13
1 O'* 1 6
14-97
Mean 1 1-31
to
Dir
117°
110°
117°
113°
107°
114°
107"
Mean 112°
N.W.
Hours...
62
222
184
__279
89
19
103
Sum 958
N.W.
Vel
6*45
7'*48
9*30
9*29
8'*38
5'*86
6'*34
Mean 7 *59
to
Dir
172°
161°
147°
151°
149°
153°
156°
Mean 156°
N.
Hours ...
69
65
67
70
8
42
38
Sum 359
N.
Vel
8'*58
13'*86
12*50
7'* 7 8
1*50
8'*g6
6-19
Mean 8'*48
to
Dir
241°
209°
197°
202°
195°
206°
200°
Mean 2073
N.E.
Hours ...
80
90
14
18
2
96
37
Sum 337
N.E.
Vel
6'-55
1 9*75
1 1*00
5*00
8'*68
1 1*30
6*61
Mean 9 *84
to
Dir
264°
233°
255°
245°
249°
236°
243°
Mean 246°
E.
Hours...
98
28
7
23
19
248
18
Sum 441
E.
Vel
1 1*58
4-80
24*50
7*50
20*50
1 1 '*31
12'*39
Mean 13*23
to
Dir
274°
279°
282°
272°
285°
304°
289°
Mean 284°
S.E.
Hours...
64
5
6
4
6
74
36
Sum 195
S.E.
Vel
13*71
12*00
Q'*00
18'*38
13'*88
11-53
15*94
Mean 12'*21
to
Dir
350°
352°
341°
346°
334°
351°
Mean 346°
S.
Hours ...
91
20
26
50
112
97
Sum 396
Maximum .........
49'-5
50’
58'
54'
43'*2
57’
40'
Hours >25'
45
39
49
35
18
9
55
Sum 250
Hours of 0
3
5
1
4
12
4
1
Sum 30
Table I. — April.
S.
Vel
12'*38
9'*88
14*1 1
11 '*23
8'*67
13*37
14'*90
Mean 12'*08
to
Dir
36°
42°
24°
19°
23°
25°
28°
Mean 28°
S.W.
Hours...
67
125
116
92
61
181
203
Sum 845
S.W.
Vel
9*86
7-50
11*72
1 4-06
5'*49
12'*45
12*13
Mean 10*39
to
Dir
. 740
61°
62°
64°
61°
63°
66°
Mean 64°
W.
Hours...
65
76
150
50
33
131
183
Sum 688
W.
~Vel
8'*73
7'*38
7'*29
8'*86
5'*33
9*38
10*70
Mean 8'*15
to
Dir
114°
117°
116°
103°
115°
110°
112°
Mean 112°
N.W.
Hours ...
115
65
54
111
126
42
98
Sum 6l 1
N.W.
Vel
6'*79
6*00
6'*20
8'*64
5'*27
6*53
9'*25
Mean 6 *93
to
Dir
154°
164°
157°
163°
155°
136°
157°
Mean 155°
N.
Hours...
60
73
93
119
78
69
55
Sum 547
N.
Vel
5'*29
5*92
6-68
13'*28
6'*30
6'*30
7*50
Mean 7'*18
to
Dir
201°
197°
206°
200°
202°
199°
184°
Mean 198°
N.E.
Hours...
49
59
89
46
175
83
2
Sum 503
N.E.
Vel
8'*20
13*98
15'*28
6-47
6'*79
6-36
o'-oo
Mean 8 * 13
to
Dir
251°
255°
250°
247°
248°
241°
Mean 213°
E.
Hours...
126
84
153
57
107
22
Sum 549
E.
Vel
12'*47
16-78
16*04
8'*73
9*52
3*55
8*64
Mean 10'*82
to
Dir
286°
288°
284°
290°
284°
292°
302°
Mean 289°*5
S.E.
Hours ...
113
153
49
100
98
45
28
Sum 586
S.E.
Vel
14' *73
16*43
14-60
10*40
13'*58
13*01
13*05
Mean 13*55
to
Dir
335°
335°
346°
338°
333°
339°
343°
Mean 338°
S.
Hours...
102
81
15
75
40
88
78
Sum 479
Maximum
45'*5
57'
46'
34'
23*5
36'
58'
Hours > 25'
17
27
43
5
0
24
40
Sum 156
Hours of 0
26
108
10
24
5
21
6
Sum 200
DE. T. E. EOBINSON ON THE SEDUCTION OE ANEMOGEAMS.
407
Table I. — May.
1857.
1858.
1859.
1860.
1861.
1862.
1863.
s.
Vel
15-31
11-09
6-55
8'-21
7'-07
9'-60
12'-39
Mean 9 ‘95
to
Dir
27°
27°
21°
17°
27°
24°
27°
Mean 24°
S.W.
Hours ...
134
165
86
204
120
158
149
Sum 1016
S.W.
Vel
6'-87
10-18
4'-32
5'-98
5'-55
9'-84
8'-67
Mean 7'-34
to
Dir
70°
71°
62°
69°
65°
64°
65°
Mean 67°
W.
Hours...
54
138
50
96
226
_174_
218
Sum 956
W.
Vel
8'*I 9
4'-72
2'-89
7'*24
4-03
3-55
6-20
Mean 5'-23
to
Dir
113°
1110
118°
108°
113°
121°
105°
Mean 113°
N.W.
Hours ...
21
59
18
130
159
105
120
Sum 612
| N.W.
Vel
3'-85
6-00
4-90
3-93
3-73
3-24
5'-02
Mean 4'-26
to
Dir
165°
159°
167°
156°
162°
157°
162°
Mean l6l°
N.
Hours ...
20
114
70
15
64
54
43
Sum 380
N.
Vel “
5-15
3-94
4-41
3-33
5-55
3-24
6-03
Mean 4'-52
to
Dir
211°
201°
198°
205°
197°
198°
207°
Mean 202°
N.E.
Hours ...
57
86
184
36
89
33
67
Sum 552
N.E.
Vel
7*91
4-01
6*36
8-35
5-55
4'"44
10'-34
Mean 6-71
to
Dir
254°
250°
246°
254°
247°
248°
235°
Mean 248°
E.
Hours ...
171
56
140
101
46
27
97
Sum 638
E.
Vel
8 '-75
5'-62
6'-87
8-10
4'-69
1-07
9-25
Mean 6'-32
to
Dir
290°
295°
293°
299°
300°
294°
305°
Mean 297°
S.E.
Hours ...
183
62
86
75
25
93
20
Sum 544
S.E.
Vel
13-49
10-77
11-93
9-76
11-90
10-31
14-27
Mean 11 -66
to
Dir
315°
337°
335°
337°
330°
336°
342°
Mean 332°
S.
Hours ...
97
36
106
86
14
98
18
Sum 455
Maximum
26'
38'
42'
28'
21'-2
30'
33'
Hours > 25'
4
1
7
1
0
7
8
Sum 28
Hours of 0
21 1
19
49
23
3
52
21
Sum 188
Table I. — June.
S.
Vel
8'-l 9
9*47
12-32
7'-2i
5'-88
7'-73
8'-51
Mean 8'-47
to
Dir
17°
24°
20°
26°
22°
35°
23°
Mean 24°
S.W.
Hours...
131
129
49
131
79
142
182
Sum 843
S.W.
Vel ~
5'-06
6-00
7'-67
7*82
4-14
6'-96
8'-31
Mean 6 -56
to
Dir
65°
69°
64°
61°
66°
65°
65°
Mean 65°
W.
Hours ...
79
190
92
165
56
193
235
Sum 1010
w.
Vel
5'-87
4'-23
4'-75
5-07
~T-iT~
5'-76
4'-54
Mean 5 -05
to
Dir
110°
107°
111°
115°
106°
111°
112°
Mean 110°
N.W.
Hours...
31
71
135
97
93
243
71
Sum 741
N.W.
Vel
3-76
5-02
3-55
3-47
3-94
11-43
4-91
Mean 5'-75
to
Dir
159°
155°
162°
154°
161°
152°
161°
Mean 158°
N.
Hours ...
58
24
70
88
115
66
62
Sum 483
N.
Vel
4'-76
2'-86
5'-72
5-15
4'-60
4-00
3'-48
Mean 4'-29
to
Dir
199°
198°
206°
201°
193°
190°
194°
Mean 197°
N.E.
Hours...
65
66
136
33
75
4
88
Sum 467
N.E.
Vel
7*94
4'-] 8
9-05
8'-12
9'-36
13-79
4'-24
Mean 6 -67
to
Dir
251°
245°
243°
249°
247°
265°
245°
Mean 249°
E.
Hours...
125
27
121
56
103
19
25
Sum 476
E.
Vel
5-36
8'-80
5-43
8'-03
6-05
13-52
6-61
Mean 7’"58
to
Dir
291°
300°
296°
287°
297°
297°
303°
Mean 296°
S.E.
Hours...
137
35
30
60
37
23
13
Sum 335
S.E.
Vel
9'-65
12-70
10-74
10-06
8'-57
9'-80
11-15
Mean 10'-28
to
Dir
315°
335°
335°
333°
339°
339°
346°
Mean 335°
S.
Hours...
88
173
82
85
129
30
33
Sum 620
Maximum
25'
32'
37'
29'
22'
48'
38'
Hours > 25'
2
10
4
2
0
18
8
Sum 44
Hours of 0
24
10
15
55
36
10
50
Sum 200
408
DE. T. E. EOBINSON ON THE SEDUCTION OF ANEMOGEAMS.
Table I. — July.
1857.
1858.
1859.
1860.
1861.
1862.
1863.
s.
Vel
8*67
6-56
7*79
4'-89
8'-62
10-53
6-00
Mean 7'-58
to
Dir
33°
24°
27°
29°
31°
27°
19°
Mean 27°
S.W.
Hours...
162
119
135
55
109
122
39
Sum 741
s.w.
Vel
7*83
6-48
6*94
4-59
6'-92
8'-31
5*19
Mean 6'-6l
to
Dir
67°
73°
64°
66°
65°
64°
68°
Mean 67°
w.
Hours...
294
191
218
110
213
254
137
Sum 1397
w.
Vel
4'-80
5-05
4'-18
1 3-80
4'-29
6-53
3-34
Mean 4'*36
to
Dir
1110
113°
107°
116°
103°
106°
115°
Mean 110° |
N.W.
Hours ...
179
120
99
230
99
141
154
Sum 1022
N.W.
Vel
5-05
3-35
2-33
2-85
2'-70
2'-06
3'-51
Mean 3'-03
to
Dir
147°
153°
152°
159°
155°
158°
157°
Mean 154°
N.
Hours ...
85
139
12
140
17
49
188
Sum 630
N.
Vel
4*45
3-14
5-51
3'-07
4-52
1-50
4'-24
Mean 3 *71
to
Dir.
214°
195°
196°
200°
197°
181°
197°
Mean 197°
N.E.
Hours...
33
71
114
78
125
2
112
Sum 535
N.E.
Vel
0'
3-46
7*19
7''50
3-81
1 8'*5
6-00
Mean 6 -51 j
to
Dir
245°
251°
237°
246°
267°
232°
Mean 246° |
E.
Hours ...
28
108
12
43
2
25
Sum 218 j
E.
Vel
0'
12-30
4'-69
6'-87
8'-85
ll'-95
6-00
Mean 7 '20 j
to
Dir
305°
288°
302°
284°
293°
298°
Mean 295° j
S.E.
Hours...
23
33
32
67
21
28
Sum 204
S.E.
Vel
10*90
10-57
12-91
5-59
14-31
11-10
13-90
Mean 1 1-08
to
Dir
356°
341°
336°
332°
252°
341°
344°
Mean 343°
S.
Hours...
5
54
23
93
67
118
33
Sum 393
I Maximum
28'
22'
32'
19'
32'
41'
22'
Hours > 25'
0
2
0
8
20
0
Sum 32
Hours of 0
5
30
15
83
20
33
47
Sum 233
Table I. — August.
S.
Vel
8'-26
7*11
9'"85
8'-36
9’54
7'-l4
8'-78
Mean 8'-43
to
Dir
24°
17°
28°
30°
26°
28°
28°
Mean 26°
S.W.
Hours...
92
75
174
119
S77
202
201
Sum 1240
s.w.
Vel
4*36
6'-01
7'*77
7-29
7'-50
5'-66
8'-82
Mean 6'-7 1
to
Dir
72°
68°
61°
70°
61°
64°
60°
Mean 65°
W.
Hours ...
90
164
242
223
195
195
202
Sum 1311
w.
Vel.......
3-09
4'-68
5'-83
4-75
6-66
3'-21
6-14
Mean 4' -91
to
Dir
119°
115°
104°
108°
101°
116°
115°
Mean 1110
N.W.
Hours ...
86
159
153
198
30
93
134
Sum 853
N.W.
~vAA7^
3-52
3'-82
1 *80
3'-39
9'*94
2-00
6'-26
Mean 4'-29
to
Dir
159°
151°
155°
151°
159°
157°
1 55°
Mean 155°
N.
Hours ...
150
52
56
84
18
65
42
Sum 467 I
N.
Vel
4'-7l
2-83
4-14
5-54
7'-20
4'-22
7'-65
Mean 5'-l6
to
Dir
200°
21 1°
200°
207°
218°
203°
203°
Mean 206°
N.E.
Hours...
124
59
88
31
5
45
32
Sum 384
N.E.
Vel
6'-55
3'*7 8
6'-80
7'”42
9*77
8'-84
6-91
Mean 6'-48
to
Dir
246°
246°
237°
252°
255°
251°
280°
Mean 252°
E,
Hours...
84
14
5
7
22
13
34
Sum 179
E.
Vel
6'-79
6'-55
2'-00
6'-39
12'-14
6'-68
6-50
Mean 5'*23
to
Dir
289°
298°
301°
296°
303°
289°
306°
Mean 297°
S.E.
Hours ...
52
70
3
33
14
44
24
Sum 240
S.E.
Vel
9'-48
1 1*47
8'-80
8'-77
15-13
10-93
15'-72
Mean 11 '-37
to
Dir
337°
333°
344°
341°
340°
335°
334°
Mean 338°
S.
Hours...
46
102
15
40
82
59
36
Sum 380
Maximum
~ 26' |
28^
33'
4Q'
28'
28'
31'
Hours >
25'
1
5
1
2
9
6
14
Sum 38
| Hours of 0
20
25
28
24:
10
39 |
10
Sum 156
DE. T. E. EO BINS ON ON THE SEDUCTION OF ANEMOGEAMS.
409
Table I. — September.
1857.
1858.
1859.
1860.
1861.
1862.
1863.
s.
Vel
9*49
12'-96
10-64
11-00
9*58
9-05
12’-47
Mean 10'-74
to
Dir
22°
18°
21°
21°
26°
25°
31°
Mean 23°
S.W.
Hours ...
193
134
204
118
194
190
165
Sum 1198
s.w.
Vel
7-'42
8'-12
8-99
5-35
6-50
5-26
1-13
Mean 6'-04
to
Dir
73°
63
70°
75°
60°
62°
65°
Mean 67°
W.
Hours ...
70
296
175
123
66
116
287
Sum 1133 |
W.
Vel
4'-27
5-12
6'-09
3'-29
4-67
~ 4'-46
8'-46
Mean 5'-19
to
Dir
109°
101°
106°
109°
109°
114°
115°
Mean 108°
N.W.
Hours...
83
59
88
112
142
101
88
Sum 673
N.W.
Vel
4'-34
7'-12
4'-00
2'-82
2'-88
3-77
9*64
Mean 4'-94
to
Dir
164°
160°
155°
156°
163°
157°
159°
Mean 159°
N.
Hours ...
75
31
30
88
34
58
54
Sum 370
N.
Vel
3'-47
6'-6g ~
5-17
4'-06
2'-70
3'-88
4-35
Mean 4'-24
to
Dir
200°
199°
204°
205°
170°
193°
193°
Mean 195°
N.E.
Hours ...
79
13
62
128
10
78
54
Sum 424
N.E.
Vel
3-30
4'-72
5-50
4'-85
4-50
5'-77
5-00
Mean 4'-64
to
Dir
252°
253°
243°
238°
239°
253°
226°
Mean 243°
E.
Hours...
42
102
26
43
2
71
1
Sum 287
E.
Vel ‘
23-55
7*70
6'-09
4'-53
14-07
8-91
13-50
Mean ll'-05
to
Dir
296°
283°
281°
301°
269°
290°
291°
Mean 293°
S.E.
Hours...
26
35
21
29
27
23
8
Sum I69
S.E.
Vel
11-58
13-75
14-20
11-48
12-61
1 1-05
10'-28
Mean 12-11
to
Dir
335°
339°
343°
349°
334°
359°
344°
Mean 343°
S.
Hours ...
116
36
82
26
244
66
38
Sum 608
Maximum
34'
32'
36'
36'
;%&? 42' •
29'
39'
Hours > 25'
5
6
10
7
27
5
7
Sum 67
Hours of 0
32
6
12
27
10
24
7
Sum 118
Table I. — October.
S.
Vel
8'-02
12-41
9-11
12-40
7*54
13-73
9-50
Mean 10'-33
to
Dir
22°
29°
20°
27°
17°
28°
21°
Mean 24°
S.W.
Hours ...
130
131
129
166
233
260
136
1 Sum 1 185
s.w.
Vel
7'-90
9^3
5'-12
1 0-62
2'-07
13-60
8'-80
Mean 7 '91
to
Dir
59°
66°
73°
71°
67°
61°
66°
Mean 66°
| w.
Hours ...
149
199
94
263
77
252
298
Sum 1332
w.
Vel.
6-17
5-43
4'-84
6-46
3'-84
8-43
5'-76
Mean 5'-85
to
Dir
109°
124°
101°
107°
115°
93°
111°
Mean 109J
N.W.
Hours ...
100
115
90
115
19
60
37
Sum 536
r n.w.
Vel !
4'-28
2-05
5-37
4-30
1-45
4'-88
9'-05
Mean 4'-44
to
Dir
165°
161°
153°
151°
140°
160°
146°
Mean 154°
N.
Hours...
7
19
46
27
24
9
8
Sum 140
N.
Vel
4'-13
5'*25
4-01
8'-59
2'-65
4'-25
2'-48
Mean 4'-48
to
Dir
205°
211°
199°
201°
214°
213°
209°
Mean 207°
N.E.
Hours ...
71
167
ill
32
43
12
9
Sum 445
N.E.
Vel
10-71
3'-58
5'-45
4'-27
6'-45
3'-65
10-42
Mean 6'-35
to
Dir
253°
240°
245°
235°
238°
250°
252°
Mean 244°
E.
Hours ...
82
L 86
120
27
37
26
80
Sum 458
E.
^Vel
9'-00
3-50
4'-81
9'-42
9 '-6 8
5-16
8'-40
Mean 7'-02
to
Dir
281°
286°
290°
314°
299°
280°
290°
Mean 292°
S.E.
Hours ...
38
6
95
4
123
25
71
Sum 362
S.E.
Vel
1 1 '*43
4'-80
12'-49
1 4-70
11-69
14'-37
13-12
Mean il'-6l j
to
Dir
335°
322°
349°
341°
340°
338°
333°
Mean 338°
S.
Hours...
46
20
59
37
165
86
102
Sum 515
1 Maximum
26'
31'
31'
38'
43'
54'
40'-5
j Hours > 25' ...
3
9
5
21
39
60
45
Sum 183°
j Hours of 0
8
47
27
2
79
8
13
Sum 1 84 1
3 i
MDCCCLXXV.
410
DR. T. R. ROBINSON ON THE REDUCTION OE ANEMOGRAMS.
Table I. — November.
1857.
1858.
1859.
1860.
1861.
1862.
1863. 1
s.
Vel
7'"46
6-33
12-81
12'-20
17'*47
8'-73
13-41
Mean 11 '-25
to
Dir
19°
27°
24°
23°
33°
24°
21°
Mean 24°
S.W.
Hours...
200
92
167
83
289
302
242
Sum 1375
s.w.
Vel
5-03
5-49
9'-22
7'-52
14-24
9-12
12-16
Mean 8'*97
to
Dir.......
72°
65°
66°
66°
68°
60°
65°
Mean 66°
W.
Hours ...
35
63
140
79
154
122
294
Sum 887
W.
Vel
4'-20
7'-49
5-91
5'-81
4'-25
3-62
9-05
Mean 5 -73
to
Dir
102°
96°
115°
106°
109°
111°
109°
Mean 107°
N.W.
Hours...
41
63
8/
11
44
35
81
Sum 362
N.W.
Vel
3-56
2'-32
4-69
4'- 1 5
4'-77
1 '-87
1 11-66
1 Mean 4'72
to
Dir
143°
151°
153°
154°
159°
159°
157°
Mean 154°
N.
Hours ...
38
73
42
2
119
16
1 9
Sum 299
N.
Vel
4'-46
1 6'-32
5'-44
7 '*84
3-54
3-25
8'-52
Mean 5'-62
to
Dir
199°
215°
212°
214°
187°
204°
202°
Mean 205°
N.E.
Hours ...
48
28
38
87
46
31
21
Sum 299
N.E.
Vel
~6'-26
8'-45
4'-38
8'-78
11-25
4'-48
| 13'-22
Mean 8'-12
to
Dir
257°
248°
255°
246°
242°
246°
258°
Mean 250°
E.
Hours . . .
107
220
31
231
4
27
1 9
| Sum 629
E.
Vel
6'-48
8'-48
12-31
To' *9 3
9'-66
6'-51
} 5'-20
Mean 8'-48
to
Dir
299°
283°
277°
292°
288°
293°
294°
Mean 289°
S.E.
Hours ...
87
131
79
130
6
47
10
Sum 490
S.E.
Vel
6'-86
15-05
1 4*41
7 *93
6'-04
10-48
1 13-58
Mean 10'-62
to
Dir
329°
339°
337°
344°
335°
342°
340°
Mean 338°
s.
Hours ...
44
39
^99
46
23
127
51
Sum 429
Maximum
26'
36"
37'
29*
75'
37'
34'
[
Hours > 25'
6
9'
19
5
90
19
30
Sum 178
Hours of 0
43
80
37
9
13
54
1
! Sum 237
Table I. — December.
S.
Vel
26-1 1
l6'-68
13-35
6'-78
18'*18
21'-98
l6'-52
Mean 17*08
to
Dir
25°
26°
28°
15°
20°
27°
37°
Mean 25°
S.W.
Hours ...
210
230
258
116
121
254
153
Sum 1342
S.W.
Vel
ll'-04
11*91
8*41
3'-06
8'-84
14-13 1
14-40
Mean 10'-20
to
Dir
69°
69°
64°
60°
64°
62°
62°
Mean 64°
w.
Hours...
175
233
167
78
182
177
335
Sum 1367
w.
Vel.
35'-70
1 0' *98
2'-92
2'-20
5'-44
16*33 l
12*71
Mean 12-21
to
Dir
95°
104°
113°
114°
107°
109° 1
105°
Mean 107°
N.W.
Hours ...
12
56
26
128
43
90 1
135
Sum 490
N.W.
Vel
O'
2*66
3-38
3'-20
4'-04
13'-96 I
8’-59
Mean 5'-09
to
Dir
151°
157°
159°
154°
154° 1
155°
Mean 155°
N.
Hours ...
3
116
38
43
62
32
Sum 294
ISL
Vel
"o'
0'
2-11
2'-37
4'-38
0'
2'-00
Mean l'-55
to
Dir
203°
223°
212°
212°
Mean 212°
N.E.
Hours ...
36
59
31
1
Sum 127
N.E.
Vel
12'-04
0'
4'-29
5-40
3-67
12-55
3-50
Mean 5'-80
to
Dir
254°
251°
255°
258°
261°
242°
Mean 254°
E.
Hours ...
3
17
62
56
18
2
Sum 158
E.
Vel
0'
17 *20 ~
14'-97
10*15
6-86
14'-26
12'-63
Mean 10'-84
to
Dir
303°
295°
294°
294°
K)
CD
O
0
295°
Mean 295°
S.E.
Hours . . .
5
37
109
61
64
36
Sum 312
S.E.
Vel
22'-26
21-95
14'-54
12'-87
14'-24
21'-68
18*96
Mean 18'-07
to
Dir
342°
332°
334°
326°
344°
340°
343°
Mean 337°
S.
Hours ...
82
205
84
127
177
57
28
Sum 760
Maximum
42'
48'
45'
38'-8
40'
45'
50'
Hours > 25'
81
102
40
15
56
106
94
Sum 494
Hours of 0
1
2
60
56
41
0
0
Sum 160
DK. T. R. ROBINSON ON THE REDUCTION OF ANEMO GRAMS.
411
The first thing which strikes one in this Table is the irregularity of the wind. It
varies in each octant ; in each octant it varies with the month, and in each octant and
month it varies with the year. As to the first of these variations, both the velocity of
the wind and the number of hours during which it blows are, in general, a maximum in
the first octant (S. to S.W.) ; they decrease from this to a minimum at octants N. to
N.E., and increase to octant 1. The products of the velocity and time at the maximum
and minimum are as 6:1. The predominance of south-westerly winds is what might
be expected from the combination of an equatorial current with the earth’s rotation ;
but it is not obvious why it is not absolute. Probably much of the change of
direction arises from circumstances local to the place of observation. Por instance,
the direction of the west coast of Ireland, which runs nearly N. and S., may occasionally
turn the S.W. currents northward ; and the mountainous ground of Antrim may divert
it here towards the east. It must also be remembered that our anemographs give only
measure of the wind at the earth’s surface, where it is at once retarded and thrown into
gigantic eddies and vortices by the effects of friction.
The experience of aeronauts shows that at a few thousand feet elevation the velocity
is often far greater than it is below, and that the direction is much more uniform. But
I do not see how this error is to be remedied. The summit of a mountain is not exempt
from it ; and though a small and lofty island, like St. Kilda, far from any extensive land,
would be better, yet even here the friction of the sea’s surface will destroy velocity. It
is possible that an anemograph at the top of a tall and slender “ stack ” would give a
much larger velocity than one at its base ; the record could be easily effected below
by telegraphy. We must remember that a current of air comports itself like one of
water, and shall be assisted in comprehending the nature of a gale by watching the
irregular movements of a river in flood. There must also be eddies in a vertical plane.
On the action of these see a valuable paper by Prof. Hennessey in Phil. Trans. 1860.
An anemograph for vertical currents might be made by a set of windmill-vanes placed
horizontal.
Secondly, in each octant the amount of wind varies with the month. It is a maximum
in January; decreases from this to July, the ratio being 2^ : 1. From this it increases
to the end of the year. There is an exception to this in March, where the daily amount
is greater than in February in the ratio of 1T3 : 1. This might seem to countenance
the vulgar notion of stormy weather prevailing near the equinoxes ; but there is no such
excess in September above October ; and in March, though the yearly maxima are higher
than in February, yet the number of hours when the velocity exceeds 25 miles is consider-
ably less. This monthly change is an obvious consequence of the change of the sun’s decli-
nation, for the zone where the easterly winds of low latitudes confine with the westerly
ones of more northern regions must shift with that to which the sun is vertical.
For the third of these irregularities, that which prevails from year to year, there can,
in the present state of our knowledge, be no certain cause assigned. It will be seen
that in the same octants the variation is very different in each month, and that the
3 i 2
412
DR. T. B. ROBINSON ON THE REDUCTION OE ANEMOGRAMS.
maxima in each octant do not belong to the same years ; while the amount of discord-
ance is so great as to almost exclude the idea of any law. I looked for one in the
direction already noticed. In 1860 the sun-spots were at a maximum, in 1856 at a
minimum ; and if they exert any influence it must have been considerably less in 1857
than in 1860. The products of velocity and time were accordingly examined in these
years, and that for 1860 is 4167 greater than in the other. But this result is reversed
by 1863, which exceeds 1860 by a still greater amount, 5223 ; and evidently many
decennial periods must be examined before any reliable conclusion can be attained as to
this influence.
The same lawless irregularity may be observed in the maximum velocities of separate
years. The highest in the period before us is 71 miles in November 1861, the lowest
19, in July 1860. Far higher velocities than these are sometimes attained, but only
for a few minutes. It holds also as to the number of hours when the velocity exceeds
twenty-five miles. As instances : in January 1863 this number is 146, in 1857 it is 23 ;
in April 1859 it is 40, in 1861 it is 0 ; in November 1861 it is 90, in 1860 it is 5. It
occurs also, though not intensely, in the hours of calm. It may have some interest to
give the mean velocity for each month irrespective of the direction.
Table II.
Month.
Velocity.
Total miles.
January
13-51
70336
February
12-82
60422
March
13-00
67691
April
11-62
51587
May
7-78
39664
June
4-24
35353
July
6-59
34343
August
7-29
35986
September
8-02
39513
October
9-12
45568
November
9*97
47671
December
12-98
166498
Here also there seems little indication of equinoctial gales. March is a trifle more
windy than February, but September less so than October. The yearly sums also
do not show any special relation to the solar spots; the total in 1857 = 79865;
in 1860 = 73067 ; but in 1863=95583. The total miles in the seven years=590672,
and the mean velocity during that time is 9*729.
II. The most obvious way of dealing with the west and south components of V is to
derive from them interpolation formulae for each year involving periodic functions of
the time, and deduce from the coefficients of these formulae in successive years some
general law. This, however, seems impracticable, for the components differ so widely
in successive years as to preclude any hope of reconciling them. As a specimen of this
discordance I give the values for the first hour of the series for January 1 : —
DE. T. E. EOBINSON ON THE SEDUCTION OF ANEMOGEAMS.
413
1857
. . . W =12-59
S= 9-81
1858
... - 6-27
22-14
1859
. . . 7-78
6-31
1860
. . . 6-80
20-91
1861
... - 3-91
- 1-21
1862
. . . 1-29
- 2-70
1863
. . . 14-62
22-65
It is evident that here there is no regular succession ; and equally so that little
dependence can be put on even the mean of the seven as representing the hour 0 for
that day. But if, as is probable, these discordances are casual, we may expect they
will disappear from the mean of a large number of observations — how large may be
estimated from the Probable Error of these observations, though, on account of the mag-
nitude of their discordances, this cannot be determined with great precision. There is
also this difficulty in the process of finding the Probable Error, that the coordinates
undergo daily and monthly variations, which must not be confounded with the casual
errors. It is therefore necessary to confine ourselves to the observations of each individual
hour during the seven years, and combine any number of these groups of seven. This
is effected by the simple means of using as the divisor n — m instead of n — 1, n being
the number of terms in the entire set, and m the number of groups. I have only
thought it necessary to make the computation for W in January and June, and I find
P E of a single observation . . + 5-901 + 3-913
P E of mean of seven .... +2-230 +1-479
P E of W in Table, mean of 217 +0-401 ±0-266
P E of mean of month ±0-082 ±0-054
The discordancy in summer is only two thirds of that in winter, and in both is so
great that the mean of seven is not to be relied on ; and even the numbers of Table III.
are not sufficiently certain. Perhaps these seven years may have been exceptionally
irregular. The discordancy of S is still greater than that of W. Evidently single hours
were out of the question ; I therefore took for each hour the mean of the month in the
first instance ; I then grouped these means for every ten days, but ultimately adopted
the entire month as the group.
Before discussing these means individually, it may be useful to give their means for
the entire period of seven years. Supposing the winter from October to March inclusive,
the summer from April to September, the day hours from 7 am. to 6 p.m., the night
from 7 p.m. to 6 A.M., we find : —
Winter Day.
Sum W=7899m,315 ; Sum 8=11239-92 ; Ann. Translation =137 38 ; D=35° 6'.
Winter Night.
Sum W=7264m,43 ; Sum S=11527-75 ; Ann. Translation=13812 ; D = 33° 25'.
414
DE. T. E. EOBINSON ON THE SEDUCTION OE ANEMOGEAMS.
Summer Day.
Sum W=3519m,23 ; Sum S=5454*50 ; Ann. Translation= 6491 ; D=32° 50'.
Summer Night.
Sum W=2831m,43 ; Sum S=5081-65 ; Ann. Translation =5 81 7 ; D=29° 8'.
Both components are more than twice as great in winter as in summer ; the day com-
ponents are greater than the night ones, except the winter S.
The sums of all are Sum W=21514”-40 ; Sum S=33303”; Ann. Trans. = 39648” ;
D = 32° 5T.
On examining the records of the components, I find that 630 hours were missed by
various accidents, so that the total number of hours is 60714; and the above sums,
X 7y-u60714h, will give for the mean hourly values W=2m,4805; S=3m,8398 ;
V=4m,5713 ; 0=32° 54' 44". The value of V shows that the wind in the first quadrant
is nearly half the total amount.
The monthly means of the components are given in the following Table (p. 415).
On examining this, Table we observe, First, that all the values both of W and S
are positive ; in other words, that in a considerable number of observations the aerial
currents from west and south have at this station a decided predominance over all the
others. Secondly , that, as was anticipated, however discordant the results of individual
hours or days may be, yet the means of from 196 to 217 present a notable agreement,
and the differences which they exhibit are evidently subject to law. If we look down
the vertical columns (which give approximate values for each hour of the middle day
of each month) we find in each a decided maximum and minimum, and another, or
even more than one of each, less in amount. The hours of these phases vary with the
months ; that of the principal maximum occurs in the winter months from noon to
3 p.m. for W ; in the summer from 9 a.m. to noon ; for S it varies less, being a little
before noon.
The principal minimum occurs in the evening, from 6 p.m. to 10 p.m., both for W
and S. The extreme diurnal ranges are greatest in March, being for W 2”T4, for
S 2m,40 ; they are least in November, being 0*74 and 0-79.
It deserves notice that during the winter months the horary values of W for the four
afternoon hours exceed those for the four that precede, the sum of the differences being
9m,95. In the summer months the reverse is the case, but the — differences are only 7m-02.
Does this arise from the great extent of land to the east of Ireland as contrasted with
the ocean to its west, and the greater evaporation from the latter in summer 1
If we examine the horizontal columns (which show the monthly variations) the
dominion of Law is still more manifest. W has a maximum in January, a minimum
in February; the greatest maximum is in March, the least minimum in April: these
abrupt changes are remarkable ; but it is possible that the great value of W in March
is abnormal, and may not occur in subsequent years. It then increases with a slight
DE. T. B. EOBINSON ON THE SEDUCTION OE ANEMOOEAMS.
415
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416
DE. T. E. EOBINSON ON THE EEDUCTION OF ANEMOGEAMS.
maximum in August and a slight minimum in November. The variation is greater
here than in the horary columns, being for hour 15 = 6m,56. The largest W is at
March 15h=6m,56 ; the least at May 15h=(H)0.
The law of S is simpler ; it has one maximum in December and one minimum in
July; its range, too, is something greater, being in hour 20 = 6m,98. The greatest
magnitude =8m*285 at December 4h, its least = 0m-82, July 19h. There is a general
agreement in the change of the two components, with one striking exception, the
maximum and minimum which W has in March and April. Such a general agree-
ment might be expected, for any air coming from the south must have a westward
motion due to the greater velocity of the earth’s rotation in a southern parallel. This
anomaly, if real, may be caused by the geographical conditions to which I have already
alluded. To them also maybe referred the fact that at May 15h W=0, though
S=2m,41, from which a sensible magnitude of the other might be expected. It must,
however, be observed that some of the changes exhibited in this Table can scarcely be
regarded as periodical. I have already pointed out that from the very great dis-
cordance of individual observations it is evident that a much greater number of them
than is afforded by a period of seven years is required to eliminate the barometric and
hygrometric influences. Yet these disturbances might be expected to be distributed
with some uniformity through the day; while the changes from hour to hour are
sometimes considerable. Thus in February 9h to 10h AW=0‘89; 16h to 17h AW
= — 0*90,; March 10h to llh AW=-1T5 ; 14h to 15h AW=094; April 10h to llh
AS= — 0'71 ; December 10h to llh AS=086. These are the largest; and it deserves
notice that they occur in winter months ; in summer there is much less abruptness
of change.
It occurred to me that some of these irregularities might be due to errors in the
records of velocity ; but this seems quite improbable. Such errors could only arise from
three possible causes.
1. Referring to my description of the anemograph in the ‘ Transactions of the Royal
Irish Academy,’ vol. xxii., it will be obvious that the track of the recording pencil might
be excentric to the brass disk which carries the paper. It was carefully adjusted when-
ever the clock was cleaned, but was liable to derangement from rough handling. The
error which would thus arise was avoided by an easy adjustment, which made the edge
of the reading alidad coincide with the right line drawn by the pencil when the clock
was wound up. It will easily appear that the readings so made are true.
2. The paper may be excentric to the centre of rotation. Let e be its excentricity,
e that of the pencil, Q the reading of any distance from the winding line, ip the angle
between that line and the line of the two centres, the correction for 6
— s(sin\J/ — 1) — (e sin\[/(— — 9)\
DR. T. E. ROBINSON ON THE REDUCTION OE ANEMOGRAMS.
417
and calling V the change of 6 in the following hour,
oe
correction of V=y cos(\f/ — 0— •JVjx sin^V;
supposing 0 = 0 ‘05 (and such an error is not probable) the maximum error would be
0m*27. This, therefore, cannot do much harm.
3. A much more serious error may be caused by the rate of the clock which moves
the pencils of the instrument. Suppose it a gaining one, the hour-circles on the paper
are less than hours, and the recorded Vs belong, not to the times to which they are
ascribed, but to periods a little in advance. The error is negligible, except for the
hour of winding-up. There the space-curve goes beyond the last hour-circle to a
distance equal to the rate in 24h, and the measured V is proportionally too large.
H + #
If the velocity were uniform, this would be corrected by multiplying V' by where
H is the hour-space, x its hourly increase ; but as this seldom is the case, the change
must be allowed for by interpolation. In all cases but the last we thus obtain
X 1
As I never have found g greater than the second term may be neglected, and the
coefficient scarcely differs from unity. In the last we have
V H+a?
n 2H + rc#
{
V'x
2H + *
H + TlX
+ V'X
(n — ])#)
"H j’
1
which may be considerably less than V. The projection of the space-curve beyond the
last hour-circle gives 24x. This excess occurred most frequently in gales from S.W.,
and was, I think, often caused by the vibration of the lofty structure which supports
the instrument. I have not applied these corrections except in a few cases when the
error was glaring. The winding-hour was at 9 a.m. in 1857 and 1858, at 10 a.m. in
the other years ; and at these hours this influence might be expected ; but on comparing
their values in Table III. with the formulae of Tables V. and VI., they seem as well
represented as any of the others*.
The discordances of these quantities would have been less striking had they been
grouped as three-hourly means ; and this was my original intention, which I abandoned
on account of a difficulty in respect of interpolation to w'hich I will refer presently.
It is, however, necessary to remark that the numbers of Table III. are merely pro-
bable values. A sensible proportion of the individual values is invariably negative for
each hour ; and my first idea was to keep the positive and negative means separate. I
tried it for January and June as extreme cases, and came to the conclusion that this
separation would be useless. The negative values occur so constantly, that they can
* I have given these details as they will he useful in case it he ever thought desirable to reduce the entire
series of their anemograms, which extends from 1847 to 1870.
MDCCCLXXV. 3 x
418
DR. T. R. ROBINSON ON THE REDUCTION OF ANEMO DRAMS.
scarcely be deemed casual. In the 744 septimates of January there are only seven in
which all the W and S are positive ; in the 720 of June there are none.
It might be expected, from the mechanism of the polar and equatorial currents, that
both components would change signs simultaneously ; but it is not so. I find that the
proportion of the combinations is : —
In January . . ^^0*589; ^^0*141; ^~0*184; 0*086.
In June . . . „ 0*406; „ 0*220; „ 0*198; „ 0*176.
The combination of -f-W with — S may arise from the influence of a continent to
the east of Ireland, and that of — W and ~f S from a north-east current whose north
component has been destroyed by friction ; but I looked for a greater frequency of
— W and — S. If we confine ourselves to consider +W, — W, +S, and — S sepa-
rately, we find : —
For January . . . Sum (-f-W)
Sum (+S)
For June .... Sum (+W)
Sum ( + S)
32121; Sum (-W)= -8315;
:42733 ; Sum (-S) =-6372.
13298; Sum (— W)= — 9002 ;
15978; Sum (— S) =-7163.
The amount of negative components does not differ very much in the two months,
but that of the positive is nearly triple in January what it is in June. Were we to
attempt to develop separately these + and — values, we should be embarrassed by the
different numbers of them belonging to each hour. Thus in J anuary the number for
— W is 47 at 2h, 69 at llh ; for — S is 41 at 2h, 56 at lh. In June, for — W it is 63
at 3h, 91 at 15h; for — S it is 65 at 2h, 98 at 9h. Supposing them developed in terms
of the time, we should still be unable to obtain any absolute values of the components
at a given epoch unless we knew the causes which produce these negative values and
the laws of their action. It is evident that the equatorial current predominates here,
but that there coexists with it a polar one, probably above, possibly collateral, which is
occasionally mixed with the other by some disturbing force — probably barometric. It
seems also that the monthly variation of the components is in a great measure limited
to the positive values. For these reasons I have confined myself to the simple means
of the entire set. But I think it might be well, in a series extending to several periods
of five or seven years, to keep them so far separate as to be able to examine whether the
occurrence of the negative values has any relation to time.
A Table like this, whose data refer to dates separated by considerable intervals, will
not suffice to give the components generally without some process of interpolation ; and
we proceed to consider this. The form universally adopted where the quantities con-
DR. T. R. ROBINSON ON THE REDUCTION OF ANEMO GRAMS.
419
cerned are periodic functions of the time-angle is that given by Bessel, in which, calling
the quantity u and the angle $, we have
w=K+A cos $+B cos 2$+C cos 3$+D cos 4$ + &c.
+ 0 sin 3 + P sin 2$ + R sin 3$ + S sin 4$+&c.
But as the monthly variations must be represented as well as the horary, a formula of
this nature including two variables would be very complicated ; and it seems best to
obtain, as proposed by Bessel, the horary formula for each month, and to regard the
constants of this formula as themselves periodic functions of the monthly time, and
develop them in similar formulas of the month-angle, <p. Stopping at terms of the
fourth order, we should have nine of these for each component ; and for a given day of
the year and hour of the day we must compute the constants for the <p of the day, and
multiply each of the last eight by the cosine or sign of the corresponding multiple of $.
The calculation of the horary constants is shortened by observing that for the angles 3,
18O + 0> 180 — 0, and 360 — 3 the sines and cosines have the same numerical value ; and
hence the calculation need only be made for the first quadrant.
Supposing the circle divided into 2 n equal parts, and that 3 contains to of these, the
u corresponding to any $ may be characterized as u, that corresponding to $ + 180 as
u , and the sum or difference of these two as 5, d .
As the cosines and sines of odd multiples of $ and 180 + $ differ in sign, but those of
even multiples agree, the expressions of A, O, C, and R will contain only d, those of the
others only s. The signs of s and d are easily determined in each case. Thus for the
first multiples of 3 the cosine and sine are + for to through the entire quadrant ; they
are — and + for n — to. For the second multiples the sine is + through the quadrant,
the cosine is + up to 45°, — through the rest ; for n — to the cosine is the same as for
to, the sine different. I take, as in the first instance, the horary division in which
n= 12, and Bessel’s formulae become
K=+4\fs+s+s .... +s j,
U 1 2 11 J
A=1+j(Z+ (d—d'j cos 15°+ ^cos 30°+ (d—d'j cos 45°+-J^Z— d^-\- (d— ^cos 75°j,
Bzr-J^js— s+-^s+s — s— s'j + ^s+s — s— s^cos 30° j,
C — d'j + p d — d — | d — d-\-d — d^j~ ] sin 45 |,
D=*{+?+i (?+?,) -i(+?J ~ (f +f) ■ -i(s+i) +++)}’
0=ti‘! ^Z+o^sin 15 +-£ (d~\~ddj + ^Z+(Zjsin 45°+ ^fZ+ ^Zjsin 60°+ ^Z+<Zjsin 75°+ fZ j,
P s+s— s\+s— s+ (s— s+s— s\cos 30ol,
l \1 11 s 71 3 9 \2 10 4 8/ J
3 k 2
420
DR. T. R. ROBINSON ON THE REDUCTION OF ANEMOGRAMS.
[d-\- d — d~ j- f d-\-d-\- d -(- d — d — <^\cos 45 1,
"1.2 10 6 \l 11 3 9 5 7/ J
S = iVfs— s+s— s— (s — s-J-s — s\ cos 30°1,
1 1 11 2 10 \4 8 5 7/ J
and so on.
These are all combinations of the groups s ± s , d^rd ; and by forming these
groups the computation is evidently much simplified.
This simplification is, however, only possible when n is an integer, and a the first arc
of the series=^ or=0.
Whatever be the value of a , Bessel’s formula fails generally to give G and U the
cosine- and sine-coefficients of the nth order. The Q correspond to u=a-\-(m— 1)^,
and this for the order becomes 1)^. Then cosine 0=cos(mz),sin 0=sine na ;
both + for odd values of m, — for even ones. Thence the nth coefficient —
u cos na= K cos w«+&c.+G cos2 na+ U sin na cos na,
1
—u cos na= — K cos na— &c.+G cos2 na-\- U sin na cos na.
2
Then summing from m— 1 to m=2w, we get
cos na S [u— u'j = (cos2 na G +sin na cos na U) X 2 n,
S (u—u^=Zn (G cos na-[- U sin na).
Here the divisor of S (u—u^ is 2 n instead of n; and these coefficients cannot he
obtained separately unless « = 0 or in which case the cosine or sine = 0.
How far the series is to be continued depends on the periodic fluctuations of the ms,
and may be found by trial, or by Bessel’s expression for the squares of the residual
errors. In any case it should not be carried further than the order as after that the
coefficients coalesce. Bessel has shown this for a= 0; and it can easily be proved to
hold good when a is a submultiple of and b a multiple of a.
For the horary groups I find the fourth order sufficient. These horary groups might
be combined in triple sets ; but, as I have said, there is a difficulty in the interpolation
due to the fact that while u1, the mean of any three, is multiplied by cosine or sine of 0,
0
the first and third components of it should be multiplied by the same functions of 6— b
and 6-\-b. This, however, may easily be corrected. Take the case of A : the effect of
three components to determine this is : —
DR. T. R. ROBINSON ON THE REDUCTION OE ANEMOG-RAMS.
421
u xcos (6— 5)+m+«£Xcos (0 -\-b)=u cos 6 cos£+m+ u cos 6 cos b— ( u — u ) sin 6 sin b
-b 0 0+b e-b 6 0+b \0+& 6-b)
= ( u +m+ u ) cos 6— ( u + u \ cos 0 versine b— / u — u \ sin 6 sin b.
\0-6 0 0+b) \0+6 0-b) \0+b 0-b)
Developing the sum and difference of the ms, which gives
u + u =2K+2A cos 6 cos 0+20 sin 0 cos 0+ 2B cos 2d cos 20+&c.,
0+b 0-b
u — u = — 2A sin 0 sin 0+20 cos 0 sin0 — 2B sin 26 sin 2b &c.,
0+5 0-b
we obtain the term
= 3u cos 6—2 versine 0{K cos 0+A cos2 0+0 sin 6 cos 0+&c.[
+2 sin2 0{ A sin2 0+0 sin0cos0+&c.f.
Summing round the circle, calling Su1 cos 6= F, and remembering that all except
S cos2 6 and S sin2 6 vanish, that each of these = 4, and 12A=3F in ordinary cases, we
have
12A=3F— 8 A cos versine 0+8A sin2 b ,
and ultimately
A X 4 (1 — -f versine b)= F.
O is given by the same formula, changing the cosines for sines in F. For higher
orders, P, it is only necessary to use jpd and j)b. In the case of D, however, the
formula must be modified ; for in this instance S cos2 =8, S sin2=0, and the expression is
D (4+-3- cos versine 40) = F. The values of the constants are : —
A (3-9091)=^+ (d—d'j sin 45°.
B (3-6428)=s-s.
0 6
C (3-2190 )=d-(d—d\ sin 45°.
0 \ 3 9/
D (5-333) =s+s — ^s+s^.
The suffixes here are the same as in
0 is 90°.
O (3-9091)=^+^+^ sin 45°.
P(3-6428)=s— s.
3 9
B (3-2190)= -d+(d+dj sin 45°.
S =0.
the preceding formulae. Thus 0 is 45°,
I have compared this formula with the observations of February and March, the
most irregular of the whole set, and the results, along with those of the preceding-
one, are given in the following Table. The numbers are the observed — the calculated
values.
422
DR. T. R. ROBINSON ON THE REDUCTION OF ANEMOGRAMS.
Table IY.
Hours.
February.
• March.
Normal.
Triplet.
Normal.
Triplet.
m
m
m
m
0
0-07
0-02
0-02
0-00
1
0-22
0-26
0-02
-0-20
2
-0-03
0-04
-0-07
-0-12
3
-0-11
-0-04
-0-07
-0-06
4
-0-02
0-08
-0-11
0-16
5
-0'03
0-02
-0-18
0-29
6
0-21
0-17
— 0-07
0-04
7
-0-17
-0-18
0-01
-0-30
8
o-oo
0-08
-0-30
-0-52
9
- 0-24
-0-23
0-01
-0-15
10
0-11
0-25
0-38
0-57
11
0-21
0-28
-0-48
-0-29
12
-0-28
-0-26
— 0-02
0-15
13
0-04
0-00
0-21
0-15
14
0*01
-0-08
-0-17
-0-32
15
-0-12
-0-25
0-28
0-31
16
0-34
0-38
-0-20
-0-01
17
-0-23
-0-13
0-05
0-01
18
-0-11
0-11
— 0"05
-0-05
19
. 0-07
0-15
0-16
-0-03
20
0-07
0-19
— 0-05
-0-06
21
0*00
-0-06
-0-09
-0-08
22
0-11
-0-03
-0-07
-0-17
23
-0-25
-0*26
0-06
-0-22
PE
+ 0-110
+ 0-123
+ 0-123
+ 0-161
The triplet combinations are not much inferior to the others, and might possibly be
sufficient ; but I prefer the latter. Even in the extreme cases of February 16 and
March 8, 10h and llh, the discordance is not as great as I anticipated from the absence
of the constant S. I tried them, omitting the terms of the fourth order, but the results
were decidedly inferior.
In considering the magnitude of some of these errors, it must be remembered that
the formula expresses only that part of the coordinates which is periodic ; and they are
the residues of other effects which do not depend on the time 0, and which disappear
from a larger series of observations ; for the other hours the errors are much smaller.
I thought of grouping the hours in pairs, which would probably have given a better
result than the triple combination; but on deducing the formula, I found it would
require more logarithmic work than the complete process. In it the coefficient of a
constant of the order has the coefficient = 6 cospxl5°, instead of- 6, as is evident
from what precedes.
DE. T. E. EOBINSON ON THE SEDUCTION OF ANEMOGEAMS.
423
The horary constants of W for the twelve months are given in
Table V.
Month.
K.
A.
B.
C.
D.
°'
P.
I R.
s.
January ...
4-571
0-058
0-234
-0-104
— 0-115
-0-211
0-133
—0-126
— 0-080
February...
2-913
-0-474
0-457
-0-199
— 0-010
-0-048
0-219
— 0-046
0-021
March
5-165
-0-645
-0-043
0-244
-0-202
-0-108
0-272
0-072
— 0-183
April
0-462
— 0-212
— 0-016
0-089
— 0-000
0-008
0-081
-0-024
0-086
May
0-594
0-161
0-044
0-098
0-021
0-458
0-127
0-055
— 0-066
June
0-837
-0-052
0-080
—0-090
0-004
0-252
0-021
0-026
0-037
July
2-104
— 0-651
0-052
0-197
-0-046
0-225
-0-033
0-104
-0-043
August ...
2-367
-0-630
0-228
0-031
— 0-114
— 0-012
0-115
-0-005
-0-105
September.
2-252
- 0-236
0-011
0-105
-0-018
0-203
0-122
-0-053
0-067
October ...
2-090
-0-274
0-159
— 0-131
-0-040
0-049
0-074
— 0-085
-0-123
November..
1-754
-0-084
0-094
0-044
— 0-068
0-046
0-112
-0-082
0-040
December..!
4-071
-0-023
-0-083
-0-015
— 0-003
0-103
0-127
0-006
0-032
The similar constants of S are given in
Table VI.
Month.
K\
A'.
1 B’-
O'.
D’.
J °-
1 F-
E'
1 B' 1
January ...
6-982
-0-131
0-170
— 0-252
-0-002
-0-143
0-049
0-089
— 0-007
February...
6-017
- 0-239
0-419
-0-108
-0-012
0-160
— 0-085
-0-109
— 0-085
March
2-976
0-012
0-311
-0-080
-0-012
0-944
-0-155
-0-009
0-058
April
2-472
-0-026
0-248
0-053
-0-112
0-561
0-070
-0-037
0-137
May
2-221
-0-252
0-142
0-142
-0-054
0-226
0-054
-0-042
-0-077
June
1-749
-0-237
0-139
0-043
— 0-015
0-379
0-155
-0-006
— 0-054
July
1-539
-0-150
0-120
— 0-015
0-080
0-287
0-124
— 0-048
-0-007
August ...
2-621
-0-176
0-241
-0-033
0-089
0-354
0-116
-0-078
-0-123
September.
3-715
-0-093
0-284
-0-037
-0-086
0-071
-0-259
-0-030
-0-057
October ...
3-834
0-289
0-104
— 0-202
— 0-018
0-217
— 0-033
-0-072
-0-081 !
November..
3-990
-0-041
0-038
— 0-013
0-006
0-081
-0-145
-0-060
0-001
December..
7-696
0-181
0-102
-0-214
-0-006
0-121
-0-100
-0-093
-0-087 !
I
The degree of precision with which these constants represent the observations will
appear from the number of errors between certain limits. W has from O'O to 0T0
inclusive, 177; from 0T1 to 0-20, 72; from 0-21 to 0-30, 33; from 0*31 to 0-40, 3;
above 0-40, 3. S has from 0-00 to 010, 172 ; from Oil to 0-20, 85 ; from 0-21 to 0-30,
27 ; from 0-31 to 010, 3; above 010, 1.
We now proceed to develop these constants in terms of <p ; but as four orders do not
give K and K' with sufficient exactness, I have carried the formula to the sixth order,
its utmost extent.
424
DE. T. E. EO BINS ON ON THE EEDUCTION OE ANEMOGEAMS.
Formula where 5=30° and a= 15°.
6A =(d—d'j cos 15+ (d—d'j cos 45 + (d~ d^ cos 75.
60=^+^ sinl5+^+<^ sin 45 + ^+^ sin 75.
6B= {5+5— /s+sHcos 30.
t 1 6 \3 4/ J
6P=^- js — S + S — 5 1 +5 — 5.
I- 1 6 3 4 -1 2 5
6C= {d-d- (d-d+d-d) } cos 45.
6R= | d-\-d-{-d-\-d— (d-\-d^ j sin 45.
6D=4{5 + S + 5+5] — (s+s).
L 1 6 3 4 J \ 2 5/
6S= { s—s— ( s—s ) 1 cos 30°.
U 6 \3 4 /J
6E=(<Z-d) sin 15° — (d — d^ cos 45°+ (d-d} cos 15°.
6T= p+^ cos 15° - (d+dj cos 45 + (d+dj sin 15.
12U=5— s— Is— 5\+5— 5.
1 6 \2 5/ 3 4
G, for reasons already given, cannot be determined.
It is, however, necessary to obviate two difficulties which interfere in the present-
instance with the accuracy of this process, but which do not affect the horary interpo-
lation. It supposes that the ms employed represent values of the coordinates belonging
to dates which correspond with a series of <p in arithmetical progression.
This is not the case ; for (1) the means of each month do not represent exactly the
coordinates belonging to the middle of that month; and (2) the angles representing the
distance of the middle of each month from the beginning of each year are not in arith
metrical progression, as is evident from the following Table, which gives these angles
=4', and also those belonging to each half month=</,.
Table VII.
Month.
+
M-
Month.
fi.
January
February
March
April
May
June
15 16-5
44 21*2
73 25-9
103 25-2
133 33-6
163 37-2
15 16*8
13 53-4
15 16-8
14 46-6
15 16-8
14 46-6
July
August
September
October
November
December
193 40-8
224 13-8
254 18-0
284 24*6
314 25-2
344 28-8
15 16-8
15 16-8
14 46’6
15 16-8
14 46*6
15 1 6-8
Both these difficulties are overcome by a process based on a suggestion of Professor
Stokes.
DE. T. E. EOBINSON ON THE SEDUCTION OE ANEMOGEAMS.
425
Let the true constants of the formula be denoted by small italic letters, so that
u=K-\-a cos d-\-o sin 6-\-b cos 24+&c.,
1
then, as the mean of u through the space D'—8=^'ud0, we have
mean u= {JK^+Jacos 6d&- j-J o sin 6d0 &c.
Let 8=$— [A ; and as all the pairs of terms are of the same form,
a cos j()8-\-o sin p8,
p p
integrating this will do for all. The integral is
which within the limits
K0-f +«
p
sinjofl
P
=k>. . . . +J™M±M_sinM-M
A p p
2a cosp^ sinj3«’ + 2 o sin/3\J/
=2K^+ p .
/3j«.-i-sinjo/x
fcos (pb+pfi)
T p
and dividing by 2p=d— 8, we obtain, calling
cos(jp4— pit)]
P 1
, cos 4 o sin 4 , 7 cos 24 _
mean w=K + a — — -f- — +6 — - — + &c.
Now we might form the n equations for u and treat them by minimum squares; but
as in this case none of the terms would vanish on summing, though all (except the one,
say «, whose square appears) are small, the labour of eliminating 12 quantities 13 times
p
over would be truly formidable. This might be evaded by substituting in each sum for
the true constants those given by the series of ®, which differ little from them, and all,
except A, are multiplied by small coefficients. This will give A a with close approxi-
p p
mation. The process may be repeated with the corrected values, but A a alone will
p
have any notable effect. Yet even with this simplification the labour is very great.
But it may be superseded thus. We have the above equation for u\ but we have also
u'= K-j-A cos pfi-0 sin p+B cos 2<p+P sin 2<p &c. ; and equating the two values,
„ , a cos 4 . o sin 4 b cos 24 n sin 24 „ , . . _ . , „
K+— ^+-y^+— 7^+^-r-^=K+A cos <p+ O sm <p+&c.
It is evident that if we put a=Ar C°S f, o=0 and s0 on, the equation would
1 cos 4 sin 4
3 L
MDCCCLXXV.
426
DR. T. R. ROBINSON ON THE REDUCTION OP ANEMOGRAMS.
be satisfied, if the factors r r ^ ^ &c. were equal in every month. They, however,
differ so little that I have thought it lawful to take their means for the twelve months.
Though this is fairly warranted, yet it seemed advisable to test it by comparing for
E the cosine constant, of the fifth order in the series for K, with the minimum square
process. It gives for E T0525 ; the second approximation, using AE alone, gives
T0305, which would be a little increased by using the corrections of the other constants,
so that the agreement is sufficient. As the factors r r will answer for any
year, I give their logarithms.
A.
O.
B.
P.
C.
E.
0-00672
0-00346
0-02156
0-02119
0-04411
0-04976
D.
s.
E.
T.
G.
U.
0-09300
0*08400
0-16622
0-11988
Not determined.
0-19731
It does not seem necessary to give the constants A, O, &c. ; but instead the secon-
dary constants of the formula w=K-{-K sin (r+0)-l-Ksin(r-|-2$)+&c., deduced from
0 0 1 1 2 2
their corrected values, are given as more convenient for computation in Table VIII.
(p. 427).
I have given the constants for the horary coefficients A, O, &c. to the 6th order for
symmetry; but in fact I do not think any of them less than (hOS need be attended
to. Even this limit is beyond what can be expected to be available when they are only
determined by the observations of seven years, as is evident from what I have already
said as to the P E of the quantities from which they are determined. Whether the
diurnal variation of the coordinates follows the same law in different septennial periods
remains to be determined ; probably it does. The constants belonging to K and K' are
<p
larger than the others, and, as derived from larger coefficients, merit more confidence.
The effect of the terms of the first and second orders, which are the chief, are similar ;
but the others present opposite phases, and would probably be modified by more
accurate determination. It is here that I think changes in successive years will probably
be found ; and were I to pursue this work further, I would combine the observations
rather differently from what I have done in the present case. I would mean the
homonymous hours of each month of each year, combine them in pairs, and mean them
to get the K of each month. I would then compute the K constants, retaining the
cosine and sine form ; and this should be continued through a few periods of the solar
spots. This would decide the question whether the wind is affected by the conditions
which modify those phenomena.
At the same time the inspection of the horary means would show whether their laws
vary with the time. Then the final constants could be determined for such intervals as
might be considered sufficient. The sine and cosine formula, though requiring more
DE. T. E. E0B1NS0N ON THE EEDUCTION OE ANEMOGEAMS.
427
Table VIII.
K= 1-3393
K=l-1203
K = 0-3354
K = 0-8488
K=l-1377
K=0-4856
K=2-4307
1
2
3
4
5
6
0
x=85°37'-4
«=12°37'-7
h=191°24'-2
! k=130°9'-3
>c=89043'-3
x=0°0'-0
1
2
3
4
5
6
A = 0-l601
A = 0-3 159
A = 0-1927
A = 0-0215
A = 0-1235
A=0-0351
A= — 0-2552
1
2
3
4
5
6
0
a=33°21'-2
a=159°44'-6
a=60°9'-0
a=l79°22'-S
I a=333°51'-8
i a = 0°0'-0
1
2
3
4
5
6
B=0-0419
B=0-1090
B=0-9878
B=0-1551
B=0-0413
B=0-0569
B=0-1014
1
2
3
4
5
6
0
jS=91°l4'-5
jS=13°56'-5
/3=333°23'-7
/3=30]°45'-l
/3=330°51'-9
/3=180°0'-0
1
2
3
4
5
6
C=0-0299
C=0-0485
0=0-1202
0=0-0427
C = 0-0387
0=0-1180
0=0-0224
i
2
3
4
5
6
0
7=314° 21'-1
7=266° 47 *5
7= 171°26'-1
7=216° 34'-8
7=153° 44'-8
7=0°0'-0
i
2
3
4
5
d
D=0-0207
D=0-0628
D=0-0399
D=0-0087
D=0-0830
D=0-0348
D= -0-0492
i
2
3
4
5
6
0
J=26l°18'*7
5 = l67°0'-0
J=25°31'-2 :
5=291°22'-8
£=229°34'-7
5=180° O'-O
1
2
3
4
5
6
0=0-1630
0=0-1296
0=0-0597
0=0-0776
0=0-1591
0=0-0342
0=0-0804
2
3
4
5
6
o
o=26l°ll'-8
o=l65°]6'3
o=l6°34'-7
o=209° 43'-0
o = 189°21,-5
o=0°0'-0
1
2
3
4
5
6
P=0-0650
P=0-0565
P=0-0069
P=0-0626
P=0-0339
P=0-0126
P=0-1142
1
2
3
4
5
6
0
«r=55a*8>5
®-=306°8'-2
'S7=48°33,-l
®=215°38'-0
^=46°45'-l
©■=0° O'-O
i
2
3
4
5
6
E=0-0209
E=0-0205
E=0-0430
R=0-0276
E=0-0621
E = 0-0186
E= -0-0095
1
2
3
4
5
6
0
P=2 98°39'‘9
p= 74°20-l
p— 204°6’-5
/3=152°52'-7
p= 148°23'-7
^=0°0'-0
i
2
3
4
5
6
S=0-0035
S=0-0339
S=0-0245
S=0-0272
S=0-0152
S=0-0282
S=- 0-0264
i
2
3
4
5
6
0
<r=l66°20'-3
<r=] 56°5'-l
cr=80°58'-6
<r=225°20'-3
tr=264°12'-8
o-=180°0'-0
i
2 1
3
4
5
6
3 l 2
428
DR. T. R. ROBINSON ON THE SEDUCTION OE ANEMOGEAMS.
Table IX. — Secondary Constants for S.
K~ 2*5130
1
K=0*8748
K=0*9444
K=0*2678
K=0*5199
K=0*3894
K=3-8177
1
2
3
4
5
6
x=93°52'*l
x=63°28'*5
x=66° 16*5
jt=150° 17*6
i=182°59f-8
k=180°0'*Q
1
2
3
4
5
6
A=0*136l
A=0*1062
A=0*0628
1
A=0*1319
1
A=0*1183
A = 0*0600
A— — 0*0749
1
2
3
4
5
8
°
a=127°43'*2
a=227°53'*9
a=195°36'*3
a=80°54'*3
a=118°31'*6
a=180°0'*0
1
2
3
4
5
6
B=0 0658
B=0*1265
B=0*0272
1
B=0*0405
B=0*0432
1
B=0*0247
B=0*1932
1
2
3
4
5
6
°
/3=5°8'*8
/S=330°3'*5
/S = 18°14'*3
j3=21 1°32'*3
/3=248°27'*0
/3=180°0'*0
1
2
3
4
5
6
6=0*1294
6=0*0590
1
C=0*0153
C=0*0737
C=0*0642
6=0*0270
C = -0*0597
1
1
1
1
5
6
0
7=290° 14*5
7=206° l6'*4
7=163° 19*2
7=252° 17*4
7=273° 32'-0
7=180°0'*0
1
2
3
4
5
6
1
1
D = 0 0284
D = 0*0455
6=0*0390
1
D = 0*0198
1
D = 0*0429
6 = 0*0179
D= -0*0083
1
2
3
1
5
i
6
1
0
J=199°28'*2
5=49° 15'*3
5=220°55'*3
5=257° 13*3
5=83°59'-9
5=180°0'*0
1
2
3
4
5
6
0 = 0*2265
0=0*1762
0=0-2199
1
0=0*1341
0=0-1469
6=0*0400
1
2
3
5
6
0=0*2715
1
1
1
1
1
0
0=324° 48'*8
0=278° 25'*5
o=211°4'*6
| 0 = 141°41'-0
o = 72°50'*9
o=180°0'*0
1
2
3
4
5
6
,
1
P=0*1098
P=0*0936
P=0*0097
P=0*0992
P=0-0699
6=0*0327
P— 0*0226
1
2
3
4
5
6
0
•87=292° 1 '*8
®-=101°28'*8
^=182°35'*5
•87=5° 40'*3
-27=43° 57 *6
■87=180°0'*0
1
2
3
4
5
6
1
R=0*0285
R=0-02l6
R=0*0407
R=0*0269
R=0*0453
R = 0*0343
R = — 0*0315
1
2
3
4
5
6
0
/9=342°57,-0
p=40°45'*9
J=39°8'*0
p=6l°35'*7
^=30° 13-3
p=0°0'*0
1
2
3
4
5
6
1
S=0-0508
S=0*0023
8=0*0452
S=0*0283
S=0*0565
S=0*0526
S=-0*0487
1
1
2
3
4
5
6
0
<r=44°29'*7
o'=280°53'*l
<r=186°38'*l
<r=95° 19*5
(r=304°41 '*1
ir=0o0'*0
1
2
3
4
5
6
DE. T. E. EOBINSON ON THE EEDUCTION OE ANEMOGKRAMS.
429
work in computing, has this advantage, that it permits the combining the constants
obtained at different periods by simple meaning, which the sine formula does not. It
also lends itself more easily to an examination of any influence which may be supposed
to change the coordinates periodically. Any such may be developed in a similar series,
and the sum or difference of the two will give the residual part which is to be accounted
for by other causes. If this residue be larger than the original periodic part, the
hypothesis must be rejected; and even though it be diminished, this is not sufficient
unless there be a priori evidence of a vera causa. As an example of this may be
mentioned one of the elements of the sun’s action. Its heating-power on a given day
depends, among other things, on the sum of the sines of its altitude during that day.
This sum
=2$™-e'dQ{sm lat. sin declin. — cos lat. cos decl. sin 6}
=2 sin lat. sin decl. X +2 cos lat. cos deck sin &,
6' being the value of Q at sunrise. If the value of this integral be computed for 12
values of <p, it can be developed in a series y=k-\-a cos <p+o sin <p-\-b cos 2 p+ &c. This
belongs to the midday of each month, and ought in strictness to be summed for the
entire month by means of the expression of deck in terms of <p ; but it is sufficient for
illustration, u is evidently diminished by y, and we have what would be found if the
altitude had no effect,
x=u-\-qyz=¥L-{-kqJrC,os <p(A+a#)-|-sin <p(0+ og'j + cos 2<p(B-J-#2')-J-&c.
If q, the measure of the altitude’s effect on the coordinates, were known, no more would
be required ; but a probable value of it is that which would make the sum of the squares
of the periodic parts of the residues or K — Jc) a minimum. This gives
<p <p
q(Sy2 - 1U2) = - S uy + 12K&
For K^=2-422 ; for lsJu= 4-723. With these I computed the series for x and x\
which need not be given, remarking merely that the coefficients of the first order are the
only ones much altered. It may suffice to give the variable parts of u, x ; u', x'.
January.
February.
March.
April.
May.
June.
July.
Aug.
Sept.
October.
Nov.
Dec.
2-109
1-016
0-778
0-032
2-758
2-630
-1-931
-1-258
-1-715
— 0*575
— 1-576
-0-299
0-438
0-680
0-217
0-886
-0-180
-0-150
-0-361
-0-929
-0-386
-1-397
1-658
0-467
3-170
1-030
2-190
0-778
-0-541
-1-092
-1-345
-0-137
-1-596
0-398
-2-068
0-420
-2-278
-0-100
-1-196
0-117
-0-102
-0-045
0-017
-1-092
0-173
-1-800
3-879
1-655
It seems from these numbers that the sun’s altitude may account for 0-27 of the
variation of W, and for 0-53 of that of S.
This discussion suggests the notion that the equatorial current which produces the
positive W and S coordinates may possibly be more constant than appears at first sight,
and that a part of these variations may be due to a current in the opposite direction
480
DR. T. R, ROBINSON ON THE REDUCTION OE ANEMOGRAMS.
caused by the solar action in the vicinity of the place of observation and varying with
the sun’s declination. Supposing qy to be that part of it due to the altitude, its mean
9
annual value would be V=2-721, about 06 of V' (page 412), and its D = 207° 8,-7.
Other periodical causes, such as the length of air traversed by the sun’s rays at different
altitudes, the difference of the earth’s daily and nightly radiations, and the amount of
watery vapour in the air, might be similarly taken into account.
I have already stated that I thought it useless to deal with the observations of single
days ; I, however, tried two experiments in this direction, which may be of some
interest, though the first of them was unsuccessful.
1. In many instances, even when the wind is moderate, there are variations in its
direction which suggest the notion that they are due to aerial whirlpools on so small a
scale that they are not likely to reach any other meteorological station.
I thought it might be possible to determine the constants of such a motion in the
following way. The curve described on such a supposition by the thread of wind which
passes the anemometer at a given station is that which would be traced by a pencil
fixed there on a plane revolving with an angular hourly velocity u round a centre which is
carried in a line inclined at the angle a to the axis of x with the hourly velocity V, | and n
being the coordinates of that centre at the origin of the time, and a the angular motion
there. It is obvious that we have
dx=dt\V cosa(l dy=dt{ V sina(l
Then at successive hours equating ^ to tangD, and dx2-\-dy\ to s, I would be able
to get values of the unknown quantities. But against this is my ignorance of the rela-
tion between cd and this distance from the centre of the circle, which is not given in any
book to which I can refer. Newton, in the vortex which he considers, gives it inversely
as the distance. It is probably nearer the inverse square. Either of these suppositions
would make direct integration impossible, so I gave up the project.
2. The other was an attempt to determine from these observations the existence of
an atmospheric tidal current. As in the case of the ocean, so in the atmosphere, the
air must be heaped up in the meridian passing through the moon, or a little to the east
of it ; and this elevation must be accompanied by a horizontal current.
Laplace (Mec. Cel. ii.) has shown that the maximum air-tidal current is 0,07532 metre
in a centesimal second *, which in English measure and time is 0T95 mile in an hour.
He, however, gives no indication of the phase of this maximum, or in what stratum of
the atmosphere it occurs. At the earth’s surface, owing to friction and other causes, it
must be considerably less than the above value, and the analogy of sea-tides is too slight
to give much assistance in the research. It may, however, authorize us to assume that
on opposite sides of the lunar meridian the directions of this current will be opposite.
* It is to be regretted that in this noble work Laplace used the centesimal division of the quadrant, and the
decimal and centesimal divisions of the day. Whatever be the fate of the metric system, it is very unlikely that
either of the others will be generally adopted.
DB. T. E. ROBINSON ON THE REDUCTION OE ANEMOGRAMS.
431
Having no data to guide me in detecting the most favourable Lunar hours, I began by
comparing the Ws for 0h, 6h, 12h, 18h, and 3h, 9h, 15h, 21h. I soon, however, found that
this involved too much labour, and confined myself to the last hour.
Calling C' the current, C'=|(W-W'\,=|/W-W'\. In this I made no attempt to
\ 21 3 / \ 9 15 /
allow for the sun’s elongation from the moon, or for their declination, nor for the
horary changes of the coordinates, as the selected lunars are nearly uniformly distributed
in each of the 24 common hours.
By a Table with the moon’s hourly motion in Bight Ascension for argument I found
the time which should be added to the Greenwich time of its culmination to obtain the
common time of the above-named lunar hours at Armagh, and entering the Journal with
these I obtained for each day two values of ^(W — W'), belonging to the upper and
lower culminations. From the irregularity of these values it might seem hopeless to
get any result ; but I pursued the inquiry in hopes of ascertaining the limits within
which the mean of a considerable number of observations (even though very discordant)
might be depended on.
I only took the first six months of the year, as the results which they gave were quite
satisfactory.
Table X.
Month.
Current.
No.
PE
Weight.
CxW.
Januarv
0*2289
404
±1-939
1-000
0-2289
The mean according to the
weight.
C'= 0-0906.
Not differing much from the
single mean.
February
0-1549
376
±1-809
1-020
0-1580
March
-0-0414
415
±1-886
1-082
— 0-0459
April
Q*
o
©
©
396
±1-737
1-190
0-0084
May
0-0844
423
±1-345
2-175
0-1837
June
0-1125
404
±1-247
2-416 ■
0-2720
0-0911
2418
±1-661
8-883
0-8051
The weights are proportional, the least, that for January, being taken as unity. It
will be observed that these probable errors are far less than those given in page 415 ; but
it should be recollected that here the variations can only occur within 6 lunar hours,
while in the other case they range through months and years. Even so there are occa-
sionally very great and startling changes when a gale bursts out suddenly or suddenly
ceases. There were two values of W— W' above 40, and three above 30. Yet with all
this I think the result is very remarkable. I do not pretend to assert that this value of
C' really represents the tidal current at these hours, though it is in the right direction
and of not improbable amount ; for it may be some uncompensated residue of the horary
changes. But it is of great importance, as giving what must be a close approxi-
mation to the real value of the average air-tidal stream, and as verifying my former
432
DE. T. E. EOBINSON ON THE SEDUCTION OE ANEMOGEAMS.
statements, that casual irregularities are eliminated from the mean of a large number of
observations. Still I think that a truer result might be obtained by omitting extremely
aberrant observations ; but it becomes a question to what extent this should be done.
I think all maybe rejected which exceed four times the largest probable error; in other
words, whose probability is less than 0-0228. This is for W— W' all above 15. The
number of these is 58, and the results after their exclusion are given in Table XI.
Table XI.
Month.
Current.
No.
PE
Weight.
CxW.
January
0-1498
386
±1-592
1*321
0*1979
The mean according to the
weights is C"= 0*0559-
February
0-2483
366
±1*607
1*317
0*3204
March
-0-0423
406
±1*726
1*266
— 0*0535
April
-0-0590
381
±1*657
1*289
— 0*0760
0*0024
May
0*0010
419
±1*262
2*438
June
0-0718
402
+ 1*204
2*496
0-1753
0*0608
2360
±1*443 10*127
0*5665
The probable errors are less, and the weights greater than in the other case, so that
C" is probably a better value than C'.
It is possible that this mode of proceeding might give the horary changes of the
coordinates more correctly than the simple comparison of the numbers in Table III. ;
but the labour of computation would be much greater.
[ 433 ]
XVI. The Croonian Lecture. — Experiments on the Brain of Monkeys (Second Series) .
By David Ferrier, M.A., M.B. , Professor of Forensic Medicine , King's College.
Communicated by Dr. Sanderson, V.P.B.S.
Received April 27, — Read May 13, 1875.
In a former memoir presented to the Royal Society the author described the results of
electrical irritation of localized regions of the brain of monkeys. This memoir contains
the details of experiments relating chiefly to the ablation or destruction of these localized
centres, with the view of determining the significance, as regards motion and sensation,
of the phenomena resulting from electrical stimulation, and for the purpose of ascer-
taining the function of those parts which give no external response to irritation. No
originality is claimed either for the idea or method of carrying out these experiments.
The plan chiefly followed in the destruction of localized regions in the hemispheres
was the application of the cautery, either in the form of a red-hot iron, or of the gal-
vanic cautery, or of Bruce’s blowpipe cautery, according to special necessities or con-
ditions. The advantage of this method is that destruction of the grey matter can be
caused rapidly and effectually, without risk of haemorrhage or interference with the
integrity of surrounding parts. By the same method a part can be severed from the
hemispheres without risk of haemorrhage.
The details of observation are given in full as the best method of indicating the course
of events following each operation and the data on which the conclusions are based.
Extirpation of the Frontal Lobes.
It has already been stated that the antero-frontal regions of the hemispheres give no
response to electrical stimulation. Only one exception to this statement is to be made
(see Exp. I.), viz. that in one case irritation of these regions caused the eyes to be turned
to one or other side, according as the electrodes were placed on the opposite hemisphere.
Experiment I.
December 2nd, 1873. — Avery lively, active, and intelligent monkey was placed under
the influence of chloroform, and the frontal extremities of both hemispheres exposed as
far back as the anterior extremity of the supero-frontal sulcus (fig. 1), the infero-frontal
regions being exposed to a corresponding extent. On electrical irritation of the upper
surface of these regions the eyes were occasionally turned to the opposite side. No results
could be observed to follow application of the electrodes to the orbital region.
The exposed portions of the hemispheres were in this instance divided rapidly by
MDCCCLXXV. 3 M
434
DE. D. FEEEIEE ON THE BEAIN OF MONKEYS.
means of a scalpel, and the cut surface touched with perchloride of iron to still the
The operation was completed at 4.40 p.m.
When the chloroform stupor had passed off, which occurred in a few minutes, the
animal sat up, but nodded off to sleep, opening its eyes faintly when a noise was made,
5 p.m. Eagerly drank some sweet tea held to its lips, but immediately went to sleep
when it was withdrawn. Took a piece of bread and butter held before its face and
began to eat, but after a bite or two went to sleep, holding the bread in its hand.
When it was awakened by cold air blown in its face, at which it expressed annoyance,
it woke up and began to eat again greedily.
5.15 p.m. The scalp was sewn up. The animal retained sensation. After the opera-
tion the animal took some food and again went to sleep.
December 3rd. — The animal is alive and well. Eats and drinks spontaneously, but fre-
quently subsides into a doze while eating. Is constantly tending to sleep when it is not
kept awake by external stimuli. It pays little or no attention to any thing going on
around unless stimuli are applied to it directly. Formerly it used to exhibit the utmost
curiosity in every thing going on around it. A lighted match held before its face caused
it to exhibit some curiosity. Touched it several times ; each time showing signs of pain
and rubbing its fingers vigorously. Formerly the sight of fire used to cause it to run
away.
December Mh. — The animal remains in much the same state, sitting quietly, feeling the
wound, which is oozing, and licking its hand. Occa-
sionally it runs hither and thither in the cage in an aim-
less manner. Often subsides into a dozing state, but is
easily roused by sounds, touch, &c. Eats and drinks of
its own accord in a mechanical way, frequently going to
sleep the while.
Retains all its senses and muscular power.
Gives evidence of sight by shrinking and holding its
hands to protect its head when threatened with a stick.
Whatever is placed in its hand is mechanically raised
to its mouth.
December 5th. — The condition is in all essential respects
unaltered. Another monkey was placed in the cage beside
it. Of this it took little or no notice. Formerly it took
the greatest interest in examining any companion placed
beside it.
The continual sleepiness continues.
Fig. 1.
r_, . Upper view of the hemispheres of the
I he animal died from exhaustion on the 7th without monkey. The shaded part in the frontal
ving exhibited any further symptoms. lob?s indicates the extent to which the
° J J 1 brain was destroyed m Experiment 1.
Post mortem Examination. — The frontal lobes were a— the supero-frontal sulcus.
DE. D. FEBEIEE ON THE BBAIN OE MONKEYS.
435
found to have been removed by a line corresponding to that described and indicated in
fig. 1.
The cut surface had fungated and was protruding through the openings in the skull.
The rest of the brain had a normal appearance.
Experiment II.
January 13 th, 1875. — A mischievous, good-tempered, and intelligent monkey was
placed under the influence of chloroform, and the frontal lobes exposed on both sides.
By means of the wire cautery the lobes were severed by a transverse line cutting across
the anterior extremity of the supero-frontal sulcus. The division was carried down to
the orbital surface, and the severed portion of brain removed.
The operation was finished at 4 p.m.
4.15 p.m. The animal drank some tea held to its lips, but lay quiet and had not yet
attempted to get up.
5 p.m. Now moves about, which it does rather unsteadily, but evidently sees where it
is going, as it avoids obstacles in its path.
5.45 p.m. Sits quietly with its head down when undisturbed, and makes scraping
movements with both hands. Expresses great annoyance when its face is blown on.
Tobacco-smoke held to its nostrils caused it to start back and run away.
7 p.m. Sits with its head down, engaged in picking at imaginary objects in front of it.
Can find its way in and out of its cage when roused to action. Turns its head round
and looks when called to, giving full evidence of its sense of hearing.
8.10 p.m. Run out of its cage when the door was opened. Runs about and jumps on
furniture when roused. Otherwise, when left to itself, it sits down and picks at imaginary
objects on the floor. Took a piece of apple offered to it and ate it.
11.15 p.m. Ran about the room when let out of its cage, occasionally stopping to pick
up things lying on the floor, and turning round to look when called to. Climbed up a
chair and then relapsed into its usual position with its head down, and began to pick
away with both hands at nothing.
January 14 th. — 10 a.m. When taken out of its cage wandered restlessly around the
room. Took a little food offered to it, and then capsized the dish. When placed in
its cage picked up some pieces of bread, and sat and ate them contentedly ; then rose
and marched round and round. After this subsided into a dreamy-like doze, and then
after a few minutes began its picking and scraping movements.
11 a.m. Is busily engaged picking up pieces of bread lying in its cage, carefully
scraping and eating them. Runs about the cage occasionally in a restless manner, and
then subsides into its quiet attitude, picking and scraping among the straw &c. in its
cage.
5.30 p.m. When let out it ran about the room for some time, jumping on chairs &c.,
and then after sitting still for a few minutes, picking as usual, started up and ran about
again in the same aimless manner.
3 m 2
436
DE. D. FEEKIEE ON THE BEAIN OF MONKEYS.
Took some food offered to it, but after eating a little set to work to scatter it all
about.
10.15 p.m. Is found clinging to its cage with hands and feet, apparently asleep, and
takes no notice of my approach.
January 15 th. — 10.30 a.m. This morning when taken out seemed unwilling to move
about. When roused and pushed, seemed to walk somewhat unsteadily, and as if its
limbs were clogged.
Thinking that the motor centres were becoming involved in softening, I chloroformed
the animal to death.
Post mortem Examination. — On examination of the brain it was found that the frontal
lobes had been cut off on both sides according to the line indicated, viz. in a line passing
transversely through the anterior extremities of the supero-frontal sulci. The plane of
section sloped somewhat from above downwards, leaving the posterior half of the orbital
surface uninjured.
The cut surface was projecting so as to protrude through the openings in the skull
and reach the under surface of the scalp.
Some degree of softening had extended from the edges of section on both sides to the
proximity of the antero-parietal sulcus, but slightly more on the left than on the right
side (see tigs. 2 & 3). The rest of the brain was round in appearance. The olfactory
bulb and tract on both sides had escaped injury.
Figs. 2 & 3 represent the upper surface of both hemispheres and side view of the left hemisphere of the
brain of the monkey. The line cutting across the frontal regions at the anterior extremity of the supero-
frontal sulci indicates the line of section of the lobes in Experiment II. The parallel lines indicate the extent
of brain-substance removed. The shading posterior to the line indicates the extent to which softening had
advanced, b = the antero-parietal sulcus (Htjxley).
DR. D. FERRIER ON THE BRAIN OF MONKEYS.
487
Experiment III.
March 16£A, 1875. — The frontal lobes of both hemispheres were exposed in a small
active and intelligent monkey, and by means of white-hot wires the frontal lobes were
severed from the rest of the hemispheres by a line passing approximately through the
anterior extremity of the supero-frontal sulcus on each side. The division, however, was
slightly further back on the left than on the right side. The operation was completed
at 1 p.m.
A few minutes after being let loose it sat up, and seeing a piece of cotton-wool lying
before it, took it up and began tearing it with its teeth. Offered a piece of apple, it
seized it and ate it.
I. 15 p.m. Walks about the room pretty steadily. There is no affection of its mus-
cular power nor of sensation ; it sees where it goes, turns its head when called to, and
smells and eats fruit offered to it.
6 p.m. Animal is found sitting quietly in its cage. It used to be very discontented at
being shut up, and kept up a continual whining. Offered some fruit, it smelt it and
ate it. When let out of the cage it ran about the room, giving full evidence of the
retention of all its special senses and powers of motion.
7 p.m. Sits in the cage diligently occupied in examining and picking its hands and
feet and woollen jacket.
Has rather a stolid look, and makes no attempt to move away when a hand is put
out to lay hold of it.
Formerly it was very timid and disliked being touched.
8 p.m. Eagerly drank some sweet tea.
When let out of its cage it walked about a little, and then sat down and went on with
its usual employment of examining and picking at its hands, feet, and coat.
9.30 p.m. Found sitting in same position at the same employment. Takes no notice
of whether the room is suddenly lightened or darkened, but goes on with its occupation
all the same.
II. 80 p.m. Found asleep on its perch. On the gas being turned up and the animal
awakened, it began to examine its hands &c. as before. The cat happening to come
into the room caused it to give a shriek and appear terrified.
March 11th. — 8.30 a.m. Ate some breakfast; came out of its cage when the door
was opened, and marched about the room. An hour or two afterwards another monkey
was placed in the cage beside it. Its companion examined it with curiosity, but it sat
quietly and made no sign of interest. Gradually sidled up to it, however, and sat
hugging it, enjoying the warmth of contact.
2 p.m. When let out of its cage it ran about a little followed by its companion.
After a few minutes sat down in a corner and began to examine and pick its hands,
feet, and tail. Makes no resistance when its companion pulls it about rather roughly
and examines its head.
438
DE. D. EEEKIEE ON THE BEAIN OE MONKEYS.
5.30 p.m. Condition remains as before. Frequently gets a tug and a bite from its
companion, who seems annoyed at its occasional restless movements.
Later in the evening when examined it exhibited no new symptoms.
March 18 th. — 10.30 a.m. Eemains as before. Sensation and voluntary motion are
unimpaired. Eats and drinks heartily, finding its own food in the cage.
When the door of its cage is opened it comes out and runs about, and then settles
down quietly in a corner. Allows itself to be touched and taken hold of, which its
companion resents very much. Has lost its former timidity and shyness. Pays no
attention to any thing going on around, but sits picking its hands and feet unless directly
disturbed, when it gets up and runs about.
8 p.m. Remains in same condition. Eats and drinks heartily.
March 19 th. — 10 a.m. Ate breakfast heartily. When taken out of its cage it ran
about the room in a wild manner, jumping on furniture. Gives a little grunt of recog-
nition when called to by name. After running about it subsided into a dull stupid-
like state, scratching its sides occasionally or the edges of the wound, which would
seem to itch. The wound looks tolerably dry and healthy.
Later it sat down by the fire close to its companion, but occasionally got up and made
some restless movements, whereupon it got a tug or bite from its companion, who
seemed to lose patience with its waywardness.
5 p.m. Found in a dozing state, but woke up and drank some tea and ate some bread
and butter, after which it again subsided into a dozing condition.
March %)th. — 9 a.m. Ate and drank. There is no difference observable as regards
sensation or voluntary motion. During the day sat quietly except when roused, when
it would get up and run about wildly for a few minutes and then subside into its sleepy
condition.
5.30 p.m. Gave a screech when the cat was brought into the room, but after a short
interval walked up to it half in terror and half showing fight.
Continued much the same as before during the rest of the day.
March 21 st. — 11 a.m. Ate some breakfast, but appears much less active than before.
Inclined to climb about along the inside of its cage.
When taken out it ran about a little and then sat down, clinging to some object.
Sees and hears as before, and other senses seem unimpaired. A few minutes after it
had been let out of its cage it returned, and began climbing restlessly on the sides of its
cage, occasionally resting quietly with its eyes closed as in sleep.
1 p.m. Was found climbing restlessly along the inside of the cage. Pays no attention
to its companion, and does not seek to sit beside it as usual. Utters a short grunt when
called to. When taken out and placed before the fire it sat perfectly still with its head
bent. On being disturbed by the movements of its companion it would get up and run
about a little.
It was observed that its movements were less free than before, and that it walked as
if its limbs were clogged.
DR. D. FEEEIER ON THE BRAIN OE MONKEYS.
439
2 p.m. Was found sprawling against the wall of the room in a corner as if it wished
to climb.
When set to move about it picked up things lying on the floor, smelt them, and occa-
sionally put them in its mouth. Eats and drinks as usual.
5.30 p.m. In attempting to drink some tea, of which it was very fond, its head was
observed to shake so that it could scarcely hold its lips to the fluid. When its head
was held steady it drank with avidity.
Eig. 4. Eig. 5.
Fig. 4 represents the upper surface of the hemispheres, fig. 5 the right, and fig. 6 the left hemisphere of the
brain of the monkey. The shaded parts in the frontal lobes in all the figures indicate the extent of destruction
of the brain-substance in Experiment III.
This paralysis agitans was taken as an implication of motor centres, and therefore the
animal was chloroformed to death to prevent complications.
Post mortem Examination. — On removal of the scalp the brain was found protruding
on each frontal region, the hernise reaching the under surface of the scalp. The sur-
440
DE. D. EEKKIER ON THE BEAIN OE MONKEYS.
faces were suppurating slightly. The edges of the bone looked healthy, and there was
no oedema of the scalp or surrounding parts.
The dura mater was of normal appearance, and stripped readily from the surface of
the hemispheres, which looked somewhat “ wet ” but otherwise normal.
On removal of the brain the base and cranial nerves were all found intact. The
olfactory tracts and bulbs had escaped injury, though the bulbs were slightly covered
with pus.
On opening the ventricles slight excess of fluid was found in them, but the ganglia
were quite normal in appearance. The anterior cornua of the ventricles had not been
penetrated.
The abnormal appearances were entirely confined to the frontal lobes. The hernial
prolongations were of the size of the openings in the frontal bone, and were bounded by
a sharp line somewhat congested, indicating the line of section of the lobes.
In the right hemisphere the line of section struck the anterior extremity of the
supero-frontal sulcus, and sloping somewhat downwards and forwards had struck the
orbital surface in a plane anterior to the superior line of section.
In the left hemisphere the line of section was situated slightly posterior to that on
the right, cutting across the supero-frontal sulcus, and sloping forwards like the right.
The posterior half of the orbital surface was intact on both sides.
The softening at the margins of the section did not extend into the antero-parietal
sulcus.
There was some softening between the lips of the longitudinal fissure at the base, but
this did not extend beyond the perpendicular plane of section.
The septum lucidum was uninjured.
The rest of the brain was intact.
An analysis of these three experiments elicits, with individual differences, certain
common and fundamental facts. They show conclusively that an animal deprived of
its frontal lobes retains all its powers of voluntary motion unimpaired, and that it con-
tinues to see, hear, smell, and taste, and to perceive and localize tactile impressions as
before. It retains its instincts of self-preservation, retains its appetites, and continues
to seek its food. It is also capable of exhibiting various emotions. The result, therefore,
is almost negative, and the removal of a part of the brain which gives no external response
to electric stimulation exercises no striking positive effect ; and yet the facts seem to
warrant the conclusion that a decided change is produced in the animal’s character and
disposition. For this operation I selected the most active, lively, and intelligent animals
which I could obtain. To one seeing the animals after the removal of their frontal
lobes little effect might be perceptible, and beyond some dulness and inactivity they
might seem fairly up to the average of monkey intelligence. They seemed to me, after
having studied their character carefully before and after the operation, to have under-
gone a great change. While conscious of sensory impressions, and retaining voluntary
power, they, instead of being actively interested in their surroundings, ceased to exhibit
DR. D. FERRIER ON THE BRAIN OE MONKEYS.
441
any interest in aught beyond their own immediate sensations, paid no attention to, or
looked vacantly and indifferently at, what formerly would have excited intense curiosity,
sat stupidly quiet or went to sleep, varying this with restless and purposeless wanderings
to and fro, and generally appeared to have lost the faculty of intelligent and attentive
observation.
Perhaps this condition may be attributed to the constitutional disturbance excited by
the operative procedure alone ; but the effects of this are capable in a great degree of
elimination ; and in the record of subsequent experiments it will be seen that after
operations of equal severity marked differences are observable according to the part of
the brain which was destroyed. The animals seem to bear the operation with com-
paratively little constitutional disturbance ; and this is testified by the fact that they
continue to eat and drink heartily within a few hours, and often less, after a large
portion of the brain has been removed.
The phenomena occurring towards the latter end of the periods of observation are
more to be regarded as signs of constitutional disturbance, and as indications of the
advance of inflammatory softening or morbid process into other cerebral regions. The
spasmodic motor affections, as well as the paretic condition seen in regard to certain
movements, are to be explained by the implication of motor centres, the nature and
position of which will be illustrated in the next series of experiments.
Destruction of Motor Areas— Begions of the Fissure of Bolando.
In my former Memoir I have related the results of electrical irritation of regions
situated in the immediate neighbourhood of the fissure of Kolando, which show that
certain definite and purposive movements of the hand, foot, arm, leg, face, and mouth
result from the electrical stimulus applied to individual areas capable of more or less
exact localization. The experiments next to be related have reference to the effect of
destruction of these centres, collectively and individually, on the power of voluntary
motion.
Experiment IV.
June 18 th, 1873. — The right hemisphere of a monkey had been partially exposed and
experimented on for the purpose of localizing the regions of electric stimulation.
The part exposed included the ascending parietal and postero-parietal convolutions,
the ascending frontal, and the posterior extremities of the three frontal convolutions.
After having been under experimentation for eight hours the animal recovered
sufficiently to sit up and take food. The wound was sewn up, and the animal placed in
its cage.
June 19 th. — The animal is apparently as well as ever, eating and drinking heartily,
and as lively and intelligent as before. No change was perceptible during the whole
of this day.
June 20 th — The wound was oozing, and the animal was less active ; but there was
MDCCCLXXV. 3 N
442
DE. D. EEEEIEE ON THE BEAIN OE MONKEYS.
The angle of the month was
Kg. 7.
no diminution of sensation or voluntary motion. It closely watched flies buzzing about,
and frequently made attempts to catch them.
Towards the afternoon it began to suffer from choreic spasms of the left angle of the
mouth and of the left hand. There was no loss of consciousness. The animal was
apparently annoyed by the spasmodic action of its mouth, and frequently endeavoured
to still them by holding its mouth with the other hand.
Towards the close of the day the spasms frequently repeated, became more intense,
and exhibited an epileptiform nature, the convulsions of the left side of the body
becoming general.
This state continued till
June 23rd. — Left hemiplegia had manifested itself,
drawn to the right, the left cheek-pouch was
flaccid and full of food, there was almost total
paralysis of the left arm, and partial paralysis
of the left leg. The pupils were equal, and
there was no paralysis of the left eyelids appa-
rently. The animal still maintained an intel-
ligent aspect, but seemed disinclined to move
on account of the powerlessness of its left side.
June 24 th. — Hemiplegia is complete on the left
side, hand, foot, and face. The animal moved by
means of its left limbs, dragging the right after it.
The animal died from exhaustion on the 27th.
Post mortem Examination. — The whole of the
exposed part of the brain was in a state of
softening and suppuration, projecting through
the opening of the skull.
The extent is indicated in figure 7.
Eig. 7 represents the right hemisphere of
the Tbrain of the monkey. The shaded part
indicates the extent of destruction of the grey
matter in Experiment IY.
c=the fissure of Kolando.
d = the postero-parietal lobule or upper end
of the ascending parietal convolution.
e = the ascending frontal convolution.
The brain otherwise was normal. The softening was confined to the surface of the
hemisphere, and did not extend to the ganglia, which were normal.
In this experiment we have a general affection of the whole of the motor region of
the right hemisphere, beginning with inflammatory irritation, which showed itself in
choreic spasms passing into general epileptiform convulsions, and ending ultimately,
as softening advanced, in complete left hemiplegia.
This result followed destruction of the cortical motor centres alone.
Experiment V.
January 5th, 1875. — A macaque of large size was placed under the influence of
chloroform, and the ascending frontal, ascending parietal, and postero-parietal convolu-
tions of the left hemisphere exposed.
Electrical irritation was applied, and the movements already related as following
DR. D. EERRIER ON THE BRAIN OE MONKEYS.
443
stimulation of these regions produced. The animal was allowed to recover consciousness
completely at 5 p.m. It remained for two hours as well as before to all appearance.
At 7 p.m. by means of the blowpipe cautery the surface of the postero-parietal
lobule (foot-centre), of the ascending parietal (hand and wrist centre), with a small
portion of the upper extremity of the ascending frontal convolution (arm and leg
centres) were destroyed.
Though the animal was quite conscious it expressed no sign of pain or uneasiness
during the process. Once during the passage of the cautery along the ascending
parietal convolution a partial closure of the fist occurred, seeming as if the heat had
caused in some degree the same effect as the electric stimulus.
On being set free the animal jumped away, but staggered and fell over on its right
side. It was observed that when the animal moved, it did so by the aid of the left arm
and left leg, dragging the right leg on the floor. When it rested, the right leg was
seen to straddle outwards, as if the power of adduction had been lost. There was no
muscular resistance to the free movement of the ankle in any direction, but there was
resistance to forcible extension of the leg. The right arm was kept flexed at the elbow,
but the wrist dropped and the hand hung flaccid. There was no resistance offered to
flexion and extension of the wrist, but decided muscular resistance to straightening
the arm. The animal made no use of its right hand to grasp, or in progression, but it
retained the power of flexing the right forearm.
The sensibility of the right side was unimpaired, as judged by the expression of pain
and annoyance when the limbs were pricked or pinched.
The great difficulty it experienced in walking, or sitting steadily upright, caused
the animal to growl in annoyance each time it staggered.
Otherwise the animal was well, and ate and drank as before within an hour after the
operation.
The animal was then subjected to an experiment for destruction of the angular
gyrus (see Exp. VIII.), and its further history and the results of the post mortem
examination are detailed under Exp. VIII.
This experiment demonstrates very conclusively that the destruction of cortical centres,
irritation of which by the electric stimulus gave rise to very definite movements of the
hand and foot, caused motor paralysis of the same movements and of none other ; and,
as will be found, the paralysis remained permanent up till the time of death.
Experiment VI.
February 26 th, 1875. — A monkey was chloroformed, and the left hemisphere was
exposed on the region which former experiments had indicated as the centre for the
biceps (/, fig. 8). By electrical irritation the region was accurately defined, and the
grey matter destroyed by means of the blowpipe cautery. The animal was conscious,
and lay perfectly quiet during the operation, though unbound. When placed on the
floor the animal sat very unsteadily ; and the cause of this was seen to be that the right
3 n 2
444
DR. D. FERRIER ON THE BRAIN OE MONKEYS.
arm hung by the right side in a state of flaccid extension. When urged to move it
used the left limbs and the right leg as before, but had lost the power of flexing the
right arm. In trying to walk, it frequently fell over on its right side.
An hour after the operation the paralytic condition of the right forearm remained
very marked ; the loss of voluntary power was
confined to the same action as was excited by
the electric stimulus.
The animal died from an overdose of chloro-
form when about to be subjected to a further
operation.
Post mortem Examination. — The only lesion in
the brain was a cauterized spot of the size of
a threepenny bit, corresponding to the bicipital
centre in the ascending frontal convolution (see
fig. 8).
These three experiments, besides others where
the same regions became involved indirectly as
the result of other experiments*, afford a simple
and conclusive proof that the movements which
are excited by the application of the electrodes
to the surface of the hemispheres in these regions are due to excitation of the grey
matter of the cortex, seeing that destruction of these same areas causes paralysis of
the same movements, while sensation remains unafiectedf.
In the first experiment the more or less complete destruction of the cortex in the
region of the fissure of Rolando caused complete hemiplegia on the opposite side of
the body, affecting all the unilateral movements capable of being called into play by
the electric irritation. In the next two, only those movements were paralyzed which had
their special centres destroyed in the cortex of the opposite hemisphere.
Fig. 8.
Fig. 8 represents the left hemisphere of the
brain of the monkey.
The shaded spot on the ascending frontal
convolution marked by the letter / indicates
the extent to which the grey matter of the
surface had been destroyed in Experiment YI.
* See Experiments VII. and X.
t I am aware that the conclusion here stated, and which seems to me well established by the above facts,
apparently stands in diametric contradiction to the conclusions which Hermann (‘Archiv fiir Physiologie,’
Band x. Hefte 2 & 3, p. 77) has arrived at from a few similar experiments on the motor centres of the brain of
dogs. He concludes that because dogs ultimately recover completely from such disturbances of motor func-
tions as are at first caused by the ablation of cortical centres, these centres cannot be motor in the true sense
of the term. Experiments on dogs, however, are not strictly comparable with experiments on monkeys ; and
the relative subordination and association of lower centres in different animals is a fact which ought to be
carefully considered. The explanation I have elsewhere given (‘West Riding Reports,’ vol. iii.) of how asso-
ciated movements, such as those of the limbs of dogs, can still be carried out through the associated action of
lower centres so long as the cortical centres of the other hemisphere are intact, is quite in harmony with the
facts Hermann gives, and is further demonstrated by the complete paralysis of voluntary motion which follows
the destruction of corresponding regions in both hemispheres in these animals.
DR. D. FERRIER ON THE BRAIN OF MONKEYS.
445
Experiments relating to the Localization of Sensory Perception* .
Certain movements of the eyes, ears, and nostrils, obtained by stimulation of certain
convolutions already described, led me to regard them as the external manifestations of
sensations thus subjectively aroused; and the following experiments were directed to
test the truth of this hypothesis, and to determine to what extent sensory localization
in the brain might be possible.
Destruction of the Angular Gyrus.
As already related, electric stimulation of this convolution caused movement of the
eyeballs to the opposite side, with a direction upwards or downwards, according as the
anterior or posterior division was stimulated, and frequently the pupils contracted and
the animal tended to close the eyes.
Experiment VII.
November 18 th, 1873. — The angular gyrus of the left hemisphere of a monkey was
exposed, and after electric irritation, causing the
movements already described, the whole of this
convolution, with the upper part of the superior
temporo-sphenoidal convolution situated between
the two limbs, was seared and destroyed with
the galvanic cautery (see fig. 9). The left eye
was then securely sealed up with plaster, and the
animal left to recover from its chloroform stupor.
A few minutes after it began to struggle a
little, as if endeavouring to rise, but was unable
to get on its legs. Half an hour after it sat up,
and began to grope about cautiously, but made
no efforts at progression. It made no sign when
a light was approximated to its eye. It did not
flinch when lifted up and its face brought quite
up to the light.
It had retained its sensation as regards hearing
and touch, starting if a noise was made, and expressing annoyance if it was pinched.
When placed in its cage beside two other monkeys, it clung to the bars of the cage,
and took no notice of its companions. It would not stir from the position it assumed.
A little later sat down in its cage, with its head covered with its hands.
An hour having elapsed, it was taken from the cage and the left eye unbandaged.
Immediately on this being done, it looked around, and seeing the door of the cage
open, ran nimbly and made its way among its companions.
* By this term, as also by the term “ sensation ” which I sometimes use, I wish to signify the fact of
conscious discrimination of impressions as distinct from the mere sensory impressions themselves.
Fig. 9.
Fig. 9 represents the left hemisphere of the
brain of the monkey.
The shading which occupies the whole of
the angular gyrus and the upper angle of the
superior temporo-sphenoidal convolution indi-
cates the extent to which the grey matter was
cauterized in Experiment VII.
446
DE. D. EEBKIEE ON THE BKAIN OE MONKEYS.
When taken out again, and the door shut, it ran back, looking at its companions,
and desirous to gain admittance.
When held np to the light it flinched and averted its head.
The transition after the bandage was removed was of a striking character, and indi-
cated an evident restoration of sight which had been lost.
Next day (Nov. 19) the animal looked perfectly well, running about, eating and
drinking as usual.
An experiment was then made with the view of ascertaining whether the blindness
of the right eye had continued. The left eye was again bandaged up as before, and
the animal placed on the floor. It immediately ran up to the cage, and putting its
hand through the bars into a dish of water began to lap it.
Sight had therefore returned, notwithstanding the destruction of the angular gyrus on
the left side.
The animal died on Nov. 24 from suppuration and necrosis of the skull, having also
become paralyzed on the right hand.
Post mortem Examination. — The angular gyrus and the ascending parietal convolu-
tions were softened, and the hemisphere fungating from the orifice in the skull. The
abnormal appearances were confined to the surface of the hemisphere. No drawing
was made of the exact extent of the softening ; but the paralysis of the right hand coin-
cided with the destruction of the ascending parietal convolution. This experiment served
to show that destruction of the angular gyrus resulted in blindness of the opposite eye,
and that this loss of visual perception was only of temporary duration, compensation
having been effected within a period of twenty-four hours.
Experiment VIII.
January bth, 1875. — The subject of this experiment was the same monkey spoken of
under the head of Exp. V.
Two hours after the destruction of the motor centres alluded to, the animal was
again chloroformed, and the angular gyrus clearly exposed, the left eye closed with
plaster, and the animal allowed to recover.
On returning to consciousness it followed my movements with its right eye, and indi-
cated its sense of hearing by turning its head and looking when called to. Took some
fruit offered to it in its left hand, and sat contentedly eating it. It seemed disinclined
to move on account of the motor paralysis of its right side.
It sat with the right leg doubled up under it, and resting the internal malleolus on
the floor. Sometimes it supported the right hand with the left. Expressed annoyance
when pinched. The animal having thus recovered from the operation of exposure of
the brain, it was taken and the angular gyrus carefully destroyed by means of the
cautery, no more than two hours having elapsed since the first operation.
When let loose, it moved about a little when nudged, but would not move of its
own accord. When forced to move, it avoided obstacles as if it still saw. On exami-
DR. D. FERRIER ON THE BRAIN OF MONKEYS.
447
nation it was found that the bandage had slipped, and that the left eye was partially
open. On this defect being remedied, it put up its left hand, and tried to pull the
bandage from the eye. On this being prevented, it sat still and would not move.
When pushed and forced to move on, it ran its head against every thing in its way.
When removed into another room it sat still with its head bent, and would not stir.
Would not come when called to.
When taken back and placed beside its cage it still refused to move, and grunted
annoyance if disturbed, or rushed with its head against any thing in its way. After
it had remained for an hour in this condition the bandage was removed from its left eye.
On this being done, it began to look around, and on being called to by name, ran to
me and tried to climb on to my knee as it had
used to do. This it did on three separate occasions.
The difference in its attitude after the bandage
was removed was as striking as in Exp. VII., and
indicated restoration of sight.
January 6th. — On account of the paralytic
condition of its right side, and the suppuration
going on in its wound, it was chloroformed to
death.
Post mortem Examination. — The postero-pari-
etal lobule, ascending parietal, and upper part of
the ascending frontal convolutions, with the an-
gular gyrus were softened and disorganized (see
fig. 10). The rest of the brain was quite normal
in appearance.
Experiment IX.
April Itli, 1875.— This animal was used for an experiment on the superior temporo-
sphenoidal convolutions on both sides. These were exposed; but previous to their
destruction the angular gyrus was exposed on the left side for the purpose of demon-
stration of the effects of destruction of this convolution to Dr. Burdon Sanderson and
Dr. Lauder Brunton. At 3.30 p.m. the angular gyrus was exposed, and its surface
destroyed accurately by means of the blowpipe cautery.
The left eye was securely closed by means of plaster, and the animal placed on the
floor.
After a few minutes it began to move about, which it did very irregularly, some-
times going backwards, and occasionally turning round and round.
4.20 p.m. The animal is more lively, but sprawls about on the floor, and does not make
any regular progression. Drank some tea held to its lips.
4.55 p.m. Answers with a grunt, or makes mouths when called to. Sprawls about on
the floor or goes backwards. When placed close to the door of its cage makes no
Fig. 10.
Fig. 10 represents the left hemisphere of
the brain of the monkey, the shaded part indi-
cating the extent to which the surface was
destroyed in Experiment Till.
448
DE. D. EEKKIER ON THE BEAIN OE MONKEYS.
attempt to enter or seek its companion, who calls for it anxiously. When urged to
move, it ran against obstacles held in its path.
It was adjudged to be blind.
5 p.m. The bandage was now removed from the left eye. After a few moments of
apparent stupor and unwillingness to move, it ran when touched, avoided obstacles
which formerly it had run against, and made its way to its cage and jumped up beside
its companion.
The animal had evidently recovered its sight.
On this being established it was again placed under chloroform, and the superior
temporo-sphenoidal convolution was destroyed in both hemispheres. The results will
be recorded subsequently (see Exp. XV. p. 461).
Next day (April 8) at 12 noon it was taken out of its cage, and the left eye bandaged
up as before, much against the animal’s will. When let loose it made a spring at me,
and then galloped away into the other room and made for its cage. Followed its
companion out of the cage a short time after, and found its way in again and jumped
on the perch. Retired from the perch when I approached making mouths.
Vision therefore had returned in the right eye.
The subsequent history and post mortem examination of this animal will be found on
p. 461 et seq. under the head of Exp. XV.
This experiment completely confirms the former two as to the fact of blindness being
caused in one eye on the destruction of the angular gyrus of the opposite hemisphere.
The important fact noted in Exp. VII. is also confirmed, viz. that within a very
short period visual perception becomes again possible with the same eye, notwith-
standing the lesion.
The next experiment relates to the effects of destruction of the angular gyrus on both
sides.
Experiment X.
January 8 th, 1875. — The angular gyrus was exposed accurately and clearly in both
hemispheres of a monkey, and the animal allowed to recover from its chloroform-stupor
2.45 p.m.
At 8 p.m the animal had almost recovered, but was somewhat unsteady. Looks around,
and turns its head when called to, and makes mouths as before.
3.30 p.m. When taken away from the fire before which it had been sitting, it ran back
to its position, looking back at me, making grimaces and mouths.
It drank with avidity some sweet tea, of which it was exceedingly fond on all
occasions. When the dish was removed to the other side of the room away from the
fire, it ran to it and drank it up.
When a light was flashed before its eyes, it turned away its head and tried to conceal
its face in its hands.
4 p.m. The animal having completely recovered from the operation, and being in full
DE. D. FEEKIEK ON THE BEAIN OF MONKEYS.
449
possession of all its powers, it was taken and the angular gyrus destroyed on both sides
by means of the cautery.
The operation was finished at 4.35.
The animal when placed on the floor uttered a cry and looked about in a scared
manner.
Pricked up its ears and cried when called to.
Sat up quite steadily, but would not move.
The pupils reacted to light.
4.55 p.m. A light flashed before its eyes caused it to wince and erect its head. When
placed beside the fire it sat up, enjoying the heat.
When removed from the fire it lay down, and would not move from its position even
when nudged.
Turned its head sharply when called to by name.
When taken hold of clung violently to me, in terror at being placed down again.
When placed beside the fire sat contentedly enjoying the heat. Made no sign of
perception when the room was suddenly darkened and lightened.
5.30 p.m. Sits quietly by the fire. A piece of apple dropped beside its hand caused
it to lay hold of it, and after smelling eat it. When taken away from the fire and
placed on a chair, lay down and refused to stir.
There is no paralysis of motion or sensation unless of sight ; and this is difficult to
ascertain beyond all doubt, as no crucial test seems applicable.
8 p.m. The question of sight was decided in the following manner. A dish of sweet
tea, of which it was fond, .was placed to its lips, whereupon it drank greedily, keeping its
mouth in the dish as it was lowered ; but on the dish being withdrawn from immediate
contact and placed on the floor quite under its nose, the animal was unable to find it,
though exhibiting a desire to do so. This was repeated several times with the same
result. On the dish being raised to its lips it drank eagerly, aid followed it with
its mouth immersed until every drop was exhausted, the dish being drawn along the
floor for some feet.
January 9th. — 11 a.m. The animal is alive and well, and retains its muscular power
and senses, except sight. It eats and drinks with avidity whatever is brought up to its
mouth, but is unable to find its food when it is removed from immediate contact.
Will not move from its place, but remains quite still with its eyes open. The pupils
are equal and active. An object waved in front of its eyes causes wincing only if closely
approximated to the eyes.
A threatened blow with a stick causes no reaction, unless when brought almost in
contact with its eyes.
The left wrist seemed slightly dropped, and not used like the other. With this
exception all the voluntary movements were unimpaired.
To avoid the complication of extension of softening to other regions, the animal was
killed with chloroform at 12 noon.
MDCCCLXXV.
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450
DR. D. PERRIER ON THE BRAIN OF MONKEYS.
Post mortem Examination. — Slight suppuration existed at the margins of the wound
and under the scalp ; and there was some oedema of the cellular tissue over the orbits.
The skull was deficient in the region of the parietal eminences.
The brain-surface corresponding to this opening was slightly elevated above the rest.
The surface of the brain was everywhere normal, except in the region of the angular
gyri.
The surface of these convolutions was destroyed on both sides. Slight softening
extended about a line into the adjoining margin of the occipital lobe on both sides,
slightly more on the left than on the right (see figs. 11, 12).
Fig. 11. Fig. 12.
Figs. 11 & 12 represent the left and right hemispheres of the monkey respectively. The shaded portions
indicate the extent of destruction of the surface of the hemispheres in Experiment X.
The lower part of the ascending parietal convolution of the right side was also
slightly involved.
The base of the brain, the ganglia, and the optic tracts were uninjured.
This experiment completely confirms the other three as to the effect of destruction of
the angular gyrus or the power of visual perception.
The slight affection of the left wrist is explained by slight invasion of the right
ascending parietal convolution by the process of softening.
These four experiments demonstrate conclusively that unilateral blindness of a complete
character results from destruction of the angular gyrus of the opposite hemisphere, and
that this unilateral blindness is only of temporary duration, provided the angular gyrus
of the other hemisphere remains intact ; while permanent blindness results from the
destruction of the angular gyrus in both hemispheres. Further proof of this will be
found in Experiment XXI.
The loss of visual perception is the only result of this lesion, the other senses and the
powers of voluntary motion being retained so long as the lesion remains confined to the
angular gyrus itself.
By the term visual perception I wish to indicate the consciousness of visual impres-
sions, and to distinguish this from mere impressions on the optical apparatus and reac-
tions which are only of a reflex nature, such as the sudden start which an animal really
DR. D. EERRIER ON THE BRAIN OF MONKEYS.
451
blind in the sense in which I use the term may make when a light is flashed before
its eyes.
Retinal impressions and reflex actions resulting from these are left unaffected by the
lesion which abolishes the perception of visual impressions.
Effects of Lesions of the Temporo-sphenoidal Lobe.
The experiments recorded under this heading relate to more or less general, as well as
limited, lesions of the convolutions of this lobe. As it is difficult to reach and localize
lesions in the individual convolutions, the exact effects of the destruction of any one
part have to be arrived at in a great measure by a process of exclusion, besides that of
direct experiment on each separate region.
The effects of electrical stimulation have been already recorded.
