PHILOSOPHICAL

TRANSACTIONS

OF THE

ROYAL SOCIETY

OF

LONDON.

FOR THE YEAR MDCCCXXXV.

PART I.

LONDON:

PRINTED BY RICHARD TAYLOR, RED LION COURT, FLEET STREET.

MDCCCXXXV.

Q
41
Ls

CONTENTS.

I. The Bakerian Lecture. — On the Proofs of a gradual Rising of the Land in certain

parts of Sweden. By Charles Lyell, Jun. Esq. F.R.S page 1

II. Note on the Electrical Relations of certain Metals and Metalliferous Minerals.

By R. W. Fox. Communicated by Davie s Gilbert, Esq. F.R.S. ... 39

III. Experimental Researches in Electricity. — Ninth Series. By Michael Faraday,

D.C.L. F.R.S. Fullerian Prof. Chem. Royal Institution, Corr. Memh. Royal
and Imp. Acadd. of Sciences, Paris, Petershurgh, Florence, Copenhagen, Ber-
lin, 8^c 41

IV. On the Determination of the Terms in the Disturbing Function of the fourth order

as regards the Eccentricities and Inclinations which give rise to Secular Inequa-
lities. By J. W. Lubbock, f^.P. and Treas. R.S 57

V. On the Results of Tide Observations made in June 1834 at the Coast Guard Sta-

tions in Great Britain and Ireland. By the Rev. William Whewell, F.R.S.
Fellow of Trinity College, Cambridge 83

VI. On certain Peculiarities in the Double Refraction and Absorption of Light exhi-

bited in the Oxalate of Chromium and Potash. By Sir David Brewster,
K.H. LL.D. F.R.S .91

VII. Second Essay on a General Method in Dynamics. By William Rowan Hamil-

ton, Member of several Scientific Societies in Great Britain and in Foreign
Countries, Andrews Professor of Astronomy in the University of Dublin, and
Royal Astronomer of Ireland. Communicated by Captain Beaufort, R.N.
F.R.S 95

VIII. Continuation of a former Paper on the Twenty-five Feet Zenith Telescope lately
erected at the Royal Observatory. By John Pond, Esq. A.R. F.R.S. . .145

IX. Some account of the Eruption of Vesuvius, which occurred in the month of August

1834, extracted from the Manuscript Notes of the Cavaliere Monticelli, Foreign
Member of the Geological Society, and from other sources ; together ivith a
Statement of the Products of the Eruption, and of the condition of the Volcano
subsequently to it. By Charles Daubeny, M.D. F.R.S. F.G.S. 8^c. Professor
of Chemistry and Botany in the University of Oxford 153

[ viii j

X. On the Atmospheric Tides and Meteorology of Dukhun (Deccan), East Indies. By

Lieutenant-Cohnel W. H. Sykes, F.R.S. L.S. G.S. Z.S. Vice-President of the
Statistical and Entomological Societies page 161

XI. Geojnetrical Investigations concerning the Phenomena of Terrestrial Magnetism.

By Thomas Stephens Davies, Esq. F.R.S. Lond. and Ed. F.R.A.S. Royal
Military Academy , Woolwich 221

XII. Researches towards establishing a Theory of the Dispersion of Light. By the

Rev. Baden Powell, M.A. F.R.S. Savilian Professor of Geometry in the Uni-
versity of Oxford 249

Appendix.

Meteorological Journal kept at the Apartments of the Royal Society, by order of the

President and Council.

PHILOSOPHICAL TRANSACTIONS.

I. The Bakerian Lecture. — On the Proofs of a gradual Rising of the Land in certain
parts of Sweden. By Charles Lyell, Jun. Esq. F.R.S.

Received October 4, — Read November 27, 1834.

At is now more than one hundred years since the Swedish naturalist Celsius ex-
pressed his opmion that the waters, not only of the Baltic, but of the whole Northern
Ocean, were gradually sinking ; and he represented their level as lowering at the rate
of forty Swedish inches in a century*. He observed that several rocks which not
long ago were sunken reefs and dangerous to navigators, had become in his time
above water ; that the sea was constantly leaving dry new tracts of land along its
borders ; that ancient ports had become inland towns ; and that old fishermen and
seafaring people could testify that at a variety of places, both on the shores of the
Baltic and the ocean, considerable changes had taken place within the time of their
memory, in the form of the coast and depth of the sea. Lastly he appealed to marks
which had been cut in the rocks before his time expressly to indicate the former level,
and the waters were observed to have fallen below these marks.

This notion of a change continually in progress in the relative level of land and
sea was at first warmly controverted, and many facts were adduced to prove that
there had not been a general fall of the waters even in the Baltic. It was supposed
by many that there might have been some error in the observations, as the Baltic,
though free from tides, is often raised for several days continuously two or three feet
above its standard level by the melting of the snow, or by the prevalence of par-
ticular winds ; and it was remarked that the altered form of the coast and the shal-
lowing of the sea might be ascribed partly to new accessions of land at points where
rivers entered, depositing sand and mud, and partly to the drifting of large blocks
by ice, which are sometimes stranded and driven up on rocks and low islands so as
to raise their height.

Playfair, in the year 1802, in his " Illustrations of the Huttonian Theory," de-

* I have used the Swedish measure throughout this paper, for the sake of uniformity, when alluding to the
measurements made by Swedes. The Swedish foot, which is divided into twelve inches, agrees very nearly
with our own, being less than ours by three eighths of an inch only.
MDCCCXXXV. B

2 MR. LYELL ON THE PROOFS OF A GRADUAL RISING OF

clared that the supposed change of relative level of sea and land in Sweden, which
appeared to him to be sufficiently ascertained, might be ascribed to the movement
of the land rather than of the waters. He observed, " that in order to depress or
elevate the absolute level of the sea, by a given quantity, in any one place, we must
depress or elevate it by the same quantity over the whole surface of the earth ;
whereas no such necessity exists with respect to the elevation or depression of the
land*." The hypothesis of the rising of the land, he adds, "agrees well with the
Huttonian theory, which holds that our continents are subject to be acted upon by
the expansive forces of the mineral regions ; that by these forces they have been
actually raised up, and are sustained by them in their present situation -f^."

In the year 1807 Von Buch, after returning from a tour in Scandinavia, announced
his conviction " that the whole country from Frederick shall in Sweden to Abo in
Finland, and perhaps as far as St. Petersburgh, was slowly and insensibly rising ;" a
conclusion to which he appears to have been led principally by information obtained
from the inhabitants, and in part by the occurrence of marine shells, of recent species,
which he had found at several points on the coast of Norw^ay above the level of the sea.

At several periods since this discussion began respecting the decline of the level of
the Baltic Sea and German Ocean, marks have been cut on the rocks of exposed cliffs,
both of islands and the main land, so as to indicate the then existing height of the
waters, the year in which the marks were made being at the same time recorded.
All these marks were examined in 1820-21 by the officers of the pilotage establish-
ment of Sweden, and a report made by them to the Royal Academy at Stockholm,
in which they declared, as the result of their measurement, that along the whole coast
of the northern part of the Gulf of Bothnia the water is lower with respect to the land
than formerly ; but that the amount of variation, or change of level, has not been
uniform. At the same time an account was given in, and published by the Academy,
of new marks which were made in the same years, 1820-21, to record the level of
the sea observed at the time of the survey.

Notwithstanding the numerous proofs recorded of the change of level, and the
high authorities who had declared in its favour, I continued, in common with many
others, to entertain some doubts respecting the reality of the phenomenon, partly
because I suspected that it might be explained by reference to more ordinary causes,
such as some of those above mentioned, and partly because it appeared to me im-
probable that such great effects of subterranean expansion should take place in
countries which, like Sweden and Norway, have been remarkably free within the
times of history from violent earthquakes. The slow, constant, and insensible ele-
vation of a large tract of land, is a process so different from the sudden rising or
falling known to have accompanied, in certain regions, the intermittent action of
earthquakes and volcanos, that the fact appeared to require more than an ordinary
weight of evidence for its confirmation. I am willing, however, to confess, after

* § 393. I § 398.

THE LAND IN CERTAIN PARTS OF SWEDEN.

reviewing- all the statements published previously to my late tour for and against the
reality of the change of level in Sweden, that my scepticism appears to have been
unwarrantable ; but it will not be disputed that too many proofs cannot be accumu-
lated to substantiate so remarkable a phenomenon.

I propose, therefore, to lay before the Royal Society the observations which I made
during- the summer of 1834, wath a view of satisfying myself in regard to the data ap-
pealed to in support of the elevation of parts both of the eastern and western shores of
Sweden. As much of the evidence could only have been derived from personal inter-
course with the inhabitants, it may be proper to mention that I was accompanied
throughout my excursion by a well-informed Swede, Mr. Johnson, who by his thorough
knowledge of the English language was well qualified to assist me as interpreter.

On my way to Sweden I examined the eastern shores of the Danish islands of
Moen and Seeland ; but neither there, nor afterwards in Scania, could I discover any
signs of a recent upward movement of the land, nor could I learn that the notion of
such a change was entertained by the natives. Proceeding northwards along the
coast of the Baltic, the first place which I visited where any elevation of land is
supposed to be going on was Calmar. This port is situated in latitude 56° 41'. To
the south of the town is the celebrated ancient castle in which was signed, in the
year 1397, the famous treaty of union between Sweden, Denmark, and Norway. The
castle is supposed to have remained in its present state from a still earlier period.
There was a fortress on the site so long ago as the year 1030*. Two round-towers
terminate the outworks of this fortress on the side of the sea ; and when I observed
that the base of one of these rested on the beach only two feet above the level of the
water, and when I found that sea-weed had recently been washed up, so as to touch
the lowest part of the building, I concluded, at first, that for the last four or five
centuries there could have been no lowering of the Baltic at this place, for otherwise

we should be compelled to suppose that part
of the tower had been originally constructed
under water. But on nearer inspection I was
led to suspect that this had really been the
case, and that the foundation was originally
subaqueous. At the height of about two feet
above the base of the tower (see sketch, fig. 1 .),
and four feet above the level of the sea, a pro-
jecting band of stone (a), one foot deep, en-
circles the tower like a hoop. This projecting
„..,,, ., A..1 e band is of smooth stone, and the stones above

a, Projecting band or hoop of stone; b, thin layers of i^<*"^ *^ "* '^ J

slabs of stone and mortar, originally perhaps built under it arC large, and with aU CVCU, drCSScd SUr-
water ; c, the beach covered by water when the sea is high. ^^^^ -g^^ bcloW tllC hOOp are many COUrSCS

of thin slabs of a different stone (b), with layers of cement between. It oc-

* See Ankaesvaed's "Work on Calmar Castle.
b2

Fig. 1.
Part of one of the round-towers of Calmar Castle

6 MR. LYELL ON THE PROOFS OF A GRADUAL RISING OF

SO that they afford a clear indication of a change in the relative level of that sea to the
amount of thirty feet since its waters were inhabited by the existing species of Testacea.
On inquiring whether any other examples had been observed of similar deposits of
shells, I was informed by Colonel Hallstrom that he had discovered them on the
farm of Orby, near Brankyrka, about three miles to the south of Stockholm. He
obligingly accompanied me to the spot, where I found strata of marl and sand fill-
ing the bottom of a valley situated in a broken tract of ground where the funda-
mental rock is gneiss. This tract of land intervenes between Lake Maeler and
the sea.