Irritation of the superior temporo-sphenoidal convolution always gave very definite
results, viz. pricking of the opposite ear, opening of the eyes and dilatation of the pupil,
with turning of the head and eyes to the opposite side.
That these phenomena were the indications of excitation of subjective auditory sen-
sations seemed probable, both from experiments on monkeys and other animals.
Stimulation of the posterior division of the third external convolution in cats, dogs,
and jackals is usually followed by sudden pricking of the opposite ear. In rodents a
similar effect results from stimulation of an homologous region.
A very marked effect I observed in the case of a wild jackal, on stimulation of the
posterior division of the third external convolution. The animal suddenly started,
pricking up both ears, and would have bounded off the table had it not been securely
fixed.
The phenomena were just such as would have resulted from a sudden alarm. A
similar result I observed in a rabbit on which I was experimenting.
That the movements resulting from irritation of the superior temporo-sphenoidal con-
volution in monkeys resemble those caused by a sudden sound is seen by the following
experiment : —
A monkey was placed on a table, and a loud whistle made close to its ear. Imme-
diately the ear became pricked up, the animal turned its head to the same side, opening
its eyes widely, while the pupils were observed to be dilated. The dilatation of the
pupils was not observed in every case when the experiment was repeated, but the other
phenomena were the same.
The effect of irritation of the lower end of the uncinate convolution (subiculum cornu
ammonis), viz. torsion and closure of the nostril of the same side, is evidently to be taken
as the indication of excitation of subjective olfactory sensations, and is precisely similar
to the effect of irritating the olfactory bulb itself, as I have ascertained by direct
experiment.
The following experiments serve to demonstrate the accuracy of the views at which I
had arrived.
3 o 2
452
DR. D. FERRIER ON THE BRAIN OE MONKEYS.
Experiment XI.
December 10£A, 1873. — The left hemisphere of a monkey was exposed in the regions
of the ascending parietal convolution, the postero-parietal lobule, the angular gyrus, and
the upper part of the superior and middle temporo-sphenoidal convolutions.
After experimentation by means of electric irritation on these regions, the temporo-
sphenoidal lobe was deeply divided with the galvano-cautery in a line nearly coinciding
with the direction of the lower temporal fissure (see fig. 13), and the substance of the
superior temporo-sphenoidal and middle temporo-sphenoidal convolutions destroyed and
scooped out throughout their upper two thirds approximately.
After the operation the animal retained sight, and apparently heard as before, as
judged by its reaction to sounds.
The condition as to smell and taste is exceedingly difficult to determine accurately.
As to smell, there is hardly any odour, pure and simple, which will cause distinct
manifestation of olfactory sensation in a monkey ; and one must study the habits of the
animal carefully, or employ some volatile substance which will cause reaction. These,
however, such as ammonic and acetic acid, act conjointly on the nerves of common sen-
sation and on the special nerve of smell. I have found, however, by careful experi-
mentation on a patient who had lost both taste and smell as the result of a blow on the
head, that ammonic and acetic acid, and particularly the latter, cause much less reaction
than they do when both systems of nerves are intact.
Confirmations of this will be found among the experiments narrated.
The reaction to acetic acid, which I frequently used to test the sensibility of the nostrils,
is only a comparative test, and reaction caused by it, when applied to the nostril, is not
to be regarded as an indication of smell ; but the absence of reaction would show that
the sensibility of the nostrils had been entirely lost ; while a less reaction in one nostril
as compared with the other would fairly indicate some abnormal condition of the nostril,
the exact cause of which is capable perhaps of explanation by other facts.
In this case the reaction to the vapour of acetic acid wTas distinctly less in the left
nostril than in the right. (The left nostril is, as will be noted, the same side as the
lesion in the hemisphere.)
As to taste, no exact experiment was made. The right side of the tongue was
touched with a rod dipped in perchloride of iron; but, owing to the nature of the
substance and the diffusion in the mouth, nothing could be ascertained accurately, though
I thought that there seemed to be less immediate reaction on the right side than on
the left.
The animal had not lost its appetite, for it drank milk and ate some food offered to it.
Hearing, as was noted, did not seem affected, as the animal reacted as usual to sounds,
turning its head, &c.
As the animal had, however, its left ear and right hemisphere intact, I plugged up
the left ear securely by means of cotton-wool, in order to ascertain whether it heard
in reality only with the right.
DR. D. FERRIER ON THE BRAIN OF MONKEYS.
453
On this being done, sounds which formerly caused the animal to prick its ear and look
round, failed to cause any reaction or excite its attention.
Sounds made by concussion caused the animal to look round, as well as the making
of any sound which likewise attracted its attention by sight.
Whether, therefore, the animal heard or not, it gave no sign of such sensations being
aroused.
It was also found that reaction to pricking and pinching was considerably less on the
right than on the left side, though not completely abolished.
The animal died next day in a comatose con- K
dition.
Post mortem Examination. — The injury to the
brain involved the convolutions to the extent
described.
The division was carried down to the hippo-
campus, which, however, was not severed ; and the
lower part of the uncinate convolution and of the
temporo-sphenoidal convolutions still remained,
^though almost severed from the rest of the
temporo-sphenoidal lobe.
This experiment only gave partial indications
of impairment of certain senses, particularly of
hearing and smell, and in some degree of tactile
sensation, and is chiefly important in relation to
the other experiments to be described.
Fig. 13 represents the left hemisphere, and
the shaded part indicates the seat of lesion in
Experiment XI. The deep shading in the
centre is intended to represent the part at which
the temporo-sphenoidal lobe was deeply divided
transversely almost as far as the hippocampus
major. The lighter shading represents the
extent to which the surface of the convolutions
was destroyed.
Experiment XII.
January 27th, 1875. — The left hemisphere of a lively and intelligent monkey was
exposed by a trephine opening in the region of the annectent gyrus connecting the
posterior limb of the angular gyrus with the occipital lobe, and the upper part of the
superior and middle temporo-sphenoidal convolutions further exposed by the bone-
forceps.
With the cautery the convolutions exposed were thoroughly cauterized and the grey
matter destroyed scooped out, while the cautery was directed horizontally inwards, so as
to divide the lobe transversely as far as possible, taking care to avoid sinking it so deeply
as to injure the crus. (See fig. 14, where the darkest part of the shading indicates the
region of the greatest depth.)
The operation was completed at 4 p.m.
After a few minutes the animal recovered from its stupor, and began to look around.
Endeavoured to get up, but staggered towards the right side. Gradually recovered
its equilibrium.
454
DE. D. EEEEIEE ON THE BE A IN OE MONKEYS.
On being placed on a chair it gave evident proof of its retention of sight by jumping
on to the table, and running to a dish containing milk, and drinking up the contents.
There is distinct reaction on both sides when a hot iron is applied to the skin. The
animal starts, and rubs vigorously the part touched.
The extent of its hearing and smell were not ascertained at this time.
January 28 th. — 10 a.m. The animal is alive and well. Ate its breakfast as usual.
Can walk and jump about, and sees distinctly, as it puts out its hand and lays hold of
objects before it.
In order to ascertain its condition as to hearing and smell, the right nostril and the
left ear were tightly stopped with cotton-wool.
When offered a piece of apple it hesitated eating it, placing it to its nostrils over and
over again, apparently as if it had difficulty in smelling.
Does not pay any attention when a noise is made, such as formerly caused it to
respond actively.
Tactile sensation seemed unimpaired on both sides.
5 p.m. The left side of the scalp has become oedematous. The left eye is partially
closed by oedema of the eyelids. Eats heartily.
Took a piece of apple offered it in its left hand.
On testing the right side by means of the hot iron there was a marked diminution of
reaction on the ear, hand, and foot of the right side, as compared with the left.
Sight continues unimpaired. Smell and hearing are considered as impaired ; smell
on the left, and hearing on the right. It is difficult to ascertain by any crucial test
whether they are gone on these sides.
January 29 th. — 10 a.m. The eyelids are cedematous. Ate some breakfast. When taken
out of its cage sat still, unwilling to move. Takes every thing offered to it in its left
hand. The animal drinks out of a dish, holding its head sideways, keeping the left side
of its lips in contact with the fluid.
On testing with the hot iron there is very marked diminution of reaction over the
whole of the right side of the body as compared with the left.
There is no loss of muscular resistance in the limbs of the right side. They do not
hang flaccid as in motor paralysis. There is no facial distortion.
The limbs are occasionally moved, but they are not used by the animal in grasping
or progression.
The foot and hand are frequently rested on the floor in irregular and what otherwise
would be uncomfortable and unnatural positions.
The animal occasionally scratches its left side with its left hand. Occasionally utters
a discontented grunt. Retains its intelligent look, and takes notice of what is going on
around it.
It was killed with chloroform at 11.15.
Post mortem Examination. — The scalp was cedematous and the wound suppurating.
From the opening in the skull a hernia cerebri of the diameter of a walnut was observed.
DR. D. FERRIER ON THE BRAIN OE MONKEYS.
455
With the exception of this appearance on the surface, the brain otherwise was per-
fectly normal in appearance.
The fungus was attached to the superior temporo-sphenoidal convolution along two
thirds of its extent.
The lower end of this and also of the middle temporo-sphenoidal convolution were
not broken down externally, but they were much congested.
The rest of the lobe was completely broken up. The lesion extended inwards, so as
to appear on the inner surface of the temporo-sphenoidal lobe, leaving only a continuity
of a narrow band between the lower and upper end of the uncinate gyrus (see fig. 15).
The hippocampus was much softened.
The occipital lobe was intact, as also the optic thalamus.
The olfactory tract and bulb were uninjured, as also the crura, corpora quadrigemina,
and corpus striatum.
This experiment is another link in the chain of evidence pointing to the association
of hearing and smell with integrity of the temporo-sphenoidal lobe — hearing on the oppo-
site and smell on the same side. The hypothetical seats of these, the superior temporo-
sphenoidal for hearing and the subiculum cornu ammonis for smell, were either disinte-
grated or cut off by the lesion described. Though the effect is not regarded as conclusive
proof of this association, it will be seen to derive importance from conjunction with
other experiments to be related. At the same time, however, the fact is again noted
that tactile sensation was almost completely abolished on the right side. This effect was
subsequent to the phenomena just observed, and apparently advanced with the process
of softening inwards towards the hippocampus and uncinate convolution.
Fig. 14.
Fig. 15.
Fig. 14 represents by the shaded part the extent
of the lesion as seen on the outer aspect of the left
hemisphere in Experiment XII. The dark shading
in the centre indicates the part at which the lobe
was deeply injured.
Fig. 15 represents the extent of the lesion, as
seen on the inner aspect of the temporo-sphenoidal
lobe.
Experiment XIII.
February 2nd, 1875. — The brain of a monkey was exposed by trephining over the
456
DR. D. EERRIER ON THE BRAIN OE MONKEYS.
region of the annectent gyrus passing from the posterior limb of the angular gyrus into
the occipital lobe on both sides.
By means of hot wires the temporo-sphenoidal lobe was divided transversely in this
region, care being taken to avoid crossing the fissure of Sylvius, and also to avoid the
crura and optic tracts.
The wires were also directed downwards and forwards, so as to break up the lobe as
far as possible in the interior. This was carried out much more completely on the left
than on the right side.
The operation was completed at 4 p.m.
4.30 p.m. The animal has recovered from its chloroform stupor, and moves about
rather unsteadily.
It evidently retained its sight, as it directed its course to the fireplace, where it sat
down to warm itself.
5 p.m. Drank a dish of tea offered to it. It sits still with its head bent on the floor,
and seems disinclined to move. It has no muscular paralysis, and can hold on by both
feet and hands. Sits, however, very unsteadily when perched on the back of a chair.
Gives no sign of hearing when called to, as it used.
There is distinct reaction to the application of a hot iron to any part of its body,
though there seems somewhat less reaction on the right side as compared with
the left.
11.30 p.m. Is more lively, and looks about intelligently, and seems to walk somewhat
more steadily.
February 3rd. — 10.30 a.m. The animal was found sitting quietly with its head bent.
On being roused and offered some milk, it drank a very little, but kept moving its lips
about in the liquid, without continuing to drink.
Made no response when a loud sound was made close to its cage.
When taken out of its cage it moved only when nudged, and then made its way to
the fire, where it sat down, holding on to the fender, enjoying the heat.
When tested with the hot iron there was found to be very decided diminution of
sensation on the right side, on ears, hands, and feet.
There was no muscular flaccidity of the limbs or distortion of the face. A shrill
sound made close to its ear caused it to start somewhat.
1 p.m. The animal was fed with milk, as it did not seem inclined to eat of its own
accord.
Made no sign of reaction when acetic acid was held before its nostrils or placed in
its mouth.
7 p.m. When acetic acid was placed within its nostrils it appeared to suffer from
irritation, and at last a kind of sneeze was effected.
With the left hand it tried to clear away the offending matter from its left nostril,
but made only a kind of attempt with the right hand to the right nostril, not succeed-
ing in localizing the seat of irritation. Opened its eyes slightly when loudly called .
DR. D. PERRIER ON THE BRAIN OE MONKEYS.
457
It uses its left hand more than the right in laying hold of any thing. Formerly it
used the right chiefly.
It is very easily knocked over by a push when it is sitting, often falling quite supine.
It was again fed, as it does not seem able to feed itself.
8 p.m. The eyelids are somewhat oedematous, more so on the right than on the left.
The animal sits leaning its weight chiefly on the left arm and leg. When knocked
over, which is done by a slight push, it recovers itself chiefly with the left arm
and leg. The right leg, when it sits, is sometimes doubled up, and rests on its
outer side. It makes no use of its right arm for any voluntary movement. The left
arm and leg are moved cautiously. Muscular resistance continues in all four limbs-
There is no facial distortion.
On being tested with a red-hot iron there was entire absence of reaction on the
right side. The left side seems to react somewhat less than before.
The animal, in struggling when acetic acid was placed in its nostrils, moved all four
limbs, but it fell repeatedly while trying to get rid of the irritation.
At 9 p.m. the animal was killed with chloroform.
Post mortem Examination. — The skull was deficient below the parietal eminences,
and the brain-substance was protruding slightly from the orifices in the skull. The
dura mater stripped readily from the brain, but underneath it there was found a thin
layer of extravasation over the region of the right temporo-sphenoidal lobe.
In the left hemisphere (see fig. 17) there was a surface corresponding to the trephine-
Pig. 16.
Pig. 17.
Pig. 16 represents the right hemisphere, and the
shaded part the extent of superficial injury in Ex-
periment XIII. The dark shading in the centre
indicates the point of greatest depth of the lesion.
The dotted lines indicate the extent of internal
softening of the medullary matter.
Pig. 17 represents the left hemisphere, and the
shading the extent of superficial lesion in Experi-
ment XIII. The deep shading in the centre indi-
cates the line of deep transverse section, and the
dotted lines indicate the extent of internal softening
of the interior of the lobe.
opening of about the size of a shilling, somewhat elevated above the surrounding surface.
The middle of this was deeply excavated, and the division extended from behind the
mdccclxxv. 3 p
458
DR. D. FERRIER ON THE BRAIN OF MONKEYS.
fissure of Sylvius below the inferior occipital fissure to the edge of the uncinate convo-
lution on the internal aspect.
In the right hemisphere the fungating mass occupied about the same extent as in the
left, but extended somewhat further backward into the occipital lobe.
The temporo-sphenoidal lobe was not divided to the same extent transversely ; but a
deep excavation occupied the centre of the fungating surface, and corresponded to the
level of the upper end of the middle temporo-sphenoidal convolution (fig. 16). The
internal aspect of the temporo-sphenoidal lobe was of normal appearance.
The rest of the brain was normal.
On examination after the brain had been hardened in spirit for 20 hours, it was found
that in the left hemisphere the transverse division extended almost to the hippocampus.
The whole of the interior of the lobe below this point was reduced to a pulp, the
softening extending to some extent between the lips of the fissure of Sylvius, and
affecting the surface of the island of Reil to a slight extent.
The grey matter of the lower half of the temporo-sphenoidal convolutions and of the
uncinate gyrus formed a sort of shell, enclosing softened medullary substance. The
hippocampus was disorganized as far as the subiculum cornu ammonis. The optic tha-
lamus was not injured.
In the right hemisphere the excavation extended to the extraventricular surface of
the optic thalamus, but the hippocampus and fornix could still be seen of normal or
almost normal appearance. The internal or medullary surface of the superior and
middle temporo-sphenoidal convolutions was softened to a slight extent below the point
of greatest depth of the wound on the hemisphere. The subiculum and the lower ends
of these convolutions are not injured externally.
In this experiment the results as regards hearing were such as to indicate abolition,
or at least considerable impairment, of reaction to stimuli which in the ordinary con-
ditions are responded to actively. So far, therefore, the theory that this is dependent
on the destruction of the superior temporo-sphenoidal convolution holds good, for this
convolution was divided or disintegrated almost completely on both sides.
The reaction to acetic acid in the nostrils is not to be taken as a sign of the reten-
tion of true smell, for it in all probability was more due to irritation of nerves of
common sensation.
The reaction, however, was decidedly diminished, and was not caused when the
vapour was held only before the nostrils.
The absence of reaction on the tongue points to impairment of the sensation of taste,
and perhaps the want of desire to eat may have its explanation in loss of this faculty.
The experiment, however, is not regarded as conclusive, and is to be taken in
connexion with other facts. It is brought out more clearly than before that the loss
of tactile sensation coincides with lesion of the hippocampus and hippocampal convo-
lution. This region was quite destroyed on the left side, and loss of tactile sensation
was observed on the opposite side ; while on the left side tactile sensation apparently
DE. D. FEEEIEE ON THE "BEATTY OF MONKEYS.
459
continued good, the hippocampus and uncinate gyrus remaining intact, or at least not
presenting any marked abnormality on the right hemisphere.
Experiment XIV.
March 9th, 1873. — The brain of a monkey was exposed on both sides in the region
of the upper part of the superior and middle temporo-sphenoidal convolutions, and red-
hot wires were passed from this point downwards and forwards, with the intention of
breaking up the grey matter on the outer aspect of the lobes as far as the subiculum
cornu ammonis. Owing to haemorrhage from the left, the destruction was made more
deeply than intended into the lobe in attempts to check it. The operation was com-
pleted at 3.30.
4.15 p.m. Is recovering from its stupor, and moves when disturbed.
4.25 p.m. Begins to sit up, but seems to have some difficulty in using its right limbs.
4.40 p.m. Tactile sensation seems gone on the right side. There is no reaction to the
application of a hot iron to the right hand or foot, but slight on the ear. The same
heat causes violent reaction on the left side.
The animal has not yet sought to move about.
4.50 p.m. Neither aloes nor citric acid caused any reaction when placed on the tongue.
Acetic acid caused no reaction when held befor the nostrils.
Tactile sensation, as indicated by reaction, is unimpaired on the left side, but there
is no reaction on the right side to hot iron or pinching.
Acetic acid caused no reaction when placed on the tongue.
No reaction to the application of a hot iron to the right side of the tongue, and little,
if any, on the left.
The animal sits up, supporting itself with its left hand and foot chiefly. Makes no
use of its right hand, but clings firmly with its left hand when about to be placed on
the floor after being taken up.
5.10 p.m. Acetic acid placed within the right nostril caused no reaction and no lacry-
mation. Placed within the left nostril caused no torsion on turning away the head, but
caused a copious flow of tears from the left eye.
5.40 p.m. Aloes nor acetic acid applied to the tongue caused any reaction.
The animal is perfectly conscious ; though it sits still, and is disinclined to move.
It gives no signs of hearing when a noise is made beside its cage.
Cutaneous sensibility of the left side remains intact ; apparently is quite gone on the
right. The animal was placed in its cage, where it lay half asleep, but immediately
roused itself when the left hand was touched.
6 p.m. While lying asleep in its cage with the tongue showing between the teeth, acetic
acid was applied to the top of the tongue. No reaction of any kind ensued. Applied
to the left nostril no movement resulted.
A hot wire applied to the tip of the tongue caused no reaction. The same stimulus
3 p 2
460
DR. D. FERRIER ON THE BRAIN OF MONKEYS.
applied to the left hand caused a sudden start, opening of the eyes, and withdrawal of
the hand.
The left side of the lip and face retained sensibility.
8 p.m. A faint reaction ensued on the application of the hot iron to the right foot.
The same stimulus applied to the hand caused no reaction. The tongue remained
absolutely insensible. The left side of the body gives active reaction.
9 p.m. I repeated these tests in presence of Dr. Lauder Brunton. The absolute
want of reaction on the right side with the exception of slight reaction of the right foot,
the retention of sensibility as indicated by reaction on the left side, the absolute insen-
sibility of the tongue to stimuli of any kind, the entire want of reaction to acetic acid
placed in the right nostril, and the copious lacrymation of the left eye when it was
introduced into the left nostril were confirmed in his presence.
Desirous to avoid further complication after this demonstration, I killed the animal
with chloroform.
Post mortem Examination. — The brain, except at the points to be described, was
everywhere normal. The base of the brain and the cranial nerves were intact. The
fifth and the Gasserian ganglion on both sides were specially examined and found intact.
In the left hemisphere there was a wound with blackened edges, of the extent seen
in fig. 18, occupying the upper part of the superior and middle temporo-sphenoidal
Fig. 18. Fig. 19.
Fig. 18 represents the left hemisphere, and the
shading the extent of the lesion in Experiment XIY.
The deep shading in the centre indicates the point
of deepest excavation, and the dotted lines proceed-
ing downwards and forwards are intended to repre-
sent the extent of internal disintegration of the lohe.
convolutions. The middle of this was excavated, and the lesion was continued into the
interior of the lobe, the whole of which was converted into a softened mass, enclosed
by a shell of grey matter on the outer and inner aspect of the lobe. The hippocampus
was injured at a point opposite the wound, and was softened throughout below this.
There was some blackened effusion within the lips of the fissure of Sylvius and
covering the surface of the island of Beil, which, however, was of normal consistence,
Fig. 19 represents the extent of lesion in the right
hemisphere in Experiment XIY. The shading indi-
cates the extent to which the grey matter was de-
stroyed.
DE. D. FEEEIEE ON THE J3EAIN OF MONKEYS.
461
and easily separable from the convolutions overlapping it. The lower part of the
ascending frontal convolution was slightly softened and congested.
In the right hemisphere the surface of the lower half of the temporo-sphenoidal
convolutions was quite disintegrated and blackened (fig. 19). The subiculum cornu
ammonis was broken up. The softening did not extend to the fissure of Sylvius. The
internal aspect of the lobe, the hippocampus, and uncinate convolution were normal,
except at the subiculum, as already described. No other injury existed in any part of
the brain.
This experiment was followed by results of a very remarkable character.
There was absence of reaction to stimuli of smell, taste, hearing, and of tactile
reaction on the right side (almost complete).
As regards the loss of tactile sensibility, we have again the apparent connexion of
this with destruction of the hippocampal region.
On both sides the subiculum cornu ammonis was broken down, and on both sides
there was absence of any reaction indicating olfactory sensation.
A peculiarity, however, existed in the comparative reaction of each nostril to the
effect of acetic acid. In the left nostril, i. e. the side on which tactile sensibility
remained, acetic acid caused a copious flow of tears from the left eye, while in the right
nostril no effect of any kind was produced. This is evidently to be ascribed to the
abolition of common sensibility as well as of true smell from the right nostril. The
lacrymation was the indication of the reflex excitation of the lacrymal gland through
the medium of tactile sensibility, which still continued unimpaired on the left side.
The absence of motor reaction, however, was an interesting fact, and serves to show how
much of the reaction caused by a pungent vapour applied to the nostril is dependent
on the integrity of true olfactory sensibility.
As regards taste, the results indicated its entire abolition. But not only taste, as
such, but also the tactile sensibility of the tongue seemed to have been destroyed.
This was noted as a remarkable phenomenon, and the tests were frequently repeated in
order that no fallacy might be allowed to remain. Not only on the right side of the
tongue, but also on the left, was this absence of reaction noted. The centres for the
tactile sensibility of the tongue on the left side seemed to have been destroyed along
with those of special sense, a fact apparently indicating their close anatomical relation
in the hemisphere. The following experiments serve to narrow the boundaries of the
lesions causing these various results as regards hearing and tactile sensation.
Experiment XV.
April 7th, 1875. — The subject of this experiment was the same monkey used for
Exp. IX.
After the animal had quite recovered from the effect of destruction of the angular
gyrus on the left side, it was again chloroformed, and the superior temporo-sphenoidal
462
DK. D. EEKBIEK ON THE BBAIN OE MONKEYS.
convolution was destroyed on both sides throughout the greater part of its extent, by
means of the blowpipe cautery passed along the surface.
An hour after the operation (6.30 p.m.) it still staggered while walking, and looked
only half awake. Made no sign when a whistle was made close to its ear or when
called loudly.
Acute sensibility existed on both sides, as determined by the application of a hot
iron. It rubbed vigorously the parts touched.
Aloes and citric acid placed on the tongue caused great annoyance and movements
of the mouth and tongue to expel the offending substance. The animal also ground its
teeth, and then got up and ran about the room, grinding its teeth, and annoyed at the
unpleasant sensation in its mouth.
Acetic acid held before its nostrils caused it to start and sneeze and rub its nose.
When not disturbed sat quietly with its head down.
8.30 p.m. Found asleep in its cage. Made no sign of perception till I laid hold of it,
when it started with a shriek. Looked up and ran to a dish of water and drank.
Again, on trying to rouse its attention, it did not look up when a loud sound was
made, though its companion looked terrified.
12.30 a.m. A loud sound made in the immediate vicinity of its cage caused a slight start.
April 8th. — 10 a.m. Animal alive and active, and jumped out of its cage when the
door was opened. Sight was good, and tactile sensation unimpaired. Various experi-
ments were made to ascertain the existence or not of hearing ; but it was difficult to
devise a test, as the animal was continually on the alert ; and it was not easy to make a
sound without in any way attracting its attention by sight. The following method was
tried. While the animal was sitting quietly by the fire, I retired to the other room,
and while watching through the chink of the half-shut door called loudly, whistled,
knocked on the door, tinkled glass, &c., without ever causing it to look round or give
any sign of having heard. I then cautiously approached the animal, and not till it saw
me did it give any sign of consciousness of my presence.
When the same experiment was repeated, while the monkey and its companion were
quietly seated by the fire enjoying the heat, it gave no sign of hearing, while its com-
panion started with alarm, and came with curiosity to ascertain the cause of the sound.
At 12 (noon) the test of sight, related under Exp. IX., was made.
8 p.m. In presence of Dr. Burdon Sanderson I repeated the various tests with the
view of eliciting signs of hearing. To all it remained without response. It seemed
unconscious of my presence when speaking close to its ear, and only started when it
caught sight of me.
April 9 th. — The animal was found weak and prostrate, and was killed with chloroform.
Post mortem Examination. — There was a considerable amount of pus underneath the
scalp and below the detached surface of the left temporal muscle. Pus was found
beneath the dura mater continuous with the collection beneath the muscle. The surface
of the brain was otherwise intact, except at the points to be described.
DR. D. TERRIER ON THE BRAIN OF MONKEYS.
463
In the left hemisphere the brain-surface corresponding to the opening in the skull to
the extent indicated by the dotted line in fig. 20 was elevated above the rest and congested.
The surface of the angular gyrus and of the superior temporo-sphenoidal convolution
was disorganized to the extent seen in the figure. The lower part of the shading
indicates medullary softening, caused by passing a hot wire into the substance.
In the right hemisphere (fig. 21) a similar dotted line indicates the extent of the
Fig. 20.
Fig. 20 represents by the shading the extent of
destruction of the grey matter of the left hemisphere
in Exp. XY. The dotted line indicates the extent
of surface exposed by removal of the bone and dura
mater.
Fig. 21.
Fig. 21 represents the extent of the lesion in the
right hemisphere in Exp. XY.
The dotted line has the same signification as in last
figure.
opening of the skull, and the extent of congestion and hernia of the surface of the
brain. The hernia was only slightly elevated above the rest of the hemisphere. The
lesion was accurately circumscribed.
The grey matter on the surface of the superior temporo-sphenoidal convolution was
destroyed throughout the upper two thirds of its extent (i. e. the extent which reacts
to electrical stimulation).
The base of the brain, ganglia, and cranial nerves were intact.
This experiment (besides confirming the fact of loss of sight by destruction of the
angular gyrus) serves to localize the effects as to hearing, which were observed to result
from extensive lesions of the temporo-sphenoidal lobe. It is obviously more difficult
to ascertain the presence or absence of the sense of hearing in the lower animals than in
man, on account of the difficulty of distinguishing between reflex action and true
sensory perception.
In the above experiments, involving destruction of the superior temporo-sphenoidal
convolution, it will be seen that, with the exception of an occasional start to a shrill
sound, in general there was an abolition of reaction to sounds which in normal condi-
tions are sufficient to excite active attention, and this while the animals were on the
alert and in full possession of their other senses.
If this absence of reaction, except where it might well he the result of reflex action,
464
DR. D. TERRIER ON THE BRAIN OE MONKEYS.
following the destruction of this region of the brain, be taken with the phenomena
resulting from electrical stimulation of the same part, we have, it appears to me, as
satisfactory proof as it is possible to obtain from the lower animals, that the sense of
hearing is localized on the superior temporo-sphenoidal convolution.
Having thus eliminated the result of destruction of this convolution from the complex
effects caused by more extensive lesions of the temporo-sphenoidal lobe, I proceed to
describe experiments tending to fix more definitely the seat of tactile perception.
Several experiments have already been detailed, which rendered it more than pro-
bable that the loss of tactile sensation was dependent on lesion of the hippocampus
major or uncinate convolution, or both.
Experiments were devised for the purpose of destroying this region without injury to
the rest of the temporo-sphenoidal lobe. To effect this seems almost impossible, consi-
dering its deep-seated and concealed position in the internal aspect of the hemisphere.
The method I at last resolved to pursue was to endeavour to reach this from the
occipital region by passing heated wires through the posterior aspect of the occipital
lobe in the direction of the hippocampus. I had first ascertained the negative effects
of destruction of the occipital lobe. These will be related subsequently.
Having made repeated experiments on the dead brain, so as to acquire knowledge of
the direction and extent to which the cautery should be pushed, I proceeded to expe-
riment on the living animal.
My first attempts were not quite successful, as will be seen, but ultimately my efforts
were rewarded with success.
Experiment XVI.
February 5th, 1875. — This, though not successful as regards the object intended, yet
presents some interesting phenomena. The left occipital lobe was exposed posteriorly,
and penetrated at the posterior extremity of the superior occipital fissure by means of
hot wires, which were directed with a view to follow the inner aspect of the temporo-
sphenoidal lobe. There was no hsemorrhage from the sinus. During the operation the
animal was observed to make sighing respiration. The operation was finished at 4.30 p.m.
The animal lay in a state of stupor for more than an hour, only making slight move-
ments when disturbed, and then with its left limbs.
7 p.m. The animal lies quiet, but indicates consciousness by grunting discontentedly
when moved. Struggles with its limbs, chiefly the left, but occasionally with the right.
On testing the cutaneous sensibility with the hot iron, reaction was decisive over the
whole of the left side, but quite abolished on the right. The animal occasionally
opened its right eye, but the left remained permanently closed. The animal passed into
a state of coma, and was found dead at 11.30 p.m.
Post mortem Examination (next morning). — It was found that the cautery, as indi-
cated by the blackened sinus, had penetrated the occipital lobe at the point mentioned,
where a round hole was situated, and on emerging had ploughed a furrow on the upper
DE. D. EEEEIEE ON THE BEAIN OE MONKEYS.
465
end of the uncinate gyrus, but then leaving the inner aspect of the temporo-sphenoidal
lobe, had ploughed off the left tubercles of the corpora quadrigemina, then penetrating
the middle of the left optic thalamus had passed inwards and emerged at the longitudinal
fissure on its basilar aspect. The corpus striatum was uninjured, as the wire had
penetrated to the inside of this ganglion.
There was no effusion into the skull, and, beyond the injury narrated, the rest of the
brain had not been injured. The optic tract of the left side had of course been
destroyed along with the left tubercles of the corpora quadrigemina, and the anterior
extremity of the sinus was situated just in front of the optic commissure.
In this the loss of sensation on the opposite side coincided with destruction of the left
optic thalamus and the injury to the tegmentum cruris.
The ptosis of the left eye indicated the destruction of the nucleus of the third nerve,
situated just below the region of the lesion in the corpora quadrigemina. As the optic
thalamus was destroyed along with part of the uncinate convolution, this experiment
of course does not warrant any conclusion as to the effect of destruction of this convo-
lution itself.
As regards the optic thalamus, and the effect of its destruction, see also Exp. XIX.
The following experiment is a repetition of the last, and was only partially successful.
Experiment XVII.
February 9th, 1875. — The left occipital lobe of a monkey was exposed as in last
experiment, and hot wires were pushed through the tip of the occipital lobe in a
direction downwards and outwards, approximately in the direction of the hippocampus
major. There was no haemorrhage of any extent.
The operation was completed at 3.15 p.m. The animal was already conscious before
the wound was dressed. It was freed and laid before the fire.
3.30 p.m. Lies by the fire breathing quietly. Pupils equal, and both eyes open. Utters
a grunt of recognition when called to, and also begins to move its tail and right hand.
Gets up, hut sits unsteadily, inclining to fall over on its right side. Reaction to hot
iron distinct on both sides of the body.
3.50 p.m. Retains sight unimpaired. Can now sit up more steadily and walk without
falling. Took a piece of apple offered to it in its right hand and ate it.
5 p.m. Took some tea, and ate some fruit. While sitting before the fire accidentally
touched the bar of the grate, on which it manifested a lively sense of pain, and rubbed
the part. The animal seems to retain all its senses and muscular power unimpaired.
9 p.m. Continues as before. Clings with right as well as left hand to its cage when laid
hold of.
When offered any thing to eat, it now uses its left hand, whereas formerly it almost
invariably employed the right. There is a distinct reaction to heat on the right side.
February 10£/i.— 10 a.m. Remains as before. Eats and drinks heartily. Sees and
hears perfectly. Reaction to hot iron still continues on both sides.
MDCCCLXXV. 3 Q
466
DR. D. PERRIER ON THE BRAIN OF MONKEYS.
No difference observed in the animal when again tested at 7 p.m.
February 11th. — 10 a.m. The animal looks much as before. The wound is suppu-
rating freely. Can see and hear, and move about. Takes every thing offered to it in its
left hand. Reaction to hot iron still continues on both sides. A sore on its right
foot seems to cause it great trouble, as it is continually biting and scratching it.
February 12tli. — 10 a.m. The animal ate and drank as before. There appeared to be
slight twitching of the right side of the body. Reaction to heat still observed on both
sides.
10.45 a.m. The animal had again a return of the twitching of its right side. The
animal was quite conscious, and did not fall. After a few minutes the animal walked
back to the fire, whence it had been removed for observation. It was now seen to drag
its right limbs somewhat.
11.40 a.m. In climbing in its cage seems to have great hesitation in using the right
hand. When taken out had a slight return of the twitching. When it had ceased
some food was placed in its right hand. Failed to grasp it, but took it with its left
hand, raised it to its mouth and ate.
4 p.m. Still continues to drag its right limbs in walking, and cannot grasp with the
right hand. There is marked diminution of reaction on the right side, as compared
with the left, when a hot iron was applied.
After this there was a return of the spasmodic twitching of the right side.
In the interval of the fits the right leg was again tested with the hot iron, and
reaction seemed to have entirely disappeared, while reaction was active when the stimulus
was applied to the left.
Towards evening the animal began to exhibit symptoms of basilar meningitis,
suffering from frequent convulsive seizures. It became comatose, and died in convul-
sions on February 13.
Post mortem Examination (February 13th, 10.30 a.m.). — The exposed posterior extre-
mity of the left occipital lobe was fungating. The dura mater stripped easily from the
surface of the brain ; but the vessels of the pia mater were injected on the left hemi-
sphere, particularly on the postero-parietal region.
The course of the wire was easily traced by the sinus it had caused, and by a line
joining the points of entrance and exit. After penetrating the occipital lobe it had
ploughed a furrow on the upper extremity of the uncinate gyrus (see fig. 22), and then,
instead of following the inner aspect of the temporo-sphenoidal lobe, had made its way
horizontally outwards through the lobe, and emerged on the outer aspect at the extre-
mity of the superior temporo-sphenoidal fissure (see fig. 23). On examination of the
brain after hardening in spirit, it was found that softening had extended from the track
of the wire, and that the hippocampus was in great measure softened down and dis-
organized.
In addition to these appearances there were signs of inflammation of the membranes
at the base of the brain, on the pons, and anterior surface of the medulla. The left
DR. D. FERRIER ON THE BRAIN OF MONKEYS.
467
optic tract was adherent to the hippocampal convolution. The dura mater in the left
sphenoidal fossa, and on the left petrous bone, and on the basilar process had a yellowish
Fig. 22.
Fig. 22 represents the lesion of the uncinate gyrus
and the direction of the sinus caused by the cautery
in Exp. XYII.
Fig. 23.
Fig. 23 represents the outer surface of the same
hemisphere, and the dotted lines indicate the track
of the cautery in Exp. XYII. The black dot at the
extremity of the upper temp.-sph. fissure indicates the
point at which the track terminated externally.
aspect. The inflammation appeared to have spread from the point in the left sphenoidal
fossa where the cautery had emerged from the brain. The optic thalamus and other
ganglia were normal, except perhaps slight extension of the inflammation up the left
optic tract to the left nates and testes.
This experiment became complicated by the results of basilar inflammation, but it is
possible to trace the course of the phenomena.
The cautery, as determined by the points of entrance and exit, seems, after ploughing
along the upper end of the uncinate gyrus, just to have missed the hippocampus and
descending pillar of the fornix. At first the effects were negative or nearly so ; but
gradually the animal began to exhibit failing sensation, as indicated by the diminution
of reaction to tactile impressions and inability to use the right hand, until ultimately
sensation became to all appearance abolished, or nearly so, on the right side. This would
coincide with the advance of softening into the hippocampus, as wras found to be the case
after death.
Whether the spasmodic affection of the right side is to be attributed to sensory
irritation excited by the progress of inflammatory softening is a question ; but it had
also a possible origin in the basilar inflammation which, extending from the left sphe-
noidal fossa, naturally would affect the left half of the pons and medulla first, and show
its effect by convulsive action of the opposite side of the body in the first instance.
This complication renders it difficult to estimate the exact effect of the lesion in the
temporo-sphenoidal lobe ; but the difference observed in the reaction of the two sides to
the hot iron strongly confirms the view that this was dependent on the lesion of the
hippocampus in the left hemisphere.
The following experiment serves to confirm this view.
3 q 2
468
DE. D. FEEEIEE ON THE BE A IN OF MONKEYS.
Experiment XVIII.
March 2nd , 1875. — A large monkey of the baboon type was chosen for this experi-
ment. As it seemed to be usually left-handed, the right hemisphere was operated on.
The right occipital lobe having been exposed, hot irons were passed through the
posterior aspect of the lobe in the direction of the hippocampal gyrus.
There was no haemorrhage of any moment.
The operation was completed at 3.15 p.m.
3.20 P.M. The animal lies by the fire, having recovered consciousness, and moves its
limbs, but has not yet attempted to get up.
3.25 p.m. When moved it opened its eyes, whence it was concluded that the crus
cerebri had not been injured.
While lying by the fire scratched its right leg with its right hand. Does not move
its left arm or left leg, whether laid on its right or left side.
3.35 p.m. There is no reaction to a hot iron on the left side. The same stimulus,
causes active manifestation of pain and rubbing when applied to the right side.
3.45 p.m. Begins to sit up and look about.
Moves only the limbs of the right side, and in sitting up occasionally falls over
on its back.
The test of the hot iron was again applied.
On the right side the slightest touch caused active reaction, and caused the animal to
rub the part touched. Applied to the left foot, the iron was kept in contact several
seconds without causing the slightest reaction, but when kept up longer a slight
retraction was caused. The same result was obtained on the left hand and the
right ear.
Pinching of the right hand and right foot caused violent reaction and slight cry. No
effect followed the strongest pinching of the left hand and foot. The left ear gave
slight reaction to pinching.
4 p.m. The animal is sitting up and looking about. Grunts when called to. Occa-
sionally falls over. Recovers itself by the aid of its right limbs. It can draw the legs
together, but the left foot is generally allowed to straddle outwards and rest on the
internal malleolus. The left arm is kept motionless in a semiflexed condition. Mus-
cular resistance continues.
4.15 p.m. When offered food it took it with the right hand, and raised it to its mouth.
Occasionally moves its left arm and leg while sitting still, but does not use them to
grasp or in progression.
The reaction to the hot iron is still persistent on the right, but gone on the left side.
The animal was occasionally seen to give a jerk of its head and grind its teeth, which
I attributed to some irritation of the fifth nerves, probably caused by inflammation of
the dura mater in the neighbourhood of the Gasserian ganglion, set up by contact of
the cautery.
DE. D. FERRIEE ON THE BRAIN OE MONKEYS.
469
4.30 p.m. The reaction to heat was again tried. A hot iron is allowed to remain in
contact with the right side without causing any reaction, except when kept so long as to
burn the part, while the slightest contact with the right side causes violent reaction and
active rubbing of the part. This was observed on the ear, hand, and foot.
There is no facial distortion.
5.45 p.m. On being placed in its cage the animal mounted its perch with difficulty, and
sat unsteadily with its head down. On turning its body a little the left leg slipped off
the perch. The animal, in recovering itself, clutched hold of the bars of the'cage with
its right hand, and though the left was placed on the bars no grasp was made with it.
Aided by its teeth and the right hand, it ultimately regained its equilibrium, and
dragged up its left leg, after having fairly got hold of the perch with its right.
Sits now holding on firmly to the perch with the right foot.
After this, on the animal shutting its eyes and going to sleep, the left foot frequently
slipped off, causing sudden grasping with the right hand on the cage until it recovered
its equilibrium.
8 p.m. The anaesthesia of the left side being again firmly established, and the animal
being otherwise well and apparently in possession of all its other, senses, the animal was
killed with chloroform, in order to avoid complication by the extension of the lesion.
Post mortem Examination. — The exposed surface of the right occipital lobe was
slightly congested. The surface of the brain, except at the point of entry of the cautery,
was everywhere else normal. There was no effusion within the skull. There was
injection of the vessels of the dura mater in the right sphenoidal fossa and over the
region of the Gasserian ganglion, extending from an inflamed spot with which the point
of the wire had come in contact.
The base of the brain and cranial nerves were normal in appearance. The crura, the
corpora quadrigemina, the optic thalami, corpora striata, pons, and medulla were unin-
jured and normal in appearance.
The cerebellum was just grazed on its right upper lobe, where the cautery had come
in contact with the tentorium in its course.
The track of the cautery was clearly traceable. It had penetrated the right occipital
lobe just at the posterior extremity of the superior occipital sulcus. Here there was a
round hole with blackened edges, about a quarter of an inch in diameter.
Emerging on the under surface of the lobe, the track appeared as a deep furrow, com-
mencing at the posterior termination of the calcarine fissure, and running along the
uncinate gyrus for about an inch. Thence following a concealed course below the surface
of the uncinate convolution, which yielded to pressure, it emerged at the tip of the
temporo-sphenoidal lobe on the orbital aspect of the lower end of the superior temporo-
sphenoidal convolution, two lines external to the subiculum cornu ammonis. On cross
section of the lobe it was found that the cautery had ploughed along the hippocampus
major.
The track of the cautery was followed with precision by the discoloration caused.
470
DR. D. PERRIER ON THE BRAIN OE MONKEYS.
This experiment indicates with precision the region in the temporo-sphenoidal whose
destruction is followed by impairment or total abolition of tactile sensation.
In the various cases in which this result
followed extensive lesion of the temporo-
sphenoidal lobe, it was found that the hippo-
campus major and the hippocampal convo-
lution were more or less extensively involved.
The destruction of these convolutions alone,
as shown by this experiment, abolishes tac-
tile sensation alone.
To ascertain the existence or absence of
this sense is surrounded with some difficulty,
owing to the fact that reflex reaction may
simulate the appearance of tactile sensation,
properly so called. The mere fact of reaction to a stimulus is no proof of the existence
of sensation.
The entire absence of reaction, however, observed in some of the preceding experi-
ments, where the hippocampal region was completely destroyed, is a strong proof of the
abolition of sensation, when it is considered that reaction was lively and marked on the
opposite side of the body at the same time.
But the loss of tactile sensation is even more conclusively indicated by the fact that
monkeys in whom the hippocampal region was destroyed ceased to use the opposite
limbs for the purposes of prehension or the exercise of the faculty of touch.
To react to tactile stimuli may signify reflex action or tactile sensation, or both ; to
touch necessarily implies the possession of the power of tactile perception.
The condition of the limbs in these cases was such as to simulate motor paralysis ; and
it is well known that Sir Charles Bell mistook the immobility of the side of the face
resulting from anaesthesia caused by division of sensory branches of the fifth for real
motor paralysis. It was pointed out by Mayo that, owing to the loss of tactile sensation,
an animal has no indication for the regulation and adaptation of its muscular movements,
and hence ceases to make them. That anaesthesia, and not motor paralysis, existed on
the side opposite the destruction of the hippocampus, is shown by the fact that a certain
degree of voluntary motion was retained. The animal (Exp. XVIII.) whose leg was
anaesthetic could replace it on the perch, though it continually tended to slip off when
the animal withdrew its attention from it.
There was no muscular flaccidity as in true motor paralysis, nor was there any appear-
ance of facial distortion, such as would have been produced by motor paralysis of one side.
It is impossible to differentiate between lesion of the hippocampus itself and of the
hippocampal or uncinate convolution. A lesion involving the hippocampus necessarily
involves the medullary aspect of the uncinate convolution, and it is impossible to destroy
the uncinate convolution without injuring the hippocampus.
Pig. 24.
Pig. 24 represents by the shading the external
extent of the lesion in the uncinate convolution, and
the dotted lines the track of the sinus caused by the
cautery in Experiment XYIII.
DE. D. FEEEIEE ON THE BEAIN OF MONKEYS.
471
In the above-mentioned experiments both these convolutions were more or less con-
jointly involved.
Owing to this difficulty, I shall speak of the two together as the “ hippocampal fold,”
and regard this as the seat of tactile perception.
We are now in a position to differentiate the various effects on sensation caused by
general destruction of the temporo-sphenoidal lobe.
As regards hearing, separate evidence is given in Experiment XY. of the localization
of this faculty in the superior temporo-sphenoidal convolution.
The absence of reaction to the usual auditory stimuli, combined with the effects of
stimulation of this convolution, afford evidence of the strongest possible character of the
localization of this sense.
The localization of smell is no less clearly indicated. Anatomically, the connexion
between the olfactory tract and the subiculum cornu ammonis, though less evident in
man, is clear in the monkey, and very apparent in the lower animals.
The effects of irritation of this region are very constant and characteristic, and are of
the same nature as direct irritation of the nostril or of the olfactory bulb itself.
Destruction of this region causes abolition or diminution of reaction to stimuli on the
same side as the lesion.
Taken together, these facts establish the localization of the sense of smell in the subi-
culum, or tip of the temporo-sphenoidal lobe.
As to the sense of taste, the positive indications are less distinct than those of smell
or hearing.
Yet the phenomena occasionally observed on stimulation of the lower part of the
middle temporo-sphenoidal convolution, viz. movements of the lips and cheek-pouches,
may be taken in connexion with lesions affecting this region, and accompanied by loss
of reaction to stimuli of taste, to afford evidence of no weak character for the localiza-
tion of taste in or near this region.
That the centres of gastatory and olfactory perception are closely related to each other
anatomically is rendered probable by the fact, often observed, of loss of taste and smell
following severe blows on the head, and particularly of the vertex. It is hot at all likely
that one and the same cause should simultaneously directly affect all the nerves which
are involved in the sensations of smell and taste ; but it is easy to understand that a
contre-coup might readily affect the integrity and functional activity of the lower end of
the temporo-sphenoidal lobe, in which the above experiments serve to localize the cen-
tral seats of these faculties.
We have thus accounted for the senses of sight, hearing, taste, smell, and touch, and
given evidence for the localization of each and all of these in the central convolutions.
Whether they are all integrated in the optic thalamus is a subject on which the
experiments I have yet made do not furnish sufficient evidence; but the following
experiment serves to prove that, in regard to tactile sensation, this is the case.
472
DR. D. EERRIER ON THE BRAIN OE MONKEYS.
Destruction of the Optic Thalamus.
Experiment XIX.
February 12th, 1875. — The left hemisphere was exposed by a trephine^opening in the
region of the pli de passage from the posterior division of the angular gyrus to the occi-
pital lobe.
With a small trocar and cannula (after the method adopted by Nothnagel in his
experiments on rabbits) the anterior extremity of the annectent gyrus was perforated
horizontally in the direction which experiments on the dead brain had taught me to
reach and destroy the optic thalamus.
After withdrawal of the trocar, a stilette with expanding wings was passed through
the cannula, and rotated so as to break up the parts with which it should come in
contact.
There was some haemorrhage from the cannula.
The operation was completed at 5.30 p.m.
5.50 p.m. The animal now is sitting up, leaning towards the right side. Makes some
movements with its left limbs.
7 p.m. The animal looks quite active and intelligent. Can move about pretty freely,
but seems weak on the right side. Does not use the right hand in taking hold of any
thing presented to it. A hot iron applied to the right hand caused the animal to wince
and rub the part touched.
8 p.m. Animal can move about. Took a piece of apple offered to it in its left hand,
and held it to its mouth with both hands. Sight and other senses do not seem affected.
8.45 p.m. A bandage was placed on the left eye in order to ascertain the condition as to
vision on the right. The bandage could not be maintained, as the animal bounced
about, knocking its head against furniture, and tearing at the bandage till it got it off.
Owing to this the condition as to sight could not be definitely tested, though the run-
ning against obstacles seemed to indicate affection of sight in the right eye.
February 13 th. — 11 a.m. The animal is much in the same condition as yesterday.
Uses all four limbs in walking, but the movements of the right are made with caution
and hesitation ; nor does it use the right hand in grasping, taking every thing offered to
it with the left.
3 p.m. Thinking that the optic thalamus had been only partially destroyed, I passed a
hot wire in the track of the cannula, so as to completely traverse the optic thalamus,
the distance &c. being carefully calculated from the result of experiments on the
dead brain.
Before the animal recovered from chloroform the left eye was bandaged, and the
animal laid before the fire.
3.10 p.m. The animal, while lying before the fire, begins to make some movements
with its left limbs. The right remain motionless. The right eye was open, and the
pupil dilated.
DR. D. TERRIER ON THE BRAIN OE MONKEYS.
473
Active reaction followed the application of a hot wire to the left side, hand, foot,
and ear.
No reaction followed application of the iron to the same points on the right side.
3.24 p.m. Begins to move about, turning towards the right side. When placed on the
back of a chair the animal clung tenaciously with the left hand and foot, but did not
grasp with the right.
The right side is completely ansesthetic. The animal, though keeping its right eye
open, apparently does not see, as it runs its head against obstacles in its way. When
placed on a chair it tumbled off, with its eye open. Muscular resistance is considerable
in the limbs of the right side. There is no trace of facial distortion.
3.40 p.m. Can flex and extend the right leg. Does so when lying down and in trying to
get up. Does not move the right limbs in walking, but drags them after the left. Turns
about aimlessly, and knocks its head against furniture &c. Sometimes goes backwards.
There is no reaction on the right side, but active on the left to hot iron.
3.55 p.m. The animal was placed on the floor, and surrounded by a circle of battery-
jars. It turned round and round, knocking its head against them, and apparently unable
to find its way out between them.
The bandage was then removed from the left eye. The animal still remained quiet
for a few minutes. When placed on the back of a chair, it quickly found its way down.
When placed beside its cage it looked about and then went in. Sight was therefore
improved or restored since the removal of the bandage.
5 p.m. The animal was observed to flex the right arm and partially close the fist while
it was sitting still. Entire abolition of reaction still continues in right. After some
minutes the animal seemed to be animated by all its former vivacity. Ate and drank
heartily. Makes active movements, turning round and round frequently to the left,
using its left limbs only.
At 5.30 p.m. the animal was chloroformed
to death, so that the exact seat of the lesion
Post mortem Examination. — From the open-
ing in the skull below the parietal eminence
there was a hernia cerebri involving the upper
part of the middle temporo-sphenoidal, annec-
tent gyrus, and lower part of the angular, and
upper end of the superior temporo-sphenoidal
convolution (see fig. 25).
In the centre of this was an opening, almost
circular, with softened edges, indicating the
point of entrance of the cannula. The surface
and base of the brain were everywhere else
normal. The cranial nerves were intact.
mdccclxxv. 3 R
Pig. 25.
Pig. 25 represents by the shading the area of
superficial injury of the left hemisphere of the
monkey in Experiment XIX. The dark central
shading indicates the orifice of the wound leading
into the optic thalamus.
474
DR. D. FEEEIEE ON THE BRAIN OF MONKEYS.
On opening the ventricles they were found free from effusion. The left optic
thalamus was disorganized.
The track of the hot iron was easily traced by its blackened appearance. It had
passed horizontally almost in the centre of the ventricular aspect of the ganglion, a line
or so beneath the surface, and completely traversing the left thalamus, had just
crossed the third ventricle and made a slight indentation on the opposite right
thalamus.
Besides this wound there was another lacerated surface situated more towards the
extraventricular aspect of the thalamus. This had been caused by the spring stilette,
which, as it had been conjectured, had not penetrated the body of the ganglion. Bound
this discoloured laceration softening had extended somewhat, but had not quite invaded
the body of the thalamus. The anterior and posterior extremities of the thalamus were
almost of normal appearance. The intervening portion was quite broken up.
The corpora ' striata and corpora quadrigemina were uninjured. The crura cerebri
were intact.
In this experiment the lesion was confined to the optic thalamus, or as far as can be
effected by such a method of experimentation.
This result, and the result of Experiment XVI., show that complete disorganization
of the optic thalamus in monkeys abolishes cutaneous sensation on the opposite side.
(As I am restricting my conclusions to monkeys, I do not here stay to discuss in detail
the results of Nothnagel’s experiments on rabbits (Virchow’s Archiv, 1874, p. 201),
which lead him to apparently contradictory conclusions. I will merely remark, on the
ground of experiment, that Nothnagel, in my opinion, is not warranted in asserting
that true sensation continues in rabbits after total destruction of the optic thalami.
Beaction to tactile stimuli, in all respects resembling sensory, such as springing forward
when the tail is pinched, or uttering screams, still continues to be manifested by these
animals after complete removal of the hemispheres.)
The retention of reaction to stimulation in the first instance in this experiment may
have been due partly to reflex action, partly to the retention of sensation ; but that
sensation was impaired was evidenced by the fact that the animal ceased to use its right
limbs as before for the purposes of prehension and touch. Here also, as in destruction
of the hippocampal fold, there was apparent muscular paralysis — but not so in reality,
as the animal could still move the limbs in some degree, and the muscles retained
their tonicity and resistance.
The interference with vision may have been due to the proximity of the lesion to the
angular gyrus and its medullary connexions, as much as to the lesion of the optic tha-
lamus, and therefore no definite conclusion is built on this fact. With regard to the
circular movements of the animal which were occasionally made, the body seemed to go
to the right or left according as the left arm was adducted or abducted.
The next experiments relate to the effects resulting from destruction or complete
removal of the occipital lobes.
DR. D. PERRIER ON THE BRAIN OE MONKEYS.
475
It has before been stated that the occipital lobes do not give any external response
to the electric stimulus.
Destruction of the Occipital Lobes.
Experiment XX.
November 21 st, 1873. — The occipital lobes were exposed on both sides in an active
and intelligent monkey.
By means of the galvano-cautery the upper surface of the exposed lobes was disor-
ganized as far back as their posterior extremity, while the left was further almost
severed from the rest of the brain by carrying the cautery perpendicularly downwards
towards the tentorium. It was not removed, however.
The operation was completed at 6 p.m,
6.15 p.m. The animal sat up spontaneously, which it did in a very unsteady manner,
and kept its head bent on the chest. Some milk was poured down its throat. Gave
evidence of retention of sight.
6.25 p.m. Moves about a little, looking about. Shows signs of pain and annoyance
when its tail is pinched. Grunts discontentedly when nudged and made to move.
8 p.m. Made to swallow some more food. When placed in the cage beside the other
monkeys it sat with its head bent, grunting when disturbed by them, and screaming
when they began roughly to examine its head.
Being obliged to be absent from London for a few days, I found on my return that
the animal had survived till the 25th. During the whole period it had maintained its
dejected and melancholy attitude, paying no attention to its surroundings, and had
shown no desire to eat or drink.
After death the occipital lobes were found disorganized, while the rest of the brain
was uninjured. The stomach and intestines were completely empty. The other viscera
were normal. No drawing was made of the brain.
In this case it might be supposed that the effects were merely due to the severity of
the operation ; but a review of the foregoing experiments will serve to indicate that
experiments involving quite as serious surgical operations were not followed by the same
depression, the animals still retaining their appetite, and eating and drinking as
before.
The results as regards motion and sensation were negative ; and the only effect which
could be noted was the general depression, and the abolition of the animal’s appetite.
Experiment XXI.
January 1 Qth, 1875. — The occipital lobes of a monkey were exposed on both sides,
and the dura mater removed from both. Owing to the rupture of a venous sinus on the
right side, cotton-wool, soaked in perchloride of iron, had to be used to stanch the
hsemorrhage, and there was reason to fear that it had in some degree injured the brain.
At 4 p.m. the left occipital lobe was separated from the hemisphere by means of
3 k 2
476
DR. D. EERRIER ON THE BRAIN OE MONKEYS.
white-hot wires passed perpendicularly downwards close to the sulcus, separating this
lobe from the angular gyrus.
4.35 p.m. The animal was let loose and laid down. After a few minutes it attempted
to sit up, and uttered a croaking sort of sound.
5 p.m. Moves about the room rather unsteadily, occasionally uttering a short cry.
Turns its head when called.
7 p.m. The animal appears to be blind. When placed on the back of a chair it would
not move, though the chair was shaken, and the animal evidently felt uncomfortable.
A piece of apple was held before it. It smelt it, and wished to lay hold of it, but made
futile grasps after it. It could not find the way into the cage when placed close to the
door.
8 p.m. It had been intended also to remove the right occipital lobe ; but owing to the
uncertainty as to the cause of the blindness, it was thought advisable to leave the right
side undisturbed, so that if the blindness were due to affection of the left angular gyrus
during the process of removing the left occipital lobe, time should be allowed for com-
pensation. The wound was therefore sewed up and dressed.
The animal, when placed on the floor, wished to return to me, but could not find
its way.
January Ylth , 10 a.m. — The animal refuses to eat. Drank some water in which its
mouth was forcibly immersed. When taken out of its cage it is seen to retain its mus-
cular power, but gropes about on the floor. The pupils are equal and of medium size,
and react sluggishly to light.
1 p.m. Tries to climb up whatever it comes in contact with. Likes to be taken up
and caressed, but cannot find its way. Still continues blind.
An ophthalmoscopic examination was attempted, but could not be carried out, on
account of the animal’s restlessness.
January 18 th. — 10 a.m. The animal looks somewhat more lively today. Ate a fig
and drank some wafer, but refused other food. Still continues blind, and moves about
in a groping manner.
At 10.30 a.m. the animal was killed with chloroform, in order to ascertain the cause
of the blindness.
Post mortem Examination. — The wound was suppurating freely.
The cut surface of the left occipital lobe was found projecting almost to the orifice in
the skull.
The exposed surface of the right occipital lobe was soft and pulpy. There was slight
extravasation on the surface of the dura mater on the right parietal region, caused by
the rupture of the sinus above alluded to.
The left occipital lobe had been cut off by a line passing perpendicularly through its
junction with the left angular gyrus (see fig. 26).
The angular gyrus was softened all along its posterior division, and just beyond the
curve (see fig. 28).
DE. D. FEEEIEE ON THE BE A IN OE MONKEYS.
477
The right occipital lobe, besides being softened on its upper aspect, was discoloured
and covered by a layer of extravasation, which likewise covered the right nates. The
nates themselves were, however, uninjured, and of normal consistence.
Fig. 26.
Fig. 26 represents by shading the extent of softening on both hemispheres of the monkey in Experiment
XXI. The transverse line on the left occipital lobe is the line of section, and the part marked by paralle lines
is the part entirely removed.
Fig 27. Fig. 28.
Fig. 27 represents the extent of softening in the Fig. 28 represents by the perpendicular line the
right hemisphere of the monkey in Experiment XXI. line of section of the occipital lobe. The part marked
by parallel lines was cut off. The shading indicates
the extent of lesion of the surface.
The posterior limb of the right angular gyrus was softened and discoloured yellow,
owing to the contact with the cotton-wool soaked with perchloride of iron which had
pressed on this part of the right hemisphere. The posterior extremity of the right occi-
pital lobe was normal in appearance, both on its upper and under surface (see fig. 27).
The optic tracts and cranial nerves were intact.
The upper part of the tentorium cerebelli on the left side was covered with pus, and
478
DR. D. FERRJER ON THE BRAIN OF MONKEYS.
the cerebellar surface beneath was yellowish in colour, but not softened. No other
lesion existed in the brain.
This experiment was unsuccessful in so far as the object of localizing the lesion in the
occipital lobes was concerned, but is a valuable confirmation of the results obtained by
former experiments on the angular gyri. In this experiment, besides the complete
removal of the left occipital lobe and extensive injury to the right, the angular gyrus
was deeply involved on both sides, not throughout, however. The lesion was, however,
extensive enough to produce total blindness ; and it further illustrates the fact that when
the angular gyrus is destroyed on both sides no compensation of visual perception
occurs.
Beyond the fact of loss of sight, which is to be attributed to the lesion of the angular
gyri, the lesions of the occipital lobes were in a great measure negative, the animal
retaining its muscular powers, and apparently other senses, and still exhibiting, though
to a less extent than before, its desire for food.
Experiment XXII.
January 22nd, 1875. — The occipital lobes were exposed on both sides in a monkey,
and the surface exposed destroyed by the cautery, which was also passed deeply into
the interior of the lobes, in order to cause as much disorganization as possible. Care was
taken not to injure the angular gyri.
The operation was completed at 3.30 p.m.
4.10 p.m. The animal after lying in a state of stupor till now begins to move, but
staggers a good deal. The eyes are open and the pupils dilated.
It indicates consciousness by turning its head when called to.
4.45 p.m. Sits quietly with its head down on its chest. It drank a little tea in which
its mouth was kept immersed. Turned fiercely round on its tail being pinched.
5.45 p.m. Gives emphatic evidence of sight. Ban away when I approached it, carefully
avoiding obstacles. Seeing its cage door open, it entered and mounted on its perch,
carefully avoiding the cat which had taken up its quarters there.
Tried to escape my hand when I offered to lay hold of it, but picked up a raisin which
I had left on the perch.
8 p.m. When not disturbed sits quietly with its head bent on its chest. Easily roused.
Does not take any food or drink offered to it.
12 midnight. Is sound asleep on its perch. Has not eaten any of the food left in
the cage.
January 23 rd. — 10 a.m. Animal found sitting in the cage with the head bent as
before. Drank a little milk held up to its lips. When removed from the cage walked
about somewhat unsteadily, and then sat down as before. The eyes are partially closed
from oedema of the eyelids. Sight continues. Made for a warm corner by the fire.
Wakes up and grunts when called to. There is no loss of motion or sensation as far as
can be seen.
DK. D. FEEEIEE ON THE BEAIN OE MONKEYS.
479
3 p.m. Still continues sitting as before. When disturbed moves very unwillingly and
apparently with great caution, as if its sight were impaired, occasionally knocking its
head against obstacles. Drank some water, but would not eat.
9 p.m. The animal remains as when last seen. Has taken no food.
January 24 th. — 11 a.m. Found lying prostrate in the cage. Killed with chloroform.
Post mortem Examination. — The exposed surface of the occipital lobes on their supe-
rior and lateral aspect was soft and pulpy and suppurating. The extent is marked by
the shading in figures 29, 30, 31. The softening extended deeply into the interior, but
did not affect the under or inner aspect of the lobes.
The angular gyrus on both sides was of normal consistence, but the grey matter had
a yellowish tint in the posterior half.
There was no effusion into the lateral ventricles.
The rest of the brain was quite normal.
Fig. 29 represents by the shading the extent of destruction of the grey matter of the occipital lobes in
Exp. XXTT.
Fig. 30.
Fig. 31.
Fig. 30 indicates the extent of softening in
the right occipital lobe in Exp. XXTT
Fig. 31 indicates the extent of softening in
the left occipital lobe in Exp. XXII.
480
DE. D. TERRIER ON THE BEAIN OP MONKEYS.
In this experiment the results as regards sensation and voluntary motion were entirely
negative. Sight became affected later ; and this can be accounted for by the proximity
of the angular gyrus to the lesion, and the commencement of pathological change in its
substance. Nothing further was to be observed, except the dull dejection and melan-
choly attitude of the animal and its persistent refusal of food.
Experiment XXIII.
March 10 th, 1875. — The occipital lobes were exposed in a small and rather weakly
monkey, and the lobes severed by perpendicular section with hot wires about a quarter
of an inch posterior to the parieto-occipital fissure, so as to avoid all interference with
the angular gyrus. The operation was completed at 4.30 p.m., the animal having by
the time the wound was dressed almost completely regained consciousness.
4.45 p.m. Begins to move about in rather a staggering manner, but exhibiting no
muscular paralysis.
4.55 p.m. Can see quite well, as it avoids obstacles, and when removed regains its
place by the fire. Twitches its ear and turns its head when called to, or a noise made.
Can sit quite steadily.
7 p.m. Sits still looking about vacantly. Will only move when nudged. Tactile
sensation is unimpaired. Sight and hearing continue. Withdrew its head sharply
when acetic acid was held before its nose. Made movements of tongue and mouth, as if
to expel it when colocynth was placed in its mouth. Circulation and respiration regular
and normal.
The animal has refused food and drink.
7.45 p.m. Drank a few teaspoonfuls of tea held up to its lips, and accidentally placing
its hand in the dish stooped and drank up the contents.
When left to itself, takes up a position with its head bent on its chest and covered
with its hands.
8.45 p.m. Remains as before. Refuses to eat or drink. When a dish of milk was
held before it in such a manner that it could not hold its head down without immersing
its mouth in the liquid, it sipped a little but wished to avert its head.
9.40 p.m. Reaction to taste again tried with aloes, and again discomfort manifested.
Turned away its head when assafcetida was held before its nostrils. Active reaction to
acetic acid. Smelt at its hand on which some assafcetida had been spilt.
12 midnight. Lies asleep in cage breathing quietly. Easily roused by a touch on
its hand, which caused it to open its eyes. Animal weak.
March 11 th. — 9.30 a.m. Found dead in its cage and rigid, death having occurred in
the night.
Post mortem Examination. — The brain was everywhere normal except in the region
of the occipital lobes. The occipital lobes had been completely divided and removed on
both sides, but more on the right than on the left. The parts removed are indicated in
figures 32, 33, 34 by the shading.
DR. D. FEEEIER ON THE BEAIN OE MONKEYS.
481
The lungs were normal, of pinkish colour. The heart was dilated, and its cavities full.
The stomach contained a few coagula of milk which it had swallowed. The other vis-
cera presented no abnormal appearance.
There was therefore nothing to account for death in the animal except the prostration
consequent on the operation in an animal of weakly constitution.
The only facts, therefore, which can be relied on as proved by this experiment are the
negative results as regards the individual senses and the powers of motion. The
abolition of appetite was not absolute, but nearly so. The occipital lobes were not
entirely removed, as will be seen by the figures.
Fig. 32.
Fig. 32 indicates by the shading the extent of removal of the occipital lohes in Exp. XXIII.
Fig. 33.
Fig. 33 indicates the extent of removal of
the right occipital lobe in Exp. XXIII.
Fig. 34.
Fig. 34 indicates the extent of removal of
the left occipital lobe in Exp. XXIII.
Experiment XXIY.
March IWi, 1875. — The occipital lobes were exposed in 'a large and strong macaque,
lively and active, but of rather a timid disposition and unwilling to be handled. With
mdccclxxv. 3 s
482
DK. D. EEEEIEE ON THE BEAIN OE MONKEYS.
hot wires the lobes were divided and removed by a line somewhat in advance of the
anterior extremity of the superior occipital sulcus, but the exact line was doubtful.
The left section sloped posteriorly, the right was almost perpendicular to the tentorium.
There was very little haemorrhage, and the operation was rapidly completed at
11.30 a.m., the animal being almost conscious during the dressing of its wound.
11.45m.M. The animal has been lying quietly looking about, but has not moved.
While this note was being written the animal sat up spontaneously, but feeling weak
and unsteady lay down again. Turned its head and looked when called by name.
Got up and tried to walk, but staggered and fell.
12.10 p.m. Oscillates while sitting up and totters when it tries to walk.
Sits near the fire, rubbing its nose and ears when they become too hot. Followed its
companion with its eyes, but cannot succeed in walking steadily to join it.
12.20 p.m. On my approaching it and making a threatening grimace at it, it turned
away making mouths at me as usual. A few minutes after ran away when I approached
it, moving now almost quite steadily.
7 p.m. Can move about freely ; but there seems to be some confusion or defect of
vision, as the animal puts out its hand to reach things without appreciating distance.
Can see its way, however, tolerably well. Smells at various kinds of food offered to it,
but refuses to eat. Refused tea, of which it formerly was very fond. Objects to being
disturbed, and sits hugging its companion, which it occasionally salutes with a tug or a
bite when it does not sit quiet.
March 19 th. — 10 a.m. Refused all food. Looks rather dejected, but otherwise is well,
retaining its muscular powers and sensation unimpaired, with the exception of slight
defect in vision, as above noticed.
The wound looks healthy, and the animal vigorous.
11.15 a.m. Licked at a piece of orange offered it, but will not eat any thing else.
Frequently treats its companion to a rough shake or bite.
5 p.m. Still refuses to eat or drink. Has taken nothing since the operation but the
piece of orange.
March 20 th. — 9 a.m. Still refuses food or drink. Sits quietly and takes little or no
interest in its companion, which runs about.
Otherwise there is no change in the symptoms, as to motion or sensation.
7 p.m. Drank eagerly a large quantity of water. Refused all kind of food.
March 21st. — 11 a.m. The animal is well and in seemingly good health. The wound
is oozing only slightly at one part, the greater part having healed up.
Came out of the cage when the door was opened and walked to the fire, before which
it sat down with a contented grunt. Still refuses to eat.
1 p.m. Greedily accepted and ate a piece of orange, which is the only thing it seems
to have any desire for. Incidentally it was observed to seize hold of its companion
(a male) and make the movements of coitus. This occurred twice. (The testicles
existed, but the penis had been amputated.)
DE. D. FERRIER ON THE BRAIN OF MONKEYS.
483
2 p.m. Drank water, but refused food.
7 p.m. Again eagerly drank cold water. Does not exhibit any desire to eat the food,
of which there is a plentiful supply in the cage. Goes occasionally and takes a draught
of water. It was once at this time observed to nibble a crust of bread, but further did
not manifest any sign of hunger.
March 22nd. — 10 a.m. Looks very dejected, sitting quietly in a corner of the cage.
Took a little water held up to its mouth, but would not eat.
7 p.m. For the first time since the operation has exhibited a distinct desire to eat by
accepting and eating a piece of bread and then drinking largely of water. This was at
the end of the fifth day. Otherwise the animal is as before.
8 p.m. Refused its former beverage tea, of which it used to be fond. Sits dejectedly
in a corner of the cage, feeling its head and licking its hand occasionally. The wound
looks well, only oozing slightly.
11 p.m. Again offered food, but refused all the food the other monkeys seemed to
enjoy. At last, on bqing offered a cold potato, it took it in its hands, smelt it carefully,
and then, as if suddenly struck by a new idea, began to eat with great gusto.
March 23 rd. — The animal looks well and less dejected than before. Walked out of
the cage when the door was opened. Retains its muscular power and senses as before.
Ate and drank several times during the day. Seems to have recovered its appetite for
its former food.
March 24 th. — The animal continues well and took its breakfast as usual.
Today it was placed in a hamper and taken to the country, to be under my obser-
vation during a short absence from London.
April 10 th. — Since last observation the animal has continued well. The wound
gradually healed up completely. The animal retained its appetite, eating and drinking
heartily. With the exception of the defect of vision, seen particularly in the want of
appreciation of distance, the animal had recovered perfectly to all appearance. It would
be difficult to say what alteration in its disposition had occurred, yet it looked duller
and less active than it used to be.
It had, however, entirely recovered from the effect of the operation, and was used for
another experiment to be recorded next (see Exp. XXV.).
This experiment is remarkable as being the only successful case I have observed of
recovery taking place after removal of a large portion of the skull and a considerable
quantity of the brain-substance.
The history of the animal offers some interesting features, and is a further illustration
of the entirely negative effect as regards motion and sensation of destruction of the
occipital lobes. The only exception was with reference to vision, which continued
impaired throughout. In the other cases when vision was lost or impaired, it was
found on post mortem examination that the angular gyrus was more or less affected.
In this case also, as will be seen from the post mortem examination (p. 486), the angular
gyrus was again the seat of lesion.
3 s 2
484
DR. D. FERRIER ON THE BRAIN OF MONKEYS.
This animal exhibited less of that dejection and depression which characterized the
other animals similarly operated on.
It is difficult to single out any one positive result of the destruction of this part of
the brain, except the remarkable aversion to food which was observed almost invariably.
This may be regarded as due to the constitutional disturbance consequent on such severe
mutilation ; but if so, it will be difficult to account for the fact that equally severe
mutilation of the frontal lobes and other parts of the brain caused little or no impair-
ment of the appetite for food.
I am disposed to think, therefore, that the aversion to food stands in causal relation
to the destruction of the occipital lobes as such, and that these lobes are somehow related
to the systemic sensations. The other animals did not live long enough to decide as to
whether this condition should remain permanent ; but in experiment XXIV. the animal,
otherwise exceptional, after remaining without food for a period of five days, again
recovered its appetite and continued to eat as before.
Thirst did not seem to have been affected to the same extent as the appetite for food.
If the systemic sensation of hunger has its seat in the occipital lobes, it is difficult to
account for the restoration of this appetite after these lobes have been removed. Yet
it is possible that compensation may have occurred by association with other senses, such
as of taste and smell. This is offered as a possible explanation ; but it must be admitted
that neither the electrical irritation of the occipital lobes nor their destruction suffice
to indicate clearly the functions which these lobes perform.
It would appear from experiment XXIV. that their destruction does not abolish the
sexual appetite. The exhibition of this appetite may perhaps have been due to irrita-
tion of some centre in proximity to the seat of lesion. Some interesting speculations
might be made with reference to these results ; but as my object in this paper has been
to restrict myself to conclusions directly deducible from my experiments, to enter on such
would be foreign to the subject.
The following experiment is interesting, and one perhaps not often capable of repetition.
Conjoint removal of Frontal and Occipital Lobes.
Experiment XX Y.
April 10 th, 1875. — The monkey which had had its occipital lobes removed on
March 18th (exp. XXIV.), i. e. twenty-three days previously, and which had apparently
quite recovered, was placed under the influence of chloroform, and the frontal lobes
removed on both sides by a line approximately traversing the anterior extremity of the
supero-frontal sulcus.
The operation was completed at 12 noon.
The animal had regained consciousness before the wound had been quite dressed.
12.10 p.m. On being let loose and placed on the floor, it sat up and began to move
about in a tottering manner. When it shook itself it fell over on its side.
12.20 p.m. Is sitting up somewhat unsteadily and gnawing at whatever comes within
DR. D. TERRIER ON THE BRAIN OE MONKEYS.
485
its reach. Occasionally suddenly puts out its hand, and frequently rubs its nostrils as
if there were some source of irritation in them.
It gives complete evidence of retaining hearing.
2 p.m. Runs away when I approach. Is not quite steady in its movements. Can find
its way into its cage as before when taken out. Sight continues as formerly.
2.80 p.m. Drank some water and ate some fruit. Sits on its perch occupied in feeling
its head and licking its hand. Seems much less timid than before ; does not seek to
move off its perch when about to be laid hold of, but resists and offers to bite. When
not disturbed sits in a dreamy sort of state, taking no notice of any thing.
4 p.m. Found sitting in the same position as when last seen, with its head bent.
Looks vacantly, and does not seem to mind an attempt to lay hold of it. When seized
it resisted, and attempted to bite, exhibiting great anger.
Ate some food offered to it. When removed from the cage it walked about restlessly
and without seeming to have any purpose. Ran away on being approached, but did
not as usual make for its cage.
12 midnight. The animal sits still and is evidently feverish, the head being swollen
and hands and feet hot.
April 11th. — 11 a.m. Found asleep in a corner of the cage. When removed it subsides
into a deep sleep and nearly falls over, but recovers itself suddenly. There is no motor
paralysis, and sensation is unaffected.
This state continued during the day, and towards night the animal fell into a state of
semistupor, and did not seem able to support itself on its legs, sprawling about occa-
sionally when disturbed. No convulsions were observed.
April 12th. — The animal was found dead in its cage at 10 a.m. partially rigid, so that
death must have occurred some hours before.
Post mortem Examination. — The scalp was cedematous, and there was a considerable
amount of pus oozing from the wound. The skull was deficient over the region of the
frontal and occipital lobes. The brain-substance at the occipital openings was adherent
by adventitious membranes to the under surface of the scalp. The left looked of normal
colour and not congested. The right was congested, and appeared as if it had received
a contusion from a fall.
From the frontal openings there protruded two livid hernise cerebri. On removal of
the dura mater, a layer of pus was found coating its under surface. This was not
adherent to the brain-substance, from which it stripped entirely.
The brain-substance had normal colour and consistence.
The roof of the orbit was also covered with pus, which extended as a thick layer into
the sphenoidal fossae, but was easily detachable and of recent formation.
The base of the brain and cranial nerves were free from signs of inflammation. There
were traces of inflammation and some degree of suppuration between the longitudinal
fissure at the occipital region and over the tentorium cerebelli. These were to all
appearance of older formation than those in the anterior part of the skull. The cere-
bellum had a normal appearance.
486
DR. D. FERRIER ON THE BRAIN OE MONKEYS.
After the brain had been hardened in spirit, it was found that the frontal lobes had
been removed by a line crossing the anterior extremity of the supero-frontal sulcus on
both sides. The plane of section sloped somewhat forwards, and the under surface of
the orbital region remained where it conceals the olfactory tracts and bulbs. The cut
surface bulged considerably and the edges of the section were softened nearly as far back
as the antero-parietal sulcus on both sides (see figures 35, 36, 37). The edges were
raised, and the vessels were injected for some distance posterior to the cut surface.
Fig. 35.
Eig. 35 represents by shading the extent of destruction of the frontal and occipital regions in
Exps. XXIY. & XXV.
Fig. 36.
Fig. 37.
Fig. 36 represents by shading the extent
of destruction of the right hemisphere in
Exps. XXIV. & XXY.
Fig. 37 represents by shading the extent
of destruction of the left hemisphere in
Exps. XXIY. & XXY.
The occipital lobes had been removed almost completely. On the left side the hemi-
sphere became rounded off just behind the posterior limb of the angular gyrus, which was
intact. On the right side the posterior limb of the angular gyrus was ragged and torn,
and formed part of the edge of the plane of section (see fig. 36).
DE. D. EEEBIEB ON THE BEAIN OE MONKEYS.
487
With the exception of the injection of the vessels of the pia mater behind the frontal
section, the rest of the brain had a normal aspect.
The most important fact demonstrated by this experiment is that the conjoint removal
of the frontal and occipital lobes exercises no effect on the powers of voluntary motion
or of sensory perception.
The results of the post mortem examination indicate that the phenomena of the second
day are not to be regarded as the effect of the removal of the frontal lobes as such, but
as due to the inflammatory complications which resulted in death.
But the fact that for many hours after the operation the animal continued to retain
its powers of sensation and of volition, proves that these faculties are independent of
the frontal and occipital lobes, and that they are associated with those parts of the brain
which, by other experiments, I have shown to be specially related to sensation and
motion.
What the positive effects were, as distinguished from the merely negative, it would
be difficult to state in exact terms. They are quite in accordance with experiments
already related as to the effect of destruction of the frontal lobes.
Without entering further into the psychological aspects of these results, I would sum
up the conclusions which seem to me to be legitimately deducible from them as follows: —
(1) Ablation of the frontal regions of the brain which give no reaction to electrical
irritation is without effect on the powers of sensation or voluntary motion, but causes
marked impairment of intelligence and of the faculty of attentive observation.
(2) Destruction of the grey matter of the convolutions bounding the fissure of Rolando
causes paralysis of voluntary motion on the opposite side of the body, sensation remaining
unaffected, while lesions circumscribed to special areas in these convolutions, previously
localized by the author, cause paralysis of voluntary motion limited to the muscular actions
excited by electrical stimulation of the same parts.
(3) Destruction of the angular gyrus (pli courbe) causes blindness of the opposite eye,
the other senses and voluntary motion remaining unaffected. This blindness is only of
temporary duration, provided the angular gyrus of the other hemisphere remains intact.
When both are destroyed the loss of visual perception is total and permanent.
(4) The effects of electrical stimulation and the results of destruction of the superior
temporo-sphenoidal convolution indicate that this region is the centre of auditory per-
ception.
(5) Destruction of the hippocampus major and hippocampal convolution abolishes
the sense of touch on the opposite side of the body.
(6) The sense of smell has its centre in the subiculum cornu ammonis or tip of the
uncinate convolution on the same side.
(7) The sense of taste is localized in a region in close anatomical relation to the
centre of smell, and is abolished by lesion of the lower part of the temporo-sphenoidal
lobe.
(8) Destruction of the optic thalamus causes complete ansesthesia of the opposite side
of the body.
488
DR. D. EERRIER ON THE BRAIN OF MONKEYS.
(9) Destruction of the occipital lobes produces no effect on the special senses, nor on
the powers of voluntary motion, but is followed by a state of depression and refusal of
food not to be accounted for by mere constitutional disturbance consequent on the
operation. The function of these lobes is regarded as obscure, but considered as being
in some way related to the systemic sensations. Their destruction does not abolish the
sexual appetite.
(10) After removal both of the frontal and occipital lobes an animal still retains its
faculties of special sense and the powers of voluntary motion.
[ 489 ]
XVII. On a Class of Identical Relations in the Theory of Elliptic Functions.
By J. W. L. Glaisher, M.A., Fellow of Trinity College , Cambridge.
Communicated by James Glaisher, F.R.S.
Received November 23, 1874, — Read January 14, 1875.
§ 1. The object of the present paper is to notice certain forms into which the series for
the primary elliptic functions admit of being thrown, and to discuss the identical rela-
tions to which they give rise. These latter, it will be shown, may be obtained directly
by the aid of Fourier’s theorem, or in a less straightforward manner by ordinary
algebra.
§ 2. Whenever we have a periodic function of x, say \px, such that yJ/x=ip(x-}-yj), it
is well known that we may assume, for all values of x,
i \ i a 2vx . a 4«r
V/ar=A0+A1 cos \-A2 cos \- &c.
/J. - fL
-j-Bi sm — +B2 sin f- &c. ;
p, y.
and if ypx be even, so that ypx=ip(—x), then B„ B2, &c. all vanish; while if \j/x is
uneven, so that \px= — \p(—x), A0, A1? &c. vanish. If ypx is such that ■tyx=-$(x-\-p),
then we have
• a 7rx . 3irx p
■d/x= A. COS kA„ cos — 4- &c.
T l y. ' 3 y. 1
. ntx „ 3ttx „
=Bj sin — + B3sm — + &c.,
according as -tyx is even or uneven.
But there is another totally different form in which ipx may generally be exhibited,
viz.
'px=<px+<p(x—{A)-±-<p(x-hft)-l-<p(x—2y,)-l-<p(x+2p)-i- &c.
or
zspx—p(x—fi)—p(a+f6)+p(x— 2fA)+p(x+2jt)— &c.,
according as yp(xA-g')=4'X or = — ipx.
The sine and cosine cannot be so expressed, but the other primary circular functions
do admit of this form, as, ex. gr., in the formulae
cot tT— — -J- ] -4 7. -J- . 0 + &c.,
X 1 x — 7T X-\-Tt 1 X — 2 7T 1 X -J- 2tT 1
1 . 1 J n
— -l- pr~ d- , ^ — &C.
-IS X + 7T 1 x — 2 or 1 r
x+2i r
3 T
MDCCCLXXV.
f
490
ME. J. W. L. GrLAISHEB ON THE THEOEY OE ELLIPTIC FUNCTIONS.
(in which, after the first term, the series proceed by pairs of terms, so that for every
term — - — there is a term — r —
x — me x + m r
Thus in general (although the sine and cosine are, as just mentioned, exceptions)
we shall have, by equating the different forms of \|/#, identities such as ex. gr. (if
is even)
Q'KOC 4l7TX
<px-\-<p(x—yj)-\-<p(x+yj)-\- &c.=Ai+A! cos — +A2cos— — j- &c.
Also, it will be seen in § 10 that in certain cases even when ipx is not periodic it may
be exhibited in the form [*)-\-<p(x +(*)-{- &c., and we shall obtain identities
in which the two sides of the equation are non-periodic.
§ 3. Before applying these principles to the elliptic functions, it is convenient to
write down at once the following eight formulae, which are to be found in the ‘ Funda-
menta Nova ’ (pp. 101, 102, &c.), and which are all placed together in Durege’s ‘ Theorie
der elliptischen Functionen’ (Leipzig, 1861), pp. 226, 227 : —
2tt f qi .7 TU qi . 37 ru , 0 )
sin am sm p^p sm ^ + &c. |,
2tt ( q Ttu qi 3mi 0 )
cosam«=jE|n^co82K+TT?cos2K+ &c.j.
cosec am u
to 4 q .to 4 q
= 2KiCOSeC2K + T=5Sln2K
4 q6 . 3to p f
r^3sm2K+ &C‘j>
7 r f to 4 q to 4 o3 3 to „
secamM=2FS|sec5s-rj^coS2-g+T^cos2K- &c.
1 7T 4*7 TO 4o2 2to d )
A — 77Trf?{ 1 — r~ ; — oCOS-^H-, , 4 COS -xf — &C. >, .
Aamw 2&'K) 1 + <p K 1 1 + g4 K j’
7T ( ,7 TU 4 fl2 . TO 4<74 . 2TO n )
cot am w=2ld cot 2K — 1+F Sm K _ 1+7* sm K ~ &c<
(1)
(2)
. 7T f 4 q TO 4o2 2to n )
A am m=2k|1 + cos k+TT? C0S X + &cj’ (3)
, 7T f TO 4^2 . TO 4g4 . 2to d ) ...
tan am ^^tan ^-pq^sm K+p^srn &c.|, (4)
(5)
(6)
(7)
(8)
wherein, of course, K .
_7tK
In what follows, let r—e~ K' , and take
ttK' ttK
P=~K » "= X’
so that
M, r=e ", and gJv=n<1.
ME. J. W. L. GLAISHEE ON THE THEOET OF ELLIPTIC FUNCTIONS. 491
» 1 i , 7 T U , Ti ll t , 7TX’ VX'
Also let ^=2K an(* z~oW’ so ^=— =— .
§ 4. The process of transformation into the form
<p%db<p(x— |W')±,P(^+jM')+ &c-
may be conveniently exhibited on (2) ; we have
2Kx
cos am ~^~ = cos am u= sec am (ui, k'), which, from (6),
'2/cK')ez-
4 r ez + e
TT~r
2 1
4rs e?z + e~
&C.
: /JIC j ez+e-2 ~(eZ~^e~z)(r — r2 -{- r3 — &c .) + {&3z + e 32)(r3— Z+r9— &c.) — &c. j
7T l
re?
/cK'|ez + e z 1 + r2e2z 1 + r2e_2z I + r4e2z-^ 1 + r4e-2,
1 1
-&c.
’&K')ez-(-e-z rez + r-1e-z
l 1
1 1 _ , 1 _&cl
+ re~z' rV + r~2e_z ' r 2e2z + r2e 2z j
'AK'
■ + r *r r* 1+r 0 ^ rir+1-J-j* C+1) rw 2 + r 0 0 rn,+2+/‘ C*-+2) j
:+-
77-S— &C.1.
The process requires that rez should be <1, that is, that u should be <2K; but as
both sides of the equation are such that they change sign without being altered in value
when u + 2K is written for u, we see that the result obtained is true for all values of u.
Thus we have
cos am 2K.r=-
' kK!\r* +r~x r*-1+r-(*-1)
for all values of x.
If in (10) we take x=0, we have
7r 2 r
4=g^+^-»+r-«-«+&c-} • • (io)
+ r~^_r"
■ + r 2
■ — &C.
or, writing K and K for K' and k, and therefore q for r,
2h'K
ic
4g , 4g2
1+g2 M + r/
which is at once seen to follow from (7), and is given by Jacobi, ‘ Fundamenta Nova,’
p. 103.
It is, of course, easy to deduce (9) directly from the infinite product
1 — cos am us
1 + cos am u
=tan 77 II
(1 — 2 q2n cos x+q*n ) (1 + 2q2n~l cos x+qin~2)
(1 + 2g,2,tcos x+qin) (1 — 2 q2n~l cos x + qin~‘2) ’
for consider
1 — 2q2n cos x 4- qin . . , (1 — q2neix) (1 — q2ne~")
1 + 2 q2n cos x + q*n’ W 1C (1 + q2neix) (1 + g,2“e_ix) '
492 ME. J. W. L. GLAISHEE ON THE THEOET OE ELLIPTIC FUNCTIONS.
Taking the logarithm and differentiating, we obtain, after a little reduction.
wif 1
K| ‘ q~*ne™—q*
o—ix I n— 2
Similarly, from the uneven factor we get
.«/. 1 . 1
g2 *»— 1g“5 q— (2»— l)g— i»l q—(2n—l)eix g2n— lg-
thus
k! m y( 1
>s am (K— u) 2KC0SeC^~’_K q-^e-1
2npix n2np—ix ry2n~ lPioc n-(2n-l)p-i
q—**e — q*n— Le™ — q
q-(2n-\)eix_q2n-\erixy
Replace u by K — u, that is to say x by \k — x, and remembering that e^—i,
e-¥*— we find
secam«=~|Sec*+22(?iei~=^+. . . ■ ■ •)}•
(9) for sec am (ui, k'), that is, for cos am u.
If the other formulae in the group (1) to (8) be transformed in the same way, viz. by
use of the identical equations
sin am u——i tan (m, k’),
A am u= cosec am (ui-\- K', kf),
we obtain the following seven formulae
-(z-l) ^+i_r-(r+i).
0 7T (r* — r~x rx~1 — r-(x-i) ^+i
y X 1 _|_ /* (X 1) ryX+lj^y* (£+1)
yX — 2 rp— (X— 2) ^.Z + 2 y— (Z + 2)
— &c.
“h pX— 2 (x~ 2) /-Z+2 J.— (Z+2)
A am 2 K# = i } -f ^ + 1 +* - (*+ 1 > + &c,
tan am 2K^=^,|rZ_i_Ir_(,_i)+^+i4-(x+i)+?J-f 4--^f)+&c7’
1 7T jrr + r-x i*-4 -f r-^-1) ,*+i + r-(*+i) |
sin am 2 Ka? 2K,|rc — r-® r1-1— rc+1— r-(:c+1)"^’ C'j’
1 7r f / ‘L ■- I ■ 1 )
cos am 2Ka' k!}sJ\rx~'^ — r_o-3) rx+^ — rx_|- — 7,_(-r_S)'^- C'J’
A am 2K« ^K,"jrr_^ + r~(z_^) 4"^+! + ,--^+*)+ + r-o-§) + &c-
• (11)
• (12)
• (13)
• (11)
■ (15)
• (16)
cot am 2Kr= — ^|yJi~^4-^:-1_^-(a:-i)+y.J+i_1r-(a;+r) + &c.j. . . . . (17)
ME. J. W. L. GrLAISHEE ON THE THEOET OE ELLIPTIC FUNCTIONS.
493
It must be remarked that in (11) and (14) the number of terms must always be
uneven; this point will be noticed at greater length further on (§ 10).
§ 5. Writing the hyperbolic sine, cosine, &c. as sinh, cosh, &c., these formulae may
also be written in a somewhat different form : thus
cos am w=5£j£/j sech sech ^(w— 2K)— sech ^7 (w+2K)+&c.j,
sin am M=^y|tanh tanh (u— 2K) — tanh gjjy (w+2K) + &c.j,
and similarly for the others.
I do not think it likely that the formulae (10) to (17) are new, but I have not
succeeded in finding them anywhere. Schellbach (‘ Die Lehre von den elliptisehen
Integralen . . . ’ Berlin, 1864, p. 38) gives the corresponding forms for du, 6l u , &c.,
but he does not allude to the similar expressions for the elliptic functions. It would,
however, in any case have been necessary for the explanation of the rest of this paper
to have written down the latter and demonstrated one of them.
§ 6. By equating the values of sin am u, cos am u, &c., as given by (1) to (8) and by
(10) to (17), we obtain a series of identities of an algebraical character ( i . e. which are
independent of the notation of elliptic functions). Thus from (2) and (10) we have
(remembering the definitions of v, &c. at the end of § 3)
kK\
cos x cos 3x cos 5x
cos 3x cos 5x
-+■
cosh % cosh ^ cosh
&c.|=^^{sech2: — sech(s— v) — sech(2; + v)+ &c.},
" ~2
+ &c. = ^ jsech 7l~ — sech ^ (# — 7r) — sech ^ (x-\-r) -f- &c.|.
This may be written (by interchanging x and z, and v) in the rather more conve-
nient form
sech x— sech (x— p) — sech (x + sech (x—2 p) -f- sech (x-\- 2p) — &c.
icx 3nx 5irx
n , cos — cos cos —
* fM3,^ + oosh^+cosh^+ )
2{X. 2 p p
In the same way, by comparing (1) and (11), we find
. %
, sin
tanh x— tanh {x— p) — tanh (x-\-(a)-\-&c.=—< -j ~r2-\-Scc. > ;
^ 1 sinh ~ sinh — — '
. tcx . 3 nx
sin — sin
and by comparing (3) and (12),
2|*
sech^-J-sech {x— ^)-j-sech (^+('A)-f&c.=--jl-{-
2irx 4%x
2 cos 2 cos
f4 _L
:o +&C.
cosh — cosh
(18)
(19)
(20)
494 ME. J. W. L. GLAISHEE ON THE THEOEY OE ELLIPTIC EUNCTIONS.
The comparison of (4) and (13) gives
cosech (x—^ + cosech (^+^) +cosech (%— if) + cosech +&c.
. . 2nx A . 4%x
4 sin 4 sm
*(.7TX ft ft )
=;]“tan7+^ 1? — +&c-
* e* + 1 e'+l >
which, on replacing x by x-\-^(Jj, becomes
, 1 OliX 1 OiU -V
cosech x-\- cosech (x— p)-\- cosech (^d-^) + &c.=-<cot— — ■ -2-2-— ~ ^2— — — See. >.
^ ^ e^ + 1 e^+l )
From (5) and (14) we deduce
. . 2nx . . 4irx
4 sin 4 sm
. irx . . 3nx
4 sin — 4 sin —
coth#— coth (x— /a)— coth (#+^)+&c.=--jcosec — — — -f 3t2 ^--{-&c. 1. (22)
^ ^ e~ — l eT-i >
The comparison of (6) and (15) gives
—cosech (x— cosech + cosech (^—2) ~~&c-
■n (
=-<sec — — -
ttx . 3 irx
4 cos — 4 cos
A . irx . . 3irx
4 sin — 4sin-
s^+l e* +1 J
which, on replacing x by becomes
cosech#— cosech {x—^)— cosech (^+i«/)+&c.=-< cosec — — &c. >.
^ ^ «* + l e^ + 1 J
The comparison of the forms for ^ ^ , (7) and (16), merely gives an equation which,
on replacement of x by x-\ --^a, is identical with that resulting from A am u, viz. (20),
while the forms of cot am u, (8) and (17), lead at once to (21).
In the expressions on the left-hand side of (19) and (22) the number of terms included
must be uneven.
It is proper to remark that the formulae for <px—<f>(x—[^) — <p(#+|W')+&c. can be
readily deduced from those for <p#+<p(#— p) -f <p(#+/a) +&c. ; thus (18) is a consequence
of (20) and (23) of (21). For ex.gr. in (20) write 2 ^ for /a, and we have
„ irx 2irx
2 cos — 2 cos
sech x + sech (x— 2^) + sech (#4-2fA)-|-&c.=^ jl-f Jr+&c. >
^ t cosh — cosh — '
2/a /a
ME. J. W. L. GLAISHEE ON THE THEOEY OF ELLIPTIC FUNCTIONS. 495
Double this result and subtract (20) from it, and we have (18). In a similar way
(23) follows from (21).
The converse proposition is not true, viz. given the value of <px—<p(x — p) — <f>(x+[t) + &c.,
we cannot deduce the value of <p#+<p(,r— jU/)+<P(#+iM') + &c-
§ 7. The results admit of being connected directly with Fourier’s theorem in the
following manner : it is of course well known that every integral of the form
or, let us write,
gives rise to a series
and that similarly from
there follows
J <p(x) cos-nx dx=A'n,
x nwx , .
1 <P(tf)cos— - dx=An,
Jo ^
<p#=- < A0+2A,cos — +2A2cos — — |-&c. > ;
\ . ni xx , „
1 <p(x) sin — dx= B„
2 (_ . 7r^ . 2ttx , D )
^=- jB, sin— +Basm — + &c. J- ;
and it will now be shown that if <px is an even function of x, and if
f <p(x)cosr^-dx=An,
then
<px -t- <p(x - (a) + <p (x + (t) + <p (x — 2(t) 4- <p(x+ 2p) + &c.
and
|A0+2A2cos^+2A4cos— +&c
<p#— <p(#— |Ea) — <p(#+^)+ <p(#— 2^) +<p(^ -f- 2f/>) — &c. jA, cos ^ + A3cos ~+&c.
also, that if <px is an uneven function of x, and if
then
and
. > . mrx
<p(x) sin — dx-.
■ B„,
<$>x + <p(x - (b) + <p (x -1- yj) + &c. = £ | B2 sin ~ + B4 sin ~ + &c.| ,
<px— <p(x— p) — <p(^-j-i«')+&c.=-iBi sin— -j-B3 sin^^+&c.l.
fj, ^ [A. [A j
(26)
(27)
It is sufficient to prove one of these formulae ; take (24). Since <px is an even function,
<px-\-$(x— ^)+<p(#+^)+<&c. (which call -tyx) is a periodic function with period and
496 ME. J. W. L. GLAISHEE ON THE THEOEY OF ELLIPTIC FUNCTIONS.
the right-hand side of (24) must be of the form
A0+A2 cos — + A4cos — +&c.
Now, <p being even,
„ . ( . . 2rmx 7
2A2m=l <p(x)cos — dx
2mm x
But
={ • • -+J- +f+I +-•} cos T dx-
i <p(#)cos dx=( <p(|— p) cos d%, on taking x=%—(a,
J-m ^ Jo P
f <p(#)cos dx=\ <p(£+/^) cos :^^-dj~, on taking x=%+(a;
Jn P Jo P
2A2m=f {<p£ + <p(£-^)+<?5(£+^)+- • • }cos^~d^
Jo r
C* , / x 2imx 7 . , p.
= ) $(#) cos — — (M7= A2m . g,
Jo ‘
unless m=0, in which case
2A0=Ao . [a,
so that (24) is proved. Formula (25) may be either obtained independently by a similar
and
thus
treatment of the integral
2Am = f <p(x) cos ^ + l)™ dx,
or it may be deduced from (24) by writing therein 2[a for [a (remarking that by this
substitution A2m becomes Am) and subtracting (24) from the double of the equation so
formed. Similar processes apply to (26) and (27).
The method by which the formulae (24) to (27) have been just obtained is the same
as that by which Sir W. Thomson (Quarterly Journal of Mathematics, t. i. p. 316)
deduced the theorem
cos 7TX-\-e~^2 cos ---• +&C.1 . (28)
■v/tt
It was after reading Sir W. Thomson’s paper three or four years ago, that I made a
list of all the suitable integrals of the form
<p(#) cos nx dx
that were given in Professor De Haan’s ‘Nouvelles Tables d’lntegrales definies:
ME. J. W. L. GLAISHEE ON THE THEOEY OF ELLIPTIC FUNCTIONS.
497
(Leyden, 1867), and deduced therefrom the resulting identities. The only formulae so
obtained which appeared of interest were, in fact, those which are given in the present
paper, viz. (18) to (23); but at the time I was not aware of their connexion with the
theory of Elliptic Functions. It was only recently, after obtaining the values of
sin am x &c. in (10) to (17), that I remarked that the resulting identities wrere the same
as those which I had previously deduced by the aid of Sir W. Thomson’s principle.
It was shown by Cayley at the end of Sir W. Thomson’s paper that the identity (28)
corresponds to
Q(ui, H(m+K\ K)\ ..... (29)
and it is singular that all the identities that follow from the method of this section thus
appear to correspond either to elliptic or theta-function transformations. Speaking
generally, the only evaluable integrals of the requisite form are derived from
J «--wcos2 bxdx=^e~* and f «""cos bx dx — a*+b*
(including as derivations the corresponding sine formulae), of which the former give rise
to theta-function relations, and the latter to elliptic-function relations.
§ 8. The integrals that produce the formulae (18) to (23), and the manner in which
the latter are obtained from them, deserve some attention. Thus
J* ~~xdx~^ cosnx(e~x—e~3x-\-e~ix—&c.)dx
1 3 5
ra2+l2 n2 + 32 ‘ n2 + 52
it rnt
=4 sech
whereby (18) and (20) follow at once from (25) and (24).
In a similar way we can show that
? °° sin nx
lo
it .nit
dx — ^ tanh —
7 r enn — 1
4 en7r + 1 ’
but the series obtained from the direct application of this integral would not converge :
and in order to deduce (21) and (23) from (26) and (27), it is necessary to express the
integral in the form
and to make use of the formulae
-Lcot|^ =sin 0+sin 20-}-sin 30+&c.,
\ cosec 0=sin tf+sin 3^ + sin 5^+&c.
This renders the process not so satisfactory from a logical point of view ; but practi-
MDCCCLXXV. 3 U
498 ME. J. W. L. (tLAISHEE ON THE THEOEY OF ELLIPTIC FUNCTIONS.
cally our knowledge that sin 0+sin 20-J-&C. and sin 0+sin 30 + &C. are the Fourier’s-
theorem equivalents of cot and ^ cosec d would be sufficient to leave no doubt of the
accuracy of the formulae so obtained.
In regard to the other two integrals required for (19) and (22), viz.
| tanh x sin nx dx and j coth x sin nx dx,
Jo Jo
it is to be observed that, stated in this form, their values are indeterminate ; for the
former
and the latter
=J0 (J- <®tt) sinnxdx’
=1 (1+^)
both of which involve cos go . But in point of fact for our purpose the co of the limit
of the integral is not arbitrary, but is to be of the form (m-\- 1)t, the lower limit being
—mir (or if we replace sin nx by sin the limits are (m+l)^ and — m[h). Taking
then m infinite,
tanh x sin nxdx
Jo
!~ cos nx~
l(B+I)>r
—2<
f n
L_~.
L
[n* + 22
r cos nx~j
(m+l)7r
n(
1
L~~J
0
(*»)*+
smnx dx— 2
„2 ,_a2~\~~„
OIU /tot/ 7
e**+l dX
— &C.|
Similarly
and therefore
.r cos nx~1Sm+1')v 1 , , n%
= T~\ --+2cosechT-
L_ n Jo n L
tanh x sin nx dx—\ tanh x sin nx dx
J — W7T J 0
r cos>nx~\m* 1 . v , n%
= k-cosech-^5
L » J0 n 2 2
m. , , I- cosraaT!(m+1),r , r cos nx~\
tanh x sm nxdx=\ - + —
L n I n J«
2 nir
•-+9rcosech ^
=t cosech
(30)
whether m be even or uneven, if n is uneven ; whence the result in (19) follows directly.
MR. J. W. L. GLAISHER ON THE THEORY OF ELLIPTIC FUNCTIONS. 499
A similar course of procedure shows that
coth x sin nx dx— nr coth — =7r< 1 + -K?
hA
'-1r
from which (22) may be derived.
In his ‘ Nouvelles Tables,’ T. 265, Prof. De Haan assigns definite values to the inde-
1 tanh x sin nx dx and 1 coth x sin nx dx ;
Jo J#
and it is noticeable that, if these values be used, they lead to the same results as those
just investigated. The reason is that the integrals in De Haan are in effect evaluated
on the assumption that cos oo = 0; and if in (30) we had, in place of the first two
terms, viz.
written
+-W+I
0+-+0+-,
n 1 n'
it is clear that the final result would have been the same.
It may be remarked that the identities (19) and (22) may be somewhat generalized
by means of the integrals
sinh ax . tt
c-5SSsm **<**=6
. , nx . ax
smh2bsm¥b
. nx ax’
cosh — + cos -r-
b b
cosh ax . x
sinh bx sm nx dx=2, b
sinh
, nx , ax
cosh -£- + cos ~r
b b
while other identities may be derived from
C ” cosh ax -w x
. cSihScos“&=4
, nx ax
cosh —j cos -y
2b 2b
, nx ax'
cosh ~r + cos -y-
b b
5 sinh ax 7r
stah TxC0snxdx=Yb
, nx , ax
cosh -^ + 008 —
b a
in which, of course, a is to be supposed less than b.
§ 9. The well-known reciprocity oif and <p in the formulae
f(n)=\ / (ir) • Jo $(X) C0S dx’ /(») = \/ (') 'Jo <P(X) sin nX dx
leads to a corresponding reciprocity in the formulae (24) to (27). Thus from the first
of the integrals we deduce that, <p and /'being both even functions, if
3 u 2
500 ME. J. W. L. GLAISHEE ON THE THEOEY OF ELLIPTIC FUNCTIONS.
<px -f <p (x — p) -f <p (x -f (t) -f- &c. =
then
fx +f{x - (l) +f(x + ^) + &c.=
and if
<px — <p(x—p) — Cp(x + p) + &c. =
then
fo—ftx—p) -f(x+p) + &c. =
^{/(0)+2/(^)cos^ + 2/(^)cos4f+&o.
^|,(0)+2,(f)coS2f+2?(^)cos^+&c.
2i/(2 *){n. V \ xr r/3*\ Q )
* -{/( ^ / 008 7+A^/C0S Y”+&ct
2 \/ (2 ir) ( / 7T \ ttx /SoA Snx 0 )
~r~ A cos 7 +*{j) cos v +&ct
Also, from the second integral, <p and /'being uneven, if
<px+<p(x— [A)+<f>(x +(*)-{- See. =
then
fx+ftx—yj) +f(x -\-p) +&c. =
and if
<px-<p(x—p) — <p(x- j-^)+&c.=
then
fx-f(x-p) -f(x+p) + &c. = ■
2 \Z(2tt) ( j, / 2%\ . 2 trx /»/ 4.7T \ . 4isx „ *
—{At) sinir+/(7) smir+&c'}’
■{HD sinf +A?) ,in?f +&c-}-
2\/(2tt
Applying these formulae to the identities (18) to (23), we see that (20) is its own
reciprocal, as also is the case with (18), (22), and (28); while (19) and (23) are reci-
procal to one another. Although Cauchy, in his memoir “ Sur les Fonctions reciproques ”
(Exercices de Mathematiques, seconde annee, 1827), has deduced, by means of his cal-
culus of residues, a theorem which is in fact (24), he does not appear to have specially
remarked the reciprocal character of the equations.
The application of the formulae presents no difficulty. For example, comparing (18)
with the first of the second pair, we have
<p#=sech x,
whence the reciprocal formula is
fx=
2) .sech
\J ^jsech sech ^7^ — sech
7 TX
~2 9
v/^-|sech - cos- + sech — cos^^-|-&c. i,
P l P P V- V- )
which, on replacing \icx and \<7r^ by x and ^ respectively, coincides with the original
formula (18)
§ 10. On looking at the formulae (18) to (23) it appears that although we have trans-
formations for sech x + sech ( x — + sech (#-f-ft<)4-&c., cosech x + cosech {x — p)
MR. J. W. L. G-LAISHER ON THE THEORY OF ELLIPTIC FUNCTIONS. 501
+ cosech (#+/«/) + &c., tanh x — tanh ( x — fx) — tanh(#-f-|M')+&c., and coth x — coth (x—fx)
— coth (,r+la.) + &c., there is none for either
or
tanh ^4-tanh(^ — j«,) + tanh
coth x-\- coth (x-[x)-\- coth (#+^)-|-&c. ;
it is therefore interesting to inquire what are the corresponding formulae in these cases.
If we write (21) in the form
2<tt ( it2 Qttqc 22 4.7 TOC |
cosech x + cosech (x -[x)-\- cosech (x-\-[x) + &c. = tanh — sin — -+- tanh — sin — - + &c. j,
and reciprocate it by the third pair of formulae of § 9, we obtain the following result,
tanh #-{-tanh (#— jO.)-|-tanh (#d-|H,)-b&c.
2ir( 7T2 . 2irx 2tt2 . 4%x „ ) .
= — ^cosech— sin — 4-cosech — sin — -f&c. >, (31)
p-l V- v- v- P ) v
which apparently ought to be the first of the two formulae sought ; but in point of fact
this equation (as can be shown by actual calculation, see § 16) is not true.
It seems natural to recur to the integral (30), viz.
r
mJ
tanh
dx
cos nx^m+1),r I- cosh#-]1
1 Jo J
2 . rnr
■- + 7T cosech -77,
n 1 v. 7
from which, since the first two terms of the right-hand member vanish when n is
even, we have
7»(m+l V
J —mix
, . 2n%x p m 2
tanh x sin = — — -\-ir cosech — ;
ju. me 1 jw,
whence ultimately, since \tt — ^0=sin 0-|--|sin 2^+^ sin 30-f-&c.,
tanh x + tanh (x—fx)-\- tanh (x -j- (x) -f &c.
=— — 1+— < cosech — sin — -1- cosech — sinJi:i:::-|-&c. . . .
**■ P l V- P f* P
but this result is not true either, and for the following reason : — Let
^x=Qx—<p (x—fx)—(p (x-{-[x) . . . +<p (x— n[x)+<p (x+np),
%x=<px+<p (x—(x) + q> (x+ix) . . . +<p (x— n(x)+<p (x+np)
2tt2 . 4 irx
and
(n infinite), and suppose <px is an uneven function of x which =1, when x— 00.
Then
4 /(x-\-fx)=—fyx+<p(x—nfx)+<p (x-\-(7i-\-\) p)
= —-tyx,
(32)
502 MR. J. W. L. GLAISHER ON THE THEORY OF ELLIPTIC FUNCTIONS.
so that -tyx is periodic ; but
X 0* +^)=X^-P (x~ np)+Q (#+(» + !) /*)
so that yjx is not periodic. Therefore we have no right to assume that between the
limits 0 and \x of x
tanh a’+tanh (x— /a) -|- tanh (x-\-p)-{-&c.
can be expressed in the form
. . 2 nx , . . 47 xx . 6nx
Al sm -f-A2 sin— -+A3 sm + &c.,
the true form being
-D • ™ I -D * 2%X , T> • 3,r X I D
fc>, sm ■ — j-J32 sm — 4-.B3 sm — -f-&c.
f p
We may, however, assume that between the limits 0 and of x
tanh x-\- tanh (x— ,«/)-)- tanh (#-|-^)-f-&c.=A1 sin ^-+A2 sin -(-&c. ;
and then
\ tanh x -T tanh ( x — p) tanh (x +//,) -|-&c. j- sin - — dx
+&c.|
tanh x sin —— fa
^(2m+l);
2, r • 2mrx 7
tanh x sm dx
r a, 2rntx^imJrl^ C 2
= — o — cos —4 ;--rs:
L 2n% p _|o Jq e +1
2mrx
sin dx
V-
= (-)n+1 cosech—.
^ > 2nn 1 2 ju.
We thus find that between the limits 0 and of x (and therefore also between
the limits — ^ and %/& of x)
4tCX
tanh tanh (x — ^)+tanh {x-\-^)-\-8c c.=“ ‘ sin ^ sin. -h &c. j-
, , 5T2 . 27ra? , 2?r2 . 4tx
cosech — sm — ■ + cosech — sm — -4-&c.
2x 2i t( 7 r2 . 2-7TX . , 27t2 . 4%x )
=- — — -{cosech — sm \- cosech — sm — +&c. >,
v- /M v- v- v- v- )
. (33)
the terms on the left-hand side being uneven in number, and such that for every term
tanh (x—np) there is also a term tanh (x-\-nyj).
If we write x+p for x in this formula (33) we increase the left-hand side by
9
tanh co -(-tanh co , that is by 2, while the right-hand side is increased by - . that is
MR. J. W. L. G-LAISHER ON THE THEORY OF ELLIPTIC FUNCTIONS.
503
by 2 also ; while if we replace x by x— (a both sides are diminished by 2 ; so that (33) is
true universally for all values of x, on the understanding that the left-hand side is
tanh #+{ tanh (#— ^)-ftanh (x-\-[/>)\ + {tanh (x— 2^) + tanh {x-\-2^)\ -f-&c.,
viz. that after the first term the series is to proceed by pairs of terms ; so that for every
term tanh (x+nt/j) there is also a term tanh(^+w^), and the whole number of terms
included is uneven. Thus for x=^(jij the series is
tanh -J- { — tanh + tanh f ^ \ + { — tanh f ^ + tanh \ + &c. ,
the value of which is unity ; and not
{ tanh — tanh ( + { tanh § p, — tanh f -{- &c. ,
which is equal to zero.
If we write for x, and suppose the terms arranged in pairs from the begin-
ning, we find
{ tanh (^-(-^j-f-tanh (x — ( fi- ) tanh tanh (^-f^)|--j-&c.
2x
^ jcosech —
. 2%x . 2tt2 . 4nx 0 )
sm — cosech — sm — + &c. y
p P ,a p )
(34)
as the unity which is introduced on the right-hand side by the change is cancelled by
the unity on the left-hand side, which results from the supposition that the number of
terms is even.
The last equation is, in fact, the relation
iZ («+K)=^7+Z(u+K', V)
(35)
(Fundamenta Nova, p. 165, and Dueege, § 69) ; for
2^ C q (ft |
Z (u)= k|]Y^2 sin 2x-\-jZ^i sin sin 6^ + &c.| ;
so that (35) becomes
2<7ri ( n (ft (ft 1
jH - sin 2 xi+Y^ sin sin 6^‘+&c- [
=2&'+£{“T=^sin sin 4z~&c- },
of which the left-hand side
=jl{(e2x-e~2x)(q+f+q5-\r&c.)-(e4x-e-4x)(q2+q6+q10+&c.)+&c.}
7r ( qe-x qe~2x q3e2x
Kjl + g'e2-* 1 ^-qe^21' 1 +§3e2jr
1 — qe2x 1 —qe~2x 1 —q3e
1 + qe2x 1 + qe~2x ^ 1 + q3e
(fe~
r^4-&C.
1 + (fe
*-r+&&cU
504 MR. J. W. L. GLAISHER ON THE THEORY OF ELLIPTIC FUNCTIONS,
and the identity becomes
tanh {x— ^) + tanh (tf-j-i^ + tanh (#_ f^j + tanh (x-\-%p)-\-&c.
z being and v being We see from this investigation also that the left-hand side
must consist of an even number of pairs of terms.
As (35) is obtained by differentiating logarithmically the formula
0 («+ K)=v/ (§,yS' 0 (»+K', K),
it follows that (34) is a form of the identity that results from differentiating loga-
rithmically
e~r' cos —— + 2e~^ cos-^-|-&c.}.