The shells are very numerous, and are for the most part imbedded in a peaty soil
containing fragments of wood. The peat has perhaps been derived from sea-weed,
large accumulations of which I saw recently heaped up in a bay of the Baltic near
Solvitzborg, intermixed with similar species of shells. The identity of the shells of
Brankyrka with those of the neighbouring sea was even more complete than at
Solna ; for in addition to the species before enumerated, I found the Neritina Jiuvia-
tilis, a freshwater shell which lives in abundance in the brackish waters of the Baltic,
and which I saw covering the rocks in the saltish water at Graso, near Oregrund.
The Baltic variety is small, and usually black ; but both in the recent and fossil
individuals it sometimes exhibits its usual variety of colours. Some specimens also
of a land shell (Bulimus luhricus) occurred with the marine at Brankyrka.

The height of these shells has been determined by Colonel Hallstrom to be seventy
Swedish feet above the Baltic ; so that they indicate a fall of the waters, or rather a
rise of the land, to that amount, since the neighbouring gulf was inhabited by this
assemblage of Testacea. But the most remarkable spot where these Baltic shells
occur in a fossil state is still further to the south, at Sodertelje (see the Map, Plate I.),
about sixteen miles south-west of Stockholm, where they are found elevated more than
ninety feet above the sea. At Sodertelje a canal was cut in 1819 across a barrier
of sand, gravel, and clay, which separated Lake Maeler from a long narrow inlet or
frith of the Baltic. The canal is, in fact, carried through the bottom of one of those
valleys so common in this district, of which the sides consist of rocks of gneiss, and
the bottom of the same covered by more recent deposits. The accompanying trans-
verse section (fig. 3.) will explain this geological structure.

Fig. 3.

Section across the valley of Sddertelje, showing the position of the new deposits in relation to the gneiss.

The boundary hills of bare rock rise to the height of two hundred feet, the newer for-
ination being in some places about one hundred feet high, while on others, as on the
site of the Lake Maren, there are hollows which sink beneath the level of the sea.

THE LAND IN CERTAIN PARTS OP SWEDEN.

In these recent strata of loam, sand, and gravel, marine shells have been found at
various altitudes, as may be seen by Colonel Nordewall's paper in the Transactions
of the Royal Academy, where a ground plan is given of the canal and the surrounding
district, of part of which I subjoin a reduced copy *. I found at the Quarnbacken
(see diagram, fig. 4.), at the height of about ninety feet above the level of the sea, the
same species of shells as those at Solna before mentioned, imbedded in a marly clay,
which derives a violet colour from the decomposition of the Mytilus edulis. Again,
the same assemblage of shells maybe seen in the Blabacken, or " blue hills," a neigh-
bouring locality, where a bed of marl about three feet deep rests on the gneiss at the
height of about one hundred feet above the sea. Here the violet colour of the decom-
posed Mi/tiliis edulis is so remarkable as to have given a name to the hill. The shells,
with the exception of the Mytilus, are in general very entire. The breadth of the
Sodertelje valley, between the opposite boundaries of gneiss, varies from about half to
three quarters of a mile ; and the newer shelly deposit, which sometimes constitutes
a nearly level platform, at the height of sixty feet or more above the canal, has
precisely the appearance of the Subapennine formations in Italy, or at the base of
the Maritime Alps, where they are seen at inferior elevations, filling the bottom of
valleys in the older rocks, or flanking hills of higher antiquity and of inclined strati-
fication. It is only by aid of the shells so exactly corresponding to those of the Baltic
that the geologist can at once decide on the comparatively modern origin of these
Swedish strata.

Fig. 4.

Plan of the Canal

of

Sodertelje

BlabacksD

rtelje

^ Quam Backen

The distance between the nearest points of Lake Maeler and the sea, now united
by the Sodertelje canal, is nearly a mile and a half English, the general line of the
canal being from north-west to south-east, and the depth of the strata cut through
varying from fifteen to more than sixty feet.

First a communication was made which united Lake Maeler with the small lake,
or mere, called Maren (see plan) ; and this passage was called the upper channel.
Here a horizontal bed of marl was passed through, of a violet colour, like that of the

* Kongl. Vetenskaps- Academiens Handlingar, 1832.

8 MR. LYELL ON THE PROOFS OF A GRADUAL RISING OF

Blabacken, and containing the Cardium edule. Besides the shells, several buried
vessels were found in this channel, some of them apparently of high antiquity, there
being no iron in them, and the planks being fixed together by wooden pegs. In an-
other place, however, an anchor was dug up, as also, in one spot, some iron nails. In
the lower channel, or that which united Lake Maeler with the bay of the sea called
Egelsta Wiken, two similar beds of marine shells were found, one at the height of
eighteen and the other of forty Swedish feet above the level of the sea.

But a much more remarkable discovery was made in the lower channel. Here the
excavation commenced in a hill, or platform, covered with a forest ; and after digging
down about fifty feet through stratified sand, gravel, and clay, they came upon what
appears to have been a small wooden house, the site of which is marked on the plan a,
fig. 4. The floor of this building was on a level with the sea. Colonel Nordewall
has stated in his account, that the mass which covered the house was thirty-four feet
thick : but he perhaps wrote ells (a Swedish ell is two feet) ; for Captain Cronstrand,
an engineer who superintended the whole excavation, and who accompanied me to the
spot, assured me that it was at the depth of about sixty- four feet. In other respects
this engineer's account agrees with that of Colonel Nordewall ; but he has enabled
me to add some particulars, which I shall now mention.

The stratification of the mass over the house was very decided, but for the most
part of that wavy and irregular kind which would result from a meeting of currents.
It contained here and there very coarse gravel, and some boulders of considerable
size. At the bottom of the whole, a mass of very fine sand was entered, in which the
appearance of the four walls of a square building was discovered. Attention was not
paid to this phenomenon soon enough to decide whether there were any remains of a
roof. An attempt was made to dig round the walls, and leave them standing ; but
the wood was perfectly decomposed, and crumbled down like dust when all support
was removed. But when they reached the level of the sea they found the timber of
the walls preserved. At the bottom, on what may have constituted the floor of the
hut, an irregular ring of stones was found, having the appearance of a rude fireplace,
and within these was a heap of charcoal and charred wood. On the outside of the
ring was a heap of unburnt fir-wood, broken up as for fuel, the dried needles of the
fir and the bark of the branches being still preserved. The building was about eight
feet square, and was supposed to have been merely a fishing-hut, occasionally resorted
to at the fishing-season. Captain Cronstrand says that the building was enveloped
with sand as fine as if blown by the wind.

I visited the nearest spot at which shells were found, in a deep drain not far from
the former site of the fossil house, (see plan, fig. 5.) and am satisfied, from their
position and from the occurrence of shells at different spots and heights in exca-
vating the " upper channel," that the strata which covered the house, like all the
rest cut through by the Sodertelje canal, were marine. It appears evident, therefore,
that this building must have been submerged beneath the waters of the Baltic to the

THE LAND IN CERTAIN PARTS OF SWEDEN. 9

depth of sixty-four feet ; and before it was raised again to its present position, which

is about even with the level of the sea, it had become covered with strata more than

sixty feet thick.

Fig. 5.

a. Site of the buried hut. h. Water in the canal, c. Bed of violet-coloured marl with Cardium edule.

If the buried vessels alone had been found, we should merely have been called
upon to suppose that they had sunk to the bottom of a fiord, which was afterwards
silted up and then upraised ; but the situation of this house seems to require far
greater changes of level. Had nothing been observed but the wooden walls, we
might have imagined that the hut was carried away during an inundation, for I was
told of a house that was floated off entire during a flood, in the north-east of Sweden,
in consequence of the artificial drainage of a lake. But the fireplace and charred
wood on the floor seem entirely opposed to such an hypothesis. To imagine a sub-
sidence of the land to the amount of more than sixty feet, and a subsequent eleva-
tion, or in other words a series of movements analogous to those by which the phe-
nomena of the Temple of Serapis have been explained, appears necessary ; yet this is
undoubtedly to assume far greater revolutions in the level of the land, since fishing-
huts were first erected in Sweden, than history or tradition would have led us to an-
ticipate. As to the fine sand in which the house was enveloped, it may be compared
to the sand which is known to collect rapidly and form a mound over wrecked
vessels which have sunk and presented an obstacle to a marine current charged with
sediment.