The formula corresponding to (33) for the hyperbolic cotangent can be shown, by a
process similar to that by which (33) was itself established, to be
. • 2-kx . ■ 47 tX
0 , 4 sin 4 sin
coth a? + coth (x— ^) + coth (a?+/») + &c.=^+^-j cot ^+-~& ^ ■+--&- + &c. [, (36)
^ ^ ^ eT — 1 en—1 ’
2x 27rjsin 2z
j«. ju. | sinh »
sm4z i o
sinh 2v~^~ C'
which holds good universally, on the same understanding, with regard to the number
and order of the terms, as that which was found requisite for the truth of (33).
§11. I now proceed to show how the identities which have been obtained in the pre-
ceding sections by elliptic functions, or by Fourier’s theorem, can be deduced from the
ordinary formulae for the cotangent and cosecant, viz.
cotx~l+^+xl%+~7r+^~+&c., (37)
co^c •■'••• (38)
by elementary algebra and trigonometry.
Thus to prove (18) we have
cosec (xJrai) = — 7—. — — - , — — — - V, -4- & c. ,
v ' > x-\ -ax x+ai—n x + ai + n 1 ’
cosec (x — ai)= — 7—. 4-&c. :
v ' x + ai x — ai — n x—ai + w 1 ’
whence, by subtraction,
2 1 — 2 — 7 — 3— / — , "T2“ 7 &c. = — cosec (x + ai) — cosec (x — ai)\.
xl-\-al {x-wf + a [x-\-Tty + ai 1 2 il v 1 ' ' n
ME. J. W. L. GLAISHER ON THE THEORY OF ELLIPTIC FUNCTIONS.
505
Now
whence
ew_e-m e~m _ i
= — 2 ieni (1 +<?2“‘ -}-e4“+&c.) ;
— cosec {x+ai)— cosec (x—ai)\=exi~a -f-e3^-3* -j-e5xi~5a +&c.
4- e-*-« -(- e-3xi-3a e. -Ut- 5a _|_ &c
and, on replacing x and a by — and we obtain the formula
r + a2 (x— jk,)2 + «2 (x + fx)2 + a2' (x — 2[x)2 + a2^ (x + 2/x)2 +
_L /
■&c.
Now from (38)
7nr _2?[? 37ivr _
= — le ^cos — (-6 * cos — -f&c.
' y y
1 1 1 1 o
— sec x— — * r~r + r~ + &c.
x — pt x — fjr x + p r af — fir
- La — .3! 4_ _&c .
—x*-(br)2 x*-(4*)2^x2-(Pr)2 ’
whence, writing xi for x,
sech x=
and
- sech (*-;»)= - (»_J»)«+ (4x)*+(*-rt« + (fr)«~ (x-rt*+ (fr)* + &C-
7T 3ir
!+(i7r)2-^ + (fw)2-r^+(^)2
37 r
— sech (x -]-(«,)= ■
+ sech (x— 2 p,)=
Lri2+&C.
(x + jx)2 + (f7r)2 ' (a? + ju,)2+(fir)2 (a? + ju.)2+(fir)
7T 37T 57T
(x - 2/x)2 + (f tt) 2 — (x — 2/x)' 2 + (pr) 2 (x — 2fx)2 + (fir) ' 2 ‘
(39)
&c.
Adding these expressions together in columns, and transforming each column by
(39), we find
sech x— sech (x— p) — sech (x+^)+sech (x— 2^) + sech (x+2^) — &c.
4-7T /
' -A" 7TX , -
3tt2
37TX
e v cos — \-e
2/x
cos
~ V- '
v y
y
47T l
( - 7TX
.?ZL2
3o rlc
—
6 ^ cos — + 6
2/a
cos —
y '
y
47 r/
^ 7TX
15ir2
37 rx
+ "7 (
6i ^ COS — + 6
‘ 2/a
COS
y '
s. y
y
D7tX
~
MDCCCLXXV.
506 MR. J. W. L. GLAISHER ON THE THEORY OF ELLIPTIC FUNCTIONS.
which, after summation of the columns,
e v 71-2? , e 2,1
— -4 cos — -)
l+e~J ^ l+e~
Bwa? . e 5i tx
COS rrj COS
1+e n
=?(
sech
TtX , , 37T2 37T2? , 5tt2 5wa?
cos — f- sech cos h sech -5— cos
?+&c-)
+ &C.
ift ft ■ Zffc ft ■ Zft ft
which is the identity (18), that was in § 6 deduced from the formula
cos am w=sec am (ui, k'),
and in § 8 from the integral
j sech x cos nx dx=^ sech
§ 12. The other identities, (19) to (23), admit of being demonstrated in exactly the
same way. The formulae of transformation, similar to (39), that are required are
a?— ft
X + fX.
a?2 + a2 (a; — ft)2 + a2 (a?+/t)2 + a
(T-$*+ «2+ ~+a*+&C- =j! (X + 2*~T
, _I® . ?ra? . 37ra?
+&c.=— (e sin — ^ sm — +&c.
ft ft
27ra? „ 4vra?
cos K2e * cos h&c.
ft 1 ft 1
! + /
a? — ft
a? -{-ft
,+&c.=^(^
. 2?ra? . 4?ra? \
sm ^ sm |-&c. ),
<*?‘4-«‘ ' (a? -ft) 2 + a2' (a? -f ft)2 + <
the first resulting from cosec (x-\-ai)+ cosec ( x — ai ), and the other two from cot ( x-\-ai )
+cot ( x—ai ). The following expressions, which are analogous to that used for sech x
in the last section, are also needed : — -
tanh x= -s
2x
! +
! + a72+^)2 + &C-,
2a?
1 2a?
COth X — “J~ o o+* 2 Trt \2 “1“ 2 To \2+* &C. 5
+ 7T2^#2 + (2tt)2 ' #2 + (3?t)2 '
1 2#
cosech <r= 5-7—2+
nf* nr>* -L- nr* 1
+ 7r2_ra?2+(27r)2 a'2+ (3tt)5
; + &C.,
all of which follow from (37) and (38) at once in the same way as that by which the
formula for sech a1 was obtained.
Only one point calls for notice in these demonstrations, viz. in the proof of (20) we
find
sech x -f- sech ( x — ju,) + sech (a+jM/)-J-&c.
27 r
t*
l-\-2e ./* cos^--j-2e
271-a? „
cos + 2 i
2tt2? 0 4%x
COS + 2(3 “ COS b&c.
P ¥■
MR. J. W. L. GLAISHER ON THE THEORY OF ELLIPTIC FUNCTIONS.
507
and in order to obtain the correct result we must replace the indeterminate series,
1 — 1 + 1 — 1 + 1 — &c., by Cases in which the method gives results absolutely erro-
neous will be noticed in § 16.
It will have been seen that the process of § 11 consists in replacing each term
of the original series by n terms (n infinite), and therefore the original expression itself
by n 2 terms. Each series of n terms formed by adding the vertical columns is trans-
formed into another series of n terms, so that we thus replace the first scheme of n 2 terms
by a second scheme of n2 terms, which latter system, being such that the columns admit
of being summed as ordinary geometrical progressions, gives the second side of the
identity to be proved.
§ 13. A question that naturally arises is to inquire what are the results which we
should obtain if, instead of using (39) and the similar formulae for the conversion of
one series into another, we were to replace at once these series by their finite summa-
tions, i.e. instead of (39) to take
x^+a* (x — fx^ + a2 (# + ju.)2-|-a2
+ &c. =^jjcosec ^ ( x—ai ) — cosec ^ (x -f- ai) j
„ nx . %ai
2 cos — - sin —
V- V-
' 2txi . a ttx . o Teai
sin2 l-sm2 —
ix fx
«. . „ irx . , ana
sin2 [- smh2 —
ix fx
We thus find
sech x— sech (x— ft) — sech (,r-}- ft)-j-&c.
sinh —
2]*
27 r nx
=— cos — ■
fX fX I . „1tx • v3
r 1 sin2 — ■+- sinh2 —
IX 2 (X
• i 3tT2
smh —
2fx
, nX
>3^
2 fx
+ &C. >,
. . (40)
while the left-hand side also
2% ( , 7T2 HX , 37T2 Znx D \
— sech cos — bsech-.r-cos — 4-&c. . . . .
fx\ 2(X fx 2ft fx 1 )
(41)
from (18). Although (40) is the identity which we have absolutely proved, we may
regard the fresh identity as being that which follows from (40) and (41), viz. (writing
for the moment x in place of and ft in place of
cos x cos Sx _ f sinh x sinh „ )
cosh %ft' cosh %[x' C C0S sin2 x-\- sinh2 j^x sin2 x + sinh2 %[x ' C‘j '
(42)
This result follows immediately from another form of the series for the cosine
3x2
508
ME, J. W. L. GLAISHEE ON THE THEOET OF ELLIPTIC FUNCTIONS.
amplitude; for on p. 113 of his ‘ Lehre von den elliptischen Integralen und den Theta-
Functionen’ (Berlin, 1864), Schellbach finds
( _ (1 _ «2s+l)
So 6,0 gx= 4 cos x 2, r-2^'co.S!i+J"'TS'
(43)
We easily see that
2KtP ( )
do 02o gx-=."—^- cos am — ^-=4< costf+p-^p cos 3#+&c.>, . . . (44)
and the comparison of (43) and (44) at once gives (42), since sin2#-J-sinh2 a= % (cosh 2 a
-y- cos 2#). The result (43) is also given in the ‘ Fundamenta Nova,’ p. 102.
It thus appears that by absolutely summing, instead of transforming, in the process
of § 11 we obtain the series of formulae which Schellbach has given on pp. 113, 114 of
his treatise, so that all the formulae and identities which arise from the transforma-
tions of the elliptic functions are algebraically exhibited by the method of § 11. It is
unnecessary to write down the series of identities analogous to (42) for the other func-
tions, as they can be easily derived as above from the values in Schellbach. It may be
remarked that (40) is a transformation of sec am (ui,k')= cos am u, but (42) is merely a
transformation of cos am w=cosam u. If, therefore, we perform the process of 11 in
reverse order (i. e. starting with the trigonometrical side of the identity to be proved,
sum the rows instead of transforming them) we obtain (42) at once.
It appears at first sight as if Schellbach’s formula
2/t'K 2Kx , t
— sec am — — = sec #4-4 cos#
7 r 7 r 1
(-)*<?*(! +g2*)
1 + 2g,2scos 2 x + qi*
(45)
gave rise to another formula for the cosine amplitude, by writing xi for x and changing
the modulus from k to k' ; but this, in fact, merely gives an expression already obtained ;
for the right-hand side of (45), on writing xi for x and e for q, becomes
which
sech #+4 cosh x
( — )* cosh S[x.
cosh 2x + cosh 2 sp.’
= sech #+£”(,— )*
cosh (x—sp) + cosh (x+sp)
cosh (x—sfi) cosh (a?-f tyt)
=sech x+X;(-Y\sech (x—sp)- 1-sech (#+5^)}.
Formulae such as (45) are the nearest approach I have met with to those numbered
(10) to (17) and the other expressions at the end of § 5 ; but (besides that an imaginary
transformation is required to reduce them to these forms) they do not put in evidence
the periodicity of the functions.
§ 14. It is perhaps desirable to place side by side, for convenience of comparison, all
the different forms into which one of the functions, the cosine amplitude, has now been
thrown. Writing, as before,
7TU 7 XU
^=2K’ z=2Kh (l~e K =«“'S r=e =e %
MB,. J. W. L. GLAISHEE ON THE THEOEY OF ELLIPTIC FUNCTIONS. 509
cos am M=Jgj eos #+y^3 cos 3#+y^5COs5;r+&c.j
■*K'
g-(l-g)
gKi-g3)
3 + &C.
1 — 2 q cos 2x + q2 1 — 2 q3 cos 2x + q6
U7(R-^J-G«)+&c-i
— AKO £ __x _.__w _T1 ,
''7'^ + r * + r Vjt J r* -\-r
= 2^/|sech2 — scch (z— v)— sech (2+j')-f&c.[
= 2AK' / sec^ 2 — 4 cos^
.( 5
ycosh 2
cosh i
cosh 2v
+ cosh 2» cosh 2 z + cosh 4v
+&c.)}
= 2M'{sech 2 “IT r cosh ^+IT^ cosh 32 — &c.| ;
while x, z , //-, y being any four quantities subject to the relations
(JjV=tt2, z=~( whence
the identities are : —
sech # — sech (x—p)— sech (x + p) + sech (x— 2^) + sech (x + 2/ca) — &c.
=sech,r— 4 cosh #
cosh -
cosh 2 ju.
( cosh 2# + cosh 2ft cosh 2x + cosh 4/x
4 cosh x , 4 cosh 3x
+ &C.1
:Sech*-^Tr+ e„+1
cosh
— &C.
2%( cosh z cosh 3z cosh 5z _ |
p | cosh ^v + cosh fv cosh -fv C’ j
sinh
+&C+.
sinh fv
[sin2,? + sinh2£v sin2^ + sinh2-|v
Another form will also be given in the next section. It is scarcely necessary to
observe that corresponding formulse and identities exist for sin am u, A am u, cosec am u,
sin am u „
a , &c.
A am u
§ 15. The identities (18) to (23) can also be proved by trigonometry in another
distinct manner, by starting from the trigonometrical sides of the equations. Thus,
for (18), from the formula
4 SeC^ l7r/3=l2 + (32 — 32 + |S* + 52 + /32 — &C-,
we have (writing z for — for brevity)
7 sech cos
4 2p. n*
3 cos z 5 cos z „
+7275 &c.
3V
+ 1
5V
+ 1
510 MR. J. W. L. GLAISHER ON THE THEORY OF ELLIPTIC FUNCTIONS,
7 sech 77- cos 32=^2
4 2 ft Ttz
5n
7 sech — cos 5z=^_
cos 3 z
3 cos 3 z
^ + 32_
W^'
7*
1ti
cos 5z
3 cos 5 z
1 — 4- 52”
,r2 + 5
I oa
1 »0
+
tn
5 cos 3z 0
-4~ To 2~? &C.
5 V „„
5 cos 5z
Vll1
rJ 'L .5-2
— &c. !
whence
2tt ( . Ti-2 ■ 3tt2 0 . 5tt2 _ D
— -jsech^ cos 2+ sech — cos 02 -f- sech cos 02+ &c.
+ &c.
8ju. ( cos .
cos 3 z
cos 5 :
“f- T72
;+P
32
■ 52
( 3 cos z
3 cos 3 z 3 cos 5 z
te*+
*
2V+s«+^+5’
7TZ 7TZ
+ &C. j_
+ ....•
^Jsinh (ijx— a?) sinh 3 (^//.— a?) sinh 5 (|)x — a?)
I cosh cosh -|jx cosh /x
2 cosh a?\ / 2 cosh 3a?
&c.|
1 +e^
) +&c.|
4 cosh a? 4 cosh 3a? „
" l+e^ + 1 +e^ ~&c-’
which, as shown in § 4,
= sech x — sech (x—p) — sech (x + + &c.
We thus in the course of the proof obtain another form for sech x — sech (x—p)
'-sech(ar+^)H-&c., viz.
o (sinh (i/*-— a?) sinh3(i^-a?) sinh 5 (ift-a?) ) .
cosh 7 jx ~ coshfp, ■+" coshf/x — «c.| V4U!
whence, in addition to the forms for cos am u in § 14, we have
it fsinhfiv— z) sinh 3 (iv— z) n )
cosam«=jg,|-oshi>— coshfy + &<=•{•
This method of proof is not so interesting as that of § 11, both because the formulae
required cannot be obtained in so elementary a manner, and also because the identities
(18) to (23) are not so directly verified, as their right-hand members are shown to be
equal to expressions such as (46), which themselves need some transformation before
they assume the desired forms. The formula
cos a? cos 3a?
it sinh (|/3tt— /3a?)
MR. J. W. L. GLAISHER ON THE THEORY OE ELLIPTIC EUNCTIONS.
511
which was required in the verification, is best obtained by deducing it from the well-
known theorem
cos a? i cos 2a? t cos 3a? t t cosh (/3x — /3a?) 1
l2 + /32 + 2* + fi* + 32 ^C’ = 2/3 sinh fir 2/8*’
from which, by writing ^/3 for 0 and 2x for x , dividing the equation so obtained by 4,
and subtracting it from (47), we find
cos a? , cos 3a? p _ n (cosh (/Sar — /3a?) 1 cosh(^/37r— /3a?))
l2 + /32 ' 39 + ^2 + &C, — 2^ ( sinh /S* 2 sinhphr j
7r j cosh(/3?r— /3a?) — cosh /3a?) cosh ^/Stt)
2/3 1 sinh /37r j
?r sinh (^/37r— /3a)
4/3 cosh
It is to be noticed that (46) is only true if x lies between 0 and /a. This may be
regarded as a consequence of the fact that (47) only holds good when x is positive
and less than 2-jt ; but the necessity for the condition is also evident from the process of
verification by ordinary algebra. Thus the expression in (46)
= 2-je x—e 3
2 cosh a?
l+e'*
2 cosh 3a? )
2e~
1+e
^-2(ex + e~x)(e-» - e~^+e-3» - &c.) + 2 (e3x+ e~3x)(e-^ - + e~9* -...)- &c.
ex + e~x 1+e2^"/1)
OpX+IL
&c°
= sech x — sech (x—p) — sech (x-+- p) -f- &c. ,
wherein we see that to justify the summations of e~x —e~3x -\-&c , and ex~* — e3(J:"M)+&e.
as ordinary geometrical progressions we must suppose x to be positive and less than [x.
Also since sech x— sech (x— p) — sech(.r+ju»)-f-&c. is periodic, while the expression in
(46) is not so, we see that the equality will not hold good beyond these limits.
I have worked out the corresponding proofs of the other five identities (19) to (23)
in the same way, but none of them call for any special remark. The process is not in
all cases exactly similar, as, ex. gr., in deducing (19) from
sinh/3i— (3 jSa+l^/3s+2e Kc’>
sin a? 3 sin 3a? 5 sin 5a? p w cosh (^/3w— /3a?)
/S2+ 12 ‘ j32 + 32 ‘ /32 + 52 C‘ 4 cosh^/3flr ’
^Sf;+5ffif,+&c-=^(sin*+ifdn3*+Isin5ji+&c-)
/x (cosh (p — 2 a) cosh2(ju. — 2a?) „ )
5r | cosh/u. cosh 2ju. ' C’j ’
we find
512
ME. J. W. L. GLAISHEE ON THE THEOET OE ELLIPTIC FUNCTIONS.
whence, since the first series on the right hand side=^T, when x is positive and less
than /A,
sing sin3z jx ( cosh (ju.— 2x) cosh 2 ([x.— 2x)
sinh^ v ' sinh-|v~*” C 2ir | cosh^ ' cosh2j&
— &c.
)
i
and
tanh x - tanh (x-p)- tanh (x + p) + &c. = 1 - 2 C0^h^x) + 2 ~ ~ &c.
The other transformations to which the method of this section leads are
coth x — coth (x—p)— coth(# + p) + &c. = 1 + 2 C0S|?0^h ^ + 2 -"cosh* 2j/~ + &c~’
cosech # — cosech (x—p)— cosech (a? ■ +/x) + &c. = 2 + 2 ^ coih|^ ^ + &c-’
cosech x + cosech (x — p) + cosech (#+,«,)-}- &c. =
secha;+ sech(#— sech(a:+/x)+&c.=
sinhft^j sinh3(^-x)
sinhfju, 1 smh-iju. 1 ’
cosh (If*— a?) Ocosh 3 (&*—#)
sinh^ju, sinhfju, ' C‘
which can be readily verified by ordinary algebra in the manner explained above. In
all these identities x must be positive and less than
§ 16. It only remains to apply the methods of §§ 11 and 15 to the identities (33) and
(36), which differ from the others by relating to non-periodic functions. Employing
the method of §11, we have
tanh x—
** +($*)*
2#
+*2+(f
+ ^-+(142 + &C.,
, ,, , 2 (d7— /*) 2(x—[l) 2
tanh(# + (a?_ft)2+(|J!r)2+(a?_p)2+(|w)2+&c.:
j_ , / , X 2(a: + /i) , 2(a? + ft) , 2(x + p) , 0
*«nl‘(a+rt_(#+/l)1+{W,-l-(le+(i),+ ( )4+(lt+rtS+,(WS+&c.
whence
tanh,r+tanh(;r— ^) + tanh(#+^)H-&c.=^ j#-1' wn2z-\-e~2v sin4s+&c.|
-J-4“ le-3" sin 254-^_6‘' sin 4z-f-&c.j
sin2z4-e_10,,sin4s-f-&c. j-
+
= j (rfps sin 2z+ sin 4z + &c-)
27r/sin2g , sin4g ( Q ^
— 7 ^ihdTv + + &C-
(48)
ME. J. W. L. GrLAISHER ON THE THEORY OE ELLIPTIC FUNCTIONS. 513
whereas the true equation is
0 'Y' Q/jr /oirj 0,2 S1T1 Az \
tanh^+tanh(^-^)+tanh(^+^) + &c.=^ + ^|gIs^+iI^+&c. j. . (49)
It is well known that if an infinite system of series be summed by rows and by
columns, the results need not necessarily be the same ; but the above is a striking
instance of such a disagreement. We should be prepared for some ambiguity from the
observation that although the value of the left-hand side is liable to a change of a unit
according as the number of terms retained is even or uneven, yet in the process of
transformation no condition whatever with regard to the number of terms in the columns
is, or can be, imposed ; but we should scarcely expect to obtain an absolutely erroneous
result by an apparently definite process.
If the same method be applied to the hyperbolic cotangent, we have
and finally
2x
which is also erroneous, the term — being omitted on the right-hand side.
The method of §15, however, yields correct results, for
2tt
— cosech2v sin 4 z
whence
+
MDCCCLXXV,
3 T
514
ME. J. W. L. GLAISHEE ON THE THEOET OF ELLIPTIC FUNCTIONS.
(by use of the formula sin 3-f-| sin 25+^ sin 30 + &C — -|0)
h 2 fc-
sinh 2/x.
lx ^sinh Q«,-2a?) 2sinh2 (^— 2a?) „ _
— I— ^ ^ sinh r
and therefore
2a?
2n /sin 2* sin 4^ ~
ft 1 fxT ysmhv sinh 2v ' ^C‘
: 1 _ 2e-21 + 2e"4*- &c. + 2 (^If
sinh (ft — 2a?) ^sinli 2(p,— S
sinh ft ' sinh 2ft
a?)
■&c.
e^—i
-f- &c
•)
=l__3l-1-l-2{(^-e-2^_2"+e-4'1+&c.)-(e4I-e-4l)(^ + e-8'1+&c.) + &c \
( g2(2:-M) e-2(i+/x) \
= tanh .z + 2|1 + ea(I_Mj — 1+e-2(*Uo + &c.|
=tanh #-f-tanh (#— ^H-tanh (a?+jM/)+&c.,
which is the true formula.
In the same way, since
2tt
2- 2-
coth * sin 2z=— <- + — ^~2+&c. >sin 2z,
!« + i 2*+4 i
we find that
2w _ , . \ 2?r , _| „sinh (ft — 2a?) , „ sinh 2 (a— 2a?) . n
-(coth. sin 2z+coth 2» sin 4* + &a)=--+l + 2 sinh(t +2 sinh 2,* + &c'
= — — 4-coth #+coth(.z— ^) + coth(a:+^)+&c.,
which is correct, and agrees with (36).
It is of course easy to assure one’s self that (48) cannot be true ; for, taking for
simplicity, and differentiating with regard to x or z ,
4 , 4 4 „ 0 ( cos 2a? 2 cos 4a? 3 cos 6a? )
(eZ + <?-x)2 + + e-(*-*>)2 + (e*+ir + C-<z+ir))a+ &C* — 0|eir_e-n + e2ff_e-2ff + <.3^_e-3*r +&C*| »’
and it is evident that if we take x>\tt and < f 7 r we should have a positive quantity
equated to a negative quantity.
I thought it of interest to actually verify numerically the truth of the formulae (33)
and (36) in one or two cases. Working with seven-figure logarithms, and taking ^ = 2,
x=%, I found that each side of (33) was =0545188, and for 2, that each side
was =0-282281 ; while for x=%, ^=2 each side of (36) was =2*07112, and for x=%,
fjj=2 each side was =4*04247 ; placing beyond doubt the correctness of (33) and (36).
It is a characteristic property of the identities noticed in this paper that in all cases
the series on both sides are convergent whatever may be the values of x and For
the actual calculation of the elliptic functions the formulse (10) to (17) would be
preferable to (1) to (8) if the angle of the modulus was very near to 90°, so that q was
MR. J. W. L. GrLAISHER ON THE THEORY OF ELLIPTIC FUNCTIONS. 515
nearly equal to unity ; but as probably the theta functions (or their transformations as
in (28)) would always afford the best means of actually calculating the elliptic functions,
I have not investigated whether (10) to (17) would present any advantages over the for-
mulae which result directly from the change of modulus from k to k ', as ex.gr. the formula
at the beginning of § 4, viz.
cos am {jTfFJ- TT~r(e‘+e") +
§ 17. There are two well-marked classes of identities that are derived from the theory
of elliptic functions, viz. pure algebraical identities, in which only one single letter is
involved, as ex. gr.
(1_2^+2^-&c.)4+(2^ + 2^+&c.)4=(1+2^+2^+&c.)4,
and what may for the sake of distinction be called transcendental identities, viz. in which
7T2
a function of (ju is equated to a function of — . To this latter class belong the chief
identities discussed in this memoir ; and if special values be assigned to x such that the
left-hand member of the equation is of the same function of p that the right-hand
member is of — , or, in other words, if the identity is of the form where gjv=ir2,
such a result is usually very interesting. The best known identity of this class is
\Zlog^(i+2+24+29+&c.)=^/logi(|+r-l-f4+r9-f«&c.) ; . . (51)
but there is another elegant formula of the same kind to which Abel has drawn
attention (CEuvres, t. i. p. 307), viz.
.■^(l+!)(l+23)(l+Ss)---=^.(l+»-)(l +«")(! +»")•••. • • • (52)
the relations between q and r being of course
log . log T — TT2.
It seems probable that all the transcendental formulae of this latter class can be
deduced from the trigonometrical identities in § 11 and at the beginning of § 12 by
elementary methods, without the introduction of elliptic-function formulae ; and it is of
some interest to verify (52) in this way.
Starting from the formula (23), which may be written
sin 3#
— x cosec
s+v__c-(*+i0
-j- &c.
we have, on differentiation with regard to x ,
x cos x cos x 3 cos 2>x „ tt2 ( ez + e~z
4 sin2#-*- 1 l+e3,x ’4~ C 2ju,2 \{ez— e_z)2
3 t 2
e8-y + e-(z_y) es+y + e-(*+y)
516 ME. J. W. L. GLAISHEE ON THE THEOEY OF ELLIPTIC FUNCTIONS.
Put #=0, and
1— ia?2
1 2 n _ir2_l -It2^
4 sin2 x~ 4 • *2(1-^2)- 4a?2 ^ 2^ 1"3^ ;
while
“ 4*2 24!
w e' + e '
2^2 [tz-e-~]
= ±(l .
! 4«2 y 2 j«,2 3 |«.2 /
so that
1 _i i _
“ 4a?2 ^ 2 4jU.2_
7T2 7t2 f c' + e-*’ e2l' + e~2‘'
2^+ !+<**+ 1 + e;v +&c- — ai ^ ^ ^_e-,)2 (e2,_e-2^a
+ &c
•}
+ e~av)(l + 2e~21' + 3e~4v-j- 4e~6v +&c.)
_ (e-** .j. e~6v)(l + 2e~iv + Se-Sv+ ±e~l*v + &c.)
+&c. \
, 7T2 7T2 f e~v 3e~3v 5e~5v 0
1 +e-v + 1 +C-3V+ 1 + c-5» +«C.
_ 1 tt2 tr
~ — fJ?
pH IP +&C.
l+e* 1+e ^
•}
whence, on integration with regard to
„ P 3^2
-^-log(l + e^)-log(l+e-3^)-&c.= — ^4- -l°g(lH-e *)— log(l + e 14 )— &c .
viz.
+ const.,
624(i_j_e-^(i . . . =C . e24^(l +e ^)(l + e“ ^ )
and C=l, as is seen by putting ; so that (52) is established.
The other identity (51), or rather the generalization of it,
4/ nr C ^ nr'Y' Anrr 'i
e~l2 +e~(x~*)2 -\-e~(x+tL)2 -\-tkc. = — < l+2<?~^cos — +2e-^ cos — +&c. > (53)
(which is much more difficult to prove by elementary methods than any of the identities
discussed in this paper), I deduced by algebraical processes from the equation in § 12,
viz. from
a a a
,x2 + ffl2^"" (x—^ + a2' (x + p)2 + a*
+&c. = -<M +2e~~cos — +2e"
- 0
COS h&C.
V-
(54)
in the Philosophical Magazine for June 1874 (ser. 4, vol. xlvii. p. 437 et seq.) ; but it
perhaps is worth while to note here what is the most natural way of obtaining it from
MR. J. W. L. GrLAISHER ON THE THEORY OE ELLIPTIC FUNCTIONS. 517
(54), viz. by help of the theorems
[e \„r~^e ’ (55)
; (56)
whence, operating on (54) with e~n and making «=0, we have at once
a/ 7 r f 3:2 (a^— fx)2 (:r-f ^,)2 'j ^ C kr& 7r2 27TX 16n27r2 4'7ZV£> 1
+ 4,2 +6- 4^2 + &c .t=Jl+2e"^cos^+2«“^cos^+&c. k
which is (53) if we take n=\.
Of the two lemmas (55) and (56) the truth of the second is seen at once, for
■>d2 / ,72 1 M \
- "«-“=(l-^+n2»4*4-&c.)<r-
= (l— mV + j^ »V— &c.)<r"
and (55) is easily established, since « being put =0 after the performance of the
differentiations.
e da2
e-a“ cos xu du
= fY~
cos xu du
✓ 7T _fi
/> 4n2
2n ,e *
But the investigation is not elementary ; and if we assume a knowledge of the integral
r
e~a2*2 cos2 bxdx—~e a2
we may as well apply it directly to prove (53) by Fourier’s theorem as explained in §7,
or employ it as Schellbach has done (‘Die Lehre von den elliptischen Integralen &c.,’
1864, p. 30). It does not seem to be easy to establish (55) without the aid of an integral ;
for, expanding in ascending powers of x , we have to show that when a= 0,
a9 , p \ ✓*■/, a2 , a* p \
e a\a a3 + «5 &C')~2ny- 4rc2+32w4 &c’j ^
and, taking the first term only, although we see at once that
.^0 i _n2& r*
da2-_~e da? 1
a Jo
11 du-
f e~n2u2du=~
2 n
yet
-n?d2 1 1 1 .2.%2 1.2.3.-
e — -s — +
— &c..
which is divergent, and cannot apparently by any simple method be so transformed that
its value when a=0 may be evident, without the intervention of an integral. Thus the
method depending upon (55), though more direct, is not so elementary as that described
in the Philosophical Magazine.
518 ME. J. W. L. GLAISHER ON THE THEORY OF ELLIPTIC FUNCTIONS.
It is curious that all the formulae of the form
<px+<p(x— j&)±<P(&+/*)+&c.= series of sines or cosines
which can be obtained by definite integrals, and which possess any interest, should be
in reality elliptic-function identities. Of course every result that can be derived from
these identities by differentiation, by multiplication by a factor and integration, &c.,
can as a rule be obtained directly from an integral, which integral itself would arise
from a similar treatment of the original integral. This is true of the identities in the
Philosophical Magazine, ser. 4, vol. xlii. pp. 422 et seq. (December 1871); and, for
example, such an integral as
f e — eric, (a— b)-\-e2a:b eric (a+b)} . . . (57)
(where erfc,z:=J e-^dx) would give rise to identities which, however, could be deduced
from (28) and (53) by a similar process to that by which (57) can be derived from
fV*2cos2 bxdx=^e->\
•Jo 2
XVIII. On Repulsion resulting from Radiation. — Part II.
By William Crookes, F.R.S. &c.
Received March 20, — Read April 22, 1875.
Contents.
Par.
Introduction 81
Improvements in the Sprengel pump 82
Horizontal index in exhausted bulb 84
Experiments with horizontal index 87
Action of hot and cold bodies on each other . . 88
Experiments on attraction at high pressures . . 95
Action through various screens 97
Pendulum apparatus with magnesium boh .... 99
Action of radiation on pendulum in vacuo .... 100
The horizontal torsion-apparatus 102
Selection of the suspending glass fibre 103
Experiments with the horizontal torsion- apparatusl 04
a. Effect of residual gas 105
Par.
b. Action of continued radiation 106
c. Action of intermittent radiation 107
d. Repulsion through various screens 109
e. Action of the electric and solar spectrum . . 110
/. The neutral point 112
Double torsion-apparatus 115
Simultaneous attraction and repulsion at same
pressure 115
Certain hypothetical explanations of the pheno-
mena 117
a. The air-current' theory 119
b. The electrical theory 120
c. The evaporation and condensation theory . . 122
81. The present paper is in continuation of one which I had the honour of reading
before the Royal Society, December 11th, 1873, and which was published in the Phi-
losophical Transactions, vol. clxiv. part 2, page 501. In that paper I described various
pieces of apparatus, chiefly in the form of delicate balances suspended in glass tubes, by
means of which I was enabled to show attraction or repulsion when radiation acted on
a mass at one end of the beam, according as the glass tube contained air at the normal
pressure, or was perfectly exhausted. At an intermediate internal pressure the action
of radiation appeared nil. Towards the end of the paper I said (70), “ I have arranged
apparatus for obtaining the movements of repulsion and attraction in a horizontal
instead of a vertical plane. Instead of supporting the beams on needle-points, so that
they could only move up and down, I suspend them by the centre to a long fibre of
cocoon-silk in such a manner that the movements would be in a horizontal plane.
With apparatus of this kind, using very varied materials for the index, enclosing them
in tubes and bulbs of different sizes, and experimenting in air and gases of different
densities up to Sprengel and chemical vacua, I have carried out a large series of expe-
riments, and have obtained results which, whilst they entirely corroborate those already
described, carry the investigation some steps further in other directions.”
82. I have introduced two important improvements into the Sprengel pump* which
* Philosophical Transactions, 1873, vol. clxiii. p. 295; 1874, vol. clxiv. pp. 509, 510. Phil. Mag. Aug. 1874.
520
ME. W. CEOOKES ON EEPULSION EESTJLTING- EEOM EADIATION.
enable me to work with more convenience and accuracy. Instead of trusting to the
comparison between the barometric gauge and the barometer to give the internal
rarefaction of my apparatus, I have joined a mercurial siphon-gauge to one arm of the
pump. This is useful for measuring very high rarefactions in experiments where a
difference of pressure equal to a tenth of a millimetre of mercury is important. By
its side is an indicator for still higher rarefactions ; it is simply a small tube having
platinum wires sealed in, and intended to be attached to an induction-coil. This is
more convenient than the plan formerly adopted (51), of having a separate vacuum-
tube forming an integral part of each apparatus. At exhaustions beyond the indications
of the siphon-gauge I can still get valuable indications of the nearness to a perfect vacuum
by the electrical resistance of this tube. I have frequently carried exhaustions to such a
point that an induction-spark will prefer to strike its full distance in air rather than
pass across the inch separating the points of the wires in the vacuum-tube. A pump
having these pieces of apparatus attached to it was exhibited in action by the writer
before the Physical Society, June 20th, 1874.
83. The cement which I have found best for keeping a vacuum is made by fusing
together 8 parts by weight of resin and 3 parts of bees-wax. For a few hours this
seems perfect, but at the highest exhaustions it leaks in the course of a day or two.
Ordinary or vulcanized india-rubber joints are of no use in these experiments, as when
the vacuum is high they allow oxygenized air to pass through as quickly as the pump
will take it out. Whenever possible the glass tubes should be united by fusion, and
where this is impracticable mercury joints should be used. The best way to make these
is to have a well-made conical stopper, cut from plain india-rubber, fitting into the wide
funnel-tube of the joint and perforated to carry the narrow tube. Before fitting the tubes
in the india-rubber, the latter is to be heated in a spirit-flame until its surface is decom-
posed and very sticky ; it is then fitted into its place, mercury is poured into the upper
part of the wide tube so as to completely cover the india-rubber, and oil of vitriol is
poured on the surface of the mercury. When well made this joint seems perfect ; the
only attention which it subsequently requires is to renew the oil of vitriol when it gets
weakened by absorption of aqueous vapour. Cement has to be used when flat glass
or crystal windows are to be cemented on to pieces of apparatus, as subsequently
described (99, 102).
It would be of great service could I find a cement which is easily applied and removed,
and will allow the joint to be subjected to the heat of boiling water for some hours
without leaking under the highest rarefactions. Hitherto I have failed to find one
which answers these requirements. I mention this in the hope that some one who
happens to read this may be in possession of the recipe for such a cement, and will
communicate it to me.
84. Before my first paper on this subject was read before the Boyal Society I
had discarded the balance form of apparatus there described, and commenced experi-
menting with bulbs and tubes in which quantitative results could be obtained. On
ME. W. CEOOKES ON EEPULSION EESULTING- FEOM EADIATION.
521
December 11th, 1873, when illustrating my paper, I exhibited to the Society many of
these new forms of apparatus. For the purposes of simple illustration, and for expe-
riments where quantitative determinations are not required, I find a horizontal index
suspended in a glass bulb the most convenient. The apparatus, with its mode of
attachment to the pump, are shown in fig. 1.
Fig. L
a, b, c, d is originally a straight piece of soft lead-glass tubing 18 inches long, f- of
an inch external and f internal diameter. At one end is blown a bulb, d e, about 3
inches diameter. The part a b of the tube is drawn out to about half its original dia-
meter, and bent at right angles. The tube is slightly contracted at c, and very much
contracted and thickened at b. At a it is also contracted and cemented by fusion to
a narrower piece of tube bent in the form of a spiral, and fitting by a mercury-joint
into the sulphuric-acid chamber of the pump. The object of the spiral is to secure
ample flexibility for the purpose of levelling the apparatus, and at the same time
having a fused joint, f g is a very fine stem of glass, drawn from glass tubing, and
having a small loop ( h ) in the middle. At each end of the stem is a ball or disk, made
of pith, cork, ivory, metal, or other substance, li i is a fine silk fibre made from split
cocoon-silk ; it is cemented by shellac at the upper end to a piece of glass rod a little
smaller in diameter than the bore of the tube, and drawn out to a point, as shown.
The contraction (c) in the tube is for the purpose of keeping this glass rod in its place ;
when properly adjusted it is secured in its place by a small piece of hot shellac, care
being taken not to cement the rod all round, and so cut otf the connexion between the
air in the bulb and that in the upper part of the tube. The silk fibre is tied on to the
loop of the glass stem at h. The length of the fibre is so adjusted that the stem and
mdccclzxv. 3 z
522
MR. W. CROOKES ON REPULSION RESULTING FROM RADIATION.
disks will hang about of an inch below the centre of the bulb ; that much having to
be allowed for the contraction of the silk when the air is exhausted.
85. The bulb-tube is firmly clamped in a vertical position, so that the index hangs
freely, and the pump is set to work, the bulb being surrounded with a vessel of water
which is kept boiling all the time exhaustion goes on. The gauge soon rises to the
barometric height ; but the operation must be continued for several hours beyond this
point, in order to get the best effects. If the bulb is not heated during the exhaustion,
the index loses sensitiveness after it has been sealed up for a few days, probably owing
to the evolution of vapour from the pith ; when, however, the precaution is taken of
heating the pith, the apparatus preserves its sensitiveness. On this account it is
necessary to tie the silk on to the loop in the centre of the glass stem, instead of
adopting the easier plan of cementing it with shellac. During the latter stages of
the exhaustion, oil of vitriol (which has been boiled and cooled in vacuo) should
gently leak into the pump through the funnel-stopper at the top of the fall-tube (44).
This covers each globule of mercury, as it falls, with sulphuric acid, and stops mercury
vapour from getting into the apparatus*. I cannot find that any vapour is evolved from
oil of vitriol.
When the exhaustion is carried to the desired degree, a spirit-flame is applied to the
contracted part of the tube at a (fig. 1), and it is sealed off. The apparatus is then
unclamped and the tube is again sealed off at b. This double operation is necessary to
secure strength at the final sealing, which can only be got by holding the tube hori-
zontally and rotating it in the flame, watching the glass to prevent it softening too
suddenly.
86. The best material of which to form the index in these bulb-tubes is pith, either
in the form of a needle or bar, or as disks at the end of a glass stem. On
December 11th, 1873, and again on April 22nd, 1874, I exhibited before the Royal
Society a glass bulb 4 inches in diameter, having suspended in it a bar of pith 3|-X-^
inches. It had been exhausted in the manner above described ; and so sensitive was it
to heat, that a touch with the finger on a part of the globe near one extremity of the
pith would drive' the bar round 90°, whilst it followed a piece of ice as a needle
follows a magnet.
To get the greatest delicacy in these apparatus there is required large surface with a
minimum of weight (75, 76). Thin disks of pith answer these requirements very satis-
factorily ; but I have also used disks cut from the wings of butterflies and dragonflies,
dried and pressed rose-leaves, very thin split mica and selenite, iridescent films of blown
glass, as well as the substances mentioned in my former paper (25). Quantitative
experiments to prove this law were attempted ; but the bulb-apparatus was found too
imperfect for accurate measurements, so another form was devised which will be described
further on (102), together with the experiments tried with it.
* By adopting this precaution it is not difficult to raise the mercury in the gauge higher than that in the
very perfect barometer hy its side, the latter being somewhat depressed by the tension of mercury vapour.
MR. W. CROOKES ON REPULSION RESULTING EROM RADIATION.
523
87. With a large bulb, very well exhausted and containing a suspended bar of pith,
a somewhat striking effect is produced when a lighted candle or other radiant source is
brought about 2 inches from the globe. The pith bar commences to oscillate to and
fro, the swing gradually increasing in amplitude until the dead centre is passed over,
and then several complete revolutions are made. The torsion of the suspending fibre
now offers resistance to the revolutions, and the index commences to turn in the oppo-
site direction. This movement is kept up with great energy and regularity as long as
the candle burns — producing, in fact, perpetual motion, provided only the radiation
falling on the pith be perpetual *. If the candle is brought closer to the bulb, the
rotation of the pith becomes more rapid; if it is moved further away the pith ceases
to pass the dead centre, and at a still further distance the index sets equatorially. The
explanation of the different movements of the pith index according to the distance the
radiant body is off, is not difficult on the supposition that the movement is due to the
direct impact of waves on the suspended body.
88. It is not at first sight obvious how ice, or a cold substance, can produce the
opposite effect to heat, cold being simply negative heat (33). The law of exchanges, how-
ever, explains this perfectly. The pith index and the whole of the surrounding bodies
are incessantly exchanging heat-rays ; and under ordinary circumstances the income and
expenditure of heat are in equilibrium. A piece of ice brought near one end of the
index cuts off the influx of heat to it from that side, and therefore allows an excess of
heat to fall upon it from the opposite side. Attraction by a cold body is therefore seen
to be only repulsion by the radiation from the opposite side of the room.
Bearing the law of exchanges in mind, several apparent anomalies in the movements
of these indices are cleared up ; and it is also easy to foresee what the movement of a body
will be when free to move in space under the influence of varying amounts of radiation.
The heat which all bodies radiate into space can have no influence in moving them,
except there be something in the nature of a recoil in the act of emitting radiation.
And even should there be such a recoil, if the body radiates heat equally all round, the
recoil will be uniform, and will not move the body in one direction more than in another.
I need therefore only consider the effect of the radiation received by a body. Here also
the influx of radiation to a body free to move in space of a uniform temperature may be
considered to be equal, and it will acquire the temperature of space without moving in
any direction.
89. The case is, however, different if two bodies, each free to move, are near each
other in space, and if they differ in temperature either from each other or from the
limiting walls of the space. I will give here four typical cases, with experiments
sufficient to prove the reasoning to be correct.
Case I. Two hot bodies, A and B, in space of a lower temperature than themselves.
The body A receives heat uniformly from space, except where the body B intervenes ;
and on this side A receives more heat, as B is hotter than the space behind it ; A will
* This experiment -was exhibited for the first time at the Royal Society’s Soiree; April 22nd, 1874.
3 z 2
524
ME. W. CROOKES ON EEPULSION RESULTING EEOM RADIATION.
therefore move from B. In the same manner it can be shown that B will move from A.
The result will therefore be mutual repulsion.
Case II. Two cold bodies, A and B, in space of a higher temperature than themselves.
Fig. 2. Case I. Fig. 2. Case II.
A will receive much heat from space, except where B cuts it off, and on that side it will
only receive slight radiation from B. A will therefore be driven towards B. In the
same manner it can be shown that B will be driven towards A ; and the result will
therefore be an apparent mutual attraction.
Case III. Two bodies, A hot and B cold, in cold space. The body A receives heat
uniformly from all sides, even from that opposite B (B being of the same temperature
as space). A will therefore not move. B receives heat uniformly from all sides, except
from that opposite A, on which side the influx of heat is more intense. The result will
therefore be that A remains stationary whilst B is repelled.
Fig. 2. Case III. Fig. 2. Case IY.
Case IV. Two bodies, A hot and B cold, in hot space. The body A receives heat
uniformly from all sides, except from that opposite B. Here the heat is less intense.
A is therefore driven towards B by the extra influx of heat on the other side of A. B
receives strong influx. of heat from all sides, and just as much from the side opposite A
ME. W. CROOKES ON REPULSION RESULTING FROM RADIATION.
525
as from any other. B will therefore not move. The result will be that A will be appa-
rently attracted towards B, whilst B will remain stationary.
The force with which the bodies A and B in these four cases will be repelled, or
apparently attracted, will vary with their distance from each other, being stronger when
they are close and weaker when they are far apart. The diminution will not, however,
follow the usual law of inverse squares, but a more complicated law.
90. Experiment proves the above reasoning to be correct. A bulb-tube was prepared
in the manner already described (84), but in it were suspended, by separate silk
fibres, two glass stems, each having pith balls at its extremity. Fig. 3 shows the eleva-
tion and plan of the apparatus. The torsion of the silk fibres was so arranged that the
pith balls a b hung freely about a millimetre from the balls c d. The glass stems were
looped in the middle, and bent so that they did not touch each other. After complete
exhaustion the following experiments were tried.
A beam of radiant heat was concentrated on to Fig. 3.
the two balls a c. When applied momentarily and
then removed the radiation simply drove the halls
apart, and immediately allowed them to come together b
again. When, however, the beam was allowed to play
upon the balls for about half a minute they became
warm and widely separated ; and upon now removing
the beam of heat the balls did not fall together at
once, but took several mfnutes to regain their original
position. This experiment therefore proves Case I.
The bulb and contents being of the ordinary tem-
perature, a spirit-flame was rapidly passed round the
bulb to warm it quickly on all sides. The balls were
thus in the condition imagined in Case II., being in a
space warmer than themselves. They immediately
came together, a touching c, and d touching b.
Many experiments were tried with the object of
proving experimentally the propositions in Cases III,
and IV. ; but with this apparatus it was found im-
possible to warm one of the balls without at the same
time producing repulsion of the ball by the beam of
radiation concentrated upon it. There is, however,
little doubt, from the experimental proof of Cases
I. and II., that the reasoning is equally correct in the
other cases.
91. With a highly exhausted bulb and light pith index, which was found to be
exceedingly sensitive to radiation, numerous experiments were tried to see if there was
any difference in action between the fingers and a tube of water of the same tempe-
526
ME. W. CROOKES ON EEPULSION RESULTING EEOM RADIATION.
rature. Many persons believe that there is a peculiar emanation or aura proceeding
from the human hand, and Baron Von Keichenbach * considered that he had proved
this to be the case. Were this true it was not impossible that the emanation would
affect the pith index. I have been unable, however, to detect the slightest action
exerted by my own or any other person’s hand which I could not entirely explain by
an action of heat.
92. A similar series of experiments were tried with various large crystals, which were
presented in different ways and with various precautions to the pith index. At first a
decided action was observed ; but in proportion as precautions were taken to eliminate
the effect of heat, so was the action seen to diminish, until very little doubt was left in
my mind that the slight residual action would have been entirely stopped had it been
possible, with the apparatus then used, to altogether eliminate the action of heat.
93. Attempts were made to see if chemical action would attract or repel the index.
I could not, however, produce chemical action close to the exhausted bulb, without at
the same time liberating such an amount of heat as to mask any other action.
94. Although I most frequently speak of repulsion by heat , and in illustrating any
of the results obtained I generally use either the fingers or the flame of a spirit-lamp as
a convenient source of radiation, it must be clearly understood that these results are not
confined to the heating-rays of the spectrum, but that any ray, from the ultra red to the
ultra violet, will produce repulsion in a vacuum. I have already mentioned this fact in
my first paper (58, 68). Experiments proving the similarity of action of all rays of the
spectrum were shown before the Physical Society on June 20th, 1874 f. They were,
however, tried with a less perfect apparatus than the one I have since used for the same
purpose, and need not be further alluded to till I describe the most recent results
obtained with the spectrum (110, 111).
95. Some experiments were tried with the object of ascertaining whether the attrac-
tion by heat, which, commencing at the neutral point (30 et seq.), increased with the
density of the enclosed air, would be continued in the same ratio if the apparatus were
filled with air above the atmospheric pressure. Two bulbs containing ivory needles
suspended by silk fibres were accordingly adjusted to show the same sensitiveness to a
hot body. One was kept for comparison, and the other was attached to an apparatus
whereby the internal air-pressure could be artificially increased by a column of mercury.
A little increase of pressure was enough to show that the sensitiveness to radiation was
greater ; and under a pressure of 14 atmosphere the superior delicacy of the ivory in the
dense air was very marked. Attempts to carry the pressure to higher points failed,
owing to the bursting of the thin glass bulbs. With a little different arrangement
no difficulty would be experienced in carrying the experiments to a much higher point ;
but hitherto the greater interest attending the vacuum experiments has prevented me
from working further in this direction. My friend and pupil, Mr. C. H. Gimingham,
* Researches on Magnetism &c., translated by Dr. Gregory. London, 1850.
t Phil. Mag., August 1874.
MR. W. CROOKES ON REPULSION RESULTING EROM RADIATION.
527
succeeded in the very difficult feat of sealing up some of these tubes under an internal
pressure of 1^ atmosphere.
96. To carry this experiment a step further bulbs containing a suspended ivory or
mica index were filled with carbonic acid gas, water, carbonic disulphide, ether, alcohol,
and other liquids. The index in carbonic acid behaved as if it were in air of somewhat
higher density than the atmosphere ; movements were also obtained when the liquids
were present, but they were so obviously due, in whole or in greater part, to currents, that
they proved nothing of importance.
97. Two other forms of the bulb -apparatus require mentioning. A thin glass bulb
was blown 2J inches in diameter (fig. 4). Inside this another bulb was blown 2 inches
in diameter, at the end of a glass tube 12 inches long. In this a light glass index with
pith terminals was suspended, and the whole was perfectly exhausted. Fig. 4 shows
the complete arrangement. In the space between the two bulbs various liquids were
enclosed, such as water, solutions of sulphate of copper, alum, perchloride of iron,
sulphate of iron, bichromate of potash, sulphate of nickel, &c. These were selected
in the hope that amongst them one would be found which would sift out the heat-rays,
and so allow me to obtain an action due to light. They, however, only affect the dark
or extreme red heat-rays, and do not affect the luminous rays which also have a heating-
Fig. 4.
0
Fig. 5.
effect. By throwing a beam of sunlight on one of the pith disks powerful repulsion was
obtained, whatever was the surrounding shell of liquid. That all these liquids allowed
528
ME. W. CEOOKES ON EEPULSION EESULTINGr EEOM EADIATION.
heat to pass through was proved with
a thermopile. Solution of sulphate of
copper was the most opaque to heat.
98. Another form of apparatus is
shown in fig. 5. Two bulbs were
blown one in the other, and they
were fused together at the necks;
to the neck a small tube was fused
for connecting with the Sprengel
pump. The space between the two
bulbs was then perfectly exhausted,
and the small tube sealed up. I
thus possessed what might be called
a spherical shell of vacuum sur-
rounding a bulb open to the air.
In this inner bulb was suspended a
pith ball on the end of a glass arm
balanced by a knob of glass on to the
other end, the suspending fibre being
protected by a glass tube fitting into
the neck of the inner bulb with a cork.
It was found that heat applied to any
part of the outer bulb passed across
the vacuum, and attracted the pith
ball (suspended in air). The sphe-
rical shell of vacuum across which
the heat passed, therefore, produced
no change of action, but simply
behaved like an extra thick glass
bulb. This experiment bears upon
the speculation in par. 81 of my
former paper on this subject.
99. Having succeeded in proving
the fact of repulsion resulting from
radiation, I was desirous of getting
some quantitative estimations of the
forces under examination. A pen-
dulum-apparatus was constructed as
shown in fig. 6. A wide glass tube
(a b) has fused to it a narrower tube
(c d), about 40 inches long; e is a
Fig. 6.
ME. W. CEOOKES ON EEPULSION RESULTING EEOM RADIATION.
529
turned mass of magnesium, weighing 42 grains, suspended by a very fine platinum
wire, the distance between the point of suspension and the centre of gravity of
the magnesium bob being 39-139 inches, so that it forms a seconds’ pendulum ; f is a
spiral made of platinum plate, fastened to two stout copper wires which pass through
the thick plate of glass b, and thence pass to a contact-key and a battery. The plate b
is cemented (83) to the end of the tube a b, which is ground flat, g is an arm fused
into the upright tube for the purpose of connecting it to the glass spiral of the pump ;
it is contracted at h for convenience of sealing off. The fine platinum wire is fastened
at its upper end to a thick wire which is sealed into the glass, and passes through to
the outside for electrical purposes (120). The distance between the pendulum bob
and the spiral is 7 millims. To ignite the spiral the current from two Grove’s cells
was used ; this brought it to a bright red heat in air, and to a white heat in vacuum.
Three feet from the pendulum a telescope was firmly clamped to the bench ;
it was furnished with a micrometer-eyepiece, with movable spider-threads and gra-
duated circle. The edge of the magnesium bob was brought into the same focus as
the traversing cross wire. Observations were taken in the following manner : — The
observer at the telescope brought the cross wire to zero, and then adjusted it to coincide
with the edge of the pendulum bob. An assistant, guided by a seconds’ watch,
pressed the contact-key down for one second, then broke contact for a second, next made
contact for the third second, and so on, alternately making and breaking contact for
either 10, 20, or 40 seconds, counting the seconds aloud. At each second the swing of
the pendulum increased ; and the milled head of the micrometer was kept turning so as
to let the cross wire keep up to the furthest point to which the pendulum vibrated.
At the end of the experiment the position of the cross wire was taken and its distance
from zero recorded.
100. Experiments were first tried in air of normal density. The pump was then set
to work, and observations were taken at different heights of the gauge. The difference
between the height of the gauge and that of the barometer gave the tension of air in
the apparatus in millimetres of mercury ; this is recorded in the first column of the
following Tables. The second column gives the greatest amplitude of the half oscilla-
tion of the pendulum in millimetres — the sign plus signifying attraction, and minus
repulsion.
Near the centre of Table I., in the second column, are five observations to which I
have affixed no sign. When trying the experiments I thought that either I had mis-
taken the direction of impulse, or my assistant had commenced to count the make-and-
break seconds wrongly, as the movement seemed to be repulsion. Never having had
repulsion at such a pressure before, I was not prepared for it ; and fearing there might
be an error, left the sign queried. Another series of observations were taken to re-
examine this point ; they are given in Table II.
It is worthy of notice in these Tables that the attraction by the incandescent
spiral is only moderate in air of ordinary density. The attraction diminishes to a
MDCCCLXXV. 4 A
530
MR. W. CROOKES ON REPULSION RESULTING PROM RADIATION.
Table I.
Tension of enclosed
air, in millims. of
mercury.
Temp. = 16° C.
Bar. =772-55 millims.
Amplitude of half
oscillation, in millims.,
at end of 40" obser-
vation.
772-55
+ 0-46
557-50
+ 0-54
472-00
+ 0-49
372-00
+ 0-39
322-00
+0-41
272-00
+ 0-28
242-00
+ 0-18
22200
+ 0-15
201-00
+ 0-11
167-00
+ 0-12
140-00
0-07 ?
114-50
0-08 ?
89-50
0-12?
70-50
0-03?
54-00
1-02 ?
48-00
+ 0-12'
37-00
+ 0-14
29-00
+ 0-14
20-00
+ 0-18
14-00
+ 0-30
9-15
+ 0-46
6-55
+ 0-66
4-65
+ 1-00
3-15
+ 1-40
2-25
+ 1-48
1-15
+ 1-72
0-75
+ 1-70
0-65
+ 1-46
0-55
+ 1-04
0-35
+ 0-64
0-25
-0-60
0-15
-1-16
-0-05
-5-90
minimum between a tension of 50 millims. and 150 millims., then rises as the pressure
diminishes, until, at a tension of 1T5 millim., the attraction is nearly four times what
it was in dense air. Above this exhaustion the attraction suddenly drops and changes
to repulsion, which at the best vacuum I could get was nearly thirteen times stronger
than the attraction in air.
The last figure in the first column requires explanation. All the others are obtained
by subtracting the height of the gauge from that of the barometer, and are positive. At
the highest rarefactions, however, I get the gauge about 0-05 millim. above the baro-
meter (85, note) ; the sign, therefore, becomes negative.
Table II. agrees in the main with Table I. The sign changes to repulsion at pres-
sures corresponding to those queried in Table I. ; the repulsion, though slight, was
unmistakable. At 102 millims. pressure the observation has a positive sign. This
looks like an error ; but as it is so recorded in my notebook, and as I was at that time
specially looking for repulsions, I do not feel justified in altering it. What I have called
ME. W. CROOKES ON REPULSION RESULTING FROM RADIATION.
531
Table II.
Tension of enclosed
air, in millims. of
mercury.
Temp. = 16° C.
Bar. =772 millims.
Amplitude of half
oscillation, in millims.,
at end of 40'' obser-
vation.
772-0
+ 0-460
770-0
+ 0-540
769-5
+ 0-570
769-0
+ 0-440
769-0
+ 0-520
769-0
+ 0-440
769-0
+ 0-450 |
565-0
+ 0-560
557-0
+ 0-540
472-0
+ 0-490 j
440-0
+ 0-550
369-0
+ 0-416
213-0
+ 0-233
207-0
+ 0-130
189-0
+ 0-180
173-0
+ 0*140
164-0
+ 0-100
162-0
-0-100
142-0
-0-120
132-0
— 0-130
127-0
-0-090
105-0
-0-140
102-0
+ 0-083
73-0
-0-130
60-0
— 0-123
56-0
-0-136
51-0
-0-030
41-0
+ 0-150
33-5
+ 0-170
32-0
+ 0-106
23-0
+ 0-110
22-0
+ 0-080
16-1
+ 0-170
16-0
+ 0-140
7-1
+ 0-380
6-0
+ 0-293
3-9
+ 0-610
1-9
+ 0-880
1-2
+ 0-755
0-9
+ 0-340
0-7
-0-740
0-6
-1-700
0-3
-3-800
0-2
-5-080
0-0
-5-680
-0-05
-6-320
the neutral point, or the point where attraction changes to repulsion, is in this series
lower than in the former. There it occurred at a tension of about 0'3 millim. of mer-
cury ; here at about 0-8. Neither does the previous attraction attain such strength,
although the ultimate repulsion is more intense. The agreement is, however, suffi-
ciently satisfactory, considering the faulty method of measurement.
There are many errors almost inseparable from this form of apparatus. The making
4 a 2
532
ME. W. CEOOKES ON EEPULSION EESTTLTINGr EEOM EADIATION.
and breaking contact by hand is not sufficiently certain, and hesitation for a fraction of
a second would seriously affect the ultimate amplitude of arc. I tried making and
breaking by clockwork, also by a seconds’ pendulum, but there were difficulties in each
plan.
Owing to the mode of suspension, there was uncertainty as to the length of the pen-
dulum. I tried to make it the right length to beat seconds in vacuo. Assuming that
I had succeeded in this, the pendulum would have executed fewer vibrations in the 40
seconds when oscillating in air, and consequently I should not have got the full benefit
from the making and breaking contact, supposing these were accurately timed to
seconds.
The battery-power varied, being stronger at the commencement, and gradually
declining towards the end of the experiment ; and even were the battery to remain con-
stant, the spiral became much hotter, owing to the removal of the air from the appa-
ratus, ranging from a bright red heat in air to a full white heat in vacuo.
Owing to the height of the centre of suspension of the pendulum from the stand of
the apparatus, the slightest deviation from the perpendicular made an appreciable dif-
ference in the distance of the weight from the spiral, and thereby increased or diminished
the effect of radiation. Thus the tread of a person across the floor of the laboratory,
or the passage of a cart along the street, would cause the image of the edge of the mag-
nesium weight apparently to move from the cross wires in the telescope.
Many of these sources of error could have been removed ; but in the mean time having
devised a form of apparatus which seemed capable of giving much more accurate results,
I ceased experimenting with the pendulum.
Before proceeding to describe the apparatus subsequently employed, I may men-
tion that a candle-flame brought within a few inches of the magnesium weight, or its
image focused on the weight and alternately obscured and exposed by a piece of card
at intervals of one second, will soon set the pendulum in vibration when the vacuum is
very good. A ray of sunlight allowed to fall once on the pendulum immediately sets it
swinging. The pendulum-apparatus above described was exhibited, and experiments
shown with it, at the Boyal Society, April 22nd, 1874, and also before the Physical
Society*, June 20th, 1874.
101. The difficulty which attended experiments with the balances and bulb-apparatus
used at first was to bring the moving part accurately back to zero, and also to measure
the deflection produced. I therefore tried several plans of giving a fixed zero-direction
to the movable index. Thus a piece of magnetic oxide of iron was cemented to one end
of the index, and a permanent magnet was brought near it. This answered pretty well,
but was inconvenient, besides not being sufficiently accurate. A bifilar suspension from
cocoon-fibres seemed likely to succeed better ; but the difficulty of suspending the rod
in this manner, so as to get exactly the same tension on each fibre, was very great, and
unless this was done there was more tendency to move in one direction than in the
* Phil. Mag., August 1874.
ME. W. CEOOKES ON REPULSION RESULTING FROM RADIATION.
533
other. When I had succeeded in suspending the needle with an equal tension on each
silk fibre, I found their elasticity to vary ; and as soon as the vacuum was approached
one was sure to contract more than the other, twisting the needle out of the axis of the
tube, and sometimes causing it to touch the side. This method of suspension was there-
fore abandoned.
By increasing the length of the needle, and also of the fibre used to suspend it, it was
possible to employ fibres with a considerable amount of torsion, and still preserve the
delicacy of the apparatus. Fine platinum wire was first tried ; but this was soon aban-
doned in favour of glass fibres, which were found to answer so perfectly that I have
since used nothing else.
102. Fig. 7 shows the form of apparatus which I have finally adopted, as combining
the greatest delicacy with facility of obtaining accurate observations, and therefore of
getting quantitative as well as qualita-
tive results. It is a torsion-apparatus in
which the beam moves in a horizontal
plane, and may be called a horizontal
torsion-balance, a b is a piece of thin
glass tubing, sealed off at the end b
and ground perfectly flat at the end a.
In the centre a circular hole, c, is
blown, and another one, c\ at the end ;
the edges of these holes are ground
quite flat, a, c, and c1 can therefore
be sealed up by cementing flat trans-
parent pieces of plate glass, quartz,
or rock-salt, a, d , and d' on to them
(83). To the centre of a b an up-
right tube, ef\ is sealed, having an arm,
g, blown on to it for the purpose of
attaching the apparatus to the pump.
h i is a glass index, drawn from circular or square (22) glass tube, and as light as possible
consistent with the needful strength. A long piece of this tube is first drawn out before
the blowpipe ; and it is then calibrated with mercury until a piece is found having the
same bore throughout ; the necessary length is then cut from this portion. jTc is a very
fine glass fibre, cemented at j to a piece of glass rod, and terminating at k with a stirrup,
cut from aluminium foil, in which the glass index, h i, rests. In front of the stirrup is a
thin glass mirror, shown at k, silvered by Liebig’s process, and either plane or concave as
most convenient. At the ends of the glass index (Ji i) may be cemented any substance
with which it is desired to experiment ; for general observations I prefer to have these
extremities of pith, as thin as possible, and exposing a surface of 10 millimetres square.
The pith may be coated with lampblack or silver, or may retain its natural surface.
Fig. 7.
534
ME, W. CEOOKES ON EEPULSION EESULTING EEOM EADIATION.
103. The preparation of the suspending thread of glass requires some care. It
should be drawn from flint glass, as this gives much tougher threads than foreign
glass. The diameter varies with the amount of torsion required ; it may be O'OOl inch
or less. I select the piece best adapted for the special experiment in the following
way : — Several threads of glass are first drawn out before the blowpipe, and a certain
number selected as being likely to answer the purpose. These are then suspended, side
by side, to a horizontal rod and equalized as to length. A piece of glass rod, about
2 inches long, which is always kept for this purpose, is then cemented by shellac on to
the end of one of the threads. Air-currents are then cut off by a glass screen, and the
thread being set in movement by a slight twist, the torsion is measured by timing the
oscillations. This having been done with each thread in succession, one is selected and
mounted in the apparatus. If it works properly, well and good ; if not, it is easy to
select a thread having the requisite amount of torsion, more or less, and substitute it for
the one first used.
In fitting up one of these apparatus, threads were drawn out which were found to
require respectively : —
44 seconds,
30 „
28 „
11 „
and
3! „
for a half oscillation when the glass weight was hung on to their ends. The one oscil-
lating in 30 seconds was first used, but was found to give insufficient torsion. The one
making half an oscillation in 11 seconds was then used, and was found to answer well.
Before I adopted this plan days were frequently wasted in the attempt to hit upon a
glass thread of the requisite degree of fineness.
104. In taking accurate observations with an apparatus of this description, it is neces-
sary to support it on a stand firmly fastened to a main wall. When resting on a bench,
or connected in any other way to the floor, there is a constant oscillation which keeps
the index from zero.
The apparatus being fastened firmly to its stand, accurately levelled, and sealed on to
the pump, a divided scale, a b (fig. 8), is placed four feet from the small mirror ; and
immediately beneath the scale is a narrow brass slit, c, illuminated by a lamp, d. In
front is a lens, e, which throws the image of the slit on to the mirror, where it is reflected
back again on to the divided scale. Here the angular movement of the bright line of
light shows the minutest attractive or repulsive force acting on the pith at the extre-
mity of the movable index.
In order to keep the luminous index accurately at zero, except when experiments are
being tried, extreme precautions must be taken to keep all extraneous radiation from
acting on the apparatus. A slightly conical paper tube, f, about 6 inches long, and
as narrow as the angular movement of the ray of light will admit of, is cemented on to
the glass window in front of the mirror ; and a similar tube, g , is cemented on to the
ME. W. CEOOKES ON EEPULSION EESULTING EEOM EADIATION.
535
quartz window in front of the pith surface on which radiation is to act. The latter tube is
furnished with card shutters, h, i, at each end, capable of easy movement up and down.
The whole apparatus is then closely packed on all sides with a layer of cotton-wool,
about 6 inches thick, and outside this is arranged a double row of Winchester quart
bottles, j, j, filled with water and covered with brown paper, spaces being only left in
front of the paper tubes. Jc and l represent the positions of the candle 140 and 280
millims. distant from the pith. The whole arrangement has the appearance shown
in fig. 8.
Fig. 8.
105. I will not discuss at present the phenomena presented when the apparatus is
full of air, or when the vacuum is imperfect, but will proceed to the effects observed
when the exhaustion has been pushed to the highest attainable degree. However much
the results may vary when the vacuum is imperfect, or when the apparatus is full of
air, I always find them agree amongst themselves when the residual gas is reduced to the
minimum possible ; and I have also ascertained that it is of no consequence what this
residual gas is. Thus I have started with the apparatus filled with various vapours and
gases, such as air, carbonic acid, water, iodine, hydrogen, or ammonia ; and at the
highest rarefaction I find no difference in the results which can be traced to the residual
vapour, assuming any to be present. A hydrogen vacuum seems neither more nor less
favourable to the phenomena than does a water or an iodine vacuum. If moisture be
present to begin with, it is necessary to allow the vapour to be absorbed by the sul-
phuric acid of the pump, and to continue the exhaustion with repeated warming of the
apparatus until the aqueous vapour is removed ; then only do I get the best results.
When pith surfaces are used at the extremities of the glass beam, they should be per-
fectly dry ; and they are more sensitive if the apparatus has held a vacuum for some
weeks, as the residual moisture in the pith will then have been absorbed by the sul-
phuric acid in the pump.
106. It was found that when a source of light and heat is suddenly allowed to shine
on the pith surface and not removed, a deflection rapidly takes place, attaining its
536
ME. W. CEOOKES ON EEPULSION EESITLTING FEOM EADIATION.
maximum in about 11 seconds ; the spot of light now returns a few degrees, and then
proceeds in the first direction to a greater extent than at first. So it goes on, by alter-
nate steps, advancing a little each oscillation, until, if the light be feeble, the index
takes up a nearly fixed position ; if, however, the light be strong, the beam is driven
against the side of the tube. In illustration of this I select the following series of obser-
vations from a large number recorded in my note-book. The horizontal figures represent
Fig. 9.
Degrees on scale, representing repulsion.
the degrees on the scale, starting from zero, where the spot of light normally rests.
The vertical figures represent the seconds during which the experiment lasted. The
zigzag line represents the oscillations of the spot of light, and shows the movement of
the pith surface under the influence of a uniform source of radiation. The time was
recorded by a chronograph. Starting from zero the spot of light is seen to have tra-
velled to 97° in 11*5 seconds ; at the end of 11 more seconds, or 22'5 seconds altogether,
it had comeback to 50°; at the end of 34 seconds the light had advanced again to 109°,
and so on. The movements are tolerably uniform as to time, taking about 11*5 seconds
for the half oscillation, but the amplitude of vibratioD is continually diminishing.
107. If, however, the light is only allowed to shine on the pith surface for 11*5 seconds
(or for as long as the spot of light takes to perform its first half oscillation), and if it is
then instantly cut off, the spot of light almost invariably returns to zero and stops there,
ME. W. CROOKES ON REPULSION RESULTING EROM RADIATION.
537
instead of swinging to the opposite side and only returning to rest after ten or a dozen
oscillations, as is the case when the beam is set vibrating by mechanical means. This
behaviour points to the return movement taking place under the influence of a force
which remains active after the original radiation is cut off, and which is only gradually
dissipated. This force is most probably from the heat which the pith has absorbed
raising its temperature ; and the steady return to zero seems to be due to the movement
being controlled by the radiation of heat by the pith.
108. A series of observations taken with another apparatus, with the object of ascer-
taining the times of oscillation to and fro, showed that the first half, or the maximum
deviation produced, whilst under the influence of radiation, occupied about the same
time as the second half, or the return swing, w7hen the source of radiation was cut off.
The following are the observations. The source of radiation was a candle, the intensity
of action being moderated by filtering the rays through glass screens.
Half oscillation,
under influence of
radiation.
Whole oscillation,
radiation being cut off
during the return, swing.- ■
8 seconds.
15 seconds.
7-5
15
7-5 ,,
14-5 „
7-5 „
15-5 „
7-5
14-5 „
7*25 „
15 .......
7*5 „
15
7'5 „
15 „
7
14 »
7 ,i
14 „
6*7 5 „
14 „
7 „
14 „
7-25 „
15 „
7
14 „
7
13*25 „
8
16
8 „
16
7-5
15 „
7
15 „
8
15 „
8*5 „
15*5 „
7’5 „
15
8
15
8
15 „
7
14 „
Mean. ..7*47 „
]
Mean... 14*77 ,,
The average time of the first half oscillation is therefore 7*47 seconds*', and of the
second half 7‘3 seconds. This small difference is not unlikely to be due to errors of
observation.
After a long series of experiments the zero gradually creeps up, showing that
one side of the apparatus is becoming warmed. The conducting-power for heat and
* % referring to paragraphs 106 and 307 it will he seen that I have put the time of the first half oscillation
as 11-5 seconds. This was with another apparatus, having a glass thread of different torsion.
MDCCCLXXV. 4 B
538
MR. W. CROOKES ON REPULSION RESULTING- FROM RADIATION.
condition of the surface (whether coated with lampblack or consisting of polished
metal) of the body on which radiation falls materially influence the movements.
109. The accompanying Table gives the results of numerous experiments as to the
effect of screens, tried with an exceedingly delicate apparatus, constructed as above
lagnesium
wire,
burnt for
•5 seconds,
distant
140
millims.
Standard
candle,
distant
140
millims.
Standard
candle,
distant
280
millims.
Copper
ball,
400’ C.,
distant
140
millims.
Copper
ball,
400° C.,
distant
280
millims.
Copper
ball,
100° C.,
distant
140
millims.
o
o
54
52
o
185
9
6
148
220
88
100
32
28
115
90
1-5
2
3-25
110
76
0
1-75
—
72
24
23
o
0-62
0
17
8
3
20
0
0
18-5
0
0
0
0
30
0
0
0
off the scale.
l o
8
72
7
—
0
0
0
29
3
—
0
0
0
Interposed sceen.
None
Rock-salt, 20 millims. thick, not very clear . .
Rock-crystal, in two pieces, 42 millims. 1
thick altogether J
Talc, clear hut very dark, 1*25 millim. 1
thick }
Plate glass, white, 2 millims. thick, one \
piece J
Ditto, two pieces
Ditto, three pieces
Ditto, two pieces, enclosing 8 millims. 1
water J
Plate glass, of a greenish colour, 10-5 |
millims. thick J
Ditto, 20 millims. thick
Alum, a clear plate, 5 millims. thick
Plate glass, slightly greenish, 40^ millims., I
and clear alum plate, 8| millims. thick. J
Calc spar, 27 millims. thick
Yery thin film of mica
Ammonio-sulphate of copper, 8 millims.
thickness of solution, opaque to rays
less refrangible than line F
Ditto, stronger solution, opaque below G.
described, the window, c' (fig. 7), being of quartz. The candle used was the kind
employed in gas photometry, and defined by Act of Parliament as a “ sperm candle
of 6 to the pound, burning at the rate of 120 grains per hour.” The distances were
taken from the front surface of the pith when the luminous index stood at zero.
They were in the proportion of 1 to 2 (140 to 280 millims.), to enable me to see if
the action would follow the law of inverse squares and be four times as great at the
half distance. No such proportion can, however, be seen in the results, the radiant
source possibly being too close to allow the rays to fall as if from a point. The figures
given are the means of a great many fairly concordant observations. Where a dash rule
is put I have tried no experiment. The cipher 0° shows that experiments were actually
tried, but with no result.
The sensitiveness of my apparatus to heat-rays appears to be greater than that of any
ordinary thermopile and galvanometer. Thus I can detect no current in the thermo-
pile when obscure rays from copper at 100° C. fall on it through glass ; and Melloni
gives a similar result.
MU. W. CROOKES ON REPULSION RESULTING EROM RADIATION.
539
110. An examination of this Table shows that the action is by no means confined to
the rays usually called heat, i. e. to the extreme- and ultra-red of the spectrum. The
strong action obtained when the light is filtered through greenish glass and alum, or
through ammonio-sulphate of copper, shows that luminous rays produce a similar
movement of repulsion.
Unfavourable weather has prevented me from obtaining good quantitative results with
the different rays of the solar spectrum ; but I have tried numerous qualitative experi-
ments which leave so doubt on my mind that any ray, from the invisible ultra-red to
the invisible ultra-violet, will produce repulsion in a vacuum. The following is an
experiment tried with the electric light. The spectrum was formed with a complete
quartz train, no glass whatever being in the path of the rays. The purity of the
spectrum was evidenced by the fact of the lines being sharp when thallium, sodium, or
lithium was put between the carbon poles. The spectrum was so arranged that any
desired ray could be thrown on to a lampblacked pith surface, screens being interposed
to cut off the action when desired. The torsion-balance was similar to the one used in
the last-named series of experiments (104), but was not quite so sensitive.
The extreme-red rays were first brought into position. On removing the screen the
luminous index moved 9 divisions on the scale. The screen being replaced, the index
returned to zero. A solution of iodine in disulphide of carbon was now interposed, and
the screen again removed. The repulsion was almost as strong as before, showing that
this liquid was transparent to the ultra-red rays.
The iodine solution was then replaced by a clear plate of alum 5 millims. thick, and
the screen removed ; a very slight movement only took place. The iodine solution was
then put in front of the alum plate, so as to subject the extreme-red rays to a double
process of sifting. No trace of action could be detected.
Whilst this double screen was in front of the pith disk, the spectrum was gradually
passed along, so as to bring the rays, one after the other, into position. No effect,
however, was produced, showing that alum and iodine solution practically obliterate
the whole of the spectrum.
The alum plate and iodine-cell were now removed, and the green of the spectrum
(the thallium line) was brought into position. The luminous index moved 6 divi-
sions. The plate of alum cut off only a small amount of this action, but the iodine-
cell brought the index to zero. This is a proof that the action in this case was not due
to the heat-rays of the spectrum, for these are practically transmitted by iodine, and cut
off by alum.
The indigo-rays were next brought into position. The spot of light moved three
divisions on the graduated scale. Alum cut off only a very little of the action ; but the
iodine-cell was completely opaque to the rays, and brought the index to zero.
Finally, the invisible ultra-violet rays of the spectrum were brought into position.
The train being of quartz these were abundant. Care was taken to keep any of the
luminous rays away from the pith disk. I think I succeeded in this ; but it was not
4 b 2
540
ME. W. CROOKES ON KEPULSION BESETTING EEOM BADIATION.
easy, owing to the fluorescence of the card and other surfaces on which stray rays fell.
The spot of light moved two divisions, which were increased to five when the invisible
rays were further concentrated by a quartz lens. The interposition of the iodine-cell
cut off the whole of the action. The alum plate cut off about half of the action, but
scarcely more than would have been cut off had a piece of colourless glass ‘of the
same thickness been interposed, and it must be remembered that the alum plate has
glass and Canada balsam on each side.
111. A similar experiment with the solar spectrum gave the following deflections,
glass prisms being used : —
Ultra-red 2
Extreme red 6
Orange 5
Green 4 -5
Indigo 3 ’5
Ultra-violet 2
Although I give the number of divisions shown by the luminous index, I attach
little importance to them, as quantitative measurements. They are only single obser-
vations, and were taken before I had succeeded in getting any thing like the same
sensitiveness I can now attain in the apparatus. As illustrations of the fact, however,
that the more refrangible rays of the spectrum act as well as the lower rays, they may
be taken as trustworthy*.
112. In my former paper on this subject I have already mentioned in detail that at
a certain point of rarefaction there is neither attraction nor repulsion when radiation
falls on the movable index (30, 43, 47, 66). I have long tried to ascertain the law
governing the position of this neutral point. My results are not yet ready for publi-
cation ; but they are shaping themselves in order, and will, I trust, lead to a true
explanation of the cause of these phenomena.
The barometric position of the neutral point dividing attraction from repulsion varies
according to circumstances ; among these may be mentioned the density of the sub-
stance on which radiation falls, the ratio of its mass to its surface, its radiating- and
conducting-power for heat, the physical condition of its surface, the kind of gas filling
the apparatus, the intensity of radiation, and the temperature of the surrounding atmo-
sphere.
When the surface exposed to radiation is pith, the neutral point is somewhat low.
I have had it vary between 50 millims. and 7 millims (30) below a vacuum. It is, how-
ever, impossible to ascertain exactly ; for a point of rarefaction can be obtained at which
the warm fingers repel, and incandescent platinum attracts. With a heavy metal in
the form of a sphere, so as to expose the smallest surface in proportion to the mass, I
* Every thing is ready to try a series of experiments with the solar spectrum, as soon as sunshine is avail-
able. The results shall he communicated in a subsequent paper.
MR. W. CEOOKES ON EEPULSION EESULTING- EEOM EADIATION.
541
have not attained the neutral point until the exhaustion was within a very small
fraction of a millimetre (43, 47) ; whilst if the metal is in the form of thin foil the
neutral point may easily be got lower than with pith.
I am inclined to believe that the true action of radiation is repulsion at any pres-
sure, and that the attraction observed when the rarefaction is below the neutral point
is caused by some modifying circumstance connected with the surrounding gas, not
necessarily of the nature of air-currents (80). As a proof of this I have not unfre-
quently obtained repulsion from radiation when the apparatus was full of air at the
normal pressure.
113. The following experiments are too few in number, and have not been varied
sufficiently as to conditions, to enable many inferences to be drawn from them.
However, they afford glimpses of a law governing the position of the neutral point.
A torsion-apparatus was fitted up similar to the one described in paragraph 102.
The beam was of glass, and at one extremity was fitted with a spring clip, also of glass,
so that different bodies could be experimented with. Disks of platinum foil, 1 centi-
metre in diameter and weighing T28 grain each, were prepared, and they were fixed
in the clip at the end of the torsion-beam, either singly or two, three, or four together,
in such a manner that while the disk exposed was always 1 centim. in diameter,
the weights should be in the proportion 1, 2, 3, 4. At the other end of the beam a
movable counterpoise was arranged, so that the length of beam from the platinum
disk to the centre was always the same.
The neutral points were as follows : — •
No. of disks.
Barometer.
Gauge.
Diff.=
Neutral point.
Differences.
1.
760
682
78
8
o
760
690
70
16
3.
760
706
54
24
4.
760
730
30
114. Two pieces of platinum, a and b , were now cut from the same sheet, each having
1 square centim. of surface, a was left the full size, but b was carefully folded in four,
so as to expose a surface of only a ^ of a square centimetre, the weight remaining the
same. The neutral points were then taken. The average of several observations
(which, however, were not quite so concordant as could have been wished) were, below
a vacuum,
a. b.
136 millims. 70 millims.
The pieces of foil were then coated with lampblack, and observations again taken.
This time the neutral points came out —
a.
66 millims.
b.
124 millims.
542
MR. W. CROOKES ON REPULSION RESULTING EROM RADIATION.
An intimate connexion is thus shown to exist between the absorbing (and radiating)
power of the surface on which radiation falls and the atmospheric tension at which the
movement is reduced to a minimum. Further experiments on this subject are in
progress.
115. It has already been said that when radiation falls on a thin surface of pith, the
neutral point is low, whilst with a moderately thick piece of platinum it is generally
high. I have constructed a double torsion-apparatus by means of which these actions can
be easily studied. Fig. 10 shows the arrangement of apparatus. It consists of a torsion-
Eig. 10.
apparatus constructed as the one shown in fig. 7 (102), with the exception of the arms
being double. Similar parts in each drawing are shown by similar letters, a b is a
piece of thin glass tubing, sealed off at the end b, and ground perfectly flat at the end
a. In the centre a circular hole (cJI) is blown, and two others are blown at the parts
c and c'; the edges of these holes are also ground perfectly flat, a, c, c\ and c" can
therefore be sealed up by cementing flat transparent plates of glass, quartz, rock-salt,
&c., a , d, d1, d" on to them. At right angles to a b , and at the parts e, d, upright
ME. W. CROOKES ON REPULSION RESULTING^ EEOM RADIATION.
543
tubes, f e, f' e', are sealed, one of them having an arm (g) blown into it for the purpose
of attaching the apparatus to the pump, h, i, h', i' are glass beams made as light as
possible consistent with the necessary stiffness, j Jc, j' Jc ' are glass fibres (103) cemented
at j, j' to pieces of glass rod, and terminating at Jc, Jd with a stirrup cut from aluminium
foil, in which the glass beams h, i, Ji', i' rest. In front of these stirrups are thin glass
mirrors ( Jc , Jc'). At the ends of the beam ( Ji , i) are cemented very thin pieces of blackened
pith, each 1 centim. square ; and at the ends of the other beam (Ji i’) are cemented pieces
of platinum foil, also 1 centimetre square. At l and l' are narrow slits, with lamps
behind them, so arranged that they send their rays of light respectively on to the mirrors
{Jc, JJ), whence they are reflected back to the divided scale to. When the torsion-beams
are riot acted on by any force, the rays of light both meet at zero (to), and there over-
lap, the slightest movement of either beam causing them to separate.
When the apparatus is full of air, a beam of radiation sufficiently wide to cover the
whole window (c") being thrown upon the plates i, Ji’, the latter are instantly attracted,
as shown by the movement of the reflected rays of light {Jc to, Jc' to). On exhausting
the tube, and trying the effect of a hot body at the central window from time to time,
it is seen that the movement of the pith surface {i) gradually diminishes, until at a
certain point of exhaustion (in this apparatus at about 50 millims. below a vacuum)
the neutral point for pith is obtained. On increasing the rarefaction the pith is
repelled by radiation, the platinum continuing to be attracted. On exhausting the air
still further (to about 28 millims.) the neutral point for the platinum surface is
obtained, higher rarefactions producing repulsion of each when radiation falls on the
pith and platinum surfaces {i, h').
At a rarefaction intermediate between the neutral point for pith (50 millims.) and
the neutral point for platinum (28 millims.), the curious effect is produced of the same
beam of radiation thrown into the window (<?") producing repulsion of the pith and
attraction of the platinum, the two rays of light {Jc to, Jc' to) each moving to the right,
and, if a piece of ice is presented to the central window, to the left. By adjusting the
internal tension of the apparatus, a point may be reached (about 40 millims. below a
vacuum) at which the repulsion of pith and the attraction of platinum are exactly
equal, and then the two rays meeting at to do not separate, but together move to the
right or left.
116. A series of experiments have been tried with a view to ascertain what influence
the state of surface of the substance submitted to radiation has on the amount or the
direction of its movement. A torsion-apparatus was prepared similar to the one shown
in fig. 7 (102), and having a thin disk of ivory at each end. One was coated with lamp-
black, whilst the other retained its white polished surface. The average of a number
of experiments showed that, under the influence of the same source of radiation acting
for the same time (15 seconds), the white ivory was repelled so as to send the lumi-
nous index 41 ‘5 divisions of the scale, whilst the blackened ivory caused, the index to
544
ME. W. CEOOKES ON EEPTTLSION EES TILTING FEOM EADIATION.
move 46-8 divisions. These experiments were, however, tried in 1873*, when I had
not succeeded in getting any thing like the delicacy I now obtain in the apparatus ; and
I propose to repeat them under varied conditions before employing the results to
found any arguments upon.
117. In my former paper on this subject (74, 75, 76, 77, 78) I have discussed various
explanations which may be given of attraction and repulsion resulting from radiation ;
and in a lecture delivered before the Physical Society f I entered more fully into the
same arguments. The most obvious explanation is that the movements are due to the
currents formed in the residual gas, which, theoretically, must be present to some extent
even in those vacua which are most nearly absolute.
Another possible explanation is that the movements are due to electricity developed
on the moving body, or on the glass apparatus, by the incident radiation.
A third explanation has been put forward by Professor Osborne Reynolds, in a paper
which was read before the Royal Society on June 18th, 1874. Referring to the results
of my experiments, Professor Reynolds says that it is the object of his paper to prove
that these effects are the result of evaporation and condensation. In my exhausted
tubes he assumes the presence of aqueous vapour, and then argues as follows : — “ When
the radiated heat from the lamp falls on the pith, its temperature will rise, and any
moisture on it will begin to evaporate and to drive the pith from the lamp. The
evaporation will be greatest on that ball which is nearest to the lamp ; therefore this
ball will be driven away until the force on the other becomes equal, after which the
balls will come to rest, unless momentum carries them further. On the other hand,
when a piece of ice is brought near, the temperature of the pith will be reduced, and it
will condense the vapour and be drawn towards the ice.”
It is not my intention to recapitulate the arguments I have already brought forward
against these three explanations. They are all fully given in my above-quoted lecture
before the Physical Society. I shall, however, adduce a few experiments which have
been devised specially with the view of putting one or other of these theories to the
test. In giving what I conceive to he reasonable arguments against the explanations
which have already been proposed, I do not, however, wish to insist upon any theory
of my own to take their place. Any theory will account for some facts ; but only the
true explanation will satisfy all the conditions of the problem, and this cannot be said
of either of the theories I have already discussed.
118. The pendulum-apparatus, described and figured in paragraph 99, was specially
devised to bear upon the air-current and the electrical theory. On referring to the
description of the experiments tried with it (Tables I. & II.), it is seen that in air the
ignited spiral produced attraction, whilst in a vacuum the same source of radiation gave
* The torsion-apparatus with ivory terminals was exhibited in action at the Meeting of the Eoyal Society,
Dec. 11th, 1873.
t Tune 20, 1874 (Phil. Mag., August 1874).
ME. W. CROOKES ON REPULSION RESULTING FROM RADIATION.
545
strong repulsion. Now the effect of raising a platinum spiral to whiteness in the air
would be to rarefy the air all round, and the suddenness of its ignition would cause the
air to be driven from it, as a centre, on all sides. Hence I was prepared to find that
the pendulum would be mechanically blown on one side by what might be likened to a
miniature explosion of heated gas. But the action was always one of attraction, whilst,
when there was no air at all present to be expanded and driven away by the hot
platinum, the action was one of violent repulsion. A possible explanation of the attraction
in air in this experiment may be given by assuming that the pendulum was driven
inwards by the rush of cold air supplying the place of that rising upwards from the hot
spiral ; but it is not likely that this action should so completely overcome the effect of
expansive action ; and, moreover, it will only account for half the phenomenon (that in
air), and leaves the still stronger action in a vacuum entirely unexplained.
119. I have tried special experiments to put the air-current theory to a decisive test.
Bulb-tubes (84) and torsion-apparatus (102) have been prepared, containing terminals of
metal, ivory, glass, mica, or pith, in the form of thin flat surfaces. These surfaces have
been placed at an angle with the plane passing through the index and suspending-
thread, in such a manner that the action of heat would he to cause currents and
drive them round like the vane of a windmill. I, however, found the action of heat
in vacuo to be repulsion, and in air to be attraction ; and the latter was even strong
enough to overcome the action of the air-currents, which could not fail to be developed
under the circumstances of the experiment.
120. The pendulum-apparatus has also been used to show that electricity is not the
cause of the attraction and repulsion. On referring to the description (99), it is seen
that the mass of magnesium forming the weight was in metallic contact with the
platinum wire which supported it, and that the upper end of this platinum wire was
fused into the glass tube, and passed thence to the outside. With this I have tried
numerous experiments bearing on the action of electricity. I have connected the pro-
jecting end of the platinum wire with “ earth,” with either pole of an induction-coil (the
other pole being more or less insulated), with either pole of a voltaic battery, and with a
delicate electroscope ; I have charged it with an electrophorus, and have submitted it
to the most varied electrical conditions ; and still, on allowing radiation to fall on the
suspended mass, I invariably obtain attraction in air and repulsion in a vacuum. The
heat has been applied from the outside, so as to pass through the glass, and also inside
by means of the ignited spiral ; and the results show no difference in kind, but only in
degree, under electrical excitement. I often obtain troublesome electrical interference
with the usual phenomena, but never of such a character as would lead me to imagine
that the normal results were due to electricity. I also obtain the normal actions
whether the apparatus has been standing insulated in the air*, or whether it has been
completely immersed in water connected electrically with “earth” or surrounded with
wet blotting-paper.
mdccclxxiv. 4 c
546
MR. W. CROOKES ON REPULSION RESULTING FROM RADIATION.
121. The following experiment was suggested by Mr. Cromwell F. Varley, F.R.S.,
who informs me that he considers the results conclusive against the electrical theory.
A torsion-apparatus was prepared, as
shown in fig. 11. The inside of the
tube ( a b) is lined with a cylinder
of copper gauze, having holes cut in
the centre ( c ) for the passage of the
supporting- thread ( d c) and the index
ray of light, and holes at each end
to admit of the plates (e,f) being
experimented with. A hole drilled
in the plate (b) allows a wire to pass
from the copper gauze to the out-
side, so as to give me electrical access
to the gauze lining. Under the
most diverse electrical conditions,
whether insulated or connected with
“ earth,” this apparatus behaves nor-
mally when heated; neither can I detect any electricity when the plate e or^is under
the influence of radiation if I connect the wire g with a delicate electroscope. In
experimenting with this apparatus I have also completely immersed it in liquids, such
as water, solutions of metallic salts, ether, disulphide of carbon, &c. The heat has
been applied in these cases by introducing a glass bulb containing water at different
temperatures and a thermometer (28). Under all these varied circumstances the
movements took place in the regular manner, and no electrical action whatever could
be detected.
122. I have already discussed Professor Osborne Reynolds’s theory of evaporation
and condensation somewhat fully in the already quoted Physical Society paper *. I
will, however, describe the following experiments, which I think prove that Professor
Reynolds has not suggested a theory which accounts for all the facts of the case, and
therefore has not hit upon the true explanation.
A thick and strong bulb was blown at the end of a piece of very difficultly fusible
green glass, specially made for steam-boiler gauges. In it was supported a thin bar of
aluminium at the end of a long platinum wire. The upper end of the wire was passed
through the top of the tube and well sealed in, for electrical purposes (120). The
apparatus was sealed by fusion to the Sprengel pump, and exhaustion was kept going
on for two days, until an induction-spark refused to pass across the vacuum. During
this time the bulb and its contents were several times raised to a dull red heat. At
the end of two days’ exhaustion the tube was found to behave in the same manner
* Loo. cit. ; also Chemical News, July 17, 1874.
Eig. 11.
ME. W. CROOKES ON REPULSION RESULTING FROM RADIATION.
547
as, but in a stronger degree than, it would in a less perfectly exhausted apparatus, viz.
it was repelled by light and heat of low intensity and attracted by cold.
A similar experiment was next tried, only water was placed in the bulb before exhaus-
tion. The water was then boiled away in vacuo , and the exhaustion continued, with
frequent heating of the apparatus to dull redness, for about forty-eight hours. At the
end of this time the bar of aluminium was found to behave exactly the same as the
one in the former experiment, being repelled by radiation.
Similar experiments, attended with similar results, were tried with a platinum and
with a glass index ; and instead of water, iodine has been put into the bulb to begin with.
It is impossible to conceive that in these experiments sufficient condensable gas or
vapour was present to produce the effects Professor Osborne Reynolds ascribes to it.
After the repeated heating to redness at the highest attainable exhaustion, it is difficult
to imagine that sufficient vapour or gas should condense on the movable index to be
instantly driven off by a ray of light or even the warmth of the finger with recoil enough
to drive backwards a heavy piece of metal.
123. It seems tome that a strong argument against Professor Reynolds’s theory (and
also against the electrical and air-current theories) may be drawn from the fact that the
repulsion in a vacuum is not confined to those red and ultra-red rays of the spectrum
which mainly produce dilatation of mercury in a thermometer, excite an electrical
current between antimony and bismuth couples, and cause a sensation of warmth when
falling on the skin, but that any ray from the ultra-red to the ultra-violet will produce
a similar effect. It cannot be reasonably argued that a ray of light, filtered through
plates of glass and alum (109), can instantly vaporize a film of moisture or condensable
gas from a surface on which it is caused to shine, or that it can produce air-currents in
the almost perfect vacuum surrounding the surface shone upon, or that it will produce
electrical excitement on such a surface.
124. Facts tested and verified by numerous experiments, but scarcely more than
touched upon in the present paper, are, I think, gradually shaping themselves in order,
in my mind, and will, I hope, aid me in evolving a theory which will account for all the
phenomena. But I wish to avoid giving any theory on the subject until I have accu-
mulated a sufficient number of these facts. The facts will then tell their own tale ; the
conditions under which they invariably occur will give the laws ; and the theory will
follow without much difficulty. In the eloquent words of Sir Humphry Davy, “ When
I consider the variety of theories which may be formed on the slender foundation of
one or two facts, I am convinced that it is the business of the true philosopher to avoid
them altogether. It is more laborious to accumulate facts than to reason concerning
them ; but one good experiment is of more value than the ingenuity of a brain like
Newton’s.”
[ 549 ]
XIX. On the Structure and Development of Myriothela.
By Professor Allman, M.D. , LL.D ., F.B.S., President of the Linnean Society
Eeceived February 5, — Read February 11, 1875.
GENERAL DESCRIPTION.
Mykiothela, of which we have as yet no satisfactory evidence of more than a single
species being known, consists of a solitary attached hydranth, carrying near its proximal
or attached end the blastostyles or appendages which give origin and support to the
gonophores (Plate 55).
Full-sized specimens (fig. 1) measure, when extended, nearly 2 inches in length.
They are then cylindrical in form, with the mouth occupying the summit of a short
conical hypostome, behind which the tentacles commence, and thence extend over
somewhat more than one half the entire length of the body ; while the proximal end of
the body is bent at right angles to the rest, is invested with a chitinous perisarc, and
gives origin to short sucker-like processes of attachment.
For some time after the animal has been removed from the sea and placed in the con-
finement of our jars, the tentacles will present the appearance of short papilliform pro-
cesses (fig. 3). This condition, however, is that only of the tentacles in a state of
contraction. When fully extended their form is very different; for they then attain a
length of nearly half a line, and present a thin cylindrical stem, terminated by a large
spherical capitulum, very well defined and distinct from the stem (fig. 2). In this
state the tentacles are kept in constant motion, the animal perpetually depressing them
and elevating them with a peculiar jerking action.
The tentacles are very numerous ; upwards of two hundred may be counted in a
single hydranth. For the greater part of their extent they are set close to one another;
but as they approach their proximal limit they not only become smaller, but are sepa-
rated from one another by greater intervals. Almost every tentacle carries a small
purple pigment spot on its summit.
The hydranth when contracted (fig. 3) becomes club-shaped or conical, and the
tentacles then pass into the state of short, thick, imbricated papillae.
The contractility of the hydranth exists chiefly in the tentacular portion. In all that
portion which carries the gonosome the contractility is much less marked. In the ten-
tacular region the contractility is shown not only in the great extent to which this part
of the hydranth can elongate and shorten itself, but in the loops and contortions, like
the writhings of a worm, into which, when fully extended, it frequently throws itself
(fig. ii).
MDCCCLXXV. 4 D
550
PROEESSOR ALLMAN ON THE STRUCTURE
The blastostyles (a, a, a , a) spring from that portion of the hydranth which lies
immediately below the tentacles. They form a dense group, surrounding the body
on all sides. They are usually somewhat clavate, or of -an elongated fusiform shape,
but are very contractile and vary much in form. Towards their free extremity they
carry several small scattered capitate tentacles ; and at the proximal side of these are the
gonophores {b, b, b), which belong to the type of simple sporosacs, and are large, of a
globular form, and carried on very short peduncles, which spring without any regular
arrangement from the sides of the blastostyle.
From the same part of the body there also spring numerous very extensile filiform
organs resembling tentacles ( c , c,c). These arise for the most part close to the base of
a blastostyle, where they occur mostly in pairs, though sometimes singly. They termi-
nate distally in a truncated sncker-like extremity. It will be afterwards seen that
these organs, which have been hitherto entirely overlooked, perform an important
function in the economy of the animal. I shall designate them by the name of
“ claspers.”
The section of the body from which the blastostyles and claspers spring is usually
somewhat swollen, and is marked by close longitudinal shallow furrows. After con-
tinuing naked for some distance beyond the proximal limit of the gonosome, the body
bends at right angles to itself, becomes clothed with a chitinous perisarc (<?.),' and fixes
itself by the extremities of short truncated processes (e) to some solid support.
The general colour of the animal is a pale straw-colour. The tentacles are almost all
tipped with a brownish-purple spot, the same colour sometimes extending over the
greater part of the tentacle, and generally also spreading in clouds and streaks over the
tentacula-bearing portion of the body. The gonophores are of a dull white, with their
distal poles encircled by a ring of purple pigment dots.
The genus Myriothela was instituted by Sars for an animal which he obtained off the
coast of Norway, and described under the name of Myriothela arctica*. He has given
an accurate, if not altogether adequate description of its external characters, and has
correctly referred it to the Hydroida. Mr. W. Stimpson, however, has pointed outf that
the Myriothela arctica of Sars is identical with an animal which Fabricius, in his c Fauna
Groenlandica,’ has described under the name of Lucernaria jyhrygia, and for which De
Blainville afterwards constituted a new genus, to which he assigned the name of Cande-
labrum. He Blainville, however, though he could have no difficulty in seeing that
Fabricius’s animal was not a Lucernaria, had notions of its affinities even less exact
than those of the celebrated author of the ‘ Fauna Grcenlandica.’ He could see no
relations between it and the Coelenterata, and asserts that its affinities are with
Sipunculus.
If the laws of priority were rigidly enforced, Sars’s name must yield to that proposed
by I)e Blainville ; but as it is plain that De Blainville knew nothing of the animal
* Sabs, Zoolog. Reise i Lofoten og Einmarken, 1849.
t See Agassiz, Cont. Nat. Hist. U. S. vol. iv. p. 341, note.
AND DEVELOPMENT OE MYRIOTHELA.
551
and was totally mistaken as to its affinities, while Saks, evidently unaware that the animal
had been previously noticed, had an accurate conception of its true zoological relations,
the name of Myriothela may fairly be accepted without any violation of the spirit which
ought to regulate biological nomenclature. And though no less an authority than Prof.
Louis Agassiz has felt himself compelled to restore De Blainville’s name, I believe that
farther confusion will be avoided, and no injustice done, by adopting the later designa-
tion of the genus.
It is quite possible that the existing accounts of Myriothela include more than one
species. At present, however, we have no evidence which would satisfy us in asserting
that more than a single species has been observed ; and the specific name assigned by
Fabricius to the first known example of the genus must accordingly be accepted.
Sars’s description is entirely confined to the external characters of the adult ; and the
first account which takes us beyond these is given by Mr. Cocks*, who describes the
young locomotive stage which he saw developed from specimens obtained on the coast
of Cornwall. Mr. Cocks’s observation has been confirmed by Mr. Alder, who, however,
has left us no published account. Mr. Hikcks, from an observation of living specimens,
has given us an excellent description of the external characters of the adult, and has
correctly pointed out the true composition of the colony, maintaining the zooidal signi-
ficance of the appendages which support the gonophoresf.
The only other notices we possess are a short one by Mr. Vigors J, who, not aware of
the previous descriptions by Fabricius and Saks, records the animal under the new
generic and specific names of Arum CocJcsii ; and one by Mr. Gosse §, who also describes
it as a new genus and species, under the name of Spadix purpurea.
The only published figures are one accompanying Mr. Cocks’s description of the
locomotive stage, a small woodcut outline by Mr. Gosse, and a characteristic figure by
Mr. Hincks.
The specimens which have afforded the material for the present memoir were obtained
at Lulworth, on the coast of Dorsetshire. They were attached to the under surface of
large stones, close to the low-water level of spring-tides.
ANATOMY.
The Trophosome. — Structure op Hydranth.
1. Endoderm.
The character of the endoderm varies according to the region in which it is examined.
Throughout the whole of the main cavity of the body it constitutes a thick layer, composed
of many cells in depth (Plate 56. figs. 1 & 2, a). The cells which form the greater part
of this endodermal layer consist of simple round masses of clear protoplasm, about
of an inch in diameter, in which a nucleus is frequently visible, and in which are immersed
* Rep. of Roy. Pol. Soc. Cornwall, 1853, p. 34. t Rep. Roy. Pol. Soe. Cornwall, 4849. ' 5 ’
t Brit. Zooph. 1868, p. 75. § Ann. Nat. Hist. 1853, and Man. of Marine Zoology, 1855,
4 D 2
552
PROFESSOR ALLMAN ON THE STRUCTURE
numerous refringent corpuscles and a few brown granules. No boundary membrane
was evident in any of these cell-bodies. At the inner or free surface the endoderm of
the whole of the gastric cavity, except in the region immediately below the mouth, forms
long conical processes, which project like villi into the cavity (figs. 1 & 2, b). These
processes, like the more external parts of the endoderm, are mainly composed of large
cells, formed of clear protoplasm, with nucleus and refringent corpuscles ; but besides
these there exist also towards the free ends of the processes numerous smaller spherical
cells (fig. 2, c ), loaded with dark-brown granules. These cells are most abundant in
the villi-like processes which are developed towards the proximal end of the body. They
form a much less coherent tissue than the large clearer cells, and may be easily isolated
under the microscope. Indeed they are constantly being thrown off, and may be often
seen to be voided through the mouth of the living animal.
Extending over the free surface of the endoderm is an exceedingly thin stratum of a
clear homogeneous protoplasm (fig. 2, d). This protoplasmic stratum is most obvious
the villi-like processes, where it has the property of developing very minute, irregular,
pseudopodial projections (eee), which are constantly changing their shape, and may
be seen under the microscope to be slowly protruded and withdrawn. The free surface
of the endoderm carries also long, very slender vibratile cilia. I believe that the thin
layer of protoplasm which extends over the free surface of the endoderm is continuous
with an interstitial undifferentiated protoplasm which exists in small quantity between
the endodermal cells. Its occurrence, with its pseudopodial extensions, on the gastric
surface of the animal is full of interest, and suggests a close analogy between the absorptive
action of the gastric surface and amoeboid reception of nutriment ; more especially when
we bear in mind that the cells between and over which the semifluid protoplasm is spread
are destitute of membrane, and that their protoplasm must be in direct relation with that
of the pseudopodial stratum.
The cilia are extremely fine and difficult of detection. They do not appear to be con-
tinuous over the whole gastric surface, but to exist only at intervals. They probably
originate directly from the proper surface of the endodermal cells, in which case they
must traverse the pseudopodial layer. They may, however, be direct processes of this
layer. Indeed it is difficult in either case not to regard them as modified pseudopodia.
True vibratile cilia, like pseudopodia, can originate only from the surface of membrane-
less protoplasm, which thus possesses, as one of its characteristic properties, the faculty
of being able to develop two kinds of processes — the non-mutable vibratile cilium and
the mutable pseudopodium.
From the gastric cavity the endoderm is continued in an altered form into the cavity
of the tentacles (fig. 2, b, & 3). Here its condition differs strikingly from that of the ten-
tacular endoderm of other marine hydroid trophosomes ; for instead of forming the clear
septate core which is so very characteristic of these, it consists of a single layer of small
round cells surrounding an open axile cavity, and so loaded with opaque granules that
the axis of the extended tentacle appears nearly white under reflected light.
AND DEVELOPMENT OE MYEIOTHELA.
553
2. Ectoderm.
Under this head I shall include, not only the proper cellular ectoderm, but the
hyaline lamella which forms its internal boundary, and is composed of a fibrillated or
muscular stratum, with a supporting structureless membrane.
The proper cellular ectoderm (Plate 56. fig. 1, c, & fig. 2, cj , li) forms a much thinner
zone than the endoderm. It is composed of two distinct strata — a superficial and a deep.
The superficial stratum (fig. 2, g) consists of small round cells, several in depth. These
are destitute of membrane, and contain abundance of yellowish corpuscles ; while on
the summit of the tentacles (fig. 3), and in irregular patches on other parts of the body,
they contain dark brownish-purple pigment granules.
Lying irregularly among these ectodermal cells, and chiefly towards the free surface
of the ectoderm, are the thread-cells (figs. 2 & 3). Two forms of thread-cells may be
distinguished, — one oviform (fig. 4, a, a'), with the invaginated sheath occupying the
axis ; the other fusiform (fig. 4, b, V), with a slightly curved axis, and having the invagi-
nated sheath oblique. Both kinds of thread-cells are formed in the interior of certain
cells belonging to the superficial layer of the ectoderm, and may be seen, some lying
free among the true cells of this layer, others enclosed in their generating-cells, and
either completely immersed in the granular matter of the cell or surrounded by a large
clear vacuole (fig. 5). No facts, however, have come to my knowledge tending to throw
further light on the mode of origin of the thread-cells.
The deep layer of the cellular ectoderm (fig. 2, h) is formed by a very remarkable tissue,
to which I shall refer under the designation of the claviform tissue. This is composed
of cells consisting of a yellowish granular protoplasm, entirely destitute of membrane,
and each drawn out into a long caudal process. They are frequently provided with an
obvious nucleus. By the union of their caudal processes groups of claviform cells (fig. 6, a)
are produced whose common stalk runs to the hyaline lamella, where it loses itself in
the fibrillated stratum ( b ). The whole forms a very soft, pulpy, and somewhat glandular-
looking tissue, easily broken down under the compressor.
Caudate cells, of apparently the same significance, were first made known by Klein-
enberg*, who discovered them in Hydra, where he believes that he has followed their
caudal prolongations into direct continuity with the fibrillee of the muscular lamella.
He regards the body of the cell as destined for the reception of stimulus from without,
and, looking upon the whole cell with its fibrilliform continuation as representing a
combined nervous and muscular system, he gives it the name of “neuro-muscle-cell.”
According to this view Hydra would represent in the phylogenesis of animals a form in
which the nervous and muscular tissues are as yet but imperfectly differentiated from
one another.
I believe that we are quite justified, with our present data, in attributing to the clavi-
form tissue the general function of a nervous system. Indeed I do not see what other
place it is possible to assign to it in the economy of the animal. In Myriothela, however,
* Hydra, eine anatomisek-entwickelungsgeschichtliche Untersuchung. Leipzig, 1872.
554
PKOFESSOK ALLMAN ON THE STEUCTUKE
I have never succeeded in tracing a direct continuity of the caudal processes of the cells
with the fibrillee of the muscular lamella. There is no doubt that the stalks of the
claviform tissue pass into the muscular layer and become intimately associated with it ;
but I do not believe that any more direct continuity with the individual fibrillee can be
here demonstrated.
KleinenberGt has further described the bodies of the caudate cells in Hydra as united
laterally with one another, and forming the outer surface of the body, while the spaces
which must necessarily lie between their caudal prolongations are occupied by a tissue
composed of small non-caudate cells, to which he gives the name of “ interstitial
tissue,” and in which he maintains that the thread-cells and the generative elements are
formed.
I can find nothing like this interstitial tissue in Myriothela ; and I believe that its
place is here taken by an undifferentiated protoplasm, through which the prolongations
of the caudate cell-clusters make their way to the muscular layer.
If we except the case of the long transitory arms of the actinula or free locomotive
stage, which will be afterwards described, the claviform tissue does not in Myriothela
come to the surface of the body. Throughout the whole of the body of the adult it
forms a deep zone, intervening between the hyaline lamella and the superficial layer of
the ectoderm, and very distinct in sections made from specimens hardened in chromic
acid.
The hyaline lamella (fig. 2, i) forms the internal boundary of the ectoderm, and is
found everywhere between the endoderm and the cellular ectoderm. It consists of
two layers, — internally (fig. 6, c ) a perfectly transparent, thin, structureless membrane,
and externally ( b ) a layer of fibrillee, which adheres closely to the structureless
membrane.
Special attention was first called to the presence of the structureless membrane
in other hydroids by Reichert*, who named it “ Stutzlamelle ; ” but he refused to admit
the existence of a true fibrillated layer. The fibrillated layer, however, is extremely
distinct in almost all hydroids. In Myriothela it can be separated, after a short macera-
tion in water, from the underlying structureless membrane. It is here composed of lon-
gitudinal fibrillee, which adhere to one another by their sides in a stratum of a single
fibre in thickness, which forms a continuous lamella, even after detachment from the
supporting structureless membrane. The fibrillee are about x 2iq0 0 of an inch in diameter,
soft, and compressible, very transparent, with a very minutely granular structure, but
otherwise apparently homogeneous. They show a convex surface when seen in profile
on the folded edge of the lamella. That they are contractile elements, forming by their
union a muscular lamella, there would seem to be little reason to doubt. They do
not, however, possess the character of true muscle-cells. So far as I was able to
trace them, they retain a uniform diameter, and show no appearance of nuclei.
As already said, I have failed to find any direct continuity between the fibrillee and
* Ueber die contractile Substanz &c. Berlin, 1867.
AND DEVELOPMENT OE MYRIOTHELA.
555
the caudal prolongations of the claviform tissue. These prolongations run to the surface
of the muscular lamella, and become there intimately united with it, so that it is per-
haps impossible to detach them without laceration ; but I cannot affirm any thing further
regarding the nature of this union. But though Myriothela does not seem to afford any
evidence of the direct continuation of the muscular fibrillae with the caudal prolonga-
tions of the claviform tissue, it cannot be regarded as in any way contradicting the
hypothesis that this tissue is destined for the reception of external stimulus — in other
words, that it represents a nervous system.
The general structure of the ectoderm of the Myriothela hydranth is that which has
been now described ; in the globular capitula of the tentacles, however, we have a most
singular modification of those structures which lie external to the hyaline lamella.
Here the place of the caudate cells is taken by a remarkable tissue, composed of closely
appressed transparent prisms, or, to speak more exactly, of greatly elongated pyramids
(fig. 3, a , & fig. 7), which are attached by their inner or apical ends to the hyaline
lamella of the capitulum to which they are perpendicular, and thence radiating out-
wards terminate at some distance from the outer boundary of the capitulum in a curved
surface, which occupies somewhat more than a hemisphere. The distal or basal extre-
mity of each pyramid is formed by a curve of greater convexity than that of the general
surface formed by their combined bases ; and this surface thus acquires a minutely
papillose appearance. The whole organ thus constituted caps the hyaline membrane
and endoclerm of the summit of the tentacle. In its structure it strongly suggests the
rod-like tissue which in higher animals we know to be associated with special organs of
sense.
Radiating from its convex surface are a multitude of slender filaments, which make
their way among the cells of the ectoderm, and terminate distally at a short distance
within the outer surface of the capitulum, where each carries on its summit an oviform,
transparent, very thin membranous sac (fig. 3, b, h & fig. 8). This sac bears, close to
its distal end, a minute bristle-like process, and is completely filled by a firm refringent
capsule, within which may be seen a transparent cylindrical cord wound in two or three
coils. The capsule (fig. 9) is easily liberated from its enveloping sac, and under slight
pressure the contained cord may sometimes be ejected through its distal end (fig. 10).
The whole assemblage of sacs, with their included capsules, forms a zone parallel to the
surface of the capitulum and a little within it (fig. 3).
The close resemblance of the capsule, with its contained cord, to a thread-cell is
abundantly obvious ; and even the external sac, with its bristle-like process, has its
parallel in the generating-cell of certain thread-cells. But besides the presence of the
filiform peduncle there are other points in which these remarkable bodies differ from
true thread-cells. The included cord does not, like the contents of an ordinary thread-
cell, consist of a wider portion continuous with a narrower one, which during ejection
becomes invaginated in the wider, but, on the contrary, possesses a uniform diameter
considerably greater than that of the filament of an ordinary thread-cell ; and instead of
556
PROFESSOR ALLMAN ON THE STRUCTURE
presenting a vast multitude of coils rolled together into a complicated mass, as in the
latter, it has only two or three such coils. Further, when ejected from the capsule
(while it still holds on by one end to the point of exit) it does not, like the filament of a
thread-cell, straighten itself and shoot across the field of the microscope, but immediately
on becoming free coils itself again into a spiral (fig. 10). Indeed I believe that the signi-
ficance of these pedunculated capsules is something very different from any which has been
hitherto assigned to the thread-cells ; and it is scarcely possible not to recognize a special
apparatus of sense in the whole structure just described, including the rod-like tissue in
which the peduncles of the sacs have their roots, and which is plainly but a modification
of the structure which forms the claviform or nervous tissue in other parts of the body.
Indeed it is impossible to overlook the striking resemblance between these pedunculated
sacs, with their enclosed capsule and cord, and the Pacinian bodies of the Yertebrata.
If this be a correct view of the nature of the structures here described, we have now for
the first time evidence which would justify us in assigning a special apparatus of sense
to a hydroid trophosome.
But with all this the resemblance between these pedunculated capsules and true
thread-cells cannot be ignored, and indeed makes us hesitate, even more than we may
have hitherto done, in regarding the latter merely as urticating organs. It is possible
that the pedunculated capsules may throw new light on the function and significance of
thread-cells ; but with no facts beyond those at present before us, we are scarcely in a
position to speculate further on this subject.
The best display of the capsules, with their investing sacs and peduncles, was obtained
from specimens which had been for twenty-four hours immersed in a solution of osmic
acid of 0T per cent., and afterwards placed in a mixture of 100 parts of glycerine with
5 parts of acetic acid ; while the most beautiful demonstration of the rod-like tissue was
found in sections which had been simply macerated in water for twenty-four hours, and
then examined, without further preparation, under the compressor. The more external
tissues of the capitulum had been softened and disintegrated by the maceration, and
were now easily separated by the simple action of the compressor ; while the firm, rod-
like tissue, offering more resistance to the decomposing action of the water, remained
beautifully isolated, with its component rods looking almost like the radiating acicular
crystals of certain forms of zeolite.
External to the zone of pedunculated capsules is a thin layer of ectoderm, which forms
the most superficial portion of the capitulum (fig. 3). This is composed of small round
membraneless cells, containing refringent corpuscles, while the summit of the capitulum
is almost always occupied by a group of small cells, containing dark brownish-purple
pigment granules. The two forms of true thread-cells already described are here deve-
loped in greater numbers than elsewhere, and may be seen scattered, without any defi-
nite order, among the more superficial cells of the ectoderm.
AND DEVELOPMENT OF M YEIOTHEL A .
557
The Gonosome.
The gonosome of Myriothela (Plate 55) consists of blastostyles with their gonophores
and of claspers.
The blastostyles (fig. 2, a , a, a ) arise from the hydranth towards its proximal or attached
extremity. They may be followed over a section occupying about one fifth of the entire
length of the extended hydranth, and spring from this region on all sides without any
very definite arrangement. They are very contractile, somewhat fusiform in shape
when extended, but more clavate in various states of contraction. Towards their free
extremities they carry several scattered tentacles resembling those of the hydranth, but
much smaller ; and where the tentacles cease to be borne the gonophores ( b , b, b) com-
mence, and continue with an irregular scattered disposition to within a short distance
of the attached end of the blastostyle.
The structure of the blastostyles resembles, in all essential points, that of the
hydranth, with the exception of their being entirely deprived of a mouth. Their
gastric cavity communicates with that of the hydranth which bears them ; the villi-like
processes of the endoderm are extremely well developed, and the spherical cells, loaded
with brown granules, which enter into the composition of these processes are very
abundant (Plate 57. fig. 14, a). The muscular lamella is well developed, and the struc-
ture of the tentacles is quite the same as in the hydranth, the rod-like tissue and
pedunculated capsules being similar in both*.
The claspers (Plate 55. fig. 2, c, c, c, and Plate 57. fig. 14, b, b), as already mentioned,
are long tentacle-like organs of a cylindrical form, slightly enlarged towards their
distal extremity, where they terminate in a sucker-like disk. They spring, like the
blastostyles, from the body of the hydranth, and mostly in pairs from two points
close to the base of a blastostyle. They have, however, no definite arrangement;
many blastostyles have no claspers at their base, and solitary claspers occur, not only
at the base of a blastostyle, but here and there at some distance from it on the body of
the hydranth.
The claspers are very contractile. Their structure differs considerably from that of
the blastostyle. The endoderm (Plate 56. fig. 11, a) is composed of an external
layer of closely applied large cells with clear contents, and an internal looser layer of
small round cells filled with brown granules, this internal layer surrounding a very narrow
axile cavity. There are no villi-like processes. The ectoderm, except in the terminal
enlargement, essentially resembles that of the blastostyles and hydranth. The muscular
* Before I had an opportunity of examining specimens of Myriothela, I regarded the appendages which
carry the gonophores not as true members of a zooidal colony, and therefore not as proper blastostyles, but as
mere peduncular organs like those which carry the gonophores in Tubularia (Gymnoblastic Hydroids, p. 383).
In thus viewing them I differed from Mr. Hincxs, who looked upon them as true zooids, having a reproductive
function, and forming with the hydranth from which they spring a compound colony (Hincxs, Brit. Hydroid
Zoophytes, p. 76). I must now abandon my former view and declare my entire agreement with Mr. Hincxs
as to the true zooidal significance of these bodies.
4 E
MDCCCLXX V.
558
PROFESSOR ALLMAN ON THE STRUCTURE
lamella ( b ) is very well developed, and is succeeded externally by a zone of claviform
tissue ( c ) overlaid by a zone composed of small round cells with nearly colourless
granular contents, and lying two or three in depth ( d ). Among these the oviform and
fusiform thread-cells are scattered in considerable abundance.
The terminal enlargement (e) of the clasper differs from its narrower portion chiefly in
the great development of the claviform tissue which constitutes the principal mass of
its substance. The caudal prolongations of the cells (fig. 12) composing this tissue are very
long, and do not unite with one another, so as to constitute botryliform groups to
the same extent as in the corresponding tissue in the ectoderm of other parts of the
hydroid ; they radiate from the hyaline lamella, and possess a considerable resemblance
to the constituent elements of the rod-like tissue in the tentacles. On the summit of
the clasper, where this organ exercises a special function of adhesion, the thread-cells so
well developed in other parts of the ectoderm are deficient.
The function of the claspers, as we shall see more particularly under the head of
development, is that of seizing, on its escape from the gonophore, the plasma mass
which is to become developed into an embryo.
The gonophores (Plate 55. fig. 2, b, b , b, and Plate 57. fig. 14, c, c, d ) show nothing like
a medusal conformation. They are simple sporosacs of a spherical form, supported on
very short peduncles, which spring without any definite arrangement from the sides of
the blastostyles. They show no definite order of arriving at maturity, the more mature
gonophores being sometimes at the distal side of the younger ones, sometimes at their
proximal side, and sometimes scattered among them. Their law of maturation is thus
strikingly different from that of the gonophores of most other hydroids, in which we find
either a constant centripetal or a constant centrifugal order in the periods of their first
appearance and of their arrival at maturity.
Myriotliela is also extremely exceptional in carrying on the same hydranth, and even
on the same blastostyle, both male and female gonophores. So far, however, as my
observations extend, the male gonophores are borne at the distal side of the female
ones. No external difference between the two can be detected beyond thefa,ct that the
mature males are much smaller than the mature females.
In the walls of the mature gonophores (Plate 57. figs. 7, 10, 12), whether male or
female, several distinct structures may be demonstrated. Most externally is a zone of
spherical cells (fig. 12, a), which for the most part contain clear colourless granules; but
towards the summit of the gonophore some of these cells are filled with purplish
pigment granules, and form a coloured circle surrounding the distal pole of the gono-
phore (fig. 14, c, c, d). Passing from without inwards, this is followed by a zone of
clavate tissue (fig. 12, b), and this by the structureless lamella ( c ) overlaid by muscular
fibrilke. These three zones are direct continuations of the corresponding elements in
the ectoderm of the blastostyle.
Lying immediately within the hyaline lamella is another cellular layer (fig. 12, d).
In its thickness this layer corresponds to the depth of a single cell. Most of the cells
AND DEVELOPMENT OF MYRIOTHELA.
559
composing it contain only clear colourless protoplasm, with some clear granules ; but
towards the distal pole of the gonophore the cells increase slightly in size, and contain
purple granules, which form a coloured ring internal and parallel to that belonging to
the outer layer (figs. 7 & 10, a). In the centre of this internal ring the layer now under
consideration is perforated by a narrow aperture, which thus lies immediately under the
distal pole of the gonophore, which is itself quite imperforate.
The last described layer encloses the mass of the generative elements (figs. 7, 10, & 12),
from which, however, it is separated by a very thin structureless membrane (fig. 12, e),
by which the whole generative mass is surrounded, and which becomes reflected over
the spadix where this is plunged into the midst of the mass of ova or spermatozoa.
DEVELOPMENT.
The first appearance of the gonophore shows itself in a minute offset of the gastric
cavity of the blastostyle. This pushes itself outwards into the ectoderm of the blastostyle,
carrying with it the endoderm, which continues to form its immediate boundary, sepa-
rated from the cellular ectoderm by the hyaline lamella ; but no well-defined external
projection has yet become apparent.
The endoderm (Plate 57. fig. 1, a), which lies over the distal end of this gastric diver-
ticulum, soon becomes excavated by a cavity of a nearly spherical shape ( b ). This
cavity, which I shall speak of as the gonogenetic chamber, is separated from that of the
diverticulum ( c ) by a considerable thickness of the endodermal layer ; but the endoderm,
which bounds it distally, forms a cellular membrane of only a single cell in thickness.
The cavity, which as yet appears quite closed, is filled with clear contents, in which no
formed matter beyond minute granules can be detected.
In the next stage the diverticulum from the Cavity of the blastostyle has increased in
size, and continuing to press the endoderm and ectoderm before it, the whole has
begun to form a well-defined hernial projection from the side of the blastostyle, while
the floor of the gonogenetic chamber has become convex ; and the chamber, which has
at the same time increased in size, presents in longitudinal section a crescentic shape.
A minute orifice has now become visible in the summit of the chamber ; and the endo-
dermal cells, which immediately surround the orifice, have become somewhat larger,
and are seen to be filled with brown pigment granules. The ectoderm continues imper-
forate, the orifice being entirely confined to the thin layer of endoderm which forms the
immediate roof of the gonogenetic chamber.
Up to this point there is nothing by which the male and female gonophores may be
distinguished from one another. We soon, however, observe a differentiation of the con-
tents of the gonogenetic chamber. In the female gonophore a layer of more consistent
protoplasm has accumulated on the free surface of the walls of this chamber (fig. 2, b),
more especially on its proximal wall or floor. Minute, clear, nucleus-like bodies may
be seen scattered through the protoplasm, and a few similar bodies float free in the more
liquid contents which still occupy the centre of the chamber.
4 e 2
560
PROFESSOR ALLMAN ON THE STRUCTURE
Following now the female gonophore in its development, we find that in the next
stage (fig. 3) both it and its included gonogenetic cavity have increased in volume, while
the floor of the cavity projects further into its interior in the form of a hollow conical
core. This is easily recognized as the spadix; on the free surface of the cavity of
the spadix (c) villi-like processes similar to those which occur in the general cavity are
abundantly developed. The gonogenetic cavity has now become uniformly filled with
a plasmatic mass (#), which is seen to consist of a multitude of nuclei (fig. 5) about
3 5\ 0 of an inch in size, each enclosing a minute nucleolus, and immersed in a minutely
granular protoplasm. An extremely delicate structureless hyaline membrane (fig. 3, d)
can now be traced over the whole surface of the generative mass, which it thus sepa-
rates from the proper endodermal walls of the gonogenetic chamber.
As yet no distinct cell-boundaries can be detected in the contents of the gonogenetic
chamber, and the nucleolated nuclei afford the only evidence of cell-differentiation.
With the enlarging gonophore, however, the protoplasm which surrounds the nuclei
increases in volume, and we soon begin to discover in it manifest cell-boundaries (fig. 4).
Every nucleus is now surrounded by a differentiated mass of protoplasm, and the cavity
of the gonophore has thus become filled with bodies which possess all the characteristic
features of true ova, each with its well-defined germinal vesicle and germinal spot and
its surrounding vitelline protoplasm.
These ova-like bodies continue to increase in size with the growth of the gonophore.
They remain for some time closely pressed against one another, having thus acquired a
polyhedral form (fig. 6) ; but they gradually become looser, assume an oval shape
(figs. 7 & VI, f), and may be easily isolated by the needle or by the mere action of the
compressor. Their germinal vesicle is now very large and distinct, and within the large
germinal spot a well-defined spherule or nucleolina may be easily detected. Though
their subsequent history differs in some points from the characteristic development of
the ovum such as is met with in other animals, we should yet be scarcely justified in
denying to them the significance of true ova.
They have no soonet attained their complete independence and acquired their full
size in the sporosac, than they begin to present a very remarkable phenomenon. They
lose their independent existence, and begin to undergo a fusion into one another ; and
when the contents of the sporosac are now liberated by rupture under the microscope,
many of these nucleolated protoplasm masses may be seen united to one another by irre-
gular pseudopodia-like extensions of their substance (fig. 8). By the gradual shortening
and thickening of these processes the little masses which they connect are drawn closer
to one another, and end by becoming completely fused together into a common proto-
plasmic mass (fig. 9). In this mass the cell-boundaries are completely lost, but numerous
nucleolated nuclei are scattered through its substance. These are almost certainly the
nuclei with their included nucleoli of the original independent protoplasm masses or ova.
The fusion commences among the ova which lie in the immediate vicinity of the
spadix, to which the masses formed by their union continue for some time to adhere by
AND DEVELOPMENT OE M YKIOTHEL A .
561
a considerable extent of their surface (fig. 7) ; while those ova which lie more towards the
periphery of the cavity continue longer distinct, but ultimately follow the same course as
the others by coalescing into compound masses.
Several such masses (fig. 10), eight or more, will thus be formed from the coalesced ova.
They detach themselves more and more from the spadix. They are now of an oval
form ; and some of them may still be seen to be connected with the spadix by a narrow
easily ruptured protoplasmic prolongation. They do not, however, entirely fill the
cavity of the gonophore ; and the narrow intervals between them, as well as the small
space which separates them from the walls of the gonophore, is occupied by a matter
which appears to consist chiefly of free nuclei and of dwindled and degraded ova, all
apparently undergoing a process of liquefaction, and doubtless an unused residuum of
the bodieshy the coalescence of which the compound masses had been formed.
If in this stage the gonophore be laid open, and the protoplasm masses, whose forma-
tion we have been tracing, be liberated under the microscope, we shall often succeed
in witnessing very minute bristle-like processes of clear protoplasm which have become
developed over their surface (fig. 11). These little processes, however, are not permanent
structures, and they will often become entirely withdrawn while the object is under
examination. They are, in fact, true pseudopodia, and are probably employed in the
nutrition of the masses from which they arise.
The contents of the gonophore, however, are intended to undergo further changes
before the period of their liberation has arrived. The separate protoplasm masses
increase in size, the residual matter which had surrounded them disappears, having
probably afforded material for their nutrition ; they begin to coalesce with one another,
and there is ultimately formed a single large plasmodium, which entirely fills the cavity
of the gonophore. When this plasmodium is examined under the compressor, the same
nucleolated nuclei which had hitherto characterized the products of the coalescence of
the ova are seen to be scattered in great numbers through its substance (fig. 13).
These nuclei, however, have already, begun to suffer a change ; for while in some the
nucleolus is still distinct, in others it has quite disappeared ; and while in some the con-
tents consist of a minutely granular matter, in others they are quite homogeneous.
When the separate protoplasm masses have all united with one another, but gene-
rally a little before they have become so completely fused together as to have their
original distinctness entirely lost, the time has arrived when the contents of the gono-
phore are to be expelled. The walls of the gonophore now begin to contract on these
contents ; and here the use of the muscular layer, which is well developed in them,
becomes at once apparent. The contained plasmodium is thus gradually forced out
through the summit of the gonophore (fig. 14, cl).
The orifice in the endodermal wall of the gonogenetic chamber is ready to aid in
giving exit to the plasmodium, but the ectoderm has been hitherto imperforate. This,
however, appears to have been becoming gradually thinner on the point immediately
over the endodermal orifice, and it is now easily ruptured at this spot by the pressure
562
PROFESSOR, ALLMAN ON THE STRUCTURE
from within. By the continued contraction of the gonophore-walls the plasmodium is
at last entirely expelled, completely enveloped, however, in a transparent structureless
membrane. This is apparently the membrane which at a very early stage had shown
itself lining the gonogenetic chamber ; it is at first of great tenuity, hut it soon acquires
considerable consistence. The empty gonophore may now be seen retracted in the
form of a shallow thick-walled cup with everted edges upon the summit of its short
peduncle (fig. 14, e)*.
The liberated plasmodium closely enveloped in its delicate structureless capsule is of
a nearly spherical form, and now lies upon the retracted gonophore, where it is usually
retained by the spadix plunged for a short distance into its mass (fig. 14 ,f). It does
not, however, continue long in this position, for the function of the claspers is soon
brought into play. These curious organs now stretch themselves out towards the
liberated plasmodium ; and as soon as they reach it they attach themselves (f) by their
sucker-like extremities to its capsule, and then by contracting pull it entirely away ( g )
from the remains of the gonophore.
Sometimes the plasmodium will be seized by only one clasper ; very often, however,
two or even three will fasten on it (Plate 55. fig. 2) ; and the plasmodium will sometimes
be seen more or less distorted by the tension thus exerted on it at the same time in
different directions.
Leaving for a while the further history of the female elements, we may now trace the
development of the male. The male gonophore resembles the female in all points
except in being about half the size of the latter ; and I could detect no difference as to
origin between the matter which in one case is to become differentiated into ova, and
that which in the other is destined for the formation of spermatozoa. In every young
gonophore I have examined, the first appearance of the matter in which sexual elements
are afterwards to show themselves is within the gonogenetic chamber which has
become excavated in the substance of the endoderm ; and it is only when the ovarian
nuclei become differentiated in the one case, and the spermatic cells in the other, that
we obtain any decided indication of the sex of the gonophore.
As we have already seen, the primitive plasma which fills the gonogenetic chamber in
the female presents after a time scattered nuclei-like bodies, which are to become the
germinal vesicles of the ova. In the male, on the other hand, such nuclei never make their
appearance, and the primitive protoplasm becomes changed into minute cell-like bodies,
which entirely fill the chamber (Plate 57. fig. 15). These little bodies are the vesicles
within which the spermatozoa originate ; but in what way the latter are produced from
them I have not succeeded in discovering. After a time the vesicles have disappeared,
and are replaced by mature spermatozoa, which now fill the cavity of the gonophore,
and which may be liberated by rupture of the latter. When thus set free they are seen
to consist of a very minute oval head, with a vibratile tail of extreme tenuity (fig. 16).
* In a single instance a gonophore with two such plasmodia ready to escape from it came under my obser-
Tation.
AND DEVELOPMENT OF MYRIOTHELA.
563
They are more minute than the spermatozoa of any other hydroid with which I am
acquainted.
By what means the spermatozoa naturally escape from the gonophore I have not been
able to determine with certainty. I could find no external orifice, nor could I detect a
thinning of the summit of the gonophore like that which in the female precedes the
escape of its contents ; and when the mature male gonophore was subjected to pressure
it was always by the rupture of the spadix and the escape of the spermatozoa through
the peduncle, which would thus carry them into the cavity of the blastostyle, that the
gonophore became emptied. It is not improbable, as we shall afterwards see, that this
is their natural mode of escape.
Returning now to the contents of the female gonophore which, just after their
escape, we had left in the grasp of the claspers, we find that by this time the coalescence
of the separate plasma masses into a single spherical plasmodium has been completed ;
and it is probable that fecundation now takes place. Hitherto we have seen nothing
which can be compared to any phenomena which we would be justified in regarding as
the immediate consequence of the action of the male element on the female ; but soon
after the liberation of the pl’asmodium and its seizure by the claspers, we find that the
whole has become broken up into a multitude of small round or irregularly shaped
masses (Plate 57. fig. 17). Some of these maybe seen still connected to one another by
narrow isthmuses of their substance, while others are quite free, and can be isolated
under the microscope. They all consist of a granular protoplasmic matter without any
distinct boundary membrane, and with numerous nucleus-like bodies immersed in their
substance. The common external structureless membrane is distinct, but it is still thin
and weak.
I must regard this breaking up of the plasmodium into separate masses as repre-
senting a true segmentation, such as in the simple ovum occurs as the immediate result
of fecundation. I have not, however, succeeded in witnessing its earlier stages, and I
cannot say whether it proceeds in accordance with the ordinary binary law of vitelline
segmentation.
How far this breaking up of the plasmodium is continued before a true histological
differentiation becomes apparent, I am unable to say, for the next stage which showed
itself (Plate 58. fig. 1) presented a marked advance on the previous ones. The seg-
mented condition had now entirely disappeared, and the developing mass had acquired
a true cellular structure, while it had become further differentiated into two distinct
layers — an external (a) layer, ectoderm, in which the cell-boundaries were with some
difficulty made out, and an internal (b), endoderm, composed of very obvious cells larger
than those of the ectoderm, and each with a clear nucleus and granular protoplasm.
This internal layer formed the boundary of a cavity ( c ) produced apparently by lique-
faction of the more central parts of the mass.
The developmental stage to which we have now arrived is thus represented by a
hollow spherical body, whose walls are formed by two layers, an ectoderm and an endo-
564
PROFESSOR ALLMAN ON THE STRUCTURE
derm, and which plainly corresponds to the planula of other hydroids. It is, however,
entirely destitute of cilia, and is still confined within its external structureless capsule ( d ),
which has now acquired considerable thickness.
We next find that the planula presents numerous minute pits distributed without
any definite arrangement over its surface (fig. 2, b, b). These are points where the
walls of the planula have begun to invaginate themselves ; and if at this time a section
be made of the planula (fig. 3), its cavity will be found to be occupied by numerous
hollow conical projections (5, b ), which radiate into it on all sides from the inner surface
of its walls. These projections are simple involutions of the walls, and are therefore
composed, like the walls themselves, of an ectoderm and an endoderm, but in an inverted
order.
If an uninjured planula in this stage be dissected out of its external structureless
capsule, which now lies loosely over it, and be subjected to carefully moderated pressure,
the internal projections will become suddenly evaginated, and will shoot out in all
directions over the outer surface in the form of hollow cylindrical arms.
The evagination wThich has thus been effected by artificial pressure takes place natu-
rally in the progress of development ; and in the next stage (fig. 4) we find that the arms
which had been formed internally by a process of involution have become external, the
embryo being still enclosed within its capsule. The ectoderm had already, by the
multiplication of its cells and the development in it of the clavate tissue, increased
considerably in thickness, and the hyaline lamella may now be seen on its inner
boundary.
Up to this period the embryo had retained its nearly spherical form ; but it now begins
to elongate itself, and assumes an oval shape (fig. 5). From its surface there project on
all sides the tubular arms, which, from their original position within the cavity of the
body, had become external by evagination ; while at one extremity of the greater
diameter the body has become truncated, and here numerous short papilliform processes
(i a ) have become developed from its surface.
The arms continue to elongate themselves, and soon present a well-defined terminal
capitulum. The papilliform processes, too, increase in number, and extend further
back on the body of the embryo, which has become still more elongated. It is
probably at this stage that the mouth is formed in the truncated end.' The embryo is
now ready to escape from its enclosing capsule, which has all along remained adherent
to the extremity of the clasper, and which now becomes ruptured, and allows the
little animal to enter on a free life in the surrounding water (Plate 55. fig. 2, d d).
The free embryo of Myriothela (Plate 58. fig. 6) is very contractile, and when fully
extended is of nearly cylindrical form, about a quarter of an inch in length, slightly
attenuated at one end so as to form a short conical hypostome («), which carries the
mouth on its summit, and more decidedly so at the opposite end, where it terminates
in a little sucker-like disk (b). The papilliform processes ( c ) have now attained the
form of the permanent tentacles, presenting a short stem with a terminal enlargement.
AND DEVELOPMENT OF MYRIOTHELA.
565
They commence just below the hypostome, and extend for some distance backwards on
the body. Springing from between the short permanent tentacles, and from a consi-
derable portion of the body which lies at their proximal side, are the long arms (d, d, d)
which made their appearance at an early period of embryonic development, and which
are destined to disappear entirely before the arrival of the animal at maturity. They
are about twenty in number, capable of great extension, and when stretched out to
their utmost (fig. 6) are in the form of long straight filaments slightly tapering towards
their distal extremities, where they terminate in a well-defined spherical capitulum.
In complete retraction they are short, somewhat ovoid bodies marked by strong
transverse rugae.
In accordance with the terminology I have already adopted in describing the early
stage of Tubularia *, I shall designate the free locomotive embryo of Myriotliela by the
name of actinula. It moves about by the aid of its long arms, whose terminal capitula
are capable of being used as suckers of attachment; while the proximal end of the body,
like that of a hydra, also admits of being temporarily attached by means of its little
suctorial disk.
After the actinula has enjoyed for some days its free locomotive existence it begins
to fix itself (fig. 7). This fixation is effected by means of the proximal sucker-like
extremity ( b ). After it has thus become stationary it continues to manifest great contrac-
tility, becoming sometimes much extended, and at other times contracted into a nearly
spherical mass. The long arms now undergo a rapid degradation ( d , d, d) ; they lose
their terminal capitula, become much shortened, and ultimately entirely disappear (fig. 8).
In the mean time the short papilliform tentacles become more numerous, extending
further backwards on the body. The proximal extremity of the animal becomes bent
at right angles to the rest of the body so as to form a sort of horizontal stolon-like foot,
from which small fleshy processes with sucker-like extremities, and having a considerable
resemblance to the claspers, are emitted. The function of these processes, however, is
very different from that of the claspers ; they serve to attach the animal permanently
to some solid support, to which they fix themselves by their extremities. Along with
the stolon-like foot they become clothed in a chitinous perisarc, and the actinula has
thus acquired all the essential characters of the adult trophosome.
The gonosome has not, however, as yet begun to develop itself ; but it soon makes its
appearance by the budding of the blastostyles and claspers from the hydranth at the
proximal side of the tentacles. From the blastostyles the gonophores are subsequently
developed in the manner already described, and the animal thus attains its complete
maturity (Plate 55).
In the histological structure of the actinula there are several points which deserve
special consideration. In the very young animal, at the time when the arms are about
to become changed from internal to external appendages, the endoderm and ectoderm
can be everywhere followed without difficulty. The endoderm is composed of clear
* Gymnoblastic Hydroids, p. 90.
4 F
JIDCCCLXXV.
566
PROEESSOR ALLMAN ON THE STRUCTURE
cells, several in depth, the most internal presenting convex surfaces to the gastric cavity,
but forming no villi-like projections. The ectoderm already consists of two zones besides
the muscular lamella — a superficial zone composed of several layers of small round cells
with clear granular contents, and a deeper zone of claviform tissue. The hyaline lamella
with its muscular fibrillse lies everywhere between the claviform tissue and the endoderm.
All these elements can be followed from the walls of the body into those of the arms.
In these the endoderm, composed of small, round, clear cells, surrounds a wide axial cavity.
When the arm has acquired its terminal capitulum, we find that the zone of claviform
tissue, hitherto simply continued into the arm from the walls of the body, has become
specially developed in the capitulum (Plate 56. fig. 13, c), and here envelops the
endoderm in a nearly spherical cap, which takes exactly the place of the rod-like
tissue in the permanent tentacles. The tissue composing this cap, moreover, is inter-
mediate in its form between the ordinary clavate tissue and the rod-like tissue ; for its
component elements do not form branching groups as in the clavate tissue of other
parts, but consist of radiating, simple, greatly elongated clavate cells, very similar to
those already described as forming the claviform tissue in the distal extremity of the
clasper, and thus affording further evidence that the rod-like tissue is only a modified
claviform tissue.
The capitulum of the actinula arm further resembles that of the permanent tentacle
in the presence of the pedunculated capsules. These differ, however, in some points
from the corresponding organs of the permanent tentacles ; for they are not more than
half their size, while the included cord is finer and longer, and is wound into closer and
more numerous coils (Plate 56. fig. 14, a). Like the cord of the larger capsules, it
continues after its emission to form a spiral, instead of straightening itself out in the
field of the microscope like the filament of the true thread-cells. The spiral, however
(fig. 14, b), is more open and more elongated than that formed by the cord ejected from
the stalked capsules of the permanent tentacles. The styliform process of the external
sac is long and slender.
When the transitory arms of the Actinula have attained their full growth, the ecto-
derm of their stem (fig. 13, a) no longer presents the two zones which were present in
their younger stages. It is the superficial zone which appears now to be wanting, so
that the clavate tissue comes to the surface. In thus becoming superficial the distal
ends of the cells composing this tissue have become wider, and lie more closely on one
another, and very often contain a large vacuole excavated in the midst of their granular
contents. Their caudal prolongations, moreover, do not seem to run into one another
to such an extent as to give rise to the botrylliform condition which characterizes this
tissue in other parts of the animal.
The endoderm of the arm (fig. 13, b) is formed externally by a tissue of large, clear,
polygonal cells containing some minute granules, which are chiefly accumulated on the
walls of the cells, while internally there is an irregular disconnected layer of small
round cells filled with brown corpuscles. The increase of the endoderm in volume
has nearly obliterated the axile canal of the arm.
AND DEVELOPMENT OE MYEIOTHELA.
567
The arm is very contractile, and, when in different states of contraction, the cells of
the ectoderm may often be seen forming irregular projections of various length and
thickness. These vary from time to time in shape and size, and look so exactly like
pseudopodial processes that without careful observation they might easily be mistaken
for them. They are, however, mainly the result of the contraction of the arm. When
the arm is shortened by the action of its contractile elements, the hyaline lamella is
thrown into irregular corrugations, and these are communicated to the superjacent
cellular ectoderm. In macerated sections of the arm the cellular ectoderm will become
disintegrated and broken down, and then the exposed hyaline lamella will often show
nearly an exact repetition of the pseudopodia-like projections. I am, however, inclined
to think that, after the contraction of the fibrillated layer has thus crumpled the hyaline
lamella and overlying ectoderm, the protoplasm of the latter exerts a certain contractility
which exaggerates the prominence of its projections, and thus to a certain extent brings
them within the category of pseudopodia.
In the ectoderm of the body of the actinula we find not only the deep clavate tissue,
but the more superficial layer of cells well developed. Here, during certain states of
contraction, pseudopodia-like projections are also formed; and I believe that these are
referable to the same cause here as in the ectoderm of the tentacles.
The proximal extremity of the actinula body is capable, as already said, of acting as
a sucker of attachment ; and here the ectoderm has acquired a considerable increase of
thickness (Plate 56. fig. 15). The increased thickness is mainly owing to the great
development of the clavate tissue at this spot. This tissue forms here a hemispherical
cap over the cul-de-sac of the gastric cavity, and the elements composing it are scarcely
at all united to one another into ramified groups. Its peculiar development here is
probably connected with a special irritability with which this part of the walls would
appear to be endowed. Over this cap the superficial ectodermal layer is continued,
forming a zone of small, spherical, membranous cells with minutely granular contents.
In the uninjured state a fine longitudinal striation may be witnessed in this part of the
actinula (Plate 58. fig. 6, b) ; it is caused by the appearance of the terminal mass of
clavate tissue as seen through the overlying layer*.
The endoderm of the stem-like proximal portion of the actinula (Plate 56. fig. 15)
closely resembles that of the transitory arms. It is composed of an external layer of
large, clear, polygonal cells, with an internal one of small round cells filled with brown
corpuscles.
GENERAL REMARKS.
I believe we are justified in regarding the claspers as true zooids rather than as mere
organs ; and if so Myriothela may be compared with Hydractinia in the extent to which
the polymorphism of the zooids is carried. We have here hydranths, blastostyles,
* A very similar appearance may be seen in tbe actinula of Tubularia, and I have now little hesitation in
referring it to a similar cause.
4 F 2
568
PEOFESSOB ALLMAN ON THE STETJCTUEE
gonophores, and claspers, all different forms of zooids, each endowed with its own
special function in the physiological division of labour, and all associated into a com-
pound colony which forms the proper zoological Individual, the logical element of the
species*. In Hy dr actinia we have hydranths, blastostyles, gonophores, and “spiral
zooids ” similarly associated. In Hydractinia , however, there is a common coenosarcal
basis which gives origin to many hydranths, as well as to the blastostyles with their
gonophores, and to the spiral zooids ; while in Myriothela the hydranth is solitary, and
the blastostyles and claspers are budded off from this.
It will be seen that the account here given of the development of Myriothela offers
no support to the view that the generative elements originate in certain cells of the
ectoderm — a view which has been defended by Kleinenberg, who, in his excellent
memoir on the structure and development of Hydra , maintains that both ova and
spermatozoa have their origin in what he calls the “ interstitial tissue ” of the ectoderm.
Neither does it support the view more recently put forward by Ed. van Beneden in his
valuable memoir on the origin of the testis and ovary f. According to the Belgian
zoologist the ova in Hydractinia always originate in the endoderm, while the sperma-
tozoa just as constantly have their origin in the ectoderm. To this observation
M. Ed. van Beneden attributes great significance ; for by adopting the highly probable
hypothesis enunciated many years ago by Huxley, that the ectoderm represents the
outer layer of the blastoderm in the higher animals and the endoderm the inner layer,
he generalizes the results of his observations on Hydractinia, and maintains that
throughout the animal kingdom the female generative system is a product of the inner
leaf of the blastoderm, and the male of the outer leaf.
From the observations on Myriothela , however, recorded above, it would seem to
follow that both ova and spermatozoa originate in a special chamber which has become
excavated in the substance of the endoderm, and that the ectoderm has nothing to do
with either.
I believe this to be the legitimate conclusion to be drawn from the appearances pre-
sented. At the same time I admit that other observers may put a different interpre-
tation on these appearances ; for it may be asserted that the material which is to become
developed either into spermatozoa or into ova is in one or both cases a product of the
ectoderm, and that it has subsequently to its origin migrated into the endoderm ; while
in proof of this the orifice which exists in the roof of the endodermal chamber will
probably be adduced and maintained to be the channel through which the generative
elements have gained access to this chamber.
Knowing the memoir of M. E. van Beneden, in which he maintains that the spermatic
* The terms Zooid and Individual are used here with the significations originally proposed hy Huxley.
The former is the “ Individual of the fifth order, Person ” of Haeckel, the latter the “ Individual of the sixth
order, Stock or Cormus ” of Haeckel.
Eduard van Beneden, “ De la Distinction Originelle dii Testicule et de l’Ovaire,” Bull, de l’Acad. Boy. de
Belgique, 2° serie, tome xxxvii. no. 5, Mai 1874.
AND DEVELOPMENT OP MYRIOTHELA.
569
mass originates as a cellular bud from the inner surface of the ectodermal layer of the
gonophore, and that this pushes itself into the endoderm and becomes afterwards cut
off from its attachment to the ectoderm, I paid great attention to the gonophores
of Myriotliela from the earliest moment when they became recognizable, but entirely
failed to detect any process resembling that described by the Belgian zoologist as taking
place in Hydractinia. In the very earliest stages of the gonophore which I could find
the gonogenetic cavity had been already formed and filled with the primitive generative
matter, and I failed to meet with any thing which would lead me to believe that this
had its origin in the ectoderm. It is true that in Myriotliela a difficulty occurs in the
observation which we do not meet with in Hydractinia ; for while the complete separa-
tion of the sexes on different colonies in Hydractinia will enable us at all times to say,
no matter how young may be the gonophore under examination, whether this be male
or female, in Myriotliela we have no certain sign by which to decide as to the sex of
the gonophore in its youngest stages, gonophores of both sexes being here borne on the
same blastostyle. It is scarcely possible, however, that among the many cases of
extremely young gonophores which I examined there were not both male and female
examples ; and in no case did I find any thing which would lead me to believe that the
origin of the generative elements in one was different from what it was in another.
The facts here noted have thus led me to maintain that both male and female elements
have their origin in the endoderm. Still, considering the difficulty of the observations,
and the fact that the appearances lie possibly open to another interpretation, I do not
desire to insist on the impossibility of the generative elements being in one or both
sexes primarily introduced from the ectoderm into the endoderm ; and I am willing to
wait for the confirmation which may be expected from further investigations.
As is well known, all the fixed hydroids pass through a free locomotive stage before
finally attaching themselves. I have elsewhere* pointed out that this free stage shows
itself under one or other of two forms, namely, that of a planula (as in the great majority of
hydroids, Campanula, Sertularia, Coryne, See.) and that of an actinula (as in Tubularia).
The free hydroid planula is a closed sac in whose walls an endoderm and an ectoderm are
differentiated, not by a process of invagination, but by one of dilamination, and in which
an oral orifice is afterwards formed by a perforation of its walls, the planula thus
becoming the gastrula of Haeckel. The external surface of the planula is almost
always clothed with vibratile cilia.
The actinula represents a form more highly organized than either the planula or the
gastrula ; for not only is a mouth always present in it, but locomotion is effected not by
vibratile cilia, but by means of external appendages in the form of tentacles or arms,
which may be either transitory or permanent.
It must not, however, be supposed that the planula stage does not exist in hydroids
whose free phase is that of an actinula. It is, on the contrary, as truly a phase of
their development as it is of that of the others : but the planula stage is then, if we
* Gymnoblastic Hydroids, p. 85.
570
PROFESSOR ALLMAN ON THE STRUCTURE
except Hydra , entirely passed within the gonophore, and the planula in such cases is
never ciliated or locomotive.
In Tubularia the planula is a non-ciliated compressed sac, developed directly out of
the plasma mass which occupies the cavity of the gonophore ; while still retained within
the gonophore it develops tentacles by outgrowths from its sides, elongates itself,
becomes perforated by a mouth, and then escapes as a free locomotive actinula destined
to undergo further changes of shape before attaining the final form of the hydroid
trophosome.
Just in the same way Myriothela passes through the non-ciliated planula stage before
it attains the form of the free actinula. In one important point, however, the actinula
of Myriothela differs from that of Tubularia, namely, in the possession of embryonic
transitory organs which take the form of long contractile arms, by which locomotion is
aided, and which entirely disappear during the subsequent course of the development.
In Hydra, too, which never presents a permanently fixed trophosome, we find a true
planula stage, the planula being here, as in the actinula-forming hydroids, destitute of
cilia. It acquires a mouth by perforation, and develops itself by continuous growth
and the emission of tentacles into the form of the adult without passing through any
intermediate actinula stage.
Properly speaking, Hydra represents a permanent actinula. Hydra (if we except the
somewhat obscure form described by Greeff under the name of Protoliydra) may thus
be assumed as the lowest known hydroid, and, in accordance with the Descent Theory,:
would be the remotest ancestral form yet discovered of the Ccelenterata.
In all cases, however, it must be borne in mind that the planula is nothing more than
the blastodermic sac after the two leaves of the blastoderm have become differentiated.
In some few cases it never clothes itself with cilia, and then it almost always remains, as
long as it continues a planula, included within the gonophore ; while in the great majority
of cases it develops cilia over its surface, and becomes free and locomotive.
Kleinenberg, finding that in the adult Hydra the entire cellular ectoderm is composed
of the caudate cells with an interstitial network of simple cells interposed between their
proximal attenuated ends, while their wide distal ends form the outer surface of. the
animal, concludes that there is here no external epithelium or epidermis. Hydra would
thus present an apparent anomaly, inasmuch as one of the most universal features in
ontogenesis — the development of an epidermal layer from the outer germ-lamella (ecto-
derm)— would seem to be absent.
This anomaly, however, is brought into agreement with the established facts of deve-
lopment by Kleinenberg, whose observations have led him to maintain that the so-called
egg-shell of Hydra is really a transformed epidermis, but, being needed only as a pro-
tective investment for the embryo, is a transitory structure destined to be cast off in the
later periods of development.
Though this may be a correct view of the state of things in Hydra, it is certain that
in Myriothela we have a perfectly distinct and well-developed layer which lies external
AND DEVELOPMENT OE MYEIOTHELA.
571
to the clayiform tissue, and forms the outer surface of the body. To this layer we must
attribute the significance of a true epidermis. It appears, however, to be absent from
the stems of the transitory arms of the actinula after these have attained their full
growth. In their early stages, while yet they are invaginated processes of the body
walls, and even for some time after their complete evagination, it is present as elsewhere ;
but during the growth of the actinula it is gradually absorbed, and then allows the
claviform tissue to come to the surface. In the capitulum of the arm, however, it never
disappears, being here needed as a protective envelope for the specially and more highly
developed sensitive structures of this part.
It is thus obvious that Myriotlielci offers no exception to the ontogenetic law, which
derives both the central nervous system and the epidermis from the outer layer of the
blastoderm.
One of the most remarkable features in Myriothela consists in the presence of the
bodies to which I have here given the name of claspers. These, as we have seen, are
tentacle-like zooids endowed with great contractility ; and no sooner is the plasma mass,
which is to become developed into the actinula, set free from the gonophore which had
hitherto confined it, than one or more claspers direct themselves towards it, and fixing
themselves to it by their sucker-like ends, hold it tenaciously during certain subsequent
periods of its development. The manner in which the claspers thus seize upon the
liberated plasmodium forcibly reminds us of the way in which the Fallopian tubes are
supposed to seize the mammalian ovum at the moment of its liberation from the
Graafian follicle.
There is something very surprising in the selective faculty thus apparently exercised
by the claspers ; for it is, as a rule, to the liberated plasma mass alone that they become
attached, while no reason whatever can be assigned why they should not seize upon some
of the neighbouring parts which are just as easily within their reach. Once or twice I
have seen a clasper fixed to some other part of the hy droid ; but this occurrence is so
rare that it cannot in any way be regarded as a manifestation of its normal function.
We have at present no data which will enable us to arrive at an absolute conclusion
as to the object gained by the seizure of the plasmodium by the claspers. It is not
improbable, however, that it is connected with fecundation. We must remember that
in Myriothela we have the very exceptional condition of one and the same blastostyle
carrying both the male and the female gonophores, and, further, that the spermatozoa
of this hydroid are remarkable for their extreme minuteness ; they are smaller, indeed,
than in any other hydroid with which I am acquainted. Now I have never seen the
spermatozoa escape spontaneously as in other hydroids from the gonophore; and when one
of the Myriothela gonophores containing mature active spermatozoa is subjected to slight
pressure, it is not through any breach of continuity in the thick external walls of the
gonophore that the spermatozoa are ejected, but through the walls of the spadix, which
appear to be easily ruptured. In this way they pass directly into the gastric cavity of
the blastostyle, and through this may be easily conducted to the base of a clasper, and
572
PROFESSOR ALLMAN ON THE STRUCTURE
thence carried through its narrow axial channel to its summit, where this has become
attached to the plasmodium just liberated from the female gonophore. When once
arrived there the spermatozoa may make their way through the terminal tissue of the
clasper, and be thus brought into immediate relation with the plasmodium, whose
investing membrane is at this time exceedingly thin and weak, a process which will be
obviously facilitated by the exceptional minuteness of the spermatozoa.
We should further bear in mind that it is not until after the seizure of the plasmodium
by the claspers that we have any evidence of the phenomenon of segmentation — a fact
which renders it highly probable that the act of fecundation also takes place subsequently
to the seizure. Spermatozoa, if searched for in the cavity of the clasper, would probably
be found there ; but, short of their detection in this situation, we have a combination of
facts about as strong as could be desired, all tending to the conclusion that the function
of the claspers is that here suggested, and offering a case in many respects parallel with
that of the hectocotyle in the Cephalopoda, or with certain phenomena of fertilization
among the Algse.
Explanation of the Plates.
PLATE 55.
Fig. 1. MyriotJielci phrygia. A group, natural size, attached to a stone; some of the
individuals contracted, others extended.
Fig. 2. Magnified view of an individual extended.
a, a , a, a. Blastostyles ; b , b, b, b. Gonophores ; c, c, c, c. Claspers ; d. Basal
portion of the hydranth invested with its perisarc ; e, e. Processes of attach-
ment.
Fig. 3. Magnified view of an individual contracted.
PLATE 56.
Fig. 1. Transverse section of the hydranth at some distance behind the mouth. Mag-
nified.
a. Endoderm ; b. Villi-like processes of endoderm projecting into gastric
cavity ; c. Ectoderm ; d, d, d. Tentacles.
Fig. 2. Portion of transverse section of hydranth, still more magnified.
a. Endoderm ; b. Villi-like processes from the free surface of endoderm ;
c, c. Small spherical cells loaded with coloured ' granules, and terminating
the villi ; d. Thin stratum of homogeneous protoplasm extending over the
free surface of the endoderm ; e, e. e. Pseudopodial processes emitted from
the protoplasmic stratum, along with which fine vibratile cilia are also seen
extending into the gastric cavity ; f. Base of a tentacle ; g. External layer of
cellular ectoderm; h. Internal layer of same (clavate tissue); i. Hyaline
lamella.
AND DEVELOPMENT OF MYKIOTHELA.
573
Fig. 3. Longitudinal section through summit of tentacle, much magnified.
a. Rod-like tissue ; b. Pedunculated capsules.
Fig. 4. Thread-cells.
a. Oviform thread-cell in its quiescent state ; a'. Same, with the filament
ejected ; b. Fusiform thread-cell in its quiescent state ; V . Same, with the
filament ejected.
Fig. 5. Cells of ectoderm of tentacle liberated at the commencement of putrescent
histolysis. In each of the two larger cells may be seen a thread-cell.
Fig. 6. A portion of the hyaline lamella with its attached clavate tissue, from the body
of the hydranth.
a. Clavate tissue ; b. Fibrillated layer of the hyaline lamella ; c. Delicate
structureless layer of the same lamella.
Fig. 7. Some of the rods of the bacillar tissue of tentacle, greatly magnified.
Fig. 8. One of the pedunculated sacs, with its contents, from the tentacle isolated.
Fig. 9. The capsule, with its contained cord liberated from the pedunculated sac.
Fig. 10. The capsule after the ejection of the cord, which is still attached by one end
to its summit.
Fig. 11. Distal extremity of a clasper.
a. Endoderm ; b. Hyaline lamella ; c. Clavate tissue ; d. External layer
of ectoderm ; e. Extension of ectoderm with its clavate tissue greatly deve-
loped over the distal end of the clasper.
Fig. 12. Isolated cells of the clavate tissue from the distal extremity of a clasper.
Fig. 13. Distal extremity of one of the transitory arms of the actinula.
a. Modified claviform tissue, which here forms the whole thickness of the
ectoderm ; b. Endoderm with axial cavity ; c. Capitulum.
Fig. 14. Pedunculated sac from the capitulum of one of the transitory arms of the
actinula.
a. The pedunculated sac with its contents still undisturbed ; b. The capsule
liberated from the sac and with its spiral cord ejected.
Fig. 15. Distal extremity of actinula, showing the peculiar development of the clavate
tissue at the extreme end (a), which acts as a sucker of adhesion.
PLATE 57.
Fig. 1. Very early stage in the development of the gonophore.
a. Offset from the endoderm of the blastostyle which has pushed itself into
the ectoderm ; b. Gonogenetic chamber filled with a granular plasma ; c.
Diverticulum from the cavity of the blastostyle ; d. Ectoderm of the blasto-
style as yet scarcely raised above the general surface.
Fig. 2. More advanced stage (female) ; the gonophore has formed a very decided pro-
jection from the external surface of the blastostyle, and the gonogenetic
chamber has begun to show a differentiation in its contents.
MDCCCLTXV. 4 G
574
PROFESSOR ALLMAN ON THE STRUCTURE
b. Gonogenetic chamber, in which the contents have become accumulated
on the walls and show imbedded nucleus-like bodies ; c. Diverticulum from
the cavity of the blastostyle ; d. Orifice in the endoderm forming the roof of
the gonogenetic chamber.
Fig. 3. A still more advanced stage of the female gonophore.
b. Gonogenetic chamber filled with a granular plasma, in which a great
number of nuclei have become developed ; c. Diverticulum from the cavity
of the blastostyle, which with its endodermal walls now projects as a spadix
into the gonogenetic chamber ; d. Very delicate structureless membrane,
which separates the generative mass from the endodermal walls of the gono-
genetic chamber.
Fig. 4. Stage still further advanced. Cell-boundaries have begun to show themselves
in the plasma of the gonogenetic chamber, and the nuclei have become sur-
rounded by differentiated masses of protoplasm.
Fig. 5. Nucleolated nuclei, isolated from the contents of the gonogenetic chamber in
fig. 3.
Fig. 6. Some of the cells forming the contents of the cavity of the gonophore in fig. 4.
Fig. 7. More advanced stage of the female gonophore. The ovarian tissue has become
looser, and now consists for the most part of detached oval masses of proto-
plasm each with a nucleus and nucleolus. Towards the centre, where they
are in contact with the spadix, some of these have coalesced into larger
masses.
a. Cellular lining of the cavity of the gonophore, w7here at the summit of
the gonophore its cells become loaded with coloured granules, forming a
purplish ring which surrounds the orifice.
Fig. 8. Some of the nucleated oval masses of fig. 7 removed from the gonophore, and
seen to have become united to one another by protoplasmic prolongations.
Fig. 9. A group of the same bodies. Between several of them the union has become
closer.
Fig. 10. Gonophore still further advanced than fig. 7. Nearly all the free oval bodies
have coalesced into a small number of large protoplasm masses.
a. As in fig. 7.
Fig. 11. Surface of one of the protoplasm masses of fig. 10, very much magnified,
showing the presence of minute pseudopodial projections.
Fig. 12. Portion of the walls of a mature gonophore (fig. 7), very much magnified,
showing details of structure.
a. External zone of spherical cells ; b. Zone of clavate tissue ; c. The fibril-
lated lamella; d. Cellular lining of the gonophore cavity; e. Very thin struc-
tureless membrane directly investing the generative elements ; f. Generative
elements.
Fig. 13. Structure of plasmodium formed by coalescence of the simple ova.
AND DEVELOPMENT OF MYBIOTHELA.
575
Fig. 14. Part of a blastostyle with gonophores, plasmodia, and claspers.
a. Blastostyle ; b, b. Claspers ; c, c. Young gonophores ; d. A mature gono-
phore, with the plasmodium escaping through its summit ; e. Walls of
gonophore retracted and everted after the liberation of the plasmodium ;
f Plasmodium liberated from the cavity of the gonophore, but still held in
in its place by the spadix, and already seized by a clasper. The plasmodia
( d andjf) present a lobed condition at the part turned towards the blastostyle,
owing to the coalescence of their constituent plasma masses being here still
incomplete ; g. A plasmodium entirely withdrawn by a clasper from its
original position on the summit of the gonophore peduncle.
Fig. 15. A male gonophore filled with the generating vesicles of the spermatozoa.
Fig. 16. Mature free spermatozoa.
Fig. 17. Structure of the plasmodium shortly after its seizure by the claspers.
PLATE 58.
Fig. 1. Planula.
a. Ectoderm; b. Endoderm ; a. Cavity of planula ; d. External structure-
less capsule.
Fig. 2. Embryo after the walls of the planula had become invaginated to form the
transitory arms.
a. Body of the embryo ; b , A Orifices of involution ; c. External struc-
tureless capsule.
Fig. 3. Section through the centre of the embryo represented in fig. 2.
a. Body of the embryo ; b, b. Arms formed by involution of the walls of
the embryo ; c. External structureless capsule.
Fig. 4. Embryo after the arms have become external by evagination.
b, b. The evaginated arms.
Fig. 5. Embryo after it has begun to elongate itself and acquire an oval form.
a. Commencement of permanent tentacles ; b,b,b. Transitory arms.
Fig. 6. Embryo after its escape from its capsule when it enters on its free life in the
surrounding water.
a. Distal extremity ; b. Proximal extremity ; c, c. Permanent tentacles ;
d, d , d. Long transitory arms fully developed.
Fig. 7. Embryo when it has begun to fix itself.
a. Distal extremity with mouth ; b. Proximal extremity with disk of
adhesion ; d, d, d. Transitory arms in process of disappearance.
Fig. 8. The embryo has definitely fixed itself, and the transitory arms have entirely
disappeared.
[ 577 ]
XX. Spectroscopic Observations of the Sun.
By J. Norman Lockyer, F.B.S., and G. M. Seabroke, F.B.A.S.
Beceived February 2, — Bead March 19, 1874.
We have the honour to communicate to the Eoyal Society the accompanying Spectro-
scopic Observations of the Chromosphere and of the Sun generally, made during the
period between the 1st October, 1872, and the 31st December, 1873.
The London observations have been made in Alexandra Road, Finchley Road, N.W. ;
the Rugby observations in the Temple Observatory at that place.
The following details are given of the instruments and methods of observation
employed.
LONDON OBSEBYATIONS.
A 6^-inch refracting telescope by Cooke, of York, mounted equatorially, was employed,
to which is attached the 7-prism spectroscope by Browning, of London, already described.
A position-circle, made by Cooke, of York, was used for obtaining the position-angle of
the prominences and of the various details of the chromosphere.
On the side towards the spectroscope the circle is provided with a pinion, which,
acting on a circular rack, causes the graduated half of the circle to rotate, the vernier
being on the fixed half attached to the telescope-body.
On the 16th of September, 1873, the prisms spectroscope was replaced by a diffraction-
grating of speculum-metal containing 6121 lines to the inch, made by Mr. L. M. Ruther-
furd, of New York, by whom it was generously placed at Mr. Lockyer’s disposal ;
the whole apparatus is only 15 inches in length, and weighs 3 lbs., while the 7-prism
spectroscope, with its mounting, is 24 inches long, and weighs lOf lbs., the principal
weight, moreover, being 18 inches from the end of the telescope. In dispersive power
the 2nd order spectrum of the grating is equal to 7 prisms, while with equal dispersive
power the grating gives much more light.
The positions of the prominences have been determined as follows : —
Standing with the back to the sun, and looking at the sun’s image on the slit plate,
the bottom of the image, being the image of the real North of the sun, is called North,
the left-hand side of the image East, the right hand West, and the top South. The
degrees are reckoned from North as zero through East to North again in the same
direction as the hands of a watch, N., E., S., W. of the image on the plate being of
course in the contrary direction to N., E., S., W. as seen directly on the sun. If,
MDCCCLXXV. 4 H
578
MESSES. LOCKYEE AND SEABEOKE ON
then, the ring of chromosphere, as seen on the slit plate, be cut at North or 0° and
straightened, we obtain a line with N. or 0° on the left hand, and extending to the
right from N. 0° through E. 90°, S. 180°, West 270°, to N. 360°.
The adjustments for recording the positions of various parts of the chromosphere as
observed with either the radial or tangential slit having been made, the telescope is
clamped in R.A., the clock set going, and the spectroscope focused for the C line.
Should a prominence be observed, the telescope is moved in R.A. or Declination,
until it appears in the middle of the field of the spectroscope, and the position-circle is
then moved until the slit is either tangential or radial to the part of the limb where
the prominence appears ; this is determined, in the case of the tangential slit, by the
narrow strip of continuous spectrum which flashes in the moment the limb of the sun
overlaps the slit exactly.
In the drawings executed in London, which accompany this paper, the positions of
the prominences have been determined as follows, viz. the smaller ones, those from 2° to
3® wide, have had the central point of their base taken for the position, those wider than
this have, in every case where possible, had the position-angle of each side determined,
and very complicated groups have had, as far as possible, their principal components
determined.
The height has been obtained by causing the slit to travel up the prominence, and
estimating how many slits high above the limb it was — a process which is easy, as there
are nearly always in the prominence details of structure which can be used as points for
measurement.
The height of each prominence is set down in slits, and the width of the slit is
measured at the end of the operation, and the true height in seconds calculated from
the measurement.
The London observations and drawings have almost entirely been made by Mr. R.
J. Friswell, Mr. Lockyer’s assistant, to whom great credit is due for the zealous and
intelligent manner in which he has taken up this branch of the research.
EUGBY OBSEEYATIONS.
The 8-g;-inch equatorial by Alvan Clark, to which is attached the ring-slit arrange-
ment, producing a virtual eclipse of the sun, described by us before this Society in
January 1873, has been used for these observations. The spectroscope attached is con-
structed on the return principle, giving a dispersion of 8 prisms of (50°. The position
of the prominences has been determined as follows : — Arranged radially round the
disk, which cuts off the light from the body of the sun, are fine platinum wires at a
distance of 10° from each other, and these being seen together with the ring of chro-
mosphere serve to fix the position of the prominences, the shape and position-angle of
which can be then easily drawn. There are four wires crossing the annulus 90° from
each other that are rather thicker than the others, and these are made to coincide with
the N., S., E., and W. points of the sun respectively by causing the upper or lower
SPECTKOSOOPIC OBSERVATIONS OE THE SUN.
579
limb of the sun’s image to traverse the disk, and then turning the instrument round
until the limb exactly passes from one wire to the opposite one ; then, on bringing the
sun’s image concentric with the disk, the left-hand wire, as seen by looking on the
disk with the back to the sun, corresponds to the East side of the sun as looked at
directly, and is therefore at the position of 90°, and the right-hand one corresponds
to the W. of the sun 270°; the lowest wire will then correspond to the North or 0°,
and the upper to the South or 180°. The direction of reckoning the degrees is as usual
N., E., S., W., or as looking directly at the sun in the contrary direction to the hands of
a clock ; but as looking on the disk with the back to the sun N., E., S., W. will be in
the same way as the hands of a clock ; and if the ring of chromosphere, as it would
appear to an observer looking at it in the annulus with the back to the sun, be cut at
N. or 0° and straightened, the appearance would be that shown in the drawings ; although
the annulus of chromosphere is looked at with the spectroscope from the opposite side
to that of the sun, the image is half inverted by a diagonal reflecting prism in the
telescope of the spectroscope, so that its appearance is the same as if looked at in the
annulus from the same side as the sun. The width of the annulus through which the
light from the chromosphere passes is such that a prominence 100" in height reaches
across the annulus, so that the height of the prominences can be judged of with fair
accuracy.
We have purposely refrained from any reduction of these observations, as we are of
opinion that such reduction will be most usefully made when the observations of the
Italian and other observers have been published, as it is hoped that the English and
foreign observations may be in some cases so complementary of each other that long
gaps may be avoided.
Notes to accompany the Maps. (Plates 59 to 64.)
(LONDON OBSERVATIONS*.)
December 6th, 1872. — Chromosphere generally 10" high.
January 1st, 1873. — Chromosphere about the usual height, except 150°-170°, where
it was low.
March 8th, 1873. — Chromosphere very hair-like in its outline, about 12" high.
Between 3.30 and 4.0 p.m. a large spot was observed between 240° and 250°, and close
to the limb. Violent action was going on. C was intensely black over the spot, and, I
think, slightly thickened ; D was very thick, and bent towards the red. The magne-
sium lines did not seem to be affected; but the two lines of b, 5166'5-f and
( Fe
* With these are included, in order of date, nine woodcuts of the more remarkable prominences, of the size
of the original drawings, which were made, some at London by Mr. Eriswell, some at Rugby by Mr. Seabroke.
The locality, date, and position-angle, which are given in each case, will enable the reader to find the places of
these prominences in the Maps.
4 h 2
580
MESSES. LOCKYEE AND SEABEOKE ON
5168-5 violently bent towards the red. 4859-1 Fe intensely
black and thick. F very black, and bent in all directions over the
region between the spots on the limb ; it was perhaps rather
thickened, but I could not be certain of this.
C T
C and F presented the above appearance on the limb near the spot. Once the bright
part of F filled up the space between 4859-1 Fe and the dark F line. This was pro-
bably only half the bright part, but I did not see it on the other side.
Another spot was close to the one in question, a little to the N. and E. of it.
London.
110°
March 8, 1873.
March 12th. — The bright line on the most refrangible side of b
in the ordinary solar spectrum scarcely affected by the spot ; b not
thickened. C gone on the edge of the spot ; F like this : —
March 17th. — A group of spots, probably those seen on the limb
on the 8th and on the sun on the 12th ; the magnesium lines were
not thickened. D is very thick, and C very black ; but it is doubtful
if it is thickened. The continuous absorption of the spot on either
side of C is very small.
March 24th. — The prominence at 230° changed a good deal in form and brilliancy.
Two spots were seen, but no satisfactory observations were obtained. One of them
seemed to give a continuous absorption only.
March 25th. — Chromosphere like the edge of a grass plot, about 15" high ; a spot
near N.E. limb. The following observations were made : —
F, 457’0.
Y
Magnesium lines not much affected.
Calcium „ near D not much affected.
„ „ in red moderately thick, but certainly not in
the same state of motion as the sodium ; scarcely any, in fact.
Hydrogen thin and scarcely disturbed.
SPECTROSCOPIC OBSERVATIONS OF THE SUN.
581
March 26th. — Chromosphere very hair-like, from 290° by 0° to 85°, except at 45°-55°.
At 20° the hairs inclined in all directions; at 290° inclined towards each other in two
masses, one on each side of 290°; at 65° sharp inclination to the prominence at 60°.
The chromosphere was also hair-like at 110°-130°, 135°-150°, 215°-245°.
March 27th. — The chromosphere about usual height, generally hairy.
March 28th. — From 90° to 180° no chromosphere seen, on account of mist and fog ;
from 180° by W. to 320° also misty, but observations made. Chromosphere hair-like
in N.E. quadrant, and about 8" to 12" high.
March 29th. — On a group of spots now in the centre of the disk the whole spectrum
appeared full of narrow strips of absorption, as though the sun were mottled. The Ca
lines enormously thickened on the left-hand spot, as seen in the spectroscope ; D formed
nearly one line, and b also appeared joined into one. Near F the absorption was so
great and general that nothing could be seen.
April 1st. — Hairy chromosphere near 10°, 30°, 70°, 90°, and 210°, at which latter
place the hairs were sharply inclined towards the prominence at 205°.
April 2nd. — The group of prominences between 210° and 225° changing considerably.
Chromosphere generally low (5" 1).
April 19th. — Chromosphere hairy, and inclined to S. at 180°-190° and 270°-280°, to
N. at 240°-250°, and straight up near 120°.
April 19, 1873.
April 21st. — Chromosphere very hairy, high, and hairs straight up at 35° to 85°.
May 1st.— Chromosphere generally hairy and rather low.
May 2, 1873.
270° 280° 290° 300°
May 2nd and 9th.— Chromosphere rather low ; on the 9th it was generally hairy,
and the hairs straight up.
May 20th. — Chromosphere very low and regular, about 6" high ; at 212^° a promi-
nence of honeycomb structure (the note says, “ looks like a coarse sponge ”) ; the two
northern quadrants not observed on account of mist.
May 22nd. — Chromosphere low.
582
MESSES. LOCKYEE AND SEABEOKE ON
May 23rd. — Chromosphere about 10", inclined E. generally from 0° to 90°, and to E.
at 105°-115°, 135°-145°, 155°-165°; straight up near 120°, 150°, 170°; a gap in it at
217°, and very low at 270°-275°.
May 24th. — Chromosphere very low at 330°-10°, and sharply inclined to the W. at
from 225°-240°.
May 31st. — Chromosphere 10"-12" high at 220°; sharply inclined to prominence
at 231°, and very hairy at 236°, so low as scarcely to be seen.
June 7th. — A spot observed. Calcium lines between C and D very thick ; D and b
very slightly or not at all affected.
Chromosphere undecided in character.
June 27th. — Chromosphere about 8".
July 7th. — Chromosphere about 10".
July 14th. — Chromosphere about 9", undecided in character.
London.
July 14, 1873.
July 16th. — Chromosphere 8"-12" high, hairy in S.E. quadrant, and inclined to the
W. ; high from 130°-140°; measured 12" here at 110°; a jet overlapped the limb, but
the prominence changed its form and it soon went off.
Much mist during observations of the two south quadrants.
July 21st. — 180°, thin, very active, vertical hairs; 186°, the same; 190°, hairs in-
creasing ; 195°, chromosphere quieter ; 200°, the same ; 205°, vertical hairs ; 210°, fuzzy;
215°, one hair longer than the rest ; 220°, masses here and there ; 225°, the same ; 230°,
fuzzy; 235°, more massive; 240°, nothing particular; 245°, chromosphere low; 250°,
very low, not hairy ; 255°, very faint.
July 22nd. — 180°-185°, hairy, but massive; 195°-205°, tongues; 215°-225°, hairy,
massive ; 225°-235°, lumpy and low ; a long cloud here connected with chromosphere
by a very faint filament ; 25°-35°, very spiky; 275°-295°, lumpy and very bright.
July 23rd. — 175°-205°, spiky, and spikes inclined to S. ; 205°-215°, very hairy, hairs
straight up ; 215°-225°, hairs inclined to S. ; 225°-235°, same inclination, more
SPECTEOSCOPIC OBSEEVATIONS OF THE SUN.
583
decided. In the N.W. quadrant the chromosphere lumpy, except near 0, where it is
spiky.
July 24th. — S.W. quadrant, the chromosphere covered with fluffy hairs ; in the N.E.
quadrant it is very spiky.
July 25th. — Only the N.E. quadrant was observed, on account of the bad light ; 0°-10°,
spiky ; 25°-35°, spiky ; 40°-50°, lumpy, with hairs all turned to N. ; 50°-60c, lumpy
and low ; 80°-90°, low and bright.
July 26th. — From 40°-90°, hairs inclined to S. ; from 30°-40°, very sharply inclined
S., the chromosphere very hairy ; N.W. quadrant, all the hairs inclined W., and high
near 350° ; S.E. quadrant, hairs to E., jets or splashes cover 3° at 110° ; S.W. quadrant,
spikes inclined to S., very decidedly at 190°.
July 28th. — Only the N.W. and N.E. quadrants were observed. In the former the
chromosphere vras hairy, and the hairs inclined to N. slightly, except at 330°, where
they were divergent. In the N.E. quadrant the hairs were generally straight up from
90° to 20°, where they were slightly inclined to W. From 10° to 0° they were straight
again.
There was a large spot nearly in the centre of the disk ; the C, D, b lines and the
chromium lines near b were not affected; the iron lines 5190-5, 5191-7, 5226-0, and
5232-0 scarcely, if at all, affected. The Ca lines near D were slightly thicker. The
spot is rather faint ; and as the general darkening of the spectrum is considerable and
the selective absorption almost nil , a cooling only would seem to be indicated.
July 30th. — In the S.W. quadrant from 262° to 270° the chromosphere or a long
low prominence was 25" high; at 310° to 316° there was another prominence, a portion
of which (about 310° to 313° or 314°) was like a coarse sponge in texture.
July 31st. — The chromosphere as a rule is low, bright, and lumpy at from 120° to
140°; there were indications of an inclination towards a prominence at 140°; at from
308° to 320° there was a smoky appearance and a slight inclination to the W.
August 7th. — The chromosphere lumpy and low from 150° to 190°; from 105° to
115° there was a very sharp inclination to E. In the S.W. quadrant it was generally
lumpy and any hairs straight up ; in the N.E. it inclined slightly to N., and was also
lumpy. There was a spot close to the base of the prominence at 309°.
August 8th. — From 90° to 70° lumpy with straight hairs ; at 48° a very low gap with
a spike in the middle of it ; there was scarcely a trace of chromosphere in the gap for
1° or 2°. From 70° to 30° the chromosphere was fumy or smoky, with hairs in the fume ;
at 23° it was very low again. From 20° to 10° it was fumy, but contained well-developed
hairs. In the N.W. quadrant it was spiky, and high at 350° to 340° ; 340° to 330° fumy ;
at 320° it was denser, and exhibited a slight inclination of its details to N. In the S.W.
quadrant the chromosphere was fumy with spikes, which latter were well developed
at 182°.
August 9th. — The chromosphere had generally a peculiar look, as though it was
584
MESSES. LOCKYEE AND SEABEOKE ON
viscous and had been drawn out into spikes. From 110° to 180° it was fumy ; from
90° to 105° there was an inclination towards E. In the N.E. quadrant it was of both
characters (spiky and fumy), and the spikes were straight up. In the N.W. it was
fumy ; in the N.W. hairy from 270° to 340°, and from 340° to 0° rather fumy.
August 13th. — Observations at 5.20 to 6 p.m., when lowness of sun stopped them ;
S.W. and N.W. with part of S.E. observed the chromosphere moderately spiky, but
its inclination indeterminate except at from 230° to 250°.
August 16th. — 90° to 115° spikes inclined E. 45° ; 115° to 180° lumpy ; spikes straight
at 120° to 130° to E. at 135°. In the N.E. the chromosphere was fumy and high, with
hairs in the fume; the same in the S.E. from 300° to 0°; from 285° to 295° the chro-
mosphere and a prominence had a spotted or mottled appearance ; about 275° spiky.
London.
320° 330° 340°
September 16th. — S.E. chromosphere hairy, with a slight inclination to the E., S.W. ;
and N.E., N.W. smoky with indistinct hairs.
September 22nd. — The chromosphere was generally smoky in appearance; at 154°
there was an exceedingly faint high prominence scarcely visible ; its height appeared to
be V 33".
September 23rd. — No particular details observable in chromosphere except at 115°,
where it was lumpy ; 253°, about, where it seemed composed of small flames ; 307°, high
and smoky. On the W. side of the large prominence at 327° to 330° the chromosphere
for 4° or 5° (222° to 227°) was hairy, and turned towards the prominence.
September 24th. — Chromosphere in S.E. and S.W. smoky and covered with irregular
tongues, not hairs. A spot was observed in which the C line was distorted and not
thickened ; D distorted and thickened ; Ca lines much thickened, but not much distorted.
When the C line was distorted D was still, and vice versd. b was distorted but not
thickened. A prominence at 304° was undergoing considerable change.
September 25th. — No particular features in the chromosphere in the S.E. and N.E.
It was high round 270°. From 315° to 325° the chromosphere was high and covered
with tongues, some 24" high.
September 26th. — A brilliant point at 109° at 2.15 p.m. ; at 3.15 p.m. not a trace of it.
In the N.W. the chromosphere was fumy with a spiky edge ; from 290° to 300° it was
15" to 20" high in the whole quadrant, and up to about 20° in the N.E. quadrant it was
inclined in the same direction, i. e. to E. down to 0°, and to S. from 0° to 20°. The C
line was seen broken over a spot.
Aug. 22, 1873.
SPECTROSCOPIC OBSERVATIONS OF THE SUN.
585
September 27th. — S.E. chromosphere smoky and covered with tongues; S.W. 180°
to 200° fumy; 230° to 240° fumy, spikes inclined to E. ; 250° to 260° chromosphere 20"
high, spikes 80". For 1° or 2° it was very low at 262°, and from 262° to 275° higher,
and inclined to prominences at 280° &c.
October 2nd. — S.E. and S.W. light very bad and chromoscope indistinct, but it
appeared to be smoky ; the same in N.E. In the N.W. the chromosphere hairy and
about 16" high.
October 15th. — Chromosphere generally 12", near 100° low (8"), and at 115° sharply
inclined to N. ; at 145° it appeared to be squirting in all directions, as though from
a hole; from 170° to 190° solid and spiky, very high and covered with tongues all
through the S.W. quadrant ; in the N.W. generally fumy, but more hairy in the eastern
part ; in the N.E. lumpy from 80° to 90°, a tuft of hairs 16" high and inclined to N. at
59°. A spot in this quadrant in which D, b, and the Ca lines are thick, but C unaltered.
October 17th. — Chromosphere very level and low (8"), but light very bad.
October 28th. — S.E. and S.W. lumpy and billowy with tongues ; N.E. and N.W.
rather more hairy.
October 30th. — Chromosphere about 8"; high, billowy, and smoky in N.E., S.E.,and
S.W. ; in N.W. the same, with a direction to W. 1
November 1st. — No details observed ; observation unsatisfactory.
November 3rd. — Only the S.E. quadrant observed ; chromosphere about 16".
November 11th. — S.W., N.W., and N.E. the chromosphere smoky with hairs; at
136° a prominence nearly separated from the chromosphere, which was fumy.
MDCCCLXXV.
586
ON SPECTROSCOPIC OBSERVATIONS OF THE SUN.
November 12th. — S.E. chromosphere billowy; S.W. 200° to 220° fumy, direction W. ;
250° to 254° very high, fumy chromosphere; 260° to 270° direction S. ; N.W. about 280°
low and bright, direction N. ; at 290° to 300° straight up ; about 340° fumy and flamy,
with a W. direction ; about 0° fumy tongues with a W. direction.
November 15th. — S.E. fumy, a few spikes straight; at 95° very billowy ; about 140°
S.W. fumy and billowy; N.W. sharp inclination to N. at 280° to 290°, and hairy at
that part ; elsewhere fumy.
December 9th. — Chromosphere rather spiky near 160° ; from 185° to 210° fluffy ;
round 213° hairy hairs straight, remainder of the quadrant billowy; round 270° very
brilliant ; D3 is very brilliant here between 265° and 272° in the lower parts of the
chromosphere.
December 12th. — From 220° round by 0° to 90° light too bad for observation ; rest
of chromosphere regular.
December 17th. — From 58° to 90° hairs have a slight tendency towards 90°. Rest
of chromosphere fumy, with a few tongues or billows.
December 29th. — Chromosphere near 20° hairy, then rather level ; at 160° spiky, and
inclined both to E. and S. ; at 200° tongues, 215° hairy, which continues to 240°.
Prominences at '241° and 244° are like wreaths of smoke ; 315° to 360° tongues inclined
towards W.
December 30th. — From 90° round by 0° to 160° light too bad for observation ; 90°
to 160° chromosphere level ; higher at 120° to 130°.
December 31st. — 0° to 90° light not good ; high at 85° ; very faint cloud at 132°; at
1.55 p.m. great changes going on in the group of prominences between 252° and
265°; chromosphere generally level.
Spots were observed on the 23rd and 29th. On the 23rd D and the Ca lines near it
slightly thickened, and D a little distorted, C and b not affected. Absorption general
rather than selective. On the 29th general absorption again characteristic, C, D, b
not affected.
It has been noted at Rugby that all the cyclones observed from the beginning of 1872
have, with one exception, had a motion of rotation, direct when in the northern hemi-
sphere, and indirect when in the southern, corresponding, therefore, to our terrestrial
cyclones.
In the Plates accompanying this paper the horizontal lines represent each one
minute.
[ 587 ]
XXI. Tables of Temperatures of the Sea at different Depths beneath the Surface , reduced
and collated from the various observations made between the years 1749 and 1868,
discussed. With Map and Sections. By Joseph Prestwich, M.A., F.B.S., F.G.S.
Received May 14, — Read June 18, 1874.
Contents.
Page
§ I. Introduction 587
§ II. Historical Narrative of Deep-sea Observations, 1749-1868 590
Ellis, Cook, Forster, Pbipps, Saussure, Peron, Krusenstern, Scoresby, Kotzebue, Wauch ope, Abel,
John Ross, Parry, Sabine, Franklin, Emil. Lenz, Beechey, Blossville, D’Urville, FitzRoy,
Graah, Berard, Du Petit-Tbouars, Yaillant, Martins and Bravais, Pratt, Wilkes, James Ross,
Aime, Spratt, Belcber, Kellett, Dayman, Armstrong, Bacbe, Maury, Pullen, Wiillerstorf,
Walker, Kiindson, Ed. Lenz, Wallicb, Shortland, Cbimmo.
Methods of Observation employed, — tbeir Relative Merits 610
Corrections for Pressure, — Du Petit-Tbouars, Martins, Aime, Miller 612
§ III. Summary of tbe preceding Observations.
Original opinions of Lenz and Du Petit-Thouars 613
Opinions of D’Urville, James Ross, and Wilkes 614
Maximum Density and Freezing-Point of Sea- water 616
Corrected Reading of Temperatures in Tropical, Arctic, Antarctic, and Inland Seas 617
§ IY. Hypotheses and Remarks of Humboldt, Arago, Lenz, and others 623
§ V. General Conclusions.
Different value of the old observations 630
Position of the Bathymetrical Isotherms : — in the Atlantic from Spitzbergen and Baffin's Bay to
the Antarctic Ocean ; in the Pacific from Behring’s Strait to the Antarctic Continent .... 631
Undercurrents of Polar Waters : — their Rise in Equatorial Regions of the Atlantic 634
Effects of the Polar deep undercurrents on the Oceanic surface-currents 635
Inland Seas dependent on local Climatal Conditions 636
Bearing of the subject on some Geological Problems 637
Final Propositions 637
Lists of Observations : — Northern Hemisphere ; Southern Hemisphere ; Inland Seas 639
§ I. Introduction.
This communication, the result of an inquiry having originally reference to the bearing
of the subject on certain geological questions, was commenced more than twenty years
ago, but abandoned for a time, partly owing to the pressure of other engagements, and
partly waiting more accurate information of the range of life at depths*. The great
impulse given to these questions by the more recent expeditions of the 4 Lightning ’
* A few of the geological questions were, however, noticed, and some of the early deep-sea temperature-
observations given, in the author’s Anniversary Address to the Geological Society of February 1871, Quart.
Journ. Geol. Soc. vol. xxvii. pp. xliii-lxxv.
4 K
MDCCCLXXV.
588
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
and ‘ Porcupine,’ culminating in that of the ‘ Challenger,’ has not only again directed
attention to the subject of deep-sea temperatures, but has led to such improved methods
of observation, that it may now seem late to bring forward the less accurate experi-
ments of former observers. It might therefore seem almost a work of supererogation,
now that the subject in connexion with these later voyages has been so ably and
zealously taken up by my friend Dr. Carpenter, to introduce these more variable older
elements into the discussion. Still the older observations, though restricted to com-
paratively limited depths, have a wide range ; and in the case of the Arctic voyages
they were obtained under conditions of so much difficulty and danger, that it may be
long before similar experiments are repeated ; while many of the original opinions evi-
dently deserve great consideration. It was, moreover, always my intention to complete
the task I had begun when time and opportunity offered ; and as Dr. Carpenter’s work
commences with the observations made by him on board the ‘Lightning’ in 1868, it
may not be out of place to have a record of all that was done in temperature-soundings*
up to that time, even as supplementary to the more exact work of later voyages.
I may also notice that, notwithstanding the superiority of the more recent observa-
tions and the inaccuracy of many of the older ones, there are a certain number of the
latter which were made with great care, and which may vie with recent experiments in
exactness ; while with respect to the others, the errors are such as may in most cases be
computed and allowed for; or merely taking the old observations as they are, the
comparative temperatures recorded at corresponding depths with the same or similar
instruments have their own special value. The older observations are also so scattered
through various narratives of voyages and in scientific periodicals, that no one can,
without much difficulty of search, form an idea of their number and interest, or of the
progress which the subject had made at the hands of the eminent men who had from
time to time engaged in the inquiry on the Continent. I purpose, therefore, to show
the state of the question at the time of the ‘ Lightning ’ expedition. For all that has
been done since, I would refer to the exhaustive papers of Dr. Carpenter j\
In former voyages the temperatures are variously noted in degrees of Reaumur,
* The few old observations of life at depths -will not now require notice.
t “ Preliminary Report,” by Dr. "William B. Carpenter, Y.P.E.S., “ of Dredging Operations in the Seas to
the North of the British Islands, carried on in Her Majesty’s Steam-vessel ‘Lightning,’ by Dr. Carpenter and
Dr. Wyville Thomson, Professor of Natural History in Queen’s College, Belfast.” Proc. Eoy. Soc. vol. xvii.
p. 168 ; Appendix, p. 197, 1868-69.
“On the Bhizopodal Eauna of the Deep Sea,” by W. B. Carpenter, M.D., Y.P.E.S. Ibid. vol. xviii. p. 59.
“ Preliminary Report of the Scientific Exploration of the Deep Sea in H.M. Surveying- vessel ‘ Porcupine,’
during the Summer of 1869, conducted by Dr. Carpenter, Y.P.R.S., Mr. J. Gwyn Jeffreys, E.R.S., and Prof.
Wyville Thomson, LL.D., E.R.S.” Ibid. vol. xviii. p. 397.
“ Report on Deep-sea Researches carried on during the Months of July, August, and September 1870, in
H.M. Surveying-ship ‘Porcupine,’” by W. B. Carpenter, M.D., E.R.S., and J. Gwyn Jeffreys, E.R.S. Ibid.
vol. xix. p. 146.
“ Report on Scientific Researches carried on during the Months of August, September, and October, 1871, in
H.M. Surveying-ship ‘ Shearwater,’ ” by William B. Carpenter, LL.D., M.D., E.R.S. Ibid. vol. xx. p. 535.
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
589
Fahrenheit, and Centigrade, and the depths are recorded in feet, fathoms, the ‘ old
French foot,’ ‘toise’*, ‘brasse,’ 4 metre,’ and the 1 yaden,’ while the longitude is some-
times that of Greenwich, at others that of Paris. I have reduced these various
measures to a common scale, adopting for temperatures that of Fahrenheit ; for length,
the English foot ; and for longitude, the meridian of Greenwich. As in these reductions
some errors may have crept in, references are given to all the original readings.
In the Lists of Observations (pp. 639-70) the degrees of temperature at depths stand
as they are recorded by the several observers, without the correction adopted for the
Sections. The place of each observation is laid down on a recent Admiralty Chart of
the world (Plate 65), in accordance with the longitude and latitude given by each
observer, without any attempt at correction, which, in some of the early observations,
may possibly be necessary.
The observations thus reduced are tabulated in three groups. Table I. gives the
deep-sea temperatures in the Northern Hemisphere from the Equator to the Polar Circle,
and in the same way Table II. gives those in the Southern Hemisphere. The observa-
tions in inland seas are given in a separate Table, No. III.
A list of temperature-soundings, made up to date, was given by Peron in 1816.
It was limited to 4 of his own, and to 16 of Forster’s and Irving’s f. In 1832
D’Urville £ gave a greatly extended list, embracing as many as 421 observations, which
he arranged according to zones of depth ; and in 1837 Gehler § published a list of 226
observations arranged according to latitude. These, I believe, constitute all the general
lists that have been published. The number of observations recorded in the present
Tables amount to 1356.
In the following pages I have given : — first, a notice of the many voyages on which
soundings for deep-sea temperatures were taken, with an account, when possible, of
the mode in which the observations were made ; secondly, a summary of the opinions
founded on these data ; and thirdly, a statement of the results obtained and of the
conclusions to be formed thereon.
Besides the error due to pressure, which, as so many of the older soundings were
made at small depths, is frequently unimportant, there is that arising from the angle of the
line from the vertical caused by currents, and another due to the tension of the rope by
strain and wet, which is sometimes not inconsiderable. I have, however, in drawing
the sections, given the depths without correction for these causes, so as to place all the
observations on the same footing, as it is but rarely, although there are exceptions,
that these particular sources of error were noticed or mentioned || .
* The Old Eoot= 12-79 inches; the Toise=76-68 inches ; the Brasse =63- 93 inches.
t Yoyage de decouverte aux Terres Australes, vol. ii. p. 327.
+ Yoyage de 1’ Astrolabe, vol. x. Chap. III. Physique.
§ Gehler’s Physikalisches Worterbuch. Sechster Band, Dritte Abtheilung, Mc-Mj, pp. 1676-82.
|| The older deep-sea soundings have been found to be liable to serious error, arising from the difficulty in
actual fixing the depth of sounding ; but in these Tables there are few of that depth to involve this particular
error ; still some of the deeper ones must be looked upon with doubt.
4 K 2
590
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
Owing to the want of a reliable self-registering thermometer, three plans were
resorted to by the earlier observers to ascertain the temperature of the sea at depths
below the surface. The first and more common plan was to bring up water from a
determined depth in sufficient quantity and with sufficient speed to prevent any material
change of temperature, and then to try it with an ordinary thermometer, although some-
times the thermometer was suspended in and descended with the water-bucket. In the
second place, the thermometer was surrounded with a non-conducting substance, and
left down a length of time sufficient to acquire the temperature of the surrounding
medium and then brought rapidly to the surface. In the third place, the temperature
was taken by means of mud or silt brought up from the bottom. On a few occasions
metallic thermometers have been tried, but not with satisfactory results. These several
plans continued in use from time to time up to a comparatively late period, until
gradually superseded by self-registering thermometers.
As the error due to pressure in the use of the latter instrument has now been deter-
mined with sufficient accuracy, most of the older observations can readily be subjected
to correction. Such correction has been applied to all the observations that have been
used in constructing the Sections, Plates 66-68 ; but, as in the Tables themselves the
original readings are given without correction, in order to obtain in any case, with a few
exceptions named, an approximately true reading, the correction given at p. 612 must be
applied. Where, from the use of proper precautions, the original readings are presumed
to be correct, they are distinguished by being placed between brackets in the Sections.
§ II. Historical Narrative of Deep-sea Observations , 1749-1868.
In this chapter I have enumerated in chronological order the various voyages on
which I have found any record of deep-sea temperatures — stating generally the course
gone over, the number of observations made, the depths attained, the methods employed.
At the end the correction for the errors attendant on these methods is determined. The
particulars of the observations taken on each voyage will be found in the Tables by
reference to Column VIII., under which is given the name of the officer in command,
or of the scientific observer accompanying the expedition. The conclusions formed by
them on these data are reserved to the next chapter.
It was about the middle of the last century that the subject of deep-sea temperatures
first began to attract attention. In 1749 Captain Ellis, on the occasion of a voyage
to the north-west coast of Africa, made two experiments at depths of 3900 and 5346 feet
in lat. 25° 13' N.*, with an instrument devised by Dr. Hales, and described by him in a
paper to the Royal Societyf. It consisted of a bucket about the size of an ordinary
pail, with valves at top and bottom, which remained open as the apparatus descended,
and closed as it ascended. He obtained in both cases readings of 53°; and he rightly
attributed this uniformity to the greater depth of water through which, in the deeper
experiment, the instrument had to be hauled, and which caused a larger gain of heat.
* Phil. Trans, for 1751-1752, vol. xlvii. p. 214. f Ibid, p, 213.
ME. J. PRESTWICH ON SUBMARINE TEMPERATURES.
591
No further attempts of the kind seem to have been made until 1772, when Cook* went,
with Forster f as naturalist, on his first voyage round the world. They each separately
record three experiments made, at depths of 600 feet, between the equator and 64° South
latitude, and they both recognized the decrease, within certain latitudes, of the tempera-
ture with depth. From some unexplained cause, the experiments were soon discon-
tinued. No mention is made either in Cook’s or Forster’s narrative of the instruments
used, except that the latter alludes (p. 45) to the use of thermometers, while Peron
speaks (p. 318) of Forster’s “ cylindre a double soupape;” so it may be presumed that
he used Hale’s apparatus with an ordinary thermometer enclosed in it. The apparatus
was left at the bottom from 15 to 30 minutes.
In 1773, on the occasion of Captain Phipps’s $ voyage to Spitzbergen, he was furnished
by the Royal Society with instructions how “ to direct his inquiries.” Sailing past
Shetland and the Faroe Islands, to the west and north coasts of Spitzbergen, he reached
80° 48" N. latitude. Dr. Irving, who accompanied the expedition, made nine observa-
tions at depths varying from 192 to 4098 feet, and extending from the German Ocean
to the north of Spitzbergen. They first of all used thermometers contrived by Lord
Charles Cavendish § in 1757. They were on the principle of overflow thermometers,
which registered the temperature by subtracting from a column of mercury of given
length the portion which passed over into an attached receiving bulb, and comparing
the instrument before and after with a standard thermometer ; but, owing to its delicacy,
difficulties of manipulation, and errors by compression, this instrument was soon
abandoned. Irving then devised a water-bottle with a coating of wool 3 inches thick,
and shutting inside with a cone of lead when at the bottom. The temperature was
taken when brought to the surface. For moderate depths the results, which are
recorded in the Tables, seem to have been tolerably correct. Those obtained with
Cavendish’s thermometer are, on the contrary, so discordant || that I have not included
* Yoyage towards the South Pole, 1772-1775. By Capt. Cook. 2nd edit. London, 1777, pp. 25, 29, 39.
t Yoyage round the World, 1772-1775, in H.M.S. ‘Resolution.’ By George Forster, F.R.S. London,
1787, vol. i. pp. 48, 50, 51.
£ A voyage towards the North Pole, undertaken hy His Majesty’s commands in 1773. London, 1774.
Appendix, pp. 141-7.
§ Phil. Trans, vol. 1. p. 308, and vol. liv. p. 261.
|| I annex them here, for the purpose of record, with the correction for compression and unequal expansion
of spirits afterwards introduced hy Cavendish and applied hy Phipps.
North Latitude.
East Longitude.
Depth in feet.
Temperature in degrees of Fahr.
| By therm.
Corrected.
Air.
1773, June 20
67 5
5 46
4680
15
26
48 5
„ „ 30 A.M. . .
70 8
10 55
708
30
31
40 5
„ „ 30 p.h. . .
70 8
10 ?
690
33
33 1
44 75
„ Aug. 31
69 0
0 18
4038
22
32
59 5
1 In this experiment the water brought up in Irving’s water-bottle gave a reading of 380,5.
592
ME. J. PEESTWICH ON STJBMAEINE TEMPEEATUEES.
them in the Tables. The general conclusion Phipps and Ieving drew was that, except
in Arctic seas, the temperature decreased with the depth.
In 1780 Saussuee made the two first observations on the temperature of the Medi-
terranean*— one off Genoa at a depth of 944 feet, and the other off Nice at a depth of
1918 feet. Both the thermometers marked 55°'8, or, allowing his correction, about
55°-5, a singularly close approach to the more recent observations of Aime and others.
Saussuee used a spirit-thermometer of Reaumue’s with a large ball, which he surrounded
with a mixture of wax, resin, and oil 3 inches thick ; and the whole was then placed
in an iron-wire cage. In both cases he sunk the thermometers at 7 o’clock in the
evening, and left them down until 7 in the morning, so that they might acquire precisely
the temperature of the surrounding water. The one sunk 1918 feet deep took twenty-
four minutes to haul in, and he inferred that this would give the true temperature
within a fraction (one fifth) of a degree. The thermometer was specially made and
graduated for the experiment ; and he had previously ascertained that after lowering it
to a temperature of 2°'3 R., and arranging so that by constant moving it traversed
1000 feet of water at 14° R. in ten minutes’ time, the instrument had only risen one
tenth of a degree, or to 20-4.
In 1800-4 a voyage of circumnavigation was undertaken by command of the Emperor
Napoleon. Monsieur F. PEEOisrf accompanied it as naturalist and physicist; but, owing
to the indifference of the officers and ill-will of the men, he was unable to make more
than 4 uncertain experiments, all in the tropical seas, and at depths only of from 320 to
2270 feet, the lowest temperature recorded being 45°-5 in lat. 4° N. M. Peeoh, not
satisfied with former methods, employed a mercurial Reaumue’s thermometer, placed in
a glass cylinder, with cotton-wool to protect it. This was enclosed in a wooden cylinder
sufficiently large to allow of a packing between the two of powdered charcoal, and then
put in a tin case, which was wrapped round with oil-cloth. The value of the results to
be obtained by such protected instruments necessarily depends, as in the case of Saus-
suee’s experiments, upon leaving the thermometer down for some hours ; but in one
case only was M. Peeon allowed to leave his apparatus down 1 hour 50 minutes, and
once he had to haul it up after five minutes’ submergence. Peeon refers to and
tabulates the experiments of his predecessors, and remarks on the same law of the
temperature decreasing from the surface downwards.
In 1803 the ‘Neva’ sailed on .a voyage of circumnavigation, under the command of
Captain Keusensteen. Touching at Falmouth, he passed round Cape Horn to the Sand-
wich Islands, Kamtschatka, Japan, and back by the Cape of Good Hope. Keusensteen
took out with him an apparatus made in St. Petersburg on the model of Hales’s; but this
was abandoned for Six’s self-registering thermometer, which, although invented in 1782,
was now for the first time employed at sea. Some thirty experiments were made by
* Voyages dans les Alpes. Neufchatel, 1796, yol. iii. pp. 153 & 196.
t Voyage de Decouvertes aux Terres Australes en ] 8Q0-4, redige par M. F. PLeox, Nat. de PExped. Paris,
1816, pp. 334-37.
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
59:
him and Dr. Horner in the tropical regions of the Pacific* * * § and the Sea of Okhotsh.
We have no description of his water-bucket, and are therefore without means of
judging of the exact value of the results. The more numerous experiments made, on
the other hand, by Dr. Horner f with Six’s thermometer admit of correction.
A subject of so much interest did not escape the attention of Scoresby ; and he gives
a Table of the twenty-four observations made by him in the seas around Spitzbergen,
during his several voyages to the Arctic Ocean between 1810 and 1822, at depths
varying from 78 to 4566 feet J. He made use of an apparatus (no doubt based on that of
Hales) consisting “of a cask capable of holding 10 gallons of water, composed of 2 inches
of fir plank, as being a bad conductor of heat.” Each end of the cask was furnished
with a valve ; these were connected with a wire so as to move simultaneously. They
opened in descending and closed in ascending. The cask was allowed to remain down
half an hour, and was hauled up briskly. A common thermometer was then used to ascer-
tain the temperature of the water so brought up. This machine soon, however, got out of
order, and he had one cast in brass, 14 inches in length by 5J inches in diameter,
which he called a marine diver. This he employed in all his experiments on and after
the 1st May, 1811. A Six’s thermometer was enclosed, which could be read off through
two glass sides in the “ diver ” on coming to the surface. The weight of the machine
was 28 lbs. He recognized in these seas a uniform though slight increase of tempera-
ture from the surface to the greatest depth he attained, the temperature at the surface
being generally 28° to 29°, and increasing in descending to 36° and even 38° (uncorrected).
In a subsequent voyage he gives, however, an experiment made 7° or 8° further south,
and off the coast of Greenland, in which the reverse held good ; the surface-temperature
being 34°, and at a depth of 678 feet 29° §.
Objections have been raised to Scoresby’s experiments, on the ground that they do
not accord with those of Martins and Bravais, which were made with more exact
modern instruments. But these observers themselves accept Scoresby’s observations as
true, subject to small corrections. The differences between them are, in fact, more
apparent than real, and arise chiefly from the circumstance that their observations were
made in the months of July and August, when the temperature of the air averaged from
35° to 45°, and that of the surface-water from 38° to 42°, whereas Scoresby experimented
in April and May, when these had temperatures respectively of 20° to 34° and of 28° to
30°, so that the relative differences between the surface and the deep waters are neces-
sarily very different in the two cases. In the experiments at depths below 2000 feet
there is little discordance after applying the corrections employed by Martins and
Bravais. The latter, however, took no depth exceeding 2854 feet, while Scoresby gives
* Yoyage round the World in the years 1803-6. English translation. London, 1813, vol. i. pp. 187 & 203.
t Horner’s observations are recorded hy Gehxer (note, p. 589). They are given under his name, and not that
of Krusenstern, in the Tables. See also the original work of Krusenstern.
± Account of the Arctic Eegions. Edinburgh, 1820, p. 187.
§ Journal of a Yoyage to the Northern Whale Fishery in the year 1822. Edinburgh, 1823, p. 237.
594
MR. J. PRESTWIC1I ON SUBMARINE TEMPERATURES.
two exceeding 4000 feet; and these were made at some distance from those of the
French observers, who experimented chiefly between Norway and lat. 76° N., whereas
Scoresby’s observations were mostly north of that latitude, and in the sea west of Spitz-
bergen as far as 80° north.
It is easy to determine the depth at which, in inland seas like the Mediterranean, the
effect of the diurnal variation of temperature ceases, but it is a much more difficult
problem in Arctic seas. Exposed to the low temperatures of an Arctic climate, the
surface-waters may continue to sink until their temperature is reduced to 250,4, the
point at which they attain their maximum of density. This, however, can only happen
in a state of perfect calm or with waters of unusual saltness, as sea-water of the usual
specific gravity freezes under ordinary conditions at 27°"4 F., though it has been shown
that in a state of perfect rest it may be reduced to 20°, or even lower before freezing.
Under these conditions, and with the complicated action of warm currents from the
south and of cold currents from the north, we must expect to find considerable variation
in the temperature of the Arctic Ocean, down, at all events, to the depths hitherto reached
of 4600 feet. Judging from the conditions prevailing in the Antarctic seas and the sea
of Baffin Bay, it seems probable that more uniform readings will be obtained at greater
depths, and that the anomalous readings in the upper strata are caused by the warmer
waters which flow in from the south tending to take at and near the surface the tempe-
rature of the air at different seasons, while the deeper part of this mass of warm water
remains unaffected ; and in the deeper channels there may be, flowing from the north,
the more permanent body of cold water produced by the winter refrigeration of the
polar seas of still higher latitudes.
Subject to the corrections for the causes before named, Scoresby’s experiments
command confidence. The effect of the corrections will be to reduce his readings where
Six’s thermometer was used, while where the water-bucket alone was used a small
addition may be generally needed.
In the mean time (1815-18) another Russian voyage of circumnavigation*, under the
command of Otto von Kotzebue, was undertaken for scientific purposes. One hundred
and sixteen carefully conducted experiments (often taken from day to day) were made
in both the great oceans and amongst the islands of the Eastern Archipelago. These
observations, many of them serial, taken at depths of from 24 to 2448 feet, were tabu-
lated in the order of date. On this voyage Kotzebue used English-made (Jones) Six’s
thermometers. They were protected by a wooden case closed with “ wire grating,” but
not in any other way, and they were fastened on the sounding-line about 6 feet above
the weight. Kotzebue considered that “ seven or eight minutes suffice to give it the
temperature of the surrounding water, and a quick or a slow pulling up has no effect
on the observation” (vol. i. p. 89).
* Entdeckungs-Reise in die Siid-See nnd nach der Berings-Strasse zur Erforschung einer nordostliehen
Durchfahrt auf dem Schiffe Rurick (Weimar, 1821), dritter Band, von dem Naturforscher der Expedition
Dr. Chamisso, Tables, p. 230 ; and Dr. Horner’s Report thereon, p. 233.
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
595
In 1816 Captain Wauchope made two observations in the Atlantic, a few degrees
north and south of the equator, at depths of 2880 and 6060 feet, and records tempera-
tures at those depths of 51° and 42° * * * §. The apparatus he used consisted of “ a series
of cases, one within the other, having valves opening up so as to allow the water to
pass through in descending, but which closed in hauling the instrument up. The
thermometer was enclosed in a glass tube in the centre of it.” Elsewhere he mentions
that the cases were J of an inch apart, except the outer one, which was ^ an inch, and
that one was filled with tallow. This was enclosed in a case of wood 1 inch thick.
The machine was 2 feet high by 10 inches in diameter. The time it took to haul
up was from twenty minutes to one hour and twenty minutes. After all, as Six’s
thermometer was used, the correction to be applied is rather that due to pressure than
to the change of medium. In measuring the depth, Captain Wauchope allowed for the
angle of the rope from the vertical.
In 1817, on the occasion of the voyage of the ‘Alceste’ to China, a few experiments
were made by Clarke ABELf in the shallow waters of the Yellow Sea. No particulars
of the methods he adopted are given.
In 1818 attention was again directed in this country to the Arctic seas, and the
‘ Isabella ’ and ‘ Alexander ’ were despatched to Baffin Bay, under the command of Boss J
and Parry; and the ‘Dorothea’ and ‘Trent’ to Spitzbergen, under Buchan and
Franklin §. As many as 72 valuable observations on deep-sea temperatures and
soundings were made by the several commanders, assisted by Sir Edward Sabine,
who accompanied Boss, and by Beechey and Fisher, who accompanied Franklin. Some
of these are recorded in the narratives of the several voyages, and the others are given
by Dr. Marcet in his well-known paper “ On the Specific Gravity and Temperature of
Sea Waters” published in 1819 1|.
Sir John Boss adopted the plan of taking the temperature of a mass of mud or silt
brought up from the bottom. For this purpose he contrived what he called a deep-sea
clamm. It consisted of “ a cast iron parallellogram ” 18 inches high by 6 inches wide
on the outside ; inside 5 X 4 in. It weighed 1 cwt., and would bring up about 6 lbs.
of mud. By this means, a bottom-temperature generally of 29°5, and in one case, at
the depth of 6000 feet, as low as 28°"75, was determined in Baffin Bay. This degree
of cold was generally corroborated by a Six’s thermometer, both instruments appa-
rently giving the same or nearly the same reading. It was on this occasion that the
* Mem. Wernerian Nat. Hist. Soc. vol. iv. p. 163.
f Thomson’s Annals of Philosophy for 1819, vol. xiii. p. 314.
+ Eoss’s Yoyage of Discovery to Baffin’s Bay in 1818. 2nd edition. London, 1819. Appendix, xi. pp. 234-236.
Appendix, xiii. p. 250.
§ Eor a Table of the temperature of the Sea at various depths, taken during Capt. Eeanklin’s Yoyage to
Spitzbergen with Captain Bxjchan, see Edinburgh Phil. Journal for 1825, vol. xii. p. 233.
|| Phil. Trans, for 1819, p. 161; Fkanklin, table vi. p. 203 ; Beechey, table vii. p. 203 ; Eishee, table viii.
p. 203; Pakby, table x. p. 205; Sabine, table xi. p. 205. These are marked ‘ m’ in the Tables.
MDCCCLXXV. 4 L
596
MR. J. PRESTWICK ON SUBMARINE TEMPERATURES.
remarkable low temperature of 25°* * * §75 F. was recorded, at a depth of 4080 feet in Davis
Straits, by Sir John Eoss and Sir Edward Sabine*.
Buchan and Franklin employed, on the suggestion of Mr. Fisher, a leaden box with
two valves, which remained open in descending, and were closed in the ascent. No
other particulars are given, but there is every probability that it was constructed on
the model of those of Hales and Scoresby. Their observations, with one or two excep-
tions, are, allowing for the difference of season (June and July), in tolerable agreement
with those of Scoresby ; but they seem less carefully made, and to require, I suspect, a
larger correction.
In 1819-20 Parry went out in command of the 4 Hecla’ and 4 Griper ’f, and pene-
trated the Arctic seas of North America as far as 113° W. long. He took several deep-
sea temperatures on board the ‘ Hecla,’ whilst Sir E. Sabine, on board the 4 Griper,’
made another series of observations. Mr. Fisher, who published an account J of the
voyage, also notes some of those on board the 4 Hecla.’
About this time Sir Humphry Davy suggested another contrivance for bringing up
water from depths, which seems to have been used occasionally by Eoss and Parry ; but
the observations with it are not specified. On the occasion of Parry’s voyage in
1819, Dr. Marcet contrived his water-bottle, which Parry appears to have occasionally
employed, especially in 1821-23 (p. xvi), 44 in consequence of the failure of the thermo-
meter when exposed to sudden changes,” although elsewhere he says (p. xiii) that the
temperature was taken, unless otherwise noticed, by Six’s thermometer. Owing to the
very small size (half a pint) of Davy’s and Marcet’s water-bottles, and their being of
metal, they were valueless for temperature-experiments §, although useful for obtaining
small samples of deep-sea water ; and they were consequently, with this exception, but
little used for the former purpose.
In Parry’s second voyage of 1821-23 1| he records a series of twenty-three experiments
made in one of the inland seas of Arctic America, at depths of from 600 to 1200 feet.
These show a temperature of from 29° to 31°*T on the surface, and a like temperature,
* On reference to Sir E. Sabine he informs me, from a note made at the time, that on bringing up the
thermometer the index marked 25f °, and that never having known it lower than 28°, he was very careful in
examining the instrument ; that both he and Captain Ross were on the spot, and that Captain Ross remarked,
in drawing it out of the tin case, which was full of water, that the mercury was close up to the index. It
fell instantly and rapidly ; hut Sir Edwakd had the same belief, that when he first looked it was close up
to the index. (See also Dr. Carpenter in Proc. Roy. Soc. vol. xvii. p. 187.)
f Yoyage for the Discovery of a North-west Passage, 1819-20, in the ‘ Hecla ’ and ‘ Griper.’ By Captain
Parry, 2nd edit, 1821, pp. 4, 5, 6, 7, 45, 115, 261, 271, 272, 273, 289, 291, 292, 293, 294, 295, 307.
+ Journal of a Yoyage of Discovery in the Arctic Regions in H.M.S. ‘Hecla’ and ‘Griper’ in the years
1819-20. By A. Fisher, Surgeon. 3rd edit. London, 1821.
§ Fisher, op. cit. p. 17.
|| Journal of a Second Yoyage for the discovery of a North-west Passage from the Atlantic to the Pacific,
performed in the years 1821-23 in H.M.S. ‘Fury’ and ‘Hecla,’ under the orders of Captain W. E. Parry.
London, 1824, p. 483.
ME. J. PRESTWICH ON SUBMARINE TEMPERATURES.
597
or one only 0o,5 less, at the bottom. As, however, there is little doubt that all these
observations in Lyons Inlet were made with Marcet’s bottle, no reliance is to be placed
on them*. In his third and last voyage of 1827 f, Parry made as many as. forty-five
observations in the seas west and north of Spitzbergen, but none exceeded 700 feet in
depth. With few exceptions, they show a lower reading than those of Scoresby. On
this occasion he reverted to the use of Six’s thermometers.
From Parry’s observing on his first voyage that his soundings were made with “ Six’s
self-registering thermometer confined in iron cases” and again, on his second voyage,
“ that he took out eight Six thermometers with iron cases” §, I was led, in conse-
quence of the low readings, to think that these cases might have been used for protection
against pressure; but Sir Edward Sabine, who was with Eoss in 1818 and with Parry
in 1819, being in the latter expedition on board Captain Clavering’s ship, the
‘Griper,’ informs me that all the observations were there made in concert between him
and Captain Clavering, and that he had with him “ half a dozen thermometers on Six’s
construction, made expressly for him by the elder Jones, each of which fitted into (and
was retained by an apparatus at top and bottom) a tinned iron cylinder pierced with holes
in the top and bottom, through which the sea-water percolated freely. .... The holes
in the top and bottom of the cylinder were rather less in diameter than a seven-shilling
piece, admitting a free current. A weight attached to the rope at some little distance
below the thermometer, caused the line to run out freely, and prevented the occurrence
of ‘ kinks ’ ” [] .
It is therefore to be presumed that the iron cases referred to by Parry were merely
to guard the instruments against accident, and not against pressure ; and on comparing
the observations made by him on board the ‘ Hecla,’ often on the same day and nearly
on the same spot, with those of Sir Edward Sabine in the ‘ Griper,’ I find them in such
close agreement as to satisfy me that such was doubtlessly the case. At the same time
* Of the 23 readings recorded, ten give precisely the same temperature at depths of 600 to 1200 feet as was
found on the surface, while the others in no instance show a difference of more than 1°, and generally of not
more than 0o,5 ; whereas an inland sea in those latitudes might he expected to show extremely low temperatures
at depths.
f Narrative of an attempt to reach the North Pole in the ‘Hecla’ in the year 1827. By Captain W. E.
Parrs'. London, 1828, Appendix vii.
X Op. cit. Introd. p. xiii. § Op. cit. Introd. p. xvi.
|| Sir Edward Sabine thus describes the mode of proceeding in making the temperature-soundings: — “The
cylinder, having the thermometer enclosed, was attached to the sounding-line, and was dropped into the sea
from the extremity of a spar run out from the side of the ship, the line to which it was attached passing round
a pulley near the end of the spar. In a similar way the cylinder when coming up from the bottom was waited
for by a boat near the end of the spar, the cylinder released, and conveyed carefully by hand in an upright
position to Capt. Clavering or myself at the gangway (or by ourselves), by whom the degree recorded by the
index was immediately noted. The record by the thermometer was then written down on the spot antece-
dently to any discussion or comment, the record being made either by Capt. Clavering or myself. The spar
from the end of which the thermometer case was dropt into the sea was always several feet distant from the
side of the ship.”
4 L 2
598
MR. J. PRESTWICH ON SUBMARINE TEMPERATURES.
there is reason to believe that thermometers of stronger make than usual, and so better
adapted to resist pressure, were used by Eoss and Parry in their voyages of 1818-19*.
The usual correction, therefore, cannot be applied to their observations of that date.
Little or none may be needed.
In 1822 Sir Edward Sabine made an observation on the temperature of the Carib-
bean Sea at a depth of 6000 feet (the actual length of rope was 7380 feet, but of this
1380 feet were allowed for slack and drift), and a reading of 450,5 F. was obtainedf.
On another occasion on this voyage, Sir Edward used a solid iron case to protect the
thermometer against pressure, but it did not prove sufficiently close to exclude water.
In 1823-26 Kotzebue commanded another voyage of circumnavigation J, and on this
occasion he was accompanied by Emil, von Lenz, who subsequently published several
important memoirs on the deep-sea temperatures and on the specific gravity of sea-
water taken on this occasion §. His observations are remarkable from their being
made at greater depths and their recording lower temperatures than any others made
up to that time, or, in fact, until long subsequently, in tropical seas. One observation,
in the Pacific, 21°T4 north latitude, indicated at a depth of 5835 feet, by his corrected
reading, a temperature of 36°*4 F., and another, 6476 feet deep, in the Atlantic, 32o,20
north latitude, gave 35°-8 F.
Although only fifteen observations were made, they were mostly at considerable depths,
and they were all taken with various precautions and subjected to careful corrections ||.
On his first voyage Kotzebue experienced so much trouble with the self-registering
thermometer, owing to the mercury passing over the index and to the shifting of the
index from jolts or shaking, that on this second voyage Lenz reverted to Hales’s
mode of taking deep-sea temperatures, using an improved apparatus arranged by Parrot,
the Kussian Academician^. The apparatus, which he termed a bathometer, was 16 inches
high by 11 inches in diameter, and held 27‘49 kil. (six gallons) of water. It had valves
at top and bottom opening upwards, and connected by a rod, to which was attached a
mercurial thermometer made specially to bear pressure, with a ball 5 lines thick.
The apparatus was covered over with four alternating layers of sheet iron and canvas,
saturated with a mixture of boiling tallow and wax, and the whole enveloped in a
cloth painted over several times. It was calculated to bear a pressure of 3000 toises
(19,150 feet), and the practice was to leave it at the bottom 15 minutes. It was
* See also ‘ Depths of the Sea,’ p. 300.
t Phil. Trans, for 1823, p. 206. See also his ‘ Pendulum and other Experiments.’ London, 1825.
t Voyage round the World. English translation. London, 1830.
§ Annalen der Physik und Chemie, Band xx. 1830, pp. 73-131; Edinb. Journ. of Science, vol. vi. 1832,
pp. 341-45 ; and St. Petersburg Ac. Sc. Bull. v. 1847, col. 65-74.
|| Physikalische Beobachtungen angestellt auf einer Reise um die Welt unter dem Commando des Capitains
von Kotzebue in den Jahren 1823-26. St. Petersburgh Acad. Sci. Me'm. i. 1831, pp. 221-334.
IF There are but few observations given in the English Translation of the Voyage (vol. i. pp. 24 & 29, and
vol. ii. p. 4), and it is not stated whether or not they are corrected. To these the name of Kotzebue is attached
in the Tables ; the others made on this voyage are ou the authority and in the name of Lenz.
MR. J. PRESTWICH ON SUBMARINE TEMPERATURES.
599
found to leak slightly ; but it was considered that the expansion of the water in coming
to the surface would compensate for this loss.
This instrument was placed in water at 67° F. (190,4 C.) until it acquired its tempe-
rature. It was then replaced with other water at 32°. Left in it for two hours, the
temperature of the water in the bathometer fell to 520,7, showing a difference, in that
time, of 14°*3, which difference Lenz further estimated would have amounted only to
7° had the apparatus passed through water ranging from 32° to 67°, instead of being
exposed to a constant temperature of 32°. Taking this as the rate of refrigeration at
given temperatures and in given time, Lenz then employed Biot’s formula for ascer-
taining the gain or loss of heat of a body placed in a medium possessing a higher
or lower temperature than itself, as the basis for calculating the correction required in
each particular observation. Corrections were also made for the depths, by allowing
on the one hand for the angle of the rope from the vertical, and on the other for the
gain in length by tension under water*.
Lenz gives a Table of his observations as originally taken, and again repeats the Table
with the corrected temperatures and depths. These two are combined in the following
Table, in which it is shown that, even with uncorrected readings, Lenz obtained on three
occasions a temperature below 4° C., while six corrected readings indicate a tempera-
ture below 3° Cent., or of from 36° to 37° Fahr.
Date.
Lat.
Long.
Depth
toises.
Angle
of
rope.
Temperature.
Time
employed
in
hauling
up the
instru-
ment.
Time
of its
remain-
ing
at the
bottom.
Corrected
observations.
At
surface.
At
depth.
Depth.
Temp.
min.
min.
toises.
1823. Oct. 10 ...
7 20 n.
21 59
w.
500
6
6
2o-8 C.
5 C.
30
15
539
2-20 C.t
1824. May 18 ...
21 14 „
196 1
„
139
10
0
26-4
16-7
6
15
140
16-36
„ >.
„
399
0
0
5-1
17
10
413
3-18
„ ».
,, j.
„
649
10
0
„
4-9
32
10
665'1
2-92
„ »
.. i.
„
„
979
25
0
„
4-6
56
15
914-9
2-44
1825. Feb. 8
25 6 „
156 58
„
179
25
0
21 '5
14
3
2
167
14-00
1825. Aug.31 ...
32 6 „
136 48
„
89
10
0
21-45
1354
4
15
89-8
13-35
„ ..
„ .i
,,
„
229
25
0
„
7-06
8
15
214
6-51
„ „
„
„
479
25
0
„
4-75
15
15
450-2
3-75
„ „
„ »
„
579
10
0
„
3-56
19
15
592-6
2-21
1826. Mar. 6
32 20 „
42 30
„
969
5
10
20-86
3-92
50
15
1014-8
2-24
1825. Aug. 24 ...
41 12 „
141 58
„
199
10
0
19-2
5-9
10
15
205
5T6
„ „
„
„
525
20
0
„
3-4
25
15
512-1
2-14
1826. Mar. 24 ...
45 53 „
15 17
192
0
0
14-64
10-56
9
15
197-7
10-36
”
” ”
383
0
0
”
10-26
13
8
396-4
9-95
t This should probably be 3° "20.
* Poggfindoeff’s Annalen der Physik und Chemie, vol. xx. 1830, pp. 78, 90, 106 ; and ‘ Bulletin Universel ’
for 1831, yoI. i. p. 275.
600
ME. J. PEESTWICH ON STJBMAEINE TEMPEEATUEES.
In 1825 an important expedition*, under the command of Captain Beechey, was
despatched by the Government round Cape Horn to the Pacific Ocean and Behring
Strait. Aided by Mr. Collie, the Surgeon, a large and valuable series of meteorolo-
gical observations were made, including ninety-seven single and serial experiments on
deep-sea temperatures in the North and South Atlantic and North and South Pacific,
ranging from lat. 56° S. to 70° N., and at depths from 30 to 5124 feet. These were
arranged in Tables according to latitude for each ocean. No very low temperatures are
recorded, but the decrease with the depth is persistent, Six’s thermometers were used,
but no particulars are given of how they were used f .
The great voyage of Admiral FitzRoy from 1826 to 1836, productive as it was of such
valuable results in other branches of science, added little to our knowledge of deep-sea
physics. Only two sets of observations, both serial, were made in the Indian Ocean at
depths of from 30 to 2500 feetj. Six’s thermometers are mentioned, but without any
other, particulars.
In 1826-29 also another important surveying and exploring expedition § proceeded
from France under the command of Captain Dumont D’Urville, aided by a staff of
scientific officers. He was instructed by Arago to pay particular attention to deep-sea
soundings and temperatures, and informed of the precautions essential in making such
observations. D’Urville proceeded from Toulon through the Straits of Gibraltar to
Teneriffe, across the Indian Ocean to Australia, New Zealand, the Eastern Archipelago,
and back by the Mauritius, the Cape, and Ascension, making observations in all the seas
he traversed, at depths varying from 50 to 6160 feet, and to the number altogether of 66,
the lowest temperature recorded being 40°. These he tabulated according to zones of
depth ; and he incorporated also in his Tables the experiments of all preceding observers,
beginning with Cook and Forster. D’Urville concluded from his observations that
in the open ocean the temperature at and below 3198 feet (600 brasses) is nearly constant
between 39° and 41° — that it might be perhaps 40° Fahr. He also supposed that a belt
of this uniform temperature existed between the latitudes of 40° and 60°. D’Urville
was evidently led to this hypothesis of a zone of uniform temperature from assuming
the greatest density of sea-water to be, as with fresh water, between 39° and 40°. His
observations in the Mediterranean confirmed those of Saussure, viz. that the wraters
of that sea, below the depth of 1000 feet, had a uniform temperature of about 55°.
In 1828 Graah made a few observations in the North Atlantic ||, but no particulars
are given of the instruments he used.
* Narrative of a Yojage to the Pacific and Behring Strait in H.M.S. ‘Blossom’ in 1825-28. London,
1831. Appendix, Table X. p. 731.
t Sir Edward Belcher, however, tells me that Captain Beechey’s thermometers “ were enclosed in copper
cases with tow above and below,” and that no protection against pressure was employed.
X Narrative of the Surveying Yoyage of H.M.S. ‘ Adventure ’ and ‘ Beagle.’ Appendix to vol. ii. p. 301.
§ Yoyage de l’Astrolabe, vol. v. of Meteorologie, Physique, et Hydrographie. Paris, 1833. Chapter III.
Physique, pp. 51*-85*.
|| Narrative of an Expedition to the East Coast of Greenland. London, 1837, p. 21.