I ought to state that I was unable to examine the remains of the house, since it was
entirely cut away, having stood, as will be seen by the section (fig. 5.), in the exact
line of the canal, the surface of the waters of which, like the foundation of the house,
were situated at about the mean level of the sea ; for Lake Maeler and the Baltic are
so nearly on a level, that when the Baltic rises two or three feet above its mean
height, the same lock at Sodertelje which usually serves to convey vessels from the
Baltic up into Lake Maeler, is used to convey them up in a contrary direction from
the lake into the sea. But although I could not see the relic of the fishing-hut itself,
I may observe that I had the advantage of conversing with the two eminent engi-
neers who were witnesses to the fact, and who, being greatly astonished at the dis-
covery, took careful notes of the phenomena at the time. They at first conceived
that the building might have been part of some well, although this seemed highly
improbable, not only from the size of the wooden structure, but from the occurrence
of springs at the surface in the immediate neighbourhood. It was only when the fire-

MDCCCXXXV. c

10 MR. LYELL ON THE PROOFS OF A GRADUAL RISING OF

place was found that they could form no other opinion than that it had been a human
habitation. In order to explain the position of beds of shells at various heights in the
strata intersected by the canal, an hypothesis was suggested by Colonel Nordewall,
in his published report, that Lake Maeler may once have been shut out from the sea
by a high barrier. Sand, gravel, and shells may then have been deposited at its bot-
tom, which on the subsequent removal of the barrier were left at their present height
above the lake. But if the shells had been submitted to a conchologist, they would
have been at once recognized as consisting for the most part of marine species, such
as do not exist in the present waters of Lake Maeler, but are characteristic of the
Baltic. Whatever doubts, therefore, may hang over the causes which brought the hut
into the extraordinary position in which it was discovered, it is impossible to reflect
on this and the other facts brought to light during the excavation of the Sodertelje
canal, without being convinced that very important movements have taken place in the
land and the bed of the sea since the Baltic was inhabited by the existing Testacea,
and even since the sea was navigated by vessels, and this country inhabited by man.

In regard to the shells, I may observe that the My a arenaria is the only one found
by me in great abundance in any part of the Baltic which I did not see among the
fossils of any of the localities already mentioned, or those afterwards to be alluded
to, further to the north. But this shell does not, I believe, extend so far north in the
Gulf of Bothnia as Sodertelje ; I could not find it even at Calmar, and further south,
at Solvitzborg, it was rare, and of very small size. The analogy, in fact, of the fossil
shells to those now living in the Bothnian Gulf is most complete : the shells are the
same species, partly freshwater and partly marine, the species taken collectively be-
ing few in number, and the marine attaining a smaller average size than in the
ocean, where the water is more salt. The Tellina Baliica is everywhere in great
abundance. Hence we may conclude, that since the time when an inland sea of
brackish water, like the Baltic, existed in the North of Europe, considerable fluctua-
tions in the position of land and sea have taken place ; a conclusion to which I
shall revert in the sequel.

The elevated position of the marine shells around Sodertelje prepares us to expect
similar deposits scattered far and wide over the valleys bordering the various branches
of Lake Maeler. Accordingly, in examining the country about forty-five miles north-
west from Sodertelje, between the towns Torshalla and Arboga, I was fortunate
enough to meet with abundance of Tellina Baltica (see the variety represented in
Plate II. figs. 3,4.) in an unctuous clay, of a deep blue colour when wet, which filled
the bottom of a valley near Lake Maeler, in a district of gneiss covered with huge
erratic blocks. This locality, which is by far the most distant from the Baltic of all
the places where similar beds with marine shells had previously been observed, lies
between the village of Smedby and Kongsor, about seventy miles from Stockholm,
and more than eighty from the general coast line. The clay is exposed to the depth
of fifteen feet, being cut through by a streamlet, which is crossed by a small bridge

THE LAND IN CERTAIN PARTS OF SWEDEN.

n

Fig. 6.

on the high road. The deposit is elevated only a few yards above Lake Maeler,
and is therefore about the same above the Baltic ; but the formation extends to
greater heights in this and adjoining low lands, as do associated beds of gravel and
sand, in which I could not detect any fossils.

After viewing these geological phenomena, I was well inclined to receive favour-
ably any probable evidence brought forward to prove that the land has been rising
in recent times in the neighbourhood of Stockholm ; but I must confess that, on
close investigation, I was disappointed in finding that several of the proofs relied
on by some writers were very equivocal. Among other facts, it has been noticed
that the level of Lake Maeler has been lowered in very modern times ; and it is clear
that the waters of this lake would appear to fall, together with the sea, if there be a
general rise of the land, since Lake Maeler joins an arm, or fiord, of the Gulf of Both-
nia at Stockholm, the salt and freshwater meeting in the middle of the city. The lake
is generally three feet higher than the sea ; but the line of separation is not constant,
and when the Baltic rises very high, its waters flow for some miles into the lake. In

that part of the town called the Rid-
darliolmen, immediately above where
the waters of the lake meet the sea,
(see Map, fig. 6.,) some of the buildings
have of late years become insecure,
because the level of Lake Maeler has
fallen, so that the piles on which the
buildings rest are not constantly under
water as of old. The tops of these
piles being now every year alternately
wet and dry, they are continually rot-
ting away. This fact is unquestionable ; and I saw the houses, which, in consequence
of this failure of support, are much rent, and out of the perpendicular.

But during the time that this change has occurred, no corresponding fall has been
observed in the neighbouring quay, or Skeppsbron, which is filled with brackish
water, and which ought to have been equally affected on the supposition of a general
rise of the land ; and we naturally, therefore, inquire whether some particular circum-
stances have not of late years given a freer outlet to the waters of Lake Maeler, so
as to cause them to sink. Now several Swedish engineers remarked to me, that the
decay of the piles had taken place since the removal of the two old bridges in Stock-
holm, which being supported on a great number of wooden piles, obstructed the free
discharge of the lake, the waters of which now pour in a rapid and unbroken current
through the large arches of the new bridge ; and secondly, they observed that the
canal of Sodertelje has formed, since the year 1819, an entirely new line of commu-
nication, by which the waters of Lake Maeler have of late years flowed out into the
sea. Can any one doubt for a moment, that if the old bridge should be restored

c 2

12

MR. LYELL ON THE PROOFS OF A GRADUAL RISING OP

and the Telje canal again closed up, the waters of the lake would immediately stand
at a higher level* ?

There are some marks in the suburbs of Stockholm which serve, I think, to set
narrow limits to the extreme amount of elevation which can by possibility have taken
place during the last three or four centuries. To one of these, the Fiskartorp of
Charles XL, I shall particularly allude, (see Map, fig. 7-,) because an attempt has
been made to draw from it the opposite inference of a rapid elevation of the land.

Map of the northern environs of Stockholm, showing the site of the Fiskartorp.

This fishing lodge is situated on a promontory surrounded on three sides by lakes
(see Map, fig. 7.)- The lodge is 131 yards distant from the nearest water, and
twenty-three feet above its level. By the side of it is a large oak, and a second one of
considerable age between it and the lake, only forty-six yards from the margin of the
water, and having its base only ten feet above the level of the lake, which at the time
that I visited it stood at least one foot below its mean height. (See Section, fig. B.)
Mr. Strom, Keeper of the Royal Woods and Forests, assured me that the age of this
oak cannot be less than four centuries. There are already some signs of decay at
its top, and its diameter at the height of five feet above the ground is four feet four

* Professor Johnston, in his paper in the Edinburgh New Philosophical Journal, No. 29, July 1833, has by
mistake represented the houses where the piles are giving way as situated on the side of the Skeppsbron instead
of the Riddarholmen.

*

THE LAND IN CERTAIN PARTS OF SWEDEN. 13

inches. As Mr. Strom is perfectly acquainted with the average rate of growth of
the oak in different kinds of soil in this country^ and has cnt down some in the neigh-

Fig. 8.

a. The fishing-house. b. The lower oak. c. Ancient site of the small cabin for fishing-tackle.

rf. The Husar Wiken.

bouring grounds which could be shown by their rings of annual increase to be more
than six hundred years old, I consider his opinion as worthy of full confidence. This
gentleman showed me an ancient plan in which the Fiskartorp and both the oaks
were laid down ; as also a small cabin, which, in the time of Charles XL, who died
in 1697, was placed between the lower oak and the lake. It was not a boat-house,
but had been merely used for preserving the oars and fishing-tackle. Being in a
state of great decay in 1824, it was removed by Mr. Strom. Now it is improbable
from what is known of the habits of the oak in this country, that the lower oak grew
close to the water's edge originally ; and if its base be now only eight feet above the
mean level of the lake, it is clear that the rise in each century must have been very
slight, although it may undoubtedly have amounted to ten inches in a hundred years,
which would accord with the estimate of the best-informed scientific men in Swe-
den, in regard to the gradual rate of the rise of land at Stockholm. Professor John-
ston appears to have confounded the cabin, which has been removed, with the Fiskar-
torp, which is still standing, the latter having been frequently repaired, as a memo-
rial of Charles XI. ; for Mr. Johnston states, that " the fishing-hut formerly stood
close by the deep water, though no longer near any spot where the favourite amuse-
ment of the monarch can be enjoyed*."

Even the lower cabin did not stand near deep water so lately as a century and a half
ago, but appears by the ancient plans to have been nearly as remote as now from the
shallow Husar Wiken. I fully agree, however, with Professor Johnston, that it ap-
pears clear from ancient documents and tradition, that the three lakes Husar, Ladu,
and Uggel, which together formed, in the time of Charles XI., what was called the
Gulf of Fiskartorp, have since grown much shallower, and have been in part con-
verted into land ; a change which may perhaps have been due, in part at least, to a
slight general upheaving of the whole country. But although I do not dissent from
Mr. Johnston's general proposition, I ought to mention here that I consider another
of his proofs derived from the neighbourhood of Stockholm as altogether untenable.
Speaking of the Bruns Wiken, a beautiful lake in the northern suburbs of the city
which skirts the woods and pleasure-grounds of the palace of Haga, (see Map, fig.7-j)

* Edinburgh Philosophical Journal, No. 29.. p. 39.

14 MR. LYELL ON THE PROOFS OF A GRADUAL RISING OF

he says, " the position of this lake shows that it has formerly communicated with the
sea, though now it is considerably above it and entirely inland. As the sea retired,
this sheet of water would also have been drained off, had it not been dammed up at
the only outlet (at Alkistan) to preserve the beauty of the promenade, one of the
finest in the neighbourhood of the city. At present it is dammed up to the height of
four or five feet, and the character of all the land around shows that in ancient times
it has been very much higher and more extensive."

Now a reader would infer from this description, that but for an artificial dam this
lake would have been laid dry ; but the fact is that it fills a deep hollow in the granitic
rocks of this district ; and the only effect of the small dam is that the mean height
of the water is somewhat more uniform throughout the year. The outlet alluded to
is at Alkistan (see Map, fig. 7.), where a slight wooden dam has been erected, so
small, that every year in the spring the water flows over it ; so that the annual ex-
treme height of the water is still the same as it would be if the dam were removed.
When I visited the spot in June, the water was two feet lower than the top of the
dam, and scarcely more than a foot above the bottom. The tract of land which se-
parates the lake from the sea is about a hundred paces broad, and is composed of
granite, over which the stream flows which issues from the lake.