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
601
Beeard, in 1831-32*, made another series of observations in the Mediterranean, and
ascertained that the temperature of about 55°, noted by Saussure and D’Urville at
depths of from 1000 to 3000, prevailed to the depth of 6400 feet.
I cannot ascertain precisely when protection against pressure on the thermometer was
first used. Parrot and LENzf made experiments on the effects of compression on
thermometers in 1832, and found that in ordinary instruments they were excessive ; but
this did not apply to Six’s self-registering thermometer, which from its form of con-
struction offers much greater resistance to compression.
It seems to me, however, that some form of protection must have been adopted by
the French several years earlier. It is true that D’Urville merely says that he was
provided with two of Bunten’s instruments, and makes no mention of the mode in
which they were used ; but on comparing his observations in the Mediterranean, where
the bathymetrical isotherms are at nearly constant levels, I find his results in such close
agreement with those of Aime, obtained with protected instruments, and so free from
variation dependent on depth alone, that I can only conclude that D’Urville’s thermo-
meters were likewise protected. In the same way I infer that Berard also used similar
instruments J. Thus their respective readings give : —
1826.
D’Frvilie.
Soundings fl062 ft. 54°*2 Fahr.
in the 1594 „ 54°-7 „
Mediterranean. L3189 „ 540,7 „
1831. 1840.
Berard. Aime.
3189 ft. 55°*4 Fahr. 1148 ft. 54°-6 Faiir.
3829 „ 55°-7 „
6377 „ 55°-4 „
For this reason I think it not improbable that the ocean observations of D’Urville
were made with the same precautions, and need little or no correction.
In 1839 Captain Wauchope§ recorded two more experiments made by him in 1836
in tropical regions at depths of 1800 and 3918 feet, showing respectively temperatures
of 52° and 43°. He also surmised that at a certain depth there might be a uniform
temperature of about 40° in all seas.
But the most remarkable voyage [| of the period was that of Captain Abel Du Petit-
Thouars between 1836 and 1839. This expedition sailed from Brest in December 1836,
touched at Teneriffe, Kio Janeiro, sailed round Cape Horn along the South- American
coast, thence to the Sandwich Islands, and back by New Zealand, Bourbon, and the
Cape. Fifty-nine observations were made ; but eleven failed owing to accidents with
* Berard’s observations are taken from Aimk’s paper quoted further on.
t Experiences de forte compression sur divers corps. Mem. Acad. Sci. St. Petersbourg, vol. ii. p. 595.
E. Marcet and De ea Eive (Bibl. Univ. xxii. 1823, p. 265) had before this shown the influence of atmospheric
pressure on the bulb of thermometers.
t On the ‘ Porcupine’ expedition of 1869 a uniform temperature was noted of 54°-7 to 550,5 in this area
of the Mediterranean at and below a depth of 1000 to 1100 feet. (Proc. Boy. Soc. 1870, vol. xix. p. 221.)
. § Edinburgh New Phil. Journ. vol. xxvi. 1838-39, p. 399.
II Voyage autour du Monde sur la Fregate ‘ La Yenus,’ Capitaine Du Petit-Thouars. Paris, 1844. Physique,
par M. nE Tessan, vol. ix. Tables, p. 385.
602
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
the instruments, and twenty gave wrong readings owing to the great pressure forcing
water into the cylinder. Amongst the successful observations, two at a depth of 6600
feet in the Pacific, and of 6000 feet off the Cape, recorded temperatures of 360,1 and
370,4 ; a third in the North Atlantic, lat. 40,23 and 6406 feet deep, gave 37°*8 F. ; while
another, at a depth of 12,271 feet near the equator in the Pacific (on which occasion
the cylinder was crushed by the pressure and the instrument broken, and the index
jammed and fixed), gave a reading of 34°*8 or 35°Fahr.
This was the first voyage in which precautions against pressure were systematically
and professedly taken ; instruments of special construction were provided. The form
adopted was Six’s thermometer, modified by Bunten, of Paris. They were enclosed
in strong brass cylinders* to protect them from pressure, and they were always left down
for half an hour. After the return of the expedition the thermometers were tried with
a standard instrument, and found to have a reading only yu to of a degree Cent,
higher than on starting. It was found, however, that the cylinder would not bear a
pressure of more than about 12,000 feet; and that at all depths it was occasionally
filled with water. In these latter cases Du Petit-Thouars used a correction of which
we shall speak presently, and gives the corrected with the uncorrected reading.
Corrections were also made for the angle the rope took with the vertical. There is
therefore every reason to suppose that the deep-sea temperatures obtained on this
voyage may be accepted as perfectly reliable.
The ‘ Bonite,’ under the command of Captain V a tel ant f, was also despatched from
France in 1836 to the Indian Ocean, Chinese seas, and the Pacific. Sixteen obser-
vations in the Atlantic and Indian Oceans are recorded at depths of from 244 to
8838 feet. The ‘ Bonite ’ was likewise provided with Bunten’s thermometers. They
were wrapped in wool and placed in a glass tube, which again was enclosed in a copper
cylinder closed by a screw at each end, and left down 18 to 20 minutes. In the first
deep sounding (700 brasses) recorded the cylinder is stated to have come up full of
water. This throws doubt on all the subsequent experiments ; and as no reference at
all is made to the state of the cylinder in the other soundings, and the readings are
more concordant with the “full cylinder” ones of Du Petit-Thouars, I think a
correction should be applied to all his deeper observations. A large number of surface-
temperatures were taken, and it was remarked again that in the Pacific the sea is more
frequently warmer than the air, except under the equator.
Another voyage J of research was undertaken by France in 1838 to the Arctic seas,
* Du Petit-Thouars gives no particulars of the construction of his instruments ; but Arago, in his report
of the results obtained on this voyage, speaks of the “ therm ometrographe de M. Punter enferme dans un etui
cylindrique en laiton de 33-4 mill, de diametre interieur et de 15-6 mill, d’epaisseur,” which I presume refers
to Du Petit-Thouars’s instruments. — Comptes Eendus, 1840, vol. xi. p. 311.
t Yoyage autour du Monde sur la Corvette ‘ La Bonite,’ Capitaine Yaillant. Geol. et Miner, par M. Che-
vxlier, pp. 232, 390-1 ; and Physique, par. M. Darondeau, ‘ Observations Meteorologiques.’
t Y oyage en Scandinavie et au Spitzberg de la Corvette ‘ La Eecherche.’ Geographie et Physique, vol. ii. p. 279.
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
603
and a series of twenty-three interesting experiments were made by MM. Martins* and
Bra vais between the North Cape and Spitzbergen, and off the west coast of that island,
in depths of from 200 to 2460 feet.
The principle of overflow differential thermometers had been revived by WALFERDiNf
in 1836 — a maximum one for the purpose of taking the higher temperatures of deep
wells and mines, and a minimum one for deep-sea soundings. These instruments were free
from the inconveniences of Cavendish’s, were of easy manipulation, and could bear jerks
without affecting the registering column of mercury. To protect them against pressure
they were enclosed in a tube of glass, of thickness proportional to the pressure to which
it would be exposed, and hermetically sealed at both ends. M. Walferdin claimed
for these thermometers greater accuracy and certainty than the ordinary self-registering
thermometers J.
These thermometers, termed “thermometres a deversement,” were used by Martins
and Bravais on their voyage to Spitzbergen, in conjunction with Six’s thermometers
(thermometrographes) modified by Bunten, of Paris. The former were enclosed in
glass tubes exhausted as much as possible, and the latter in copper tubes, evidently
not strong enough, as they “almost always came up full of water.” To ensure accuracy,
they employed in all these observations two instruments of each sort, and in some cases
as many as four, and took the mean of each set. When sunk to the bottom they were
raised 1 metre from it, and left there for an hour. Sometimes the thermometrographs
were not protected ; and in that case, or when the tubes were full of water, a correction
was applied, of which we shall speak further on. A correction was also used for the
angle of the rope with the vertical. M. Martins states that he had much more confi-
dence in Walferdin’s thermometers than in Bunten’s. I find, however, that, taking
the 18 observations made with sets of the former, the average variation for each set
amounted to 0O-45 Cent., or, averaging the variation of each of the 52 instruments
employed, to 0°T6 C., while the 10 observations with 23 instruments of the latter give
respectively 0°T8 C. and 0o,08 C. ; but M. Martins shows that while the mean of the
differences is 0°T9 C. at depths not exceeding 131 metres, it is reduced to 0o,06 C. at
depths of 640 to 870 metres. The readings, on the whole, of Walferdin’s instru-
ments are very slightly lower than those of Bunten’s ; as they were more relied on by
the observers, I have given them in the Tables in preference to the others.
But notwithstanding the successful use of Walferdin’s instruments on this voyage,
* Voyage de £ La Eecherche,’ Geogr. et Phys. vol. ii. (Memoire sur les Temperatures de la Mer Glaciate a la
surface, a des graudes profondeurs, et dans le voisinage des glaciers du Spitzberg, par M. Charles Martens)
pp. 342-5. Tableau IV. f Bull. Soc. Geol. de France for 1836, vol. vii. pp. 193 & 354.
t He instances a case of a well at Saint-Andre where, at a depth of 830 feet, two of his instruments gave
170,96 C. and 170,93 C. respectively; whereas two self-registering instruments gave 19°-2 C. and 16°-8. The
latter were affected both from water getting into the case and from lowering of the index by shaking. In
another case, two of his instruments both registered 230,5 C., and two thermometrographs 23°-45 and 23o-50,
while another of the latter had its index displaced by the shaking of the line. — Ibid. vol. ix. p. 255, vol. xii,
p. 166, and vol. xiii. p. 113.
MDCCCLXXV. 4 M
604
ME. J. PRESTWICK ON SUBMARINE TEMPERATURES.
and the mention of them approvingly by Pouillet* and ARAGof, I cannot find that they
were again used, although a modified form contrived by M. Aime was employed by him
in his researches in the Mediterranean in 1840-44.
In 1838 a few observations were made in the Indian Ocean by the Rev. J. H. Pratt J.
An American expedition made the round of the world in 1839-42 under the command
of Captain Wilkes, who gives twenty-eight § deep-sea temperatures at depths of from
60 to 5100 feet in the South Pacific and Southern Oceans, in one case recording
a temperature of 270,5 at a depth of 1420 feet in the latter sea. The subject was
afterwards [| further discussed by Captain Wilkes in a separate paper, in which he
expressed an opinion that there existed a zone of the uniform mean temperature of
390-5 Fahr. It would appear that Six’s thermometers without protection were used.
In the same year (1839) a very important expedition was despatched from this country
to the Antarctic seas under the command of Captain Sir James C. Ross. A special
code of instructions was drawn up by a Committee of the Royal Society. Numerous
results of great value were obtained, especially those relating to the soundings and sea-
bed of the Antarctic Ocean. As many as 161 deep-sea temperature-observations are
recorded, chiefly in the Southern and Antarctic Oceans, with a few in the Atlantic and
Indian Oceans % They vary in depth from 12 to 7200 feet; some of the soundings
were much deeper.
These temperature-soundings claim particular notice in consequence of the undue
weight which has been attached to them. In starting Sir James Ross took with him
a supply of Six’s thermometers ; but he gives no description of how they were used, or
what precautions were adopted **. The observations also are not tabulated, but are
scattered through the work without plan or order ; and it is at times difficult to fix
on their exact position, date, &c. It would appear that, owing to want of protection
and the great depths at which they were used, all the instruments he took with
him from England were broken by the time he reached the Southern Ocean.
* Elements de Physique, 5th edit. vol. ii. p. 653. f (Euvres completes, vol. mi. p. 626.
t London and Edinb. Phil. Mag. 1840, vol. xvi. p. 176.
§ United States Exploring Expedition, 1839-42. London, 1845, vol. i. pp. 137, 139, 230, 309, 310 ;
vol. ii. pp. 290, 293, 299, 332 ; and vol. iii. Appendix I.
|| “ On the Depth and Saltness of the Ocean,” American Journal of Science and Arts for January 1848, p. 41.
*[[ A Voyage of Discovery and Research in the Southern and Antarctic Regions. London, 1847, vol. i.
pp. 34, 130, 166, 167, 168, 170, 180, 200, 222, 231, 267, 280, 306, 309, 313, 317, 321 ; and vol. ii. pp. 35,
52, 53, 55, 133, 138, 140, 141, 147, 156, 193, 195, 200, 214, 216, 227, 228, 282, 322, 351, 356, 358, 363,
369, 374, 379, 382, 384.
** Dr. Hooker, who accompanied the expedition, informs me that no precautions were taken against pressure,
hut that to prevent breakage “ the thermometers were enclosed in a copper cylinder. Sometimes two thermo-
meters were placed at different points of the same line (say 500 and 1000 fathoms), at others the line was
drawn up and sunk again to a greater or less depth. The first fathoms of the line were spun yarn, the next of
3 plies of the same, the rest whole line.” It was hauled in by the whole ship’s company. Dr. Hooker also says
“ that the average length of time, speaking entirely from memory, during which the thermometers were left at
the depths reached was a quarter of an hour.”
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
605
He then wrote to England for stronger registering thermometers, which were sent to
him in Australia, but of which he gives no particulars further than stating that they
were stronger. Before receiving these, he apparently renewed his observations with
instruments obtained in Australia. Consequently it is probable that each of these sets
of instruments were of different construction, and may require a different correction —
those used during the first part of the voyage a larger correction than those used during
the latter period. In the absence of sufficient information this cannot be attempted ;
and the general formula given further on has been applied to the correction of all his
observations I have had occasion to use in the construction of the sections.
With regard to the observations themselves, they may be also sometimes open to
objection in consequence of the great difficulties under which they were so constantly
taken. The severe cold, the inclemency of the weather, and the tediousness of the
operation are all elements of possible error to be taken into account. The one cause
may have led at times to the shifting of the index, and the other to some want of accu-
racy in the reading ; for I cannot conceive it possible for any set of thermometers to have
recorded, in the innumerable cases mentioned, the same one and uniform temperature
of 39°‘5 at and beyond a certain depth. Even supposing a uniform temperature of that
exact degree did exist at certain determined depths, it is in the highest degree impro-
bable that any instruments would give the exact same record. There is not only the
risk of shifting of the index, but there is the certainty that the ordinary imperfection
and variation of the instruments would most certainly prevent it. With the greatest
care and with standard instruments especially selected, MM. Martins and Bravais, out
of ten sets of observations each made with two, three, or four thermometers, only give
one instance in which the readings of two of them agree. In the other cases they
differ from 0°T to 1° Fahr.
Nevertheless, apart from this point, and supposing them to be approximately correct,
the observations of Sir James Boss are, from their number, depth, and position, very
valuable, and, subject to correction, they furnish fairly available results, although,
from the cause before mentioned, it may not be certain whether the correction applied
gives the true reading in all cases within one, two degrees, or in some cases possibly
more. Owing also to this use of unprotected instruments Boss came to the same con-
clusion as D’Urville with respect to the existence of a zone of a uniform surface-
temperature in given latitudes, and likewise with respect to the persistence of the same
uniform temperature of 390,5 Fahr. at given depths in the great oceans. In this opinion
he seems to have been biassed, similarly with his predecessors, by the belief that the
density of sea-water was, like that of fresh water, greatest at that temperature.
In 1840-44 M. Aime made a series of important observations on the temperature of
the air and sea between Marseilles and Algiers*. The experiments, which were carried
on for a series of years, proved that the diurnal variations of temperature in the Medi-
* “Memoir© sur la temperature de la Mediterranee,” Annales de Cliimie et de Physique, 1845, 3me ser.
vol. xt. p. 1 ; and Comptes Eendus for Sept. 1844.
4 m 2
606
ME. J. PEESTWICH ON STJBMAEINE TEMPEEATUEES.
terranean ceased at a depth of 60 feet, and the annual variations at a depth of from
1150 to 1300 feet. At this point Aime found a uniform temperature of 54°-7, and
was of opinion, from the observations of Berard, that no increase took place at greater
depths. This degree he showed to be the average of the mean temperature between
Toulon and Algiers, of the months of January, February, and March.
In order to determine whether the decrease of temperature was gradual, or whether
the instrument passed through warmer strata, Aime also used a thermometer which
was let down upright and reversed at the bottom of the soundings. This he termed
a “ thermometre a retournement.” Besides these, Aime employed the ordinary self-
registering thermometer with an enlargement in one part of the tube to remedy the
inconvenience of the quicksilver passing over the index. These several instruments
were enclosed in copper cylinders strong enough to resist the pressure to which they were
subjected. For moderate depths he preferred a glass tube hermetically sealed * * * §.
In 1845 Captain (now Admiral) Spratt made 15 observations f from the surface to
a depth of 1260 feet, in the Grecian archipelago, and obtained results in perfect
accordance with those of Saussure and Aime in the Western Mediterranean. He
afterwards made a more extended series of observations (34 in all) and to greater depths
(7440 feet) in the eastern basin of the Mediterranean from Malta to Egypt J. Admiral
Spratt at first used Six’s thermometer ; but finding that the index often moved, he
resorted, in shallow seas of the archipelago, to the plan of taking the temperature of the
mud brought up from the bottom by means of a sound formed of iron tubing. This plan,
Admiral Spratt considered, gave more reliable results than the other. In every case in
Forbes’s Yll.th zone, or between 1080 and 1200 feet, the mud indicated a temperature
of 55°*5 ; and he concluded that there was no reason to suppose the temperature to be
lower than 55° at any depth under 1800 feet. In the deeper waters he reverted to the
use of Six’s thermometer.
Captain (now Admiral Sir Edward) Belcher gives a series of eight observations he
made in mid-Atlantic when crossing the equator in 1843, at depths of from 1800 to
6000 feet§. Sir Edward informs me that a much larger number were made, but that
they were not published at the time and have been unfortunately lost, with the exception
of the few others recorded by Sir James Ross||. Sir Edward Belcher also mentions
that he had a water-bottle of great strength, with two enclosed thermometers specially
made by Carey, and that these instruments “ were tested continuously between 1835
and 1846, and never found to vary from each other or from the standard which I
[Sir E. B.] now possess, and which belonged to the Old Board of Longitude. They
* Eor a description of his instruments see op. cit. Ann. Chim. et Phys. pp. 6-12.
f Phil. Mag. for 1848, p. 169.
± The Nautical Magazine for 1862, p. 9. Admiral Spkatt has also obligingly communicated to me the
twenty-two unpublished observations to which is attached “ u ” in the Tables.
§ Narrative of the Yoyage of H.M.S. ‘ Samarang’ during the years 1843-46. London, 1848, vol. i. p. 9.
|| Antarctic Yoyage, vol. ii. p. 53.
ME. J. PRESTWICK ON SUBMAEINE TEMPERATURES.
607
were out in 1852-54, exposed to all the Arctic variations of temperature, and are still
perfect. They were made to go inside the water-bottle, and not subjected to jerks of
the line, which we found often moved the indices”* * * §.
In 1845-51 Captain Kellett, in his voyage f to the Pacific and Behring Strait, made
38 observations to depths of 3000 feet, several of them serial, some in mid-Atlantic,
others in the Pacific, ranging from near the Equator to Behring Straits, and seven in
the Arctic Ocean beyond. Six’s thermometers without protection were used.
Lieutenant (afterwards Commander) Dayman, who served on the surveying-ship
‘ Rattlesnake,’ made a series of one hundred and ten observations in the Atlantic,
Indian, and Southern Oceans, at depths generally of from 1000 to 2000 feet J.
While the readings given by other observers who used unprotected self-registering
thermometers agree fairly well among themselves, those recorded by Dayman are much
higher in proportion. But as he gives no particulars of his instruments, or of the mode
in which they were used, it is- not possible to say how the difference arises or what the
error may be ; it seems uniformly too high by 1° or 2°. There are also anomalies in
the lists, which leads me to suppose that the readings of the lesser and greater depths
have sometimes been transposed. The readings, however, have a certain independent
value inter se as furnishing comparative temperatures at corresponding depths.
Sir A. Armstrong §, who was with Captain McClure on his memorable voyage along
the coast of Arctic America, records three observations made on the voyage out round
Cape Horn, and three in the Arctic Ocean after passing Behring Strait. No mention
is made of the thermometers, except that they were Six’s “ self-registering.”
In the series || of “Reports” to the Government of the United States much valuable
information is given with respect to the temperature of the seas off the North-American
coast, and especially of the Gulf-stream at various depths. As the original observations
are, however, not recorded, but only the diagrams founded on them, I am unable, with
two or three exceptions, to give any tabulated details, and must refer to the “ Reports ”
themselves for fuller information. Owing to the depth of the Gulf-stream off the
American coast, the lines of bathymetrical isotherms lie at very variable depths. The
* With respect to the mode of conducting the observations. Sir Edward Belcher says, “ The deep-sea tem-
peratures were observed only in calms. The thermometers were all handled by myself, and eased overboard
with the greatest care. The hauling-in was not subject to jerks, as it was done by the aid of a boat astern,
the ship drifting by currents, sometimes one to two hundred fathoms from the boat, and great caution observed
in getting them detached (by myself) and read off instantly.”
t Yoyage of the ‘Herald,’ Captain Kellett. By Berthold Seehan. London, 1853, vol. i. pp. 7, 92, 94,
vol. ii. p. 107.
+ Narrative of the Yoyage of H.M.S. ‘ Rattlesnake,’ Captain Stanley, 1846-50. By John Macgillivray.
London, 1852. Appendix I. vol. i. ; and Edinb. New Phil. Journ. for 1852, vol. lii. p. 267.
§ A Personal Narrative of the Discovery of the North-West Passage, by Alexander Armstrong, M.D.,
R.N., H.M.S. ‘ Investigator,’ Captain McClure, 1850-54. London, pp. 19, 43, 65, 150, 216.
|| See Report of the Superintendent of the United States Coast Survey for 1854, by Professor Bache.
Also those for succeeding years.
608
ME. J. PRESTWICK ON SUBMARINE TEMPERATURES.
stream forms, as is well known, a trough of warm water, from below which the cold
water rises up as a wall in approaching the coast.
Captain Maury has given* incidentally a few deep-sea temperatures made by the
U. S/Coast Survey (Dunsterville, Brooke, and Rodgers) during the few years previous
to the publication of his work ; but it is a subject which he does not treat so fully as other
points of ocean physics. It is not stated what instruments were employed.
On the voyage of H.M.S. 4 Cyclops’ in 1857, forty-one important observations were
made by Captain Pullen in the North and South Atlantic, Indian Ocean, and Red Sea, at
depths of from 2400 to about 16,000 feetf. It was on this voyage that the first regular
precautions against pressure were taken in this country. Captain Pullen was furnished,
by order of the late Admiral FitzRoy, with some instruments constructed purposely for
deep-sea observations, the object of which was explained in the following memorandum,
communicated to me by Captain Pullen : —
“ In Six’s self-registering thermometer, the long bulb, filled with spirits of wine, is so
delicate, that under a great pressure of ocean it is more or less compressed, and drives
the spirit against the mercury, which is thus acted on not only by temperature, but by
the mechanical pressure of sea-water.
“ With a view to obviate this failing, Messrs. Negretti and Zambra undertook to
make a case for a we&k bulb, which should transmit temperature, but resist pressure.
“ Accordingly a tube of thick glass is sealed outside of the delicate bulb, between
which and the casing is a space all round, which is nearly filled with mercury.
“ The small space not so filled is a vacuum, into which the mercury can be expanded,
or forced, by heat or mechanical compression, without doing injury to, or even com-
pressing, the inner and much more delicate bulb.
“This provision is meant to guard against possible compression of even the outer
glass, strong as it is.
“ One may ask, Why not strengthen the inner tube, the bulb, at once, so as to be
equal in power of resistance to the outer casing ? Mr. Glaisher and the makers say
no ; the bulb will yield a little, on account of its length, be it even as strong as the
outer case. (Signed) “ Robert FitzRoy, Admiral.
“May 19th, 1857.”
With these instruments Captain Pullen made a series of observations, and was the
first in this country to confirm the observations of the continental observers that so low
a temperature as 35° existed in the depths of intertropical seas. In reply to my inquiries,
Captain Pullen informs me that, after comparing the deep-sea thermometers with
standards kept on deck and setting the indices, “ they were placed in copper cylinders,
* The Physical Geography of the Sea. By M. T. Maury, LL.D., U.S.N., 11th edit. London, 1857, pp.
53, 261, 263, and Appendix, p. 351. The last edition of 1874 gives no new facts.
t Twelve of these are given in Proc. Roy. Soc. vol. ix. p. 189, and the others are abstracts from
Captain Puuleej’s MS. Journal, of which he has kindly given me the particulars ; to these latter “ u” is attached
in the Tables.
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
609
with a valve at each end both opening upwards, so that on going down a column of
water passed through. On arriving at the depth, and you commence hauling in, these
valves close, thus cutting off a portion of water at that depth, which was brought up
and tested for density and its then temperature. Indices read off both from maximum
and minimum scale and noted. But I have often- found that the maximum index
shifted, showing a different reading from what it stood at when started. Now whether
this would affect the minimum side is a question.”
Captain Pullen thinks not. But there are inequalities in some cases so apparent
that they can hardly be accounted for, except by a shifting of the index. In one
instance, in fact, while the thermometer at 7890 feet indicated 41°*, the index, owing
to rough weather, had shifted to 67° at a depth of 11760 feet. Captain Pullen speaks
also of some of the instruments being more regular in their indications than others.
After, however, eliminating those readings, which are evidently too high (marked with
a ] in Tables), the value of the other observations remains unaffected.
The Austrian Expedition of the ‘Novara’ in 1857-60 j*, under the command of
Admiral Yon Wullerstorf, made an extraordinary number of daily meteorological
observations, from which it is difficult to extract the few scattered notices respecting the
temperature at depths. Although they amount to 33 in number, they are mostly at
depths under 1000 feet, and none exceed 1500 feet. They embrace eleven observa-
tions in the Mediterranean to depths of not more than 760 feet.
It was apparently on this occasion that the water-bucket was last used. All that is
said on the subject is that “ for these observations a wooden cylinder furnished with
valves was generally employed; but an English apparatus has also frequently been made
use of, which consists of a similarly constructed copper cylinder, with an easily affected
maximum and minimum thermometer, so that by it water was not only brought up from
a depth, but also the highest and lowest temperatures of the layers of water through
which the sounding was made were ascertained.” No other particulars are given, and
no mention is made in the several observations of which instrument was used. Wul-
lerstorf’s observations, as I read them, differ so greatly from those of other observers,
that I can only attribute it to some undetected source of error. The readings seem
much too high and out of proportion with the others ; but still they have a certain
value in their comparative temperatures.
In 1859 Captain KundsonJ made four temperature-soundings between Iceland and
Greenland, at depths of 1200 to 1800 feet; and in 1861 Dr. Ed. Lenz§ records a
* In two other cases also the hottom-temperature is recorded as higher than those at lesser depths.
f Eeise der osterreichischer Eregatten ‘Novara’ urn die Erde in 1857-59. Wien, 1862. Naturw.-phy-
sikalischer Theil, 139-449.
+ “ "Voyage of the War Brig ‘ Queen’ from Iceland to Greenland,” in the Papers translated for the Hydro-
graphic Office, Washington, 1871.
§ Meteorologische Beohachtungen auf den Atlantischen und Grossen Ocean an den Jahren 1847-49. Angestellt
von dem Dr. Ed. Levz, berechnet von E. Lenz. Nov. 1861. Bulletin de l’Academie Imp. des Sciences de St.
Petersbourg, tom. v. p. 129 (1863).
610
ME. J. PRESTWICH ON SUBMARINE TEMPERATURES.
series of observations made in the North and South Atlantic, at a uniform depth of
360 feet, the importance of which consists in showing, as Horner and Kotzebue had
previously done, that near the equator the water at and beneath the surface is colder
than a few degrees further north and south. Six’s self-registering thermometers were
used. No protection mentioned.
Dr. Wallich* gives, in 1862, one temperature-observation at a depth of 600 feet,
on the well-known occasion of the deep-sea soundings between England and America.
Between 1860 and 1868 the several other expeditions undertaken to obtain deep-sea
soundings in different parts of the world for telegraphic purposes afforded favourable
opportunities for temperature-observations. Such were those obtained in 1868 by Capt.
SHORTLANDf between Bombay and Aden, which are recorded in a series of means. They
extend in one case to the depth of 13,020 feet, and give a reading of 33°*5, and in
another, more westward, to 7800 feet, with a reading of 36°. These readings have, I pre-
sume, been corrected from the original observations.
Again, in 1868 Commander Chimmo $ made a series of observations on the American
side of the North Atlantic, at depths extending to 12,000 feet, and recording tempe-
ratures of 42°. It is merely stated that the experiments were made with “new and
delicate thermometers,” which were without protection, and the readings are un-
corrected.
In August 1868 the 4 Lightning ’ sailed on the first of that series of deep-sea researches
which, conducted under the combined superintendence of Dr. Carpenter and Professor
Wyville Thomson, with the addition afterwards of Mr. Gwyn Jeffreys, and followed
up systematically in subsequent voyages, have already yielded sudi valuable and impor-
tant information on the natural history and physics of the depths of the sea.
Regarding the relative merits of the several methods employed by the early observers,
a few words may be said. The water-bucket, when properly constructed, of sufficient
size, and when well handled, was not badly contrived to determine the temperature at
moderate depths. It was free from the errors of pressure and index to which thermo-
meters are liable. The errors depend upon the size of the apparatus, the proper
closing of the valves, the rapidity of hauling in, and the difference of temperature
between the bottom- and surface-waters. When the latter is not great the error can
be but small ; and such is the case in those Arctic seas where it has been chiefly used.
As so considerable a number of observations were made with this apparatus by Scoresby
and Franklin, it might be desirable to determine by experiment the amount of correction
required to adjust the error of this particular apparatus.
In the case of Lenz’s bathometer, he made a series of experiments to determine
* The North- Atlantic Sea-Bed, 1862, p. 145.
t Admiral Sherabd Osborx, “ On the Geography of the Bed of the Atlantic and Indian Oceans and Medi-
terranean Sea,” Journ. Roy. Geogr. Soc. 1871, vol. xli. p. 58.
I Proc. Roy. Geogr. Soc. 1869, vol. xiii. p. 92.
ME. J. PRESTW1CH ON SUBMARINE TEMPERATURES.
611
the corrections necessary for his several observations. He showed that a variety of consi-
derations have to be taken into account with Hales’s water-bucket or any similar appa-
ratus, and that the scale of corrections must vary with the latitude and the depth.
Thus in lat. 21° 14' N., with a surface-temperature of 79°-5 F. and at a depth of 2635 feet,
his corrections amounted to 4° F., while in lat. 45° 53', with a surface-temperature of 58°*3
and at a depth of 2524 feet, they amounted only to 0O-6 F., and, again, for the lesser
depths of 898 and 1252 feet in the same latitude respectively to 0O-4 F. and to 0o,6 F.
The same corrections cannot, however, be applied to the observations of Ellis, Cook?
Forster, Irving, Scoresby, Franklin, and Wauchope ; for in the case of the first three
and of Franklin the apparatus was not protected by any other non-conducting sub-
stances ; in the case of Wauchope’s and Scoresby’s later experiments the correction
must be applied to the enclosed Six thermometer ; and in Irving’s the small size o^
the apparatus, although protected, necessitates a larger correction. It is, nevertheless,
satisfactory to note, from the regular decrease in the value of the corrections from the
equator to the pole, that in the higher latitudes, where Hales’s apparatus has been most
used, the special corrections needed for that apparatus diminish to their minimum, and
are so small that probably 0o,5 to 1° would cover all the errors of observation made by
the foregoing explorers. The main error for correction is that due to pressure in those
instances where a Six’s thermometer has been used in conjunction with Hales’s appa-
ratus.
The second plan, that of sinking an ordinary thermometer, protected and surrounded
by some substances which are bad conductors, has been but little used, as it requires so
much time. Independently of this, and for moderate depths, it is trustworthy and
useful, and some of the results, as those of Saussure, may be accepted as closely accurate.
The third plan, that of taking the temperature of mud or silt brought up from the
bottom, has the advantage that it secures the possession of a body having the exact
bottom-temperature ; but it has the disadvantage of small bulk, and therefore of being
more influenced by the temperature of the water through which it has to pass. For
moderate depths, however, the error can only be small.
The first and last of these methods, whatever their inconveniences, had but one main
source of error — causing a gain where the surface-temperature is higher, and a loss
where lower, than that at depths. Only in one instance, however, was the necessary
correction accurately estimated. But with the introduction of the self-registering ther-
mometer two sources of error (the one occasional and uncertain in amount, arising from
shifting of the indices; and the other fixed and definite, resulting from pressure)
were introduced. Owing also to the want of standard instruments, the observations
made on the several voyages have had in themselves different degrees of value, dependent
on the care with which the instruments were made, and on the precautions with which
they were used. As such precautions were, it is evident, usually enforced, and Admi-
ralty instruments were generally used, a considerable uniformity of result has been
nevertheless maintained ; and the readings on the different voyages agree sufficiently
MDCCCLXXV. 4 N
612
MR. J. PRESTWICH ON SUBMARINE TEMPERATURES.
well amongst themselves to allow, with reasonable success, of the application of the
same correction to all, excepting those of Dayman, and perhaps one or two others, which
require larger corrections, and Wullerstorf’s, which are uncertain.
With these few exceptions, and admitting slight qualifications for each particular case,
the larger number of the early observations may, subject to a correction for pressure, be
accepted as approximately accurate. The need of this correction for pressure was, as I
have before observed, noted so early as 1823; but it was not until the voyage of ‘La
Venus ’ that the necessary precautions were professedly taken against it, and that expe-
riments were made to estimate its amount. Such estimates were then made by Du Petit-
Thouars in tropical seas, subsequently by Martins and Bravais in arctic seas, and after-
wards by Aime in an inland sea. The results of the several calculations are as follows : —
Du Petit-Thouars made experiments with a protected and an unprotected thermo-
meter at a depth of 1000 brasses or 1620 metres, which is equal to a pressure of 162
atmospheres, and he was led to adopt a coefficient of 0o,01 Cent, per atmosphere as the
measure of correction needed for unprotected thermometers. This gives 1° C. per 100
atmospheres, or of 1°*8 F. per 3200 feet, or 1° Fahr. = 1780 feet.
Ch. Martins concluded from his experiments, which were on a more limited depth,
that a coefficient of 0°T3 Cent, per 100 metres, or of lo,30 C. per 1000 metres* (equal
to 20,3 Fahr. per 3280 feet, or 1° for every 1426 feet), was required.
Aime, again, from experiments in the Mediterranean with his special thermometro-
graphs, came to the same conclusion as Du Petit-Tiiouars, viz. that for the pressure of
every 100 atmospheres the instrument required a correction of about 1° Cent.
These conclusions agree very closely with the more recent researches of Dr. Carpenter
and the late Dr. Miller. The latter showedf that under a pressure of 2-^ tons (or 374
atmospheres) per square inch, Six’s unprotected self-registering thermometers of three
different constructions gave readings from 7°*5 to 10° Fahr. too high. Excluding the
effects of the small amount of heat evolved from the water by compression (or some
undetermined cause), which was found equal to 0o,9, the mean error ^of the three was
80,6 F. — 0O-9 = 7O-7 ; and, taking the pressure of one ton as equivalent to a depth of 800
fathoms, this would be equal to a rise of 1° F. for every 1560 feet. But in those expe-
riments one instrument (Six’s, with a spherical bulb) gave a variation of 2° in excess of
the one with cylindrical bulb and of the Admiralty instrument. Now, as the two latter
are of the forms almost always used, and Bunten’s instruments had also a cylindrical
bulb, it is a question whether the one with spherical bulb should not be excluded. In
that case the reading of the other two gives a mean of 8°F. — 0o,9 = 7°T as the error for
pressure of 2-| tons, or equal to 1° Fahr. for every 1690 feet.
It is true that considerable variation was found to exist in the effects of pressure on
* M. Martins took the differences between each of the protected and unprotected “ thermometrograph.es,”
and these he diminished in each case by 0°T, — “ quantite egale a la poussee de l’index.”
t Proc. Roy. Soc. for 1869, vol. xvii. p. 485 : see also Proc. Roy. Soe. for 1870, vol. xviii. p. 409 ; and Com-
mander Dayis, R.N., ibid. p. 347.
MR. J. PRESTWICH ON SUBMARINE TEMPERATURES.
613
some other instruments ; but with the care taken in the construction of our best ther-
mometers, and of those of Buntef, which were generally employed, the chances of
greater variation than that here indicated are reduced to a minimum*.
The foregoing estimates show that with good instruments the effect of pressure equals
an increase of about 1°F. for every 1400 to 1800 feet of depth ; and in adopting a coeffi-
cient of 1° F. for every 1700 feet as the necessary correction of all the observations in the
Tables, excepting those made with protected instruments or corrected by the original
observer, and excepting also those before named as requiring larger corrections in con-
sequence of using unfit or unsuitable instruments or instruments of a different class, I
feel that I am below rather than above the true measure of allowance.
§ III. Summary of the preceding Observations.
Although the early observers noted the decrease of temperature with the increase of
depth, it was not until 1823-26 that Lenz proved that this decrease held good to the
greater depths of temperate and tropical seas, and that the water at depths in the open
oceans was but little above the zero of Centigrade.
The substitution of the self-registering thermometer for the older methods led for a
time, owing to the neglected error of pressure, to a retrograde course ; for the voyages
of Beechey, Kellett, and others which followed between 1826 and 1836, while they
added largely to the number of observations at greater depths, gave, in so doing,
increased importance to the error, from the circumstance that the pressure on the
instrument not only counterbalanced the effect of the greater cold at increased depths,
but often gave readings (uncorrected) somewhat higher at those depths than at lesser
ones. From this cause, and from inattention to the different properties of sea- and
fresh water, an erroneous conclusion was drawn from observations otherwise valuable,
which for a time greatly retarded the progress of ocean physics.
The first to fall into this error was D’Urville, who, misled by the coincidence of
temperature obtained by him in some of his deepest soundings, and of the nearly like
minimum temperature (4° to 5° C.) so frequently recorded (with his unprotected ther-
mometers) by Beechey and others at greater depths, concluded, in ignorance apparently
of Lenz’s observations, that this uniformity of temperature was the result of a general
* With, respect to these variations, Dr. Carpenter, after speaking of the results obtained on the ‘ Porcupine ’
expedition with the Mtller-Casella instrument, observes: — “With these results, obtained with thermometers
upon which complete reliance can be placed, those obtained last year with the best ordinary thermometers are
found to be in close accordance, when the proper correction for pressure is applied to them.” He then instances
two cases in which experiments were made on both expeditions at nearly the same places and in nearly
similar depths. In one case, at a depth of 550 fathoms, the difference exceeded the estimate by about 1°,
in the other, at a depth of 550 fathoms, it amounted to 2°-2 E., or was “ exactly equivalent to the correc-
tion for pressure at that depth in the unprotected thermometers.” Dr. Carpenter concludes : — “ This very
near accordance gave us, of course, a feeling of great satisfaction in our last year’s work; and it fully justified
our conclusion that, whatever might be the pressure-correction required by the instruments then employed, it
would not affect the differences obtained at nearly approximating depths.” (Proc. Roy. Soc. vol. xviii. p. 455.)
4 N 2
614
ME. J. PRESTWICK ON SUBMARINE TEMPERATURES.
law dependent on the maximum density of water, which he supposed to be alike in
fresh and salt water; and he consequently assumed that a temperature of about 4°-4 C.
(40° F.) prevailed below a certain depth in open seas*, and that in both hemispheres
there was in certain latitudes a zone from the surface downwards of like uniform
temperature f.
On the other hand, we have seen that in 1836-39 Du Petit-Thouars fully confirmed
the observations of Lenz, that a temperature of from 35° to 37° existed at depths in both
the great oceans. Arago, in commenting on these results, testifies to their accuracy
and importance, and remarks that “ the observations collected by the ‘ Venus ’ will
occupy a distinguished place, on account of their number and exactness, and of the
great depths at which they were taken.” He also observes that, low as some of the
readings are, yet all errors must be positive, and that they place on reliable grounds the
great fact of the prevalence of the same low temperatures at depths in the Pacific as
well as in the Atlantic, and in the equatorial regions of both oceans ; and he especially
dwells on the circumstance that they tend effectually to disprove the hypothesis which
had been advanced, that at great depths there existed a uniform and common tempe-
rature of 40°F.$
It appears, nevertheless, that so little was known of what had already been done and
written, that Sir James Ross fell into the very same errors as D’Urville had made
thirteen years before. Unfortunately in this case his conclusions were accepted without
examination by distinguished writers in two popular works on Physical Geography, and
obtained a currency for which it is difficult to account §. Although Sir James Ross’s
experiments were in themselves valuable, they required both detail and corroboration,
and his conclusions were evidently based on an assumption for which there was no
warrant. And yet, while his important and positive facts as to the persistence of life to
great depths failed to receive the attention they deserved, his physical fallacies were
received almost without a question. As with his predecessor, D’Urville, Sir James
found in his more numerous and deeper observations that the unprotected thermometer
commonly marked a temperature of and about 39° to 40° ; and taking the maximum
density of fresh water to be 39°-5, he applied the same reasoning to the open seas as had
already been applied to freshwater lakes, and assumed, exactly as D’Urville had done,
that a uniform temperature of about 39°*5 prevailed at depths varying with the latitude,
and that a belt of water of that temperature, extending from the surface downwards,
encircles the globe between the 50th and 60th degrees of south latitude, or, as he more
definitely fixes it, in a mean latitude of about 56° 26' S. [(
* Yoyage, p. 62. f Ibid. p. 59.
} “ II faut done esperer que le fameux nombre +40,4 si etourdiment emprunte aux observations a la surface
et au fond des lacs d’eau douce de Suisse cessera de paraitre dans les dissertations ex prof esso, comme la limite
au-dessous de laquelle la temperature du fond des mers ne saurait jamais descendre.” (Yoyage de ‘La Yenus,’
Physique, vol. v. p. 22 ; and ‘ (Euvres Completes,’ vol. ix. p. 254.)
§ I may, however, remark that their mention of the subject is incidental, and confined merely to giving the
facts on Ross’s authority.
|| “It is therefore evident that about this parallel of latitude there is a belt or circle round the earth,
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
615
Wilkes, who also explored the Antarctic seas in 1838—42, took the same view, and
for the same reasons as D’Urville, Wauchope, and Eoss, of the existence of a deep-sea
and of a belt of water of the uniform temperature of 390-5 F.
Commenting on the general results of this great American expedition, Biot discusses*
the question of deep-sea temperatures. He remarks that serial observations should in
all cases be made, “ that the instruments ought to be protected against pressure by
surroundings of great strength and resistance,” and that they should be left a consi-
derable time at the bottom. Comparing the observations of Eoss with those of
Du Petit-Thouars, Scoresby, Parry, and Martins, he shows their want of agreement.
He says that the experiments of Eoss depend entirely on his instruments, “ of which
he had no means of knowing and judging ( aucun moyen d' appreciez)” while he knew
those of Du Petit-Thouars and Martins to have been prepared with every care. For
Eoss, he remarks, “ the uniformity of temperature at the bottom of the sea is a necessity; ”
and he trusts that some steps may be taken to verify his observations, for between them
and those of other observers there is, he remarks, “ a complete incompatibility.”
With respect to the freezing-point and point of greatest density of sea-water, these
properties were first more particularly investigated by Dr. Marcet in his well-known
paper on the subject published inl819f. Dr. Marcet ascertained that he could lower
the temperature of sea-water (at 1-027 sp. gr.) to 27°, and even, when in large vessels and
kept perfectly still, to 18° or 19° F., before freezing, but that when it froze it always rose
to 28°; and he states that his experiments “ uniformly led him to the conclusion that
the law of greatest specific density at 40° did not apply to sea-water, but that, on the
where the mean temperature of the sea obtains throughout its entire depth, forming a boundary, or kind of
neutral ground, between the two great thermic basins of the oceans. To the north of this circle the sea has
become warmer than its mean temperature, by reason of the sun’s heat which it has absorbed, elevating its tem-
perature at various depths in different latitudes. So that the line of mean temperature of 390,5 in latitude
45° S. has descended to the depth of 600 fathoms ; and at the equatorial and tropical regions this mark of the
limit of the sun’s influence is found at the depth of about 1200 fathoms, beneath which the ocean maintains its
unvarying mean temperature of 39°-5, whilst that of the surface is about 78°.
“ So likewise, to the south of the circle of mean temperature, we find that, in the absence of an equal solar
supply, the radiation of the heat of the ocean into space occasions the sea to be of a colder temperature as we
advance to the south ; and near the 70th degree of latitude we find the line of mean temperature has descended
to the depth of 750 fathoms, beneath which again, to the greatest depths, the temperature of 39°-5 obtains,
whilst that of the surface is 30°.
“ The experiments which our limited time and means admitted of our making serve to show that the mean
temperature of the ocean at present is about 39°*5, or 7| degrees above the freezing-point of pure water, and
as nearly as possible the point of its greatest density. But it would be indispensable that this temperature
should be ascertained to the tenth part of a degree ; and as we now know where we may send any number of
thermometers down to the greatest fathomable depths without an alteration of temperature, even to that small
amount, this desideratum might be very easily obtained.” (Boss’s ‘ Yoyage to the Antarctic Kegions,’ vol. ii.
p. 375.)
* Journal des Savans, 1849, p. 69.
t “ On the Specific Gravity and Temperature of Sea-water,” Phil. Trans, for 1819, p. 161.
616
ME. J. PRESTWICH ON SUBMARINE TEMPERATIJEES.
contrary, sea-water gradually increased in weight down to the freezing-point, until it
actually congealed.” Other experiments led him to fix this point of greatest density at
22° F.
Erman* in 1828 fixed the maximum density of sea-water of 1*027 specific gravity at
25° F., and found likewise that it did not reach its maximum before congelation. Still
more conclusive were the more elaborate experiments of Despretz j* in 1837. Taking
distilled water at a temperature of 20° C. and sea-water of the specific gravity of 1*027
at 20° C., he successfully determined the following important points : —
Cent. Eahe.
O O
Maximum density of freshwater +1 =39*2
,, sea-water —3*67=25*4
Point of congelation of sea-water —2*55=27*4
Temperature of sea-water during congelation . . . —1*88=28*6
He also showed that the freezing-point and the point of maximum density were pro-
portionate to the quantity of saline matter in the water, and that both therefore varied
with the degree of salinity of the sea.
The effects of pressure and the properties of fresh and salt water were therefore per-
fectly well understood previous to the date of Ross’s voyage. How, then, the unsup-
ported opinion of one who, though a most able and enterprising navigator, had not any
pretensions to an exact knowledge of physical science could have been accepted by
scientific writers of so much eminence is a singular fact. I can only account for it by
the circumstance that the subject had not been made in this country one of special
investigation, and therefore the results of Ross’s work had not been questioned by any
competent special authority. In fact they had never been discussed.
The observations of Leez, Hu Petit-Thouaes, and others, combined with the
researches of physicists, had sufiiciently established the law of the decrease of tempe-
rature with the depth to 2° to 3° above the zero of Centigrade in the temperate and
tropical zones of both the great oceans ; and their conclusions could hardly be consi-
dered as seriously affected by the unsupported though ingenious hypothesis of D’Urville
and Ross. Lenz had obtained, by means of his bathometer, with corrections for change
of medium, the low readings given at p. 599 ; and subsequently Du Petit-Thouars by
means of protected thermometers had obtained directly, without correction J, amongst
a number of others at lesser depths, the following deep-sea temperatures : —
* “ Nouvelles Recherches sur le maximum de densite de l’eau salee,” Annales de Chimie, xxxviii. p. 287.
•f* “ Recherches sur le maximum de densite de l’eau pure et des dissolutions aqueuses,” ibid. Ixx. p. 5.
J Others of his observations were corrected. On his return his thermometers were found to give too, high
a reading by -A to -A of a degree Centigrade, so that his observations may require a further slight deduction
to this extent.
ME. J. PRESTWICH ON SUBMARINE TEMPERATURES.
617
Temperature
Lat.
Long, of
Paris.
Depth.
Metres.
r
at depth.
-A
at surface.
North Atlantic . .
o
4
23 N.
28 26 W.
1950
3-2 C.
27 C.
South Atlantic . . -j
'25
10 S.
5 39 E.
1620
3
19-6
1620
25*6
.39
51 S.
41 57 E.
3*2
North Pacific . . . j
i 4
32 N.
136 54 W.
3740
1-7
27-2
1790
2-5
11-7
51
34 N.
159 21 E.
!
f 0
55 S.
99 27 W.
1790
3
26-5
27
47 S.
98 0E.
1620
2-8
23-8
South Pacific and In-
dian Ocean . . 1
! 37
42 S.
112 38 E.
1620
3
16-7
43
47 S.
81 26 W.
810
4-1
13-2
( »
99
99 99
1790
2-3
99
The rate of decrease recorded by the observations of Du Petit-Thouaes was con-
firmed within certain limits for lesser depths by those of Kotzebue, Beechey, D’Ueville,
Vaillant, and others, and for greater depths by some of the later observations of
Captain Pullen, who obtained in the
Temperature
Lat.
Long.
Depth,
fathoms.
r
at depth.
\
at surface.
Indian Ocean . . .
5.
31 S.
6i 31 E.
2330
35 F.
84 F.
|
[26
46 S.
23 52 W.
2700
35
/ 5
South Atlantic . . \
i 30
6
20 14
400
4o‘5
74*5
99
99 99
1200
38-2
99
These various submarine temperature observations in the several great Oceans, taken
in conjunction with the corrected readings for others adopted by Du Petit-Thouaes and
De Tessan, showed that, whether in temperate or tropical regions, approximately : — j
The temperature at surface being according to latitude . 60 to 80 Fahe.
At from 1000 to 2000 feet it was from 40 to 60 „
„ 2000 to 5000 „ „ 37 to 40 „
„ 5000 to 12000 . . 35 to 37 „ (or less)
Other corrected readings give equally low or still lower temperatures.
On the other hand, in the Arctic seas, the observations of Scoeesby and of Martins
and Beavais showed that the temperature of the upper strata, down to a depth of 200
to 300 feet, varies greatly with the season, ranging from 8 to 10 degrees above to 3 or 4
degrees under 32° F., and that with increasing depth a more uniform higher temperature
prevailed. Scoeesby, whose experiments were conducted further northward and west-
ward, found this latter temperature to be generally 3° or 4° above the freezing-point of
fresh water, or 7° to 8° above that of sea-water. His two deepest experiments (to the
N.W. of Spitzbergen) give the following results : —
618
MR. J. PRESTWICH ON SUBMARINE TEMPERATURES.
Temperature.
Lat.
Long.
Depth.
Uncorrected.
Corrected.
79 4 N.
5 38 E.
4380 feet.
37 Fahr.
34*5 \
78 2 N.
0 10 w.
4566 feet.
38 „
35-41?
M. Martins’s chief experiments were, on the other hand, between the North Cape
and Spitzbergen, from 71° to 76° N. lat. The deepest temperature sounding was in
73° 36' N. and 20° 53' E., in which instance Walferdin’s thermometer registered at 2854
feet 320,2 F., and Six’s thermometer, corrected for pressure, gave 310,6. This latter is
the only recorded instance in the open sea where his reading was below zero of Centigrade.
His most northern observations, viz. in 76° 13' N. and 12° 48' E., at 1296 feet, and
another in the same place in 2103 feet, gave respectively 330,4 and 320,3 ; while one of
Scoresby’s, in 79° N. and 5° 40' E., at 2400 feet gives, corrected, 340,6 F., and another in
76° 16' N., 9°E., at 1380 feet, not far from Martins’s position, gives, without allowance
for pressure (for in this case Six’s thermometer does not appear to have been used), a
temperature of 330-3.
Martins, however, states that on approaching the land in Magdalena Bay, instead
of a submarine temperature above zero, he found that in depths of from 110 to 136
metres the temperature of the water was always below zero ; that these bottom-
waters there had, in fact, a temperature of — 10,75 C. to — -1°‘91 C. (280,6 F.), that of
the surface being 0°T to 1°*2 Cent.*
The results obtained in another section of the North Atlantic are very different
and of much interest. The observations in Davis Strait and Baffin Bay by John Ross
and Sabine indicate that, after passing the point where the diurnal and annual variation
cease, there is a gradual decrease of the temperature with the depth to a point
approaching in places to that of the maximum density of sea-water. Even taking the
readings without correction f, they show : —
From 1000 to 2000 feet, a temperature of 32 to 29-5 Fahr.
„ 2000 to 3000 „ „ 30 to 29
„ 3000 to 4000 „ „ 29 Fahr.
„ 5000 to 6000 „ „ 28f „
Besides these, Parry noted, in 680<29 N. lat. and 63°-43 W. long., at a depth of
4854 feet, a temperature of 27°, and, as before mentioned, Ross and Sabine have
recorded J, in 66° 50' N., 61° W., at a depth of 4080 feet, a temperature of 25f°§.
In the Antarctic seas the observations of Cook, James Ross, and Wilkes show that the
temperature from the surface down to 600 or 1000 feet varies from 28° to 32°. At greater
depths there are, with few exceptions, only the experiments of Ross ; and these cannot,
* Op. cit. p. 332. f Probably but very little is needed, anti, pp. 597 and 598.
+ Marcet, Phil. Trans. 1819, pp. 169 & 205. § This may be rather doubtful (see, however, note, ante, p. 596),
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
619
for reasons before given, be accepted without reserve. Still they are available after
correction for pressure ; and the readings then indicate thermal conditions very similar
to those which obtain in Arctic seas. To take one of the most southern series of
observations, at a spot in the Antarctic Ocean where no soundings were obtained, at a
reputed depth of 24,000 feet : —
Temperature.
Lat. Long.
Depth.
Uncorrected. Corrected for pressure.
68 32 S. 12 49 W.
Surface (March)
30-8 Fahr.
30-8 Fahr.
900 feet.
33
32-4
1800 „
35-5
34-4
3600 „
38'7
36*5
4500 „
39-4
36*6
5400 „
39
35-8
6300 „
39-5
35*8
Again, another nearer the South Polar land, and
in soundings : —
63 49 S. 51 7 W
Surface (Feb.).
32 F.
32 F.
600 feet.
32-2
32
900 „
33-2
32-6
1800 „
35*5
35-6
2700 „
36-4
35
3600 „
37-3
35-2
7200 „
39-5
35-2
Still further and closer to another part of the Antarctic continent we have : —
77 49 S. 162 36 W. Surface (Feb.). 28-5 F. 28-5 F.
1740 feet. 30-8 29-8
There is only one observation of Du Petit-Thouars in the Southern Ocean for
comparison with those of Boss. As the cylinder came up full, I give the reading with
the correction : —
59 48 S. 79 56 W. Surface (March). 42-9 F. 42-9 F.
2657 feet. 39 37-5
The conditions, therefore, prevailing in the open Arctic and Antarctic seas are appa-
rently closely analogous, — the temperature at a distance from land increasing with the
depth until it rises to 35° to 36° F. at 2000 to 3000 feet, below which it seems to remain
nearly stationary at about the same temperature ; while closer to the land and at less
depths it falls nearer to the freezing-point of sea-water (see note, posted, p. 635).
The temperatures at depths in inland seas were found at an early period to be very
different to those of open seas ; and it is singular that the very first observations made
mdccclxxv. 4 o
620
ME. J. PBESTWICH ON STTBMAEINE TEMPEEATTJEES.
in the Mediterranean by Saussuke in 1780, of 550,8 F. at 944 feet, and 55°-5 at
1918 feet, remain substantially correct to the present day. It was, however, D’Urville’s
more extended observations in 1826 that made better known the fact that the tempe-
rature decreased from the surface down to 200 brasses (1066 feet), below which it
remained constant at about 13° C., or between 54° and 55° F. Still his greatest depth
did not exceed 3189 feet; but Berard in 1831 extended the observations to a depth of
6377 feet, and still found the same degree of temperature.
Aime further showed, from a series of soundings made during 1840-44 in the western
basin of the Mediterranean, between Marseilles and Algiers, that the diurnal variation
of temperature ceases to be sensible at 16 to 18 metres, and the annual variation at
300 to 400 metres. The mean of his series of observations gave the following results : —
Mean Annual Temperature of the Mediterranean at different depths.
Depth.
Temperature.
Extreme monthly variations.
Surface.
18*2 Cent.
10°-2 Cent.
25 metres.
16-3
6-3
CD
o
14-4
2-8
100 „
13-7
2-0
200 „
13-0
1-0
350 „
12-6
0-0
This temperature of 12°-6 (54°-7 F.) he showed to be that of the mean of the winter
months (or rather that of the months of January, March, and April) of the area; and
he was of opinion that the same temperature obtained at greater depths, referring
in support of that opinion to other and deeper soundings by Berard. The fol-
lowing observations by the latter, made between the Balearic Islands and Algeria, are
extracted from D’Urville’s tables : —
Depths of |SurfaCein August
AT rwom nDT*
variable •<
temperature. |
Depths of
uniform <(
temperature. |
November
At depth of 40 brasses in October
55 10 55 55
„ 600
600
750
1200
November
June
November
June
27-1 Cent.
14-6
16-5
14-9
13
13
13
13
This gives the rather higher reading of 55°*4 at depths ; but whether arising from
Berard using less perfect instruments or from an actual difference of temperature on this
southern side of the Mediterranean, is uncertain. The marked agreement between the
observations of Berard in 1831-32 and those of the ‘Porcupine’ expedition in 1870,
leads me to suppose that the latter may be the influencing cause.
D’Urville’s observations, which were made further north in the western Mediter-
ranean than those of Berard, agree more closely with those of Aime. Thus he found —
MR. J. PRESTWICH ON SUBMARINE TEMPERATURES.
621
At a depth of 300 brasses in March a temperature of .
33
600
33
33
12-7 Cent.
12-6
The only temperature-observations made in the eastern basin of the Mediterranean
previously to 1869, with the exception of two of Wullerstorf, are those of Admiral
Speatt. They extend from Malta to Alexandria, and from the Grecian archipelago to
the Gulf of Syrtis, forming for this section of the Mediterranean a series complemental
to those made in the western section by D’Urville, Berard, and Aime. The results he
obtained are also, when corrected, in close agreement with those of these several
observers. His first experiments were made in ZEgina Bay in 1845, in connexion with
the natural-history researches of Edward Forbes, and extended only to a distance of
three miles from shore. Allowing for a gain of 0o-5 or 1° in hauling lip the silt, the
corrected readings will then give as the general results : —
For Forbes’s Zone I. (1 to 12 feet) a temperature of . 55 to 82 Fahr.
„ „ II. (at and near 120 feet) . . . . 69 to 70
„ „ III. ( „ 330 feet) . . . 56 to 57
„ „ VII. ( „ 1260 feet) . . . 54-5 to 55
Three other experiments in the seas of Greece gave him the following readings : —
O
1080 feet (four miles off Nio) . . 55*51 or, allowing for gain in hauling
1200 „ (seven miles off Andros) 55’5 > up through warmer waters,
1260 „ (three miles off iEgina) 55*5 J of from 54°*5 to 55°.
In the shallower waters of the archipelago he found “ the temperature of the
intermediate depths between 100 fathoms and the surface range from 55° to 76°, and,
indeed, in the summer season sometimes up to 80° and 86° in the littoral waters of
enclosed gulfs and shallow bays.”
A set of serial observations off Crete, made later with unprotected self-registering
thermometers, gave readings as under (these, when corrected for pressure, agree, with
the exception of the fourth, which seems a doubtful reading, very closely with those of
Berard in the southern portion of the western Mediterranean basin*): —
Temperature at depths in the Mediterranean off the N. W. Coast of Crete.
Uncorrected. Corrected for pressure.
Surface in the month of June
o
. . 73 Fahr.
73° Fahr.
At a depth of 120 feet .
. . 68
67-9
„ 300 „ . . .
. . 63
62-7
„ 600 „ . . .
. . 59f
59-4
„ 1200 „ . . .
. . 59f (?)
59?
„ 7440 „ . . .
. . 59±
55-2
Admiral Spratt says that he found this temperature of “ about 59° in all depths from
300 down to 2000 fathoms.” In the extreme eastern portion of the Mediterranean
* Nautical Magazine for 1862, p. 10 ; e Travels and Researches in Crete’ (London, 1865), vol. ii. App. p. 332.
4 O 2
622
MR. J. PRESTWICH ON SUBMARINE TEMPERATURES.
there are, however, indications of a higher temperature, as the following observations,
taken, the first three in November, and the last in April 1861, show : —
Deep-sea Temperatures off the Coast of Egypt , west of Alexandria.
Uncorrected. Corrected.
At a depth of 180 feet 71 Fahr. 70‘9 Fahr.
„ 300 „ 68 67*8
„ 600 „ 62| 62-1
„ 1620 „ 59§ 58-5
Admiral Spratt concluded that “ the minimum temperature of their (Eastern Medi-
terranean, Grecian archipelago, Sea of Marmora, and Black Sea) deeper parts correspond
nearly with the mean annual temperature above them.” This apparent discrepancy
between Amfi and Admiral Spratt evidently arises from the circumstance that the one
bases his conclusion on observations made with protected and the other with unpro-
tected thermometers, which gave too high a reading. Subject to correction the results
are closely concordant, and both give approximately the mean sub-winter temperature.
The observations of Aime and others thus proved that in this great inland sea the
influence of the variations of temperature at the surface ceases at a depth of from
1000 to 1200 feet, and that below that line a uniform temperature of from 54° to 55°*5
prevails in the western basin, and one possibly 0O-5 to 1° higher in the eastern basin of
the Mediterranean.
Some deep temperature-observations have also been made in two other nearly closed
seas — the Red Sea and the Sea of Okhotsk, — the latter by Dr. Horner in 1803, and
the former by Captain Pullen, with his protected thermometers, in 1858.
The mean winter temperature of the air in the Red Sea may be a little under
70° Fahr. The following observations are not serial, but were taken at intervals in
various parts of that sea (see Table III. p. 667).
Temperatures at depths in the Bed Sea.
Surface in the months of March and April . . . 78° to 86° Fahr.
At 300 feet 77
„ 2552 „ 71
„ 4068 „ 70-5
In the Sea of Okhotsk, where the mean winter temperature is doubtlessly under 20° F.,
the observations were only carried to a depth of 690 feet, with the following results : —
Temperature at depths in the Sea of Okhotsk.
Uncorrected.
Corrected.
Surface in the month of August
. . . 46-4
46-4
At 108 feet
. . . 31-6
31-6
„ 360
28-8
„ 690 „
28-6
Parry’s observations in Lyon’s Inlet are excluded, for the reasons before given (p. 597).
ME. J. PEESTWICH ON STTBMAEINE TEMPEEATUEES.
623
§ IV. Hypotheses of Humboldt, Arago, Lenz, and others.
Such is a summary of the results obtained between the years 1749 and 1868. From
time to time they had been commented on by some of the most eminent physicists of
the time, and the cause of the low temperatures prevailing in the depths of tropical seas
discussed.
Humboldt, so far back as 1812, and again in his subsequent works* * * §, contended that
“the existence of those cold layers in low latitudes proves the existence of an under-
current flowing from the poles to the equator.” In support of this hypothesis, he showed
how it explained the fact, first noticed by Franklin and Williams f, that the water on
shoals in the Atlantic was many degrees lower than that surrounding them, from the cir-
cumstance that the deeper cold water, flowing and rising over them, displaced the warmer
surface-waters J. These observations were afterwards confirmed by Hu Petit-Thouars,
Vaillant, and others. He was further of opinion that “ in the narrower seas, as well
as in the tropical seas which cover the cold waters from Arctic regions, all the mass of
water is in a state of movement.”
Humboldt also contested the conclusions of those who considered that the ocean is
salter under the equator than at a distance from it, and showed that while in lat. 0° to
14° the specific gravity was T0272, it was 1-0282 in lat. 15° to 18°, and 1-0278 in lat.
30° to 40°. Nor did he fail to note § that the equatorial zone is not the hottest water
zone ; but that two hotter zones lie a few degrees N. and S. of it.
Humboldt subsequently [| thus summarized the question as it then stood : —
“ As fresh and salt water do not attain the maximum of their density at the same
degree of temperature, and as the saltness of the sea lowers the thermometrical degree
corresponding to this point, we can understand how the water drawn from great depths
of the sea during the voyages of Kotzebue and Du Petit-Thouars could have been
found to have only the temperature of 37° and 36°-5. This icy temperature of sea-water,
which is likewise manifested at the depths of tropical seas, first led to a study of the
lower polar currents, which move from both poles towards the equator. Without these
submarine currents the tropical seas at those depths could only have a temperature
equal to the local maximum of cold possessed by the falling particles of water at the
radiating and cooled surface of the tropical sea. In the Mediterranean the cause of the
absence of such a refrigeration of the lower strata is ingeniously explained by Arago,
* ‘ Voyage 5 : Eelation Historique (Paris 1814), vol. i. p. 73. Climatologie Asiatique (Paris 1831), p. 560.
1 Kosmos,’ Otto’s translation, 1849, vol. i. p. 307.
f On the Use of the Thermometer in Navigation. Philadelphia, 1792.
J He instances, for example, a case noticed by himself on the “ Signal Bank” off Eerroll, where he found
the water to have a temperature of from 54°-5 to 56° F., while the water immediately around was from 59° to
59°-6 F.
§ Ann. Chim. et Phys. xxxiii. 1820, p. 40.
I] Kosmos, vol. i. pp. 308, 309 (Sabine’s translation, pp. 295, 296).
624
ME. J. PBESTWICH ON SUBMARINE TEMPEEATUEES.
on the assumption that the entrance of the deeper polar currents into the Straits
of Gibraltar, where the water at the surface flows in from the Atlantic Ocean from west
to east, is hindered by the submarine counter-currents, which move from east to west,
from the Mediterranean into the Atlantic The zones at which occur the
maxima of the oceanic temperature and of the density (the saline contents) of its waters
do not correspond with the equator. The two maxima are separated from one another,
and the waters of the highest temperature appear to form two nearly parallel lines north
and south of the geographical equator. Lenz, in his voyage of circumnavigation, found
in the Pacific the maxima of density in 22° north and 17° south latitude, whilst its
minimum was situated a few degrees to the south of the equator. In the region of calms
the solar heat can exercise but little influence on evaporation, because the stratum of air
impregnated with saline aqueous vapour, which rests on the surface of the sea, remains
still and unchanged.”
Similar views were adopted by D’Atjbuisson in 1819*. The whole subject of Oceanic
circulation was again discussed from a fresh point of view by D’Urville f in his account
of the results of his voyage of 1826. After arguing (p. 62) that in open seas the tempe-
rature at and below 600 brasses (3198 feet) is nearly constant between 4° C. and 5° C., and
that perhaps it may be 4°-4 C. (40° P.), he significantly remarks that in the zone
10° on each side of the equator some particular cause seems to occasion in the water
“ up to 100 brasses a more sudden and rapid cooling than would have been expected.”
He afterwards (p. 64) proceeds to say that the mass of the equatorial waters, slowly
diminished by evaporation, may give rise to a slow and continuous ascensional movement
of the lower colder waters, and these so displaced make room for other waters coming
from the polar regions, so that “ it is rather a transport, nearly in mass and very slow, of
the deep waters of high latitudes towards the equator.” The point of departure he con-
sidered to be between 40° and 60° lat. ; and he inferred that the deep cold waters (at
40°) are there directed periodically in two “ insensible currents,” the one towards the
equator and the other towards the pole.
AragoJ in 1838, reporting to the French Institute on a scientific expedition then in
course of preparation to the coast of Africa, thus expresses his opinion : —
“ La temperature des couches inferieures de l’ocean, entre les tropiques, est de 22° a
25° centigrades au-dessous du plus bas point auquel les navigateurs aient observe le ther-
mometre a la surface. Ainsi, cette couche si froide du fond n’est point alimentee par la
precipitation des couches superficielles. II semble done impossible de ne pas admettre
que des courants sous-marins transportent les eaux des mers glaciales j usque sous
l’equateur.
* Traite de Geognosie (Strasbourg, 1819), p. 450.
t ‘ Yoyage de 1’ Astrolabe, 5 Sect. Meteorologie, Physique, et Hydrographie, chap. iii. pp. 51 *-85*. Paris,
1833.
t “Instructions concernant la Me'teorologie et la Physique du Globe, par M. Arago, Courants Sous-marins,”
Comptes Eendus, 1838, part 2, tome vii. pp. 212, 213.
ME. J. PBESTWICH ON SUBMAEINE TEMPEEATUEES.
625
“ La consequence est importante. Les experiences faites au milieu de la Mediter-
ranee, la fortifient. Cette mer interieure ne pourrait recevoir les conrants froids, prove-
nant des regions polaires, que par la passe si resserree de Gibraltar ; eh bien ! dans la
Mediterranee, la temperature des couches profondes n’est jamais aussi faible, toutes les
autres circonstances restant pareilles, qu’en plein ocean; on peut meme aj outer que nulle
part cette temperature du fond de la Mer Mediterranee ne parait devoir descendre au
dessous de la temperature moyenne du lieu. Si cette derniere circonstance vient a se con-
firmer, il en resultera qu’aucune partie du flux glacial venant des poles ne franchit le
seuil du detroit de Gibraltar.
“Lorsque M. le Capitaine D’Urville partit, il y a quelques annees, pour sa premiere
campagne de ‘ l’Astrolabe,’ j’eus la pensee qu’il pourrait etre utiie de rechercher si les
phenomenes de l’ocean, quant a la temperature des couches profondes, se presenteraient
dans toute leur purete des qu’ on se tr ourer ait a Vouest du detroit. L’Academie voulut
bien accueillir mon voeu. Sur sa recommandation expresse, quelques observations de la
nature de celles que je desirais, furent faites a peu de distance de Cadiz. Eh bien ! elles
donnerent precisement ce qu’on aurait trouve dans la Mediterranee.
“ Ce fait curieux semble se preter a deux explications differentes. On peut supposer
que le courant polaire se trouve completement refoule par un courant sous-marin dirige
de la Mediterranee vers l’ocean, et dont l’existence est appuyee sur divers evenements de
mer. On peut supposer aussi que la saillie si forte de la cote meridionale du Portugal ,
ne permet pas au flux d’eau froide venant du nord, de s’inflechir jusqu’a angle droit pour
aller atteindre les regions voisines de l’embouchure du Guadalquivir.”
Again*, in reporting on the observations of the ‘ Venus,’ Arago saw no other expla-
nation of the low deep-sea temperatures recorded in tropical seas, but “ the existence of
submarine currents carrying to the equator the bottom-water of the icy seas.”
It is, however, to Lenz (who had, in his previous papers of 1831 and others, concluded
that the temperature of the ocean decreases with the depth, rapidly at first and then
gradually, until a point of about 36° F. was reached, when it became insensible) that
we are indebted for a more special review and discussion of all the facts known up
to 1845 f. Speaking of the earlier observations made on the temperature of the sea
at great depths, he observes: — “The greater number of these observations, with the
exception of those made by myself, were taken with thermometrographs, and especially
with Six’s thermometers. It is, however, to be observed that all instruments of this
kind are liable to a source of error which hitherto investigators have not borne in mind,
viz. the compression of the vessel or the bulb which contains the thermometrical
substance (spirits of wine), particularly by the enormous pressure in depths of several
thousand feet. I was witness of a series of experiments on the action of strong pressure
on a thermometer-bulb, which Parrot undertook in order to ascertain the influence of
* Comptes Eendus, 1840, vol. xi. p. 311.
t “ Bemerkungen iiber die Temperatnr des "Weltmeeres in. yerschiedenen Tiefen, yon Emu,. Lenz,” Bulletin
Acad. Sci. St. Petersburg, y. (1847), cols. 65-74.
626
MR. J. PRESTWICH ON SUBMARINE TEMPERATURES.
a strong pressure on different substances, and which he has made known in the
‘Memoirs of the Academy of St, Petersburg’ (vi. serie, Sc. Math. Ph. et Natur., t. ii.
p. 595, 1832). It is there mentioned that a pressure of 100 atmospheres caused the
thermometer to rise about 20o,5, without the temperature having altered in the least,
as was shown by a second thermometer which was protected from pressure by a brass
cylinder.”
Lenz proceeds to remark that it necessarily follows that thermometrographs (although
in such instruments the effect would be much less owing to their form of construction)
exposed in the sea to pressures of 100 to 200 atmospheres must give too high a
reading, and that the circumstance of the indications in so many deep soundings
remaining uniform, or sometimes increasing with the depth, proves the influence of
compression.
Reviewing the data furnished by different observers and by himself, and assigning to
them, if not an actual, at all events a relative and comparative value for corre-
sponding depths, Lenz notices the circumstance that they all point to the existence
of a belt of water at and near the equator cooler than at a short distance to the
north and south of it; and in illustration of this he takes the consecutive series of
observations at nearly the same depths made by Kotzebue in 1815-1818, at short
distances apart over a great length of the Atlantic ; and he gives a Table, of which the
following is an abstract : —
Zones of
latitude.
North Atlantic.
South Atlantic.
Mean
depth.
Mean
temperature.
Mean
depth.
Mean
temperature.
feet.
°F.
feet.
°F.
0 to 3
435
58-2
480
57
3 „ 6
460
57-8
405
56-4
6 „ 9
400
58
351
61-5
9 „ 12
390
59-4
426
62-7
12 „ 15
390
58-2
351
60-8
15 „ 18
408
66-7
305
60-3
18 „ 21
468
68-2
378
61-7
21 „ 24
414
69-2
420
63-2
24 „ 27
432
69
27 „ 30
403
65-7
30 „ 33
390
60
33 „ 36
447
62-2
36 „ 39
418
61-2
39 „ 42
438
58-5
45 „ 48
458
53-6
This, he observes, shows a rapid rise of the isothermal planes in approaching the
equator; and taking a definite isotherm of 140,5 C., he gives the following diagram, in
which he shows that this plane, which in lat. 45° to 48° N. lies at a depth of 350 feet,
sinks gradually to 640 feet in lat. 23° to 26°, and then, rising more abruptly as it
MR. J. PRESTWICH ON SUBMARINE TEMPERATURES.
627
approaches the equatorial regions, reaches to within 390 feet of the surface in lat. 12°
to 15° N *
* Although Kotzebue’s observations in the Pacific did not furnish him with the same number of data, he
thought there was yet evidence of the same condition prevailing there also ; but the observations were much
scattered over many parallels of longitude and were made in various currents. The results were : —
Latitude.
6 to 9 N. . .
Mean depth,
feet.
600
Mean temperature.
°F.
. . . . 56
9 „ 12
499
. . . • 62
12 „ 15
558
61-3
15 „ 18
498
. . . . 69‘5
18 „ 21
402
. . . . 69-3
27 „ 30
450
64
30 „ 33
600
62
33 „ 36
600
51-8
36 ..39
600
52-7
Dr. Horxer had previously noticed, in
the Atlantic, this anomaly of s
a. proportionally lower tempers
depths near the equator than 5° S. and 10° N. of it, but without offering
any explanation, and gave a :
means of some of Krusextern’s observations, of which the following is an extract : —
April 20
No. of Obs. Lat.
to 26 5 17 15 S.
Long. Depth,
o / feet.
3 20 W. 342
Temp.
°F.
55-4
27
„ 30 4
10 24
12 2
396
56-2
30
„ 4 M 5
5 12
17 5
402
53-3
May 3
„ 10 8
0 43 N.
20 28
444
52 -5
10
„ 16 7
4 51
24 38
450
5 2-5
15
„ 19 5
9 34
29 38
402
52-7
20
„ 24 5
19 30
35 7
426
61-0
25
„ 30 6
31 0
36 30
426
58-7
31
„ 6 J 5
40 30
29 40
408
54-2
4 P
Edinb. Phil. Journ. 1822, vol. vi. p. 161.
MDCCCLXXV.
628
MR. J. PRESTWICH ON SUBMARINE TEMPERATURES.
Lenz then proceeds to observe : — “ The form of the submarine isothermal line which
I have drawn leads us of itself, on the first glance, to an explanation of this striking
phenomenon.
“ The mass of water in the tropics, warmer down to a certain depth from the sun’s
heat, cannot maintain its equilibrium with the colder waters of the middle and higher
latitudes : a flow of the warmer water from the equator to the poles must necessarily
take place on the surface ; and this surface-flow must be supplied at the equator by a
flow of colder water from high latitudes, which at first would flow in an almost hori-
zontal direction, but which under the equator must rise from below to the surface. In
this manner, in the northern hemisphere, a great vertical circulation takes place in the
ocean, which has its direction above from the equator to the pole, and below from the
pole to the equator. Since these flows or currents moving in opposite directions are
distinguished by their different temperatures, we obtain in the submarine isotherm an
indication of the direction of the lower portion of this flow. A corresponding flow, but
moving in the opposite direction, takes place in the southern hemisphere ; so that in a
zone surrounding the equator where both are united, the water flows almost in the
direction from below up to the surface ; and thus one meets with cold water in much
shallower depths than in those two zones north and south which lie immediately
adjoining, and which, in fact, is shown by the observations.
“ It is not my intention to enter here upon the question, how the original direction
of this current to the surface becomes greatly altered by the diminution of the speed of
rotation and by the influence of the wind, so that the water first arrived at the polar
regions by considerably circuitous ways, or how the lower portion of the current was
drawn westward by the entrance of bodies of water into latitudes of greater speed of
rotation ; in any case the last influence will be very much diminished by the opposition
of the west bank of the ocean, in comparison with the corresponding diversion or
drawing away which the air-currents undergo. It is sufficient for me to have furnished
in the figure of the submarine isothermal line proof of the current from the pole to the
equator in the depth of the ocean. It would be highly desirable that future navigators
should enlarge our knowledge on this point, by a larger number of observations with
one and the same instrument, or with corrected instruments, which could be accom-
plished with very little trouble and in a very short time. If they would be satisfied
with letting down the thermometrographs at always one and the same depth of some
100 fathoms, this observation would be made in fifteen minutes; and in any case, by a
frequent repetition of it, results would be arrived at, especially in latitudes ranging
from 40° N. to 40° S., which would be far more instructive for physical geography than
the observations hitherto made, where one proceeded or reasoned more on the deter-
mination of the diminution of the temperature than upon compared determinations of
different places.
“ From a current underneath of colder waters from the poles to the equator, some
important conclusions arise, viz. : —
MR. J. PRESTWICH ON SUBMARINE TEMPERATURES.
629
“ 1. The diminution (pointed out) of temperature everywhere up to latitude 60° with
the increase of depth, in direct opposition to the conditions observed on dry land.
“ 2. My numerous determinations of the salinity of the ocean have shown that the
maximum of the salinity does not occur at the equator, but invariably some degrees
north and south from it (in the Atlantic at 23° N. and 17° S.). I have endeavoured to
explain this condition from the greater evaporation in these latitudes, which is compre-
hensible from the cooperation of the trade-wind, in opposition to the region of calms at
the equator (see Mem. de lAcad. Sc. Math. Ph. et Nat. t. i. p. 507). According to the
above, I do not, however, doubt that also the slight salinity of the uprising polar water
in the region of calms contributes materially to this condition.
“ 3. It is a point which has been determined by Humboldt, John Davy, and others,
that the water of the ocean is colder at the surface over shallows than at some distance
from them over very great depths. This phenomenon, the explanation of which hitherto
has not been found to be satisfactory (Gehler’s New Lexicon, t. vi. 3. p. 1687), is a
simple consequence of the current of colder water at depths from the pole to the
equator ; for if this runs against any obstruction, such as a shallow would present, it
will rise along it as upon an inclined plane, and approach nearer the surface, and in
this manner the surface will be cooled down.”
A little later Pouillet*, who does not, however, seem to have been aware of Lenz’s
researches, remarks : — “ It seems certain that there is in general a surface-current
carrying towards the polar seas the warm water of the tropics, and a lower current
bringing back from the poles the cold water of the polar regions ; but these currents
are modified in their direction and intensity by a number of causes which depend on the
depth of the sea-basins, their configuration, and the influence of winds and tides.”
I have already referred to Biot’s criticism of Boss’s work. Beasoning afterwards on
the different temperatures shown to exist throughout all seas, and on the impossibility,
in consequence, of any portion of it being in a state of rest, he observes f : — “ The exist-
ence and the initial direction of these constant currents presupposes three things : first,
a permanent cause of movement which forces the polar waters towards the equator ;
secondly, a constant exterior afflux supplying the great polar streams at the origin and
along their course ; and lastly, some exhausting cause or outflow, preventing the final
accumulation of their products ” (p. 79). Biot, however, in consequence, apparently, of
the doubts he felt respecting the accuracy of temperature observations at depths, owing
to the anomalous results of Boss’s, hesitates to admit “ the inference that the bottom of
the sea was occupied by a layer of cold water proceeding from the poles and which is
unceasingly renewed” (p. 71), and attaches more weight as a cause of this circulation
to the inequality of mean pressure of the atmosphere in different latitudes.
Buff J gave in 1850 a good general summary of the question as it then stood.
* Elements de Physique, 5 ed. vol. ii. p. 666 (1847).
t * Journal des Savans ’ for 1849.
t ‘ Physics of the Earth,’ translated by Hofmann. London, 1851, pp. 172-74.
4 p 2
630
ME. J. PEESTWICH ON STJBMAEINE TEMPEEATUEES.
A few years later Emil von Lenz* described the observations made by Dr. Edward
Lenz during a series of voyages across the Atlantic to the west coast of South America
at a small but uniform depth, and with the same instruments throughout. For some
reason not explained, the temperatures in the low latitudes of the South Atlantic are
not given.
North Atlantic.
South Atlantic.
Lat. N.
1
Long. W. Feet deep.
1
Temp,
at depth.
Surface.
Lat. S.
Long. W.
Feet deep.
1 Temp,
at depth.
Surface.
1 38
27 360
58-2 E.
81-4
° '
o
3 14
21
61 „
80
6 9
23
60 „
84
6 52
22 „ +
58-2 „
80
13 28
28
360
72-8
80-2
25 35
37
66-3 „
72-5
17 17
19 2 (32 ?)
9r
76-6
84
31 48
36
64-3 „
73
30 13
46
64
77
35 35
17 „ t
62-6 „
63-6
33
72 (52 ?)
52
56
35 37
35
60 „
68-4
53 12
58
43
51
35 39
34
61 „
67-8
55 19
62
41
48-4
40 40
27 | „
56 „
62-6
56
64
»
41
46
On these he remarks, “ The number of observations here are so few, that no valid
general conclusions can be drawn from them ; I only mention that this attempt was
substantiated by me in results made public on an earlier occasion (Bull. Phys. Math. v.
1847); viz. that at the equator, or rather in the region of calms, one finds a notably
more rapid diminution of temperature at increased depth than even in the tropic or
subtropical zone. We also see here that at 4° N. lat. the temperature at 60 fathoms
decreases from 21° R. to 12° R., but at 28° (321) lat. only to 14°*8 ; and it is first at
36° lat. in this depth that one finds nearly the same temperature as at the equator,
viz. 120,6 Reaumur. In the Southern Atlantic Ocean, the conditions of temperature at
depths appear to approximate more nearly to the equator than in the Northern, pos-
sibly in consequence of the northern inclination of the region of calms.”
§ V. General Conclusions.
It is evident that the old observations (all before 1868) have very different degrees
of value. In laying down the lines of Section of the Bathymetrical Isotherms on
the Admiralty “ Track Chart ” of the world, I have selected those observations which
appear the most reliable, and which at the same time offer the most continuous series
over the greatest number of parallels of latitude, such as the observations of Kotzebue
in the North and South Atlantic, and those of Dayman J in the South Atlantic and
* “ Meteorologische Beobachtungen auf dem Atlantischen und Grossen Oceane in den Jahren 1847-49
angestellt von dem Dr. En. Lenz, verechnet von E. Lenz,” Bull. Acad. Imp. Sci. St. Petersbourg, iv. 1863,
p. 130.
t These numbers do not quite agree with the text, where they stand as “ 420 ” and “ 180.”
X Only the correction for Dayman’s observations should probably be rather higher than that for the others.
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
631
Indian Oceans, subject to, as the correction for pressure, the deduction of 1° Fahr. for
every 1700 feet of depth. As the ‘Challenger’ expedition will supply ample data
regarding the deeper temperature-soundings in the intertropical seas, the scarcity of
them in the earlier voyages is of less importance. Those, on the contrary, collected
on the many Arctic and Antarctic voyages under circumstances of so much difficulty,
and which bear in so essential a manner upon the intermediate areas, are fortunately
much more complete. The lines of Section have therefore been so selected as to
embrace the chief observations of the several explorers in both the Arctic and the
Antarctic seas. For this purpose two lines traverse respectively the length of the
Atlantic and of the Pacific, and two others are run through the Indian and Southern
Oceans.
Section No. 1 first traverses the North Atlantic from the top of Baffin Bay to the
equator in long. 20° W., and shows the low submarine temperatures prevailing in the
higher latitudes on that side of the Atlantic. The bathymetrical isotherm of 35° F.
seems on this line not to extend beyond lat. 63° N. Soundings have been made in
Davis Strait and Baffin Bay between lat. 60° and 77° N. to the depth of 6000 feet, and
everywhere the temperature decreases with the depth down to 29° and 28°, or even 27°,
and in one instance so low a degree as 250,75 F. has been recorded. The isotherms of
40°, 50°, and 60° F. in the western area of the Atlantic have likewise a less northward
extension than in the eastern area traversed by Section No. 2 ; while that of 70° F.,
which is affected by the Gulf-stream, extends further north.
Section No. 2, which commences in the seas around Spitzbergen, exhibits, to depths
within the annual influence, a temperature as low, if not lower, than in No. 1, while
below that the temperature, on the contrary, down to the depths hitherto tried (not
quite 5000 feet) increases with the depth. Owing to the great diurnal variations of
temperature at the surface or to currents, the fluctuations in the upper strata are
frequent and rapid. From 1000 down to 3000 feet the temperature is more uniform
at 33° to 34°, and reaches, at 4500 to 4600 feet*, 34° to 35° F. or possibly 36°. Off
the coast of Greenland the one experiment of Scoresby shows a decrease of tempe-
rature to the full depth tried, viz. to 280,5 (corr.) at 708 feet.
From the Spitzbergen seas, the bathymetrical isotherm of 35° F. gradually falls until
the latitude of about 50° N. is reached, when its depth is twice what it is in lat. 76°
to 80°. About lat. 40° N. it appears to have attained its maximum depth of about
11,000 feet, at which it remains to lat. 30°, from about which point it again rises gra-
dually, lying in lat. 12° at a depth of about 8000 feet, and reaching probably still nearer
the surface at the equatorf . The isotherm of 40° F., which, in this north-eastern part
of the Atlantic, extends as far as lat. 72° to 73° north, reaches its maximum depth
of about 6000 to 7000 feet between lat. 50° to 30° N., and rises to between 3000
* Scoresbt’s deepest sounding was in 76° 30' N., 4° 48' W., 7200 feet, no bottom.
t The depths of these isotherms in the Atlantic will no doubt require correction ; but this will not affect their
relative position and general bearing.
632
MR. J. PRESTWICK ON SUBMARINE TEMPERATURES.
and 4000 feet near the equator. Of these two and other lower isotherms in tempe-
rate and tropical seas the older observations afford, however, very few data, and we need
say little. We wait for those of the ‘ Challenger.’
Of the bathymetrical isotherms of 50°, 60°, 70°, and 80° F., the data are more
ample. They seem respectively to set in about lat. 60°, 50°, 25°, and 12° N., and the
first two to attain their greatest depths between lat. 40° and 20° — the isotherm of
50° F. falling to 3000 feet, and that of 60° F. to 1200 feet. They then rise, and from
lat. 12° N. to the equator, the isotherm of 50° F. comes within 1000 to 1200 feet of the
surface, and that of 60° F. from 300 to 400 feet.
In the South Atlantic, on the line of section No. 1, which now crosses over to the
eastern area of the South Atlantic, the bathymetrical isotherms seem to be prolonged
southward more nearly on the same level that they have near the equator — the isotherm
of 50° lying at from 1000 to 1400 feet, between lat. 7° and 40° S., and that of 60° F.
at 500 or 600 feet. In the western area (sect. No. 2) the isotherms of 50°, 60°,
and 70° F. are much more irregular, sinking in lat. 10° to 20° to about 3000, 1800,
and 500 feet, and then rising and ending, as in the other line of section, in about
lat. 40° and 45° S. But while, on the whole, the higher isotherms range rather further
south in the western than in the eastern area, the isotherm of 35° F. is in both prolonged
further south, on a nearly uniform level of from 7 000 to 8000 feet, between lat. 20° and 65°.
The Pacific Sections (Nos. 3 & 4) exhibit a much lesser number of observations, but
still sufficient to draw some general conclusions. Starting in one case in the Arctic
Sea north of Behring Strait, and in the other in the sea south of Behring Strait, one
line of section (No. 3) passes through the Eastern Pacific to the equator in long. 120° W.,
and the other (No. 4) through the Western Pacific to the equator in long. 180° W.
North of Behring Strait the sea is so shallow that the observations barely pass beyond
the limits of diurnal variations. The width and depth (180 feet) of that strait itself
are also so small that the intercommunication through it between the polar seas and
the North Pacific can have little or no effect on the thermal condition of the latter;
nevertheless it may be a question whether the submarine isotherm of 60° F. in that
ocean extends beyond the lat. of 40° to 45° N., and the isotherm of 50° F. beyond
about lat. 55° N., being about 5° less in either case of their northern range in the
eastern area of the North Atlantic; while the isotherm of 35° F. disappears, as in the
western division of the Atlantic, between lat. 60° to 70° N., instead of having the more
indefinite northward range it has in the open North Atlantic.
These isotherms also, instead of the remarkable rise which they present near the
equator in the North Atlantic, exhibit in the North Pacific a gradual decline to the
equator, where, judging from the few data we have at our disposal, they seem to lie —
that of 60° F. at 800 to 1000 feet, of 50° F. at 2000 to 2500 feet, of 40° F. at 4000
to 5000 feet, of 35° F. at 7000 to 8000 feet respectively, and pass the equatorial zone
without rise or apparent change of level.
On the other hand, in the South Pacific the conditions are much more like those of
MR. J. PRESTWICH ON SUBMARINE TEMPERATURES.
633
the South Atlantic. In the Eastern division (section No. 3) the isotherms of 60° F. and
50° F. are on a nearly uniform level from the equator to about 35° to 45° S. lat., and
extending apparently not quite so far southward as in the Atlantic. In the Western
division of the Pacific (section No. 4) the several isotherms seem to lie rather deeper,
and the isotherms of 60° and 50° F. to extend some degrees further south. But we again
have, as in the South Atlantic, the same expansion of the isotherms of 40° and 35° F.
as they range southward, the latter having in lat. 65° S. a depth of 6000 to 7000 feet;
from this point it rises rapidly, or is displaced by colder waters, as it approaches the
Antarctic continent.
Section No. 5, which crosses the Indian and Southern Oceans from 20° N. to 40° S.,
exhibits conditions analogous to those which obtain in the Pacific, though the isotherms
of 40° and 35° appear to lie deeper, viz. at depths of about 9000 to 12,000 feet at the
equator. They are then prolonged nearly on the same level to about 12° north, and
thence to rise as they approach the head of the Arabian Gulf, where they are lost in
the heated surface-waters. In the other direction the three higher isotherms on this
line of section maintain a more nearly uniform relative depth of about 200, 500, and
1500 feet, — that of 80° F. terminating in about lat. 20° S., that of 70° F. in lat. 30° S.,
and that of 60° F. in lat. 39° S. At this point the isotherm of 50° F. lies at a depth
of about 1500 feet, that of 40° F. at 4000 to 5000 feet, and that of 35° F. may be at
about 7000 to 8000 feet. In this section we have no data south of 40° S. lat.
Section No. 6 traverses the Southern Ocean more to the eastward. We there still
find the higher isotherms terminating in nearly the same parallels of latitude ; but we
can follow the lines of 40° F. and 35° F. further south — the former at a depth of about
4000 feet in lat. 53° S. and becoming lost in about lat. 65° S., and the latter rising and
disappearing in about lat. 70° S. South of this is a zone in which the temperature
of the sea to the depths (1800 feet) yet tried is 30° and 33° F. (corr.).
In the preceding observations the position of the bathymetrical isotherms can only be
taken as an approximation to the truth, though they are, there is reason to hope, rela-
tively correct. The deeper isotherms have possibly too high a degree, and the upper
ones, it must be borne in mind, are, in different meridians, subject to the action of
many causes that may produce aberration, such as displacement by the action of surface-
currents, which will vary according to their depth ; while another manifest cause,
affecting more especially the lower isotherms, arises from the inequalities of the
sea-bed, whereby the lower cold strata are deflected and driven nearer to the surface —
an effect not only due to submarine banks and some islands, but caused also by conti-
nental shores, as on parts of the southern coasts of Africa and of South America*.
Independently, however, of these local variations, certain general conditions have
been clearly established by the researches we have had occasion to review, — such as
the presence of a stratum of water at and below 35° extending from the Arctic and
* When this takes place the temperature of the sea at or near the surface will be found to become lower on
approaching the shore, against which the colder undercurrent rises. Their existence may thus be proved.
634
MR. J. PRESTWICH ON SUBMARINE TEMPERATURES.
Antarctic seas to the equator, and which no doubt has justly been attributed to deep
undercurrents carrying the waters of the poles to tropical regions, and the probable rise
of these polar waters to the surface in the equatorial zone of the Atlantic. The
source of those glacial waters in the North Atlantic lies, probably, in the Arctic Ocean ;
and the question arises as to the channels by which they travel southward. The
comparatively high temperature of 34° to 36° at depths in the seas around Spitzbergen
shows that, although a deep body of cold water may move down the east coast of Green-
land, the channels of the comparatively shallow sea between Norway and Spitzbergen
are entirely, and of the deeper sea between Spitzbergen and Greenland in great part,
occupied by a body of warmer water from the south (for without renewal the degree ot
heat could not be maintained), pn the other hand, the constant low temperature at
depths in Baffin Bay, and the southward drifting of the large low-sunk icebergs, show that
that sea and Davis Strait afford a passage to a deep glacial current derived from the Arctic
seas of North America. Issuing from these comparatively narrow channels this body
of cold water unites with that passing down the east coast of Greenland, and flows
southwards, over the great depths of the Atlantic, apparently to the equator.
In the South Atlantic, on the contrary, the channel of the deep-seated glacial water
is coextensive with the wide expanse open to the Antarctic seas, so that an unbroken
undercurrent of such waters may occupy the one broad bed of that ocean.
These two great undercurrents of the Atlantic, flowing respectively from the north
and the south poles towards the equator, must eventually meet ; and, judging from the
rise of the bathymetrical isotherms and the low temperature of the sea immediately
beneath the heated surface-waters in the equatorial regions, it is probable, as suggested
by Lenz, that the meeting is there, and that it is that which in part determines, in
conjunction with the excessive evaporation, the surging-up of the polar waters, though
other causes presently to be referred to may assist. In whatever way effected, the
waters which thus rise to the surface in the equatorial zone necessarily tend to disperse
and escape into other areas, whether by a slow movement in mass, or by more rapid
currents in shallower and more definite channels, or by both causes combined.
The course of these deep Arctic and Antarctic undercurrents or streams in the Atlantic
may be influenced by another cause ; viz. by the west to east trend of the South-
American continent from the Caribbean Sea to Cape St. Roque, and by that from east to
west of the African continent along the coast of Guinea — projections which both
contract the width of the Atlantic, and present barriers which may help to deflect side-
ways and upwards, on the one (American) side the southward flow of the Arctic waters,
and on the other (African) side the northward flow of the Antarctic waters, in a
manner analogous to that which takes place on shoals and islands.
It is not my intention to enter upon the discussion of the course and magnitude of
the Gulf-stream ; but I would suggest whether or not the initial start of that great
current, together with the others which originate or acquire new power at the equator,
such as the Guinea, the South Equatorial, and the Brazilian currents, may not be cradled
ME. J. PEESTWICH ON STJBMAEINE TEMPEEATUEES.
635
by this surging-up of Arctic and Antarctic waters at or near the equator ; while other
portions of those great bodies of water are deflected back and imperceptibly return the
one to the north polar and the other to the south polar seas — in masses unaffected by
the more active shallow drifts and currents sweeping over their surface, and whose
course is influenced by trade-winds and the earth’s rotation ; for while the cold waters
are found so comparatively near the surface in the equatorial regions, the presence,
at depths, in both the polar seas, of bodies of water having a temperature far above
not only that of the winter but the annual temperature of those latitudes, is equally
well proved. Thus although the mean annual temperature of Spitzbergen does not
exceed 18° F. (and Dove estimates'* the normal mean temperature of latitudes 80°
to 90° at 4°*5 F.), we find that in the seas surrounding that island there is a submarine
temperature of 34° to 35°, if not rather higher. In the same way in the Antarctic regions
and in latitude 60° to 70° we there also find a submarine temperature nearly as highf.
Thus there is a rise of from 6° to 8° Fahr. in descending from the surface to depths
of 3000 feet to 4000 feet in the open polar seas, whereas in like depths in the equa-
torial regions of the Atlantic there is a fall of not less than 40° F., extending at greater
depths to about 50° F.
There is every reason to believe that the open seas of the north polar regions are due,
as suggested by Maury and others, to the influence of warm southern waters, though
this is not, as supposed by those authors, owing to the action of the Gulf-stream J, but
to the surging-up of these deeper warm strata ; and in the same way the open sea found
by Cook, Weddell, Boss, and others, after passing the first barrier of ice in the south
polar seas, may be due to a similar cause. The great body of water at 32° to 35° or
36° F. extending to the depth of 4000 to 5000 feet or more, and passing by Spitzbergen,
must ultimately be displaced and deflected by the colder and denser waters between 32°
and 250-4 of the polar regions, and rise to the surface ; and as the influx is constant, an
equilibrium can only be maintained by an efflux as great to other areas. By Behring
Strait, owing to its narrowness and shallowness, comparatively none passes ; but the
surface-currents through Smith Sound, and the more intricate channels amongst the
islands of the North- American coast and so down Baffin Bay, and that down the east
coast of Greenland, originate doubtlessly with these effluent waters. The temperature-
soundings to depths of 1000 feet in Baffin Bay are in accordance with this view ; for
after passing the stratum affected by the diurnal variations, the water to about that
depth, although there is no surface-current from the south, has generally a temperature
of from 30° to 34°, while that at greater depths sinks at places to a point very closely
* The mean summer temperature of Spitzbergen, according to Dote, is 34°‘5 E.
t If, as we have reason to think, the observations of Sir James Eoss should require a larger correction than
others, then the isotherms in the Antarctic and Southern Oceans will have to be raised, and the isotherm of
35° will be replaced by one of 33° or 32° E.
+ At the same time there cannot, I think, he any doubt of the influence of the Gulf-stream, as a shallow
current, on the seas and northern shores of the British Islands and Norway.
MDCCCLXXV. 4 Q
636
ME. J. PKESTWICII ON SUBMARINE TEMPERATURES.
approaching to the freezing-point or to that of the maximum density of ordinary
sea-water. Moving in the same direction as the great body of colder water which it
overlies, the warmer surface-water has a greater velocity than it, and moves over it
as a surface-current — the causes which effect its impulsion being of a more energetic
character than those which originate during the colder months of the year with the
descent of the dense waters and their slow outward propulsion in a deep undercurrent.
In the Pacific Ocean the great breadth of open sea, and the almost entire exclu-
sion of the waters of the north polar seas, have produced conditions very different from
those which obtain in the Atlantic. The temperature-soundings are too few to lead to
any certain conclusion ; but, so far as they go, they seem to show that there is no uprising
of cold undercurrents at the equator. The observations referred to by Lexz are so scat-
tered and at such small depths, that they may have been affected by the action of the
great cold current which passes northward up the west coast of South America, and is
deflected westward at the equator, and by various other surface-currents.
In any case, the remarkable rise of the bathymetrical isotherms in the North
Pacific, which cannot be accounted for by any current passing through Behring Strait,
leads me to infer that the Antarctic waters pass under the whole length of the Pacific,
and are thrown up by the barrier presented at its northern extremity by the American
and Asiatic coasts. Some of the great currents of the North Pacific may owe their
origin to, while others seem to be strengthened by, these distantly derived waters.
Nor is it easy to account in any other way for the rise of the isotherms of 35° and
40° E. at the head of the Arabian Sea after traversing the deep bed of the Indian Ocean.
The high temperature of the surface-waters, however, prevents the effects being so
apparent in the upper strata of that sea. Again, the causes which influence the great
currents of the North -Indian Ocean appear to correspond with the area of surging-up,
as they approach the Asiatic continent, of the south-polar undercurrents.
The cause of these phenomena in both hemispheres is, in all probability, connected
with the intense cold of the polar regions, — the mean annual difference of from
7 0° to 80° F. between the polar and the intertropical regions forming a permanent
disturbing cause, owing to the alteration of density to which the affluent waters are
unceasingly subjected*. It is a cause, also, which, from the variation in the density of
the surface-water in winter and summer, must materially influence the operation of
the currents generally, both at the Arctic and Antarctic regions, during the different
seasons of the year, increasing the outflow from the polar seas in the cold months,
and the influx in the warmer, whence the outflowing current through Behring Strait in
the winter or spring, and the inflowing current in the summer. For the same reason
we should expect to find the general circulation more active in the one season than in
the other. But the discussion of these interesting questions is not our object.
In no way are the effects of the remarkable interchange between the polar and equa-
torial waters in the great oceans more conspicuous than in the comparison of the
* According to Dove the mean temperature of the equator is 79°*8 and of the pole 20,2.
ME. J. PRESTWICH ON SUBMARINE TEMPERATURES.
637
thermal conditions of those oceans with those of inland seas — the one so dependent on
local climatal influences, and the other subject to influences so distant; for whereas it
is the winter c#ld of the latitude which regulates the one, it is the cold of the polar
winters which affects the other. Thus the temperature of from 54° to 55° F. at depths
in the Mediterranean below the influence of the annual variations is that of the sub-
winter months of that area, as that of 70° is for the Red Sea. But the most striking
case is the sea of Okhotsk, where, in the parallel of Great Britain, but with a winter-
cold under 20°, or possibly under 15° F., we have a nearly enclosed sea, of which the
submarine temperature at 200 to 700 feet in the month of August is under 29° F.,
or nearly 2° below zero of Centigrade, the surface-temperature being 47° F.
These questions have necessarily a very important bearing on many geological
problems, especially those connected with climates and the distribution of species.
For example, it is probable that the increased severity of the climate noticed within the
historical period on the east coast of Greenland may arise from that elevation of the
land which is shown, by the presence of raised beaches and marine remains at heights
of from 50 to 300 feet or more on the north-western coast of Greenland41 and amongst
the islands of the Northern-American archipelago beyond Baffin Bay, to have taken
place at a comparatively recent period ; for this, by lessening the width and depth of
the many small straits opening into Baffin Bay, has thrown a larger volume of the
polar waters into the other channels, as that between Greenland and Spitzbergen, and
has thus had the effect of increasing and strengthening the ice-bearing current from
the north which passes down the east coast of Greenland. The amelioration of climate
towards the close of the Quaternary period may also have been locally greatly influenced
by the elevation of the land and shallowing of the seas around Britain and Norway,
by which any flow over this area of the deep polar currents has been diverted.
The cognate questions also connected with the southward range of an Arctic fauna
or the northward range of a tropical fauna, and, to compare the water with the land,
the insular-like character of the fauna of inland seas (all so liable to changes with any
alteration in the direction and volume of those deep and obscure f undercurrents to
which we have been referring, or by their ingress into seas before closed), are of the
highest importance in the consideration whether of the later or of the older geolo_
gical phenomena of the globe. They are, however, beyond the immediate range of
this paper, which I submit as a starting-point for further research.
To conclude, the observations recorded in these pages, after subjecting the readings
to the necessary corrections, show : —
1. — a. That a stratum of water at and under 35° F. extends beneath the Atlantic from
the Arctic to the Antarctic seasj; and, as it traverses all the parallels of latitude
* There is the same evidence of recent elevation on the coasts of Behring Strait.
t Using the word in contradistinction to “ conspicuous ” surface-currents, such as the Gulf-stream, the
effects of which are well known, and have so often been reasoned upon in connexion with geological phenomena.
t This has now been more fully established by the recent expeditions of the ‘ Porcupine ’ and ‘ Challenger.
4 q 2
638
ME. J. PRESTWICH ON SUBMARINE TEMPERATURES.
irrespective of the surface isothermals, it must have an origin dependent not on local
influences, but on others at a distance — such, in fact, as accord only with polar influences.
b. That in the North Atlantic the two channels through which the deep-seated
cold polar waters pass southward are Baffin Bay and the sea near the east coast of
Greenland; while the shallower seas immediately west of Spitzbergen, and between
that island and Norway, are occupied to their entire depth by warmer waters flowing
northward, from equatorial regions, towards the pole.
2. That in the North Atlantic the isotherm of 36° extends further in the polar seas
than in the South Atlantic ; but in both its rise is masked by the extreme climatal
variations and by surface-currents.
3. — a. That in the equatorial regions of the Atlantic the deep-seated north and south
polar waters, either owing to their meeting, or from impinging against projecting
continental coasts, or from irregularities in the sea-hed, or from the several causes
combined, are deflected and surge up at the surface, as shown by the rise of the bathy-
metrical isotherms.
• b. That the main portions of the upper strata of these surging waters flow slowly
en masse from this equatorial zone towards the poles — such bodies of water moving
independently of the drifts and surface-currents by which they are traversed and chan-
nelled.
4. — a. That in the Pacific there is a similar deep stratum of cold water at and under
35°, extending from the Antarctic Ocean to Behring Sea without rising, as in the
Atlantic, at the equator.
b. That in the North Pacific the submarine temperature is as low as or lower than
in the open North Atlantic in the same latitudes.
c. Consequently, as the body of cold water in the North Pacific cannot be of north
polar origin (comparatively none passing through Behring Strait), there is reason to
believe that the south polar waters traverse the whole length of the Pacific, and rise
against the coasts bounding that ocean on the north.
5. That in the same way the Southern and Indian Oceans are underlaid by the
cold waters proceeding from the Antarctic seas, which surge upwards as they approach
the Asiatic coast.
6. That there the surging-up of polar waters in the great oceans, and of tropical
waters in Arctic and Antarctic seas, is intimately connected with some of the great
surface-currents which originate, or acquire additional force, in equatorial and polar
seas, although the ultimate course of these currents may be influenced and determined
by the action of the prevailing winds and by the movement of rotation of the earth.
7. That the temperature at depths in inland seas is governed by local causes, and
tends in each case to assimilate to (or as near as the physical properties of water will
allow) that of the mean winter or sub-winter temperature of the place.
MR. J. PEESTWICH ON SUBMARINE TEMPERATURES.
639
Tables of Submarine Temperatures of the Great Oceans and Inland Seas, taken
between 1749 and 1868, arranged according to the Latitudes in each Hemisphere, and
reduced to English measures and Greenwich Longitude.
References to the original observations will be found in § II., in notes to the several voyages (given in order of date). Those
alone to which (w) is attached are from unpublished documents. Those also where (M.) is added to the name will be found in
Marcet’s paper {ante, p. 595), and not in the works of the original observers.. The temperature-readings are given as recorded by
each observer. To obtain an approximately true reading, it is necessary to apply the correction named at p. 612, excepting
the observations of Lenz (and Kotzebue, 2nd voyage), Du Petit-Ti-iouars (when stated “cylinder sound”), Martins, Aime,
Shortland, Vaillant (in part), D’Urville (in part), and some of Pullen’s, and probably Ross’s and Parry’s of 1818-19. The
correction consists in a deduction of 1° Kaiir. for every 1700 feet of depth. The figures in parentheses attached to Du Petit-
Thouars’s observations give his original corrections of temperature and depth. A separate list of the voyages on which the
observations were taken will be found, in connexion with the names in column VIII., in “Explanation of Map,” p. 671.
Table I. — Northern Hemisphere.
I.
II.
Bate.
III.
North
Lati-
tude.
IY.
Longi-
tude of
Green-
wich.
Y.
Sea.
YI.
Bepth
in feet.
YII.
Temperature in
degrees of Fahr.
Yin.
Name of
observer.
At
depth.
Surface.
Air.
I.
Mar., 1S28...
O O
99 40 w.
N. Pacific ...
480
71
0
83
83
Beechey
„ „
„ „
„ „
960
63-5
3-
22 Apr., 1825...
O ?
179 43 w.
N. Pacific ...
4800
45-5
837
Kotzebue, 2d.voy.
4-
May, 1824...
Near the
above place
N. Pacific ...
6000
36-5
86
5-
6 May, 1818...
0 7
20 26 w.
N. Atlantic ...
339
59-1
83-3
84-1
Kotzebue
5«.
21 Apr., 1848...
0 30
N. Pacific
6000
43.5
80*5
Belcher
6.
Oct., 1836...
0 33
8 16 E.
1ST. Atlantic . . .
3918
43
787
Wauchope
7’
6 May, 1818...
0 36
, 20 29 W.
N. Atlantic . . .
416
58
83-3
847?
Kotzebue
8.
5 Sept., 1772...
0 52
8 w.?
N. Atlantic . . .
510
66
74
7S'S
Forster
9'
8 Aug., 1828...
1
126 40 E.
N. Pacific . . .
1541
54-8
82-4
8l '2
D’Urville
IO.
12 Jan., 1847...
1 5
22 32 W.
N. Atlantic . . .
2010
52
83
77
Dayman
IJ.
12 May, 1816...
1 17
177 ^ W.
1ST. Pacific
1800
55
82-5
83
Kotzebue
12.
1847-49 1
17 w.
N. Atlantic . . .
360
58-2
81-4
E. Lenz
13-
8 May, 1818...
1 58
21 6 w.
N. Atlantic . . .
467
57'5
82-6
74 .
Kotzebue
14.
2 Dec., 1857...
2 20
28 44 w.
N. Atlantic . . !
4080
46-2
80
Pullen
*5-
,, „
„ 1,
c„ „
„ ,,
6480
38-5
„
16.
4 Feb., 1829...
2 30
1910 w.
N. Atlantic . . .
5101
43-6
80-5
79-2
D’Urville
*7-
9 May, 1818...
2 32
21 13 W.
N. Atlantic ...
480
58-5
84-3
8 1 -8
Kotzebue
18.
5 Feb., 1829...
3
19 IO W.
N. Atlantic . . .
2657
45-6
78-8
80-5
D’Urville
i9.
„ „
,, ,,
1594
59
83-2
82-8
20.
10 May, 1818...
3 S
21 24 W.
N. Atlantic ...
480
58‘9
84-5
84-4
Kotzebue
21.
1847-49
7. 14
21 W.
jSj\ Atlantic • • •
360
61
80
ID. Lenz
11 May, 1818...
j r
3 3°
21 53 w.
N. Atlantic ...
463
59
83
79'3
Kotzebue
23.
6 Feb., 1829...
3 3°
19 20 W.
N. Atlantic . . .
53
80-2
81
80-5
D’Urville
24.
„
„ •,
„ »
133
79-5
„
I5'
„ ».
„ „
n ii
266
70-8
26.
„ 1.
„ „
11 11
531
67;8
8i-8
27.
„ „
„ „
797
65-3
82
8i'S
,,
28.
„ >.
19 IOW.
1062
60-6
81
807
28a.
22 May, 1803...
3 27
14s w.
N. Pacific ...
600
60-2
82
lg
Krusenstern . . .
29.
23 Sept., 1858...
3 37
160 52 E.
N. Pacific ...
1200
7L2
85-8
82-8
Wiillerstorf
30.
22 Feb., 1804...
4
16 ? w.
N. Atlantic . . .
2274
45-5
88
88*3
jPeron
3i-
22 Sept., 1858...
4 2
l6o 41 E.
N. Pacific ...
600
81-6
84-8
8r6
Wiillerstorf
| 32.
30 Dec., 1838...
4 H
1 91 2 E.
Indian Ocean
1 600
70
827
82
Pratt :
IS.
Remarks.
\ Under the Equator 8° west of
J the Galapagos Islands.
1 JustN. of theEquator, between
\ the Sandwich Islands and
J Australia.
Between Brazil and Sierra Leone.
1° W. of Albemarle Island.
Gulf of Guinea. Rope vertical.
Between Brazil and Sierra Leone.
(Between the coast of Guinea
\ and Ascension.
In the Straits of Molucca.
In mid-ocean. W. of No. 7.
N. of Island of New Nantucket.
Near the Island of St. Paul.
Not far from No. 10.
1 In soundings : 90 miles off the
J Island of St. Paid.
In mid-ocean ; between the
■ north-west of Bra til and the
coast of Guinea.
imong the Society Islands,
f Between Marshall and Salo-
[ mon Islands.
Therm, remained down lh 15m.
Near the Caroline Islands.
Between Sumatra and Ceylon.
640
MR. J. PRESTWICK ON SUBMARINE TEMPERATURES.
Table I. — Northern Hemisphere (continued).
L
II.
III.
IY.
• Y.
VI.
YII.
Yin.
IX. J
Bate.
North
Lati-
Longi-
tude of
Green-
Sea.
Depth
in feet.
Temperature in
degrees of Fahr.
Name of
observer.
Remarks.
tude.
At
depth.
I
Surface.
Air.
wich.
33-
12 May, 1818...
O /
22 42 W.
480
§3 |
82-5
0
77-1
Kotzebue
In mid-ocean, between the
1 Deo., 1857...
28 42 w.
6000
42-5
80
Pullen
l coasts of Guinea and of
9000
39-4
Guayana.
36.
24 May, 1S39..
4 2 3
26 06 W.
N. Atlantic . . .
6398
(5151?)
42-S
(39-7)
8o-6
77 ’5
DuPetitThouars
Cylinder full of water.
37-
” ”
” „
” ”
6398
(6037 ?)
37-8
”
” ”
Cylinder sound.
3S.
39-
27 June, 1837...
13 May, 1818...
4 32
4 33
134 34 W.
24 1 1 w.
N. Pacific ...
N. Atlantic . . .
12273
471
35
57-9
81
82-6
78-8
81-9
DuPetitThouars
Kotzebue
Instrument crushed. Index fixed,
f Between Island of St. Paul
[ and Sierra Leone.
40.
Oct., 1823...
5
22 ? w.
N. Atlantic . . .
3000
43-2
83-8
Kotzebue, 2d voy.
In mid-ocean : near No. 33.
41.
42.
19 Deb., 1804...
7 Jan., 1847...
5 *
1 3 ? w.
22 19 w.
N. Atlantic . . .
N. Atlantic . . .
1280
2040
48-6
49
8/
83
90
82
Peron
Pflvma.n
Therm, remained down lh 50m.
f Mid-ocean, between Brazil and
( Sierra Leone.
43-
14 May, 1818...
6 Jan., 1847...
15 May, 1818...
1847-49
26 9 IV.
22 34 W.
27 34 W.
23 W.
22 39 W.
479
56-5
82-9
82
s3'9
79
8r8
Kotzebue
Between Guayana and Liberia.
In mid-ocean: near No. 42.
r
2166
50
Dayman
45-
46.
47-
48.
414
55-9
81-9
84
84
80
Kotzebue
j- Between Guayana and Liberia.
6 9
N. Atlantic ...
360
60
E. Lenz
5 Jan., 1847...
1847-49
N. Atlantic . . .
1110
51
82
Dayman
(Between Sierra Leone and
\ Guayana.
Between Cape-Yerd Is & St. Paul.
6 s2
N. Atlantic . . .
420
58-2
E. Lenz
49-
24 Nov., 1800...
7
20 W. ?
N. Atlantic
320
61-2
86
Peron ■
Therm, broke and replaced.
50.
16 May, 1818...
7 J3
28 32 W.
N. Atlantic . . .
368
58
81-5
82-3
Kotzebue
In mid-ocean, between Brazil
51*
10 Oct., 1823...
7 20
2i 59 w.
N. Atlantic . . .
3435
35-9
78-5
Lenz
J and Sierra Leone.
52.
16 Mar., 1858...
7 47
^ 93 18 E.