I shall now pass to the country around Upsala, about forty miles north-north-west
of that around Stockholm last described (see general Map, Plate I.). In its geologi-
cal structure it resembles that of Stockholm, the fundamental rocks being here also
gneiss and granite, partially covered with newer deposits and with erratic blocks ;
but near Upsala there is a much larger quantity of clay in the overlying formation.
A section of this clay is well seen at Ulfva on the banks of Fyrisa, a spot which I
visited with Mr. Marklin of Upsala. The thickness of clay here exposed in a vertical
section is between thirty and forty feet, and the river is probably as much more above
the level of the sea. This stiff blue clay reminded me much of the Subapennine clay
of Italy, In some parts it contains no shells; but in others the Tellina Baltica entire,
with both its valves and the epidermis, is very abundant. It is precisely the same va-
riety of this shell as I found before near Torshalla (see p. 10, and Plate II. figs. 3, 4.).
The Mytilus edulis also occurs, often much flattened, and occasionally covered with
the small white flustra now so commonly attached to it in the Baltic. In some of
the associated strata there is much vegetable matter, exactly resembling sea-weed.
I could find none of the littoral shells which I before mentioned as associated with
the Mytiltis and Tellina near Stockholm.

One of those ridges of sand and gravel which I have before described as being
frequent in Sweden, passes through the suburbs of Upsala, running in the usual di-
rection nearly north and south. Its summit, according to the barometrical measure-
ment of Professor Wahlenberg, rises more than a hundred feet above the river which
flows at its base. Its structure ia laid open in large pits, one of them about seventy
feet deep ; and these sections show that the mass consists for the most part of a con-

THE LAND IN CERTAIN PARTS OF SWEDEN. 15

tinued series of thin layers of sand, loam, and gravel, in part horizontal, but in some
places, and for a limited space, inclined at an angle of more than fifty degrees, with
numerous small vertical rents occasionally traversing the beds. Whether these have
been occasioned by subterranean movements, or during the drying and settling of
the mass when it was first raised above the waters, is a point on which I can offer
no conjecture. The inclination of the strata, resembling that in gravel-beds, I attri-
bute chiefly to original inequalities in the mode of its deposition. Here, as in other
places, I could find no fossils in the beds of pure sand and gravel, nor did I meet
with any in the blue clay which seems to crop out from beneath the sand at the
bottom of the hill. But fortunately, near the castle at Upsala a thin bed of violet-
coloured marl, full of shells, has been cut through at the bottom of a gravel-pit near
the top of the ridge. This marl, which forms a horizontal layer only three inches
thick, is within about twelve feet of the summit of the ridge, and about eighty above
the sea. It contains the Mytilus edulis, Cardium edule, Tellina Baltica, LiUorina
llttorea, Paludina ulva ? Both above and below this marl are strata of gravel, and
some of the overlying beds contain round boulders a foot or more in diameter.

This is the only place in Sweden where I met with any fossils in the midst of one
of the sand-oasar, or ridges of sand and gravel. The fact of finding the recent shells of
the Baltic in such a position appears to me of the highest interest, especially because
on the summit of this, as of other ridges, I found large erratic blocks resting imme-
diately on the uppermost layers of gravel or fine sand. In that part of the ridge
south of the town called Palacksbacken, these blocks are abundant, and are on the
very summit, appearing to be all superficial, for I could find none in situ in the deep
gravel-pits which intersect the ridge. I examined these blocks in company with Pro-
fessor Wahlenberg, and found them to consist of angular masses of gneiss and gra-
nite, the larger ones rarely exceeding nine feet in length ; but we measured one
which was no less than sixteen feet long, thirteen high, and eight broad. It follows,
therefore, that by whatever cause these enormous fragments of granite rocks have
been conveyed to their present sites, some of them at least have been transported
thither since the Baltic was separated from the ocean and inhabited by the existing
species of Testacea.

I may observe also, that the occurrence of layers of marl containing littoral
shells, as above described, in the midst of a stratified ridge of sand and gravel, is
opposed to the theory of those geologists who refer the formation of such ridges to
a violent flood or debacle rushing from the north. The perfect preservation of the
shells at Upsala, and the repeated succession of thin alternating layers of gravel,
sand, and loam, which are seen almost everywhere, imply a gradual, and at times a
very tranquil, deposition of transported matter. If I am asked for a more probable
hypothesis in the room of that to which I object, I may state that these ridges ap-
pear to me to be ancient banks of sand and shingle, which have been thrown down
at the bottom of the Gulf of Bothnia, in lines parallel to the ancient coast during the

16 MR. LYELL ON THE PROOFS OF A GRADUAL RISING OF

successive rise of the land ; or in other words, during the gradual conversion of part
of the gulf into land. I conceive that they may have been formed in those tracts
where a marine current, flowing as now, during the spring when the ice and snow
melt, from north to south, came in contact with flooded rivers rushing from the con-
tinent, or from the west, charged with gravel, sand, and mud. According to this
view, these large Swedish ridges may be compared to smaller banks known to have
been formed within the last five or six centuries on the eastern coast of England, at
points where a prevailing marine current from the north meets rivers descending from
the interior, or from the east. In such situations the river, instead of entering the
sea in a straight line, is deflected at a right angle, and runs from north to south
between the land and the new-formed sand-bank. The deep narrow breaches which
occasionally occur in many of these ridges in Sweden, precisely resemble those which
a flooded river or an inundation from the sea sometimes makes through our smaller
banks above alluded to. If this explanation be admitted, I conceive that the steep
escarpments often presented on both sides of the oasar or ridges of sand, may be almost
entirely due to their original form, and not to subsequent denudation. As to the
manner in which the erratic blocks have been lodged on the highest parts of these
sand-banks, I fully adopt the opinion of those who believe them to have been carried
by ice, respecting the agency of which I shall have more to say in another place.

The low meadows near the town of Upsala are not many feet above the level of Lake
Maeler, the most northern arm of which reaches near to that place, which is distant
about fifty miles from Sodertelje, before alluded to, at the south-eastern extremity
of the same lake. If the opinion, therefore, of the rise of the land be well founded,
the whole of Lake Maeler, and the low lands adjoining, must have been covered
with salt water at no very remote period in history. Professor Wahlenberg pointed
out to me a meadow to the south of Upsala in which the Glaux maritima and the
Triglochin maritimus now flourish, plants which inhabit salt marshes bordering the
sea. These same species have, it is true, been found in the interior of Germany and
France near saline springs ; but in the country of Upsala there are no salt springs ;
and this botanical phenomenon seems to confirm the opinion that the salt waters
have only receded in very modern times from these lands, and that the rains have not
yet had time to dissolve and wash away all the salt which may have been originally
precipitated when this tract was laid dry.

Oregrund.
The next region which I examined was the coast near Oregrund, a port about forty
miles north-east of Upsala. During the survey of 1820, before alluded to, a mark was
made near this place on the rocky cliffs of Graso, a long narrow island which lies op-
posite to Oregrund. On my visit to this island I was accompanied by Lieut. Olof
Flumen, a gentleman of the pilotage establishment, who cut the mark in 1820. It
is much to be regretted that neither he nor any other observer, as far as I could learn.

THE LAND IN CERTAIN PARTS OF SWEDEN.

17

had visited these spots since the marks were made. No place could have been better
chosen for the purpose : the letters and lines, which are still as fresh as if newly
made, have been cut upon the vertical face of a cliff of gneiss, which is free from
lichens, and which plunges to the depth of about three fathoms perpendicularly be-
neath the water. I subjoin a sketch

(fig. 9.) which I made of the rock and
mark as they appeared on the 1st of
July 1834. A vein of granite, com-
posed of felspar and quartz, traverses
the gneiss in an oblique direction above
tlie mark. The rock is stated by Brun-
CRONA to be in latitude 60° 18' N. It
is situated at the south of Strandtorpet
and north of Karingsundet. The length
of the horizontal line is twenty inches
and a half; the figures express that
the mark was cut on the 13th day of

Fig. 9.

Mark at Graso near Oregrund.

the ninth month (September) in the year 1820, and the runic letters at the beginning
and end of the line are the initials of Olof Flumen.

At the above date the horizontal line was exactly at the level of the sea on a calm
day, when the water was supposed to be at its standard level. When I visited the
place on the 1st of July 1834, the line was five inches and a half above the surface of
the water ; and Lieutenant Flumen and the seamen thought that a slight wind which
was then blowing from the north-north-west, directly down the sound between Ore-
grund and Graso, caused the water to be an inch or two higher than it would have
been had the sea been as perfectly calm as on the day preceding my visit. 1 found
the pilots, both here and at other places on this coast, to be of opinion, that notwith-
standing the fluctuations of level caused by the wind, a person well accustomed to
this sea can decide whether, on a particular day, the water is an inch or two above
or below its standard level. There had been several calm days without wind before
I arrived at Oregrund, and I was assured that the sea was in a state of rest similar
to that of the day which had been chosen fourteen years before for making the mark.
Before we came to the spot, both Lieutenant Flumen and the boatmen expressed
their persuasion that I should find the sea below the mark, because they declared
that either the waters of the gulf were always sinking, or the land on this coast was
gradually rising. To confirm this opinion the sailors pointed out several rocks which
they well remembered to have been barely covered with water in their younger days,
or about forty years ago, but which now rise between one and two feet above the
w^ater. Among others they took me to a small insulated rock in the sea, opposite
Domaskarsund, which they recollected to have once been nearly two feet lower, at
which time the neighbouring channel, which I saw nearly dry, had allowed a loaded

MDCCCXXXV. D

18 MR. LYELL ON THE PROOFS OF A GRADUAL RISING OF

boat to pass. So strong is the conviction of the fishermen here, and of the seafaring
inhabitants generally, that a gradual change of level, to the amount of three feet or
more in a century, is taking place, that they seem to feel no interest whatever in the
confirmation of the fact afforded by artificial marks, for they observed to me that
they can point out innumerable natural marks in support of the change ; and they
mentioned this as if it rendered any additional evidence quite superfluous.