Indian Ocean
510
6S-8
818
8r8
Wiillerstorf
Near the Nicobar Islands.
S3-
22 Nov., 1800...
8 ^
Par. of Cape
Verd Isl.
| N. Atlantic
532
77
86-5
86
Peron '
Therm, down only 5m.
54-
14 Sept., 1858...
158 IO E.
N. Pacific ...
1200
66-5
84-5
82
Wiillerstorf
Amongst the Caroline Islands.
55-
5 Mar., „ ...
8 29
93 33 h.
Indian Ocean
480
78-2
83
80-3
”
East of Nicobar Islands.
56.
57-
3 Jan., 1847,..
13 Nov., 1817...
S 55
8 59
22 38 w.
155 36 E.
N. Atlantic . . .
N. Pacific ...
1146
600
59
S2
87
78
85
Dayman
Kotzebue
In the parallel of Sierra Leone.
J Between the Badack and the
\ Mariana Islands.
58.
59-
6 July, 1826...
12 May, 1846...
9
20 40 W.
97 w.
N. Atlantic . . .
2125
41-2
80-3
87
76-8
84
D’Urville
7° W. of Sierra Leone.
N. Pacific ...
60
85
Kellett
120
83
61.
180
81
„
62.
240
„
„
63.
300
66
*
53
Between the Galapagos Islands
and Acapulca, Mexico.
64.
65.
66.
600
1200
1800
4S
67.
68.
2400
46
;;
3000
44
”
69.
”
14 Nov., 1817...
9 20
155 l6 E.
N. Pacific ...
150
77
83
84
Kotzebue -
Amongst the Caroline Islands.
7°.
15 Nov., 1817...
9 26
154 59 E.
N. Pacific ...
90
79
87-4 j
857
Kotzebue
1
71
300
591
51-4
49-5
58-4
[Between the Badack and the
f Mariana Lslands.
72'
»
414
73-
» 99
17 May, 1818...
9 27
29 7 W.
N. Atlantic . . . |
606
79’2
”
80
”
Kotzebue
1
j
(Between tbe Cape-Yerd and
( St. ^aul Islands.
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
641
Table I. — Northern Hemisphere (continued).
I.
II.
III.
IY.
Y.
YI.
I
YII.
YIII.
IX.
Longi-
Temperature in
Date.
Lati-
tude of
Sea.
Depth
degrees of Pahr.
Name of
Eemarks.
Green-
in feet.
observer.
tude.
At
depth.
wich.
| Surface.
Air.
|
12 Apr., 1828...
Bay of Benga
531
0
63
86
86
Blosseville
| Off the north coast of Ceylon, j
76
77
7S
47
17 Not., 1817
153 17 E.
29 9 W.
NT. Pacific
438
57-4
51
84-2.
s3’5
Kotzebue
N. of the Caroline Islands.
Aug., 1816...
IO I4
N. Atlantic . .
5796
80
Wauehope
Corrected depth 2880 feet.
79
18 Not., 1817...
152 07 E.
N. Pacific ...
366
59-9
83-9
83-2
Kotzebue
j- N. of the Caroline Islands.
n 4
827
So.
19 ,,
150 56 E.
492
56-6
837
81.
18 May, 181S...
n 35
30 56 W.
N. Atlantic ...
393
59-4
78-8
79'8
„
S.W. of Cape-Verd Islands.
20 Not., 1817...
T T 4-7
T cn on i?
N. Pacific ...
. 516
63
84
84-2
Kotzebue
.j. . .
1 .Between the Mariana and the
83.
30 Aug., 1858...
11 55
I49 53 E.
„ „
270
84-8
84-5
83-8
Wiillerstorf
J Caroline Islands.
83a.
3 Sept., 1836...
11 59
hi 55 w.
4266
42-8
-g.g
81
Vaillant
1 Between Mexico and the Mar-
s35.
84
4 „
2133
49
80
82'4
i' quesas Islands.
21 Not., 1817...
12 28
I49 06 E.
468
66-9
83-3
8ri
Kotzebue
f Between the Mariana and the
| Caroline Islands.
]
85
22 July, 1843...
12 36
25 35 IV.
N. Atlantic ...
900
52 i
7915
James Boss
86
1800
47-6
140 miles W. of Cape-Verd
87.
.. I!
„ ,,
„ „
8100
39-5
„
„
> Islands. No soundings in
11,100 feet.
88.
„ „
„ „
moo
39-6
„
,,
J
89.
Before 1857
T„ 9
78 w. ?
Caribbean Sea
1440
48
83
Dunsterville . . .
9°.
„ „
„ „
2316
43
[Quoted by Maury without date
91'
» „
,, „
„ ),
„ ,,
2700
42
„
| or exact position.
92.
„ „
, , ,,
„ „
3000
43
J
93-
Apr., 1859...
13
48 IO E.
Gulf of Aden
7200
45
8i‘5
Pullen ( u )
In soundings.
94-
19 May, 1818...
13 24
32 2 W.
N. Atlantic . . .
393
58-1
76-5
777
Kotzebue
f Between Cape-Verd Islands
\ and Guayana.
94a.
95'
27 Mar., 1837...
13 27
83 20 E.
Bay of Bengal
N. Pacific ...
3200
46
78-8
78
Vaillant
Uncertain.
22 Not., 1817...
147 l8 E.
396
69-9
Kotzebue
E. of the Mariana Islands.
96.
97-
13 Dee., „
13 51
13 52
II9 36 E.
145 II E.
China Sea . . .
561
61-5
82-2
«4'5
837
West of Luzon.
23 Not., ,,
N. Pacific ...
270
71-1
827
j Between the Mariana and the
Philippine Islands.
”
98.
Mar., 1828...
14 22
99 35 IV.
N. Pacific ...
600
57
88
91
Beechey
99-
1200
1 Off the south-west coast of
100.
1800
48-5
f Mexico.
IOI.
2400
49-5
J
102.
Apr., 1859...
14 26
54 5 e-
Arabian Sea. . .
9000
43-5
82-5
Pullen (u)
fin soundings. Entrance of
| the Gulf of Aden.
103.
28 June, 1826...
15
22 40 TV.
N. Atlantic . . .
425
64-8
73'+
73 ‘4
D’Urville
E. of the Cape-Verd Islands.
104.
28 June, 1858...
I5 5
Il8 3 E.
China Sea . . .
510
83
847
84-5
Wiillerstorf,
IV W. of Luzon.
105.
106.
2 Jan., 1847...
15 28
*5 5i
16 5
23 22 VV.
N. Atlantic . . .
1080
53
73
76-5
75
Dayman
E. of the Cape-Verd Islands.
W. of Cape-Verd Islands.
1 Between Mexico and the Sand-
20 May, 1818...
Jan., 1827...
32 56 TV.
N. Atlantic...
384
77-8
Kotzebue
107.
r33 35'"'-
N. Pacific ...
1992
49
76
Beechey
J
108.
» „
2592
45
J wich Islands.
109.
1 Dec., 1817...
16 32
140 56 E.
N. Pacific ...
534
68-7
82-5
827 ■
Kotzebue
f Between the Mariana and the
[ Philippine Islands,
- no.
12
l6 A2
II9 26 E.
China Sea . . .
483
60-1
80*5
West of Luzon.
no a
11 Sept., 1836...
Apr., 1859...
l6 47
1 15 40 TV.
64 21 E.
N. Pacific . . .
6930
42-4
847 '
Vaillant l
3° N.W. 'of No. 835.
hi.
16 57
Arabian Sea. . .
11280
44-4
82
Pullen (w) ]
[n soundings.
1 12.
10 Oct., 1827...
i7 5
83 12 E.
Bay of Bengal
1647
50-4
857
?°'5 ]
Blosseville (
Iff the Circars coast.
^3.
8 July, 1857...
17 19
29 50 TV.
N. Atlantic ...
1200
60-3
8o-8
78'9
Wiillerstorf 1
W of the Cape-Verd Islands, j
642
ME. J. PEESTWICH ON SUBMARINE TEMPEEATUEES.
Table I. — Northern Hemisphere (continued).
I.
II.
Date.
III.
North
Lati-
IV.
Longi-
tude of
Green-
wich.
V.
Sea.
VI.
Depth
in feet.
VII.
Temperature in
degrees of Eahr.
VIII.
Name of
observer.
IX.
Remarks.
tilde.
At
depth.
Surface.
Air.
1 14.
115.
1 15^
2 Dec., 1817...
O /
0 /
139 14 E.
27 I w.
119 47 e.
II9 53 E.
34 24 w.
I34 20 E.
I34 l8 E.
137 56 E.
23 18 W.
456
480
3733
70-2
60-5
42-4
60
68-6
42
O
2 IVI
^0
Kotzebue
f Between the Mariana and the
( Philippine Islands.
bl.W. of Cape-Verd Islands.
In sight of Luzon.
W. of Luzon.
June, 1825...
29 Jan., 1837...
11 Dec., 1817...
17 30
17 54
jST. Atlantic . . .
76-5
77
78
82
Beechey
Vaillant
82 2
Kotzebue
11 7-
21 May, 1818...
10 Not., 1836...
18 21
N. Atlantic...
N. Pacific ...
432
3182
78-8
80
77*7
8i-5
79
79-6
68
Vaillant
Between SenegalandMartinique.
1
„ 27
18 25
18 40
4261
40-6
71-8
70
57
67
54
48
1 Between the Philippine and
j the Mariana Islands.
3 Dec., 1817...
81-5
73
Kotzebue
121.
jnn
1 Jan., 1847...
N. Atlantic . . .
468
1068
Dayman
| N. of the Cape-Yerd Islands.
123.
Mar., 1827...
1851
163 58 E.
N. Pacific ...
600
79‘5
75
Beechey
1200
Between Lamira and the Mar-
125.
126.
1860
i' shall Islands, Polynesian
Archipelago.
E. of the Mariana Islands.
Mar., 1827...
18 51
18 53
l6l 30 E.
I48 54 E.
1IA E.
N. Pacific ...
2520
1200
44
79
70* C
76
82
Beechey
'
Feb. 1804...
Indian Ocean
420
58
/y d
72*2
Horner
Off the N. W. coast of Australia.
128.
4 Dec., 1817...
19 20
T
I34 32 E.
132 15 B. .
130 35 E.
35 10 w.
83 30 w.
I55 59
N. Pacific ...i
270
70-9
67-1
67- 6
68- 5
45*5
8o-8
79-8
Kotzebue
1
129.
130.
I3I-
132.
I33-
*34-
I3S-
136.
5 ,, ,,
19 44
19 44
r9 59
20 30
21 06
21 13
438
1 Between the Mariana andPhi-
j lippine Islands.
6 „ „
498
77‘3
22 May, 1818...
13 Not., 1822...
N. Atlantic . . .
471
79
76-2
76-9
Kotzebue
In mid-ocean.
Caribbean Sea
7476
83
77
71
7Q* C
Sabine :
Corrected depth 6000 feet.
Cylinder sound.
J Between the Canaries and
\ Cape-Verd Islands.
9 July, 1837...
31 Dec., 1846...
18 May, 1824...
N. Pacific ...
1ST. Atlantic . . .
531
1158
55*4 |
61
76
66
DuPetitThouars
Dayman
21 14
164 E.
JST. Pacific ...
898
61 ’5
Lenz
2635
37-6
37-3
36-4
/y d
...
(Between the Sandwich Islands
[ and the coast of China.
4236
]3g’
5835
J
23 May, 1818...
13 Jan., 1837...
June, 1825...
Not. 1804...
21 40
22 2
36 14 w.
N. Atlantic . . .
368
68-8
75-8
70-2
767
71-6
Kotzebue
/Between Canaries and West-
1 39-
140.
141.
M-ia
1415
19 33 w.
'll 14 w.
I32 E.
N. Atlantic . . .
1ST. Atlantic . . .
2657
(1607 ?)
240
50
63
DuPetitTbouars 1
Beechey
]_ Indian Islands.
Cylinder full of water.
4° W. of Cape Blanco.
1 Between the Loo-choo and the
J Mariana Islands.
z3
N. Pacific . . .
300
74-2
74
Horner
780
60-2
” 99
”
The later observations
in the Indian Ocean by Capt. Shortland are given
as a whole without separate particulars : —
1868. ,
Between Jan. 28 j
and Feb. 12 ... [
Between Kooria-Moor
(17° to 20° lat. N. !
Innfr. EA
ia and Bombay
and 45° to 70°
( 600
3000
6000
9000
60
50-9
42-8
35 ‘3
75
74'5
Shortland
1
1 Mean of all the observations'
between these dates.
Feb. 22 to March 6 |
Between Kooria-Mooria and Aden
(13° to 17° lat. N. and 45° to 55°
lonp1. EA
12240
, 13020
f 600
3000
6000
33-7
33-5
67-7
54-2
454
76-5
78-8
„
1 Mean of the observations be-
r tween these dates.
1
( 7800
36
”
)
ME. J. PRESTW1CH ON SUBMARINE TEMPERATURES.
643
Table I. — Northern Hemisphere (continued).
I.
n.
III.
IY.
Y.
YI.
YII.
YHI.
IX.
North
Lati-
Longi-
Temperature in
Date.
tude of
Green-
wich.
Sea.
Depth
in feet.
degrees of Pahr.
Name of
observer.
Remarks.
tude.
At
depth.
Surface.
Air.
141c
June, 1804...
0 ,
O i
178 E.
N. Pacific ...
O
76*4
O
78
0
1 Horner
300
70-8
I Between the Sandwich Islands
| and Japan.
750
62
4 1
T
24 May, 1818...
36 51 w.
N. Atlantic . . .
471
696
76-9
77
Kotzebue
In mid-ocean.
1 7A4
May, 1827...
23 6
124 52 E.
China Sea ...
55*5
80-5
82
Beechey
■44-
145-
1860
47
1 Off the east coast of Formosa.
2100
45
” ”
146.
30 Dec., 1846 ...
,, n 07
N. Atlantic ...
396
66
69
68
Dayman
1 Between the Cape-Yerd and
1140
61
J Canary Islands.
22 June, 1804...
On the N.
tropic.
178 4E.
N. Pacific ...
150
76
78
Krusen stern ...
...
300
71
1 Between the Sandwich Islands
» =,
.. >.
» ,7
7. >7
7.
77
J and Japan.
147c
750
62-6
)(
J
148.
June, 1826...
24 57
163 21 W.
N. Pacific ...
1200
67
77
76
Beechey
f Between Sandwich and
1 Gardner Island.
T 1 9
8 Feb., 1825...
25 6
25 13
156 58 W.
25 12 W.
1070
57*5
71
Lenz
N. of the Sandwich Islands.
150
1749 ...
N. Atlantic . . .
3900
53
84
84
Ellis
| 43m to haul up.
I5I-
5346
152J
25 May, 1818...
25 23
37 w.
|N. Atlantic ...
435
68-9
76
76
Kotzebue
1 Between the Canaries and the
I53-
1847-49 ...
25 35
37 w.
N. Atlantic . . .
360
66-3
72-5
E. Lenz
J W. -India Islands.
I54*
Dee., 1827...
25 38
117 48 w.
N. Pacific ...
300
62
63
62's
Beechey
J55-
n „
»
7,
900
50
„
! 3° distant from the coast of
156.
„
„ 7,
77 77
1260
47'5
„
„
j Lower California.
i57.
„ 7,
„
.7 „
>7 >7
1860
47-5
„
„
J
158.
June, 1853...
Off Cape
26
Florida.
N. Atlantic ...
3300
49
Bache
12 miles E. of the lighthouse.
\ Between Africa and the West-
158ft
June, 1803...
37 w.
N. Atlantic . . .
420
65-7
74-2
Horner
1 586
i59.
1200
63
J India Islands.
6 June, 1846...
26 38
133 26 w.
N. Pacific ...
60
69
71
70
Kellett
160.
120
68
„ j
161.
180
68
! 162.
163.
” ”
„ „
240
300
68
68
”
Between Lower California
164.
165.
600
645
( and the Sandwich Islands.
1200
50
j
166.
1800
46
167.
2400
44-5
168.
3000
43
7
168 a
Not., 1804...
27
147 w.
N. Pacific ...
180
70-8
78
Horner
168 b
540
64-7
[l0° N.E. of the Sandwich
168 0
600
64-4
[ Islands.
ma
720
64-4
J
169.
4 Mar., 1829...
27
3 i 40 w.
N. Atlantic . . .
2657
51-2
69-3
68
D’Urville !
Between Teneriffe and Bermuda.
170.
27 June, 1857...
27 2
24 7 w.
N. Atlantic . . .
600
72-2
74*4
73’8
Wiillerstorf
| No soundings in 24,300 feet.
171.
” „
” ”
1440
63-7
”
4 R
MDCCCLXXV.
644
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
Table I. — Northern Hemisphere (continued).
I.
II.
III.
IY.
Y.
YI.
|
YII.
YHI.
Date.
North.
Lati-
Longi-
tude of
Green-
wich.
Sea.
Depth
in feet.
Temperature in
degrees of Eahr.
Name of
observer.
tude.
At
depth.
Surface.
Air.
172
9 Nov., 1857...
O 1
27 31
O 1
21 39 W.
N. Atlantic . . .
3000
0
50
0
72
0
Pullen ( u ) . . .
173
,,
>.
.. „
4800
44-5
„
„ (u) ...
174
26 May,
1818...
27 38
37 10 w.
N. Atlantic . . .
448
65-7
74'5
75
Kotzebue
175
22 Sept., 1817...
27 50
152 21 w.
N. Pacific . . .
30
75
77
76-1
Kotzebue
176
„
„
,; „
„ „
„ „
60
74-5
„
„
177
„
„
„ „
„ »
,, „
150
73-7
„
178
„
„ „
11
» 11
300
67-2
„
„
179
„
„ »
„ ii
» >,
600
61
„
„
180
„
„
„ »
„ „
» »
1200
51-5
„
„
181
June, 1826...
28 22
172 i7w.
N. Pacific ...
900
57
76-5
77
Beechey
182
1854 |
95 miles
Cana
off Cape ]
veral. J
N. Atlantic . . .
2100
50
82?
Craven
183
30 Dec.,
1846...
28 34
18 38 w.
N. Atlantic . . .
780
63
67
66
Dayman
184.
June,
1826...
28 52
*73 9 w-
N. Pacific ...
2400
47
78
81
Beechey
185.
„
„
„ »
.. „
3600
41
„
„
186.
V
„ „
„ „
4704
42-8
„
„
„
187.
10 Oct.,
1837...
29 32
34 40 w.
N. Atlantic . . .
8838
44
75
79
Vaillant
188.
1 June,
1816...
29 24
160 34 E.
N. Pacific ...
600
62
74
75
Kotzebue
189.
„
„
„ >»
.» J.
„ „
1800
52-5
„
„
„
190.
17 Nov.,
1837...
29 25
118 51 W.
N. Pacific ...
2657
43-3
65-3
69-5
DuPetitThoua
190a
June,
1803...
3°
40 w.
N. Atlantic . . .
90
70-2
72-5
Horner
190 b
„
„
„
„ „
180
68-5
»
1 90c
„
„
„
„
, , „
378
65-7
,,
190 d
»
„
„
840
62
„
190c
„
„
„
,, ,,
1020
62
„
19°/
„
,,
„
„
,, ,,
1200
62
,,
„
191.
27 May,
1818...
3° 3
37 24 w.
N. Atlantic . . .
368
66-5
73
75‘5
Kotzebue
192.
25 Oct.,
1815...
30 12
15 14 w.
N. Atlantic . . .
1176
56-3
74‘3
74' 3
Kotzebue
*93-
22 June,
1857...
30 50
23 6 w.
N. Atlantic . . .
576
67
71
7*
Wullerstorf. . . .
*94-
23 July,
1817...
31 1
123 46 E.
Yellow Sea . . .
240
65
74
76
Abel
195.
1847-49 ..
31 48
36 w.
N. Atlantic . . .
360
64-3
73
„
E. Lenz
196.
31 Aug., 1825...
32 6
136 48 w.
N. Pacific . . .
578
56
70A
Lenz
197.
» >,
„ „
1364
43-6
„
„
198.
„
„
„ „
2870
38'8
*99-
»
„ »
„ „
3773
35-9
200.
6 Nov., 1857...
32 13
19 5 w.
N. Atlantic . . .
2400
51-5
7°'5
„
Pullen
201.
6 May,
1826...
32 20
42 30 w.
N. Atlantic . . .
6470
36
697
Lenz
202.
28 May, 1818...
32 36
36 35 w.
N. Atlantic . . .
393
671
72
727
Kotzebue .......
203.
1844?
32 46
165 53 w.
N. Pacific ...
600
55-7
Belcher
204.
205.
900
1800
52-7
48-1
>> 9 }
206.
2700
3600
43-2
43-2
207.
. ” ” |
IX.
Eemarks.
1 Between the Canaries and
J Cape-Verd Islands.
In mid-ocean.
1.6° N.E. from the Sandwich
| Islands.
) .
Off Bunker Island.
Exact position not given.
W. of the Canaries.
I N. of Bunker Island ; Poly-
j nesian Archipelago.
f Between the Canaries and
[ Elorida.
1 7° N.N.W. of the Sandwich
I Islands.
Cylinder full.
1
Between the Canaries and
[ Bermuda.
( Between the Canaries and
[ Madeira.
f Between the Canaries and
[ the Azores.
E. of Chusan.
Between the Azores and West-
India Islands.
distant from the
ast of Japan.
]
[About 3
j south i
J
f Between Madeira and the
[ Canaries.
1 Between Madeira and Ber-
J muda.
Between the Sandwich and the
)■ Aleutian Islands. Quoted
j by Jas. Boss, vol. ii. p. 53.
ME. J. PEESTWICH ON SUBMARINE TEMPERA TUBES ,
645
Table I. — Northern Hemisphere (continued).
I.
11.
III.
IY.
Y.
YI.
VII.
VIII.
IX.
Date.
North
Lati-
Longi-
tude of
Green-
wich.
Sea.
Depth
in feet.
Temperature in
degrees of Eahr.
Name of
observer.
Eemarks.
tude.
At
depth.
Surface.
Air.
zo’ja
2076
July, 1804..
33
O 1
I70 E.
N. Pacific . .
330
1200
60-5
53-6
O
70*2
O
Homer.
1 Between the Sandwich Islands
J and Japan.
208.
7 June, 1857...
33 38
14 4 w.
N. Atlantic . .
720
59-6
69
68*6
Wullerstorf
Between Madeira and Morocco.
209.
29 May, 1818...
June, 1826...
34 34
34 Si
35 55 w.
165 39 E.
452
62
69*2
78
69-3
69
Kotzebue
Between Bermuda and Spain.
1
1920
54-7
Beechey
” „
3450
4560
43
43-5
1 Between Japan and the Sand-
j wich Islands.
17 Dec., 1846...
{
34 S2
about ]
16 24 w.
792
61
61
59
Dayman
N. of Madeira.
213a
214.
215.
35
62
80
IVTaiipy.
Bottom of Gulf-stream.
June, 1826...
35°?J
35 11
165 21 E.
N. Pacific ...
900
72
78
Beechey
| In mid-ocean.
1500
216 .
4 June, 1857...
35 20
8 55 w.
N. Atlantic . .
420
59-6
65‘5
66-8
Wullerstorf
Near the Strait of Gibraltar.
217.
1847^9 ...
35 35
35 37
35 39
35 4i
35 5i
17 w.
35 w.
34 w.
35 iaw.
147 38 w.
N. Atlantic . . .
180
62-6
63-6
68 ’4
67-8
74’5
72-2
E. Lenz
N. of Madeira.
218.
360
60
S.W. of the Azores.
219.
360
61
S.W. of the Azores.
220.
30 May, 1818...
N. Atlantic . . .
445
62-3
69-9
75
Kotzebue
7° S.W. of the Azores.
221.
14 Sept., 1817...
N. Pacific ...
24
72
Kotzebue
222.
48
70-9
223.
90
681
224.
150
57-6
225.
300
54
Between the Sandwich Islands
and the coast of California.
226.
600
51
227.
2448
42-8
228.
18 Sept., 1817...
36 9
148 9 w.
N. Pacific . . .
150
571
7i*9
73
Kotzebue
229.
„ „
„ „
„ »
600
52'8
„
,,
230.
„ „
1800
44
;
231.
24 July, 1817...
36 24
37 3
122 59 E.
160 43 e.
Yellow Sea . . .
90
67
”
75
Abel
S. of Staunton Island.
232.
6 June, 1816.,
N. Pacific . . .
60
59 "5
61
63
Kotzebue
]
233.
,,
150
56 -8
I Between the Polynesian Archi-
[ pelago and Kamtschatka.
234.
600
52-7
235-
1800
43
1
J
236.
31 May, 1818...
37 9
37 3°
34 31 w.
122 40 E.
N. Atlantic . . .
378
62-2
687
69
67
67
73
Kotzebue
5° W. of the Azores.
I
237.
25 July, 1817...
Yellow Sea ...
90
66
Abel
238.
120
62
72
}- Upper part near the coast.
1
j
W. of Fayal.
Gulf ofPetchili.
239-
26 „ „ ...
37 38
38 9
121 34 E.
33 8 w.
120 20 E.
90
66
74
687
240.
1 June, 1818...
N. Atlantic . . .
445
61 '5
68 ’9
74
61
Kotzebue
241.
27 July, 1817...
38 12
Yellow Sea . . .
90
72
Abel
242.
June, 1826...
38 55
165 48 E.
N. Pacific ...
1080
44
64
Beechey
1 Between the Polynesian Archi-
J pelago and Aleutianlslands.
243.
2280
41-5
244.
16 Oct., 1815...
39 4
13 8 W.
N. Atlantic...
828
55
69-1
72-5
Kotzebue
245.
576
56
} 4° W. of Lisbon.
246.
2 June, 1818...
39 15
39 27
31 3 w.
12 57 W.
N. Atlantic . . .
432
601
67- 5
68- 5
65
lid-ocean ; W. of the Azores.
247.
15 Oct., 1815...
N. Atlantic . . .
600
55-7
Iff the coast of Portugal.
4 e 2
646
ME. J. PRESTWICK ON SUBMARINE TEMPERATURES.
Table I. — Northern Hemisphere (continued).
I.
II.
III.
IY.
Y.
YI.
North.
Longi-
Date.
tude of
Sea.
Depth
tude.
Green-
wich.
in feet.
248.
1847-^9 ...
O 1
40 4O
0 1
27 w.
S’. Atlantic . . .
360
249.
24 Aug... 1825...
41 12
14 1 58 w.
Sf. Pacific ...
1308
250.
„ ..
>>
>» .»
„ ,,
3263
250a
1854 ...
\ 160
miles off f
N. Atlantic . . .
120
251.
„
J Nan
tucket. \
„ „
5400
252.
May, 1825...
41 20
14 40 w.
S. Atlantic . .
840
253-
19 Aug., 1837...
41 42
162 42 E.
N. Pacific ...
1066
(905D
254.
4 June, 1818...
41 43
27 23 w.
ST. Atlantic . . .
442
255.
::
GO
0
42 32
34 5 8 w.
S'. Atlantic . . .
4688
256.
18 Aug., 1837...
42 1
163 38 E.
N. Pacific . . .
1066
(640 ?)
256a
15 July, 1868...
43 3°
38 50 W.
N. Atlantic . . .
600
2565
„ »
„ „
i) ,,
1800
256c
„ .>
„ »
„ „
6000
256(7
Sept., 1868...
43 4°?
38 O W.?
ST. Atlantic . . .
600
256c
„ „
„ „
„ „
„ „
2400
256/
„ ,,
„ „
,, ,,
6000
256 9
„ »
„ „
„ „
12000
256 A
29 Aug., 1868...
44 3
48 7 w.
N. Atlantic . . .
300
256 i
„ »
„ ».
,J J>
„ „
6000
25 6?
July, 1868...
1 West
ern edge of
Bank of f
3000
256#
„ „
)
Newfound
land. \
6000
2567
” ”
| Betw
een Flemish
Grand
G-ap and 1
Bank. J
1500
257.
21 Aug., 1837...
45 5
161 48 E.
N. Pacific ...
958
(479?)
258.
30 June, 1846...
45 3°
133 w.
N. Pacific . . .
60
259.
„ „
„ ,,
120
260.
,, „
,, „
„
180
261.
„ ,,
240
262.
„ »
„ »
„ „
300
263.
„ >,
„
„ „
600
264.
>» „
„ „
„ „
1200
265.
>. ,,
„
„ ,,
1800
266.
„ f)
,, „
„ „
2400
267.
„ ,,
„ „
„
„ „
3000
268.
,26 May, 1826...
45 53
15 17 w.
N. Atlantic . . .
1252
269.
,, „
„ 5,
»
2524
270.
. 6 June, 1818..
45 57
21 23 w.
N. Atlantic . . .
357
270 a
s Sept., 1804..
47
158 E.
N. Pacific ...
480
270 1
>12 Sept., 1868..
47 u
23 14 W.
IN. Atlantic . . .
12000
271.
7 June, 1318..
47 18
20 30 W.
N. Atlantic . . .
402
272.
47 32
20 24 W.
462
YII.
Temperature in
degrees of Pahr.
depth.
56
41-2
35-8
67
35
58
41-2
586
46
41-5
62
52
42
59
49
43
42
43
39'5
39-5
403
39-2
48
48
48
47
47
45
42
42
42
42
50-7
49-9
54-7
42
54’5
54-7
62-6
66-5
64
58
64-1
61
58-6
61
60
5°
547
5®
YIII.
IX.
Name of
Remarks.
observer.
E. Lenz
Lenz . . .
Beechey ....
DuPetitThouars
Kotzebue
Vaillant
DuPetitThouar:
Chimmo
Chimmo
N. of the Azores.
"I Between the Sandwich Islands
J and British Columbia.
| Exact position not given.
6° W. of the coast of Portugal.
Cylinder sound.
4° N. of the Azores.
Between Portugal and New York.
\ South of Kamtschatka. Cylin-
J ders sound.
Soundings in 13,680 feet.
DuPetitThouars
Kellett
58‘3
Lenz
6o*6
65
TCofczfihufi
60
Horner
Chimmo
60
607
Kotzebue
60-3
6r3
”
Near the Grand Bank of New-
| foundland.
J
| Soundings in 9900 feet.
I Soundings in 9000 feet.
South of Kamtschatka. Cylin-
ders sound.
10° W. of the mouth of the
Columbia River, Oregon.
Near the Bay of Biscay.
Between Portugal and Azores.
Between Ireland and the
Azores.
ME. J. PEESTWICH ON SUBMARINE TEMPEEATIJEES.
647
Table I. — Northern Hemisphere (continued).
I.
II.
III.
IY.
Y.
YI.
YII.
YIII.
IX.
North
Lati-
tude.
Longi-
tude of
Temperature
in
Date,
Sea.
Depth
degrees of Eahr.
Name of
Eemarks.
Green-
wich.
in feet.
At
depth.
Surface.
Air.
observer.
9 June, 1818...
19 42 w.
N. Atlantic . . .
451
54°2
62-5
6o‘4
I\< >t zcbue
\
1
10 „
48 2
17 56 W.
54-2
62
62-3
I Between Ireland and the
1 Azores.
*75-
11 „
48 8
15 33 w.
480
52-3
62-5
63-5
276.
12 „
48 22
13 45 w.
429
51-1
63-8
69-9
J
277.
13 „
10 50 w.
492
52-1
59'5
68
5° W. of the Scilly Isles
278.
May, 1845 ...
48 45
6 19 w.
N. Atlantic . . .
498
52
57
59
Beecliey
Entrance of British Channel.
>79.
19 July, 1850...
5°
170 w. ?
N. Pacific ...
1080
40
51
5°
Armstrong
No soundings. S. of Aleutian Is.
280.
18 Sept., 1837...
51 34
l6l 41 E.
N. Pacific ...
5872
(57411)
36-4
53
51-8
DuPetitThouars
Cylinder sound.
280a
Lsi
52
Tfin f
312
43'1
Horner
Off Petropaulovski.
'I
Oct., 1826 ...
163 39 w.
N. Pacific . . .
600
39
47'5
46
Beechey
2S2.
j3
39-7
1200
L, , , „ _ „ . , .
! 0 to tlie b.ih. oi the Aleutian
j Islands.
283.
2136
40-7
284.
2736
40
)
285.
11 June, 1773...
55?
0 37 w.?
N. Atlantic . . .
192
49
51
55
Phipps
North Sea; off Whitby.
286.
4 June, 1819...
27 May, 1819...
55 1
56 59
35 36 w.
24 33 w.
N. Atlantic . . .
1500
44-5
44-2
48-5
43
49
Parry
No soundings.
287.
6120
45'5
Between Ireland and Greenland.
288.
25 „ „
57 4
57 42
17 52 w.
14 16 w.
600
49
5o
49' 5
5°'5
5°
Near Rockall. Marcet’s bottle.
28,
290.
24 „
28 „ „
840
780
47.7
48
”
Do. do. In soundings.
Marcet’s bottle used.
57 26
25 16 w.
49
49
291.
5 May, 1828...
57 35
36 36 w.
N. Atlantic . . .
660
44-4
46-4
5i'3
Graali
Betw. Ireland and Newfoundland .
292.
17 June, 1819...
57 5i
41 5 w.
N. Atlantic . . .
1410
39
4°'5
4i'5
Parry
Off the south of Greenland.
*93-
July, 1827...
58 48
175 2 E.
N. Pacific . . .
600
45
54
57
Beecliey
41-5
[off the Siberian coast; Beh-
f ring Sea.
294.
1200
295.
1962
40-5
296.
2652
40-5
J
297.
17 June, 1819...
58 52
59
48 12 W.
44 w.
N. Atlantic . . .
1740
38-7
38'S
39
38'5
40
Parrv
Entrance to Davis Strait.
298.
23 May, 1818...
N. Atlantic . . .
480
37
Sabine (M.)
No soundings. Off C. Farewell.
299.
1860 ...
59 27
26 41 w.
N. Atlantic . . .
600
48-5
48
44
Wallich
Soundings in 7560 feet.
300.
301.
30 June, 1859...
59 35
59 4°
38 9 w.
47 46 w.
N. Atlantic . . .
1800
44'4
44-6
37
...
Kiindson
Off S. of Greenland.
18 June, 1819...
N. Atlantic . . .
1560
39
35
Parry
f Entrance to Davis Strait.
{ No soundings.
302.
3°4-
12 June, 1773...
60
O 10 E ^
N. Atlantic . . .
390
44
5°
40
5°
37
Phipps
Off Shetland.
4 Oct., 1818...
60
58 w.
Davis Strait .
5400
35‘7
Sabine (M.)
No soundings.
3°5-
8 Aug., 1859...
60 10
36 21 W.
N. Atlantic . . .
1800
45
48'6
Kiindson
Parallel of Cape Farewell.
306.
7 Sept., 1773...
60 14
2 30 E.?
N. Atlantic . . .
336
50
57
60
Irving
Between Shetland and Norway.
307.
29 June, 1859...
60 27
35 34 w-
N. Atlantic . . .
1800
44-1
48
Kiindson
Parallel of Cape Farewell.
308.
27 Oct., 1818...
61
7 w.
N. Atlantic ...
2820
47
49'5
5°'5
Sabine (M.)
No soundings.
308a
14 Aug., 1858...
62?
55 w.?
Baffin’s Bay. . .
150
31-5
38
Walter.
1
308J
„ V
„ „
300
29-5
„
( Doubtful about position.
308c
„
„ ,,
684
30
J
309.
310.
311-
July, 1827...
61 10
176 32 E.
N. Pacific . . .
30
60
120
41-5
38
29-5
43'5
45
Beechey
) Off theooost of Siberia; north-
f ern part of Behring Sea.
J
1
648
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
Table I. — Northern Hemisphere (continued).
I.
II.
III.
IY.
Y.
YI.
Pate.
North
Longi-
tude of
Sea.
Depth
tude.
Green-
wich.
in feet.
312
July, 1827...
61 10
176 32 E.
N. Pacific . . .
120
313
77 79
„ „
„ ,,
99 39
180
314
77 77
„ „
,3 ,9
33 99
180
3J5
„ „
9, 3,
99 99
312
316
77 f7
39 9,
600
317
97 77
,, „
93 33
93 33
1200
318
11 Oct., 1820 ...
6l II
31 12 W.
N. Atlantic . . .
1920
319
28 June, 1859...
61 12
33 w.
N. Atlantic . . .
1200
320
27 Oct., 1818 ...
61 48
1 52 w.
N. Atlantic . . .
2838
321
1 June, 1818...
63 50
55 3° w-
Davis Straits.
870
322
3 Sept., 1823 j
64 to
64 qo?
84 to
85 w.?
f Arctic Ame-
[ rica.
} 900
323
>, „
„
3, „
" 1080
324
4 Sept. „
,, „
„
33 33
600
325
»
„ »
„
39 93
840
326.
„ 39
„
93 93
1020
327.
»
„ 33
33 99
1200
32*-
5 Sept., „
33 33
99 33
960
329.
6 Sept., „
3, ,3
„
690
.33°-
»
3, „
„
750
331-
»
3, ,3
„
39 39
780
332-
»
33 33
„
„ „
810
333-
7 Sept., „
33 33
„
„ „
600
334-
„ 33
„
33
630
335-
»
,3 ,3
„
39 39
690
336.
»
33 33
„
33 99
744
337-
8 Sept., „
33 3>
„
33 39
636
338.
„ „
39 33
648
339-
»
» 39
39 33
660
34°.
„
„
39 39
720
341.
9 Sept., „
„ „
„
93 93
600
342-
»
„ „
„
93 33
720
343-
10 „
„ »
„
33 33
840
344-
11 „
33 9,
„
99 9 9
720
345-
4 Sept., 1773...
65 ?
2 21 E.
N. Atlantic . . .
4098
346.
26 Sept., 1818...
65 5°
59 30 W.
Davis Strait. . .
1860
347-
24 Sept., 1818...
66 35
5 33 E-
N. Atlantic . . .
1560
348-
24 Sept., 1818...
66 38
5 44E.
N. Atlantic . . .
1560
349-
19 Sept., 1818...
66 50
61 w.
Davis Strait...
600
35°.
»
„ „
„
39 99
1200
351-
» „
»
33 33
2400
352.
»
„ „
„
39 33
4080
353-
21 Sept., 1820...
67 38
59 1 w.
Davis Strait. . .
1200
354-
20 „
68 12
60 50 w.
” ”
1908
YII.
Temperature in
degrees of Eahr.
At
depth
44-2
437
47
32
30
30
30-5
31
30-5
30- 5
31- 4
29- 5
307
30
30
30- 5
29-5
29- 5
30- 2
29
29-6
297
295
30
30
30
30
40
29
41-5
41*5
30
29
29
2575
33-2
33
47'5
46-4
49
36
3°
3°'S
3°
3i
3°'5
3°'5
317
3°
3°'7
3°'S
3°'S
3i
29'5
30-2
3i
30
3°'5
3°
297
3°
3°'5
3°
3°
55
34
43
43 '5
33
34'5
32
YIII.
Name of
observer.
Beechey
IX.
Eemarks.
Off the coast of Siberia ; north-
ern part of Behring Sea.
[bottle used,
Parry |15°W.ofCapeFarewell. Marcet’s
Ktindson Fal'GWe11
Parry (M.) N. of the Shetland Island;
Parry (M.).
Parry
Beset in ice, in and near Lyon
Inlet, Pox Channel, Hud-
son Bay. Soundings were
obtained in each case at a
further depth of from 30 to
100 feet. Marcet’s water-
bottle supposed to have been
used.
Phipps
Sabine (M.)...
Franklin
Beechey (M.)
Sabine (M.)...,
Between Iceland and Norway.
Soundings in 2220 feet.
> Between Iceland and Norway,
Soundings in 4500 feet.
f Boss & Sabine
l (M).
Parry In soundings. Marcet’s
Parallel of Disco Island.
[used.
bottle
ME. J. PEESTWLCH ON SITBMAEINE TEMPEEATUEES.
649
Table I. — Northern Hemisphere (continued).
I.
II.
III.
IY.
Y.
YI.
YII.
Yin.
IX.
North
Longi-
tude of
Temperature
in
Date.
Sea.
Depth
in feet.
degrees of Eahr.
Name of
observer.
Eemarks.
tude.
Green-
wich.
At
depth.
Surface.
Air.
355-
11 Sept., 1820...
68 19
66 05 w.
Davis Strait...
876
34:
32
34
Parry
)
1 Near the American coast.
356.
357-
990
J
18 „
68 24
63 08 w.
Davis Strait...
1908
30
3°
29
”
Near mid-channel.
3 j8.
15 „
68 24
63 32 w.
63 48 IV.
1020
3°-S
3i
11
No soundings in 3660 feet.
Six’s therm, used. In soundings.
35,
16 „
68 29
4854
27
J
34
Parry & Fisher.
360.
17 Aug., 1855...
68 42
174 27 w.
Arctic Ocean .
120
38
45
48-6
Rodgers(Maury)
I Off the Asiatic coast. Sound-
J ings very near the bottom.
361.
168
40-2
„
„
9 Sept., 1820...
69 24
67 05 IV.
Davis Strait. . .
210
31
. 32'5
34
pnVTO
f Between Disco Island and Cape
idirj
\ Kater.
363-
364-
Aug., 1827...
19 Aug., 1850...
70 2
70 30?
164 40 w.
148 w. ?
126
37
49
29?
57
33?
Beechey
Off Icy Cape.
No soundings.
Arctic Ocean .
540
295
Armstrong
365.
4 July, 1839...
70 40
23 36 E.
Arctic Ocean .
567
39
40
Bravais
Bay of Hammerfest.
366.
15 July, 1839...
70 40
23 35 E.
Arctic Ocean .
390
39-5
41
48
Martins
1 Bay of Hammerfest. Tempe-
640
39
J rature at bottom.
368.
6 Sept., 1820...
70 47
67 56 w.
Baffin Bay . . .
456
31-3
33
72
Parry
369.
37°.
J
v Near the American coast.
1170
31-5
22 Aug., 1839...
71 1
23 23 E.
Arctic Ocean .
266
391
45
45
Martins
^ Off N. coast of Norway, bottom
371.
788
38'9
j temperature.
372-
10 Au g., 1855...
71 16
176 5 IV.
Arctic Ocean .
90
31'6
38*2
3715
Rodgers(Maury)
1 Between Kellet Land and Sibe-
373-
,, >7
77 7,
„ „
186
34
„
„
77 77
J ria, being near the bottom.
374-
14 Aug., 1855...
71 21
175 22 W.
Arctic Ocean .
60
33-4
44
45
Rodgers(Maury)
| The next day’s reading gave
375-
»
77 77
7. .7
77 77
150
37-3
J 3° higher.
376.
3 Sept., 1820...
71 24
70 58 IV.
Baffin Bay . . .
528
33
35‘5
38
Parry «
In soundings.
377-
9 Sept., 1850...
71 30?
120 W.?
Arctic Seas . . .
• 210
29?
35?
Armstrong
i Amongst ice, Prince of Wales
378.
77
» >7
» 77
450
31?
J Strait.
379-
13 Aug., 1855. . .
72 2
174 37 W.
Arctic Ocean .
120
34
43'7
45'2
Rodgers( Maury)
| Within 2 feet of bottom.
380.
77 77
77 77
240
41
„
„ »
381.
6 Aug., 1822...
72 7
19 II w.
Arctic Seas . . .
708
29
34
32
42
Scoresby . . .
Off the east coast of Greenland.
382.
2 Sept., 1820...
72 9
73 58 w.
Baffin Bay . . .
450
32-2
33
Parl7 ,
Marcet’s bottle used.
383.
7 Sept., 1818...
72 16
71 18 w.
Baffin Bay . . .
6000
28-7
35
33
Sabine (M.). ...
Soundings in 6000 feet.
384-
385.
6 Sept., 1818...
7 Sept., 1818..
72 22
72 22
73 06 w.
73 S8 w.
Baffin Bay . . .
Baffin Bay . . .
1476
6000
30
28-7
36
35
41
Parry (M.)
J ohn Ross
j-Near Pond’s Bay.
386.
6 Sept., 1818...
72 23
72 55 w.
Baffin Bay . . .
1476
30
36
37
Sabine (M.)
No soundings.
387-
21 Aug., 1839...
72 29
19 54 E.
Arctic Ocean .
531
40-1
43'4
43-8
Martins
1 Between Norway and Bear
388.
77
77 (j
1279
38-5
J Island.
389.
5 Sept., 1818...
72 37
74 6 w.
Baffin Bay . . .
1140
30'2
35
35'5
Sabine (M.)
Soundings in 1140 feet.
39°.
5 Sept., 1818...
72 39
74 3° w.
Baffin Bay ...
1140
30-2
35
39
Parry (M.)
West side of the Bay.
391.
28 July, 1849 ...
72 51
163 w.
Arctic Ocean .
30
33
36
Kellett(Seeman)
392.
77
7, 77
77.
77 77
60
32
,, ,,
1
393-
77 77
„
,7
90
29
I
394-
7, „
.7
120
29
» 7,
j Off the American coast, near
j the ice-pack.
395-
77 ,7
77 77
130
29
77 77
396.
>7 77
„
180
29
„
7,
1
397-
7. „
7. 77.
”
” „
210
29-5
„ „
J
650
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
Table I. — Northern Hemisphere (continued).
I.
II.
III.
IY.
Y.
YI.
YII.
YIII.
IX.
North
Longi-
tude of
Temperature
in
Date.
Sea.
Depth
in feet.
degrees of Pahr.
Name of
observer.
Remarks.
tude.
Green-
wich.
At
depth.
Surface.
Air.
398.
1 Sept., 1820...
72 55 ?
75
19 w.?
Baffin Bay . . .
660
O
30-2
0
3°'5
3i
Pond Bay. Marcet’s bottle used.
399*
400.
73
73 35
90
w.
Prince Begent Inlet,
f Lancaster Sound: soundings in
\ 1260feet. Marcet’sbottleused.
14 Aug., 1819...
I w.
Baffin Bay . . .
1110
34
34
39
Parry
401.
402.
20 July, 1839...
1 Sept., 1818...
73 36
73 38
n n
52 E.
19 w.
2854
32-2
42-2
35
42*2
Martins
Mean of four experiments.
77
Baffin Bay . . .
750
30-5
36
Parry (M.)
Near Pond Bay.
4°3-
8 Aug., 1838...
73 52
16
23
Arctic Ocean .
1010
36-3
4i'8
34‘ 3
Bravais et Mar-
tins
/ Mean of two experiments. Be-
[ tween Norway and Bear Is-
No soundings. [land.
404.
30 Aug., 1818...
74 4
79
w.
Lancaster Sd.
1410
29-2
36'5
37
Sabine (M.)
4°5-
Aug., 1818...
74 20?
80
w.?
Baffin Bay . . .
3900
29
John Boss
| Entrance of Lancaster Sound.
406.
51
74 8
4044
29-5
4°7-
Sept., 1818...
74 2*
112
48 w.
Arct. America
630
32
31-2
34
Parry (M.)
f Entrance to Banks Strait. In
[ soundings.
408.
18 July, 1838...
74 45
!5
E.
Arctic Ocean .
1493
34-5
39'2
37'3
Bravais et Mar-
tins
1 Mean of two experiments. Be-
J tween N orway and Bear Isl.
409.
6 Nov., 1819...
74 47?
no
48 w.?
Arct. America
30
30
28
j6
Parry
- South of Melville Island.
9 „
48 w. ?
15 E.
30
31
28
J
6 July, 1818...
74 48
10
Arctic Ocean .
204
34-5
34
36
Franklin
f At bottom ; near land. Query,
1 lat. 79° 48' ?
412.
18 July, 1818...
74 5°
59
30 w.
Baffin Bay . . .
1182
29-5
32
37
Parry (M.)
Off the Greenland coast.
413-
19 Aug., 1839...
74 52
12
57 e-
Arctic Ocean .
397
37-8
41-2
39-8
Martins
1 Bottom temperature. Between
4H
1598
33-4
J Norway and Spitzbergen.
415.
29 Aug., 1818...
74 58
77
42 w.
Baffin Bay . . .
1020
31
36
34
Tarry (M.)
Near Lancaster Sound.
416.
29 Aug., 1818...
27 Aug., 1820. . .
74 59
7 C 0
76
37 w.
Baffin Bay . . .
Arct. America
1020
564
31
31-7
36
34
31
Sabine (M.)
Soundings in 1020 feet.
In soundings. Marcet’s bottle
/j *
418.
10 Sept., 1818...
75 14
3
53 E.?
Arctic Ocean .
4536
36
35
37
Franklin (M.)..J
Between Spitzbergen and Iceland.
419.
14 Aug., 1818...
75 5°
66
w.
Baffin Bay . . .
1200
30-1
32
38
Sabine (M.)
1 Melville Bay; soundings in
420.
„ »
„
2532
29-7
„
„
J 2700 feet.
421
3 Aug., 1818...
75 52
63
w.
Baffin Bay . . .
2490
29
34
38
Sabine (M.)
Melville Bay. Soundings.
26 July, 1839 . . .
16 E.
Arctic Ocean .
2395
32-7
38-2
38-2
Martins
/Mean of four experiments;
\ bottom temperature.
423
424
14 Aug., 1818...’
75 56
”
66
31 W.
Baffin Bay . . .
1200
2532
30-2
29-2
32
36
Parry (M.)
| Melville Bay.
42s
25 July, 1839...
9
5I E.
Arctic Ocean .
2142
32
38-2
38
Martins
[Mean of two experiments.
[ Bottom.
426
1 Aug., 1818...
76?
62
W.?
Baffin Bay . . .
to J-1
0 0
29-5
29-5
John Boss
| Top of Melville Bay.
427
2 „ „
75 51
62
59
„ „
428
76?
65
w.?
„ „
2730
29'5
„
Near Melville Bay.
429
25 Aug., 1818...
76 8
i
21 w.
Baffin Bay . . .
324
29-5
32-5
3i'5
Sabine (M.)
Soundings in 336 feet.
43°
25 Aug., 1818...
76 8
/«
31 w.
Baffin Bay ...
324
29-5
32.
3r5
Parry (M.)
f In soundings. Entrance to
[ Jones Sound.
43i
18 Aug., 1839...
76 13
48 E.
Arct. Ocean A.
308
37-2
40-4
...
Martins
-1 Between Bear Island and Spitz-
432
1296
334
bergen. Mean of two expe-
” ” .
”
r riments.
J Mean of four experiments:
433
2103
32-3
434
435
9 April, 1810...
76 16
9
O E.
Arctic Ocean .
300
31'3
28-8
12
Scoresby
, at bottom.
738
33-8
L In ice, 1° S.W. of Spitzbergen.
436
1380
33-8
99
J
437
438
23 Apr., 1810...
76 16
10
50 E.
Arctic Ocean
120
28
28-3
16
Scoresby
300
28-3
l Frozen up.
99
439
738
30
J
44°
24 Aug., 1818...
76 22
77
38 W.
Baffin Bay . . .
600
30-2
3r5
33
Parry (M.)
Near Cobourg Island.
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
651
Table I. — Northern Hemisphere (continued).
I.
II
Date.
III.
North
Lati-
IY.
Longi-
tude of
Y.
Sea.
YI.
Depth
in feet.
YII.
Temperature in
degrees of Fahr.
Yin.
Name of
observer.
IX.
Eemarks.
tude.
Green-
wich.
At
depth.
Surface.
Air.
441
44Z
24 Aug., 1818..
23 Apr., 1811...
76 22
76 33
76 34
O /
77 38 w.
77 10 w.
IO E.
Baffin Bay . .
Arctic Ocean
1440
612
120
29-5
29-5
31
0
3i'5
32
30
O
33
36
25
Parry (M.)
Scoresby
Near Cobourg Island.
Entrance of Smith Sound.
\
240
35
1
! Frozen up : off the S.W. of
[ Spitzbergen.
445-
360
34
600
34'7
1
J
447-
448.
449-
4S°-
24 Aug., 1818...
26 May, 1818...
25 July, 1839...
76 35
76 48
76 57
78 w.
12 26 E.
13 29 E.
Baffin Bay . . .
Arctic Ocean .
Arctic Ocean .
600
1440
4200
515
30 '2
29*5
43
37*4
3r5
33
37'8
33
29
37'3
Sabine (M.)
f Franklin &1
t Buchan.../
Martins
j. Entrance of Smith Sound.
( Off S. of Spitzbergen. Frank-
J lin ascribes the high tem-
j perature to the water-bucket
|_ being examined in the cabin.
1 Mean of 2 expts. each : off Spitz -
J bergen ; bottom temperature
451.
1040
347
1 May, 1811...
77 15
8 IO E.
Arctic Ocean .
120
29-3
29*3
l6
Scoresby
\
453-
240
29'3
1
| In ice : off the W. coast of
j Spitzbergen.
454-
360
30
45 5-
600
30
1
)
456.
20 May, 1813...
77 4°
2 30 E.
Arctic Ocean .
300
29-3
29
3°
Scoresby
] Amongst floes; between Spitz-
J bergen and Greenland.
457-
660
31
458.
459-
460.1
461.
15 Aug., 1839...
7 June, 1817...
14 Aug., 1839...
20 May, 1816...
77 43
78 2
78 41
79
12 IIE.
O IO W.
9 39 E-
5 40 E.
Arctic Ocean .
Arctic Ocean .
Arctic Ocean .
Arctic Ocean .
397
4566
321
78
34-3
38
31
36*4
32
. 34*7
29
35'9
36
36*3
34
Martins
Scoresby
Martins
Scoresby
Mean of 4 expts. : at bottom,
f Ice near : between Spitzbergen
/ and Greenland.
Mean of 4 expts. : at bottom.
'I
I
462.
33-8
463.
342
34*5
(Moored to a floe, N.W. of
j Spitzbergen.
464.
600
36
465.
2400
36
”
J
Amongst floes.
4 expts. *i off Magdalena Bay,
1 expts. J Spitzbergen.
At bottom.
| West coast of Spitzbergen.
466.
21 May, 1816...
79 4
79 33
5 38 E.
10 54 e.
Arctic Ocean .
4380
38
Scoresby
467.'
13 Aug., 1839...
Arctic Ocean .
213
404
34*2
29
357
38
Martins c
468.
34*1
469.
47°.
26 June, 1818...
3 Aug., 1839...
79 44
In
9 33 E.
Magdalena
Arctic Ocean .
Bay.
90
79
, 361
34
32*4
34
33’2
35
38*6
FrankL & Buck. .
Martins
170(7
28*6
471-
4 June., 1827...
79 49
79 49
15 II E.
15 17 E.
Arctic Ocean .
441
459
471
29*2
38
43
43
44
41
43
43
Parity
472.
5 June, 1827...
Arctic Ocean .
29*7
29*8
3°'5
Parry
474-
480
29*8
3*
475-
492
28*7
476.
492
30
Beset in the ice : off the north
j coast of Spitzbergen.
I 477-
507
408
29*5
31
30
1
478.
6 June, 1827...
79 49
15 22 E. .
Arctic Ocean .
30
Parr
I
479-
408
29
39
1
480.
408
30
|
481.
408
29*2
39
38
j
30'5 :
4 s
MDCCCLXXV.
652
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
Table I.-^-Northern Hemisphere (continued).
I.
II.
III.
IV.
V.
VI.
VII.
VIII.
IX.
Date.
North
Longi-
tude of
Sea.
Depth
in feet.
Temperature in
degrees of Pahr.
Name of
observer.
Eemarks.
tude.
Green-
wich.
At
depth.
Surface.
Air.
482.
483.
6 June, 1827...
79 49
O 1
15 22 E.
Arctic Ocean .
408
29‘2
3°'5
3°'5
O
37*5
38
Parry
456
29-5
'l
484.
504
30
-Q
* ‘
”
485.
408
29-5
29'7
*
486.
420
29'7
32
41
38
487.
438
30
30
474
29'2
31
”
489
7 June, 1827...
79 5°
15 3° E-
Arctic Ocean .
312
29
3i-5
38
pov1,v
ITdllj
312
29
3 2
40
315
30
33
37
452
318
29-5
3I-5
31
Beset in the ice : off the north
318
29
39
41
• coast of Spitzbergen.
191
324
30
3°'5
4°‘5
+95
29
336
3i-5
4i
496
336
30
.
42
31
497
348
29-8
39
49 8
384
29
41
j j
•JT-C
/inn
408
30
49 y
500
J J
31
40
468
29'5
501
8 June, 1827...
70 CO
T5 30 E.
Arctic Ocean .
288
28-8
30
42
Parry
502
312
29
32
40
303
31'5
321
29-2
AO
”
5°4
25 June, 1818...
79 5i
IO E.
Arctic Ocean .
102
34
33
34
Frankl. & Buch.
1 N.W. of Spitzbergen. Sound-
505
„
„
360
34
33
34
„ »
J ings.
506
5°7
29 June, 1818...
79 5i
IO E.
”
102
114
34
34
34
34
39
37
” »
| Near the land in a current.
508
27 June, 1818...
79 5li
„
432
34'5
3+
36
„ „
Near ice.
5°9
510
5”
512
513
19 May, 1827...
79 55
13 46 E.
Arctic Ocean .
372
29
28'5
28
13
Parry
-i
426
28
1- Beset : N. of Spitzbergen.
18 May, 1827...
79 56
I3 39 E.
Arctic Ocean .
570
30
Parry
'I
432
28'5
28
15
30
1 Beset : N. of Spitzbergen.
21 June, 1818...
79 56
II 30 E.
Arctic Ocean .
114
31
3$
Frankl. & Buch.
Ice around ; bottom.
5*4
20 „
79 58
II 25 E.
„ „
144
31
3i-5
30
„ ,)
At bottom ; beset.
5T5
23 June, 1818...
79 59
IO 12 E.
Arctic Ocean .
126
32-5
3r5
30
Frankl. & Buch.
Beset.
516
22 „
80
II 14 E.
„ „
198
31
3°
3°
„ „
Beset : off the land.
5J7
518
519
7 June, 1816...
80
5 E.
13 5 E.
Arctic Ocean .
720
36-3
297
40
Scoresby
Beset : N.W. of Spitzbergen.
16 May, 1827...
80 1
Arctic Ocean .
564
29’5
287
28-5
28
18
Parry
576
28 "5
187
L Beset : N. of Spitzbergen.
520
521
522
15 ”
606
690
498
30
15 May, 1827...
22 July, 1818...
80 4
12 39 E.
Arctic Ocean .
2,0* C
Parry
N. of Spitzbergen.
At bottom : N.W. of Spitzbergen.
80 13
II 31 E.
Arctic Ocean .
35-8
j
41
Frankl. & Buch.
5'23
21 „ „
80 14
II 12 E.
11 »
570
35*3
32'5
41-5
„ „
At bottom. „ „
524
80 15
II 36 E.
” ”
438
36-8
32-5
37
” ”
At bottom. „ „
ME. J. PEESTWICH ON SUBMAKINE TEMPEEATUEES.
653
Table I. — Northern Hemisphere (continued).
|l
II.
III.
IV.
V.
VI.
VII.
VIII.
IX.
North
Tnnci
Temperature
in
Date.
tude of
Sea.
Depth
degrees of Pahr.
Name of
observer.
Eemarks.
tnde.
Green-
wich.
in feet.
At
depth.
Surface.
Air.
525-
25 July,
1818...
80 18
II 40 E.
Arctic Ocean .
549
36
32‘5
34
Frankl. & Buch.
At bottom.
526.
7 „
„
80 18
II IO E.
„ »
720
36
33
35
„ n
527.
10 „
„
80 19
II 24 E.
,, „
714
36
32
,> »
528.
8
„
80 20
II IO E.
„ „
780
36-5
3i-5
35
„
529.
9 „
80 20
IO 55 E.
660
35*5
3°'S
3°'5
,,
North-west of Spitzbergen. At
530.
12 „
„
80 20
II 7 E.
„ »
870
35-8
32
36
,,
bottom : beset. The tem-
perature of the air is taken
531.
26 „
„
80 20
II 25 E.
„
330
36
32-5
36
„ ,,
from Marcet.
S32-
20 „
,,
80 21
IO 12 E.
„ „
648
35'5
32'5
34*5
533-
11 „
„
80 22
IO 30 E.
>, ,,
720
36
32
40
.. ,,
534-
13 „
„
80 22
IO 2 E.
„ „
1410
35‘5
32
4°'5
,,
j
535-
13 July,
1818...
80 22
II E.
Arctic Ocean .
1302
37
32"5
Franklin (M.)...
N. of Spitzbergen : rocky bottom.
536.
„
„
„
IO 55 E.
» ,,
1422
35'5
31-5
40
N. of Spitzbergen : beset.
537-
19 July,
1818...
80 24
II 14 E.
Arctic Ocean .
618
36'5
3i‘5
4i
Frankl. & Buch.
\
538.
14 „
„
80 26
IO 45 E.
,, „
1398
35-5
32
39
» „
539-
16 „
„
80 26
II 25 E.
„ „
103S
36‘3
36-5
39
„ „
At bottom : beset.
I
54°-
18 „
„
80 26
IO 30 E.
„ „
1986
36
32-5
36
„ „
)
541-]
9 July,
1818...
80 26
II 38 E.
Arctic Ocean .
720
36
3i
35
Franklin (M.)... :
N.W. of Spitzbergen : beset.
542.
15 July,
1818...
80 27
IO 20 E.
Arctic Ocean .
1188
36
32
38
Frankl. & Buch.
1 At bottom : beset.
543-
17 „
„
80 27
II E.
„ „
1710
35-5'
34
” ”
J
544-
15 July,
1818...
80 28
IO 20 E.
Arctic Ocean .
1110
36-2
32‘5
Franklin (M.)...
Beset.
545-
546.
547-
548.
4 Aug.,
14 June,
15 „
1773...
80 30
80 47
80 49
l6 E.
Arctic Ocean
360
39
36
31
30
20
32
26
Phipps
Under the ice.
1827...
l8 22 E.
Arctic Ocean .
570
29 ’8
Parry
19 7 E.
450
29
27
26
|>N. of Spitzbergen.
492
28-6
y
Note. — The observations where it is said that Marcet’s water-hottle has been used are not reliable. There is an ambiguity in
the few remarks in Wuelerstorf’s ‘Voyage of the Novara ’ “On the Temperature and Density of Sea-water at Depths,” which
perhaps should exclude those observations also. The irregularity of the readings would seem to indicate that the temperature is
rather that at time of taking the specific gravity than that at time of emersion of the apparatus. Some may be about right,
others much wrong.
4 s 2
654
ME. J. PEESTW1CH ON SUBMARINE TEMPEEATUEES.
Table IT. — Southern Hemisphere.
I.
II.
Date.
III.
South
IY.
Longi-
tude of
Y.
Sea.
YI.
Depth
in feet.
YII.
Temperature in
degrees of Eahr.
YIII.
Name of
observer.
IX.
Remarks.
tude.
Green-
wich.
At
depth.
Surface.
Air.
*•
May, 1804...
5 Mar., 1858...
0 0
0 13
0 1
146 0 w.
58 26 E.
Pacific
Indian Ocean
1200
7980
O
57-5
41
O
84'5
8l
°
Horner
Pullen (w)
[lands.
10° N.W. of the Marquesas Is-
North of Seychelles Islands.
2.
1176*
67?
r Weather bad, and readings
3-
„ „
,, „
„ „
14280
40
,,
uncertain.
A.
7 Feb., 1838...
0 31
97 19 vv.
S. Pacific
2656
45
807
84^2
DuPetitThouars
Cylinder sound.
5-
30 Dec,, 1857...
0 46
82 43 E.
Indian Ocean
(1706?)
720
77.4
82
81-6
Wiillerstorf
In mid-ocean.
6.
5 May, 1818...
0 53
20 28 W.
S. Atlantic ...
480
57 "3
83
83
Kotzebue
Between N. Brazil and Guinea.
8 Feb., 1838...
° 55
97 7 w.
S. Pacific
5872
37-4
797
86
DuPetitThouars
Cylinder sound.
7 a.
-
May, 1804...
4 May, 1818...
1 5
2 17
146 vv.
19 50 w.
S. Pacific
S. Atlantic . . .
(2296?)
600
480
59
571
82-5
83
82-5
Horner
Kotzebue
Near No. la.
In mid-ocean.
9-
7 Aug., 1845...
2 32
30 53 w.
S. Atlantic . .
2400
50-5
78
80
Kellett
Soundings in 17,970 feet.
IO.
23 Mar., 1843...
2 32
8 11 vv.
S. Atlantic ...
1800
46
79
Belcher
V
II.
„ „
„ „
2400
38?
„
„
12.
„ „
” »
99 99
„ „
3000
46
„
,,
13‘
» »
3600
45'5
„
^ Between Ascension Island and
the coast of Guinea.
14-
„ „
4200
46
„
IS-
,, ,,
„ „
4800
45
„
„
1 6.
,, „
„ >>
„ „
5400
40-2
„
,,
17.
„ „
6000
42-7
,,
J
18.
14 Jan., 1847...
2 37
26 15 vv.
S. Atlantic ...
1608
53
80
79
Dayman
Between St. Paul and Ascension.
19.
Sept., 1816...
3 26
7 39 E-
S. Atlantic . . .
8610
42
73
Wauchope
/ Off the coast of Congo. Cor-
[ rented depth 6060 feet.
20.
3 May, 1818...
3 42
18 41 w.
S. Atlantic . . .
426
56
82-6
83‘5
Kotzebue
Between Brazil and Guinea.
21.
28 Sept., 1827...
Aug., 1836...
3 48
3 58
128 7 E.
i 37 w.
S. Pacific
S. Atlantic ...
425
1800
74
52
83
73
8 1 *6
D’Urville
Wauchope
Amongst the Molucca Islands.
32“ to haul in.
*3.
18 July, 1827...
2 May, 1818...
4 42
5 8
I 52 40 E.
17 14 W.
S. Pacific
S. Atlantic . . .
212
378
81
57 '6
83'2
8i'6
85'1
82
D’Urville
Kotzebue
Off New Ireland.
In mid-ocean.
-5-
15 Jan., 1847...
5 9
27 51 VV.
S. Atlantic ...
918
54
80
78
Dayman
1 East of Juan Fernando. Kead-
26.
„ „
»
„ „
1758
60
„
J ing probably reversed.
28 Feb., 1858...
5 3i
61 31 E.
Indian Ocean
13980
35
84
Pullen (m)
In soundings.
27rt.
10 Mar., 1836...
5 59
24 35
S. Atlantic ...
3733
43-7
79'5
79'5
Yaillant
Cylinder full.
28.
1 May, 1818...
6 35
15 34 w.
S. Atlantic ...
339
59
8i'5
817
Kotzebue
N. of Ascension.
29.
26 Feb., 1858...
7 12
60 52 E.
Indian Ocean
12000
38-2
8i’5
Pullen (u)
No bottom at 13,524 feet.
3°.
21 Dec., 1838...
7 29
85 l8 E.
Indian Ocean
600
78
83
82-5
Pratt
1 Between Sumatra and the
3i-
20 „ „
7 54
85 20 E.
240
81-5
84
82-5
..
J Mauritius. „ , ,
[Islands.
31a.
32-
July, 1839...
16 Jan., 1847...
7 54
7 55
112 53 W.
29 II W.
S. Pacific
S. Atlantic ...
2700
1098
44-5
74
80
79
Dayman
Between Peru and Marquesas
L Between Ascension and Brazil.
33-
„
»
..
1638
47
„
J
34-
30 Apr., 1818...
8 15
14 3 VV.
S. Atlantic ...
367
64
8o'3
8o-3
Kotzebue
Near Ascension Island.
35-
17 Oct., 1858...
8 21
162 56 E.
S. Pacific
300
83-5
84-2
83-2
Wiillerstorf.
36.
37-
” ”
” ”
600
900
81-1
”
’’
East of the Salomon Isles.
38.
1
» ”
” ”
1140
73-8
”
J
MR. J. PRESTWICK ON SUBMARINE TEMPERATURES.
655
Table II. — Southern Hemisphere (continued).
L
II.
III.
IY.
Y.
.VI.
VII.
VIII.
IX.
South
Lati-
Longi-
tude of
Temperature
in
Date.
Sea.
Depth
in feet.
degrees of Eahr.
Name of
observer.
Remarks.
tude.
Green-
wich.
At
depth.
Surface.
Air.
O i
30 38 w.
0
0
39-
8 Dec., 1857...
9 3°
S. Atlantic ...
5280
41-5
80
Pullen (m)
Soundings in 7680 feet.
40.
29 Apr., 1818...
9 ,39
S. Atlantic ...
420
601
79'4
807
Kotzebue
f Between Ascension and St.
\ Helena.
41.
19 June, 1839...
IO?
Off Peru
S. Pacific
498
57
63
Wilkes
Latitude estimated.
42.
23 Feb, 1858...
10 54
58 44 E.
Indian Ocean
2640
5P5
83
Pullen (u)
1 No bottom in 7920 feet. Pro-
43-
5280
41-5
1 bable error in reading of
j last depth, from shifting
44-
,, ,,
7920
51-5?
,,
J of index.
45-
28 Apr, 1818...
TT TT
II 21 W.
S. Atlantic ...
432
65-5
78-5
807
Kotzebue
f Between Ascension and St.
[_ Helena.
46.
47-
April, 1836 ...
15 July, 1839...
12
97 e-?
Off Callao
2178
45
FitzRoy
Near Keeling Island.
1800
51
67
Wilkes ....
} Latitude estimated.
48.
18 „
T'J 9
1740
50
70
77’2
J
49-
27 Apr, 1818...
12 30
9 58 w.
S. Atlantic ...
368
59-8
787
Kotzebue
f Between Ascension and St.
[ Helena.
So-
23 May, 1837...
12 39
77 7 w.
S. Pacific
682
55‘7
67-8
64-4
DuPetitThouars
Cylinder sound : in soundings.
Si-
17 Jan, 1847...
12 49
32 23 w.
S. Atlantic ...
354
80
81
79
Dayman
Off the coast of Brazil.
52-
1847-49
13 28
28 w.
S. Atlantic ...
360
72'8
8o'2
E. Lenz
Between Bahia and Ascension.
S3-
22 May, 1837...
13 5°
76 41 w.
S. Pacific
688
55'4
65
68
DuPetitThouars
f Cylinder sound : off Pisco
l 'Bay.
54-
S4«-
55-
26 Apr, 1818...
December . . .
14 12
7 55 w-
31 w.
S. Atlantic ...
339
62
75'6
78
77
74
Kotzebue
North of St. Helena.
IS
IS 3
S. Atlantic . . .
360
74'6
Horner
3 June, 1843...
23 14 w.
S. Atlantic . . .
5400
40-3
James Ross
L No soundings in 27,600 feet.
56.
„
„
,> „
7200
39'5
„
J
57-
19 Jan, 1847...
15 5
34 44 w.
S. Atlantic . . .
1356
59
80
79
Dayman
1 Off Bahia, Brazil : reading
S8.
59-
60.
1902
62
J probably reversed.
)
13 Apr, 1816...
i5 *6
133 42 w.
S. Pacific
60
79
80
79'8
Kc tzebue
120
79
| North of the Low Islands ;
6l .
300
78'8
Y or 15° E. of the Society
I Islands.
62.
600
63.
1200
56
j
64.
6S-
27 Oct, 1827...
15 4°
IS 54
120 50 E.
10 23 W.
Indian Ocean
2136
46’2
82^4
807
D’Urville
Between Australia and Java,
f Cylinder sound : near St.
[ Helena.
8 May, 1839...
S. Atlantic ...
1066
536
74’5
74'8
DuPetitThouars
66.
28 July, 1826...
16
26 40 W.
S. Atlantic ...
960
51 -5
73-6
71-6
D'Urville
Between St. Helena and Brazil.
67.
24 Apr, 1818...
16 14
5 7 w.
S. Atlantic . . .
276
62-8
74' 3
727
Kotzebue
Near St. Helena.
68.
28 Oct, 1827...
16 40
17 55
120 20 E.
Indian Ocean
1068
69’3
82-8
8i’6
D’Urville
Off N.W. coast of Australia.
69.
23 Apr, 1818...
3 8 w.
S. Atlantic ...
327
581
737
75
Kotzebue
S.E. of St. Helena.
70.
1S47-A9
17 17
192(32?)
,,
360
76'6
84
E. Lenz.
Apparent error of longitude.
71.
11 Nov, 1827...
17 3°
I35 20 E. ?
Indian Ocean
1602
55-8
8o'i
78-8
D’Urville
J Probable error of longitude,
[ should be 114° 20' E.
29 Oct, „ ...
20 Jan, 1847...
17 3°
17 48
120 20 E.
640
73-8
8o-6
81
Near the Rowley Shoals.
Off the coast of Brazil.
73-
36 20 W.
S. Atlantic ...
792
67
80
Dayman
74-
29 July, 1839...
17 54
I 12 53 W.
8. Pacific
2700
44-5
74
Wilkes
/ Amer. Journ. Sc, January,
\ 1848. In mid-ocean.
75-
30 Oct, 1827...
18
1 19 50 E.
Indian Ocean
480*
75'5
78-8
8o'i
D’Urville
1 Near the north-west coast
76.
77-
78.
506*
76'8
80-3
79
j of Australia.
4 Aug, 1839...
”g9
120 W.?
S. Pacific
300
74
75
Wilkes
•N
600
73'5
(Between the coast of America
79-
1200
61
j and the Society Islands.
1800
]
50
656 ME. J. PRESTWICH ON SUBMARINE TEMPERATURES.
Table II. — Southern Hemisphere (continued).
I.
II.
III.
IY.
Y.
YI.
.YII.
Yin.
IX.
South
lati-
tude.
Tonoi
Temperature
in
Date.
tude of
Sea.
Depth
degrees of Eahr.
Name of
observer.
Remarks.
Green-
wich.
in feet.
At
depth.
Surface.
Air.
81.
31 July, 1857...
18 7
O 1
37 16 w.
S. Atlantic . . .
240
75-8
76A
74‘5
Wiillerstorf ... 1
Off the coast of Brazil.
82.
7 Aug., 1839...
S. Pacific
600
75
77
Wilkes
) .
10 14
«3-
7 Apr., 1816..
18 17
124 56 w.
S. Pacific
750
68-5
78-5
79-2
Kotzebue
| In mid-ocean ; between the
84.
750
68
79-6
80
}■ Marquesas and Easter
” ”
11 11
0/ 0
70*2,
Island.
«5-
78-5
71 11
11 11
/y *
1
1200
54
/-
80
79 D
87.
Jan., 1826...
18 38
r.A 1 w
1410
70
76
76-5
Beechey
Near Clermont Tonnerre Isl.
J Between St. Helena and the
22 Apr., 1818...
I 25 w.
S. Atlantic . . .
393
62-8
73
Kotzebue
L Cape.
19 IS
89.
14 Dec., 1857...
19 34
27 19 w.
S. Atlantic ...
2400
53
76
Pullen (u)
[Between Bio Janeiro and
9°.
„ »
„ >.
» »
4800
38-5
„
,»
| St. Helena.
91-
7200
41-2?
»
D’Urville
f E. of Eodriguelsl. Thermo-
23 Sept., 1828...
20
Indian Ocean
6194
45-3
73'4
71 '2
I meter wrong ; too high.
Amongst the Friendly Islands.
93-
174 IO w.
17 Apr., 1827...
S. Pacific
1602
51-7
77-8
73-8
20 20
94-
21 Jan., 1847...
37 58 w.
S. Atlantic ...
876
59
80
78
"DayTuan
1 Off the coast of Brazil.
95-
50
J
11 11
1000
»
11
96-
16 Feb., 1858...
20 14
59 35 e-
Indian Ocean
2880
50-5
80
Pullen (u)
1 Off the east coast of Mau-
97-
„ .»
„
» »
» V
5610
40
„
| ritius.
98.
„ „
„ ,,
» »
„ „
8250
40-5?
„
„
J
99.
31 July, 1829...
20 32
S. Atlantic . . .
426
69-4
72'6
ir’TTvyillft
Near Martin-Vaz Island.
29 20 w.
O 54 E.
71
7r8
Kotzebue
J Between St. Helena and the
L Cape.
20 Apr., 1818...
20 33
S. Atlantic . . .
367
60-8
73'5
lOO.
July, 1825...
20 3 8
38 46 W.
S. Atlantic ...
2760
43-5
73
71
Beechey
Near the coast of Brazil.
IO I.
3 May, 1847...
20 42
58 47 E.
Indian Ocean
840
74
77
76
Dayman
103.
57
) E. of the Mauritius.
1800
11 11
104
Feb., 1826...
21 19
140 23 W.
1200
58-5
8i5
76
Beechey
I
[ Between the Society Islands
[ and Pitcairn Island.
10s
1800
51
19 17
11 ii
106
2400
45
J
” ”
if 11
11 11
11 11
”
”
Wiillerstorf
/Between the Society and
107
6 Feb., 1859...
21 51
149 59 w.
S. Pacific
1080
713
8r6
82-4
\ Tubuai Isles.
108
18 May, 1847...
21 53
cfi /i c e
Indian Ocean
1092
63
77
77
Dayman
Near the Isle of Bourbon.
109
18 Jan., 1819...
22 31
40 31 w.
S. Atlantic ...
600
69-5
74'7
Wanchope
Near the coast of Brazil.
I IO
17 Feb., 1837...
23 30
43 21 w.
S. Atlantic ...
373
60
72-5
74‘3
D uPetit Thouars
Cylinder full.
July, 1825..
23 32
41 12 w.
S. Atlantic ...
1200
56
75
71
Beechey
Off Bio Janeiro.
112
15 Sept., 1857...
33 49
O 39 w.
S. Atlantic . . .
840
56-3
57'5
55
Wiillerstorf
(Entered in wrong place.)
J Between Bourbon and Ma-
11 3
31 July, 1837...
- . _
54 20 e.
Indian Ocean
4740
43
7° '4
Vaillant
\ dagascar.
z4 /
69*8
19 May, 1847...
24 16
56 58 E.
Indian Ocean
1092
71
75
76
Dayman
S. of Isle of Bourbon.
1 14
605
76-5
Beechey
Near Elizabeth Island.
Dec., 1825...
24 35
127 W.
S. Pacific
1440
76
116
27 Sept., 1772...
24 44
24 54 W.
S. Atlantic ...
480
68
70
72-5
Forster .........
Between Brazil and the Cape.
117
6 Aug., 1857...
24 54
43 10 w.
S. Atlantic . . .
84
72-8
72*2
72-3
Wiillerstorf.
118
1 May, 1839...
(morning)
1 May, 1839...
(noon)
25 10
7 59 E-
S. Atlantic . . .
5316
37-4
67-3
69
DuPetitThouars
1 1st cylinder sound: south of
l St. Helena. 2nd cylinder
”9
” ”
” ”
5316
40-4
(37-4)
67-2
67-5
Beechey
J full. Corr. 1=1790° feet.
120
Apr., 1828...
25 30
-Q
S. Pacific
600
69
80
80
1
IOd ^ vv.
l To the N.E. of Easter Island.
1200
58
122
” ”
19 99
”
11 11
”
J
1860
50
” ”
” ”
”
” ”
’’
ME. J. PBESTWICH OX SUBMAEIXE TEMPEEATUEES.
65'
Table II. — Southern Hemisphere (continued).
I.
II.
III.
IY.
Y.
YI.
yh.
Yin.
IX.
South
Lati-
Longi-
tude of
Temperature
in
Date.
Sea.
Depth
in feet.
degrees of Eahr.
Name of
observer.
Bemarks.
t-ude.
Green-
wich.
At
depth.
Surface.
Air.
J,,
Apr., 1S2S...
O l
25 30
108 w.
S. Pacific
2460
44
80
80 .
Beechey
To the N.E. of Easter Island.
124
31 Mar., 1S40...
25 4°
160 E.
S. Pacific
60
70
75
Wilkes
125
»
„ ,,
„
„ „
120
72
„
„
126
»
„ „
„
„ »
180
73
„
„
127
»
.. ,,
240
71*5
„
„
128
» „
„ »
„
„ „
300
72
„
„
129
»
» »
360
71?
„
130
„ „
,,
„ „
420
71-5
„
i,
(Between New South Wales
j and New Caledonia.
I3I
„
„ „
,,
„ „
480
71-5
„
132
„ »
„ „
„ „
540
695
„
133
„ „
„
„ „
600
73?
134
»
„ „
„
„ „
1200
63-5
„
13s
» »
„ ,,
1800
56
„
„
136.
„ „
„
2400
52
„
137-
„ „
„
>, j>
3000
49
,,
„
13s.
1 May, 1847 ...
25 48
61 6 E.
Indian Ocean
990
62
74
Dayman
1 Between Mauritius and Isl.
139.
»
„ „
1920
59
„
„
/ of Amsterdam.
140.
4 Feb., 1847...
26 7
40 30 \v.
S. Atlantic ...
1386
60
77
66
Dayman
1
141.
„ „
2106
51
„
l Off the coast of Brazil.
142.
20 May, 1847 ...
26 9
58 45 e.
Indian Ocean
840
63
7i
74
Dayman
1 S. of the Mauritius. Beading
143-
» »
„ „
2160
73
„
„
J probably reversed.
144-
22 May, 1850 ...
26 34
JOI 28 w.
S. Pacific
660
65
7Z
71
Armstrong
1 Between the Society Islands
x45-
» «
>, „
1110
53
„
„
J and Chili.
146.
Nov., 1825...
26 36
112 40 W.
S. Pacific
2598
44
74' 5
7i
Beechey
j
M7-
» .. .
„ „
„ „
3240
43
„
„
j- W’est of Easter Island.
148.
»
„ „
3840
44-5?
„
J
149.
29 April, 1839...
26 36
7 32 e.
S. Atlantic . . .
5315
41-7
68
69-8
DuPetitThouars 1
Cylinder full ; near the Cape.
IS°.
19 Dec., 1857 ...
26 46
23 52 w.
S. Atlantic ...
16200
(3_8-5)
35
75
Pullen
fin soundings-; descent lhour;
14 Feb., 1839...
( ascent 2 hours.
151.
26 47
98 30 E.
Indian Ocean
5316
42-8
73-8
74-3
DuPetitThouars 1
Cylinder full ; in mid-ocean.
30 Sept., 1838...
(5200)
(38-7)
152.
26 53
174 31 W.
S. Pacific
5316
45-2
667
66 7
DuPetit Thouars (
Cylinder full; Kermadec Island.
28 April, 1847 .
(4987)
(42-1)
153.
26 56
57 31 e.
Indian Ocean
1200 ;
60
74
Dayman . .
154.
2100
57
70
1 South of Mauritius.
J
IS5-
27 Nov., 1827...
27
98 40 E.
Indian Ocean
1605
52-3
7°'5
69
D’Urville ]
Between Mauritius and Australia.
IS6.
Nov., 1825...
27 17
” ”
103 VV.
S. Pacific .
600
64-5
68-5
66
Beechey
'I
'SI-
1260
51-5
[ Between the Society Islands
f and Chili.
158.
„ „
5?
1800
46
65
j
159-
5 Feb., 1847 ...
27 21
38 I W.
S. Atlantic ...
1092
76
73
Dayman
1 Between the Biver Plata and
160.
„ „
5? ,,
2052
51
J the Isl. of Tristan d’Acunha.
161
15 May, 1836...
27 30
41 E.
Indian Ocean
30
74-5
75-6
FitzRoy
162
48
74-2
[Between Natal and Mada-
i9
163
„ „
108
74
( gascar.
164
„
120
74
”
”
658
ME. J. PEESTWICH ON STJBMAEINE TEMPEEATUEES,
Table II. — Southern Hemisphere (continued).
I.
II.
III.
IY.
Y.
YI.
YII.
YIII.
IX.
South
Longi-
tude of
Temperature
in
Date.
Sea.
Depth
degrees of Eahr.
Name of
observer.
Eemarks.
tude.
Green-
wich.
in feet.
At
depth.
Surface.
Air.
165.
15 May, 1836...
O /
27 30
O i
41 E.
indian Ocean
168
0
73
O
75-6
0
Ki tz"R,oy
240
72-5
!
288
71
Southern entrance of Mozam-
168.
300
70
bique Channel, between Ma-
” ”
”
dagascar and Natal. The
169.
170.
450
68
4th, 7th, 8th, and 10th ob-
600
64-5
servations, on being repeat-
”
” ”
| ed, gave exactly the same
171.
172.
173.
174.
i75-
1200
58-5
I results. The 1st, however,
I gave 74’4.
1800
55-5
2400
52-5
j
2520
52
j
21 May, 1847...
61 9 E.
Indian Ocean
1998
54
73
69
Dayman - --
f Between Madagascar and Isl.
( of Amsterdam.
176.
11 Feb., 1839...
27 47
100 20 E.
Indian Ocean
5316
37
74-8
76-2
DuPetit Thouars
Cylinder sound. W. of Aus-
(5282)
tralia.
177.
24 May, 1847 ...
28 1
67 28 E.
Indian Ocean
1716
54
69
67
Dayman
1 Between Mauritius and the
99,
28 6
63 30 E.
57 18 E.
1800
53
69
73
68
J Island of Amsterdam.
1 Between Madagascar and Isl.
179.
27 April, 1847 ■
28 16
Indian Ocean
1260
60
70
Dayman
180.
2160
57
j of Amsterdam.
181.
April, 1828 .
28 40
96 w.
S. Pacific
600
71
74
73
Beechey i .
1
182.
1200
53
(Between Valparaiso and Eas-
183.
” ”
” ”
”
” ”
1800
49
f ter Island.
184.
2400
45
185.
14 Dec., 1857 ...
28 4s
84 48 E.
Indian Ocean
720
63-7
69-9
677
Wiillerstorf
f Between Madagascar and Aus-
( tralia.
186.
4 Oct., 1838 ...
28 49
177 18 W.
S. Pacific
5316
44.7
67
66-2
DuPetit Thouars
Cylinder full. Near No. 152.
387.
(3740?)
(42-6)
27 July, 1827...
29 13
12 54 W.
S. Atlantic ...
1655
50-4
66-6
69-5
Blosseville
Between the Cape and Paraguay.
188.
18 Nov., 1827...
19 20
107 30 E.
Indian Ocean
4378
40
73‘4
7 1 '2
D’Urville. .
(Entered in wrong place.)
189.
13 Dec., 1857...
29 25
85 2 E.
Indian Ocean
720
68
69-i
66-6
Wiillerstorf
Between Natal and Australia.
19°.
26 April, 1839 .
29 33
10 57 E.
S. Atlantic ...
6396
41-2
66-z
627
DuPetit Thouars
f Full ; between the Cape and
\ Tristan d’Acunha.
191.
25 May, 1847...
29 49
67 14 E.
Indian Ocean
(6133)
2160
(37-6)
54
66
66
Dayman
| Between Madagascar and Isl.
\ of Amsterdam.
I92.
10 Aug., 1826...
3°
22 40 TV.
S. Atlantic
1602
50
63-6
59
D’Urville
Between the Cape and Uruguay.
193.
7 Dee., 1828...
30
44 20 e.
Indian Ocean
1602
58-8
72-8
73*6
f Between Madagascar and the
[ Cape.
I94-
17 Aug., 1826...
30
1 3 40 w.
S. Atlantic ...
1494
51-8
64
55'4
In mid-ocean.
195.
21 Dec., 1857 ...
30 6
20 14 w.
S. Atlantic ...
2400
43-5
74'5
Pullen (m)
)
196.
„
„ »
„ „
4800
40-2
! Mid-ocean ; between the Cape
f and Brazil.
197.
„ „
» „
7200
38-2
„
)
198.
1847-49
30 13
. 30 13
46 \v.
56 50 E.
S. Atlantic . . .
360
64
61
77
71
Otf coast of Uruguay.
''Between Mauritius and the
199.
, 26 April, 1847 .
Indian Ocean
972
65
|Fh Lenz
Dayman
200,
5) ,,
1698
60
J Cape.
'I
201,
Nov., 1825...
30 21
89 34 W.
S. Pacific
600
62 ‘5
63
66-5
Beechey
202,
1320
50
(Between Easter Island and
j Valparaiso.
” ”
”
”
97 .
203.
1920
45-2
J
)
204,
.13 April, 1818...
■ 3° 39
14 27 E.
S. Atlantic ...
150
661
67'S
68
Kotzebue
205
300
60-8
1 West of the Colony of the
f Cape ; northern part.
JJ
” ”
”
206,
1200
49-5
”
”
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
659
Table II. — Southern Hemisphere (continued).
I.
II.
in.
IY.
Y.
YI.
VII.
VIII.
IX.
South
Lati-
Tono-i
Temperature in
Date.
tude of
Sea.
Depth
iu feet.
degrees of Eahr.
Name of
observer.
Eemarks.
tude.
Green-
wich.
At
depth.
Surface.
Air.
O l
36 48 W.
0
O
2°7'
8Eeb„ 1847...
30 52
S. Atlantic . . .
1200
61
73
71
Dayman
1 In mid-ocean ; parallel of Uru-
208
2160
51
I guay.
209.
8 March, 1840.
45 miles
W. of Cape.
S. Atlantic ...
762
45
56
65
James Boss
210.
10 „
60 miles
„ 77
„ »
1200
43-5
61
64
,,
t Lat. and long, not given.
211.
7 „ „
i2omiles
„ „
77 77
2400
?
70
7i
,,
J
212.
31 29
45 57 w.
S. Atlantic . . .
1860
46-5
66
62
Beech ey . .
Off the coast of Uruguay.
2X3.
23 March, 1839.
3i 33
33 3°e.
Indian Ocean
5316
39'5
75-2
72-2
DuPetitThouars
Cylinder sound ; off Natal.
2 I A..
9 Dec., 1828...
32
35 5° B-
Indian Ocean
(4659)
2136
56-4
7°'4
66-5
D’Urville
f Between the Cape and Mada-
\ gascar.
Midway between the Cape and
Western Australia.
215.
26 May, 1847 ...
68 6 e.
Indian Ocean
2040
55
65
65
Dayman
2x6.
27 Jan., 1859...
32 21
157 18 w.
S. Pacific
1200
60-3
73-x
71-2
Wiillerstorf,
Between AustraliaandYalparaiso.
217.
7 Oct., 1838...
3* 5i
176 42 E.
S. Pacific
5316
44.4
61-3
66'2
DuPetitThouars •
Cylinder full. N. of N. Zealand.
(4692)
(41-7)
12 June, 1827...
32 54
II 26 W.
S. Atlantic ...
2455
56-4
72
72-5
Blosseville '
Between the Cape & Rio Janeiro.
2X9.
1847-49 ...
72(52?) w.
360
59
56
E. Lenz
Apparent error in longitude.
220.
16 Dec., 1828...
16 „
33
30 20 E.
Indian Ocean
801
1014
64-2
69
697
69
D’Urville
1 Off the S. coast of Natal.
221.
33
29 20 E.
77 77
742
72-3
J
24 Mar., 1818...
33 14
29 59 E.
Indian Ocean
870
62-7
71-9
76-1
Kotzebue i
On the Bank off the Cape.
223.
9 Peb., 1847...
33
36 54 W.
S. Atlantic ...
1104
60
70
68
Dayman
1 Between Monte Video ajjd the
22^.
!! ,
1944
50
/ Cape.
225.
1 Mar., 1840...
33 23
7 41 E-
S. Atlantic ...
600
56
70
71
James Boss
226.
„
,, „
» »
7,
900
53-2
„
„
| Vol. ii. p. 53. In mid-ocean
227.
„
„ „
7 7 77
1800
47-4
}■ between the Cape and the
228.
43
1 Island of Tristan d’Acunha.
” ”
77 77
77 77
2700
,7
„
|
229.
„
„ ,,
„
77
3600
41-7
>
230.
24 Apr., 1837...
33 26
72 03 w.
S. Pacific
853
49-1
54'7
51-8
DuPetitThouars
f Cylinder sound ; soundings in
l 960 feet. Off Valparaiso.
231.
27 Mar., 1827...
33 3°
175 50 E.
S. Pacific
3204
44-5
69-3
68-2
D’Urville i
North of New Zealand.
232
233.
11 Aug., 1841...
33 32
167 40 E.
S. Pacific
900
1200
53
51
James Ross
] In soundings on a bank be-
” ”
77 77
J- tween New Zealand and
234.
>, »
>, „
77 77
1800
48-1
„
N. S. Wales.
233.
>, „
7,
2400
45-3
J
236.
9 Aug., 1841...
33 4°
164 l8 E.
S. Pacific
900
55‘8
59
James Ross
} Between New Zealand and
*37
„ !>
„ „
1800
49-7
„
J N. S. Wales.
*3»-
10 Aug., 1841...
33 41
166 23 E.
S. Pacific
12
58-7
597
James Ross
239.
». »
» »
„ 77
77 77
300
57-6
240.
,, „
» ”
,7 „
„ „
600
567
.7
.7
Between the North Island of
241.
» „
„ »
77 77
77 77
900
53-6
,,
New Zealand andNewSouth
242.
» »
» »
„ „
1800
49-5
7.
.7
Wales. No bottom in 4920
feet.
243-
» »
» >,
77 77
77 >7
2700
45-6
„
244.
„ „
„ „
7. ,7
>7
3600
42-7
„
245.
„ »
„ „
•77 .7
77 7,
4500
40-4
„
„
J
246.
27 May, 1847...
33 48
70 HE.
Indian Ocean
2100
54
63
63
Dayman Between the Cape and Australia.
247.
17 Dec., 1828...
34
27 20 E.
Indian Ocean
334* ,
66-9
69-5
74'2
D’Urville Near Algoa Bay.
248.
26 Mar., 1818...
34 2
28 12 E.
1
Indian Ocean
324
64
71'1
72
Kotzebue On the Bank off the Cape.
4 T
MDCCCLXXV.
660
ME. J. PRESTWICH ON SUBMARINE TEMPERATURES.
Table II. — Southern Hemisphere (continued).
L
II.
III.
IY.
Y.
YI.
YII.
YIII.
IX.
South
Lati-
Longi-
tude of
Temperature
in
Date.
Sea.
Depth
in feet.
degrees of Eahr.
Name of
observer.
Remarks.
tude.
Green-
wich.
At
depth.
Surface.
Air.
O 1
0
0
249.
24 Apr., 1847...
34 24
54 14 E.
Indian Ocean
942
60
64
60
Dayman
1 Between Island of Amsterdam
250.
251.
1772
58
J and the Cape.
1
19 Nov., 1838...
34 34
l6l 2 E.
S. Pacific
4264
40-8
65
65'3
DuPetitThouars
(3347?)
1 Between New Zealand and
252.
? „
34 37
17 1 IE.
” ”
3214
(2920)
42-8
627
6l'2
” ”
J Sydney. Cylinder sound.
253.
24 Feb., 1847...
34 42
4 15 W.
S. Atlantic ...
2184
51
70
69
Dayman
1 Between St. Helena and Tris-
254.
2S5-
256.
3900
44
J tan d’Acunha.
12 Oct., 1772...
12 Oct., 1838...
34 48?
34 54
600
58
59
62
60
Forster
In the parallel of the Cape.
Soundings N. of New Zealand.
174 5 E.
S. Pacific
1607
50-5
6o-8
DuPetitThouars
(951 ?)
256a
20 April, 1836...
34 57
52 30 w.
S. Atlantic . . .
266
55
62'2
567
Vaillant
| Entrance of Bio de la Plata.
25 65
257.
35 1
35
250
60-6
6l
62-6
1 June, 1847...
80 56 E.
Indian Ocean
2076*
55
59
61
Dayman
(Between the Cape and King.
I George’s Sound.
258.
19 Dec., 1828...
35
23 20 E.
Indian Ocean
378
60-4
68-2
707
D’Urville
S.W. of Algoa Bay.
259.
21 Dec., 1828...
35
l8 20 E.
S. Atlantic ...
694
59-6
67-6
68
Off the Cape.
260.
4 Oct., 1826...
35
Ill 20 E.
Indian Ocean
480
56-3
57
59-8
„
Off the S.W. of Australia.
261.
„
35 7
118 5 e.
»
229*
58
62
58
,,
Off King George’s Sound.
262.
27 Mar., 1818...
35 i7
22 56 E.
Indian Ocean
516
51-7
68-i
77'5
Kotzebue
Off the Cape.
263.
10. Feb., 1847...
35 *1
35 31 W.
S. Atlantic ...
1008
62
68
68
Dayman
1 Between Monte Video and
49
264.
265.
1854
1170
J Tristan d’Acunha Island.
25 Feb., 1847...
35 28
3 6 w.
S. Atlantic ...
54
69
68
Dayman
] Between the African coast and
266.
2010
46
j Tristan d’Acunha Island.
267.
4 Jan., 1827...
35 3°
137 20 E.
S. Pacific
1869
46-2
66-3
63'4
D’Urville
Off South Australia.
268.
17 Feb., 1847...
35 3°
19 34 w.
S. Atlantic ...
1290
58
69
64
Dayman
1 Between the Cape and Monte
269.
270.
2196
2100
61
J Yideo. ? Beading reversed.
28 May, 1847...
35 33
72 6 E.
Indian Ocean
55
60
6l
Dayman
(Between the Mauritius and
\ the Island of Amsterdam.
271.
20 Dec., 1858...
35 34
175 31 E.
S. Pacific
1020
60
67
637
Wiillerstorf ...
N. of New Zealand.
272.
5 Sept., 1826...
36
33 20 e.
Indian Ocean
1174'
55-4
62-1
59
D’Urville
Off Natal.
273.
27 Oct., „
36
121 20 E.
„ „
1708
45 *3
56-6
54‘9
„
Near King George’s Sound.
274.
23 Feb., 1847...
36 4
4 53 w.
S. Atlantic . . .
1230
61
67
62
Dayman
1 Between the Cape and Monte
275.
2070
48
( Yideo.
”
276.
277.
29 May, 1847...
16 Feb., 1837...
36 6
36 7
74 15 E-
21 4 vv.
Indian Ocean
2100
52
CQ
60
Dayman
Near the Island of Amsterdam.
1 Between the Cape and Monte
S. Atlantic ...
1176
55
66
59
Dayman
27S.
279.
2016
47
( Video.
5 Feb., 1858...
36 11
54 12 e.
Indian Ocean
3600
46-8
66-5
Pullen (u)
(Between the Cape and Island
280.
„ »
„ » 1
„ „
„ „
6000
40-8
„
j of Amsterdam.
281.
13 Apr., 1847...
36 17
26 43 E.
Indian Ocean
1290
62
68
61
Dayman
282.
2160
60
J- South of Algoa Bay.
283.
20 Sept., 1857...
36 22
5 39 e-
S. Atlantic ...
1320
53
51-8
56-8
Wiillerstorf
f Between Tristan d’Acunha
[ and the Cape.
284.
29 Oct., „ ...
36 22
17 34 e.
600
63-3
63-5
59*9
„
South of the Cape.
285.
286.
5 Mar., 1847...
36 22
13 40 E.
S. Atlantic . . .
1302
2202
52
46
68
66
Dayman
I
” ”
99 99
” ”
” ”
”
”
99
>Off the Cape.
287.
6 Mar., 1847...
36 24
14 42 E.
S. Atlantic ...
882
65
JO
71
Dayman
1704
J
288.
56
”
” ”
” ”
99
”
ME. J. PEESTWICH ON SUBMARINE TEMPEEATUEES.
Table II. — Southern Hemisphere (continued).
661
I.
II.
Date.
III.
South.
Lati-
tude.
IY.
Longi-
tude of
Green-
wich.
Y.
Sea.
YI.
Depth
in feet.
YII.
Temperature in
degrees of Fahr.
Yin.
Name of
observer.
At
depth.
Surface.
Air.
289.
17 Eeb., 1827...
O i
36 30
O 1
I76 40 E.
S. Pacific
907
50-8
0
6S'S
64'2
D’Urville
290.
15 Feb., 1847...
36 3I
24 7 W.
S. Atlantic ...
1164
58
64
63
Dayman
291.
„ »
„ »
v >.
» »
2034
45
„
„
292.
27 Jan., 1839...
36 36
Il8 28 E.
Indian Ocean
5316
37
64-2
637
DuPetitThouars
(5282)
293.
4 Mar., 1847...
36 41
12 IE.
S. Atlantic ...
1128
55
64
66
Dayman
294.
„ »
„ »
1968
46
„
„
295.
6 June, 1847...
36 42
97 54 E-
Indian Ocean
1920
51
56
55
Dayman
296.
18 Eeb., 1847 ...
36 47
18 47 W.
S. Atlantic . . .
768
57
68
54
Dayman
297.
».
„ „
„ „
» »
1542
50
„
298.
3 Mar., 1847...
36 47
IO 24 E.
S. Atlantic- ...
1248
54
66
63
Dayman
299.
„
„ »
„ »
2088
46
„
„
„
30 Oct., 1857 ...
tR tt v
900
52
^35
62-2
w iillei’storf
301.
13 Eeb., 1847 ...
36 50
27 50 w.
S. Atlantic . . .
1290
62
66
66
Dayman
302.
„
„
„ „
„ ,,
2220
45
„
„
„
3°3-
14 April, 1847...
36 53
; 27 49 e.
Indian Ocean
1290
65
69,
66
Dayman
3°4-
,. »
„ ,,
„ „
„ „
2160
56
„
„
3°5-
26 Eeb., 1847 ...
36 57
I 31 w.
S. Atlantic . . .
1170
53
67
65
Dayman
306.
„ „
„ >,
)J „
„ „
2010
49
„
307.
18 Feb., 1827 ...
37
176 20 E.
S. Pacific
801
57' 7
67*1
64'2
D’Urville. .
308.
12 July, 1841 ...
37 *o
I5I 36 E.
S. Pacific
3300
46-2
60
James Boss
309.
11 „
17 miles
off C. Howe.
S. Pacific
1752
49-7
59
59
„
310.
July, 1828...
37 20
48 47 w.
S. Atlantic . . .
600
57
60
57
Beech ey
311.
„ »
„ >.
1140
56-5
„
„
„
312.
„
„ „
„ „
.» „
1740
48-5
„
„
3*3-
12 Eeb., 1847...
37 20
30 58 w.
S. Atlantic ...
1230
57
66
69
Dayman
3X4-
„ „
„ »
„ „
2130
45
„
„
„
3i5-
13 Jan., 1827 ...
37 30
157 20 E.
S. Pacific
3257
42
67
65-5
D’Urville
316.
8 Feb., „ ...
37 30
178 55 E.
1922
46
67-4
657
3*7-
1 Feb., 1839 ...
37 42
114 58 E.
Indian Ocean
5315
37'4
62'2
6ri
DuPetit Thouars
(5282)
318.
19 April, 1847...
37 49
39 5°e-
Indian Ocean
1596
51
59
64
Dayman
319.
„ »
„ „
,, „
„ ,7
1896
53
„
320.
21 Eeb., 1847 ...
37 54
10 28 w.
S. Atlantic ...
1230
53
62
59
Dayman
321.
„ „
77 77
2070
43
„
„
„
322.
1 Sept., 1826...
38
24 20 E.
Indian Ocean
587
54-7
63*2
547
D’Urville
323-
„
„
» »
77 77
2776
41-3
„
„ ‘
324.
21 Nov., „ ...j
38
149 20 E.
S. Pacific
934
5 r ) ' 4
60
6o'S
325-
19 Eeb., 1847...
38 7
16 43 W.
S. Atlantic ...
2220
48
63
65
Dayman
326.
16 April, 1847 .
38 8
32 54 e.
Indian Ocean
768
64
69
69
Dayman
327-
„ „
„ 77
» »
77 7i
1668
60
„
77
328.
3 Dec., 1857 ...
38 9
77 46 E.
Indian Ocean
720
55-4*
567
54
Wullerstorf
329.
15 April, 1847 .
38 10
29 39 E.
Indian Ocean
1230
67
69
67
Dayman
3 So-
» „
„ ”
„ „
77 77
2100
58
„
„
SS1-
26 Eeb., 1837 ...
38 12
33 4° w-
S. Atlantic ...
2132
37-4
62*3
71-6
DuPetitThouars
(1968?)
IX.
Remarks.
North of New Zealand.
| In mid-ocean.
/ Cylinder sound. Near Eng
\ George’s Sound.
) S.W. of the Cape.
/ Between Amsterdam Island
\ and Australia.
1 Between the Cape and Buenos
J Ayres.
| S.W. of the Cape.
S. of the Cape.
\ Between Tristan d’ Acunha and
J Monte Video.
Off Algoa Bay.
1 Between Tristan d’ Acunha
J Island and the Cape.
North of New Zealand.
Off Port Jackson: no soundings.
In soundings.
1 Off Bio de la Plata.
1 Between La Plata and the
J Cape.
/Between New Zealand and
\ New South Wales.
Near the N.E. of New Zealand.
S. of Cape Leeuwin, Australia.
1 Between the Cape and Crozet
J Island. ? Beading reversed.
\ Between the Cape and La
/ Plata.
S.W. of Algoa Bay.
Bass’s Strait.
Between La Plata and the Cape.
1 Between Port Natal and
J Prince Edward Island.
Near the Island of Amsterdam.
South of Algoa Bay.
Cylinder full : in mid-ocean.
4 t 2
662
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
Table II. — Southern Hemisphere (continued).
I.
II.
III.
IV.
V.
VI.
VII.
VIII.
IX.
South
T on o-i
Temperature
in
Date.
tude of
Sea.
Depth
in feet.
degrees of Eahr.
Name of
observer.
Eemarks.
tude.
Green-
wich.
At
depth.
Surface.
Air.
45 36 E.
0
0
332.
21 April, 1847...
38 13
948
55
60
66
Dayman
1 Between the Cape and Island
333-
333«
1758
52
J of Amsterdam.
27 Feb., 1847 ...
38 22
0 28 V.
S. Atlantic . .
1152
55
62
64
Dayman
1 In open ocean.
2028
45
1 Mar., 1847...
38 25
S. Atlantic ...
1170
48
55
56
Dayman
\ Between the Cape and Gough
2010
44
J Island.
336.
337-
38 30
38 3°
I45 l6 E.
75 44 w.
58
602
63-6
55'5
65'3
54
D’Urrille .
In Bass’s Strait.
Oct., 1825 ...
540
51
Deeehey ...
1200
44-5
'I I
339-
1800
45-5
Off the south coast of Chili.
2400
44
j
34i-
26 Not., 1857...
38 41
77 45 E-
Indian Ocean
720
55*4
56
54'7
W tiller storf
Near the Island of Amsterdam.
10 Not., 1826...
39
39 4
141 50 E.
123 22 E.
1708
47-5
56-2
6o-8
63-6
587
D’Urville
Off the S. coast of Australia.
Cylinder full. S. of Australia.
343-
23 Jan., 1839 . . .
S. Pacific
1870
48-5
(47-5)
DuPetit Thouars
344-
27 Not., 1841...
39 16
177 25 W.
S. Pacific
900
53-5
58
James Boss
\
345-
346.
1800
49-2
| Off the east coast of the North
V Island of New Zealand : no
2700
46-8
” ”
”
soundings.
347.
3600
44-9
348.
Aug., 1825...
39 3i
45 2 w.
S. Atlantic . . .
1482
55
59
47
Beechey
J
Open ocean.
349-
15 Mar., 1839...
39 5i
44 17 E-
Indian Ocean
5316
(3051 ?)
37-8
78
8o-6
DuPetitThouars
Cylinder sound. Open ocean.
350.
12 June, 1847...
39 57
40 44
1 18 E.
Indian Ocean
1920
45
54
48
Dayman
S. of King George’s Sound,
j To the N.W. of Kerguelen I.
351-
14 Not., 1857...
60 8 E.
Indian Ocean
Wullerstorf
\ No soundings in 37,020 feet.
352-
14 June, 1847...
40 46
123 26 E.
S. Pacific
2280
50
53
49
Dayman
South of W. Australia.
353-
11 Not., 1857...
40 52
49 57 E.
Indian Ocean
600
54-9
54' 3
477
Wullerstorf
j Between the Cape and Ker-
1 guelen Island.
In Cook Strait.
Off La Plata.
354.
20 Jan., 1827 ...
40 58
41
173 5 E.
54 35 w.
S. Pacific
32*
63-5
64-4
59
65
D’Urville
355-
5 April, 1850 .
S. Atlantic ...
900
40
Armstrong
356.
2 Feb., 1827...
40 31
41 56
176 48 E.
55 6 w.
S. Pacific
506*
58-7
63*2
65
627
D’Urville
Cook’s Strait, New Zealand.
Cylinder full.
357-
2 Mar., 1837...
S. Atlantic ...
1066
38-5
6o*8
DuPetitThouars
(591?)
358.
4 Jan., 1827...
42
17 1 E.
S. Pacific
534
55-8
63
61
D’Urville
Near the W. coast of N. Zealand.
359-:
Sept., 1825...
42 2
46 8 w.
S. Atlantic ...
1200
41
47
Beechey
In the parallel of Bio Negro.
360.
27 Dec., 1838...
42 34
153 IO E.
S. Pacific
5316
43-5
557
55'4
DuPetitThouars
Cylinder full.
(3904?)
(41-4)
361.
17 Jan., 1839 ...
43 2
131 54 e.
S. Pacific
5872
44-6
55'4
53*6
DuPetitThouars
S. of Australia; cylinder full.
(41-2)
362.
26 March, 1843.
43 10
14 44 E.
S. Atlantic ...
1800
44
53
52'7
James Boss
| Between the Cape of Good
363.
2700
41-1
364-
„ „
„
6300
39-8
„
„
(r Hope and Bouvet Island:
no soundings.
365.
»
7200
39-5
„
)
366.
17 Dec., 1827...
43 25
1 5 miles
I47 7 E.
e. of Cape
S. Pacific
160*
2250
55-6
48
CO
D’Urville
Off east coast of Tasmania.
36 6a\
367-1
9 July, 1S47 ...
16 April, 1836...
Pillar
jy
43 47
79 6 w.
S. Pacific
2656
39-3
55
557
53
55' 5
DuPetit Thouars
Tasmania.
1 Off the Isle of Chiloe. Cy-
J linder sound.
368.
..
1
•I
5872
36-1 1
55'4
55
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES,
663
Table II. — Southern Hemisphere (continued).
I.
II.
III.
IY.
Y.
YI.
YII.
Yin.
IX.
South
T nn O'i
Temperature
in
Date.
tude of
Sea.
Depth
in feet.
degrees of Eahr.
Name of
observer.
Eemarks.
tude.
Green-
At
depth.
wich.
Surface.
Air.
369.
O /
o
o
O
27 Mar, 1843...
43 52
13 23 E.
S. Atlantic ...
900
44
47'5
49*8
Jame3 Boss
370.
„ „
» .»
77
1800
40-3
„
(Between the Cape and Bouvet
371-
»
„ ,,
77 77
2700
39-8
„
„
C Island.
372-
„ ,,
3600
39-5
J
373-
8 Jan, 1816...
44 47
57 31 w-
S. Atlantic ...
1176
38-8
54‘9
57-6
Kotzebue
f Between Monte Video and the
\ Falkland Islands.
374-
5 Mar, 1837...
45 38
61 10 w.
S. Atlantic ...
160
48-2
57'5
59
DuPetitThouars
)
(8 A.M.)
213
424
j Cylinder sound. In sound-
375-
„ (7 A.M.)
JJ 1,
JJ »
' 57‘2
55'4
}- ings N. of the Falkland
376.
„ (6 A.M.)
„ »
,,
374
413
„
55
j Islands.
377-
„ (noon)
„ „
374
41'3
58-6
63
77 77
j
37»-
Sept, 1825...
46 15
51 53 w.
S. Atlantic . . .
1680
41
5i
SS
Beechey '
N.E. of the Falkland Islands.
379-
380.
14 Not, 1840...
?
9
S. Pacific
900
1800
49-8
48
51
46-8
James Boss
Two days’ sail south of Van
” ”
”
> Diemen Land : no sound-
381.
7,
2700
46-5
„
[ ings.
382.
„ >»
„ ..
77 7,
3600
45-6
„
„ „
J
383-
Sept, 1825...
47 18
' 53 30 w.
S. Atlantic ,.
1620
44.7
49'8
43
Beechey
[Open sea to the N.E. of the
384.
3618
39-2
385-
4398
40-1
f Falkland Islands.
386.
5124
394
J
387.
4 Dee, 1841...
49 J7
172 28 w.
S. Pacific
900
48-7
53
49'7
James Boss
388.
„ ».
„ 7,
„ „
2700
44-5
,,
389
„
„ „
3600
422
„
„ „
[Near Antipodes Island. No
i soundings in 6600 feet.
39°
„ ,,
4500
41
„
„ „
391
„ „
5400
40-2
„
„ „
392
.. >.
„ „
6300
40
„
„ „
J .
392
Feb, 1804...
52
68 w.
S. Atlantic . . .
330
46
53'4
43
Horner
Off Patagonia.
393
2 April, 1841...
52 10
136 56 E.
South’n Ocean
900
42
James Boss
394
1800
41
Between Australia and the
395
» „
„ „
„ „
,,
2700
40
,,
„ „
> Antarctic Land. Soundings
in 9240 feet.
396
„ „
„
3600
39-8
J
397
23 Dec, 1772...
52 26
53 12
9
S. Ocean
600
34-5
32
51
33
Forster
20° south of the Cape.
S.E. of the Falkland Islands.
398
1847^9
55 w-
S. Ocean
360
43
E. Lenz
398
9 May, 1836 ...
16 Sept, 1842...
53 47
54 4i
62 45 w.
55 22 w.
S. Atlantic ...
957
39-2
41
39'5
38
33’5
Vaillant
Off Terra del Fuego.
1 In soundings. 10° east of
399
S. Ocean
900
39-8
James Boss
4°o
„ j.
1680
398
J Cape Horn.
401
10 Jan, 1840..
55? .
V
157 E.?
?
S. Ocean
1800
39
43
32
Wilkes
|
1
1 402
22
1920
j Off Macquarie Island. Mud
at bottom of No. 402.
I403
16 „ „ ..
2
157 46 E.
5100
31-5
3i
J
1 4°4
16 Mar, 1839..
55
65 \V.
2400
37
44
Near Le Maire Strait.
4°5
15 Dec, 1772..
55 8
55 9
22 E. ?
S. Ocean
600
34
32
39 ?
Cook
Amongst ice : S. of the Cape.
l 7 7
I 4°
30 Mar, 1841,
I32 28 E.
S. Ocean
900
39
38'5
James Boss
40
,, „
„ 71
„
1800
395
Open ocean, on the parallel
Y of Macquarie Island : no
[4°
«' ”
>. ,>
.7 77
2700
39-8
soundings.
j 4°
” ”
V
3600
1 39-8
J
664
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
Table II. — Southern Hemisphere (continued).
I.
II.
III.
IY.
Y.
YI.
YII.
YIII.
IX.
South
Tmo.
Temperature
in
Pate.
tude of
Sea.
Depth
in feet.
degrees of Pahr.
Name of
observer.
Eemarks.
tude.
Green-
At
depth.
mch.
Surface.
Air.
O l
0
o
0
410.
13 Dec., 1841...
55
149 20 w.
S. Ocean
900
39-6
39
42-5
James Boss
1
411.
» ,,
?l ,,
,, ,,
1800
399
„
„
! Between Cape Horn and New
j Zealand : no soundings.
41a.
13 Dec., 1841...
„ „
„ „
35
2700
39-7
39
42-5
55
4*3-
3600
397
t)
J
414.
1847-49
55 J9
62 W.
360
41
48-4
17, T ip.n 7, , , .
\
f Between Cape Horn and the
[_ South Shetlands.
415.
23 Dec, 1772...
55 2°
3I 30 E.
600
345
33
Cook
f Near ice : between Cape and
3 -
1
[ Enderby Land.
416.
18 Sept., 1842...
55 4°
63 8 w.
S. Ocean
18Q0
37-2
40*2
31-9
James Boss
5
to soundings.
417.
20 Deo., 1842...
55 48
54 40 w.
S. Ocean
900
40
40
45 '4
James Boss
419.
” ”
” ”
” »
”
1800
2700
396
396
»
”
” ’
Between the Falkland Islands
" ”
” »
"
”
”■ ”
J- and Elephant Island: no
420.