The sea deepens rapidly near the coast at Oregrund, and there is twenty-eight
fathoms water in the bay. Along the shore is a broad band of bare gneiss traversed
by granite veins, which ramify in every direction, and consist chiefly of felspar in
large crystals. In many places this sloping band of bare rock, having a smooth sur-
face, extends up for a hundred paces from the sea, covered only with a scanty coating
of lichens. The gneiss, where it approaches within eighteen paces of the sea, is so
smooth and polished that it is difficult to walk upon it. The surface swells into those
rounded flattened forms which are so common in the forests in the interior of Sweden,
where grass is frequently unable to establish itself on so hard a foundation. Not
even lichens can grow in some parts where veins and beds of quartz appear ; but trees
take root in the clefts of the granite and gneiss, rising amidst vast erratic blocks,
resembling those which, in equal numbers and of equal dimensions, crowd the greater
part of the shores and islands of the Bothnian gulf.

From Oregrund I went on to Gefle, about forty miles to the north-west. In a low
part of the intervening country, near the village of Skjerplinge, I came to a large
tract of stiff blue clay, like that near Upsala, covered with sand six or eight feet deep.
In the clay I found the Mytilus edidls and the Tellina Baltica. I was informed that
marine shells are met with abundantly at a much higher level in a hill of sand near
Skjerplinge, where also, according to tradition, a large iron ling, such as ships are
attached to, was formerly found fixed in the soil.

My attention was repeatedly called to low pastures from one to three miles inland,
where the old inhabitants or their fathers remembered that boats and ships had
sailed. The traveller would not have suspected such recent conversions of sea into
terra Jirma ; but there are few regions where a valley newly gained from the sea may
J80 rapidly assume an air of considerable antiquity. Every small island and rock off
this coast is covered with wood, and it only requires that the intervening channels
and fiords should dry up and become overspread with green turf for the country to
wear at once an inland aspect, with open glades and plains surrounded by well-
wooded heights.

Among other stories of wrecked vessels found in the interior, I was told at Gefle
that a vessel and an anchor had been found in a hill of sand and gravel at Uggleby,
sixteen miles from the sea, in the parish of that name. Colonel Hallstrom tells me
that similar traditions are common in Finland, and that a wreck is said to have been
found there at Laihela, two miles from the sea.

On both sides of the river at Gefle I found land gained from the sea, within the

THE LAND IN CERTAIN PARTS OF SWEDEN. 19

memory of persons now living ; and its gradual extension here, and in other places to
the north and south, is attributed by the natives to a slow but constant change in the
relative level of land and sea. In this place the deposition of fluviatile sediment must
cooperate with other causes ; but the shallowing of the water and its conversion into
land are too universal to be explained by sedimentary accumulations alone. Prepa-
rations are making to remove the harbour farther from the town, in consequence, as
I was assured, of the continued fall of the water rendering it every year more difficult
for ships to reach the ancient wharfs.

I visited two marks near Gefle, one of them cut in 1731 in the island of Lofgrund,
twelve miles north-east of that port, and another made in 1820, about six miles farther
north. The first of these marks (that of Lofgrund *) was carved by one Rudberg in
1731, on a fixed rock of mica-schist, in the middle of a small sheltered bay on the
east side of the island. The mica-schist is very hard and full of garnets, the highest
part of the rock being only four feet above the water, and its length and breadth
about fourteen feet. There is a depth of water of about seven fefet and a half on the
side where the mark is made. The annexed sketch (fig. 10.) will give some idea of
the outline of that side of the rock and of the mark.

Fig. 10.
Rock in the Harbour of Lofgrund.

a. The upper mark. h. The lower mark.

The horizontal line, which is somewhat irregularly cut, is known to have been
originally made at the mean water-level. When I measured it on the 3rd of July
1834, this line was two feet six inches and a half above the mean level of the water ;
but as the wind was blowing from the east-north-east, the chief pilot of Gefle, who
accompanied me, declared that 1 ought to add at least four inches more in order to
express the full diff*erence of the ancient as compared to the present level of the sea.
It will appear that I had afterwards good reason to believe that this estimate was not
exaggerated. Even when this allowance is made, the fall, in the space of somewhat
more than a century, is not quite equal to three feet. There is a lower horizontal
mark two feet five inches long, irregular and without any date^, which, when I ex-

* Sometimes called Lofgrundet, the final et being the definite article in Swedish.

d2

20 MR. LYELL ON THE PROOFS OF A GRADUAL RISING OF

amined it, was washed and almost covered by the ripple on the surface of the water.
It is not enumerated by Bruncrona as among those which were cut in 1820 ; but
my boatmen and the fishermen on the island said it was cut in 1820. Although
occasionally covered by the small waves, it was one inch and a half above the mean
level of the water, and would probably have been four inches or more above it on a
calm day.

It has been observed that lichens grow nearly to the water's edge on the rocks
skirting the Gulf of Bothnia, and certainly the lower border of this line of vegetation
often appears very distinct when viewed at a short distance ; the rock below, where
it is alternately wet and dry, remaining of its natural colour, which is usually very
much contrasted with that of the surface, where it is coated with lichens. Now it has
been proposed to measure and note the distance of this line of vegetation above the
sea, and then to determine, after a certain lapse of years, the rate of elevation of the
land, by observing how much lower the lichens have descended. With a view of
furnishing data to 'future observers for such comparisons, I endeavoured, at Lof-
grundet and other places, to ascertain the height of this line of vegetation, but without
success, for it always appeared to me undefinable. Not only is it very uneven, but
sometimes, after passing over a space of bare rock, we come down again to some
straggling lichens growing luxuriantly nearly to the water's edge.

Von Buch mentions in his Travels* that he found a large quantity of fine-grained
red sandstone, used as a building-stone, at Gefle, containing small nodules of asphal-
tum. He was told that these stones were found nowhere in situ, but were thrown
up by the sea upon the skar, or that line of rocks and islands which bounds the coast
off Gefle. I found the shore of the isle of Lofgrund strewed over with these schis-
tose red-sandstone blocks. They have the form of large flat slabs, with angular
edges, as if they had been just taken from a quarry. They were exposed to a hot
sun, and the black pitchy matter was oozing out abundantly from numerous pores.
The planes of stratification presented those undulations called ripple-marks. On my
inquiring from whence they came, I was assured by the fishermen that a fresh supply
of such masses was brought to the coast from time to time by the sea. I remarked
that their size was such that the waves could not have power to move them, that
there were no rocks like them in the neighbourhood, and that they were not rounded
by attrition as if rolled at the bottom of the sea. One of the fishermen replied
that the ice might have brought them, and he undertook to show me much larger
blocks which had been stranded recently on different parts of the skar. I accord-
ingly went to a small island called Hvitgrund in order to see proofs of this fact,
and there I observed blocks of red granite, five or six feet in diameter, perfectly free
from lichens, amidst other blocks of various sizes which were coloured grey, white,
and black, by a coating of these plants. The sailors named other spots where I might
see much larger blocks, perfectly bare, or only beginning to be covered, amidst

* Vol. ii, chap. v. French edition, p. 303.

THE LAND IN CERTAIN PARTS OF SWEDEN. 21

thousands which, having probably lain for a great many years at the same height
above the mean level of the sea, had entirely changed their colour. They declared
that they well knew the exact date of the arrival of some of these blocks, which they
observed would in time become as well coloured (or as thickly clad with lichens) as
those older ones among which they had been thrown. On my demanding whether
any of my informants had seen great stones floated by ice, they admitted that they
had not ; but the chief pilot stated that the drift ice on this coast is often packed so
as to be eighteen feet thick, different sheets from five to six feet in thickness being
driven one over the other ; and when this happens, fragments of rocks might be
frozen in and floated off* on a rise of the water or a change of wind. The more usual
mode, however, of explaining the manner in which ice operates is somewhat different.
When the sea freezes in winter to the depth of about five or six feet, detached
masses of rock lying on shoals are necessarily frozen in. Afterwards, when the water
rises on the approach of summer, the ice, being buoyed up, lifts with it these stones,
and they may then be transported by floating ice-islands to a great distance.

The next mark which I examined was that of St. Olof's Stone in Edsko (or Edsjo)
Sund*, in the parish of Hille. There was no one at Gefle who was present in 1820
when the mark was cut, and unfortunately it is imperfectly and even incorrectly de-
scribed in Bruncrona's Report. St. Olof's Stone is an immense erratic block, about
thirty-six feet high above the water, forty long, and thirty broad, with precipitous
and in some places overhanging sides. It consists of micaceous schist with garnets.
It is situated in lat. 60° 52' N. The mark is cut on the precipitous south-east side, at
the base of which there is about a fathom's depth of water.

Bruncrona, in his Report, states that the mark consists of a horizontal line, upon
which the date of the year 1820 is carved. Directions were probably given by him to
this effect, but they have only been in part executed, for there is neither a horizontal
nor vertical mark, but only two irregular lines to the right of the figures, as shown in
the annexed sketch. It is also stated in the Report, that Fig. ii.

the water stood 1*92 foot under the lowest edge or base
of the ciphers. Now unfortunately, the base of the let-
ters do not form a perfectly horizontal line, the bottom
of the last cipher being three quarters of an inch below
the bottom of the figure 8. On the evening of July 3rd,
I found the water-level to be exactly two feet below the
base of the cipher, or the 0. The wind was blowing from the east-south-east, so that
the water in the Sound, according to the pilot's opinion, was four or five inches above
its level of equilibrium.

As this was the third time 1 had been told that the sea was several inches above
its standard height, I determined to pass the night in Edsko, in hopes that the wind
might fall, and that I might have an opportunity of repeating my observation during
* Colonel Bruncrona has called this Assiasund, but it is not known by this name at Gefle.

22 MR. LYELL ON THE PROOFS OF A GRADUAL RISING OF

a perfect calm. At a very early hour the next morning the wind shifted to the north-
north-west, and fell almost entirely, so that when I revisited St. Olof s Stone the sur-
face of the water was perfectly smooth. I then found the level of the sea, as the pilot
had expected, 3j inches lower than on the preceding evening. This circumstance
gave me much confidence in the opinion which he had previously expressed, that the
water at Lofgrund was three or four inches above its standard level at the time of
my observation.

The result, then, of my second visit was, that on a moderately calm day, with a slight
wind blowing north-north-west, I found the level of the water, on July 4, 1834, two
feet three inches and a half below the bottom of the 0, at the end of the figures
1820, or 3'58 inches lower than the water in the year 1820, supposing the measure-
ment to have been then taken from the base of the last cipher. If it was taken from
the base of the figure 8, then the difference between the water-level at the two periods
compared would be three quarters of an inch greater.