„ „
„ „
,, „
„
3600
39-4
„
„ „
soundings.
421.
„
„ , ,
„ „
„
4500
393
„
„ „
422.
,, „
„ „
„
6000
39-5
„
„
„ „
'
423.
424.
425.
426
Sept., 1825...
55 5 8
72 10 w.
600
42-5
43‘5
37
Beechey . . . .....
1
1380
42-5
[Off the south coast of Terra
1980
40-5
f del Fuego.
2580
41-6
1
427
. 1847-49
56
56 20
64 w.
148 8 w.
360
41
46
35‘8
17 Benz
East of Oa.np. Horn.
14 Dec., 1841...
S. Ocean
900
38
41
James Boss
]
j- In mid-ocean : no soundings.
429
” „
” ”
1800
to 7200
39-7
” ”
43°
43i
18 Mai-., 1843...
56 41
6 s w.
S. Ocean
900
1800
35'2
36 '8
33‘5
33-2
James Boss
1 In mid-ocean, between Bouvet
” ”
" "
” ”
}. Island and Sandwich Isl. :
432
» •>.
„ 33
» »
»
2700
37'8
»
»
» >
1 no soundings.
433
„
„ „
,,
3600
39.
„
„
„ „
J
434
5 April, 1837...
56 58
82 16 w.
S. Ocean
13124
?
44-6
42-6
DuPetitThouars
Cylinder crushed : index fixed.
(12828)
435
21 Dec., 1840...
57 5*
I70 30 E.
S. Ocean
1380
39-5
42
39
James Boss.
436
23 Mar., 1837...
58 32
73 z9w.
S. Ocean
2132
39 ’5
44
45
DuPetitThouars
Near No. 443. Cylinder sound.
(1608)
300
437
23 Mar., 1842...
58 36
104 40 IV.
S. Ocean
40-8
4T
32
James Boss
|
438
„ , „
» ,,
„ „
„
600
40-8
„
»
„■
439
» „
» „
» ..
t,
900
40-7
tt „
! BetweenDoughertylslandand
44°
„ »
„ „
tt ,,
„
1800
40-8
„
„
( Cape Horn : no soundings.
44 1
„ „
tt tt
„
2700
40-5
„ •
,, ,,
|
442
„
„ ,,
„
3600
40
„
„
„ „
J
1
443
1 April, 1837...
58 4°
79 15 w.
S. Ocean
2657
3S-6
42-4
42-4
DuPetitThouars
Cylinder full.
(1870)
444
28 Mar., 1S42...
58 55
83 16 w.
S. Ocean
900
40-S
42
40
James Boss
445
„ „
„
„
1800
40-8
[ Open sea to the S.W. of Cape
446
„ »
„ »
„ „
„
2700
40-5
„
„
f Horn.
447
„ ,,
„ »
,, „
3600
40
„
„
„
/
'
448
22 Dec,, 1840...
59
171 E.
S. Ocean
900
38-5
37
37'4
James Boss
\
|
449
>, „
J9
„ „
,,
1800
39-5
}J
[Between New Zealand and
45°
„
„ tt
2700
39-7
„
f South Victoria Land.
1
45 1
tt „
”
3600
.39-7
”
J
ME. J. PEESTWICH ON SUBMAEINE TEMPEEATUEES.
665
Table II. — Southern Hemisphere (continued).
I.
II.
III.
IY.
Y.
YI.
VII.
yiii.
IX.
South
Lati-
Longi-
tude of
Temperature
in
Date.
Sea.
Depth
in feet.
degrees of Eahr.
Name of
observer.
Eemarks.
tude.
Green-
wich.
At
depth.
Surface.
Air.
59 4S
79 56 w.
Q
0
0
452
26 Mar., 1837...
8. Ocean
2657
39
42-9
42-4
DuPetitThouars
Near his last. Cylinder full.
(2395)
453-
25 Mar., 1841...
60 22
131 28 E.
S. Ocean
900
37
35
34'4
James Boss
1
454-
,, „
„ ,,
„
„
1800
38
„
,,
J
^ Between Australia and Adelie
453-
„ . „
„ ,,
„ „
„
2700
39-5
„
„
„
Land : no soundings.
456.
„ ..
„ „
3600
40-5
J
457-
458.
Mar., 1839...
61 ?
55 w.?
22 30 \y.
1800
33
36
Wilkes
Off Elephant Island.
In mid-ocean : no soundings.
22 Eeb., 1843...
61 30
S. Ocean
4500
39-2
32
30
James Boss
459-
SMar., 1842...
62 15
163 50 w.
S. Ocean
600
32-2
35
32
James Boss
1
460.
900
35*5
Between the Society Islands
461.
>,
„ „
„ „
1800
372
„
„
1
and Antarctic Continent.
Erom the surface to 600 ft.
462.
„
„ „
„ „
„
2700
38-5
„
„
„
the temperature was 30o,8.
463.
„ „
„ .»
3600
39
„
„
J
464.
465.
1839
63 ?
57 w.?
174 30 E.
600
29
29
3°
28
Wilkes
Near the South 'She.tla.nrls.
27 Dec., 1840...
63
S. Ocean
900
35-5
3*'9
James Boss
I
Between New Zealand and
466.
„ »
„ „
„
1800
38-2
„
- S. Victoria Land: no sound-
467.
„ „
„
3600
39-7
,,
„
„
ings.
468.
4 Mar., 1839...
63 28
63 47
55 w.
151 34 w.
S. Ocean
600
30
31
30
Wilkes
See Amer. Journ. of Sc. Jan. 1848.
469
20 Dee., 1841...
S. Ocean
900
35 -6
277
James Boss
470.
,, ,,
„ „
, , ,,
1800
38-4
Amongst ice. Between Dou-
471.
„
„ „
» »
„
3600
40
„
„
[ gherty Island and South
] Victoria Land. Soundings
472.
>.
„ »
” ...
4500
39-6
„
„
„
in 10,200 feet.
473-
„
„ >,
,,
5400
39-8
„
'
1
474-
8 Eeb., 1843...
63 49
51 7 w.
S. Ocean
600
32-2
32
33
James Boss
475-
900
332
476.
„ „
„ „
„ „
„
1800
35-5
,,
„
„
Near Louis Philippe Land,
Antarctic Continent. Off
477-
» •>
2700
36- 4
37- 3
”,
the pack. No soundings
in 7260 feet.
478
»
„ „
.. ..
99
3600
„
„
„
479
„ „
„ »
.. ..
„
7260
39'5
480
481
18 Mar., 1841...
63 5i
151 47 E.
S. Ocean
900
1800
35-5
37-5
30-4
287
James Boss
>
I Between Van Diemen Land
» »
j. »
!. 1.
1 and South Victoria Land.
482
„ „
2700
38-5
17
j Near the pack: no sound-
483
„ „
„ „
„
3600
392
/
I iugs-
484
18 Jan., 1843...
63 59
54 35 w.
S. Ocean
900
30
32
James Boss
f Off the pack : soundings in
[ 1260 feet.
I
485
21 Mar., 1841...
64 7
140 22 E.
S. Ocean
900
34
30-8
27
James Boss
>
486
„
1800
36'5
„
„
[Near the pack: no soundings.
487
„
..
2700
38
„
,,
,,
j N. of Adelie Land.
488
„ „
„ »
. 3600
38-7
55
7
489
13 Jan., 1773...
64 30?
39 E-?
S. Ocean
600
32
33'5
36
Cook
N.W. of Enderby Land.
490
30 Dec., 1840...
64 38
I73 IO E.
S. Ocean
900
35-2
3i
32-2
James Boss
49 1
n
1800
37-2
Between New Zealand and
492
2400
”
h South Victoria Land. Sound-
1. »
»
38-8
..
..
i
ings in 9360 feet.
493
” ”
” ”
”
3600
398
”
J
666
ME. J. PEESTWICH OH STJBMAEINE TEMPEEATTJEES .
Table II. — Southern Hemisphere (continued).
I.
II.
III.
IY.
Y.
YI.
YII.
Yin.
IX.
South
T(mo-
Temperature
in
Date.
tude of
Sea.
Depth
in feet.
degrees of Eahr.
Hame of
observer.
Eemarks.
tude.
Green-
wich.
At
depth.
Surface.
Air.
494-
6 Mar., 1841...
O l
64 51
164 45 B.
S. Ocean
3600
0
37-2
29-2
0
31
James Boss
No soundings.
494®
12 Feb., 1840...
64 57
1 12 16 E.
S. Ocean
1500
30-5
31
Wilkes
f Near the ice-barrier. No
\ soundings.
495
3 Jan., 1842...
66 34
156 22 W.
Antarctic O.
6300
396
28
31'1
James Boss
In the pack.
496.
3 Mar., 1842...
67 28
174 27 w.
Ant. Ocean ...
900
34-2
33
32-3
James Boss
497-
„ >,
„ 77
„ ' 77
1800
35’5
„
„
„
[ No soundings. Not far from
j icebergs.
498.
„ 77
7, 77
„ »
77 77
2700
37’5
„
■„
499.
77 77
„ „
77 77
3600
38
„
„
J
500.
S°i.
7 Jan., 1841...
68 17
I75 21 B.
Ant. Ocean . . .
900
1800
37'5
38-2
28
28
James Boss
] Not far from icebergs. Ap-
proaching the Antarctic
502.
77 77
77 77
2700
39-2
77
»
continent.
5°3-
7, 7,
3600
39-8
„
„
)
5°4-
5°5-
2 Mar., 1841...
68 27
68 32
167 42 E.
12 49 W.
2400
36
28 -2
27
Tames Ross
Ditto. No soundings.
3 Mar., 1843...
Ant. Ocean . . .
900
33
30-8
29-4
James Boss
506.
„ 77
77 77
1800
35-5
„
,,
5°7-
3600
38-7
Between Louis Philippe Land
4500
39-4
. and Enderby Land. No
508.
7, 77
” „
’7
»
»
soundings in 24,000 feet.
5°9-
„
„ „
„ „
,7 7,
5400
39
„
„
„
510.
„ ,7
77 ,7
„ „
77 77
6300
39-5
„
„
J
511-
512.
9 Feb., 1842...
7° 39
174 31 W.
Ant. Ocean ...
900
1800
32-1
35
28
27-9
James Boss
| To the N.E. of S. Victoria
”
”
t Land. Near the pack : no
5I3-
”
,> „
”
2700
35-8
»
7,
1 soundings.
5i4-
„
„ >,
77 77
„ ..
3600
37-6
„
„
J
5I5
18 Jan., 1841...
72 57
176 6 E.
Ant. Ocean . . .
900
33-8
30
3i
James Boss
\ In the parallel of Mt. Sabine,
516
„ 7,
„ „
„ ..
1380
34-6
„
„
J S. Victoria : no soundings.
5i7
15 Feb., 1842...
75 6
172 56 E.
Ant. Ocean ...
1740
32
30
25U
James Boss
Off S. Victoria Ld. : in soundings.
518
1 Feb., 1841...
77 5
171 33 W.
Ant. Ocean . . .
900
33
3*
27 ?
James Boss
1 Off the perpendicular ice-bar-
1500
33-2
l rier. Appearance of land
5I9
” .»
77 7,
»
”
j beyond : in soundings.
520
29 Jan., 1841...
77 47
176 43 E.
Ant. Ocean . . .
900
33
31
28
James Boss
113 miles off the ice-wall.
521
” „
” ”
” ”
” ’ ’’
1800
34-2
”
j Soundings in 2460 feet,
f Off the perpendicular ice-bar-
522.
23 Feb., 1842...
77 49
162 36 W.
Ant. Ocean ...
1740
30-8
28-5
25
James Boss
] rier. Appearance of land
[ beyond.
Addenda. — Omitted Observations of Capt. Kellett.
13 Dec.,
Depth
in feet.
At depth
60
66° F.
120
180
63
300
60
600
55
1200
51
1800
52
2400
46
3000
46
15.-19° 10' S. ; 77° 17' W.
Temperature
Air.
65° F.
20 Jan., 1846.-0° 18' S.; 83° W.
Temperature
At depth.
75° F.
70
67
65-5
62-5
54
51
48
47
Surface.
68° F.
Surface.
76° F.
ME. J. PRESTWICH ON SUBMARINE TEMPERATURES.
667
Table III. — Submarine Temperatures op Inland Seas*.
The Mediterranean.
I.
II.
Date.
III.
Position.
IY.
Deptli
in feet.
Y.
Temperature in
degrees of Fahr.
YI.
Name of
observer.
YII.
Remarks.
At
depth.
Surface.
Air.
8 Oct., 1780..
Western Division.
944
69
66
Saussure
1 Thermometers left down 12
J hours.
16 „ „ ..
Off Cape della Causa, near Nice..
41° N. lat. 5°‘20E. long
1918
68-5
58-5
57-i
569
61-3
22 Mar., 1829..
3204
547
57- 6
58- 1
D’Urville
\
23 „ „ ...
41° N. lat. 2°-20E. long
1602
1
5-
6.
27 Apr., 1826...
27 „
40° N. lat.' 4°'50 E. long
1602
54'5
623
59- 6
657
63-6
63-8
65-9
60- 8
293
563
7-
5 May, „
8 „
1068
54-2
64-1
63
59'2
6o‘5
6o'8
_ Between the coast of France
and Straits of Gibraltar.
1335
57‘4
21 „
106*
565
IO.
9,9!
106*
61-3
26 „
119*
58-3
3 June ,,
112*
59'2
55-4
627
69-8
737
797
797
8o-8
66*5
75'2
74‘3
83-2
13.
14.
15.
26 June, 1831 . . .
Between Mahon and Algiers
6408
Berard
>
27
3204
55-4
23 July, 1832...
14 miles N.E. of Bougie
3850
557
16.
9 Aug., „
10 miles N. of Bougie
267
56-3
17.
23 „
8 miles E.N.E. of Bougie
267
55'4
89-9
737
75"2
72
607
59
Between the Balearic Isles
and Algeria.
18.
23 Oct., „
40o,41 N. lat. 2°-10 E. long
373
58'8
70-8
72
68
19.
213
618
20.
106
69
21.
15 Nov., 1831...
Off Cape St. Martin
3204
55-4
67-1
58'3
74'5
22.
4005
55 ’4
July, 1844...
Between Marseilles and Algiers . . .
3
73-4
Aime
24.
33
68
25.
49
662
Mean of July (evening) ob-
servations. The mean tem-
[ perature of the air in July
26.
65
65'5
27.
82
644
| is 75°.
28.
98
63-5
J
29.
Mar., 1844...
3
57-4
57'5
Aime
3°.
6£
57-2
31.
33
57
Mean of March (evening) ob-
servations. The mean tem-
perature of the air in March
32.
46
56-8
33-
59
56’6
is 58°'l.
34-
566
35-
' 1841-1844 ...
f Between Marseilles and Algiers ;
\ exact position not specified . . .
82
61-3
647
644
Aime
36.
164
58
These numbers give the mean
I annual temperatures result-
[ ing from the total of his
observations.
37-
328
56-7
3s*.
656
55-4
39-
1148
54-6
)
”
* A few observations of D’Urville, marked thus, have F affixed in the original. Possibly this may mark “ Fathoms; ” but in
the absence of information the reduction is for “ Brasses,” which is the measure he otherwise used.
MDCCCLXXV. 4 U
668
MR. J. PRESTWICH ON SUBMARINE TEMPERATURES.
Table III. — Inland Seas (continued).
The Mediterranean (continued).
I.
II.
Date.
III.
Position.
IV.
Depth
in feet.
V.
Temperature in
degrees of Fahr.
At
depth.
Surface.
Air.
Western Division (continued).
40.
9 May, 1857...
38° 36' N. lat. 13° 41' E. long. . . .
720
58-8
6r6
6l
41-
11 „
38° 51' N. lat. 10° 36' E. long. . . .
750
57-2
60
62
42.
15 „ „
37° 56' N. lat. 3° 47' E. long. . . .
750
56-4
62-2
64-5
43-
„ ..
„ „
648
61-2
„
„
44.
19 „ „
36° 2'N. lat. 4° 2' W. long....
750
59-2
62-6
63-2
45-
24 „ „
36° 8' N. lat. 5° 21' W. long. . . .
60
601
59‘z
63-S
46.
30 „
36° 7'N. lat. 5° 22' W. long....
270
58-4
6r5
64-8
47-
2 June, ,,
36° 33' N. lat. 4° 34' W. long. . . .
72
56-4
57-6
66-2
Eastern Division.
48.
4 May, 1857...
39° 33' N. lat. 18° 51' E. long. . . .
180
58-2
61
61
49-
» „
300
60-1
„
„
50.
5 „
38° 21' N. lat. 16° 56' E. long. ...
150
60-8
61-5
6o-5
51.
July, 1845 ...
Egina Gulf
12
82
88
52.
60
78
c?.
120
69
jj
54.
210
62
55.
450
56
56.
780
55'5
C7.
12
80
84
58.
60
76
59.
120.
69
60.
210
61
6l.
330
57
62.
1260
55'5
62(3!.
23 July, 1846...
N. Division of Archipelago
30
76
86
62 b.
60
69
62 c.
150
62
62 d.
300
58
6ze.
600
55
63.
Aug., 1847...
OffNio
1080
86
64.
Off Andros
1200
55-5
65-
25 July, 1847...
Grecian Archipelago
60
74
78
86
66.
„ »
„ „
120
74
„
„
67.
» »
„ „
360
64
68.
„ »
„ „
540
64
„
„
69.
, „
720
56
„
„
70.
20 Sept., 1852...
Off Crete
60
72
75
76
71
„ »
„ „
300
59
„
„
72.
„ „
„ ;
720
56
„
,,
73-
14 June, i860...
Off Crete
60
68
73
80
74-
” „
” ”
120
68
1 ”
”
VI.
Name of
observer.
Spratt
Spratt
Spratt (u)
Spratt .
Spratt .
Spratt .
Spratt .
VII.
Remarks.
Between the Straits of Messina
and Straits of Gibraltar.
Between the Ionian Islands
and Sicily.
} A mile and a half from shore.
y Three miles from shore.
Between Euboea and Skyros.
Four miles from shore.
Seven miles from shore.
[Southern division of Greek
[ archipelago.
North coast o'f Crete.
1 About 50 miles west of Ceri-
l zotta, on the N.W. coast of
I Crete.
ME. J. PBESTWICH ON STJBMAEINE TEMPEEATUEES.
669
Table III. — Inland Seas (continued).
The Mediterranean (continued).
I.
11.
Date.
HI.
Position.,
IV.
Depth
in feet.
V.
Temperature in
degrees of Fahr.
VI.
Name of
Observer.
At
depth.
Surface.
Air.
14 June, 1860*
180
68
0
73
0
80
Spratt
76
300
63
77
600
59f
78
1200
59J
7440
591
80
25 Aug., 1860...
60
81
82
88
Spratt
81
120
79-J
82
180
781
83
300
77
84
600
73
85
May, 1861...
Between Malta and Tripoli
1770
62
62
68
Spratt.
86
21 Eeb., 1861 ...
120
62
61
64
Spratt
87
300
62
1740
62?
89
27 Feb., 1861...
Gulf of Syrtis
300
61
60
56
Spratt .. ..
9°
600
611
91
6 April, 1861...
Arabs Gulf W. of Alexandria
120
61|
62
68
Spratt
92.
1800
591
93-
April, 1861...
Off the coast of Egypt
120
611
63
6S
Spratt .
94.
1620
591
95.
15 Nov., 1861...
Off the coast of Egypt
180
71
73
69
Spratt
96.
300
68
9 7.
480
64
98.
600
62J
99-
15 Feb., 1861...
65 miles from Malta
180
59-|
60
57
Spratt ( u ) S
100.
»
,, „
600
59-1
„
„
IOI.
15 Feb., 1861...
55 miles S.W. of Malta
300
59
59!
Spratt ( u )
102.
„
,, „
900
59
„
,,
103.
15 Feb., 1861...
150 miles S.S.W. of Malta
120
60
60
104.
300
59 i
Spratt (u) . ^
„ j
104a
11 June, 1860...
150 miles E. of Malta
60
72 i
74
75
Spratt (u) \
I05-
n n
120
69
106.
180
63
107.
300
59|-
108.
600
58J
109.
7200
58f
no.
17 Nov., 1853...
Sea op Marmora
60
551
55*
61
Spratt (u) N
hi.
j> ,,
300
54
1 12.
17 Nov., 1853...
Sea of Marmora
60
56
60
113.
300
54A
p ()
1 14.
5 May, 1854...
Black Sea, Bourgas Gulf
60
49
52
68
» 1
Spratt (u) O
VII.
Bemarks.
About 50 miles west of Ceri-
zotta, on the N.W. coast of
Crete.
About 2 or 3 miles from the
About 200 miles west of Ben-
ghazi.
1 180 miles S.E'.'of Malta. No
J soundings in 6000 feet.
- Near the coast.
- Off Alexandria.
Off Arabs Tower, west of
S.W. of Malta.
Between Malta and the Greek
archipelago.
10 miles distant from the pre-
ceding. Soundings in 1320
feet.
* The observations of Admiral Spkatt before 1860
were made with Six’s self-registering thermometer.
were made on mud brought up from the bottom. Those in and after 1860
4 u 2
670
ME. J. PEESTWICH ON STJBMAEINE TEMPEEATUEES.
Table III. — Inland Seas (continued).
Eed Sea.
I.
II.
Date.
III.
North
Lati-
tude.
IV.'
Longi-
tude of
Green-
wich.
Y.
Sea.
YI.
Depth
in feet.
YIL.
Temperature in
degrees of Fahr.
VIII.
Name of
observer.
IX.
Remarks.
At
depth.
Surface.
Air.
0
0 •
0
115.
1 March and J
13 19
42 53 E.
Eed Sea
570
74-5
85
Pullen (m)
Near Strait of Bab-el-Mandeb.
116.
/ Apr., 1858 \
15 18
41 43 E.
240
77
86
Near the Islands of Dhalak.
117.
„
16 59
40 5 E.
300
77
86
Between Eas Debeer (Nubia)
118.
17 49
40 2 E.
„ „
3342
70-5
80
l and Ghumfooda, on the
1 19.
„ „
38 57 E.
„ „ j
1392
70-5
86
Arabian coast.
120.
„ „
20 57
37 29 E.
..
1800
71
83-5
1 Off Jeddah.
121.
j » 11
22 1
38 l6 E.
„
2552
71
78
J
122.
..
23 30
36 58 E.
4068
70-5
77'5
Between Berenice and Yembo.
I23.
„ „
27 33
Jubal Strait
2892
70
72
Top of Eed Sea.
1
Sea of Okhotsk.
May, 1804
46
144 E.
Sea of Okhotsk
360
32
2d.'6
Horner
Near the N. coast of Japan.
August
53
I44 E.
480
30
JT
55-8
Horner
Off the north end of Saghahen.
126.
August
53
152 E.
84
446
46-4
Horner
96
36-5
108
31-6
I 2Q.
126
29-3
Between the Island of Sagha-
■ lien and the coast of Kamt-
1 3°.
11 11
180
29
I!
schatka.
1 3 1.
360
29
132.
660
29
I33-
»
„ „
690
29
”
”
ME. J. PRESTWICH ON SUBMARINE TEMPERATURES.
671
Explanation of Map.
PLATE 65.
This Map is reduced, so far as relates to the hydrographical details, from the last
edition of the Admiralty ‘ Chart of the World for Tracks.’
On this the observations recorded in Tables I., II., and III. are laid down according
to the latitude or longitude given by the original observers. A few corrections have
been made in the Tables since the Map vras engraved. In the case of these or any
other discrepancies*, the Tables give the correct reading. In the Mediterranean only
a portion of the numbers (without the initials) are given for want of space.
The numbers in the Map correspond with those in the Tables, and the name of the
observer is indicated by initial letters as under. The name of the ship is added for
convenience of reference :
§11., in the order of date.
the fuller particulars and titles will be found
in the text,
A. Armstrong . . .
Voyage of the ‘ Investigator ’ . . . .
. 1850-54.
a. Abel
On the Voyage of the ‘Alceste’
. 1817.
B. Beechey . . . .
Voyage of the ‘ Blossom ’ *
. 1825-28.
is Belcher . . . .
Voyage of the ‘Sulphur’
. 1836-46.
99 99
Voyage of the ‘ Samarang ’
. 1843-46.
Bl. Blosseville . . .
See D’Urville
. 1828.
Ba. Bache
United States Coast Survey for 1854 . . .
. 1854.
C. Cook
Voyage of the ‘ Resolution ’ and ‘ Adventure ’
. 1772-75.
c. Ciiimmo
See note, p. 610
. 1868.
cr. Craven
See Bache
. 1855.
D.f D’Urville ....
Voyage de ‘ L’Astrolabe ’
. 1826-29.
d. Dayman . . .
Voyage of the ‘Rattlesnake ’
. 1846-47.
Ds. Dunsterville . . .
See Maury.
E. Ellis
On a Voyage to the Coast of Africa . . .
. 1749.
F. Franklin & Buchan .
Voyage of the ‘ Dorothea ’ and ‘ Trent ’ . .
. 1818.
F, FitzRoy . . . .
Voyage of the ‘ Adventure’ and ‘ Beagle ’
. 1826-36.
f. Forster ....
Voyage of the ‘Resolution’
. 1772-75.
G. Graah
Expedition to the East Coast of Greenland .
. 1828.
H. Horner . . . .
See Krusenstern’s Voyage
. 1803-6.
I. Irving
See Phipps’s Voyage
1773.
K. Kotzebue ....
Voyage of the ‘Rurick’
. 1815-18.
99 99 ....
V oyage of the ‘ Predpriatie ’ (see Lenz)
. 1823-26.
* The whole group of observations to the west and north of Spitzbergen are placed rather too far (from
|° to 1°) north.
t D should have stood for Dayman and U for D’Urville ; as it is, U stands for D’Urville in the north
hemisphere and D in the south hemisphere.
672
ME. J. PKESTWICH ON SUBMARINE TEMPERATURES.
K. Kellett . . ■ . . Voyage of the ‘ Herald’ 1845-51.
k. Kundson .... Voyage of the ‘ Queen ’ 1859.
Kr. Krusenstern . . . Voyage of the ‘ Neva’ and £ Nadeshda ’ . . . 1803-6.
L. Emil. Lenz . . . With Kotzebue on his 2nd Voyage .... 1823-26.
36. Ed. Lenz .... On Voyages in the ‘Atcha’ 1847-49.
M. Martins & Bravais . Voyage de ‘ La Recherche ’ 1838.
Ma. Maury Physical Geography of the Sea .... edit. 1857
P. Parry Voyage of the ‘Alexander ’ 1818.
„ „ Voyage of the ‘ Hecla’ and ‘ Griper’ .... 1819-20.
,, „ Voyage of the ‘ Fury ’ and ‘ Hecla ’ .... 1821-23.
,, „ Voyage of the ‘ Hecla ’ 1827. .
P, Pullen .... On the Voyage of the ‘ Cyclops ’ 1857-59.
Phipps (see Irving) . Voyage toward the North Pole (the ‘Racehorse’) 1773.
p. Peron Voyage sur les Corvettes ‘Le Geographe,’ ‘Le
Naturaliste,’ et ‘ Le Casuarina ’ 1800-4.
pr. Pratt On a Voyage to India 1840.
R. John Ross . . . Voyage of the ‘ Isabella’ 1818.
J?. James Ross . . . Voyage of the ‘ Discovery ’ and ‘ Research ’ . . 1839-43.
Ro. Rodgers .... See Maury 1855.
Si Scoresby .... Various Voyages (the ‘ Esk ’ and ‘ Baffin ’) . . 1810-22.
S. Sabine. .... . . With Ross in 1818, and Parry in 1819 . . . 1819.
Sh. Shortland . . . On the Voyage of the ‘ Hydra ’ 1868.
T. Du Petit-Thouars . Voyage de ‘La Venus’ 1836-39.
U. D’Urville . . , Voyage de ‘ L’ Astrolabe ’ (see D) 1826-29.
V. Vaillant .... Voyage de ‘ La Bonite ’ 1836-39.
W. Wullerstorf . . Voyage of the ‘ Novara ’ 1857-59.
W. Wauchope . . . See notes, pp. 595 & 601 1816 & 1836.
Wi. Wilkes .... United States Exploring Expedition (the ‘ Vin-
cennes ’ and ‘ Peacock ’) 1839-42.
Wa. Walker .... On the Voyage of the ‘ Fox ’ 1858.
The other numbers in italics mark (in feet) the further depth to which some of the
soundings have been carried. Where they have reached the bottom a stop (.) is added;
where, on the contrary, the soundings have not reached the bottom, the sign + is
added.
The many other voyages for scientific purposes sent out by the English, French, and
American governments during the period here described contain many very numerous
meteorological observations, but no observation on submarine temperatures, unless I
have inadvertently overlooked any.
MR. J. PRESTWICH ON SUBMARINE TEMPERATURES.
673
Explanation of Sections.
PLATES 66, 67, & 68.
The position of the sections will be found on the Map, and the initials attached to
the numbers have the same reference on both.
In the absence of observations in the direct line of section some of those at a short
distance on either side are included.
The vertical lines indicate the position and depth of the temperature-soundings,
and the figures in italics connected with them give the temperature at the surface and
at depths in degrees of Fahrenheit. The other figures on the top line mark the degrees
of latitude. The stronger figures in italics relate to the probable position of the bathy-
metrical isotherms generally.
The separate numbers at depths indicate the depth in feet to which soundings have
been made in any latitude, the sign -j- showing that no bottom has been reached.
All the observations used in the Sections have been subjected to correction for pres-
sure, as adopted p. 612, viz. by making a deduction of 1° Fahr. for every 1700 feet
of depth, exclusive of the observations of Lenz, Du Petit-Thouars (such of them as
are given in parentheses in the Tables), Martins, Pullen (in part), and those of Eoss,
Parry, and Sabine of 1818-19, which are taken, for reasons before given, as recorded
by the original observers. It is possible that in some instances (as, for example,
James Eoss) a larger correction might be necessary, and that in the Antarctic seas the
isotherm of 35° F. should be replaced by one of 33° or 32°*; but this will not much
affect the correction for the more numerous observations at lesser depths.
All the depths are given, for the sake of uniformity, without correction for angle
of rope, as that could only possibly be known in but few cases. The importance, how-
ever, of a correction for this also will be evident by reference to the large allowances
which Du Petit-Thouars f has often thought it necessary to make in his soundings, the
corrected readings being given between parentheses. Only in 21 cases does he record
“ the angle of the line from the vertical ” as 0 ; in the other 38 cases he found it to vary
from 10° to 67°; and he estimated the difference caused by the latter extreme case as
equal to a reduction of the observed depth of 5872 feet to a corrected depth of 2296 feet.
The want of information on this point is one reason for taking, as we have done, a
minimum correction for pressure.
Where the observations are sufficiently numerous the bathymetrical isotherms are
laid down in continuous lines. The dotted lines indicate the probable prolongation of
the isotherms, on the supposition that there are no disturbing causes ; but it must be
borne in mind that the isotherms (the lower ones especially) are liable to rise with every
* Should some of the observations of the ‘ Challenger ’ be fonnd to correspond in position with any of those
recorded in these pages, they will furnish a measure whereby to correct these or those of other observers.
t See also the corrected depths of Lenz (ante, p. 599) and of Wauchope, 1816, and Sabine, 1822 (Tables).
674
ME. J. PEESTWICH ON STJBMAEINE TEMPEEATUEES.
important irregularity (banks, shoals, &c.) in the bed of the ocean, and the upper
isotherms may be variously deflected by surface-drifts and currents.
It is probable that in some of these Sections (as, for example, in the North Pacific,
Sect. 4, and in the South Atlantic, Sects. 1 & 2) the irregularities of curvature may be
exaggerated, owing to the want of uniformity in the instruments used by the different
observers, and by the necessity of using a general correction for all.
Very little was known before 1868 of the deep bed of the Atlantic. The few indi-
cations of the ocean-bed given in the sections are taken from notices in the several
voyages above recorded and from Maury. In the higher north latitudes we have the
soundings of Ross, Kane, Scoresby, and Martins. In section No. 2 the greater depths
of Scoresby are in the sea west of Spitzbergen, and the lesser ones of Martins between
Spitzbergen and Norway, which accounts for the break in continuity of depth.
The position of the bathymetrical isotherms and the indications of the sea-bed are
confined strictly to observations anterior to 1868.
[ 675 ]
XXII. A Memoir on Prepotentials. By Professor Cayley, F.B.S.
Eeceived April 8, — Eead June 10, 1875.
The present Memoir relates to multiple integrals expressed in terms of the (s+1) ulti-
mately disappearing variables (x . . z, w), and the same number of parameters (a . . c, e ),
and being of the form
C § dzr
J {{a-x)*. . + (c-z?+
where g and dzs depend only on the variables (x . . z, w ). Such an integral, in regard
to the index \s-\-q_i is said to be “ prepotential,” and in the particular case q=—^ to
be £; potential.”
I use throughout the language of hyper-tridimensional geometry : (x . . z, w) and
(a . . c, e) are regarded as coordinates of points in (s-j-l)dimensional space, the former
of them determining the position of an element qdm of attracting matter, the latter
being the attracted point ; viz. we have a mass of matter = ^ distributed in such
manner that, dvr being the element of (s-f-1)- or lower-dimensional volume at the point
{oc . . z, w), the corresponding density is g, a given function of (x . . z, w), and that the
element of mass gdvr exerts on the attracted point (a . . c, e) a force inversely propor-
tional to the (s+2g'4'l)th power of the distance {(a— x)2 . .-\-(c — z)2-\-{e — w)2\i. The
integration is extended so as to include the whole attracting mass J qdvr ; and the integral
is then said to represent the Prepotential of the mass in regard to the point (a . . c, e).
In the particular case s— 2, q= — the force is as the inverse square of the distance,
and the integral represents the Potential in the ordinary sense of the word.
The element of volume dvr is usually either the element of solid (spatial or (s-j-1)-
dimensional) volume dx . . dz dw, or else the element of superficial (s-dimensional)
volume dS. In particular, when the surface (s-dimensional locus) is the (s-dimensional)
plane w=0, the superficial element dS is =dx . . . dz. The cases of a less-than-s-dimen-
sional volume are in the present memoir considered only incidentally. It is scarcely
necessary to remark that the notion of density is dependent on the dimensionality of the
element of volume d zu : in passing from a spatial distribution, qdx . . .dz dw, to a super-
ficial distribution, § dS, we alter the signification of g. In fact if, in order to connect
the two, we imagine the spatial distribution as made over an indefinitely thin layer or
stratum bounded by the surface, so that at any element dS of the surface the normal
thickness is dv, where dv is a function of the coordinates (x . . . z, w) of the element dS,
the spatial element is =dv dS, and the element of mass q dx ... dz dw is =% dv dS; and
mdccclxxv. 4 x
676
PROFESSOR CAYLEY ON PREPOTENTIALS.
then changing the signification of g, so as to denote by it the product g dv, the expression
for the element of mass becomes § dS, which is the formula in the case of the superficial
distribution.
The space or surface over which the distribution extends may be spoken of as the
material space or surface; so that the density g is not =0 for any finite portion of the
material space or surface ; and if the distribution be such that the density becomes =0
for any point or locus of the material space or surface, then such point or locus, consi-
dered as an infinitesimal portion of space or surface, may be excluded from and regarded
as not belonging to the material space or surface. It is allowable, and frequently con-
venient, to regard q as a discontinuous function, having its proper value within the
material space or surface, and having its value =0 beyond these limits; and this being
so, the integrations may be regarded as extending as far as we please beyond the material
space or surface (but so always as to include the whole of the material space or surface) —
for instance, in the case of a spatial distribution, over the whole (s-f-l)dimensional
space ; and in the case of a superficial distribution, over the whole of the s-dimensional
surface of which the material surface is a part.
In all cases of surface-integrals it is, unless the contrary is expressly stated, assumed
that the attracted point does not lie on the material surface ; to make it do so is, in
fact, a particular supposition. As to solid integrals, the cases where the attracted point
is not, and is, in the material space may be regarded as cases of coordinate generality ;
or we may regard the latter one as the general case, deducing the former one from it
by supposing the density at the attracted point to become =0.
The present memoir has chiefly reference to three principal cases, which I call
A, C, D, and a special case, B, included both under A and C : viz. these are : —
A. The prepotential-plane case; q general, but the surface is here the plane w= 0,
C qdx ... dz
J {{a-x)*... + {c-z)* + e*}is+9'
B. The potential-plane case; q= — and the surface the plane w— 0, so that the
integral is
qdx ... dz
Si
(a — x)2 . . .+ (c— ,s)2 + e2}2S 2
C. The potential-surface case; q=—^, the surface arbitrary, so that the integral is
q dS
J {(a— x)2. . . + (<?— zY+ {e—wf}hs~k
D. The potential-solid case; q=—\, and the integral is
PROEESSOK CAYLEY ON PREPOTENTIALS.
677
It is, in fact, only the prepotential-plane case which is connected with the partial
differential equation
(&_ d?_
\flfa2 * ’ ‘ ^ dc2'
de2' e
Y=0,
considered in Green’s memoir ‘On the Attractions of Ellipsoids’ (1835), and called
here “ the prepotential equation.” For this equation is satisfied by the function
l
|a2... + C2 + e2}i*+?’
and therefore also hy
l
{(a-^)2... + (c-z)2 + e2}is+9’
and consequently by the integral
f g dx . . . dz (A)
J {(a-x)‘2... + {c-z]2 + e2}>s+q
that is hy the prepotential-plane integral ; but the equation is not satisfied by the value
{{a—xf. . .+ (c— z)2 + (e — w)2}is+g
nor, therefore, hy the prepotential-solid, or general superficial, integral.
But if ^=— 1, then, instead of the prepotential equation, we have “the potential
equation ”
(* + *.£W_0.
and this is satisfied by
and therefore also by
Hence it is satisfied by
{a2. . . + c2 + e2}2*’"2
1
{(a— x)2. . . + (c— z)2+ (e— m;)2}2* 2
dz dw
C qdx . .
J Ua— x]2. . . + (c-
{(a— x)2. . . + (c— z)2 + (e— w)2}is 2’
(P)
the potential-solid integral, provided that the point (a ... c, e) does not lie within the
material space : I would rather say that the integral does not satisfy the equation, but
of this more hereafter ; and it is satisfied by
f ; rn
J {(a — x)2. . . + (c— z)2 + (e— w)2}2* 2’ ' '
the potential-surface integral. The potential-plane integral (B), as a particular case of
(C), of course also satisfies the equation.
Each of the four cases give rise to what may be called a distribution-theorem ; viz.
given Y a function of (a . . . c, e ) satisfying certain prescribed conditions, but otherwise
arbitrary, then the form of the theorem is that there exists and that we can find an expres-
4x2
678
PROFESSOR CATLET ON PREPOTENTIALS.
sion for g>, the density or distribution of matter over the space or surface to which the
theorem relates, such that the corresponding integral V has its given value, viz. in
A and B there exists such a distribution over the plane w=0, in C such a distribution
over a given surface, and in D such a distribution in space. The establishment, and
exhibition in connexion with each other, of these four distribution-theorems is the
principal object of the present memoir ; but the memoir contains other investigations
which have presented themselves to me in treating the question. It is to be noticed
that the theorem A belongs to Green, being in fact the fundamental theorem of his
memoir of 1885, already referred to. Theorem C, in the particular case of tridimen-
sional space, belongs also to him, being given in his ‘Essay on the Application of
Mathematical Analysis to the theories of Electricity and Magnetism’ (Nottingham, 1828),
being partially rediscovered by Gauss in the year 1840 ; and theorem D, in the same
case of tridimensional space, to Lejeune-Dirichlet : see his memoir “ Sur un moyen
general de verifier l’expression du potentiel relatif a une masse quelconque homogene
ou heterogene,” Crelle , t. xxxii. pp. 80-84 (1840). I refer more particularly to these
and other researches by Gauss, Jacobi, and others in an Annex to the present memoir.
On the Prepotential Surface-integral. — Art. Nos. 1 to 18.
1. In what immediately follows we require
dx . . .dz
(x2. . , + x2 + d
,2\*s+?’
limiting condition x1 . . R2, the prepotential of a uniform (s-coordinal) circular
disk*, radius It, in regard to a point (0 ... 0, e) on the axis ; and in particular the value
is required in the case where the distance e (taken to be always positive) is indefinitely
small in regard to the radius R.
Writing x—r% . . . z=r%, where the s new variables £ . . . £ are such that £2. . .+£2— 1,
the integral becomes
r r*-'drdS r rR r°~ldr
J (r2 + e2f+q' ~J „ (r2 + e2f+^
where dS is the element of surface of the s-dimensional unit-sphere £2. . .+£2=1 ; the
2(IU)S
integral J dS denotes the entire surface of this sphere, which (see Annex I.) is — ~plg-
The other factor,
rR rs~]dr
Jo +
is the r-integral of Annex II.
* It is to be throughout borne in mind that x . . . z denotes a set of s coordinates, x . . . z, w a set of s+ 1
coordinates ; the adjective coordinal refers to the number of coordinates 'which enter into the equation ; thus,
x2 . . . -\-z2-\-w2—f2 is an (s+l)coordinal sphere (observe that the surface of such a sphere is s-dimensional) ;
x2 . . . +z2=/2, according as we tacitly associate with it the condition w— 0, or w arbitrary, is an s-coordinal
circle, or cylinder, the surface of such circle or cylinder being s-dimensional, but the circumference of the circle
(s— l)dimensional; or if we attend only to the s-dimensional space constituted by the plane iv=Q, the locus
may be considered as an s-coordinal sphere, its surface being (s— l)dimensional.
PROFESSOR CAYLEY ON PREPOTENTIALS.
679
2. We now consider the prepotential-surface integral
V=f
J {{a-xf... + [c-zY
y+{e-wyys+q
As already mentioned, it is only a particular case of this, the prepotential-plane integral,
which is specially discussed ; but at present I consider the general case, for the purpose
of establishing a theorem in relation thereto. The surface (s-dimensional surface) S is
any given surface whatever.
Let the attracted point P be situate indefinitely near to the surface, on the normal
thereto at a point N, say the normal distance NP is=a* ; and let this point N be taken
as the centre of an indefinitely small circular (s-dimensional) disk or segment (of the
surface), the radius of which R, although indefinitely small, is indefinitely large in com-
parison with the normal distance s. I proceed to determine the prepotential of the
disk ; for this purpose, transforming to new axes, the origin being at N and the axes of
x ... z in the tangent-plane at N, then the coordinates of the attracted point P will be
(0 . . .0, »), and the expression for the prepotential of the disk will be
V _ f q dx . . .dz
J{A.. + ^+ 2}is+s’
where the limits are given by x2 . . .-f-;s2<R2.
Suppose for a moment that the density at the point N is =§', then the density
throughout the disk may be taken =§', and the integral becomes
dx . . .dz
r=o' r — -
where instead of g' I write g ; viz. g now denotes the density at the point N. Making
this change, then (by what precedes) the value is
2(ri)s rR rs~'dr
r(*s) Jo {/•2 + 82}is+9'
q= Positive. — Nos. 3 to 7.
3. I consider first the case where q is positive. The value is here
2(P1)S 1 J r^sTV/ f xi~'dx
(1+tf)5'
or since is indefinitely small, the ^-integral may be neglected, and the value is
_J_ (Tl)Tg
_82!?r(is+?)'
Observe that this value is independent of R, and that the expression is thus the same
as if (instead of the disk) we had taken the whole of the infinite tangent-plane, the
* s is positive ; in afterwards writing s=0, we mean by 0 the limit of an indefinitely small positive quantity
680
PEOFESSOE CAYLEY ON PEEPOTENTIALS.
density at every point thereof being =g. It is proper to remark that the neglected
terms are of the orders
JLjYi-Y3 /_^\2?+2
’ VeJ ’
(ri)Tg
so that the complete value multiplied by a2q is equal to the constant g + ^ + terms
s g \ 2 q / S \ 25'"^2
of the orders ( ’(e) ’ &c*
4. Let us now consider the prepotential of the remaining portion of the surface ;
every part thereof is at a distance from P exceeding, in fact far exceeding, R ; so that
imagining the whole mass jg dS to be collected at the distance R, the prepotential of
the remaining portion of the surface is less than
jgdS '
Es+2? ’
viz. we have thus, in the case where the mass J g dS is finite, a superior limit to the
prepotential of the remaining portion of the surface. This will be indefinitely small in
comparison with the prepotential of the disk, provided only is indefinitely small
compared with Rs+2?, that is s indefinitely small in comparison with R1+5?. The proof
assumes that the mass J* § cZS is finite ; but considering the very rough manner in which
the limit was obtained, it can scarcely be doubted that, if not universally, at least
for very general laws of distribution, even when jg d S is infinite, the same thing is true ;
viz. that by taking s sufficiently small in regard to R, we can make the prepotential of
the remaining portion of the surface vanish in comparison with that of the disk. But
without entering into the question I assume that the prepotential of the remaining
portion does thus vanish ; the prepotential of the whole surface in regard to the inde-
finitely near point P is thus equal to the prepotential of the disk; viz. its value is
_ 1 (T$yTq
(±s+qy
which, observe, is infinite for a point P on the surface.
5. Considering the prepotential V of an arbitrary point (a ... c, e) as a given function
of (a . . . c, e) the coordinates of this point, and taking (x ... z, w) for the coordinates
of the point N, which is, in fact, an arbitrary point on the surface, then the value of V
at the point P indefinitely near to N will be =W, if W denote the same function of
(x . . . Zf w) that Y is of (a ... c, e). The result just obtained is therefore
or, what is the same thing,
vv-^r(iS+?)’ y-uJ’
_r(|s+?) ,
e-lrijTs 0 • ■
PEOFESSOE CAYLEY ON PEEPOTENTIALS.
681
As to this, remark that V is not an arbitrary function of (a . . . c, e) : non constat
that there is any distribution of matter, and still less that there is any distribution of
matter on the surface, which will produce at the point (a . , .c, e), that is at every point
whatever, a prepotential the value of which shall be a function assumed at pleasure of
the coordinates (a ... c, e). But suppose that V, the given function of (a ... c, e), is
such that there does exist a corresponding distribution of matter on the surface (viz.
that V satisfies the conditions, whatever they are, required in order that this may be the
case), then the foregoing formula determines the distribution, viz. it gives the expression
of that is, the density at any point of the surface.
6. The theorem may be presented in a somewhat different form ; regarding the pre-
potential as a function of the normal distance a, its derived function in regard to a is
2g (Tl)Tg
g22+i s’ r(±s+g)’
that is
and we thus have
___j_ 2(rJr)T(g+i) .
82j+1 f P(^S + g) ’
dw_ _J_ 2(r^r(g+i)
ds 8*«+ r(i* + g) ’ Is— uh
or, what is the same thing,
§=■
r(is+g)
2(r^r(g+i)
da .
d W
where, however, W being given as a function of (x . . . z, w), the notation requires
explanation. Taking cos «... cos y to be the inclinations of the normal at N, in the
direction NP in which the distance a is measured, to the positive parts of the axes of
(x . . . z ), viz. these cosines denote the values of
dS dS
dx ' ’ ' dz ’
each taken with the same sign + or — , and divided by the square root of the sum of
the squares of the last-mentioned quantities, then the meaning is
dW dW , dW
~di=S coS“---+^c°sy.
7. The surface S may be the plane w= 0, viz. we have then the prepotential-plane
integral
J{(«-
qdx . . .dz
x)^..+{c-z)2 + e*}is-,I,
. . (A)
where e (like s) is positive. In afterwards writing e=0, we mean by 0 the limit of an
indefinitely small positive quantity.
The foregoing distribution-formulse then become
e=wf(eS,W)-’ W
682
PROFESSOR CAYLEY ON PREPOTENTIALS.
and
r (fr+g)
*(T*)T(a+i)
e=0
(A*)
which will be used in the sequel.
It will be remembered that in the preceding investigation it has been assumed that
q is positive, the limiting case q=0 being excluded ■j*.
q——\. — Nos. 8 to 13.
8. I pass to the case q-=.—\, viz. we here have the potential-surface integral
gdS
{{a—xf ... + (c— 2)2- f (e—w)’2}is
(C)
it will be seen that the results present themselves under a remarkably different form.
The potential of the disk is, as before,
2(ri)s T r*~ldr
e rjs J(rs+ss)s-*’
where § here denotes the density at the point N ; and the value of the r-integral
-d/t . , . s2 s4 \ r*»r±
=R(l+term5 in ^ ^ . . .)
Observe that this is indefinitely small, and remains so for a point P on the surface ;
the potential of the remaining portion of the surface (for a point P near to or on the
surface) is finite, that is, neither indefinitely large nor indefinitely small, and it varies
continuously as the attracted point passes through the disk (or aperture in the material
surface now under consideration) ; hence the potential of the whole surface is finite for
an attracted point P on the surface, and it varies continuously as P passes through the
surface.
It will be noticed that there is in this case a term in V independent of a ; and it is on
this account necessary, instead of the potential, to consider its derived function in
regard to a; viz. neglecting the indefinitely small terms which contain powers of
a T
•g, 1 write
(tV __2(ri)«+1
da r(is-i) ?■
The corresponding term arising from the potential of the other portion of the sur-
face, viz. the derived function of the potential in regard to a, is not indefinitely small ;
and calling it Q, the formula for the whole surface becomes
dV _ 2(ri)s+1
t This is, as regards q, the case throughout ; a limiting value, if not expressly stated to he included, is
always excluded.
PROFESSOR CAYLEY ON PREPOTENTIALS.
683
9. I consider positions of the point P on the two opposite sides of the point N, say
at the normal distances a', a", these being positive distances measured in opposite direc-
tions from the point N. The function V, which represents the potential of the surface
in regard to the point P, is or may be a different function of the coordinates {a . . , c, e)
of the point P, according as the point is situate on the one side or the other of the
surface (as to this more presently). I represent it in the one case by V', and in the other
case by Y" ; and in further explanation state that a' is measured into the space to which
Y1 refers, a" into that to which V" refers; and I say that the formulse belonging to the
two positions of the point P are
2(ru-)s+i
dW
da"
=Q!'—
2(ir)*+i
where, instead of Y', Y", I have written W', W" to denote that the coordinates, as well
of P' as of P", are taken to be the values (x...z,w) which belong to the point N. The
symbols denote
dW' dW , , dW ■
-d?=lu cosa'.-.+^-cos/,
dW dW" ,, , dW"
-W—^cosx"-+-dFcos /■
where (cos a! . . . cos y') and (cos a" . . . cos y") are the cosine inclinations of the normal
distances a', a" to the positive parts of the axes of (x . . . z) ; since these distances are
measured in opposite directions, we have cos u"= — cos a1 . . . cos y"= — cos y'. If we
imagine a curve through N cutting the surface at right angles, or, what is the same
thing, an element of the curve coinciding in direction with the normal element P'NP",
and if s denote the distance of N from a fixed point of the curve, and for the point P' s
becomes while for the point P" it becomes s—W's, or, what is the same thing, if
s increase in the direction of NP' and decrease in that of NP7, then if any function 0
of the coordinates (x . . . z, w) of N be regarded as a function of s, we have
d@_d@ d®_ d®
ds da' 5 ds da" ’
10. In particular, let 0 denote the potential of the remaining portion of the surface,
that is, of the whole surface exclusive of the disk ; the curve last spoken of is a curve
which does not pass through the material surface, viz. the portion to which 0 has
reference, and there is no discontinuity in the value of 0 as we pass along this curve
through the point N. We have Q'= value of ^ at the point P', and Q"= value of
at the point P" ; and the two points P', P" coming to coincide together at the point
MDCCCLXXV. 4 Y
684
PROFESSOR CAYLEY ON PREPOTENTIALS.
N, we have then
d©
V ~~din ~ dP
,yi 6?© <?©
1 ~W’ ~ ~ds'
dW' dW' dW" dW
We have in like manner = — -y- ; and the equations obtained above
may be written
dW' _d® 2(ri)s+1
ds ~ ds ~ r(is-i) St
dw"_^© 2(ri)s+i
ds ~ &+r(i* -*)£»■
in which form they show that as the attracted point passes through the surface from
the position P' on the one side to P" on the other, there is an abrupt change in the
dW dV
value of or say of the first derived function of the potential in regard to the
orthotomic arc s, that is in the rate of increase of V in the passage of the attracted
point normally to the surface. It is obvious that if the attracted point traverses the
surface obliquely instead of normally, viz. if the arc s cuts the surface obliquely,
there is the like abrupt change in the value of
Reverting to the original form of the two equations, and attending to the relation
Q'-f-Q"=0, we obtain
dW' dW" _-4(Vj)s+1
da' ds" r(^-i) &
or, what is the same thing,
r(^-j) /dW dw"\
Z— “4(ri)s+1 \ ds' + ds" )
(C)
11. I recall the signification of the symbols: — ■V,,V,Aare the potentials, it may bedifferent
functions of the coordinates (a . . . c, e) of the attracted point, for positions of this point
on the two sides of the surface (as to this more presently), and W', W" are what V', V"
respectively become when the coordinates [a . . . c, e) are replaced by (x ... z, w ), the coor-
f dW' dW" .
dinates of a -bint N on the surface. The explanation of the symbols ~^r is given
a little above ; § denotes the density at the point (x . . . z, w).
12. The like remarks arise as with regard to the former distribution theorem (A) ;
the functions V', V" cannot be assumed at pleasure ; non constat that there is any dis-
tribution in space, and still less any distribution on the surface, which would give such
values to the potential of a point (a . . . c, e) on the two sides of the surface respectively ;
but assuming that the functions V', V" are such that they do arise from a distribution
on the surface, or say that they satisfy all the conditions, whatever they are, required in
PROFESSOR CATLET ON PBEPOTENTI ALS .
685
order that this may be so, then the formula determines the distribution, viz. it gives the
value of g, the density at a point (x, . . . z, w) of the surface.
13. In the case where the surface is the plane w= 0, viz. in the case of the potential-
plane integral,
ydx . . . dz
{(« — a?)2. . . + (c— ar^ + e9}** i
(B)
(e assumed to be positive) ; then, since every thing is symmetrical on the two sides of the
plane, V' and Y" are the same functions of (a .. . c, e), say they are each=V ; W', W"
are each of them the same function, say they are each = W, of (x ... z, e) that V is of
(a . . . c, e), and the distribution-formula becomes
_rgs-i) /dw\
§ 2(ri)s+1 V de)eJ
(B)
viz. this is also what one of the prepotential-plane formulae becomes on writing
therein
q= 0, or Negative. — Nos. 14 to 18.
14. Consider the case ^=0. The prepotential of the disk is
f-w(logE+N_logs"-);
and to get rid of the constant term we must consider the derived function in regard to
s, viz. this is
2(r*)« i
r ^ •*>
and we have thus for the whole surface
dV _ 2(Tj)«l
d* u 2 T%s
where Q, which relates to the remaining portion of the surface, is finite ; we have thence,
writing, as before, W in place of V,
dW
da z
2(r*)«
'2 TU ’
or say
T$s ( dW\
- 2(ri)s '
ds .
15. Consider the case q negative, but —q<\- The prepotential of the disk is here
2 fro (R-22 , . risrw )
and to get rid of the first term we must consider the derived function in regard to a,
viz. this is
2(ri)T(g+l).
* 2 r(**+j) ’
4 y 2
686
PROFESSOR CAYLEY OX PEEPOTEXTIALS.
whence for the potential of the whole surface
=Q— S'
2(ri)sr(?+i)
? r(is-ts) 5
where Q, the part relating to the remaining portion of the surface, is finite. Multiplying
by s2?+1 (where the index 2y+l is positive), the term in Q disappears ; and writing, as
before, W in place of V, this is
# da -
2(ri)*r(<?+i)
r \s + q ’
or say
r(fr+g)
2(T*)T(g+l)
(s'5
dW\
d* .
viz. we thus see that the formula (A*) originally obtained for the case q positive
extends to the case q=0, and q= — , but —q<j>; hut, as already seen, it does not
extend to the limiting case q=
16. If q be negative and between — ^ and —1, we have in like manner a formula
dV
da
=Q— «
2(Tl)T(g+l) _2?_1 .
r(t»+*)
but here 2g'+l being negative, the terms22 ’Q does not disappear:
to be treated in the same way as for q=—^, and we arrive at
dW ,
■w+*
Il2q+1
dW")
da" )
4(T±yT(q + l)
r(is+q)i e;
the formula has
viz. the formula is of the same form as for the potential case q= —
formula does not hold good in the limiting case q— — \.
17. We have, in fact, here the potential of the disk
whence
2(rip (R2 9. ri? )
— r(i«) f j 2 “* loS 8 r(i*-i)/ ;
w 2{T^y
da~Q r(iS-l) g(2gl°g*)i
Observe that the
since in the complete differential coefficient a + 2s log s the term s vanishes in compari-
son with 2s log s ; and then, proceeding as before, we find
i dw1 i dW" -8(r±y
s' log s' da1 a" log a" da" T (^s — 1 ) ^ ’
but I have not particularly examined this formula.
18. If q be negative and > — 1 (that is, —§'>1), then the prepotential for the
disk is
_ (rj)‘/R-»g , ±s + q R~2g~2
~ ? T-gS y~2q' 1 -2q-2
and it would seem that in order to obtain a result it would be necessary to proceed to
a derived function higher than the first ; but I have not examined the case.
PROFESSOR CAYLEY ON PREPOTENTIALS.
687
Continuity of the Prepotential-surface Integral. — Art. Nos. 19 to 25.
19. I again consider the prepotential-surface integral
f &
J {{a-xf. . . + {c-zf+
in regard to a point (a . . . c, e) not on the surface ; q is either positive or negative, as
afterwards mentioned.
The integral or prepotential and all its derived functions, first, second, &c. ad infinitum ,
in regard to each or all or any of the coordinates (a . . . c, e) are all finite. This is cer-
tainly the case when the mass j %dS is finite, and possibly in other cases also ; but to fix
the ideas we may assume that the mass is finite. And the prepotential and its derived
functions vary continuously with the position of the attracted point (a . . . c, e), so long
as this point in its course does not traverse the material surface. For greater clearness
we may consider the point as moving along a continuous curve (one-dimensional locus),
which curve, or the part of it under consideration, does not meet the surface ; and the
meaning is that the prepotential and each of its derived functions varies continuously as
the point (a . . . c, e) passes continuously along the curve.
20. Consider a “ region,” that is, a portion of space any point of which can be by a
continuous curve not meeting the material surface connected with any other point of
the region. It is a legitimate inference, from what just precedes, that the prepotential
is, for any point (a . . . c, e) whatever within the region, one and the same function of the
coordinates {a . . . c, e), viz. the theorem, rightly understood, is true ; but the theorem
gives rise to a difficulty, and needs explanation.
Consider, for instance, a closed surface made up of two segments, the attracting
matter being distributed in any manner over the whole surface (as a particular case
5+1 = 3, a uniform spherical shell made up of two hemispheres) ; then, as regards the
first segment (now taken as the material surface), there is no division into regions, but
the whole of the (5+l)dimensional space is one region; wherefore the prepotential
of the first segment is one and the same function of the coordinates (a . . . c, e) of the
attracted point for any position whatever of this point. But in like manner the prepo-
tential of the second segment is one and the same function of the coordinates (a . . . c, e)
for any position whatever of the attracted point. And the prepotential of the whole
surface, being the sum of the prepotentials of the two segments, is consequently one and
the same function of the coordinates (a . . . c, e) of the attracted point for any position
whatever of this point ; viz. it is the same function for a point in the region inside the
closed surface and for a point in the outside region. That this is not in general the case
we know from the particular case, 5 + 1 = 3, of a uniform spherical shell referred to above.
21. Consider in general an unclosed surface or segment, with matter distributed over
it in any manner ; and imagine a closed curve or circuit cutting the segment once ; and
let the attracted point (a. .. c,e) move continuously along the circuit. We may con-
sider the circuit as corresponding to (in ordinary tridimensional space) a plane curve of
688
PROEESSOK CAYLEY ON PREPOTENTIALS.
equal periphery, the corresponding points on the circuit and the plane curve being
points at equal distances s along the curves from fixed points on the two curves respec-
tively ; and then treating the plane curve as the base of a cylinder, we may represent
the potential as a length or ordinate, Y=y, measured upwards from the point on the
plane curve along the generating line of the cylinder, in such wise that the upper
extremity of the length or ordinate y traces out on the cylinder a curve, say the prepo-
tential curve, which represents the march of the prepotential. The attracted point may,
for greater convenience, be represented as a point on the prepotential curve, viz. by the
upper instead of the lower extremity of the length or ordinate y ; and the ordinate, or
height of this point above the base of the cylinder, then represents the value of the
prepotential. The before-mentioned continuity-theorem is that the prepotential curve
corresponding to any portion (of the circuit) which does not meet the material surface
is a continuous curve, viz. that there is no abrupt change of value either in the ordinate
y(=V) of the prepotential curve, or in the first or any other of the derived functions
dy d^y
&c. We have thus (in each of the two figures) a continuous curve as we pass
(in the direction of the arrow) from a point P' on one side of the segment to a point
P" on the other side of the segment ; but this continuity does not exist in regard to the
remaining part, from P" to P', of the prepotential curve corresponding to the portion
(of the circuit) which traverses the material surface.
22. I consider first the case^=— ^ (see the left-hand figure): the prepotential is
here a potential. At the point N, wdiich corresponds to the passage through the
material surface, then, as was seen, the ordinate y (=the Potential V) remains finite
and continuous; but there is an abrupt change in the value of that is, in the
direction of the curve : the point N is really a node with two branches crossing at this
point, as shown in the figure ; but the dotted continuations have only an analytical
existence, and do not represent values of the potential. And by means of this branch-
to-branch discontinuity at the point N, we escape from the foregoing conclusion as to
the continuity of the potential on the passage of the attracted point through a closed
surface.
23. To show how this is I will for greater clearness examine the case (s + l)=3,
in ordinary tridimensional space, of the uniform spherical shell attracting according to
the inverse square of the distance ; instead of dividing the shell into hemispheres, I
divide it by a plane into any two segments (see the figure, wherein A, B represent the
PROFESSOR CAYLEY ON PREPOTENTIALS. 689
centres of the two segments respectively, and where for graphical convenience the seg-
ment A is taken to be small.
We may consider the attracted point as moving along the axis ocx', viz. the two
extremities may be regarded as meeting at infinity, or we may outside the sphere bend
the line round, so as to produce a closed circuit. We are only concerned with what
happens at the intersections with the spherical surface. The ordinates represent the
potentials, viz. the curves are a, b , c for the segments A, B, and the whole spherical
surface respectively. Practically, we construct the curves c, a , and deduce the curve b by
taking for its ordinate the difference of the other two ordinates. The curve c is, as we
know, a discontinuous curve, composed of a horizontal line and two hyperbolic branches ;
the curve a can be laid down approximately by treating the segment A as a plane
circular disk ; it is of the form shown in the figure, having a node at the point corre
sponding to A. [In the case where the segment A is actually a plane disk, the curve
is made up of portions of branches of two hyperbolas ; but taking the segment A as
being what it is, the segment of a spherical surface, the curve is a single curve, having
a node as mentioned above.] And from the curves c and a, deducing the curve b, we
see that this is a curve without any discontinuity corresponding to the passage of the
attracted point through A (but with an abrupt change of direction or node corresponding
to the passage through B). And conversely, using the curves a, b to determine the
curve <?, we see how, on the passage of the attracted point at A into the interior of the
sphere, in consequence of the branch-to-branch discontinuity of the curve a, the curve
c, obtained by combination of the two curves, undergoes a change of law, passing
abruptly from a hyperbolic to a rectilinear form, and how similarly on the passage
of the attracted point at B from the interior to the exterior of the sphere, in conse-
quence of the branch-to-branch discontinuity of the curve b, the curve c again
undergoes a change of law, abruptly reverting to the hyperbolic form.
690
PROFESSOR CATLET ON PREPOTENTIALS.
24. In the case q positive the prepotential curve is as shown by the right-hand
figure in p. 688, viz. the ordinate is here infinite at the point N corresponding to the
passage through the surface ; the value of the derived function changes between
-j- infinity and — infinity ; and there is thus a discontinuity of value in the derived
function. It would seem that when q is fractional this occasions a change of law on
passage through the surface, but that there is no change of law when q is integral.
In illustration, consider the closed surface as made up of an infinitesimal circular
disk, as before, and of a residual portion ; the potential of the disk on an indefinitely
near point is found as before, and the prepotential of the whole surface is
_i JI TO,V
n
where V15 the prepotential of the remaining portion of the surface, is a function which
varies (and its derived functions vary) continuously as the attracted point traverses the
disk. To fix the ideas we may take the origin at the centre of the disk, and the axis
of e as coinciding with the normal, so that s, which is always positive, is =+e; and
the expression for the prepotential at a point (a ... c, e) on the normal through the
centre of the disk is
,(rp*.rg v
(±e)22 -f r(is+g')i" 1
viz. when q is fractional there is the discontinuity of law, inasmuch as the term changes
from
( + <?)2
to
i-ey
but when q is integral this discontinuity disappears. The like
considerations, using of course the proper formula for the attraction of the disk, would
apply to the case q=0 or negative.
25. Or again, we might use the formulae which belong to the case of a uniform (s+ 1)-
coordinal spherical shell (see Annex No. III.), viz. we decompose the surface as follows,
surface = disk residue of surface;
and then, considering a spherical shell touching the surface at the point in question
(so that the disk is in fact an element common to the surface and the spherical shell),
and being of a uniform density equal to that of the disk, we have
disk = spherical shell— residue of spherical shell ;
and consequently
surface = spherical shell — residue of spherical shell+residue of surface;
and then, considering the attracted point as passing through the disk, it does not pass
through either of the two residues, and there is not any discontinuity, as regards the
prepotentials of these residues respectively ; there is consequently, as regards the pre-
potential of the surface, the same discontinuity that there is as regards the prepotential
of the spherical shell. But I do not further consider the question from this point of view.
PROFESSOR CAYLEY ON PREPOTENTIALS.
691
The Potential Solid Integral. — Art. No. 26.
26. We have farther to consider the prepotential (and in particular the potential) of
a material space ; to fix the ideas, consider for the moment the case of a distribution
over the space included within a closed surface, the exterior density being zero, and the
interior density being, suppose for the moment, constant ; we consider the discontinuity
which takes place as the attracting point passes from the exterior space through the
hounding surface into the interior material space. We may imagine the interior space
divided into indefinitely thin shells by a series of closed surfaces similar, if we please,
to the bounding surface ; and we may conceive the matter included between any two
consecutive surfaces as concentrated on the exterior of the two surfaces, so as to give
rise to a series of consecutive material surfaces ; the quantity of such matter is infini-
tesimal, and the density of each of the material surfaces is therefore also infinitesimal.
As the attracted point comes from the external space to pass through the first of the
material surfaces — suppose, to fix the ideas, it moves continuously along a curve the
arc of which measured from a fixed point is =s — there is in the value of V (or, as the
dV
case may be, in the values of its derived functions &c.) the discontinuity due to the
passage through the material surface ; and the like as the attracted point passes
through the different material surfaces respectively. Take the case of a potential,
q— — ^ ; then, if the surface-density were finite, there would be no finite change in the
dV
value of Y, but there would be a finite change in the value of ; as it is, the changes
are to be multiplied by the infinitesimal density, say g, of the material surface ; there is
consequently no finite change in the value of the first derived function ; but there is,
or may be, a finite change in the value of and the higher derived functions. But
there is in V an infinitesimal change corresponding to the passage through the successive
material surfaces respectively ; that is, as the attracted point enters into the material
space there is a change in the law of V considered as a function of the coordinates
(a ... c, e) of the attracted point ; but by what precedes this change of law takes place
without any abrupt change of value either of V or of its first derived function ; which
derived function may be considered as representing the derived function in regard to
any one of the coordinates a . . ,c,e. The suppositions that the density outside the
bounding surface was zero and inside it constant, were made for simplicity only, and
were not essential ; it is enough if the density, changing abruptly at the bounding
surface, varies continuously in the material space within the bounding surface*. The
* It is, indeed, enough if the density varies continuously within the hounding surface in the neighbourhood,
of the point of passage through the surface ; but the condition may without loss of generality be stated as in
the text, it being understood that for each abrupt change of density within the bounding surface we must
consider the attracted point as passing through a new bounding surface, and have regard to the resulting-
discontinuity.
4 z
MDCCCLXXV.
692
PROFESSOR CAYLEY ON PREPOTENTIALS.
conclusion is that V', V" being the values at points within and without the bounding
surface, V' and V" are in general different functions of the coordinates (a ... c, e) of
the attracting point; but that at the surface we have not only V'=V", but that the
first derived functions are also equal, viz, that we have
dV'__dW dV' d\" dV dV"
da da ’ dc dc 5 de de
27. In the general case of a Potential,
T7 p dx . . . dz dw
V {{a-xf . . . + {c-zY + (e-wfYa~i ’
if g does not vanish at the attracted point (a ... c, e), but has there a value g'
different from zero, we may consider the attracting (s-fl)dimensional mass as made
up of an indefinitely small sphere, radius s and density g', which includes within it the
attracted point, and of a remaining portion external to the attracted point. Writing
V to denote^ • • • +^2+^2’ then, as regards the potential of the sphere, we have
VV= —
4 (Hr)
r(**-
T)?
(see Annex III. No. 67), and as regards the remaining portion
VV=0 ; hence, as regards the whole attracting mass, VV has the first-mentioned value,
that is we have
(-
\da 2
d2
1 A 1 Y \ V— _ 4(IA)S ,
da2 ‘ ‘ ' ' dc2' de2) P(is— i) ^ 5
where g* is the same function of the coordinates (a ... c, e) that g is of (x ... z, w) ;
viz. the potential of an attracting mass distributed not on a surface, but over a portion
of space, does not satisfy the potential equation
(d2 . d2 d2\~.r „
d#- • • +^+^yv=0’
but it satisfies the foregoing equation, which only agrees with the potential equation
in regard to a point (a. . .c,e) outside the material space, and for which, therefore,
g' is =0.
The equation may be written
S'=
r (js-j) / d*
4(Pi)s+1 V®2 ‘ ' ’
+ dc2^de2> V’
or, considering V as a given function of (a ... c, e), in general a discontinuous function
but subject to certain conditions as afterwards mentioned, and taking W the same
function of {x ... z, w) that V is of {a ... c, e), then we have
S=
r(-b-j)
4(ri)s+1
. . (D)
PROFESSOR CAYLEY ON PREPOTENTIALS.
693
viz. this equation determines § as a function, in general a discontinuous function, of
(x ... z, w) such that the corresponding integral
may be the given function of the coordinates (a ... c, e). The equation is, in fact, the
distribution-theorem D.
28. It is to be observed that the given function of (a ... c, e) must satisfy certain
conditions as to value at infinity and continuity, but it is not (as in the distribution-
theorems A, B, and C it is) required to satisfy a partial differential equation ; the
function, except as regards the conditions as to value at infinity and continuity, is abso-
lutely arbitrary.
The potential (assuming that the matter which gives rise to it lies wholly within a
finite closed surface) must vanish for points at an infinite distance, or more accurately
it must for indefinitely large values of a2 . . . -j -c2-\-e2 be of the form, Constant -f- by
(a2 . . . -\-c2-\-e2)is~i. It may be a discontinuous function ; for instance outside a given
closed surface it may be one function, and inside the same surface a different function
of the coordinates (a ... c, e) ; viz. this may happen in consequence of an abrupt change
of the density of the attracting matter on the one and the other side of the given closed
surface, but not in any other manner ; and, happening in this manner, then V', V" being
the values for points within and without the surface respectively, it has been seen to be
dV' dY" dY' dY" dY' dY"
necessary that, at the surface, not only V'=Y", but also ~de~~de'
Subject to these conditions as to value at infinity and continuity, V may be any function
whatever of the coordinates (a ... c, e) ; and then taking W, the same function of
(x ... z, w ), the foregoing equation determines g>, viz. determines it to be =0 for those
parts of space which do not belong to the material space, and to have its proper value
as a function of (x ... z, w ) for the remaining or material space.
The Prejpotential Plane Theorem A. — Art. Nos. 29 to 36.
29. We have seen that if there exists on the plane w = 0 a distribution of matter
producing at the point (a ... c, e) a given prepotential V (viz. V is to be regarded as a
given function of (a . . . c, e)), then that the distribution or density g> is given by a
determinate formula ; but it was remarked that the prepotential V cannot be a function
assumed at pleasure ; it must be a function satisfying certain conditions. One of these
is the condition of continuity ; the function Y and all its derived functions must vary
continuously as we pass, without traversing the material plane, from any given point to
any other given point. But it is sufficient to attend to points on one side of the plane,
say the upperside, or that for which e is positive ; and since any such point is acces-
sible from any other such point by a path which does not meet the plane, it is suffi-
cient to say that the function V must vary continuously for a passage by such path from
any such point to any such point ; the function Y must therefore be one and the same
4 z 2
694
PROFESSOR CAYLEY ON PREPOTENTIALS.
function (and that a continuous one in value) for all values of the coordinates (a ... c)
and positive values of the coordinate e.
If, moreover, we assume that the distribution which corresponds to the given potential
V is a distribution of a finite mass §gdx . . . dz over a finite portion of the plane w=0,
viz. over a portion or area such that the distance of a point within the area from a fixed
point, or say from the origin {a ... c) = (0 ... 0), is always finite ; this being so, we
have the further condition that the prepotential V must for indefinitely large values of
all or any of the coordinates (a ... c, e) reduce itself to the form
(j 'qdx . . . dz)+(a? . . . -\-c2+e2f+q.
The assumptions upon which this last condition is obtained are perhaps Unnecessary ;
instead of the condition in the foregoing form we, in fact, use only the Condition that
the prepotential vanishes for a point at infinity, that is when all or any one or more
of the coordinates (a .. . c , e) are or is infinite.
Again, as we have seen, the prepotential V must satisfy the prepotential equation
(£. + *L+£-+-J— i\y_o
[da1 ’ ’ ■ +*'+**+ 2}+l de) V — U'
These conditions satisfied, to the given prepotential V, there corresponds on the plane
w= 0, a distribution given by the foregoing formula, and which will be a distribution
over a finite portion of the plane, as already mentioned.
30. The proof depends upon properties of the prepotential equation,
, *
d 2 2(7 + 1 d
de 2 ^ e de
w=o,
or, what is the same thing,
say, for shortness, □ W=0.
Consider, in general, the integral
dz de e2q+
• • +
/dwy , ,
(dwy]
U)+l
{ de ) }
taken over a closed surface S lying altogether on the positive side of the plane c=0,
the function W being in the first instance arbitrary.
Writing the integral under the form
dx ...dzde ( e2q+
dW d W
dx dx
+ ^+1
dz dz ~
dW dW\
de de J'
we reduce the several terms by an integration by parts as follows :■
PROFESSOR CAYLEY ON PREPOTENTIALS.
695
. dW
term in ^
is = j dy..
.dzdeWe»+‘^-§dx..
dW
dz
is — j* dx . .
dW C
, . ..de We2*+1^f— dx. ,
..dzde W^ |
dW
de
is — \dx. .
, . ..dzWe^~-^dx. ,
Write d$ to denote an element of surface at the point (x ... z, e); and taking
a ... y, & to denote the inclinations of the interior normal at that point to the positive
axes of coordinates, we have
dy . . . dzde=—dS cos a,
dx
dx
and the first terms are together
de=—dS cosy,
dz=—dS cosS ;
dW
dW
• c°s 7+-^ C0SM
W here denoting the value at the surface, and the integration being extended over the
whole of the closed surface : this may also be written
where * denotes an element of the internal normal.
The second terms are together
= -J* • • • • • • +1 t)+s(^‘- T)}=-j**.**WDW.
We have consequently
= (dx ...dzdee2«+1 W □ W.
31. The second term vanishes if W satisfies the prepotential equation nW=0 ; and
this being so, if also W=0 for all points of the closed surface S, then the first term also
vanishes, and we therefore have
where the integration extends over the whole space included within the closed surface ;
whence, W being a real function,
d W
dx
=0,
^-0 ^-0
U’ de — u’
696
PROFESSOR CAYLEY ON PREPOTENTIALS.
for all points within the closed surface ; consequently, since W vanishes at the surface,
W=0 for all points within the closed surface.
32. Considering W as satisfying the equation □ W=0, we may imagine the closed
surface to become larger and larger, and ultimately infinite, at the same time flattening
itself out into coincidence with the plane e=0, so that it comes to include the whole
space above the plane e=0, say the surface breaks up into the surface positive infinity
and the infinite plane e=0.
C dW
The integral le2?+1W ~^g~dS separates itself into two parts, the first relating to the
surface positive infinity, and which vanishes if W = 0 at infinity (that is, if all or any of
the coordinates x . . . z, e are infinite); the second relating to the plane e=0 is
jw (^2g+l~[pJ dx . . . dz , W here denoting its value at the plane, that is when e=0,
and the integral being extended over the whole plane. The theorem thus becomes
= -Jw ^+1^Pj dx . . . dz.
Hence also if W = 0 at all points of the plane e=0, the right-hand side vanishes,
and we have
J*’-
dz de e2q+l
dw y
dx ) '
■ +
+
Consequently a^=0 . . . ^-=0, ^—=0, for all points whatever of positive space; and
therefore also W=0 for all points whatever of positive space.
33. Take next U, W, each of them a function of (x . . . z, e ), and consider the
I'
7 7 7 , , dV dW
rfW rfU dW^
dz dz
de de /’
taken over the space within a closed surface S ; treating this in a similar manner, we
find it to be
= -Je22+1 W ^ cZS-Jcte ...dz
de e2q+l WqU,
where the integration extends over the whole of the closed surface S ; and by parity of
= -jV+1 U^S-j^. . . dzdee2q+l UnW,
with the same limits of integration ; that is, we have
|V'+1 W^dS+jjdx...dzde. e2q+\W □ U=jVs+1U ^ dS +jjdx ...dzde. e2?+,U □ W,
PROFESSOR CAYLEY ON PREPOTENTIALS.
697
which, if U, W each satisfy the prepotential equation, becomes
j>-w^s
And if we now take the closed surface S to be the surface positive infinity, together
with the plane e=0, then, provided only U and Y vanish at infinity, for each integral
the portion belonging to the surface positive infinity vanishes, and there remains only
the portion belonging to the plane e=0 ; we have therefore
fe2«+'w~ dx... dz=^e2q+1JJ ~ dx . . . dz,
where the functions U, W have each of them the value belonging to the plane e=0 ,
viz. in U, W considered as given functions of (x ... z, e) we regard e as a positive quan-
tity ultimately put =0, and where the integrations extend each of them over the whole
infinite plane.
34. Assume
TT 1
U_ {(«-#... + (c-*)2H he8}1-*-*’
an expression which, regarded as a function of (x ... z, e), satisfies the prepotential
equation in regard to these variables, and which vanishes at infinity when all or any
of these coordinates (x ... z, e) are infinite.
We have
dU — 2{\s-\-q)e
{(a-xf. . . + (c-*)2 + e2}is+2+1 ’
and we have consequently
=j>«u^<zs.
w
-2 {\s+q)eiq^
{(a-xY... + {c-zY + e*}
12tis+®~1
dx ...dz
=f(-£.
dx ... dz
){(«—«) 2. .. + (c— z)2 + e2}i
where it will be recollected that e is ultimately =0 ; to mark this we may for W
write W0.
Attend to the left-hand side ; take V0 the same function of a ... c, e=0, that W0 is of
x ... z, e=0 ; then first writing the expression in the form
^ r — 2 (-^s + q) e^i^dx . ..dz
°J {{a—xf. . .+ (c-.z)2 + e2}*s+9+I’
write x=a-}-e<' . . . z=c-\-e%, the expression becomes
— V f ~ 2 (a* + g)e2g+2 • esd£ • • • dt
°J W
i(i+r...+§*)}i*+*+i
= -2(i5+2)V0jjI
+ |2... + ?2}5W
where the integral is to be taken from — oo to + go for each of the new variables !;...£.
Writing f=m . . . £=ry, where a2. . .-|-y2=l, we have -d\ . . . d%=rs~1dr dS also
£2. . . + £2=r2, and the integral is
rs~'dr
(l+r2fs+9+1’
rs~1dr
(l+r2fs+9+1’
698
PROFESSOR CAYLEY ON PREPOTENTIALS.
where JcZS denotes the surface of the s-coordinal unit sphere a2. . .-f-y2=l, and the
/-integral is to be taken from r=0 to r= oo ; the values of the twro factors thus are
1 ,Q 2(ri)s ,
dS — 5 and
(i+r2k
msT(g + l)
T(i«+J? + 1)'
Hence the expression in question is
2(r2)s ir^r(g + l) _ -2(r^)sr(g + l)
T1S r(*«+2+i)’ - r(is+9) V(
and we have
J('
>2?+l \
dx ... dz
-2(Ti)T(g + l)
r ms+Ai v°-’
de J0 {(a-x)*... + (c-z)*+e*\is+q r(*s + ?)
or, what is the same thing,
V„=
f -rfb+§) ,
!
0
V 2(ri)T(fir+l)l
V.4 de)
J { (a— x)*. . . + (c-
-zY + e2)is+q
35. Take now V a function of (a . . . c, e) satisfying the prepotential equation in
regard to these variables, always finite, and vanishing at infinity, and let W be the same
function of (x ... z, e ), W therefore satisfying the prepotential equation in regard to
the last-mentioned variables, and consider the function
r r(i*+9)
'r'™)
| dx ... dz
\ 2(T*)T(?+1)I
J 1 {a— x)2. . . + (c— z)2 +
e2f+q '
where the integral is taken over the infinite plane e=0; then this function (V — the
integral) satisfies the prepotential equation (for each term separately satisfies it), is
always finite, and it vanishes at infinity. It also, as has just been seen, vanishes for any
point whatever of the plane e=0. Consequently it vanishes for all points whatever of
positive space. Or, what is the same thing, if we write
V=
q dx ... dz
{[a-xf... + (c-*)2 + e2}|s+ff’
(A)
where g is a function of (x . . . 2), and the integral is taken over the whole infinite plane,
then if V is a function of (a . . . c, e) satisfying the above conditions, there exists a cor-
responding value of g ; viz. taking W the same function of (x . . . 2, e ) which Y is of
(a . . . c, e), the value of g is
T(l s + q)
2(T*)T(? + 1)
(A)
where e is to be put =0 in the function e2q+1^-. This is the prepotential-plane theorem ;
viz. taking for the prepotential in regard to a given point (a, ... c, e)fi function of (a ... c, e )
satisfying the prescribed conditions, but otherwise arbitrary, there exists on the plane
<2=0 a distribution g given by the last-mentioned formula.
PROFESSOR CAYLEY ON PREPOTENTIALS.
699
36. It is assumed in the proof that 2^+1 is positive or zero; viz. q is positive, or if
negative then — q >* ; the limiting case q=—\ is included.
It is to be remarked that by what precedes, if q be positive (but excluding the case
^=0) the density § is given by the equivalent more simple formula
The foregoing proof is substantially that given in Green’s memoir on the Attraction
of Ellipsoids ; it will be observed that the proof only imposes upon V the condition of
vanishing at infinity, without obliging it to assume for large values of (a . . . c, e) the
foim +“+e«r*'
The Potential-surface Theorem C. — Art. Nos. 37 to 42.
37. In the case q= — writing here V we have precisely, as in the
general case,
jV ^ dS+jjdx ... dzde WVU=ju ^ dS+^dx ...dzde UVW ;
and if the functions U, W satisfy the equations VU=0, VW=0, then (subject to the
exception presently referred to) the second terms on the two sides respectively each of
them vanish.
But, instead of taking the surface to be the surface positive infinity together with the
plane e=0, we now leave it an arbitrary closed surface, and for greater symmetry of
notation write w in place of e ; and we suppose that the functions U and W, or one of
them, may become infinite at points within the closed surface ; on this last account the
second terms do not in every case vanish.
38. Suppose, for instance, that U at a point indefinitely near the point (a ... c,e) within
the surface becomes
1 .
{{oc— a)2. . . + [z— c)2 + (w— e)2}is_" ’
then if V be the value of W at the point (a... c , e), we have
J dx . . . dz dw W V U = ‘ V J dx . . . dz dw V U ;
and since VU = 0, except at the point in question, the integral may be taken over any
portion of space surrounding this point, for instance, over the space included within the
sphere, radius R, having the point (a . . . c, e) for its centre ; or taking the origin at this
point, we have to find ^dx . ..dz dw VU, where
U=
\xz. . . +
and the integration extends over the space within the sphere x2. . .+52+w2=R2.
MDCCCLXXV. 5 A
700
PROFESSOR CAYLEY ON PREPOTENTIALS.
39. This may be accomplished most easily by means of a particular case of the last-
mentioned theorem ; viz. writing W — 1, we have
J^S+J<fe...^cZwVU=0,
or the required value is = — j ^ over the surface of the last-mentioned sphere.
We have, if for a moment r2—x2. . .-\-z2+w2,
dU /x d
z d w d\ _ / x d
z d w d\
t dJJ
dU
da \rdx"
' r dz' r dw) ’ l r dx'
‘ r dz' r dw i
V' dr ’
dr 9
that is, — 1, ^ ; and hence
da rs Rs
where JcZS is the whole surface of the sphere x2 . . . +z2+ w3=It2, viz. it is =RS into
the surface of the unit-sphere^2. . . -\-z2-\-w2= 1. This spherical surface, say
cd2 i9
JUZ is — ri(s+1)»
4 (ny
(s-i)T%{s-iy
Jdu 4(ri)s+i
-j- dS— px(/_-i), and consequently
f dx . . . dzdwV
J r(is-i)
40. Treating in like manner the case where W at a point indefinitely near the point
(a, . . . c, e) within the surface becomes
l
— {{x-af. . . + (0- c)2+ («,— e)2}^’
and writing T to denote the same function of (a, . . . c, e) that IT is of (x ... z, w), we
have, instead of the foregoing, the more general theorem
Jw ^ <ZS+ Jfe . . dz dw WVU-ifij^A V
=Jxi^<JS+j’&...*fcuvw-i|pA)T,
where in the two solid integrals respectively we exclude from consideration the space
in the immediate neighbourhood of the two critical points (a ... c, e) and (a . . . c, e)
respectively.
Suppose that W is always finite within the surface, and that U is finite except at
the point (a ... c, e ), and moreover that U, W are such that VTJ=0, VW=0, then
the equation becomes
f„ju JO 4(rw+lT7. rTT<iw 70
PROFESSOR CAYLEY ON PREPOTENTIALS.
701
In particular this equation holds good if U is = xy. +
41. Imagine now on the surface S a distribution gdS producing at a point (a' . . . c', e')
within the surface a potential V', and at a point (a" . . . c", e") without the surface a
potential Y"; where, by what precedes, Y" is in general not the same function of
(a" . . . c", e ") that V' is of (a! ...</, e').
It is further assumed that at a point (a ... c, e) on the surface we have Y'=Y" :
that V', or any of its derived functions, are not infinite for any point (a' .. . d, d)
within the surface :
that V", or any of its derived functions, are not infinite for any point ( a " . . . c", e")
without the surface :
and that Y"=0 for any point at infinity.
Consider Y' as a given function of (a. . . c, e) ; and take W' the same function of
(x . . . z, w). Then if, as before,
U=
then
{(a— a?)2. . .+ (c — z)2+ (e — w)2}*s
(£•■+£+£)»-».
Similarly, considering Y" as a given function of (a ... c, e) and take W" the same
function of (#-. . z, e). Then, by considering the space outside the surface S, or say
between this surface and infinity, and observing that U does not become infinite for any
point in this space, we have
I
dW"
dx"
dJJ
rd8=)W"~dS;
and adding these two equations, we have
CTT/dW , dW"\ 7C1 C /„7dU , _x„, dU\ 7_ 4(TiY+1tt,
J U(- -M+Wr) *=J (W^+W"&®) dS-T&k) V'
But in this equation the functions W' and W" each of them belong to a point
(x . . . z, w) on the surface, and we have at the surface W'=W", =W suppose; the
term on the right-hand side thus is dS, which vanishes in virtue of
d\ J dU A .
d^^ds1 T = v ’ ana the e(luation thus becomes
J
(dW dW"
\ dx' ‘ dx"
dS
that is, the point (a . . . c, e) being interior, we have
-T($s—$)/dW dW"\
4(ri)s+1 \dx,Jr~dx]l )
dS
{ (a - xf. . . + (c - zf + (e - wyys~ * *
5 A 2
702
PROFESSOR CAYLEY ON PREPOTENTIALS.
Iii exactly the same way if (a ... c, e) be an exterior point, then we have
is-fPJv ;
and adding, and omitting the terms which vanish,
that is,
4(ri)s+1v„
r(i*-i)v ’
-r(is-i) /dw' dw"
4(riy+1 v d8' d8"
dS
(a— x)2...(c — z)2 + (e—w)2ys~s'
42. Comparing the two results with
§dS
(a—x)2. . . + (c— z)2+ (e— w)2}lS~*’
we see that V', V" satisfying the foregoing conditions, there exists a distribution § on
the surface, producing the potentials V' and V" at an interior point and an exterior
point respectively ; the value of g in fact being
§=-
TQs-i) id W' dW \
4(ri)s+1 V da' + dx" )’
(C)
where W', W" are respectively the same functions of (x ... z, w) that V', V" are of
(«...<?, e).
The Potential-solid Theorem D. — Art. No. 43.
43. We have as before (No. 40),
jw ^ dS-t- jit . . . dzdw WVU-
= Ju w ds + f<& ■ • • * trvw-ipA^ T,
where, assuming first that W is not infinite for any point (x ... z, w) whatever, we have
no term in T ; and taking next U = — — — ■ — — - — - — 7 ,ot i._i as before, we have
& {(a-x)2. .. + (c-zf + (e-w)2ys 2
VU=0 ; the equation thus becomes
JW W dS~ jU 7F V=f* * dw UVW^
where W may be a discontinuous function of the coordinates (x . . . z, w), provided only
there is no abrupt change in the value either of W or of any of its first derived functions
^ viz. it may be any function which can represent the potential of a solid
mass on an attracted point (x ... z,w); the resulting value of V W is of course discon-
PEOFESSOE CATLET ON PEEPOTENTIALS.
703
tinuous. Taking, then, for the closed surface S the boundary of infinite space, U and
W each vanish at this boundary, and the equation becomes
-(ri)l^V= Ux... dz dw UVW ;
r(i«— i) •/
viz. substituting for U its value, and comparing with
g dx . . . dz dw
{(«— xy. . .+(c— zy+(e— wyy
where the integral in the first instance extends to the whole of infinite space, but the
limits may be ultimately restricted by g being =0, we see that the value of g is
W being the same function of (x ... z, w) that V is of (a ... c, e), which is the theorem D.
Examples of the foregoing Theorems. — Art. Nos. 44 to 49.
44. It will be remarked, as regards all the theorems, that we do not start with known
limits ; we start with V a function of (a ... c, e), the coordinates of the attracted point,
satisfying certain prescribed conditions, and we thence find g, a function of the coordinates
(x...z) or (x...z,w), as the case may be, which function is found to be =0 for
values of (x . . . z) or (x ... z, w) lying beyond certain limits, and to have a determinate
non-evanescent value for values of (x . . . z) or (x ... z,w) lying within these limits ; and
we thus, as a result, obtain these limits for the limits of the multiple integral V.
45. Thus in theorem A, in the example where the limiting equation is ultimately
found to be x2 . . . -f -z2=f2, we start with V a certain function of a2 . . . -f -c2{=%? suppose)
and e2, viz. Y is a function of these quantities through 9, which denotes the positive root
of the equation
the value in fact being V=j t~q~l(t-\-f2)~isdt, and the resulting value of g is found to
be =0 for values of (x ... z) for which x2 . . . +z2>/2. Hence V denotes an integral
J {{a— a?)2... + (c— ^)2 + e2}^+2’
the limiting equation being x2 . . .-\-z2=f2, say this is the s-co ordinal sphere.
And similarly, in the examples where the limiting equation is ultimately found to be
x2- z 2
j2... + ^2=l, we start with Y a certain function of #, ...c, e through 6 (or directly
and through 0), where 0 denotes the positive root of the equation
704
PROFESSOR CAYLEY ON PEEPOTENTIALS.
and the resulting value of $ is found to be =0 for values of {cc . . . z) for which
x 2 . z2 -j
dx . . .dz
{{a-x)\ .. + (c-zf+ e2)^
™2 ,,2
the limiting equation being say this is the s-coordinal ellipsoid. It is
clear that this includes the before-mentioned case of the s-coordinal sphere; but it is,
on account of the more simple form of the ^-equation, worth while to work out directly
an example for the sphere.
46. Three examples are worked out in Annex IV. ; the results are as follows : —
First, 0 defined for the sphere as above; ^ + 1 positive;
Jfczz
J {(a—x)2...- 4
dx. . . dz
,2 li*+2
-xy...+(c- zy+e*y
over the sphere x2 . . . +y2=f2,
=ST wfflfft-'-'V+f )-***■
This is included in the next-mentioned example for the ellipsoid.
Secondly, 0 defined for the ellipsoid as above ; g'-j-l positive ;
f (l-t-
. — Ts 1 dx . . .dz
Y—\ ' f
h2)
J {{a—x)2 . .
. + {c-z)2+e2)is+2
a?2 z2
over the ellipsoid
1
This result is included in the next-mentioned example ; but the proof for the general
value of m is not directly applicable to the value m= 0 for the case in question.
Thirdly, 0 and the ellipsoid as above ; y + l positive; m— 0 or positive, and apparently
in other cases.
V=f (
,1+P"
gt\ 2+«
\a-xf..
. + {c-z)2 + e2\is+2
: the ellipsoid as above.
(ri)sr(i+g+m)
— rGs+^)r(i+m) v
d 2
f+r
,3 p2\ m
• • • t+e)-Ht.
And we have in Annex V. a fourth example ; here Q and the ellipsoid are as above :
the result involves the Greenian functions.
PEOFESSOE CATLET ON PEEPOTENTIALS.
705
47. We may in the foregoing results write e=0 ; the results, writing therein s + 1 for
s, and in the new forms taking (a . . . c, e) and (x . . . z, w) for the two sets of coordinates
respectively, also writing q—\ for q, would give integrals of the form
P pdx...dzdw
J {{a—xf.. . + (c~^)2+(e— w)2ps+2
for the (s-j-l)coordinal sphere and ellipsoid x2 . . . + z2 -\-w2 =f2 and J2 • • • + f2+^2 = l>*
say these are prepotential solid integrals; and then, writing q=—\, we should obtain
potential solid integrals, such as are also given by the theorem D. The change can be
made if necessary ; but it is more convenient to retain the results in their original
forms, as relating to the s-coordinal sphere and ellipsoid.
There are two cases, according as the attracted point (a . . , c) is external or internal.
.X2
For the sphere: — For an external point > /2 ; writing e — 0, the equation ^^=1
has a positive root, viz. this is ; and 0 will have, or it maybe replaced by, this
value y2—f 2 : for an internal point n2<f2 ; as e approaches zero, the positive root of the
original equation gradually diminishes and becomes ultimately =0, viz. in the formulae
0 is to be replaced by this value 0.
«2 c2 . .
For the ellipsoid: — For an external pointy. . . +^>1; writing e=0, the equation
Ci~ (& ' ' ...
. . . +fl_j_^2=:l has a positive root, and 6 will denote this positive root: for an
internal point p . . . < 1 ; as e approaches zero the positive root of the original equa-
tion gradually diminishes and becomes ultimately =0, viz. in the formulae 6 is to be
replaced by this value 0.
The resulting formulae for the sphere x2 . . . -\-z2=f 2 may be compared with formulae
for the spherical shell, Annex VI., and each set with formulae obtained by direct inte-
gration in Annex III.
We may in any of the formulae write q=—^, and so obtain examples of theorem B.
48. As regards theorem C, we might in like manner obtain examples of potentials
relating to the surfaces of the (s-J-l)coordinal sphere x2 . . . -J -z2-\-w2=f2, and ellipsoid
00^
7s* ••+*«+ F=1’ or say to spherical and ellipsoidal shells ; but I have confined myself
to the sphere. We have to assume values V' and V" belonging to the cases of an
internal and an external point respectively, and thence to obtain a value g, or distribu-
tion over the spherical surface, which shall produce these potentials respectively. The
result (see Annex VI.) is
706
PROFESSOR CAYLEY ON PEEPOTENTIALS.
over the surface of the (s+l)coordinal sphere x2 . . . -\-z2-\-w2=f2,
2(ri)s+i/s i
— r(Js + l) for exterior point z>f
and
2{TVS+H° 1
— ^(4 + 4 f^~x ^or in^eri°r P°int *</,
where %,2=a2 .. .-\-c2-\-e2. Observe that for the interior point the potential is a mere
constant multiple of f.
The same Annex VI. contains the case of the s-coordinal cylinder#2 . . . -\-z2=f2, which
is peculiar in that the cylinder is not a finite closed surface, but the theorem C is found
to extend to it.
49. As regards theorem D, we might in like manner obtain potentials relating to the
(s-f l)coordinal sphere x2 . . . -\-z2-\-w2=f2 and ellipsoid^ . . . +p+-p=l; but I confine
myself to the case of the sphere (see Annex VII.). We here assume values "V7 and V"
belonging to an internal and an external point respectively, and thence obtain a
value g, or distribution over the whole (s+l)dimensional space, which density is found
to be =0 for points outside the sphere. The result obtained is
v C dx...dzdw
Ji («-*)2 • • - + (c-z)*+ (e-w)2}^
over (s+l)coordinal sphere #2. . .-\-z2-\-w2=f2,
(T-s')s+i fs+l
==j'{ls + -?-) x7-1 ^0r ex^er^or P°int *>f
=TJfs>+f { + \)f2 — ( 2 5 — f°r interior point z<f,
where 7?=d? . . .-J -c2-\-e2.
The remaining Annexes VIII. and IX. have no immediate reference to the theorems
A, B, C, D, which are the principal objects of the memoir. The subjects to which they
relate will be seen from the headings and introductory paragraphs.
Annex I. Surface and Volume of Sphere x2 . . .jrz2jrvf=f2. — Nos. 51 & 52.
51. We require in (s-f-l)dimensional space, J dx ... dz dw, the volume of the sphere
x2 . . .-\-z2-\-w2=f2, and J cZS, the surface of the same sphere.
Writing x=f\Z%. . . z=f\/%, w=f*/ co, we have
dx ...dz dw= -Ti fs+1 d\... d% du,
with the limiting condition § . . . ; but in order to take account as well of the
negative as the positive values of x ... z, w, we must multiply by 2S+1. The value is
therefore
=/*+i jr*... ••<*?*».
PROFESSOR CAYLEY ON PREPOTENTIALS.
707
extended to all positive values of such that | . . .+£+<"< 1 ; and we obtain
this by a known theorem, viz.
(JUp+i
Volume of (s+l)dimensional sphere =/'s+l +
Writing x=fB, . . . z=f%, w=fco, we obtain dS=fsd%, where is the element of
surface of the unit-sphere £2 . . . + £2 + <y2=l ; we have element of volume d%. . .d% da
—Vs dr d%, where r is to be taken from 0 to 1, and thence
that is,
J d\ . . . d% dr X dt= dZ,
§dZ=(s+l)§dt... dtd», =2(^+1)^
2(ri)s
J2(ri)s+1
^S= surface of (s -f- ljdimensional sphere =/ s
52. Writing s— 1 for s, we have
(W
Volume of (s— ljdimensional sphere=/s p/ig^_-f
Surface of do. =fs 1 "p^ ,
which forms are sometimes convenient.
Writing in the first forms s+l = 3, or in the second forms s=3, we find in ordinary
space
Volume of sphere=/3 =f3 — — — =z—f~,
r J r(f) J f.i.VTr 3
and
Surface of sphere=/2 —f2, =4 nf2,
as they should be.
Ts~^dv
Annex II. The Integral 1 ^8+g8 ^s+q. — Nos. 53 to 63.
53. The integral in question (which occurs ante, No. 2) may also be considered as arising
from a prepotential integral in tridimensional space ; the prepotential of an element of
mass dm is taken to be=J^-2, where d is the distance of the element from the attracted
point P. Hence if the element of mass be an element of the plane z — 0, coordinates
(x, y ), being the density, and if the attracted point be situate in the axis of z at a
distance e from the origin, the prepotential is
xt f pdxdy
V J (a?2+y2+e2)j*+2'
For convenience it is assumed throughout that e is positive.
MDCCCLXXV. 5 B
708
PEOFESSOE CAYLEY ON PEEPOTENTIALS.
Suppose that the attracting body is a circular disk radius E, having the origin for its
centre (viz. that bounded by the curve a?-\-y2= E2); then writing oc=r cos 0, y=r sin 8,
we have
„ C grdrdQ
V_ jp + e2)^+2’
which, if § is a function of r only, is
r %rdr .
| ('r2_|_e2ji«+2 >
and in particular if %=rs~2, then the value is
1 dr
(r2 + e2)^+2’
the integral in regard to r being taken from r= 0 to r=E. It is assumed that s— 1 is
not negative, viz. it is positive or (it may be) zero. 1 consider the integral
p r*-1 dr
Jo (r2 + e2)iS+25
which I call the r-integral, more particularly in the case where e is small in comparison
with E. It is to be observed that e not being = 0, and E being finite, the integral con-
tains no infinite element, and is therefore finite, whether q is positive, negative, or zero.
54. Writing r=e\/ v, the integral is
the limits being
E2
v^s~ldv
.V)is+i’
and 0.
In the case where q is positive this is
viz. the first term of this is
vis-'dv
(T+wji*+2;
2 r &+qy
and the second term is a term expansible in a series containing the powers 2q, 2q-\-2,
e 2 i
&c. of the small quantity as appears by effecting therein the substitution v=~; viz.
the value of the entire integral is by this means found to be
)vas + q) 1
ii xq~l dx )
\T(±s+q) J0 {l+x)is+qy
55. In the case where q is =0, or negative, the formula fails by reason that the ele
becomes infinite for indefinitely large values of v.
v^s — * d/V
ment tv , of the integrals
(l+v)is+2
rs
Eecurring to the original form \ ~ it is to be observed that the integral has a
Jo v +e )s 2
PROFESSOR CAYLEY ON PREPOTENTIALS.
709
finite value when e=0; and it might therefore at first sight be imagined that the factor
(r2+e2)_is“? might be expanded in ascending powers of e2, and the value of the integral
consequently obtained as a series of positive powers of e2. But the series thus obtained
is of the form e21c{ r~2q~2 th~ldr, where 2q being positive, the exponent — 2q— 2k— 1 is
for a sufficiently small value of Jc at first positive, or if negative less than — 1, and the
value of the integral is finite ; but as Jc increases the exponent becomes negative, and
equal or greater than —1, and the value of the integral is then infinite. The inference
is that the series commences in the form A+Be2+CV . . . , but that we come at last when
q is fractional to a term of the form K.e~2q, and when q is =0, or integral, to a term of
the form Ke-2? log e, the process giving the coefficients A, B, C . . . , so long as the expo-
nent of the corresponding term e°, e2, e4 . . . is less than — 2 q (in particular #=0, there is
a term Jc log e, and the expansion-process does not give any term of the result ), and the
failure of the series after this point being indicated by the values of the subsequent
coefficients coming out = oo.
56. In illustration, we may consider any of the cases in which the integral can be
obtained in finite terms. For instance.
Integral is Jr(r2+e2)* dr , =^(r2- \-e2)*, from 0 to R,
=^(R2 + ef-^3;
viz. expanding in ascending powers of e this is
=iR3+pte2...-^3,
or we have here a term in e 3. And so,
s=l, q=- 2,
Integral is §(r2-\-e2fdr, = ( \r2 + \e2)r\/ r2 + e1 -f f e4 log (r + y/ r2 + e1) , from 0 to R,
=(iRs+|^)E */W+e>+§e' log B+ ^±1 ;
viz. expanding in ascending powers of e this is
:1R4+|RV. . . + f e4 log
or we have here a term in e4 log e.
57. Returning to the form
i
vis~ldv
(1+v)
and writing herein v=- — -, or, what is the same thing, #=— L_ , and for shortness
x i+u’
* Term is |e4log— , =fe4/log~ + log 2V which, 5 being large, is reduced to log 5.
\ e ) e D b e
5 b 2
710
PROFESSOR CAYLEY ON PREPOTENTIALS.
x=
R2’
R2’
■ H 2
el
the value is
=±e~29^ xq~\l —xf^dx,
where observe that q— 1 is 0 or negative, but X being a positive quantity less than 1,
the function — xfs~l is finite for the whole extent of the integration.
58. If 2=0, this is
=1
Jx X
2 Jy X
=ilogX
\dx
where observe that in virtue of the change made from ^(1— x)is~l to ^ {1 — (1—
(a function which becomes infinite, to one which does not become infinite, for #=0), it
has become allowable in place of \ to write ( — f .
Jx Jo Jo
When e is small, the integral which is the third term of the foregoing expression is
obviously a quantity of the order e 2 ; the first term is ^log ^d-log-y/ 1+ which,
neglecting terms in e2, is =^log — , and hence the approximate value of the r-integral
>R yS-lflr
Jo (r* + e*T
or, what is the same thing, it is
. R n T1 7 1 —yr
=log7— H
where the integral in this expression is a mere numerical constant, which, when -|s— 1
is a positive integer, has the value
i_Li _i__! ;
and neglecting this in comparison with the logarithmic term, the approximate value is
PROFESSOR CATLET ON PREPOTENTIALS.
711
59. I consider also the case q= — l ; the integral is here
j* a?-*(l - { 1 ■ - (1 )dx
=e(X-i-l)+±e{1x-$\l-(l -x)*-l\dx;
Jx
and the first term of this being =\/ e2+R2 — e, this is consequently
=\/^2+62+i^r x-%\l — (1— xfs~'\dx— c(l+| f x~l { 1 — (1 —xfs~ 1 1 dx).
Jo Jo
As regards the second term of this we have
-2x-^l-(l-x)^-1}+2(is-l)jx^(l-x)^-2dx=jx-i{l-(l-x)^-1ldx;
or taking each term between the limits 1, 0,
+
viz. this integral has the value
o ,
TR ys-'dr
Jo {r* + e
a , is consequently
=VR2+e2+^£ x~?{l — (l-xf~'\dx-e r(^z|y’
which is of the form
1
say the approximate value is
R (l-f terms in . . A—e
R— e
R2’ R4’
nis-l) ’
where the first term R is the term dr, given by the expansion in ascending powers
of e2 ; the second term is the term in 0~2?. And observe that term is the value of
x~i(l—xfs~ldx,
Jo
calculated by means of the ordinary formula for a Eulerian integral (which formula, on
account of the negative exponent — §, is not really applicable, the value of the integral
being =co ) on the assumption that the T of a negative q is interpreted in accordance
with the equation T{q-\-^)=qTq ; viz. the value thus calculated is
r(-i)r(is) _
2 r(is-i) ’ r(i«— i)
on the assumption r^= — -|E( — ; and this agrees with the foregoing value.
712
PROFESSOR CAYLEY ON PREPOTENTIALS.
60. It is now easy to see in general how the foregoing transformed value
xq~Hl — x'fs~ldx> where q is negative and fractional, gives at once the value of the
Jx
e2
term in e~2q. Observe that in the integral x is always between 1 and X (=e8 a
positive quantity less than 1) ; the function to be integrated never becomes infinite.
Imagine for a moment an integral f xadx, where a is positive pr negative. We may con-
Jx
r*l fX _ jl+a
ventionally write this =1 xadx— i xadx, understanding the first symbol to mean ,
Jo Jo l+«
X1 + “ jl + a QlJ
and the second to mean ; they of course properly mean — — —
and
X1+“_o]
+ «' J A * l+« l+«
but the terms in 01+“, whether zero or infinite, destroy each other, the original form
, in fact, showing that no such terms can appear in the result.
In accordance with the convention we write
f xq~\l — xfs~'dx={ xq~'(l — x)is~'dx— f xq~l(l— x)¥~'dx ;
Jx Jo Jo
and it follows that the term in e~2q is
\e~2q f xq~\l —x)¥~ldx,
this last expression (wherein q, it will be remembered, is a negative fraction) being
understood according to the convention ; and so understanding it the value of the
term is
i/,-2?
“2 r wwr
where the T of the negative q is to be interpreted in accordance with the equation
T(q+l)=qTq; viz. we have r^ + l), =g(g + i) F(g~l-2), &c., so as to make the
argument of the T positive. Observe that under this convention we have
r^IYl— a)— or the term is -e~2q — - —
i^i(i q)— sin??r, oi tneterm is 2e . sin q7[ r(is+?)r(l-?)
61. An example in which -|s— 1 is integral will make the process clearer, and will
serve instead of a general proof. Suppose q= — y, ys — 1 = 4, the expression
( x^ (1— x)4 dx = ( (x~*— 4#“^+ 6^— 4x&-t-x?r) dx
^0 Jo
is used to denote the value
_7_1A T 42. _ 7l 7_
1 3 T^13 5T 27
— 7.2401 -75
7/ 1 2. j 6_ 1 j 1_\ 7/ 44 i 1 6_\ _
— / ^ — 1 — 3 -f is'- 5 ~r 2 7b — H — 27 — 5 i- 13b — 5.13.27’ “5 . 13.27'
PROFESSOR CAYLEY ON PREPOTENTIALS.
713
But we have
r^rg _r5r(-p
24T(-|)
-I5
62. The case of a negative integer is more simple ; to find the logarithmic term of
\e~2q\ x^1 (l—cc)1*'1 dx,
Jx
we have only to expand the factor (1— xfs~l so as to obtain the term involving x~q ; we
have thus the term
TU
r-d.
) e m-fl
vy
l0£
r(i-g) r(is+g) X’
1 / R2\ R / e*
where log ^=log ( j, =2 log — +2 log v 1 80 that neglecting the terms ii
R-
&c. this is =2 log — , and the term in question is
r^s
i R
log — .
-( ¥* 2?r(i-g)r(is+?)^ e-
The general conclusion is that q being negative, the r-integral
fK r3-1 dr
Jo (r2 + e2)*s+2
has for its value a series proceeding in powers of e 2, and which up to a certain point is
equal to the series obtained by expanding in ascending powers of e 2 and integrating
each term separately ; viz. the series to the point in question is
R-2« is + g R-29-2 is + ?.is + ? + 1 R-2J-4 4
-2 q 1 — 2q — 2 6 1.2 -2q-4.e ' ’
continued so long as the exponent of e is less than — 2 q ; together with a term K<?-22
when q is fractional, and Ke~2q log ~ when q is integral ; viz. q fractional this term is
_i,-2g rj*rg _ jgj rfr
— r (is + q)’~- singTT r(is + g)r(l-g)»
and q integral, it is
-(“) e r(i-?)r(is+g)10^'
63. It has been tacitly assumed that \s-\-q is positive ; but the formulae hold good if
\s-{-q is=0 or negative. Suppose is 0 or a negative integer, then F(|-s-]-^) = oo ,
and the special term involving e~2q or e~2q log e vanishes ; in fact in this case the
r-integral is
714
PEOFESSOE CAYLEY ON PEEPOTENTIALS.
where (r2+e2)-cis+s) has for its value a finite series, and the integral is therefore equal to
a finite series A+Be2+Ce4+&c. If \s-\-q be fractional, then the T of the negative
quantity l-s-j-# must be understood as above, or, what is the same thing, we may, instead
(r1)2
of r(-|s-l-g'), write s-n 5 thus, q being integral, the exceptional term is
_r v, -a, rja sin (fr + g)?r • f(l —q — ^s) , R
— t—)e (T^T{l-q) i0& e ’
for instance, s=l, q=— 2, the term is
or, since r§=f . ^
result.
, sin ( — hr) Tf . R
^~ri)».ra Iog7-
ri, and T3=2, the term is -f-fe4 log^, agreeing with a preceding
Annex III. Prepotentials of Uniform Spherical Shell and Solid Sphere. —
Nos. 64 to 92.
64. The prepotentials in question depend ultimately upon two integrals, which also
arise, as will presently appear, from prepotential problems in two-dimensional space, and
which are for convenience termed the ring-integral and the disk-integral respectively.
The analytical investigation in regard to these, depending as it does on a transformation
of a function allied with the hypergeometric series, is I think interesting.
65. Consider first the prepotential of a uniform (s+1) dimensional spherical shell.
This is
(a — a?)2 . .
dS
+ (c — z)2+ (e— M>)2ps+S’
the equation of the surface being x2 . . . +z2+w2=/2; and there are the two cases of an
internal point, a2 .. . -\-c2-\-e2 <f2, and an external point, a2 . . . -\-c2-\-e2>f2.
The value is a function of a2 . . . -fi c2-\-e2, say this is =z2 ; and taking the axes so that
the coordinates of the attracted point are (0 ... 0, z), the integral is
d S
^2...+*2+(x-w)2p+2’
where the equation of the surface is still x2 . . . -{-z2-\-w2=f2. Writing x=f% . . . z=j%,
w=fco, where |2 . . . -\-%2-\-a2=l, we have dS = or the integral is
>(/2-2x/«> + x2)i*+2-
Assume %=px, . . . %=pz, where x2 . . . -\-z2= 1 ; then p2-\-a2=l. Moreover, d\ . . . d£,
—ps~l dp d%, where d% is the element of surface of the s-dimensional unit-sphere
x2 . . . -\-z2— 1 ; or for p, substituting its value \/l — a2, we have dp = > anc^ thence
PROFESSOR CAYLEY ON PREPOTENTIALS.
715
dl . . . dl)= — (1— a2)is~l u dco d%. The integral as regards p is from p= — 1 to +1, or as
regards co from 1 to — 1; whence reversing the sign the integral will be from oj— - 1
to -f 1 ; and the required integral is thus
C1 (l-q^lfrrfS (1 —W-'d*
—J J _ , (f - 2k/0J + K2) *s+2’ ■«/ J (/2 - 2*> + K2) **+2’
2(ri)*
where J d% is the surface of the s-dimensional unit-sphere (see Annex I.), == ^1$ >
and for greater convenience transforming the second factor by writing therein co= cos 6,
(f1)®
the required integral is — into
n/sp sin 5-1 $ dd
J 0 (/2-2x/cos 0 + X2)is+«’
which last expression ^including the factor 2 f% but without the factor the ring-
integral discussed in the present Annex. It may be remarked that the value can be at
once obtained in the particular case s= 2, which belongs to tridimensional space, viz. we
then have
Y 2tt/'2 r sinJdd
~ J J 0 (/2-2x/cosfl + x2)2+1
= i^(/*-2*/cos«+*V
=i I
which agrees with a result given, ‘ Mecanique Celeste,’ Book XII. Chap. II.
66. Consider next the prepotential of the uniform solid (s + l)dimensional sphere,
f dx ... dzdw
V ~ J {{a-w)2...+ (c-zf +{e-w) 2}ii+2’
equation of surface x2. . . -]-z2-\-w2=f2, and the two cases of an internal point x<f,
and an external point z>f (a2 . . . -\-c2-j-e2=z2 as before).
Transforming so that the coordinates of the attracted point are 0 . . . 0, «, the integral
J{x2... +z2 + (x-wflis+q’
where the equation is still x2. . . -\-z2-\-w2=f2. Writing here x=r% . . . z=r%, where
£2 . . • +£2=1, we have dx . . . dz=rs~1 drdX, where d% is an element of surface of the
.s-dimensional unit-sphere |2. . . -f- £2=1; the integral is therefore
4
1 dr d1*dw
{r2+ (:
J J{>-s+(*-i
w)2\is+*
drdw
w)2^s+i’
where, as regards r and w, the integration extends over the circle r2 -\-w2=f 2 . The value
mdccclxxv. 5 c
716
PEOEESSOE CAYLEY ON PEEPOTENTIALS.
of the first factor (see Annex I.) is = 4 2' ; and writings, x in place of r, w respectively,
I 2s
2(TiV .
the integral is =■ pjf ■ into
k
ys~l dxdy
or we have
J{(a?->c)2 + j/2}is+2
over the circle x*-\-y‘2=f‘2; viz. this last expression (without the factor r^J is the disk-
integral discussed in the present Annex.