It is much to be regretted that in the printed account of the cutting of this and
other marks in the year 1820 — 21, no exact mention is made of the state of the sea and
direction of the wind. I was merely assured generally that calm days were chosen,
and circumstances avoided which are known to cause the Gulf to deviate from its stan-
dard level. This precaution I know to have been carefully attended to at Oregrund.

Mr. Von Hoff, in his important work entitled " The History of Natural Changes on
the Earth's Surface proved by Tradition," has objected to the marks cut on the rocks
of this coast that they were made on loose blocks, which may have been heaved up
from their position by the sea and ice*. But the greater number of the marks have
been set on fixed rocks ; and even where this is not the case, the proof derived from
such enormous masses as St. Olof 's Stone is quite unexceptionable. I ought, how-
ever, to add, that Mr. Von Hoff has, in the third volume of his work just published,
withdrawn his opposition to the validity of the evidence in favour of the rise of land
now going on in the Baltic -J-.

Before I pass from Gefle to another part of Sweden, I may state that Colonel Hall-
STROM, to whom we are indebted for an interesting article on the marks made to de-
termine the rate of change of level in the Bothnian gulf:}:, informed me that the
inhabitants of the opposite coast of Finland are as fully persuaded as those between
Gefle and Torneo that either the waters are falling in their country or the land rising.
The same gentleman observed, that notwithstanding the fluctuations of level in the
Baltic at certain seasons, he never happened to examine any of the ancient marks,
either on the Swedish or Finland side of the gulf, without finding the water below the
marks. He also gave me some marl of a violet colour, which he had lately brought
from Nadendal, near Abo, in Finland, found at the height of sixty feet above the level

* Geschichte der Veranderungen, Part I. p. 425.

t Ibid. vol. iii. p. 316.

X Kongl.Vetenskaps-Academiens Handlingar, Stockholm, 1823, p. 30.

THE LAND IN CERTAIN PARTS OF SWEDEN. 23

of the sea near the coast. It is composed principally^ like that before mentioned near
Stockholm and Upsala, of the decomposition of the Mytilus edulis, but also contains
perfect specimens of the Tellina Baltica, Littorina Uttorea, L. rudis, and Paludina ulva.

o

The castle of Abo on the Finland coast has been cited by several writers* as
proving that the ground on which it stands has not been elevated, that building
being many centuries old and yet close to the water's edge. But Colonel Hallstrom
assured me that the base of the walls is ten feet above the water ; so that the castle
may be four centuries old, and yet there may have been a gradual rise of the land at
that point to the amount of more than two feet in a century.

Not being able to visit Sundsvall, 1 applied by letter to Mr. James Dickson, resi-
dent at that port, who at my request put a series of questions, which 1 had drawn up,
to the most experienced pilots and fishermen on their return in November last from
their fishing-stations in the Gulf of Bothnia. In their answers they stated :

1st, That they could not conceive the possibility of the land rising, but were of
opinion that the sea had been sinking gradually in the Gulf of Bothnia, the fall du-
ring the last thirty years amounting to two feet, or thereabouts :

2ndly, They had never seen any of the marks cut in the rocks in 1820 ; but from
other appearances they inferred that the fall of the waters in the last fourteen years,
in the neighbourhood both of Sundsvall and Hernosand, was from six to eight inches :

Srdly, They had found it necessary in their own time, in consequence of the re-
tiring and shallowing of the waters, to remove their stations or fishing-posts nearer
to the sea :

4thly, They could point out examples of large blocks of rock which had been
moved and even conveyed from one place to another by ice, both on the shores of the
islands of the Gulf of Bothnia and on those of the main land.

I shall now pass over from the shores of the Baltic to the opposite coast of Sweden
between Uddevalla and Gothenburg, a district from 250 to 300 miles south-west of
that before described, and about three degrees of latitude farther south. The deposits
containing recent shells at Uddevalla, raised in some spots to the height of more than
two hundred English feet above the sea, have long been celebrated ; as also the dis-
covery, made by M. Alexandre Brongniart^ of barnacles attached to elevated rocks
of gneiss on the spots where they must have grown. I was desirous of seeing this
phenomenon, as it appeared to me that it might throw some light on the time which
has elapsed since the shelly beds were raised from the sea ; for if the Balani had been
exposed in the open air ever since the emergence of the rocks to which they were
fixed, it could hardly be supposed that the time had been indefinitely great, since in
that case the shells must have been decomposed. The fact recorded by M. Brongniart
was, I believe, observed at Capellbacken, immediately south of Uddevalla, where there
is a narrow valley in the gneiss, the bottom of which is filled up with a great deposit
of shells, sand, and clay, which rise, according to Hisinger, at their greatest eleva-

* Se? Von Hoff, Part I. p. 438.

24 . MR. LYELL ON THE PROOFS OF A GRADUAL RISING OF

tion 206 English feet above the sea*. I searched in vain for the Balani round the
boundary of gneiss at its contact with the beds of shells, as also on some insulated
rocks of gneiss which had been newly laid bare by the workmen, the shelly matter
being removed as materials for the repair of the roads. I presume, however, that it
was in just such a situation as that last mentioned that M. Brongniart found the
adhering barnacles; for under similar circumstances I afterwards found them in
another place, called Kured, about two miles north of Uddevalla -f-. Here a mass of
white shells has been laid open to the depth of forty feet, in a quarry resembling
singularly, when seen at a distance, one of our chalk-pits. Although now two
miles from the nearest sea, and a hundred feet or more above it, they evidently
fill what has once been a narrow channel, or fiord, bounded by rocks of gneiss.
The deposit now forms a flat inland meadow, the fertility of which is contrasted
with the steep and barren rocks which rise above it on all sides. It consists here
almost exclusively of broken and entire shells, which lie in thin strata. They have
been used largely both for making lime and for road materials ; and the removal of
part of them has exposed a ledge and precipice of gneiss, which they must previously
have covered to some depth. Adhering to the face of this precipice, I found the
circular supports of many large Balani. Some of these supports (see Plate II.
figs. 38, 39.) were three quarters of an inch in diameter ; and being white, they spotted
the rock, so as to present at a distance exactly the appearance of lichens. I also
found in horizontal clefts between the rocks pendent barnacles, fixed to the roof so
firmly that I was able to break off pieces of the hard gneiss on which the shells still
remained attached. In some places small zoophytes {Cellepora} Lam.) were ad-
hering to the rock or to the Balani ; and I also found some of the Cellepores with
the support of the Balani partially covering them. These corals and adhering shells,
therefore, must have grown upon the gneiss before the accumulation of drift shells
had filled up this valley, once a submarine hollow. I had always imagined that the
shelly formations near Uddevalla resembled ancient beaches of the ocean which had
been upraised, but they are in fact stratified formations of sand, clay, and gravel, and
in several places almost entirely of shells, which have filled up at some former period
the deep bays and fiords of a sea like that now bounding this coast. The quantity
and variety of the shells at Capellbacken, Kured, and Bracke reminded me of the
deposits of Grignon and,Damerie in the Paris basin ; but it is curious to reflect, that
although the shells are almost equally well preserved in both these regions, they are
specifically so distinct, that in the one it is scarcely possible to find a recent species,
while in the other nearly all, perhaps every one of the species, belong to the German
Ocean. The list of the shells which I collected here in one day will be found at the
end of this paper ; and although it will probably give but an imperfect idea of the

* Anteckningar, &c., v. p. 81.

t M. Beongniart says that he found the barnacles " un peu au dessus de I'amas coquillier," (Tableau des
Terr. p. 89) ; but this may refer to what then remained of the shelly mass.

THE LAND IN CERTAIN PARTS OF SWEDEN. 25

entire number which might be found, it will serve to show that a considerable variety
exists here.

The difference of this assemblage of shells from the fossils which I had before ex-
amined near the shores of the Baltic was very striking. A considerable proportion
of the whole mass, especially at Kured, was made up of the loose valves of a large
barnacle (Balamis tulipa, — see Appendix), to which I imagine the large supports be-
long which covered the surface of the gneiss at Kured. These supports exhibit a
number of concentric rings of growth, often very regular (see Plate II. figs. 38, 39.).
When the animal died, the shell seems to have been easily broken off from the rock,
and we must suppose successive crops of them to have been supplied for ages before
such enormous heaps of stratified shells were amassed. The Balanus sulcatus is also
very common, of a large size, remaining entire, with its support. Some of these I
saw fixed to the rock as before mentioned ; but generally they are found adhering to
valves of the Mytilus edulis, or large valves of the Pecten islandicus, of which last
the colour is preserved. Not one of these Balani, nor any species of that genus, in-
habits the Baltic. The shell next perhaps in abundance to the large Balanus is Saxi-
cava rugosa, of which the valves are often of extraordinary thickness, and must have
belonged to very aged individuals. The two valves are sometimes united ; but I
never found them lodged in any cavity either of a rock or zoophyte : perhaps they
may have inhabited the roots of large sea-weeds. (See remarks on this shell in the
Appendix.) The thick shells of Mi/a truncata are also in great quantity ; and the
Mytilus edulis four or five times larger than in the Baltic, and retaining much of its
colour. A Fusus also {Murex Rumphius, Mont.) occurs in profusion.

I found at Uddevalla many bivalve shells, in which small holes had been drilled by
predaceous Trachelipodes, whereas among the fossils near Stockholm and Upsala I
could never meet with a single bivalve so perforated ; and there are, I believe, no
zoophagous Mollusca now living in the Baltic.

From Uddevalla I went to the small island of Gulholmen (see Map), in the parish of"
Morlanda, part of the coast not far from Uddevalla, where Celsius declared, at the
beginning of the last century, that the sea was sinking. On my way I crossed Orust,
an island about fourteen miles in diameter, consisting chiefly of micaceous schist, form-
ing low hills a few hundred feet high, resting upon which, at different elevations, are
beds of sand, gravel, and clay, sometimes entirely destitute of shells, but often inclos-
ing many recent shells, for the most part the same species as at Uddevalla, but with
the addition of the Ostrea edulis and Cerithium reticulatum. I met with some of these
fossils between Hogan and Morlanda in a blue clay, which seemed to lie at a higher
elevation than any of the shells near Uddevalla. The features of the scenery in the
interior of Orust are precisely such as we might suppose the present coast to exhibit
if it should be lifted up with its small islands, rocks, and friths, and if the intervening
level flats, where sand, mud, and shells are known to be now accumulating, should
be laid dry. An account was given me of the finding of an anchor near Morlanda,

MDCCCXXXV. E

26

MR. LYELL ON THE PROOFS OP A GRADUAL RISING OF

in a valley, the lower part of which had gained considerably in extent, within the
memory of persons now living, by the retreat of the waters. In descending to EUelos
on the eastern coast, opposite the island of Gulholmen, I observed shelly deposits
about fifteen feet above the level of the sea, in which were many specimens of the
Ostrea edulis, Saxicava rugosa, Cerithium reticulatum, and other shells, some of which
I had seen at Uddevalla, and others cast up on the shores in Orust.