67. We find for the value in regard to an internal point x<f,
Y=r(is|r|^w) /,+ 'JW-
which in the particular case q— — is
ere
It may be added that in regard to an external point a >f, the value is
v=r<p^lS;i¥=?) ■2C''+’ - JJ
which in the same case q= — 1 is
where the ^-integral is
o V — s + 1 v —8 — 1 v~s+l
and the value of V is therefore
(pip+l fs+ 1
_r (*«+*) x®-1*
d 2 d? d*
Recurring to the case of the internal point; then writing V=^... an<^
observing that V(;s2)=4(^s+A), we have
VY=-
4(ri)sH
T&s-i
(in particular for ordinary space s+l = 3, or the value is — 7^, = — 4r, which is right).
v w
PROFESSOR CAYLET ON PREPOTENTIALS.
717
68. The integrals referred to as the ring-integral and the disk-integral arise also from
the following integrals in two-dimensional space, viz. these are
C yt-'dS C ys-ldxdy
J + J {{x-xF + y*}***’
in the first of which dS denotes an element of arc of the circle x2-\-y2=f'2, the integra-
tion being extended over the whole circumference, and in the second the integration
extends over the circle x2-\-y2=f2 ; y*~l is written for shortness instead of viz.
this is considered as always positive, whether y is positive or negative ; it is moreover
assumed that s — 1 is zero or positive.
Writing in the first integral x=f cos 6, y~f sin Q, the value is
» f I ^
—J J (/2 — 2 x/ cos 9 + *2)is+2 ’
viz. this represents the prepotential of the circumference of the circle, density varying as
(sintf)8-1, in regard to a point x=x, y= 0 in the plane of the circle; and similarly the
second integral represents the prepotential of the circular disk, density of the element at
the point (x, y)=ys~l , in regard to the same point x=x, y— 0, it being in each case assumed
that the prepotential of an element of mass gd& upon a point at distance d is = J^.
69. In the case of the circumference, it is assumed that the attracted point is not on
the circumference, z not =f; and the function under the integral sign, and therefore the
integral itself, is in every case finite. In the case of the circle, if z be an interior point,
then if 2^—1 be =0 or positive, the element at the attracted point becomes infinite;
but to avoid this we consider not the potential of the whole circle, but the potential of
the circle less an indefinitely small circle radius s having the attracted point for its
centre; which being so, the element under the integral sign, and consequently the
integral itself, remains finite.
It is to be remarked that the two integrals are connected with each other ; viz. the
circle of the second integral being divided in rings by means of a system of circles con-
centric with the bounding circle A’2-f-?/2==/’2, then the prepotential of each ring or annulus
is determined by an integral such as the first integral ; or, analytically, writing in the
second integral x—r cos d, y=r sin 0, and therefore dxdy=rdrdQ, the second integral is
(sin d$
+ k2 — 2 xr cos
0)^+2’
viz. the integral in regard to 6 is here the same function of r, z that the first integral is
of/, z ; and the integration in regard to r is of course to be taken from r— 0 to r=f.
But the ^-integral is not in its original form such a function of r as to render possible
the integration in regard to r ; and I, in fact, obtain the second integral by a different
and in' some respects a better process.
70. Consider first the ring-integral, which writing therein as above x=f cos 0,
5 c 2
718
PROFESSOR CAYLEY ON PREPOTENTIALS.
y—f sin 0, and multiplying by 2 in order that the integral, instead of being taken from
0 to 2sr, may be taken from 0 to w, becomes
_o n, C (sin Q)s~ldQ
J J(/2-2x/cose + x2)is+9'
Write cos then sin \0=*Jl—x, sin 0=2#T1 — x)1 ; d6——x~\ 1—x) *dx\
cos 0= — 1 -j- 2# ; 0=0 gives x=l, 0=w gives #=0, and the integral is
=2-i fs f1 aP~\l -af-'dx
Jo {(f+x)2 — 4x/a?}is+2’
_ 2s-1/* a#*-1 (\—oofs~'dac
~(f+*)s+ 21 Jo (1 -ux)is+q ’
4xf
if for shortness u~ (obviously u< 1).
The integral in x is here an integral belonging to the general form
II(a,0, 7, w)=f XT*1 (l—xy~l (1 — ux)' ydx,
viz. we have
2-5—1 fs
Ring-integral =— ~ ' U(^s, \s+q, u).
yj+x)
71. The general function II(a, 0, y, u) is
n (a, 0, 7, «)=r ^|yF(a, 7, a+0, u),
or, what is the same thing,
F(a, 0, y, = IT(a, 7~a> ft w)>
and consequently transformable by means of various theorems for the transformation of
the hypergeometric series ; in particular the theorems
F(a, 0, 7, m)=F(0, «, 7, u),
F(a, 0, 7s «)=(!— “)y-B_#,F(y— a, 7—0, 7, u) ;
and if v= /1 — ^1— Q what js the same thing, u—- 4 x/v- , then
Vl+V'l-M/ (l + '/v)2’
F(a, 0, 20, u)=( l+\/ v)2* F(«, a— 0+^, v) ;
in verification observe that if «t=l then also v=l, and that with these values, calcu-
lating each side by means of the formula
ir7r(y-«-/3)
T(«,0, 7, 1)— r(y_a)r(y-/3)
rr/ O n r«TQ8-y)
n(«, 0, 7, i)— r(a+/g_yp
the resulting equation, F(a, 0, 20, l)=22aF(a, a— 0+|-, 0+?r, 1), becomes
rg0r(<3-«) r(0+i)r(2/3-2«)
r(20-«)r0~ z r(2j8-«)r(0-a+i)’
PROFESSOR CAYLEY ON PREPOTENTIALS.
719
that is
T2/3 02a Y(2{3-2ct)
r/3r(/3+i) — 1 r(/B-a)r(s -«+i)’
which is true, in virtue of the relation
Y2xY\ o2j — i
ra?r(«“+-^)
72. The foregoing formulae, and in particular the formula which I have written
F(a, (3, 2j3, u)=(l-j-\/v)2aF(a, a— /3-j--^-, /3+-|, v), are taken from Rummer’s Memoir,
“ Ueber die hypergeometrische Reihe,” Crelle , t. xv. (1836), viz. the formula in question
is under a slightly different form, his formula (41) p. 76 ; the formula (43), p. 77, is
intended to be equivalent thereto ; but there is an error of transcription, 2a — 2/3 + 1, in
place of /3+^, which makes the formula (43) erroneous.
It may be remarked as to the formulae generally, that although very probably
II(a, (3, y, u ) may denote a proper function of u, whatever be the values of the indices
(a, (3, y), and the various transformation- theorems hold good accordingly (the T-function
of a negative argument being interpreted in the usual manner by means of the equation
r.r=^r(l+#), =X^J+ ^ r(2+tf) &c.), yet that the function U(a,(3, y, u ), used as de-
noting the definite integral 1 oca~l (1— (1 —ux)~ydx, has no meaning except in the
Jo
case where a and (3 are each of them positive.
In what follows we obtain for the ring-integral and the disk-integral various expres-
sions in terms of H-functions, which are afterwards transformed into ^-integrals with a
superior limit go and inferior limit 0, or ; but for values of the variable index, q
lying beyond certain limits, the indices a and (3 , or one of them, of the Il-function will
become negative, viz. the integral represented by the Il-function, or, what is the same
thing, the ^-integral, will cease to have a determinate value, and at the same time, or
usually so, the argument or arguments of one or more of the T-functions will become
negative. It is quite possible that in such cases the results are not without meaning,
and that an interpretation for them might be found ; but they have not any obvious
interpretation, and we must in the first instance consider them as inapplicable.
73. We require further properties of the II-functions. Starting with the foregoing
equation,
F(a, (3, 2/3, w) =(!+>/ «)2aF(a,a— /3+i, /3 + i v ),
each side may be expressed in a fourfold form : —
F(a, 0, 2/3, u)
=F(/3,a, 2/3, u)
=(1— m)p_“ F(2/3— a, /3, 2/3, u)
— (1 _ uf-o- Y(cc, 2/3 - a, 2/3, u)
(l+xA;)2“F(a,a-/3+i,/3+A v)
=(1 +\/ v )2a F(a— /3+-|, a, /3-f^, v)
= (1+xA;)2“ (1 -«)*"«» Ffl3-a+i, 2/3 — a, (3+± v)
= (l+N/^(l-^-2“F(2/3-a,/3-a+i,/3+i,i;),
720
PROFESSOR CAYLEY ON PREPOTEN TIALS.
where, instead of (l+\/ v)2a (l—vyp~2a, it is proper to write (1+^/ vf°J (1 \J v)2/3~2“; and
then to each form applying the transformation
we have
F(a, /3, y, w) — par(y— a) 7 w),
r«r(2j3-«) ^ — & u)
Yj3 T/3 n(/3, (3, a, u )
=(l w)3 a r(2/S-«)r« — a’ a?
= (1 - uf-a yr-r^_ a) n(a, 2/3 — a, 2(3- a, u)
— (i+\/^)2a rar(/3— «+^) n(«, /3 a+!>a /^-H2>w)
=(l-}~\/'y)2“ r(2j3 — a) ^(a 2/3 cc,k,v)
=(l-sr\/v2p 2“ p^_a+ijpa n(/3— a+i) 2/3 — a, ?;)
= (1 +\/ ^ (1 — y)2^ 2a r(2/3-«)r(«-/3 + i) n(2/3 — a, a— ^+-2 5 /3 — a+^, y)’
I select on the left-hand the second form, and equating it successively to the four
right-hand forms, attending to the relation ^^-^-=2 1-23 T|, we find
n(3,0,<vO=(i+\AO2a 21-23 r«r|?!+i) n(«,j9-«+*,«H3+*,«)
— (!+>/ -y)2a2 l~v r(«-^+f)r(2/3-«)n^~ — a>a> ^
= (l + \/y)2,3(l— \Zv)2fi 2“21 2Pp^_f +\)ra HO — a+-|, a, 20— a, v)
= (1 + \A0213 (1 — \/ VY? 2a21 ^r(2/3 — a) r(a— /3 + i) ^(2/3— a, a— /3 — a + tt).
Putting herein a.=\s-{-q, the formulae become
n(is,|s,|s+!?!»)=(l+\/ vy+'Q 2l_i Tiis+q-fT^-q) n(ls+?>i— 2>i+?>*) • • • CO
=(iW'v)^2'~ ra+r^_g)n(i+g,^-g,i»+g^) • • (IL)
=(l+yi)'(l-^)-2*2'-'r5^J7T?yn(|-2)is+f.i*-?.»)- • -(ra-)
=(l+v^)-(l -^)-» 2- r(is-;)ri+g) n(^-g' i+g- * -g. »)' • -(IV.)
PBOEESSOB CAYLEY ON PKEPOTENTIALS.
721
where observe that on the right-hand side the IT-functions of I. and IV. only differ by
the sign of q, and so also the Il-functions of II. and III. only differ by the sign of q.
We hence have
n(|s,|s,is-2v «0=(l+^)s-2? VY>
and comparing with (IV.),
n(te is, is+q,u)= is, 1 s-S, «).
Ring-integral
(/+*)
u).
4*/
where gives, as well in the case of an exterior as an interior point, a conver-
4?c/*
gent series for the integral ; but this series proceeds according to the powers of xy2.
We may obtain more convenient formulae applying to the cases of an internal and an
external point respectively.
f K
75. Internal point %<f, tjl—u—j—, and therefore v=p.
n(is,is,is+2,«)= ~!-i +4)
= (~t) 2‘"'r(i+s)r(is-s) n(i +2.is-2>is+Sy5)
= (t") (V) 2"'r(i-«)r(i*+S) n(*
=Yt)' +*t -4Y
where the Il-functions on the right-hand side are respectively
_/>+i f 1afr+g-1(l— , x)-i~idx
—J J0 (P—x?x)i+*
_/s+22
j Jo (/2— x2a?)i®+?
3 X~1~i (1 — x)is+q~l dx
(f*-K*xp-i
=/*- j
—f-n+i T a^~g+1(l-J?)g~^
Jo (/2-*V)-^
dx
=(/3)ii [p-Ht+r-^y-Ht+fr^-’dt
f-2q + l
= (/*-**)- 2?
the if-forms being obtained by means of the transformation x=j^p—^, ; viz. this gives
1—x p—y}^
1 x~t+p -K*’J
whence the results just written down.
i p -*2 f2_y2T_(p^m±n dT_ (/»-*)*
— t+f-K2 ’aX — (t+p-K 2)2’
PEOEESSOE CATLET ON PEEPOTENTIALS.
We hence have
Ring-integral
/
-(/*-**)«*
f
~(p-*rq
= f
= f
TjsTj
r(i«+gOr(±-g)
i>ri
r(i+?)r(is-?)
r(W)r(i*+s)
T^s-q)T(i + g)
J t*s+*-1(t+f2—z^is+q(t+f2)-,!-*dt
JV* (t+f*-x*)'-* (t+f)-i°-qdt
JV*-* (*+/W)-^ ( t+f)~is+9dt
r 1 ( t +/2 - o-^-? (t +f)q~i dt.
As a verification write z=0, the four integrals are
f &+<-'dt _/2?_1 r(^+g)r(i-g)
Jo ( t+f*f+i ’ r(i>+ij ’
r _f2?_s r(j+g)r(^-g)
Jo ( t+pf+ *’ 1 r(i«+i) 5
f” ^~q~ldt _r-2q-s r(j~g)r(2g + g)
Jo ( t+pf+i ’ r(|s+i)
fr-i-'dt r(js-g)r(i+g)
Jo (*+/2)is+i’ 1 r(i«+i) »
and hence from each of them
-p. . . ,i
Rmg-mtegral =pq r(fc+fj>
which is in fact the value obtained from
Ring-integral = ~rr
lfs
'(/+«)
on putting therein z=0 ; viz. the value is
2®-1 r1 i, v, , 7 i 2®-ir^s.r^s
= 7^ Jo ^ ^ —VIP =f* W *
76. External point \/l—u=^~, and therefore v=rL.
*+f
n(is, is, , w)=^a±/^
-e?0
oi-8 rrAisi « 1 a i_|_/> /2\
2 r(^+g)r(i-g) n(,2s+^ 2 <b 2+^ -2;
risr" n(*+s>fc-j>
r(i + ??)E(is— g)
= Cat) (^r) 21"!r(iS-#(H?) n(is-2> i+<z,
PROFESSOR CAYLEY ON PREPOTENTIALS,
where the rT-functions on the right hand are respectively
_ fiqfr+g-ifi-afl-g-frfe
Jo (x2-/2tf)9+*
_ +2g r^g-*( \-x)*-i-'dx
Jo (x2-/2«)^ + «
“* Jo
~Z Jo («2-/^)-g+i
we have then
723
=-^=jy, y _r*+’{t+F-*?F*'-'(t+F)-<-* at,
j,s+2q /»“
=v=jt’ £_/"* v+f-**)’-1 (t+fyi-’dt,
= (x‘- r. _Jr^>
V-2J+1 F“
=S?r^J M ;
fsKi-s TUoTa F"
Eing-integral=-j^p; r(^+ =)r(\_g) j ^J-^t+f-xJ-^t+f)-’-* at
fs ruora F“
= r (i + q) r (Is - q) JK2_/?_i (^+/2-^)’“21 {t+f)~is-qdt
= /* rft4)r(i+?)£/rg~l v+r-*r'-i v+fy^at
fsy\-s r+sF1 F”
=W^cTl r (^- ?) r (i + ?) JK2_/2r is_?^ at.
Observe that in II. and III. the integrals, except as to the limits, are the same as in
the corresponding formulae for the interior point.
If in the ^-integrals we put t-\-x2— f2 in place of t, and ultimately suppose x inde-
finitely large in comparison with/’ they severally become
f’(<+*5-/i)-i'+#<!’+s',(<+*2)“!"i to=\’~, SrsSi=*ss" —
Jo J 0 I'+^j 1 l2S + tJ
yy+^-pr- <!+i (<+^)-*-^=/^p ,=**- **%!%-*.
and they all four give
Ring-integral ;
. r nsn
■xs + 2q F(i,9 + i)’
which agrees with the value
AYY n(i», *s, is+j, ^5), =~^‘ n(is, is, is+2, oj
when j is indefinitely large.
MDCCCLXXV.
724
PBOFESSOR CAYLEY ON PREPOTENTIALS.
77. We come now to the disk-integral,
£ ys~1dxdy
J {(*-*)* + y»}**+*’
over the circle x2-\-y2=f 2. Writing x=z+g cos<p,y=g sin <p, we have dxdy=% dg d<p,
and the integral therefore is
Jsin®-1 <p dg dQ
— ^ ’
where the integration in regard to g is performed at once, viz. the integral is
=rzyV2?) sins_i $ ^ ’
or multiplying by 2, in order that the integration may be taken only over the semicircle,
y= positive, this is
=fz~q J (?1-22) sin*_1 Q
the term (§'~2i) being taken between the proper limits.
78. Consider first an interior point »<f. As already mentioned, we exclude an
indefinitely small circle radius s, and the limits for q are from § ==s to g>=its value at the
circumference; viz. if here x—f cos#, y=fsxn.O, then we have /"cos Q=z-\-q cos <p,
f sin 0=q sin <p, and consequently
cos 0,
• * / ■ A /Sin ^
sin <p =- sm 6, =
? \/x2+/2— 2xf cos I
1 / /«-* sin"-1 6
\{x2+/2-2x/cosflps+?-1
As regards the second term, this is = — sin®-1 <p (ftp, <p=0 to <p=?r, or, what is the
same thing, we may multiply by 2 and take the integral from <p=0 to <p = ^. Writing-
then sin <p = s/ x, and consequently sins_1 <p (ftp = |#s_1(l — x)-i dx, the term is
gl-2 q
— ~TZTq r(|g4-lp an^ the value °f the disk-integral is
_fs~l C sin5-1 6 d<p e1-2?
_ i — (1J (*9+/2 — 2x/cosS)*s+2-1 | — q F(|s-f£)-
PROFESSOR CAYLEY ON PREPOTENTIALS.
725
Bat we have
and thence
that is
/sin 0 fcosd—x
sin cos<p= ,
/ sin 9 2 7 /(/— x cos'd) d&
tan <p = -/ — i — , sec2 <p d<p =-¥7 7 — 42 ;
r /cos0 — x’ r r (/cosfl — xy ’
d<p =
f(f—x cos
or, what is the same thing,
f{f—x cos Q)dO
-/2 + x2— 2x/cos 0’
M(/2-^) + (/2 + x2-2x/cosfl)} .
/-fx2 — 2x/cos 0
^/s_1 (*”■ sins_I0{(/2— x2) + (/2 + x2-2x/cos (
{/2 + x2 — 2x/cos 0}is+2
ill!? r^ri
i— 1
and the expression for the disk-integral is therefore
i-srJ.
79. Writing as before cos x, sin See., and this is
= (i— 5) (x +/)*+ 2«-2{^+/)2 n^5’ + W) + n(iS’ as> a5 + 2'— 1, M)| — iZTg r(|s+|)*
As a verification observe that if z=0, each of the Il-functions becomes
= | (1 — ®)2 dx, — ;
2,2s-2 z1-2? risris . fi~2i rj-sri
hence the whole first term is= --- . — ps — , viz. this is=^— — rrx2 anc^
complete value is
■~<1
i-q r(is + |)
l ru ,, ri
x 2& 1 2 j f\-2 a 5l-22)
~i-g
vanishing, as it should do, if/=e.
80. In the case of an exterior point %>f the process is somewhat different, but the
M1
result is of a like form. We have
Disk-integral = (g!1-22— g1-2a)sin*-1p d<p,
gi referring to the point M' and to the point M. Attending first to the integral
jy~22 sin4-1 <p d<p, and writing as before/cos 6=z+§ cos cp,f sin Q=g sin <p, this is
rs_ 1 r sin*-^ d<p
_ ■ ' J I X2 +/2 - 2 xf cos 0 }*s+2
5 d 2
726
PROFESSOR CAYLEY ON PREPOTENTIALS.
1 ~ j Csin s_10{(/2 — x2) + (/2 + x2— 2x/ cos
V J (y,2_[_x2 — 2/k cos 0)is+2 ’
the inferior and superior limits being here the values of 5 which correspond to the points
N, A respectively, say $+a, and 0= 0; hence, reversing the sign and interchanging the
two limits, the value of — jV-22sin®-10 d<p is the above integral taken from 0 to a. But
similarly the value of +J^1_2? sins-10 is the same integral taken from a to -k ; and for
the two terms together the value is the same integral from 0 to tt ; viz. we thus find
Disk-integral =xn^J ^ (/> +»»-2/S,cos8)fr+« 1
viz. writing as before cos x &c., and y, this is
= (i — q)(x + /)•+ 22-2{ ~ (x +/)* • iS5 2S + ^ w)+n(is, Is + g-— l)j.
81. As a verification, suppose that z is indefinitely large : we must recur to the last
preceding formula ; the value is thus
. — cos0
viz. this is
f
— (i _ ~g) xs+2g- 1 J ^ sin*~ — cos + [1 — (s+ 2g) cos25] >dt
where the integral of the first term vanishes ; the value is thus
= (l^yx»+2gfo sinS_1 P “ 0 + 2?) cos2^] d6,
where we may multiply by 2 and take the integral from 0 to |. Writing then
sin fi=\/ x, the value is
= (i 4)*s+2gJ0 1 “ O+M1 s) K1 “
1 l(«+2 g)\ _ r^ri \-g
J’-ms+i)' i*+¥
and hence the value is
_/8+I rigTj
viz. this is=^yj*y5_1 dxdy , over the circle x2-\-if=f2, as is easily verified.
82. Reverting to the interior point z < /',
1 1 4- /
where the integral is— (
PROFESSOR CAYLEY ON PREPOTENTIALS.
727
2«-2 A-
7-
g'-22 risrj
=(i-g)(^+/r^{yT^ n^’ **+& w)+n(^, *», fc+j-1, ^)j-r=^r#+|) ;
then reducing the expression in { \ by the transformations for Il(-Js, \ s , tt) and the
like transformations for II(^s, ^5, — 1, u), the term in ^ [ may be expressed in the
four forms : —
2- . (7+*)5+2*-2 int0
r(is+9)r(i-?) f+*~ ^ mt0
21-® r^r2 (/+ x)s+2 g~2 • t
[(l-^n(i+?> is-!, i*+q,£) n(-i+j, \s-i+ 1,
risri (/+»)‘-1(/-»)
into
r(i-g)r(is+§-) /s_22
[n(i-s, is+2, is-g,f) + (i-^)^^1 fc+j-i.
nm (/+«)—(/-«)■-« .
“ r(i«-?)r(i+g) /-!« lnt0
j^n^s— —fi) js— / j+1, — i+£, f — J-
83. The first and fourth of these are susceptible of a reduction which does not appear
to be applicable to the second and third. Consider in general the function
(i -.>)n(«, & l -ft ®)+ ^ n(*-i, g+ 1, -ft v) ;
the second II-function is here
f xa~2(l— x . l—vxfdx ;
viz. this is
=^ZI i1 ~x • 1 x'-'-il-x.l-vxydx,
or, since the first term vanishes between the limits, this is
=^^xa-\(l-x.l-vxy-l(l+v-2vx)dx,
=_£_{(! +<,)]}(«, j3, 1-/3, v)-2v. fV(l-ar.l -vxf~ldx\.
728
PROFESSOR CAYLEY ON PREPOTENTIALS.
that is
=(1— a?a_1(l— x.l — vxy~ldx— 2J vx.X°-~l{\ - x.l—vxf hJx,
=2^ #a-1(l — a+-1(l — vxfdx.
«-l
(i-v)U{u, 3, 1-/3, v)+-j-n{*-l, 3+1, -3, «)=2n(a, 3, -3, «).
We have therefore
(i-p)n (is+q, is, |-2, -i+2>|)
=2Tl++2, i-2, — i+2, ;
and from the same equation written in the form
n(«— 1, 3+1, —3, v)+~j(l—v)n(u, 3, 1-3, v)=2^r-l n(a, 3, —3, v),
we obtain
n^s -g, i+fi', i— S'j j2^+T^r+(l— 2+1, — t+2> f— 2>p)
=2(rglHg?)n(lg-g+1^ -i+^ i-?» /*)•
84. Hence the terms in [ ] are
_ 2=->r*sri (/+*)*+s*-2 i_„ _ij_„ *!\
~ r(i«+g)r(i-ff) ' /s+2*-2 ’n\2 +^2 ^ 2+?,/7’
-r(is-q+mi+g) 7^ AV q+ ’ 2+^’2 q,fV‘
respectively, and the corresponding values of the disk-integral are
Y{§-q)T(\s+q)fl 2!?-n(2S+£, 2 <b .»+&/*)
-r+ri ff-^y-29 tWi , 1 , 1 *a\ e'-2? r+rf
r(i« ,g+i)r(T+ff) W ) • nVs~2+1’ “2+^’ 2_??’/y ~i-< z^FH)’
which we may again verify by writing therein «=0, viz. the Tl-functions thus become
r(j*+g).r(j-y) d r(+-g+i)r(-i+g)
r(++i) r (*.+*)
and consequently the integral is
— _1 r^r2 / gl-2?\
s1-2? r$«r£
■wr(*.+tf
<2\ gi-2? m«r-i
PROFESSOR CATLET ON PEEPOTENTIALS.
729
85. But the forms nevertheless belong to a system of four ; from the formulae
n(a, j3, y, v )
r«r/3 t x
= r7r(a+/B-y) a> v)
= (1— vy~y 11(0, a, a-}-|3— 7, v )
= (l — v)13 yp^a + (8— y)ry n(a+^ — y, y, 0, v ),
writing therein a=^-s+g', 0=-^— y= — 1+g1, we deduce
n(is+^5 \ — q, —\+q, v )
r ( - 1 + gfr (is- 1 + i ) n(-i+^ j+1, t>)
n(|— q, is+q, &—q+ 1, v)
-*+& W, *);
and the last-mentioned values of the disk-integral may thus be written in the four forms:
rd-^rjli+g) /1_2? n(is+^ I-?, -term in s,
-r**r£
r(i+s)r(i*-?+i) ^ 2? n(~2+^ \s-q-\-l, 2 «+2»/*)
W+j) - „ ,
r(i+ff)r(V-ff+i)(^“/) -i+2.W»7*) “ ” ;
and since the last of these is in fact the second of the original forms, it is clear that if
instead of the first we had taken the second of the original forms, we should have
obtained again the same system of four forms.
86. Writing as before x=~ -L — &c., the forms are
° t+J~ — K- ’
nsTi
T{i-q)T^s + q)
■ri*ri
(Z2-*2)1
lP+i-'(t+fa—x*j-*+*'l(t+f *)-*-' dt— term in s,
riK^rtV-g+i)/"1^2-^1-2! r?+? ( t+r-*?T * (*+/2)-^ „
JV*“* (£+/2-*2)-*+i (i5+/3)-is+^1^- „
( #s"? (^-f/2-^2)-Js-2 (^-f/2)“i+? —
r(|-g)r(is+g) J
-ri*r*
r(iS-g+i)r(i+?)
730
PROFESSOR CAYLEY ON PREPOTENTIALS.
87. The third of these possesses a remarkable property: write mf instead of f, and
at the same time change t into m2t, the integral becomes
f(i + q) fs+ 1 £ t~g-*\m2(t-\-f2)—z2\~q+i(t+f2)~is+q-1dt—term. in g ;
and hence writing or m= 1+jj and therefore m2== 1 + 2 |f, the value is
-2+1
m-q)V(ls+g)fS+J0 *"*"*{ t+r-*2+jr(t+f^\ in e.
Hence the term in (f is
=S/into expression /* £
where the factor which multiplies If is, as it should be, the ring-integral ; it in fact
agrees with one of the expressions previously obtained for this integral.
88. Similarly for an exterior point x>f', starting in like manner from, Disk-integral
2«— 2 fs
x ^rr/i n i „ i,
= (X __ g^(x +/)'+*-* 1 ~ n(ia, is, ls+q, w) + n(-l5, Is, ls+g-1, u)
and reducing in like manner, the term in \ } may be expressed in the four forms
' ( *+f)S+2q ~2 into
r(is + ?)T(i-?) ks+2*~2
[-(1-J2)n(i«+ff, i-q, 1 n(ls+g-l, f-g, -i+g,{J)],
9I-. r+i+ (x+/)-+2^-2 .
" m + Q)r(x2s-q)
[— C1— 5)n (*+& *s-*' S)+i~ n(-i+g,is-g+i,is+g-i,Q];
gi-#-.- r jsTj : (x+fY-w.-fy^ {
[-n (i-q, h+q, is-q, £) + (l-g) i^-1 n(*-g, is+q, \s-q, Q],
2J + 1
91- Mr into
rc^“g)r(*+g) U / l J
[-n(ls-?,i+?,i-2,£W(l-f) n(|S-2+l, -1+2, 1-2,5)]-
PEOFESSOE CAYLEY ON PBEPOTENTIALS.
731
89. For the reduction of the first and fourth of these we have to consider
-(l-#)n(«, 0, 1-0, v)+~ n(«-l, 0+1, -0, v);
viz. this is
( — 1+v + l+v)^ x . 1 -vxY~ldx— 2^ vx . xa~\ 1—x. 1 —vxf-'dx,
=2v . . 1 -vxf-'dx,
=2 v . II(a, 3 + 1, — 3+1, v ) ;
that is,
-(i-»)n(«,0,i-0,»)+^n(a-i,0+i, -0,!))=2®n(«,0+i, -0+1, »).
[I repeat for comparison the foregoing equation,
+(1 -V) n(a, 0, 1-0, «)+?=i n(a-l, 0+1, -0, «)=2II(a, 0, -0, V);
by adding and subtracting these we obtain two new formulae] ; for reduction of the
fourth formula the equation may be written
-n(«-i, 0+1, -0, v)+(i-v)£i . n(«, 0, 1-0, ®)=-2 At vn(a, 0+i-0+i, 4
90. But it is sufficient to consider the first formula ; the term in [ ] is
=r|^nh> (^)'+!,'a5 n(*+* *-**+*$,
and the corresponding value of the disk-integral is
rjsrj ++I
which we may again verify by taking therein z indefinitely large ; viz. the value is then
pispj, fs+l
=f(fr+|) «*+ as above. It is the first of a system of four forms, the others of which
are
r+r| ++1
r(i+?)r(+-?+i) *s+2?
,/s+i
■■ r(|s+?)r(|-g') x*+2?
y^+i
~r(is-g + l)r(^ + g')
is+2,~2^5
o-r) ’
And hence, writing as before x=
t+P-K?
t .
&c., the four values are
5 E
MDCCCLXXV.
PROFESSOR CAYLEY ON PREPOTENTIALS.
-T(*.+ff)r(*-?)
— r(*+ff)r(4*-gr+i)
—r(is+g)r.(|-?)
_ TLsri
— r(i«-?+i)r(^+y)
f+1 £ r?-^+/2-^)-^+/2)~|,+?-1^,
^ £J_//-is-?(^/2-^)is-?(^+/2)?-f^
where we may in the integrals write t-\-v?—f2 in place of t, making the limits co , 0 ;
but the actual form is preferable.
91. In the third form for f write mf, at the same time changing t into mt ; the new
value of the disk-integral is
rioru C”
Writing her emf=f-\-hf, that is m=l+j, m3=l+-y, and observing that if —
be positive, the factor (m2(t-\-f2)—x2)~q+‘ vanishes for the value t — at the lower
limit, we see that on this supposition, — 2+i positive, the value is
=rsr+^K) ? " LS’~>{t+f-x2+T ;
viz. the term in ^ is =$/ into the expression
that is into
r(i* + <z)r(i-?)
which is in fact = of into the value of the ring-integral.
92. Comparing for the cases of an interior point %<f and an exterior point %>f, the
four expressions for the disk-integral, it will be noticed that only the third expressions
correspond precisely to each other ; viz. these are : interior point, k <f; the value is
r(i*+?)r(j— q)
(t+f at
e1-2?
\-q r(is-f-g)’
where, if ([ be positive (which is in fact a necessary condition in order to the appli-
cability of the formula), the term in e vanishes, and may therefore be omitted : and
PROFESSOR CAYLEY ON PREPOTENTIALS.
733
exterior point, «>/*; the value is
differing only from the preceding one in the inferior limit z3 —f '2 in place of 0 of the
integral. We have ^ — q positive, and also -^s + g' positive; viz. q may have any value
diminishing from to — the extreme values not admissible.
Annex IV. Examples of Theorem A. — Nos. 93 to 112.
93. It is remarked in the text that in the examples which relate to the s-coordinal
sphere and ellipsoid respectively, we have a quantity 0, a function of the coordinates
(a. . . c, e) of the attracted point ; viz. in the case of the sphere, writing a2 . . . -{-c2=z2,
we have
X2 e2
/2 + <
and in the case of the ellipsoid
= 1,
c*
'¥+6
e*
+ T = 1,
/2 + 6-
the equation having in each case a positive root which is called 3. The properties of
the equation are the same in each case ; but for the sphere, the equation being a quadric
one, can be solved. The equation in fact is
and the positive root is therefore
6=\{e2-\-fc2 —f2 +\/ (e2-}-z2 —f 2)2+ ^e2f2 [ •
Suppose e to gradually diminish and become =0; for an exterior point, x>f, the
value of the radical is =x2—f\ and we have for an interior point, ?-<f the
_j_ K 2
value of the radical, supposing e only indefinitely small, is =/'3 — a3 -fy 2 _ ^ e2, and we
have 3 =-| e2 ^1 4y2 ~l~ , =~J—^ or, what is the same thing, ^ = ^1— viz. the
positive root of the equation continually diminishes with e, and becomes ultimately =0.
If « or e be indefinitely large, then the radical may be taken = e1 + *.2, and we have
0 indefinitely large, =e2-\ -y2.
94. Every thing is the same with the general equation
/2 + <
...+
A2-f 0
= 1
the left-hand side is =0 for 0—zn , and (as 3 decreases) continually increases, becoming
infinite for 3 = 0; there is consequently a single positive value of 3 for which the value
is =1 ; viz. the equation has a single positive root, and 3 is taken to denote this root.
5 e 2
734
PROFESSOR CAYLEY ON PREPOTENTIALS.
In the last-mentioned equation, let e gradually diminish and become =0 ; then for an
exterior point, viz. if
($“ C2 G/2 C2
ja--- +^2>1, the equation • • • +^jTfl = 1
has (as is at once seen) a single positive root, and 0 becomes equal to the positive root
a2 c2
of this equation ; but for an interior point, ot j-2. . . +^<1, the equation just written
down has no positive root, and 0 becomes =0, that is the positive root of the original
equation continually diminishes with e, and for e=0 becomes ultimately =0; its value
• • £2 / £2\
for e small is in fact given by -q— ^1 —p . . . — ^ J . Also a ... c, e or any of them inde-
finitely large, 0 is indefinitely large, =a2 . . . -\-c2-\-e2.
95. We have an interesting geometrical illustration in the case s+l=2; 0 is here
determined by the equation
_?!_ i J!_ _i_ e__!.
#2 ^2
viz. 0 is the squared 2-semiaxis of the ellipsoid, confocal with the conic p-{-p=l, which
■ a? b2
passes through the point ( a , b, e). Taking e=0, the point in question, if p-\-p>l, is a
point in the plane of xy, outside the ellipse, and we have through the point a proper
a2 b 2
confocal ellipsoid, whose squared 2-semiaxis does not vanish ; but if then the
point is within the ellipse, and the only confocal ellipsoid through the point is the
indefinitely thin ellipsoid, squared semiaxes (f2, g2, 0), which in fact coincides with the
ellipse.
96. The positive root 6 of the equation
a2 ^
has certain properties which connect themselves with the function
0, . . 4+A2)-i.
We have (the accents denoting differentiations in regard to 6)
„ e2
r =0
where
Vdl 2 a
J da Q+f2 U’ daT~ J' 0+/2’
T/— C' | g
(/2 + 0)2‘ ' ’ ‘ (A2 + 0)2 ‘
02’
and we have the like formulae for . . . — ,
ac ae
We deduce
PROFESSOR CAYLEY ON PREPOTENTIALS,
and to this we may join, jj being arbitrary,
[ M_2_
•» * _L r! o T I
6 + + J2 da 0 + v) + h9 dc~^~ d -f-r] de J ^9 -\-J9. 6 + >] +F
Again, defining Vt0, Ud as immediately appears, we have
r7 „ A$\2 , (dty 1 ,T, 4
- \da) •••+(&)> -F • 4J’ - J'
and passing to the second differential coefficients, we have
<m 2 8ffl2 4a2J"
^-J'(fl+/2)_J/2(S +/2)3- J,3(0 +/2)2’
+/:
where
J" =— 2
(0 +/2)3 + (0+A2)3+ 03}’
with the like formulae for ... ^4, 44- Joining to these 2g + 1 ~, we obtain
rfe2 de9 ° e de J'0
, rf2fl , <Z20 , 2g + l
D ~ y«?a2 ' • • + dc2+ie2 + e de)’
2 f 1 1 l + (2g + l))
” J'{0+/2--- “i“fl + A2"t" 0 j
8 4P'
-F2(“iJ,')-F (J')’
where the last two terms destroy each other ; and observing that we have
i/_L_
©— 2 \Q+f2- - • ^Q+h9^ 0 )'
the result is
4©'
J'©*
97. First example. y?—d? . . . -fc2, and 0 is the positive root of ^p-Fg-=l.
* V is assumed = j -\-f2)~isdt, where g'+l is positive.
Jd
I do not work the example out ; it corresponds step by step with, and is hardly
more simple than, the next example, which relates to the ellipsoid. The result is
p = 0, if ,x9 , . . -j-z2''*/2,
r(fr + g) ns (-
f-(ri)sr(?+i)/ y
l...+z9\« .
if w\..+zWf:
? 1
( x9...+z9\
| dx . ..dz
l f J
J{(a
—sc)9. . . + (c—
z)9 + e9}^
hence the integral
736
PEOEESSOE CAYLEY ON PEEP OTEN TI A L S .
taken over the sphere x2 . . . -j -z2=f2,
a2 c2 e2
98. Second example. 0 the positive root of . • • +p+g+ y = 1 ’■> #+1 positive.
Consider here the function
V= f F'-'it+f*. . . t+h2)~idt;
this satisfies the prepotential equation. We have in fact
dV_ d6_' fV_ dH , (My
da da ’ da 2 da 2 ® \^« y ’
rf2V ri2V
with the like expressions for ; also
Hence
2q + l d\ 2q + 1 dd
e de M e de’
□ V=-©D^-0'V^
or, substituting for and their values, this is
Moreover V does not become infinite for any values of (a . . .c, e), e not =0 ; and it
vanishes for points at oo ; and not only so, but for indefinitely large values of any of the
coordinates (a. . . e, e) it reduces itself to a numerical multiple of ( a 2. . . + c2+e2)_*s+?;
in fact in this case 0 is indefinitely large, =a2. . . + c2+e2: consequently throughout
the integral t is indefinitely large, and we may therefore write
that is
V=r
The conditions of the theorem are thus satisfied, and we have for § either of the
formulae,
?=
m* + q)
(e2?W)0, g =
~r(jg+g)
2(ri)T(9 + i)
(in the former of them q must be positive; in the latter it is sufficient if <2+1 be
positive).
ROEESSOR CAYLEY ON PREPOTENTIALS.
737
99. We have W the same function of (x . . . z, e) that V is of [a ... c, e) ; viz. writing
for the positive root of
f + l'" +F+A+X = 1’
the value of W is
= f #_?_1(^+/2- • • t + h^dt.
z^
Considering the formula which involves e2?W, — first, if -p . . .+^>1, then when e is
= 0 the value of X is not =0 ; the integral W is therefore finite (not indefinitely large),
and we have e2?W=0, consequently g=0.
xi zi
But if to . . . 1, then when e is indefinitely small, X is also indefinitely small;
/p2 ^2
viz. we then have - = 1 — . . . — the value of W is
w =(/. . . A)-'f t-’-'dt, =(/. .
and hence
r(|g+g) i
e-(ri)<r9-}
r(jg+g)
~(nyT(q+i)
(/.../»)-'( 10...
100. Again, using the formula which involves (e2q+i ; we have here = — 0
or substituting for © and je their values and multiplying by e2q+1, we find
dV
e2q+iyL=2e2q+2Q-'Jl-'Q,
de ’
:2^+2S ? 2 [(y2 + (jp • ■ • + (0+/*- • • 0 + #) K
and therefore
e*q+X de —2e*,+i'A V 2 [(/2 + A)2* • • +(A2 + A)2+A2] 1 (A+/2- • • *•
Hence, writing e=0, first for an exterior point or p. .. X is not =0, and
the expression vanishes in virtue of the factor e2q+2 ; whence also g = 0; next for an
QC^ Z ^ . 6^ 1 / X‘ ^
interior point or j2 - • • +^<1, X is =0, hence also — 2=- ^1— j2. . . —jpj is infinite ;
x 2
and neglecting in comparison with it the terms &c., the value is
2(0 (/-/0-
=2(10,
738 PEOEESSOE CAYLEY ON PEEPOTENTIALS.
and we have as before,
r(i* + g) //> 7iH/i or a?y
e-(ri)*r(S+i) (/• • • 7i) [}~f* ■ ■ ■ -*) •
101. Hence in the formula
V— f §dx. . .dz
J {(a-x)*...+(c-zr+e*}**+9
_ ie ^ 9 ’ ‘
§ has the value just found, or, what is the same thing, we have
[ (-?■
zq\q
J | {a— a?)2. .
. + (c-*)2 + e2ps+2
over ellipsoid • • • +|g=l,
=(rr'(i,+g71) (/• • • 7*)j 'j-'-V+f ■ ■ ■ t+hT'dt.
102. We may in this result write e=0. There are two cases, according as the
a2 c2
attracted point is exterior or interior: if it is exterior, j? . . . +p> 1? $ will denote the
positive root of the equation y2 + g • • • +/^rg = l ; if it be interior,^ • • • +^2 < 1? $ will
be=0 ; and we thus have
1 f h*
dx ... dz
^-x)K.. + {c-zf\^
==^f~(^ + g)1^ (/• • • 70j] ^"?-1(^+/2 • • • t+tf^dt, for exterior point^2 . . . +^>1,
= ~r^ + g)^ (/* ‘ ^2_1(*+/2 • • • t-\-h2)~Ht, for interior point Jg . . . +%< 1 ;
but as regards the value for an interior point it is to be observed that unless g be nega-
tive (between 0 and —1, since 1 + g is positive by hypothesis) the two sides of the
equation will be each of them infinite.
103. Third example. We assume here
where
V= dt I“T
Je
1 = 1
T=rs",(^+/2 . . . t+h2)-\
PROFESSOR CAYLEY ON PREPOTENTIALS.
739
and, as before, 6 is the positive root of the equation
/ >2 /»2 0*2
T — 1 __Z _ — 0
j*+rmm h*+d v — u-
^s-\-q is positive in order that the integral may be finite ; also m is positive.
104. In order to show that V satisfies the prepotential equation □ V = 0, I shall, in
the first place, consider the more general expression,
V=r dt Im T,
Jo+ri
where tj is a constant positive quantity which will be ultimately put =0. The functions
previously called J and 0 will be written J0 and 0O, and J, 0 will now denote
J, =1-,
+ >)+/2"'
cz e *
1 + ij + h~ +
0, =(Q+v)-*-'(0+,+f . . . ;
whence also, subtracting from J the evanescent function J0, we have
say this is
=’(i
+f '.«+*+/
. . . +
6 + n? .6 j-y + Ii2
and we have thence, by former equations and in the present notation,
a dd
d + ri+pda
_ | 6 — — P
2 • • • T A _I_ _j_ J.2 r/„~r A ■ J- T • i ,
S + >i + A2 dc'd + v\ de J0‘
V^=f,
v n
□ 0=
J0'©0 *
In virtue of the equation which determines 0, we have
cl\
^=J
-J"0
*+/
da
and thence
MDCCCLXXV.
4a2
, \ dd i
(“8+1+/V0* |
rffl I
da J
— Jm0
rfa2’
with like expressions for . . .
5 F
740
PROFESSOR CAYLEY ON PREPOTENTIALS.
Also
and hence
2q + ldV r * _
-V *=J„ <BmI
10+ri
2q+l
2,
t
e de
□ V
=f 4-
Je+>i L
2m
l ■ 1 + (2g+
tf+A2’*' t
t +/2
+m(m- 1) I- . 4{^ . . . +^+£}t]
+4mJ «-©(' ? - 4—5 ^_i
/<W\3
0^(G«) ••• + (^c) +(*))
— jm0
cm rfgfl 2g + l
da* ’ ’ ' ' dc*' de*' e del’
105. Writing I', T' for the first derived coefficients of I, T in regard to t, we have
T t “ i
“(*+/*)* ' * * *** (t + h*)^ 22’
and the integral is therefore
~ 2\t+p”’^t+h^ t )■-
£ dt[2mlm-1 T+m(m-l) I”-2 . 4I'T ) .
=r dt( 4m Im~ 1 T' + 4m(m — 1 ) Iw_2 1'T),
= 1 ^4m^(Iro-1T);
= — 4m Jm- 10.
d
Hence, writing (J’B 0 )' instead of ^ (JWi ©), we have
□ V — — 4m Jm-X0
. T / a dd c dQ e dQ\
+4roJ 0(«+,+/ss5---+9+v^s+jt'<*;
viz. this is
-(Jm©)'
— Jm0 D0;
□ V=— 4mJra-10
Jo
-4(J»0)'i
+4J"®I4
PROEESSOR CAYLEY ON PREPOTENTIALS.
741
or, instead of (J“©)', writing J'©+Jm©', this is
□ V=-^^(J’_2P+J)_j^-(0'0t-00'o).
We have here
( i 2 1) fl 21)
J'-2P+J=«2j (fl+,+^*-(fl + ,+/s)(fl+ys) + (T[7^)-- • +e2j(9 + #“(0 + rj)fl + fi5}
=tf-
=jj2 . Q, suppose.
Also ©'©„—©©„' contains the factor jj, is = ??M suppose.
106. Substituting for J, J7— 2P+J, and ©'©0— ©@0' their values 77P, ??Q, and j?M, the
whole result contains the factor nm+\ viz. we have
f t
Kfl+ZW + i+Z*)*
(fl + AW + ’J + ^2)‘
□ V=-
4»jw+1 P”
and if here, except in the term t]m+\ we write q=0, we have
“ 4-e2 -J
2’
u
W+fT'
~(fl + A2)2
a2
(fl+/2)4*'
r‘ 2
. . + £
^(0+A2)4
e _ 1 T w
‘ M ’ — 6^0 >
»-i-« r ®
M=0O0O"-0O'2,
and the formula becomes
□ v= -4^+1 Jo,ni-2|iJo'"0o+ J0'(©o"-^) j ;
or (instead of J0, 0O) using now J, 0 in their original significations,
J=l-
this is
or, what is the same thing,
□ V = - 4ym+1 Jte-2|l J'"0+ J' j,
-A2)2^fl2J
(9 + A2)'
viz. the expression in { } is
— f a? ■ C2 , c2] . xr a« c2 , e2-| f 1
L(0 +/2j4- (fl + A2)4t- fl4J f 2 +y2)2- * ’ "T (fl + A8jS -T g2J |_(fl +^2) 2-
We thus see that q being infinitesimal □ V is infinitesimal of the order t]m+1 ; and hence
jj being =0, we have
□ V=0;
5 p 2
742
PROFESSOR CAYLEY ON PREPOTENTIALS.
viz. the prepotential equation is satisfied by the value
V=C dt lmT,
where m -f- 1 is positive.
107. We have consequently a value of g corresponding to the foregoing value of V
and this value is
____ TQs + g) (c^dW\
S 27rKT(2 + l)\ de ) e=0’
where, writing X for the positive root of
vve have
1—JL- ,
A+/2
--=0,
x + A2 x
W=jJW
we thence obtain
eL=fV-?~(
1
de J* t \
v, £ p/2 ^ P
-l\
\ *+/2
X + /i2 X/ '
multiplying by e2?+1, and substituting for ^
we have
I Im7T'”+0^T2+^/
^ «,*) I1 ' ' X+h2'>'i’
PA2)2+X2j
2g2?+2
X^+2"
( X<1
W+pf"-+^+h^)
where the second term, although containing the evanescent factor
1-
X -) -f~ X -(- Id’ X
is for the present retained.
108. I attend to the second term.
xi £2
1°, Suppose j2...-}-^>l, then as e diminishes and becomes =0, X does not become
zero, but it becomes the positive root of the equation
PROFESSOR CAYLEY ON PREPOTENTIALS.
74;
factor
l1 X+/2"' a + A2 a)’1S-°-
2°. Suppose then as e diminishes to zero, A tends to become =0, but ^
x2 z 2 e2
is finite and =1— — . . — — , whence is indefinitely large; and since -
z2
(a + A2) 5
p-- w * (A+/8)2
becomes =^... +74, which is finite, the denominator may be reduced to and the term
therefore is
x2
— 2 1
■-STT. -ni.-y
which, the other factor being finite, vanishes in virtue of the evanescent factor
l_ &
A +/2 A + A2 A /
Hence the second term always vanishes, and we have ( e being =0)
de
109. Considering first the case ^...+^>1, then as <? diminishes to zero, A does not
become = 0 ; the integral contains no infinite element, and it consequently vanishes in
virtue of the factor e2q+2.
yz _ zz
f2'" l'h2
But if then introducing instead of t the new variable f, =fi, that is
t=%, and writing for shortness,
£ £
R=l-
/2+£
A2 +
the term becomes
=Jrf|. 2m(R-f)—g’(/*+| ...4*+'
where, as regards the limits corresponding to t=cc , we have £=0, and corresponding to
i—'k we have | the positive root of R— £=0. But e is indefinitely small ; except for
indefinitely small values of |, we have
£j, and (>+f. ■**+£)'=(/•• • *)- ;
and if g be indefinitely small, then whether we take the accurate or the reduced
744
PBOEESSOE CAYLEY ON PEEPOTENTIALS.
expressions, the elements are finite, and the corresponding portion of the integral is
indefinitely small. We may consequently reduce as above ; viz. writing now
R=l-
the formula is
/2-. A„
<?<*' • 2m(E -9*-'£t/ . . . h)~\
= — 2m(/. ..h)-' . f « . e(E-|)— ;
Jo
citing the integral becomes =R,?+mf duuq(l—u)m~\ which is
r(i+g)r(m) m m
' r(l + g, + m) ’
that is, we have
and consequently
that is
^d_w=_2(f h).K
r(i+g)r(i+w)
r(l + g + m) ’
r(2s+?) or -p 7A-i f(i +5,)r(i +to)
2(ri)T(l + g) J * T(\+q + m) ’
— ( -f 7A-I r(¥s+g)f(l +m) T?9+>»
? 1/ • • • n) (ri^r^+g+m) 5
viz. g has this value forvalues of ( x...z ) such that butis=0 if ^...-f^>l.
J h J h
110. Multiplying by a constant factor so as to reduce g to the value R?+m, the final
result is
q+m
•~Tf)
■_c (*-£••
J [(a— »)2...H
. ~\2 I
the limits being given by the equation
~2
- .. + -=1
is
if- rfp-'-' - ~7uPt+f’- ■ ■ t+h^’
where 6 is the positive root of
0+/2 e+^2 fl
eo-f..
z\ ?+>»
-p) *•••*
J {{a—xf.
In particular if e=0, or
PEOEESSOK CAYLEY ON PEEPOTENTIALS.
745
there are two cases,
«2
exterior, -,2 .
, ,2
interior, ^ .
is positive root of 1— ^ . . .— -^=0,
‘l J
. + p<l, Q vanishes, viz. the limits in the integral are oo , 0 ;
q must be negative, 1 -\-q positive as before, in order that the ^-integral may not be
infinite in regard to the element £=0.
It is assumed in the proof that m and 1 -\-q are each of them positive ; but, as appears
by the second example, the theorem is true for the extreme value m— 0; it does not,
however, appear that the proof can be extended to include the extreme value q= — 1.
The formula seems, however, to hold good for values of m , q beyond the foregoing limits ;
and it would seem that the only necessary conditions are \s-{-q, 1-f m, and 1 -\-q-\-m,
each of them positive. The theorem is in fact a particular case of the following one,
proved, Annex X. No. 162, viz.
J { (a— a?)2... +
■si *•••*
[c—zY + e2]
j S+q
over the ellipsoid
where <r denotes : assuming <pu=(l — u)q+r‘
J + 1 hz + t t
<r)x)dx,
, we have
<p(<r + (1 — a)x) = (1 — a)q+m(l — x)q+r>
and the theorem is thus proved.
111. Particular cases :
rZ
m= 0
f (l dx...dz
. \_V„ -Z2 (Tj)«r(i + g)rf
’ J[(a-xY- + (c~zY + e2]is+q~ T(is + g) KJ "
h)\ dtt-q-\t+p...t+}f)-K
Cor. In a somewhat similar manner it may be shown that
f X 2 £2\®
(rj)«r(i+g)
P(2S+?)
{{a— a?)2...+ (c— ^r)2 + e2}
Multiply the first by a and subtract the second, we have
SIFT,— •(/■••*) V . . «+*»)-*•
1 — 72 — 12) ifl—x)dx...dz
{(a—xY... + {c—zY + e2Y
or writing q-{- 1 for q, this is
Jr P"- h*.
-Tt\ f> • ^^+/2- • • < + *>
t+r
f X*2 2,2\?+1
{a~x')dx . . dz
j-q-\t+f\..t+V)-h
_lL__(ri)*r(2.+g) (f h)rdf
{(a-xp.. + (c-zY+e*}is+q+1 T&s + q + l) X t+p
and we have similar formulae with (instead of (a— x)) . . . c— z, e in the numerator.
746
PEOFESSOE CAYLEY ON PEEPOTENTIALS.
112. If 77i=l, we have
1 —
f%" h*
dx . . .dz
\[a-xf... +(c-z)* + e‘2}is+«
(rj)T(2+g)
r &+q)
which, differentiated in respect to a, gives the (a— ^formula ; hence conversely, assuming
the a—x, . . .c—z, e formula, we obtain by integration the last preceding formula to a
constant pres, viz. we thereby obtain the multiple integral =C+ right-hand function,
where C is independent of (a ... c, e) ; and by taking these all infinite, observing that
then d—co , the two integrals each vanish, and we obtain C=0.
In particular s= 3, g= — 1, then
Jt
dx dij dz
(a— x)2 + {b— y)‘2+ (c— z)2 + e2j
p *+*’)•*»
which, putting therein e=0, gives the potential of an ellipsoid for the cases of an
exterior point and an interior point respectively.
Annex Y. Green’s Integration of the Prepotential Equation
(*
\ do? ’
P.P 2 g+1 d
' dc2' de2' e
* V:
:0.— Nos. 113 to 128.
113. In the present Annex I in part reproduce Green’s process for the integration of
this equation by means of a series of functions analogous to Laplace’s Functions, and
which may be termed “ Greenians ” (see his Memoir on the Attraction of Ellipsoids,
referred to above) ; each such function gives rise to a Prepotential Integral.
Green shows, by a complicated and difficult piece of general reasoning, that there
exist solutions of the form V =0<p (see post, No. 116), where <p is a function of the s
new variables a, 3 ... y without 6, such that \7(p=zcp, z being a function of Q only ; these
functions <p of the variables a, 3 ... y are in fact the Greenian Functions in question.
The function of the order 0 is <p= 1 ; those of the order 1 are <p=a, <p=/3 . . . <p=y ;
those of the order 2 are <p=a(3, See., and s-functions each of the form
2"{ A a? -fi B32 • • • + Cy2 } + D.
The existence of the functions just referred to other than the s-functions involving the
squares of the variables is obvious enough ; the difficulty first arises in regard to these
s-functions ; and the actual development of them appears to me important by reason of
the light which is thereby thrown upon the general theory. This I accomplish in the
present Annex ; and I determine by Green’s process the corresponding prepotential
integrals. I do not go into the question of the Greenian Functions of orders superior
to the second.
114. I write for greater clearness (a, b . . .c, e ) instead of (a ... c, e) to denote the
series of (s + 1) variables; viz. ( a,b...c ) will denote a series of s variables; corre-
sponding to these we have the semiaxes (f, g .. . h), and the new variables (a, (3 . . . y) ;
PEOFESSOE CATLET ON PEBPOTENTIALS.
747
these last, with the before-mentioned function 8, are the s-j- 1 new variables of the problem ;
and for convenience there is introduced also a quantity g ; viz. we have
d —
h=s/f+d (3,
c=\/h2-\-Q y,
g,
where l=a2+32 . . . +y2+s2.
That is, we have 8 a function of a, b ...<?, e determined by
a2 b2 c~ e2 ..
• • • +a2Ts+I= 1 ’
and then a, (3 ... y are given as functions of the same quantities d,b...c,e by the
equations
2 a- n* b2 2 C2
/2 + 0’ P — ff2+s- ■ • 7 — +
also g, considered as a function of the same quantities, is
Z2 b2 c2
115. Introducing instead of a, b . . . c, e the new variables a, (3 . . . y, 0, the transformed
differential equation is
, d2\ . n dV
40
?X_i_2 — (sA-2a-\-^ ^ ^ \ _i_ w n
</02+^ dd + r .. -/i2 + sJ+vv_u,
where for shortness
VV=W—’-
h2
** • • • -/TTfi 72+!
1 f r-
/+H /2+s
*2-(32...
'id +6 y
2+i
d2Y
7 do.2
d2 Y
tf/32
■ 1 f /2_ 2 _^A2 2 ,
20 rf2V
-y— Z5 — &C.
/2 + 0 .^2 + 0
+/W« {-2?-'2-i» .. . +aqr9)} « ^
U‘S
+?^Fsi_2^-2■“', • • ■ +to)} 1 3
rf/3
MDCCCLXXT,
748
PEOFESSOE CAYLEY ON PEEPOTENTIALS.
Also
dV
e*q+1^-e = —Qi+1e2q+2U—
Jl
_*y y-y
72 + A j \j
V 1 dV
\P + 6 “ da •
+
l (W dV\
+ d y dy A db ,
116. To integrate the equation for Y we assume
V=0<p,
where 0 is a function of 6 only, and <p a function of a, /3 ... y (without 6), such that
V<P=/£<P,
x being a function of 0 only. Assuming that this is possible, the remaining equation to
be satisfied is obviously
Y2© . „ d ©
40
^ +2^{22+2+o(-?54s...+/AJ)}+*©-0-
Solutions of the form in question are
<P=1 , *=0,
C _ o<7_ o.
:a , *=-
p+t
<p=(3 , *= „
V+r” a2+a
o_a0 ;r- ■- 1 i-grr-2 5 ®_l
V * /2 + 0./ + 0 V2+S ' | ^ ^2 + 3'" A2 + 0)’
-u 1 /_ 2y— 2— 6 l •
1 ^ /2+* /+e)
and it can be shown next that there is a solution of the form
<p=|(Aa2+B/32. . . + Cy2)+D.
117. In fact, assuming that this satisfies V<p— ;s<p=0, we must have identically
+^Ti{-prs *‘-F- ■■■■ -]&+}
+4* + #{_ jP P'”— 5,2+1}
Q )
-_A_|
p+n
— s— 2<7— 1 +
* V + 0 ^A2 + 0
+^«{“s_22_1 +7^9--+FT«}
/i2 + 0
/2 + 9 1 g 2
+*{l(Aa2+Bj32... + Cy2) + D [;
PROEESSOB CAYLEY ON PREPOTENTIALS.
749
*
so that from the term in a2 we have
/2 + S
B/2
C/2
>+fl.^+r" /2+s.a2+
r = 0
or, what is the same thing,
A|-22-3-Apj . . ■++*— RT+'O} -b JA . .
with the like equations from /32 . . . y2; and from the constant term we have
r+o
4-B— . . .+^“+-*0=0.
^ o2 + 0 ^A2 + 0
118. Multiplying this last by/2, and adding it to the first, we obtain
a{-22-2 D=o :
fiz. putting for shortness this is
A{2^+2 + Q+M/2 + 5)}+«/2D=0,
B{2^+24-0+|x(/ + 0)}+*/D=O,
and similarly
C|2^+2 + Q+i47i2 +Q)}+^2D=0,
and to these we join the foregoing equation
/2+g+^S • • -+FT0 — «D=0.
Eliminating A, B . . . C, D we have an equation which determines z as a function of Q ;
and the equations then determine the ratios of A, B . . . C, D, so that these quantities
will be given as determinate multiples of an arbitrary quantity M. The equation for *
is in fact
P _L f
(/2 + 0){2? + 2 + O + i«(/2 + 0)l + (/ + 0){2? + 2 + O + i«(/ + 0)} ' '
A2
(A2 + 0){2? + 2+O + i«(A2+0)}
and the values of A, B . . C, D are then
M/2 Mg2
MA2
+1=0
M
2g + 2+O + ix(/2 + 0)’ 2g + 2 + fl + ijc(/ + 0)’ 2g + 2 + 0 + ±x(A2 + <
values which seem to be dependent on d: if they were so, it would be fatal to the success
of the process ; but they are really independent of 0.
119. That they are independent of 0 depends on the theorem that we have
(2g + 2 + O)*0
" 2q + 2-
5 g 2
750
PROFESSOR CAYLEY ON PREPOTENTIALS.
where x0 is a quantity independent of 0 determined by the equation
> + <
lq + 2 + fr o/2 2q + 2 + ±x0g
2 • +
2q + 2 + ±x0h*
+i — o,
(x0 is in fact the value of x on writing 0=0), and that, omitting the arbitrary multiplier,
the values of A, B . . . C, D then are
/2 £2 A2 _1 .
2q + 2 + \x0P' 2q + 2 + \K0g*'> ' ' ' 2g + 2 + i^0A2’ x0 *
or, what is the same thing, the value of <p is
- i/2*2 ■ W , PV . i
2g + 2+^0/2'r2!? + 2+^o5r2* - ■^r2q + 2 + ^P *0*
120. [To explain the ground of the assumption
_(2£+2 + %
/6— 2q+ ’
observe that, assuming
2g+ 2 + 0 + |x(/2 + 8) _ 2f/ + 2+n + ^(/ + 5)
2g' + 2 + ix0/2 — 2g + 2+i?f0/ ’
then multiplying out and reducing, we obtain
i*0(22+2 + <W-f ) + (2ff+2) • 0 ;
viz. the equation divides out by the factor g2—f2, thereby becoming
x0(2q + 2 + Q) - (2$+ 2> + i**o0= 0,
that is, it gives for x the foregoing value : hence clearly, x having this value, we obtain
by symmetry
2?+2+Q+i*[f +0), 2?+2 + Q+ W+«)> • • • 2j+2 + Q+A*(7 f + 6),
proportional to
2^+2 +ix0f, 2q+2+±x0g\ . . . 2q+2+ W>2 ;
viz. the ratios, not only of A : B, but of A : B . . . : C will be independent of 0.]
121. To complete the transformation, starting with the foregoing value of x, we have
so that we have
2?+2+a+Hf +0)=(2?+2+fi) . :
A\2q+2 + iz„f\+*tfT)=0,
B\2q+2+i^f-}+y.^D=0,
Cj22+2+|*tA3»+Vi!D=0,
_A , B_ , C (2g + 2 + OKP
/* + 0"1V + fi ' ’ ‘ + 2g + 2— — U>
PROFESSOR CAYLEY ON PREPOTENTIALS.
751
Substituting for A, B, . . . C their values, this last becomes
JD
2 q + \
XnD
viz. this is
2 0 )
2q + 2 + ik0Q\2q+2 + i*of2~f + 0$ ' ' ' ~ 2q + 2-^0&\2q + 2+^~
-2?+2-i^ {22 + 2 + Q}=0;
■ ■ ■ +{2 ?+1^^-FT8}+22+2+Q=0;
or substituting for O its value, and dividing out by 2^+2, we have
v+0;
°q + 2 + U0f2 ^2q + 2 + ±x0g‘
2 * ’ • + 2j + 2 + ±x0A2 + 1 —
the equation for the determination of z0.
122. The equation for z0 is of the order s; there are consequently s functions of the
form in question, and each of the terms a2, 02, . . . y2 can be expressed as a linear func-
tion of these. It thus appears that any quadric function of a, (3, ... y can be expressed
as a sum of Greenian functions ; viz. the form is
A
+Ba-{-&c.
-{- C«3 -f- &c.
[D,/ l/2*2 - W . . _i_\
^ ^ 2q + 2 + A*0'/2 ^ 2? + 2 + ^ * ' • 2q + 2 + x<)
+D"( „ „ „ )
(s lines),
viz. the terms multiplied by D', D", &c. respectively are those answering to the roots
z0', z", ... of the equation in z0.
The general conclusion is that any rational and integral function of a, 0, ... y can be
expressed as a sum of Greenian functions.
123. We have next to integrate the^ equation
40
^(22+2 +j^rQ+^rQ . . . -zQ= 0.
Suppose z— 0, a particular solution is 0 = 1 ;
72+a
7 + <
. . — 72^^ , a particular solution is — _V/' + ^ . — .
in fact, omitting the constant denominator, or writing 0=v//"+^, ancl therefore
d© l l
~ 2 \//2 + ~~4(/2 + 0)i’
752
PROFESSOR CAYLEY ON PREPOTENTIALS.
the equation to be verified is
(/*H-9)
V/2+e]
' 27+2+/4a+/T9-'
' ’ +A*T"fl]
i j
f 9
9 1
+ V^+9j
!~2^-2 ~/ + 9 • *
• “AM^j
-29
Again, suppose (value belonging to <p=a/3, see No. 116), a parti-
cular solution is ? • in fact omitting the constant factor, or writing
/2+£2...+ A2 ’ ° &
and therefore
®=s/f*+6*/f+6,
21 V/2+0 vy+flf
^2Q -| f y^+fl
+ ■
V/2+<
4( (/2 + 9)i^ *//“+« vV + 9 (^+«)«
the equation to be verified is
a/ + S i 2 V/2 4-9 I
1 (/2 + 9)f'r V^ + fl V^2 + fl (/ + 0)if
-[_ / V/ff2 + 9_|_ V//2 + e\{9f7 I 2-h— — — -1- — 1
+v^ti+~wtq ;h+2+/2+^2+9- - • +>+9/
+ \//2+^\A2-M |/2"+ 9.^ + 0 +^T9 (_2^
2^ 2 ^
z ^*+r
9 '
’• “ A2-^
2/7 2 ^
z p+r-
■•+wTi,
or putting for shortness Q==y2q^-|-^p0 • • • this is
_9_vV±9 , A 's/P + Q I / vV2 + fl | V/'~^V9r/±9_LO\
(/2 + 9)* V/2 + 6 vy + 0 (£2 + 9)* + ^ ;
2 ^ . I . Vff2 + 9 / 0/7 q\ i v!/2'+9/ Otf 2-4- ^ o\ — 0
which is true.
And generally the particular solution is deduced from the value of <p by writing therein
V7¥T9 _ vy+9 vra
V/2+£2 . • • + A2’ V/2 +/...+ A2’ ‘ * ' V/2+/... + A2
in place of a, 0, . . . y respectively : say the value thus obtained is @=H, where H is
what <p becomes by the above substitution.
124. Represent for a moment the equation in 0 by
PROFESSOR CAYLEY ON PREPOTENTIALS.
753
and assume that this is satisfied by Q=H§zd0, then we have
and therefore
"(Sf j,«M+a“*+HS)
+2 Hs)
=0 j
(8«f + 2PH),+4flH|=0;
viz., multiplying by 5, this is
or
^(H’*)+ipH>*=0,
viz. substituting for P its value, this is
Wz Te + h (2#+: 2' • • • + W+e) =l °*
H fc— 03-2
V/2+
and
Hence, integrating,
©=CH
v^+o.^+fl. ..**+*’
Q-v-'dO
C an arbitrary constant,
X arbitrary,
H2 V/2 + 0./ + 0...#J + 0’
where the constants of integration are C, X ; or, what is the same thing, taking T the
same function of t that H is of 6 (viz. T is what <p becomes on writing therein
V/2+*
y .y - + 1
^h^ + t
s/P+tf- • - + ^2 V/2 +/ . . . + X2 V/2+/...+A2’
in place of a, j3, . . . y respectively), then
_nn t q ldt
}e T2 + t .'gWt TJp+i*
where x may be taken =co : we thus have
T7 ^ htt f"
V=@<p = — CH(pJ
Recollecting that
T2 X/f2 + t.C,Z + t...h? + t
so that for 0=co we have a2+b2 . . . +c2+e2=^, the assumption x=co comes to making
V vanish for infinite values of (a, b,...c, e ).
754
PROFESSOR CAYLEY ON PREPOTENTIALS.
125. We have to find the value of § corresponding to the foregoing value of V ; viz.
W being the value of V, on writing therein (x, y,. . .z) in place of (a, b, . . . c), then
(theorem A)
r(j»+g) / t,w\
?- 2(ri)T(j+l)^ it);
Take X the same function of (x, y,. . .z,e) that 6 is of (a, b, . . .c, e), viz. A the positive
root of
. i y I i
/2 + a“^2 + a* • • tA2 + a a-
and (|, 7>i, . „ . r) corresponding to (a, (3, . . . 7, s), viz.
S— ,/.7'o t /3-r T‘--£— jhi , T> T— V^1'
■2T yi ^.2
"t/2 + A~/ + A * ’ * _ A2 + A’
V^+a’ V/+a'.‘ v^2+Y
so that W is the same function of (|, r„...X) that Y is of (a, (3, . . . 0): say this is
t-i-'dt
--CAxf/j^ t2 V/2 + ^./ + ^.“
then we have for § the value
A2 + *’
r(^+g)
e-2(r*)T(j+i)
/i2?2 \ -1 / 1
1 ^dW n dW
/i2 + A / •\/2 + A<= ^•••+/i2 + A^’ J
where e is to be put =0.
126. Suppose e is =0, then if ^+^...+^>1, X is not =0, hut is the positive root
of
- +
/2 + A / + A" A2 + A
P ' f
V
2 ~2 / /v>2 ,,2
rv • • • + =1> r5 —\f 1 — r 'i , 7 TTTTT" * •
/2 + a #2+a A2+a
a?2,?/2
is =0, and we have
f=0, viz. g is =0 for all points outside the ellipsoid + ^ • •+T2=1»
J 9 ' 1
But if then on writing e=0, we have A=0, r*=-
J 9 K ;
0 B(^ + g) . . q+1e-q+2 A / 1 £ dW _i_ 1 dW , ■ 1 9* 9 dW\
^~2^T(q + l)-A A«+1V\/2? € V ^ ^ d? " A=0
- r(i*+g) ^
2^r(g+i)- A • \/2 5 d£ ^ </? ^A=(,’
= -CA0^0.+
2A-?-1
A02/^...A
4>o i
Aofg...h’ W+l’
where term in ( ) is
PEOEESSOE CAYLEY ON PEEPOTENTIALS.
755
Hence
r(js + g) 2CvJ/0 ( e2
5 o„is'
r |2c^o_A2y
27riT(g + 1) ’ A0/<?. . .h \ \)
__-r(^+g) 2C4/0 a» f
2^V(q + 1) 'A 0fy. ..h \ p / " * AV ’
where \J/0, A0 are wliat \|/, A become on writing therein k=0. It will be remembered
that A is what H becomes on changing therein d into X ; hence A0 is what H becomes
Moreover \|/ is what <p becomes on changing therein a, (3 ... 7 into 77 . . . £ : writing
X=0, we have il=g . .. £=|; hence \I/0 is what <J5 becomes on changing therein
a, (3 . . .y into . P. And it is proper in <p to restore the^ original variables by
writing , ■ X — ^ in place of a, fi . . . y.
v72+fl V/+0 V/*2-M /
127. Recapitulating,
V='
qdx . . .dz
\{a-xY... + {c-zY + e^
where, since for the value of V about to be mentioned g vanishes for points outside the
ellipsoid, the integral is to be taken over the ellipsoid
— +— =1
and then (transferring a constant factor) if
T-M+Duf h) H.r ,
v r(is+?) -A.U “fjj T » Vi+/s...(+s*
the corresponding value of § is
where A0 is what H becomes on writing therein ^=0, and \f/0 is what 41 becomes on writing
^ ~ in place of a . . y.
f 'l
128. Thus putting for shortness D.=t~g~1(t-\-f2. . . t + h2)^, we have in the three
several cases ?=1, <P= respectively,
H=l,
<■= (1-f.
y v=
' AV 5 V
H_ Vr+0
V/2...+a2’
^ ( 55
„ )s v=
” - ^
TT V/2 + 9. + S
/2...+A2 ’
f=^( „
„ )«, v=
» - aifcfW+tadt’
MDCCCLXXY.
5 H
756
PROFESSOR CAYLEY ON PREPOTENTIALS.
and for the case last considered
, A2c2
a =__f/!±L_ ■ ' 2^2+9 . i
* 2? + 2 + K/2--'^2g + 2+iJc0/2 *0’
H — i/2(/2 + ^). _| — |#Y*2 + fl) _ J_ ^ me function with. £ for 0,
2? + 2 + ix0/2 ^2g + 2 + iKo/*2 x0’
^0 =
^9 • • • +
2? + 2 + K/2 2q + 2 + ±x0h2 x0’
\r
• • •+;
0 2q + 2 + ±x0P • ' * r2g + 2 + Wi2 *o’
where *0 is the root of the equation 2g + 2^-/2 . • • +2g + 21j_^2 + l=Q,
?= l1-/-! • • -$)**•’ v=flI^r (/- • • w* . . *+*)-*.
Annex YI. Examples of Theorem C. — Nos. 129 to 132.
129. First example relating to the (s-fl) coordinal sphere x2 . . . -\-z2-\-w2=f2.
Assume
TTI M TTIt M . . . .
Y=y... +c»+^)*<->’ v =^” (a constailt)>
these values each satisfy the potential equation.
V' is not infinite for any point outside the surfaces, and for indefinitely large distances
it is of the proper form.
V" is not infinite for any point inside the surface; and at the surface Y'=Y".
The conditions of the theorem are therefore satisfied ; and writing
we have
?rfS
(a-a?) . . . + {c-z)*+ (e-w)2
r(*«-*) (dW> dW"\
z— 4(r \
W'=
M
(a?2...+^2 + w;2)^-i’
w„ M , dW" A
W"=^; hence -^-=0,
&_ z d w d\ M
M ~ V dx • * ' +/ ofe+/ j ...** + le*)*"*
(s-l)j(a?2... + z2 + w2) M
= (z2... +z2 + zv2)is+i ’
where
PBOPESSOB CAYLEY ON PEEPOTENTIALS.
757
which at the surface is =-
(s— 1)M
f* '
Hence
(g-i)r(jg-D.M r(jg+j).M
4(r^)s+i/s
2(r ±y+'f
2(r *)•+*/'
(viz. g is constant).
130. Writing for convenience M=^r^+Iy a constant which may be put =1),
also a2 . . . + c2-f e2=%2, we have and consequently
8/dS
(e— wy\
2 lis~i
=2(r(ir+i)'/ ^ f°r exteri°r p°int *>/»
2(rh!+1/ss/ i , . , . . , -
= 2 x for interior point « </.
i (,2s + 2) /
By making a ... c, e all indefinitely large we find
P/<®=
2(ri)s+i/ss/
r(^+i) 5
viz. the expression on the right-hand side is here the mass of the shell thickness hf.
Taking s= 3 we have the ordinary formulae for the Potential of a uniform spherical
shell.
131. Suppose s=3, but let the surface be the infinite cylinder x2-\-y2—f2. Take here
V'=Mlo g^o2+b2, Y"=M log/,
each satisfying the potential equation ^2+ = 0 ’ hut Y', instead of vanishing, is
infinite at infinity, and the conditions of the theorem are not satisfied ; the Potential of
the cylinder is in fact infinite. But the failure is a mere consequence of the special
value of s, viz. this is such that s— 2, instead of being positive, is =0. Keverting
to the general case of (s-j-1) dimensional space, let the surface be the infinite cylinder
x2 . . . -\-z2=f2 ; and assume
V~(«^..+C2P~ i); Y"=J^ (a constant)>
these satisfy the potential equation ; viz. as regards V', we have
■£+£) v-°>
that
jf-+h)r=o.
dc 2
Y' is not infinite at any point outside the cylinder, and it vanishes at infinity, except
indeed when only the coordinate e is infinite, and its form at infinity is not
=M -p(a2.. . +c2+e2)^"1>.
V" is not infinite for any point within the cylinder ; and at the surface we have V'= V".
5 h 2
758 „
PROFESSOR CAYLEY ON PREPOTENTIALS.
We have
where
r(^-i) /dW dw"\
’~“4(r|)*+I \ da' + da" )•
dW'
da' z
(s 2) (««... +«8)M _(s_2)M dW" n
— at the suriace ; -^-=U,
and therefore
(**+...**)* /<
' (s-2)r(is-i)M
4(ri)s+1/s
(viz. g is constant) ;
or, what is the same thing, writing M = (s— l C’ w^ence S-ty and writing also
a2 . . . + c2=z2, we have
dfdS
(a—x)2 . . . + (c—z)2+ (e— wYY
4(TX)s+lfs-nf 1 . , ^
= (g_2)r4s— i) tf=* for an extenor Pomt ;i>h
4(ri),+]/s-.8/ i ^ x ^
= (s_2)r(l^-i)/^ for interior point *</.
132. This is right; but we can without difficulty bring it to coincide with the result
obtained for the (s-f-l)dimensional sphere with only s— 1 in place of s ; we may in
fact, by a single integration, pass from the cylinder x2 . . . -\-z2=f2 to the s-dimensional
sphere or circle x2 . . . -\-z2f 2, which is the base of this cylinder. Writing first dS=d'%dw,
where (72 refers to the s variables [x ... z) and the sphere x2 . . . -\-z2=f2; or using now
dS in this sense, then in place of the original d&> we have dSdw : and the limits of w
being co , — co , then in place of e—w we may write simply w. This being so, and
putting for shortness (a— x)2 . . . -\-{c — z)2—A 2, the integral is
J-. J (A»+«*)K-
and we have without difficulty
dco
r
i r£r$(«
.. (A*+*d*)1(*“1) A-2 Fi(s-1) •
[To prove it write w— A tan 3, then the integral is in the first place converted into
As_-
coss 3QdO, which, putting cos 6=\/ x and therefore sin Q=*yi— x, becomes
=A f vf-v-'dx,
which has the value in question.]
Hence replacing A by its value we have
AriJ.5-2) C SfdS
F}(s — !) J I (a— x)2. . . + (c-
4^T(i).f-1 8/ f
^)2P(S“2) (s -l)\(a*...+c?fs-2) fs~2
PEOFESSOE CAYLEY ON PEEPOTENTIALS.
759
that is
Ji
SfdS 4%'-sfs~l if ft 1
{a-xY . . . +(c-zY\*s-2)-(s-2)m°-2)\(a*. .. + c*fs~2) 01
1 1
” r is \ (#...+<*)*-*> 01 f~
viz. this is the formula for the sphere with s — 1 instead of s.
Annex YII. Example of Theorem D. — Nos. 133 & 134.
133. The example relates to the (s+l)dimensional sphere x2 . . . -\-z2-\-w2=-f2.
Instead of at once assuming for V a form satisfying the proper conditions as to conti-
nuity, we assume a form with indeterminate coefficients, and make it satisfy the con-
ditions in question. Write
V=— 2 for a2... -\-c2 + e2>f2;
[a? . . . + c2 + e2)2 2 J
=A [a2 . . . +c2-f-<?2)+ B for a2 . . . + c2 + e2 <f2 :
In order that the two values may be equal at the surface, we must have
_pi=A/2+B,
dV
and in order that the derived functions &c. may be equal, we must have
— (s— l)aM
fs
=2A«, &c.
viz. these are all satisfied if only --^-,^=2A.
We have thus the values of A and B, or the exterior potential being as above
M
the value of the interior potential must be
=^fa+t)-(»-i).a8-^8+e8
The corresponding values of W are of course
M M (n , fl «2. . . + 22 + w2)
(*...+•.+-)•* and M(is+ t)-(f-w) 7 }’
and we thence find
^=0 if of ... -\-z" -\-w2
rfr-p , i\> M
§ ~ 4(fi)s+1 ^ 4v2S 2A2S+3/f ys+u — (r^)4'+l /s + 1
if x2 . . . -\-z2-\-w2 <f\
760
PBOEESSOK CAYLEY ON PBEPOTENTIALS,
("pns+i
Assuming for M the value x|y/*+1, the last value becomes § = 1 ; and writing for
shortness ar . . . +c2+e2=;s2, we have
_ (IAp+> .f+i
, for exterior point z>f,
worked out by the theorem ; this is in fact what is done in tridimensional space by
Lejeune-Diriciilet in his Memoir of 1846 above referred to.
Annex VIII. Prepotentials of the Iiomaloids. — Nos. 135 to 137.
135. We have in tridimensional space the series of figures — the plane, the line, the
point; and there is in like manner in (s-j-l)dimensional space a corresponding series
of (s + 1) terms; the (sfi-l)coordinal plane — the line, the point: say these are the
homaloids or homaloidal figures. And (taking the density as uniform, or, what is the
same thing, =1) we may consider the prepotentials of these several figures in regard to
an attracted point, which, for greater simplicity, is taken not to be on the figure.
136. The integral may be written
which still relates to a (s-fl)dimensional space: the (s+1) coordinates of the attracted
point instead of being (a . . . c, e) are (a. .. c, d ... e,u) ; viz. we have the s' coordinates
(a . . . c ), the s— s' coordinates (d. . . e), and the (s+l)th coordinate u : and the integration
is extended over the (s—s') dimensional figure w~ — co to -f-oo,...£= — oo to +oo .
And it is also assumed that q is positive.
It is at once clear that we may reduce the integral to
v=^
{ (a-a?)2...+ (c— ^)2 + M2H-^y2... + ^2}'s+?,
dw ... dt
say for shortness
dw ... dt
(A2 + w2... + *2)ii+?’
where A2, ={a—x'f...Jr{c—zf-\-u2, is a constant as regards the integration, and where
the limits in regard to each of the s — s' variables are — oo , -|-oo .
We may for these variables write . . .r£, where |2. ..-1-^2=1 ; and we then have
PEOFESSOE CAYLEY ON PEEPOTENTIALS.
761
iv2. . .+£2==7’2, div . . . dt=rs~s'~1dr dS, where dS is the element of surface of the (s-s1)-
coordinal unit-sphere £2. . . -j-£2=l. We thus obtain
V=
p rs-s'~ lfo
){A2 + r2ps+s
where the integral in regard to r is taken from 0 to go , and the integral J dS over the
surface of the unit-sphere ; hence by Annex I. the value of this last factor is = \ 2j —f .
The integral represented by the first factor will be finite, provided only \s’ -\-q be positive;
which is the case for any value whatever of s' if only q be positive.
The first factor is an integral such as is considered in Annex II. ; to find its value we
have only to write r= A x, and we thus find it to be
1 n T” xis-^s'~ldx . 1 ^r^(s— + g)
— (A2)^+? 2 Jo (X V1Z,=As'+2?‘ r(is + gr) ’
and we thus have
v L (ra-T&'+g)
v-a,+29. T{¥+q) »
(rp-Tay+g) i #
r(i* + g) \ {a -xf. . . + [c-zf + id p5'* 9
137. As a verification observe that the prepotential equation □ V=0, that is
/ dz ,^1 , i d2 , d* ,2q + l <Ay__n.
\dcd * dc* dd2 ' de2 du2 u du) ’
for a function V which contains only the s'+l variables (a . . .c, u) becomes
. \d2,d2.2q+\ d\y_Q
\dcd ‘ dcz. dud u du) 5
which is satisfied by V a constant multiple of \{a—x)2. .Jr{c—zf-\-id\^~s'~q.
Annex IX. The Gauss-Jacobi Theory of Episplieric Integrals. — No. 138.
138. The formula obtained (Annex IV. No. 110) is proved only for positive values
of m ; but writing therein ^=0, m= — ^ , it becomes
dx ... dz
57
T dt.tr1 (
1 t . ,
_ C2 e\
J \
< t+f
t + fd t)
a formula which is obtainable as a particular case of a more general one
dS
(- ^ -2(r wrdi 1
) \{*Jx...z, w)2f r(i«)J_A — Disct. { (*XN • • • Z, W, T
r)2+^(X2...+z2+w2+T°-)^
762
PBOEESSOB CAYLEY ON PBEPOTENTIALS.
(notation to be presently explained), being a result obtained by Jacobi by a process
which is in fact the extension to any number of variables of that made use of by
Gauss in his Memoir ‘ Determinatio attractionis quam exerceret planeta, &c.’
(1818). I proceed to develop this theory.
139. Jacobi’s process has reference to a class of s- tuple integrals (including some of
those here previously considered) which may be termed “ epispheric ” : viz. considering
the (s+1) variables (x...z,w) connected by the equation x2...-\-z2+w2= 1, or say they are
the coordinates of a point on a (s+l)tuple unit-sphere, then the form is JU^S, where
dS is the element of the surface of the unit-sphere, and U is any function of the 5+1
coordinates : the integral is taken to be of the form { . , ^ — — rr-pu,
and
then
Before going further it is convenient to remark that taking as independent variables the
s coordinates x...z, we have dS=^'x where w stands for + */l —x2...—z2; we must
dw ~
in obtaining the integral take account of the two values of w, and finally extend the
integral to the values of x ... z which satisfy x2. . .+z2< 1.
If, as is ultimately done, in place of x . . .
value of d$ is = 7-? where w now stands for +
we write -
respectively, then the
\/]
xd
72"'
— ~ ; we must in
w ' v /*"’
finding the value of the integral take account of the two values of w, and finally extend
the integral to the values of x
which satisfy^
140. The determination of the integral depends upon formulae for the transformation
of the spherical element <7S, and of the quadric function (x, y . . . z, w, l)2.
First, as regards the spherical element dS ; let the s + 1 variables x, y . . . z, w which
satisfy x2-\-y2 . .. z2-\-w2= 1 be regarded as functions of the s independent variables
then we have
X,
y •
• • *5
w
dx
dy
dz
dw
HP
dQ ’
’ ‘ dP
HQ
dx
dy
dz
d
df’
* * dtf
dtp
dx
dy
dz
dw
w
# *
■ ■
dty
we
effect
on the s+
dQdxp . . . iTv}/, =
d(03 <P *)
d$ d<p . . . d\ p, for shortness.
w) a transformation
x,y
X Y
’T’ T*
Z W
• T> y ’
PEOEESSOE CATLET ON PEEPOTENTIALS.
763
thus introducing for the moment s+2 variables X, Y, . . . Z, W, T, which satisfy iden-
tically X2+Y2 ... +Z2+W2 — T2=0, then considering these as functions of the fore-
going s independent variables 6, <p, ... ip, we have
d S=
l
Ts+1
X, Y ... Z, W
dX dY dZ dW
dd’ d&"‘ dQ
dd dtp ...dip=
1 d(X,Y...Z, W)
T 1 B (3, p ■ • • *)
dd dtp ... d-\r
dX dY dZ d W
d<p ’ d<p ' ’ ' d<p’ d<p
dX dY dZ dW
dif /’ dv[/ " d\J/ d\f/
141. Considering next the s+2 variables X, Y, . . . Z, W, T as linear functions (with
constant terms) of the s+1 new variables or say as linear functions of the
s-}-2 quantities «y, 1, which implies between them a linear relation
«X + 6Y . . . +cZ+dW + eT=l ;
and assuming that we have identically
X2+Y\ . . +Z2+W2-T2=r-H2 • • • +r+*2-l,
so that in consequence of the left-hand side being =0, the right-hand side is also =0;
viz. j] a are connected by
i2+;j2...+r+"2=l:
let dX represent the spherical element belonging to the coordinates a. Con-
sidering these as functions of the foregoing ^independent variables Q, cp, . . . ■ty, we have
d%=
7) . .
.. £
CO
d$
dr,
. dX
dw
dd’
dQ
dw’
ud
d£
dr,
%
dw
dp?
dp
dp’
dp
dk
dr,
dco
dp’
dip
. .
dip’
dip
142. We have in this expression u, each of them a linear function of the
s+2 quantities X, Y, . . . Z, W, T ; the determinant is consequently a linear function of
s -j- 2 like determinants obtained by substituting for the variables any s-J- 1 out of the s-j-2
variables X, Y . . . Z, W, T ; but in virtue of the equation X2-f-Y2 . . . + Z2-f W2— T2=0,
mdccclxxv. 5 i
764
PROFESSOR CAYLEY ON PREPOTENTIALS.
these s-j-2 determinants are proportional to the quantities X, Y . . . Z, W, T respec-
tively, and the determinant thus assumes the form
«X + b Y . . . + cZ + d W + eT .
T
where A is the like determinant with (X, Y, . . . Z, W), and where the coefficients
a,b, . . . c, d, e are precisely those of the linear relation «X-j-&Y . . . +cZ-|-dW-}-eT=l ;
the last-mentioned expression is thus =q? A, or, substituting for A its value, we have
_ 1 d (X, Y . . .Z, W) , ,.
rp ^(j) a. . . j,*) dQd<p...d\ p;
d{&, <P- ■ ■4’,
viz. comparing with the foregoing expression for dS we have
JS=±dX,
which is the requisite formula for the transformation of dS.
148. Consider the integral
{*Jsc, y . . .z,w, l)2}*®’
which, from its containing a single quadric function, may be called “ one-quadric.” Then
effecting the foregoing transformation,
and observing that
x,y..
X Y
T’ T’
Z W
T’ T’
W,1)S=L(*XX, Y...Z,W,T)2,
the integral becomes
4
J)(*XX, Y...Z, W, T)4
where X, Y . . . Z, W, T denote given linear functions (with constant terms) of the s+1
variables q . . . £, &>, or, what is the same thing, given linear functions of the s + 2 quan-
tities g, j? . . . £, 1, such that identically X2-)-Y2. . . 4-Z2ff-W2 — T2=|2 + ^2. . . -f-£2-|-<y2— 1.
We have then £2-|-jj2 . . . 4-£2+£y2— 1 = 0, and d$ as the corresponding spherical
element.
144. We may have X, Y . . . Z, W, T such linear functions of <y, 1 that not
only
X2+Y2 . . . + Z2-|-W2-T2=f -H2 . . . + £2+*,2-l
as above, hut also
(*XX, Y, . . . Z, W, T)2=A£2+1V . . . +C£2+ EW2-L ;
PROFESSOR CAYLEY ON PREPOTENTIALS.
765
j{Ap + Bi)2.. .+C?2 + EW*— l;-'s’
where the s+2 coefficients A, B . . . C, E, L are given by means of the identity
-(fl+A)(*+B) . . . (3+C)(5+E)(3+L)
=Disct.|(#XX, Y . . . Z, W, T)2+ 0(X2+Y2 . . . + Z2+W2-T2)} ;
viz. equating the discriminant to zero, we have an equation in 0, the roots whereof are
—A, — B . . . — C, — E, — L.
The integral is
j*T
which is of the form
(A-L)£2 + (B-L>,2. .. +(C— L)£2 + (E — L>2ps’
dt
' f. ^ ,
J {a^ + brf. . . +c?2 + ew2}2
where I provisionally assume that a,b ... c,e are all positive.
145. To transform this, in place of the s-fl variables f, q . . . a connected by
£2+?72 . . . +£24-‘*>2=l, we introduce the s+1 variables x,y . . ,z,w such that
9 9
t==KWc.
where
and consequently
g2=a|2+5jj2 . . . +c%2-\-ew2,
X2+y2... -\-Z2 + W2 = l.
Hence writing d$ to denote the spherical element corresponding to the point
(x,y...z, w), we have by a former formula
^S= — Ml \/7j .. .$\/c,us/e) d6 d ^ d,
f+1
( ab .. . ce ■)*
dt
or, what is the same thing,
{a^ + br?... +c^2 + ecu2 }2<s+1) (ab...ce) 4
dS.
Hence integrating each side, and observing that J dS, taken over the whole spherical
surface x2-\-y 2. . . -{-z2 -\-w2=l, is =2(r^)s+1 -rT(^-s-f-^-), we have
Ji
Kny
a^ + br)*. . .c?2 + m2p(s+1)“T(is + i) * (ab . . . cef
5 I 2
766
PROFESSOR CATLET ON PREPOTENTIALS.
146. For a,b...c,e write herein a + 6, b + Q . . . c+5, e-\-6 respectively, and multi-
plying each side by Q2~\ where q is any positive integer or fractional number less than
% s , integrate from 5=0 to 5=oo . On the left-hand side, attending to the relation
|2+^3. . . -]-£2+02=l, the integral in regard to 5 is
r* dt
Jo ^2+0p+1)’
where g2, =a^2-{-bif . . . -j-c£2-j-ea2, as before is independent of 5; the value of the
definite integral is
__r(K* + l)-g)r(0) 1
r±o+i) gs+1-22’
which, replacing by its value and multiplying by dS, and prefixing the integral sign,
gives the left-hand side ; hence forming the equation and dividing by a numerical factor,
we have
+ c£2 + eco2)-
o/Tu.y+i p00
= r^r4(s + 1 ) - q 1 o . . . t+c .
and in particular if q— — then
dl, _2(ri)s
+ct? + eWfs~ I>
( dt. . . . t-\-c. t-\-e)~\
or, if for a ... c, e we restore the values A— L. . . C — L, E— L, then
C d s
J(A02...+C?
f "■ ^+A-L • ■ • *+c-L • ‘+E-in
f dt ■ ("+A • • • i+C . <+E . t+ L)-» ;
viz. we thus have
^w-=2-W' Ldt(t+A ■■■t+c- (+E • <+L^
where t-\- A . . . t-\-C . tf-j-E .£+L is in fact a given rational and integral function of t ;
viz. it is
= -Disct.{(*XX . . . Z, W, Tf+t(X\ . . +Z2+ W2-T2)}.
147. Consider in particular the integral
dS
here
{' diS _
J { (a- faY ...+ ( c-hzy + ( e - kwy + Z2 ps ’
(*JX . . . Z, W, T)2-K(X2. . . + Z2+W2-T2)
= («T-/X)2. . . +(cT-hZy+(eT-my+l2T2
+t(X2. . . +Z2+W2-T2)
:(/2-K)X2. . . +(h*+t)Z2+(Z?+t)W2+(a\ . . +c2+e2+l2-t) T2
— 2«/XT . . . 2<?AZT-2^WT;
PEOFESSOE CAYLEY ON PEEPOTENTI ALS .
767
viz. the discriminant taken negatively is
I *+/»... ,-af
fj -|— 7&2, — ch
— af ... — ch —(a2. . . +c2+e2+l2)+t
which is
— t -\~f " . . . . t-\-Jc2 ^ t — (l2 . . . — C2 — 6 2 — h
+
a9P
t+p"
cVi2 e2F \
't + hZ + l + k*)’
-t . ( t+f 2 . . . t+h 2 . t+k2)
=7+A...7-|-C.7+E.7+L,
and consequently - A . . . — C, — E, — L are the roots of the equation
t+p ••• Z-M9 Z+F Z“ ■
148. The roots are all real ; moreover there is one and only one positive root. Hence
taking — L to be the positive root, we have A . . . C, E, — L all positive ; and therefore
a fortiori A— L, . . . C — L, E— L all positive, which agrees with a foregoing provisional
assumption. Or, writing for greater convenience 6 to denote the positive quantity — L,
that is taking 6 to be the positive root of the equation
have
a9 c2 e2 Z2 „
i~6+P ’ ' ' — $ + It 1 ~ f+¥~ 0 — U’
f',„_ dS
J +(c — hzf-\-(e — kwf + l^\2S
=38*0 -
\J t • t+P- •■t+h?.t+k'i( 1 — f+p • • • “
Z + A2 t + & t
y
or, what is the same thing, we have
AH
dx ... dz
f • • -h J +w{(a— xf . . . +(c— ^)2 + (e + /cw)2 + Z2}5
* (1_^ • • ■ -rh-fi-i) A* • t+r. . .t+v. <+m
where on the left-hand side w now denotes
. . a?2 ^2 ,
tion is j:2 . . .
149. Suppose 7=0, then if
aA f a • • •
and the limiting e^ua-
768
PROFESS OE CAYLEY ON PREPOTENTIALS.
the equation
i_ _ 6 __ e n
0+/2'-- 0 + A2 0+F
has a positive root differing from zero, which may be represented by the same letter 0 ;
but if
«2 c2 e2 1
/2 • • ' + A2 + A*<1»
then the positive root of the original equation becomes =0; viz. as l gradually dimi-
nishes to zero the positive root d also diminishes, and becomes ultimately zero.
Hence writing 1=0, we have
dS
{{a-fxf. . . +{c-hzf + (e-kwy}i*
or, what is the same thing,
dx . . .dz
™s-
+ w{(a— <r)2. . . +(c— z)z+(e + Aw)2}2®
wr.<
dt 1-
Q now denoting the positive root of the equation
q/ l gl
1~Q+p‘ • • “0 + F- 0 + F=0,
t+li1 . t+Tc2)^,
^•••+^+F>lor<l.
a2 e2
In the case • +^<1? the inferior limit being then 0, this is in fact Jacobi’s
theorem (Crelle, t. xii. p. 69, 1834) ; but Jacobi does not consider the general case where
l is not =0, nor does he give explicitly the formula in the other case
n a2 , c2 e2
1=0, . . . +A2+Ii>-L-
A2 1 A2'
150. Suppose Jc= 0, e being in the first instance not =0, then the former alternative
holds good ; and observing, in regard to the form which contains +w in the denomi-
nator, that we can now take account of the two values by simply multiplying by 2, we
have
dS 2 C dx ... dz
I {{a-fxf.. . + (c-hzf + e*\is’ /.../il|M2... + M2 + «sF!
(w on the right-hand side denoting 'y/i—^3 ... —p, and the limiting equation being
a?2 z 2
j2 • . • + p=l), each
PROFESSOR CAYLEY ON PREPOTENTIALS.
769
'<-(*+/’•• -«+m
w C * c • •
where 0 is here the positive root of the equation 1—f^p • • • ~f^p~ y=0, which is the
formula referred to at the beginning of the present Annex. We may in the formula
write 0=0, thus obtaining; the theorem under two different forms for the cases
p • • • > 1 and < 1 respectively.
Annex X. Methods of Lejeune-Dirichlet and Boole. — Nos. 151 to 162.
151. The notion that the density § is a discontinuous function vanishing for points
outside the attracting mass has been made use of in a different manner by Lejeune-
Dirichlet (1839) and Boole (1857) : viz. supposing that g has a given value f{x .. . z )
within a given closed surface S and is =0 outside the surface, these geometers in the
expression of a potential or prepotential integral replace g by a definite integral which
possesses the discontinuity in question, viz. it is =f{x . . . z) for points inside the surface
and =0 for points outside the surface ; and then in the potential or prepotential integral
they extend the integration over the whole of infinite space, thus getting rid of the
equation of the surface as a limiting equation for the multiple integral.
152. Lejeune-Dirichlet’s paper “ Sur une nouvelle methode pour la determination
des integrates multiples ” is published in ‘ Comptes Rendus,’ t. viii. pp. 155-160 (1839),
and Liouv. t. iv. pp. 164-168 (same year). The process is applied to the form
1 d dxdydz
da}{ (a-x)* + {b-yf+ (c-*)*}**-”
over the ellipsoid ^+^+^2=1 ; but it would be equally applicable to the triple inte-
gral itself, or say to the s-tuple integral
C dx . . .dz
or, indeed, to
(c-*y
dx ... dz
{ {a— x)2 . . . + (c— z)2 + e2l
li»+s
over the ellipsoid jr2 . . . +p=l ; but it may be as well to attend to the first form,
more resembling that considered by the author.
153 . Since z. 1 cos \<p dq> is =1 or 0, according as X is < 1 or > 1, it follows that
^ 0 T
the integral is equal to the real part of the following expression,
*J0 ^ 9 ) Ua-x)*...
\{a-x)z. . . +(c - s)2?
770
PKOPESSOB CAYLEY ON PEEPOTENTIALS.
where the integrations in regard to x ... z are .now to be extended from —go to + co for
each variable, A further transformation is necessary : since
1 l
-=Yre~r7!i j d-Aj . 1 e"*, a positive and r positive and <1,
writing herein (a—x)2 . . .-\-(c—zf for <r, and \s-\-q for r, we have
.. •■■ ■ 1 1 rlxl
and the value is thus
O
g-Qs+q)
J dx... dz ,
nT^sH-g)
where the integral in regard to the variables (x . . . z) is
=#«*- +^jdx^ (++^>+3a**i- . . . j dzA o+ty-wi ;
=eliV£
-e f^+v,
f*t+9
and the like for the other integrals up to the 2-integral. The resulting value is thus
sin <p
‘7lT(^S + 9') 1
d-Aj ■As+2_1 e^4G+/^','+p+fc2'/') — ,
+/**... ?+***’
which, putting therein 4'=^, ^ dt, is
eft
/-2-1
s/p + t...h* + t J0
j e^^f2+t ' ’ ’ +*‘+t) sin i p . <jd2_1 <7<p.
’ n
154. But we have to consider only the real part of this expression; viz. writing for
a' 2 c2
shortness a=j^~t . . . we require the real part of
e~iq” J eicr<f . <p2_1 sin <p dcp.
Writing here for sin © its exponential value^-. (ei<p —e i<p ), and using the formula
e~qni j d<p . <pq~l . (o- positive),
and the like one
elni jo d(P • <P2-1 ^ (<r negative)
(in which formulse q must be positive and less than 1), we see that the real part in
question is =0, or is
Tg sin (g + l)7r 7r 1
2(1— (r)* 5 ~2Y(\—q) (1 — tr)«’
according as cr > 1 or <r < 1.
PROFESSOR CAYLEY ON PREPOTENTIALS.
771
155. If the point is interior, . . . 4-^< 1, and consequently also a< 1, and the value,
writing (T-^)2 instead of 7 r, is
=r'(is+})r(i-}) (/• • • 0 • (i-Ar---A<) •
^2 ^»2
But if the point be exterior, -p. • • • + ^> 1, an<^ lienee, writing 0 for the positive root
a2 c2
of the equation, <r=l ; viz. 0 is the positive root of the equation • • + ^2qr§—l> ^ien
£=0, a is greater than 1, and continues so as t increases, until, for t=6, <r becomes =1,
and for larger values of t we have <r < 1 ; and the expression thus is
(nr
r(Wg)r(i
h* + t
dt . . . t+h*)-i (1
viz. the two expressions in the cases of an interior point and an exterior point respec-
tively give the value of the integral
dx...dz
{{a-x)*...+{c-z)*}is+q
This is in fact the formula of Annex IV. No. 110, writing therein e=0 and m=—q.
156. Boole’s researches are contained in two memoirs dated 1846, “On the Analysis
of Discontinuous Functions,” Trans. Boyal Irish Academy, vol. xxi. (1848), pp. 124-139,
and “ On a certain Multiple Definite Integral,” do. pp. 140-150 (the particular theorem
about to be referred to is stated in the postscript of this memoir), and in the memoir
“ On the Comparison of Transcendents, with certain applications to the theory of
Definite Integrals,” Phil. Trans, vol. 147, for 1857, pp. 745-803, the theorem being the
third example, p. 794. The method is similar to that of, and was in fact suggested by,
Lejeune-Dirichlet ; the auxiliary theorem made use of in the memoir of 1857 for the
representation of the discontinuity being
f(x)
t
j J da dvds cos\(a—x—ts)v-\-\i7r\visi lf{a),
which is a deduction from Fourier’s theorem.
Changing the notation (and in particular writing s and for his n and i) the
method is here applied to the determination of the s-tuple integral
'=^dx...
n
( X 2 ^2\
(where <p is an arbitrary function) over the ellipsoid
157. The process is as follows : we have
<p(/2- + p) !
•••+A2— 1-
{ (a-Xf...+ (c-z)* + e2\*s+l1 (is + q)
T
du dv dTvis+qtis+q~l
cos^u-^...~-r((a-x)\..+(c-z)2+6?)v)+i(is+q)7rj(pu;
5 E
MDCCCLXXV.
PROFESSOR CAYLEY ON PREPOTENTIALS.
ATI
viz. the right-hand side is here equal to the left-hand side or is =0, according as
. . . — |— < 1 or >1. V is consequently obtained by multiplying the right-hand side by
j 'l
dx . . . dz and integrating from — oo to -fco for each variable.
Hence, changing the order of the integration,
V :
' orVIL
irT^s + q)
r
du dv dr vls+qrls+q lQu . O,
where
Now
if
Q=J&...*cos|^m— e\— yt+T((a— *)*■•■+(«— *),})»+2(i«+2)*|-
fi+<a-«y=i*£z r + ^ ... r+T^,
&—X— f*Ta
% 1+/V
j, n h\c
...
158. Substituting, and integrating with respect to £ ... £ between the limits — oo , -f oo
we have
(/. ..h)t0S (/ 2 ^ C2T \ I 1 )
Q=(i+7^..:i +^)V- C0Sir~^T~n7V --r+v;) b+M :
or, what is the same thing, writing i in place of r, this is
n (f...h)-jfist* U a2 c2 e2\ . i )
Q=t/4<...tf+qw-c” {\u-rTr-wTrj)v+^\’
that is, writing
have
a1 c _i_e
a~fr+t"^w+i^rT
v=T®j,.,n>**
or, writing 7rs_1=I (F^)s, this is
TT
— f dt ■ f dudv . fl?cos{(%— <r)v-\-\qr\<pu
AVSS + 99 Jo Vjo Jo
159. Boole writes
du dv dqcos\(u— (?)v-\-\q7r\<$>u= <p(<r) ;
viz, starting from Foukiek’s theorem,
^ du dv cos(w — <r)v . <pw=<p(<r)
(where <p(c ) is regarded as vanishing except when <j is between the limits 0, 1, and the
limits of u are taken to be 1, 0 accordingly), then, according to an admissible theory of
m;
t~q~lvq cos{{u— <r)v + ^q7r}<pu .
PROFESSOR CAYLEY ON PREPOTENTIALS.
773
general differentiation, we have the result in question. He has in the formula - instead
of my t ; and he proceeds, “ Here <r increases continually with s. As s varies from 0 to oo ,
<t also varies from 0 to oo . To any positive limits of <r will correspond positive limits
of s ; and these, as will hereafter appear [refers to his note B], will in certain cases replace
the limits 0 and oo in the expression for V.”
160. It seems better to deal with the result in the following manner, as in part shown
p. 803 of Boole’s memoir. Writing the integral in the form
V = (^1 + J dudt dv . vq cos|(m—
effect the integration in regard to v ; viz. according as u is greater or less than <r, then
f" 7 „ \ . i i r(<7 + 1) sin {q-\-\)n n
l dv . pgcos{(M— <7)v-\-\qr\=— .q+1 — — , or 0,
Jo \U G" )
and consequently, writing for a its value,
7 r
= r(-g)(W-<r)^1
, or 0 ;
P + t'" h* + t t' ®U’
or 0 as above k
Y==r(-;)r»+g)j’J, du dt
161. To further explain this, consider t as an ^-coordinate and was a ^-coordinate;
«=. “ .. .4-— L
J P+x
for positive values of x, this is a mere hyperbolic branch, as shown in the figure, viz.
#=0, y=co ; and as x continually increases to oo , y continually decreases to zero.
The limits are originally taken to be from u=0 to u— 1 and £=0 to £=oo , viz. over
the infinite strip bounded by the lines £0, 01, 11 ; but within these limits the function
under the integral sign is to be replaced by zero whenever the values u, t are such that
«2 c2 e2
u is less than viz. when the values belong to a point in the shaded
774
PROFESSOR CAT LEY ON PREPOTENTIALS.
portion of the strip ; the integral is therefore to be extended only over the unshaded
portion of the strip ; viz. the value is
v- ffW-.ft)
T(-q)T(is + q)
dll dt .
the double integral being taken over the unshaded portion of the strip ; or, what is the
same thing, the integral in regard to u is to be taken from u — (saY
r+t
from u—g ) to u— 1, and then the integral in regard to t is to be taken from t=d to
t— oo, where, as before, 0 is the positive root of the equation <7=1, that is of
rp P (P
P+Q ^A*+r Q
162. Write u=G-j-(l — g)x, and therefore u— <r=(l — g)x, 1— u—(l — <r)(l — x) and
du=(l — a)dx\ then the limits (1, 0) of x correspond to the limits (1, g) of u, and the
formula becomes
Y=r(?;)rar+g)r^- f'V+f’-t+vrK <>{H-(l-r>
where a is retained in place of its value ~ — . .. + 4^+t- This in a form
J z ~rt tlz 4 * t
(deduced from Boole’s result in the memoir of 1846) given by me, Cambridge and
Dublin Mathematical Journal, vol. ii. (1847), p. 219.
If in particular <pu=(l— u)q+m, then <p{cr+(l— <r)#}=(l — G)q+m(l— x)q+m, and thence
f x~q~l {<pff + (l— G)x}dx—{1— G)m( x~q~\l—x)q+r
Jo Jo
r(-g)r(i+g+w)
~ r(i+?w)
and thence restoring; for g its value, we have
ndx.
fi °)m >
• *^-(*+/*...*+v)-(i -j,
-\-t
h2+t t
( a?2 ziy+m
V-p-'-w) dx-dz
\(a-x)*... + {c-z)* + e*\is+q
. This is in fact the thee
its general form ; but the proof assumes that q is positive.
over the ellipsoid A.„.-j-£_=l. This is in fact the theorem of Annex IV . No. 110 in
J h
INDEX
TO THE
PHILOSOPHICAL TRANSACTIONS
FOR THE YEAR 1875.
A.
Abel (F. A.) and Noble (Capt.) (see Noble).
Allman (G. J.). On the Structure and Development of Myriothela, 549. — General description, 549 ;
anatomy, 551 ; the gonosome, 557 ; development, 559 ; general remarks, 567 ; explanation of the
plates, 572.
Armagh Observatory , reduction of anemograms taken at, 403.
B.
Bessel’s determination of the law of a periodic phenomenon (see Chambers).
Brain, localization of functions of/ 433 (see Ferrier).
C.
Cayley (A.). On Prepotentials, 675.
Cephalopoda, development of, 38 (see Lankester).
Chambers (C. and F.). On the Mathematical Expression of Observations of Complex Periodical Phe-
nomena ; and on Planetary Influence on the Earth’s Magnetism, 361. — Application of the processes
to determine whether there are any periodic variations of magnetic disturbances corresponding to the
orbital or synodic periods of certain planets, 379; appendix, demonstrations of certain formulae,
394 ; specimen calculation of Bessel’s coefficients, 400.
Contraction of slags in cooling, 205.
Crook.es (W.). On Repulsion resulting from Radiation. — Part II., 519 (for contents see p. 519).
Croonian Lecture, 433 (see Ferrier).
MDCCCLXXV. 5 L
776
INDEX.
D.
Development of ovum in mollusca, 1; of teeth in Newt &c., 285; in Ophidia, 297.
E.
Egg, development of, in mollusca, 1 (see Lankester).
Elliptic functions, 489 (see Glaisher).
F.
Ferrier (D). The Croonian Lecture. Experiments on the Brain of Monkeys (Second Series), 433.
— Extirpation of the frontal lobes, 433 ; destruction of motor areas — regions of the fissure of
Rolando, 441 ; experiments relating to the localization of sensory perception — destruction of the
angular gyrus, 445 ; effects of lesions of the temporo-sphenoidal lobe, 451 ; destruction of the
optic thalamus, 472 ; destruction of the occipital lobes, 475 ; conjoint removal of frontal and occi-
pital lobes, 484 ; conclusions, 487.
G.
Gallapagos Islands, tortoises of, 259 (see Gunther).
Glaisher (J. W. L.). On a Class of Identical Relations in the Theory of Elliptic Functions, 489.
Gunpowder, researches on fired, 49.
Gunther (A.). Description of the Living and Extinct Races of Gigantic Land-Tortoises. — Parts I.
and II. Introduction, and the Tortoises of the Gallapagos Islands, 251. — Introduction, 251;
description of the Gallapagos tortoises, 259 ; explanation of the plates, 282.
H.
Haughton (S.). On the Tides of the Arctic Seas, 317. — Part IV. On the Tides of Northumberland
Sound, at the Northern Outlet of Wellington Channel, 317 ; Part Y. On the Tides of Refuge
Cove, Wellington Channel, 331 ; Part VI. Tides of Port Kennedy, in Bellot Strait, 339.
Hennessey (J. B. N.). On the Atmospheric Lines of the Solar Spectrum, illustrated by a Map drawn
on the same scale as that adopted by Kirchhoff, 157.
K.
Klein (E.). Researches on the Smallpox of Sheep, 215 (for contents see p. 215).
L.
Lankester (E. Ray) . Contributions to the Developmental History of the Mollusca, 1. — Of Pisidium, 1 ;
Aplysia, 13 ; Tergipes, Polycera, Tethys, Neritina, Limax, and Limnceus, 28 ; general considerations,
32 ; the ovarian egg of Loligo and Sepia, 38 ; explanation of plates 1 to 4, 12 ; 5 to 10, 36 ;
11 & 12, 46.
Lassell (W). On Polishing the Spectra of Reflecting Telescopes, 303.
Lockyer (J. N.) and Seabroke (G. M.). Spectroscopic Observations of the Sun, 577.
INDEX.
777
M.
Magnetism, planetary influence on the earth’s, 379 (see Chambers).
, terrestrial, 161 (see Sabine).
Mallet (R.) . Addition to the paper “ On Volcanic Energy : an attempt to develop its true Origin and
Cosmical Relations/5 205.
Mollusca, developmental history of, 1 (see Lankester) .
Myriothela, structure and development of, 549 (see Allman).
N.
Noble (Capt.) and Abel (F. A.). Researches on Explosives — Fired Gunpowder, 49 (for contents see
p. 49).
0.
Ophidia, structure and development of teeth in, 297.
P.
Periodical phenomena, disentanglement of simple, in observations of complex, 361 (see Chambers).
Planets, influence of, on the earth’s magnetism, 379 (see Chambers).
Potentials, a generalization of, 675 (see Cayley).
Prepotentials, 675 (see Cayley).
Prestwich (J.) . Tables of Temperatures of the Sea at different Depths below the Surface, reduced and
collated from the various observations made between the years 1749 and 1868, discussed, 587 (for
contents see p. 587) .
R.
Radiation, repulsion resulting from, 519 (see Crookes).
Robinson (T. R.). Reduction of Anemograms taken at the Armagh Observatory in the years 1857-63,
403.
S.
Sabine (Sir E.). Contributions to Terrestrial Magnetism. — No. XIV., 161.
Sea-temperatures at different depths, 587 (see Prestwich).
Seabroke (G. M.) and Lockyer (J. N.) (see Lockyer).
Smallpox of sheep, 215 (see Klein).
Spectrum, solar, as affected by terrestrial absorption, 157.
Sprengel pump, improvements in, 519.
Sun, spectroscopic observations of the, 577.
778
INDEX.
T.
Teeth, development of, in Newt &c., 285 ; in Opliidia, 297 (see Tomes).
Telescopes, on polishing the specula of reflecting, 303 (see Lassell).
Tides of the Arctic Seas, 317 (see Haughton).
Tomes (C. S.). On the Development of the Teeth of the Newt, Erog, Slowworm, and Green Lizard, 285.
On the Structure and Development of the Teeth of Ophidia, 297.
Tortoises, gigantic land-, 251 (see Gunther).
Volcanic energy, 205 (see Mallet).
V.
w.
Wind, reduction of observations of, at Armagh, 403.
(/Vw & tyt
0 0 ~s
LONDON:
PEINTED BY TAYLOE AND FEANCIS, EED LION COUET, FLEET STEEET.
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Phil. Tram. 1875. Plate 53.
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MERCURY VENUS. . THE EARTH
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TEMPERATURE -SECTIONS in the INDIAN and SOUTHERN OCEANS
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