In regard to the island of Gulholmen, Celsius tells us that in his time forty pilots,
none of whom were under sixty years of age, having been assembled there, had una-
nimously declared to one Mr. Kalm that there was only fifteen feet depth of water in
places where in their youth there had been eighteen feet. He also mentions that one
of the pilots pointed out a small rock near Gulholmen, then rising two feet above the
water, which, when he was a child, was not visible *.

The present inhabitants, as far as I conversed with them, are entirely ignorant of
any such statements having been recorded a century ago ; but on my demanding
whether the water stood now at the same level as in their younger days, they unani-
mously declared that it did not. Mr. Bruncrona, in his memoir before cited, men-
tions that on an insulated rock called Gulleskar, near the harbour of Gulholmen,
there was an iron ring to which ships were moored, and that this ring, when mea-
sured in 1820, was eight feet above the level of the water. Unfortunately, no parti-
culars are given; and as both the chief pilot of 1820 and another who assisted him
in the measurement were dead at the time of my visit, I could not ascertain with
certainty from what point of the ring they had begun their measurement, nor the
means they had taken to secure accuracy. Having obtained the assistance of Johan
WuNSCH, now chief pilot, I found the point where the ring is fixed into the rock to
be only seven feet five inches above the level of the sea, which was then declared to
be at its usual level, a very slight wind only blowing from the north-north-west, and
there being never any tides in the sea here. The iron ring, which has remained for
more than half a centuiy in its present place, is fifteen inches in diameter, and the
top of it stands more than eighteen inches above the level of the rock when it is
erect, in which position I found it, thus (see fig. 12), having been so placed for the sake

Fig. 12.
Summit of the Gulleskar, with the Ring.

* Celsius, Observations on the Diminution of the Waters of the Baltic and German Ocean.— Trans. Roy.
Acad, of Sweden.

THE LAND IN CERTAIN PARTS OF SWEDEN. 27

of drying the fresh paint, with which it had been just covered ; but the islanders
suppose the measure to have been taken from the bottom, or point where the staple
enters the rock, which seems most probable. Curiosity led a great many of the
inhabitants to accompany me ; and when I declared that the height of the ring was
seven inches less above the water than that recorded by Bruncrona, many of the
older men with one accord pronounced this to be impossible, and said that the for-
mer observation must have been incorrect, for that the sea must, on the contrary,
have fallen since 1820. Some of them affirmed that the pilot who received orders in
1820 to make the measurement was ignorant in what manner to proceed, the place
of the ring not being perpendicularly over the water, and he having no instrument
for levelling, so as to ascertain that the line which he first carried out from the ring
was strictly horizontal. Whether there was any foundation for this charge I cannot
pretend to decide ; but I mention it as proving that the islanders believe that there
is a change of level going on. It may be useful to those who may make future
measurements to state what length of line it required to reach from the iron staple
of the ring to the nearest point of the rock to which the sea comes up, this point
being now exactly in the direction north-west and by north of the ring. I stretched
the rope from one angle to another of the rock, not applying it to the surface of the
intervening hollows, and found its length to be fifteen feet five inches and a half. As
the GuUeskar, however, is by no means well chosen for the facility of observations, I
had a new mark cut on the face of a vertical cliff on the south side of the harbour,
about a hundred yards from the post-house. I subjoin a copy of the mark, the lower
part of which was cut in my presence, and which the chief pilot pro-
mised to see completed. The horizontal line was cut six inches above
the water-level, and the vertical line at the right end of it, six inches in
length, was terminated at the bottom by a short cross line, which the
surface of the water just covered. The vertical depth of water below
the mark was four feet two inches and a half. I may suggest, that
whenever horizontal lines or any marks are made, like that of St. Olof 's Stone be-
fore mentioned, not at the level of the sea, but at a certain height above it, on a ver-
tical face of rock, there should always be a perpendicular line cut down to the then
existing level of the water, to facilitate subsequent observations and prevent mistakes.
Marks cut at given heights above the standard level are perhaps the best, as they are
not concealed by a temporary rise of the water.

Before leaving Gulholmen I visited the Skefverskar, an isolated rock which, ac-
cording to the testimony of several old people, was always covered, except at very low
water, about forty years ago. In their younger days, before the year 1799, when the
present church of Gulholmen was built, they went to church at Morlanda, and passed
near this rock, the exposure of the summit of which was a well-known sign to them
of a particular state of the weather. This rock is now always seen except when the
sea is very high. I found the highest point of it to be sixteen inches above the level

E 2

]

Fig. 13.

c

/<?

T.

\8

/

'it,

28

MR. LYELL ON THE PROOFS OF A GRADUAL RISING OF

of the water ; and its extreme length from east to west, including a detached point at
one end, measured fifty-two feet four inches and a half.

From Gulholmen I went to Marstrand, an island about twenty miles to the south,
in order to observe another of the marks enumerated by Bruncrona. I first re
crossed the ferry at Svansund to the main land, and then passed to that of Tjufkil,
which leads to Koon. On the shore at Tjufkil I found a bed of oysters and other
shells, five or six feet thick, with pebbles intermixed, rising to the height of sixteen
feet or more above the water. The oysters, which were ingreat number, all belonged
to the Ostrea edulis, which is taken on this coast ; and the other shells were the same
as at Uddevalla and EUelos, with the addition oi Anomia striata. This shelly deposit
has been ovei-whelmed by a great fall of rock from the steep heights of gneiss behind,
some of the fragments which cover the shells being about nine feet square.

Not far from the harbour at Marstrand is an artificial channel, which, in the year
1770, was cut through an isthmus which formerly connected two parts of Koon
island. The excavation was made through a mass of clay and sand with shells, simi-
lar to that of Tjufkil, already mentioned ; so that there can be no doubt that there
must originally have been a natural passage in this place. One Captain Constant,
who superintended the digging of the channel in 1770, caused a mark, of which the
following is a sketch, to be hewn on the face of a vertical rock of micaceous schist
on the shore of Koon, nearly opposite Marstrand.

Fig. 14.
Mark at Koon Island, near Marstrand.

An horizontal line, ten inches long, is seen twenty-one inches below the bottom
of the last cipher. This line I found to be just ten inches above the level of the

THE LAND IN CERTAIN PARTS OF SWEDEN. 29

water. My observation was made on the 19th of July 1834, sixty-four years after
the mark was cut. Now my boatmen stated that the horizontal line was origi-
nally intended to express the lowest level to which the sea fell at the time of dig-
ging the Koon canal ; and this information was confirmed by Mr. O. J. Westbeck,
who resides in the immediate neighbourhood. On my applying to this gentleman to
learn whether the water at the time of my observation might be considered as un-
usually low, he said that as the wind was easterly, the sea was certainly below its
mean level, but it had by no means reached its extreme point of depression, for there
still was water in the Koon canal, immediately opposite his villa ; whereas, after the
prevalence of a strong easterly wind for two days, the sea falls so low that certain
parts of this canal are dried up. He suggested, therefore, that by measuring the depth
of water in those parts of the canal which dry up, and adding that depth to the ten
inches which I had already obtained below the mark only half an hour before, I
should ascertain the point of extreme low water as compared to that of 1770. We
accordingly found that the water in the places alluded to was fourteen inches deep ;
so that the lowest water now is two feet below the maximum of depression sixty-four
years ago. Mr. Westbeck said that he had always heard from his father that the
mark, which was cut the year he was born, was intended to express the lowest level
of the sea during the digging of the canal in 1770.

I have already stated that there is no tide on the coast here, a circumstance which
seems very extraordinary ; but all the pilots and seamen agree in asserting the fact.
A strong wind off the shore causes the water to fall two or three feet, and to rise as
much if it be in the opposite direction. Notwithstanding these occasional oscilla-
tions, the inhabitants pretend to determine whether the sea is two or three inches
above or below its standard level. I was shown here, as at other places, rocks which
forty or fifty years ago could rarely be seen, but are now permanently above water.
I was also told of numerous rocky channels where boats could once pass, but which
had now grown too shallow, and of meadows which were yielding from time to time
a larger quantity of hay, in consequence of their increased extension on the side
towards the sea.

I know not how much further to the south the same signs of a rise of the land have
been observed, but it is certain that the narrow frith in which the port of Gothenburg
is situated has been gradually filling up, in such a manner as would happen if the same
cause of change was cooperating there with the deposition of river-sediment. It is
well known that in the sixteenth century the ancient port was placed twenty miles
further up, and called Lodese ; and this was afterwards removed further down, and
called New Lodese, to distinguish it from what remained of the more ancient har-
bour. But now the newer of these places is called Gammle Staden, or the old town,
and is a mile or more above Gothenburg.

On the banks of the river at Gothenburg I found a deposit of blue clay, filled with
a great variety of recent marine shells. Among others, Lutraria compressa ; Mactra

30 MR. LYELL ON THE PROOFS OF A GRADUAL RISING OF

subtt-uncata, very abundant ; Tellina solidula ; Donax trunculus ? Dillwyn ; Cyjrrina
Islandica, Fenus gallina, Cardium edule, Littorina littorea, Turritella terehra, RosteU
lana pes pelicani, and Buccmum reticulatum. This part of the estuary is now always
filled with fresh water, except on rare occasions, and for a short time, when a strong
wind drives the sea up the river, and causes the water to rise six feet, in which case it
becomes brackish. At different heights above the sea, in the valley of the Gotha Elf,
between Gothenburg and Trolhattan, marine shells have been found similar to those
of Uddevalla.

Some persons who have been long resident in Gothenburg pointed out to me, as a
proof that the water was falling there, that the rocks several feet above the highest
water-mark were bare and uncoloured, by which they meant that no lichens grew
upon them.

A similar remark had been made to me at Tjufkil, Svansund, and other places on
this coast. It seems probable that some species of lichen may require a much longer
time to establish themselves on newly exposed rocks than others ; and I could ob-
serve distinctly, near Gothenburg, that some kinds approached nearer the water's
edge than others, and that the variety of species became greater and the colour difr
ferent on ascending to greater heights. It would therefore be an interesting point for
a geologist sufficiently skilled in botany to determine whether the extent of the lichens
and mosses downwards towards the water on this coast, where the rocks are supposed
to be always rising, presents different phenomena from the line of vegetation on other
coasts, where the relative level of the land and sea is known to have remained sta-
tionary.

On many parts of the eastern coast, above described, the sea freezes in severe
winters in the Skar ; that is to say, among the rocks and islets which skirt the main
land, and where there is almost always still water. As I have before mentioned the
accounts which I received of the transporting power of ice in the Gulf of Bothnia,
it may be well to state some facts bearing on the same subject which I learnt at
Gothenburg. In the harbour of that port there are a great number of strong wooden
piles, called dolphins, three or four feet in circumference, the lower parts of which
are sunk to a considerable depth in the mud, and firmly fixed in it, so that vessels
may be moored to their tops. As these dolphins are annually frozen in, it is found
necessary to break the ice round them ; but sometimes this has been neglected, and
Mr. Harrison, the English Vice-Consul, informed me, that on such occasions he has
known a great number of the piles drawn up together out of the mud six feet per-
pendicular, a rise of the river having caused the ice to float up to that amount.

Mr. Westbeck of Marstrand, to whom I have already alluded, mentioned to me,
that having been formerly employed in the Swedish Diving Company for thirty years,
he had opportunities of witnessing the extraordinary power of ice to lift up from the
bottom of the sea and remove to a distance very heavy masses. In two instances the
ice collected round sunken vessels which were under his charge, and having frozen

THE LAND IN CERTAIN PARTS OF SWEDEN. 31

round them, floated them off with their cargo and ballast from shallow into deep
water.

I shall now state some general conclusions to which I have been led by the obser-
vations above described. It is evident from the position of the fossil shells of recent
species on the coast of the Baltic between Gefle and Sodertelje, and on the shores of
the ocean between Uddevalla and Gothenburg, that the tract of land (see Map,
Plate I.) which once separated the two seas in this region was much narrower at a
comparately modern period. Shells like those of Uddevalla have not only been found
a few miles due east of that place, but as far inland as Trolhattan in digging the
canal there*; and still further in the interior, about fifty miles from the coast at
Tusenddalersbacken, and other places near Lake Rogvarpen in Dalsland, on the west
side of Lake Wener (see Map, Plate I.). Of these fossils an account will be seen in
the works of Mr. Hisinger, to whom we are indebted for a valuable geological map
of the whole of the south of Sweden. They are found in Dalsland about as far above
the sea as near Uddevalla, or about two hundred feet high ; so that when they were
deposited, we must suppose the whole of that extensive Lake Wener, the surface of
which lies at an inferior level, to have formed part of the ocean. On the other hand,
when the marine shells of the environs of Upsala, Stockholm, and Torshalla lived in
the Baltic, we must suppose the whole of Lake Maeler to have been a bay of that sea.
Now the distance between the nearest points of Lakes Wener and Maeler is only
about seventy English miles, whereas there is more than three times that distance be-
tween Stockholm and Uddevalla, the nearest points at which the two seas now ap-
proach each other in the same direction. It is very desirable that Swedish geologists
should pursue this subject still further, and ascertain precisely how far the shells of
the two seas can be traced inland in opposite directions.

In crossing from Stockholm to Sodertelje, Arboga, Orebro, Mariestadt, and We-
nersborg to Uddevalla, I passed the summit level of the country, about half-way be-
tween the Baltic and the ocean, near Bodarne, where the hills, as Von Buch remarks,
do not probably exceed five or six hundred feet in height. I found erratic blocks
scattered widely over the whole of this country, but they were much larger and more
numerous on the eastern than on the western watershed. There were also deposits
of stratified sand and gravel on the heights, but I was never able to discover any
shells in them, nor in the blue clay in the lower grounds bordering the lakes, except
very rarely, and these were of freshwater species ; as, for example, at the place before
mentioned near Lake Maeler not far from Torshalla, between Smedby and Kongsor.
It will naturally be asked, whether the appearance of the interior is generally such
as would agree with the hypothesis of a gradual rise, according to which we must
suppose that every tract has in its turn been first a shoal in the sea, and then for a
time a shore. It appeared to me, on comparing both the eastern and western coasts
and their islands with the interior, that the geological appearances and physical

* See Hisinger's Anteckningar, vol. iv. p. 42.

32 MR. LYELL ON THE PROOFS OF A GRADUAL RISING OF

features of those parts of the country which I examined answered well to all the
conditions of such a theory. In passing from Gefle to Fahlun, and from thence to
Sala, I found the number of erratic blocks very great, as now on the islands and
shores of the Bothnian Gulf; whereas on the opposite or western coast they are
smaller in size and quantity, both in the interior of the country around Uddevalla
and Gothenburg, and at the sea-side in the contiguous Skiir. I saw some considerable
l)ouiders overlying the deposits of recent shells at Capellbacken near Uddevalla, a
phenomenon analogous to that described near Upsala, where these huge erratic blocks
repose upon the sand-hills, characterized by fossil shells of Baltic species. The trans-
portation, therefore, of these rocky fragments into their present position continued
after the period when the modern shelly formations of both coasts were accumulated ;
and it may be inferred from several facts mentioned in this memoir, that the drifting
of such blocks may now be going on by means of ice every year. I am at a loss to
conceive from what data some geologists have inferred the simultaneous dispersion
of the erratic blocks of the North of Europe ; but it would carry me into too wide a
digression should I endeavour to controvert that theory. I can, however, confirm the
statement of Professor Hauswann, that, in the ridges of sand and gravel, the largest
blocks occur in the highest parts of each ridge ; a fact which seems to me to point
to the mode in which they may have been drifted into their present position. For if
these ridges were originally sand-banks in the sea, as the marine shells found in
some of them incline me to believe, the summits of such banks would have arrested
the progress of ice-islands which might transport fragments of rock in the man.ner
before suggested.

In regard to the proposition, that the land in certain parts of Sweden is gradually
rising, I have no hesitation in assenting to it after my visit to the districts above al-
luded to. Independently of the geological proofs derived from strata containing recent
shells, the evidence in favour of an upward movement consists of two kinds : first, the
testimony of the inhabitants ; and secondly, the altered level indicated byartificial marks
cut in the rocks. More than one generation has passed away since Celsius recorded
the stories of pilots, fishermen, and the inhabitants of the two opposite coasts at Gefle
and Gulholmen respecting the increased extension of land and apparent sinking of
the sea. It was at the same places that I heard precisely similar accounts from per-
sons now living ; so identical, indeed, that if related, they would appear mere repe-
titions of the words of Celsius, with scarcely any change except in the names of the
witnesses. But I am aware, from what I myself experienced when reading formerly on
this subject, that it is not easy to convey to the minds of those who do not visit the
country, the impression made by the testimony now under consideration, deriving as
it does almost all its weight from an accumulation of minute particulars, each, sepa-
rately considered, of but small importance.

From what I saw at Calmar and Stockholm as compared with Oregrund and Gefle,
I have no doubt that the rate of elevation is very different in different places ; and in

THE LAND IN CERTAIN PARTS OF SWEDEN. 33

the south of Scania I could not ascertain, either from the testimony of the inhabitants
or from any appearances on the coast, that the slightest change of relative level can
be detected. The difference of about three feet in a century, indicated by the mark
at Lofgrundet, and of about two feet in sixty-four years, by that of Marstrand, are
in such complete accordance with the results of the surveys of Bruncrona, Hall-
STROM, and others, as to lead me to place entire reliance on the conclusions to which
they have arrived from a larger number of data, and respecting a territory of much
gi-eater extent. The slight amount of difference between the level of the sea and the
marks of 1820 which I observed at Oregrund and Gefle, although corroborating the
same result, are undoubtedly in themselves of small value ; and a difference of level
amounting only to about four or six inches may be easily attributed to accident or
the particular state of the weather at the time of my visit. Subsequent observers
might find the same marks submerged beneath the waters ; but I nevertheless be-
lieve, that if the summer season and a calm day be selected, so that the circumstances
shall correspond with those under which the marks were originally cut, there will be
found to have been a real depression of level, to the amount of several inches, in the
course of the last fourteen years.

Be this as it may, I may be allowed to congratulate the scientific world that this
wonderful phenomenon is every day exciting increased attention among the philoso-
phers of Sweden, and especially of Professor Berzelius, who, in his reports to the
Academy of Sciences at Stockholm, has already recorded many valuable observations
on the levels of the water of Lake Maeler at different seasons, and who is understood
to be now exerting himself to secure more frequent observations in future of the marks
in the Bothnian Gulf. It is only by multiplying such measurements, and repeating
them within short intervals of time, that we shall be able to determine whether the
movement of the land be oscillatory or always in one direction, and whether it be in-
termittent or constant.

Appendix.

List of Fossil Shells from the Country near Stockholm.

Names. Observations.

TeUina Baltica. Var. a. The variety of this shell, found fossil in sand and marl at
PI. II. figs. 1. & 2. Solna, Brankyrka, and Sodertelje, where it is associated

with littoral shells, is smaller, thinner, and deprived of
epidermis, resembling those which I collected in the sand
on the shores of the Gulf of Bothnia and at Solvitzborg.

MDCCCXXXV. F

34

MR. LYELL ON THE PROOFS OF A GRADUAL RISING OF

NameB.
TelUna Baltica. Var. h.
PL II. figs. 3. & 4.

2. Cardium edule.
Pl.II. fig. 6.

Var.

3. Mytilus edulis.

4. Littorina littorea. {Tur-
bo littoreus, Linn.)

5. Littorina rudis.
rudis.)

{Turbo

6. Littorina crassior. {Tur-
bo crassior).

7. Paludina ulva} PI. II.
fig. b. a.b. c.

Observations.
This variety of T. baltica was found in stiff blue clay
between Smedby and Kongsor (see page 10), as also at
Ulfva, near Upsala (see page 14). It is larger, thicker,
and covered with a strong green epidermis ; but there is
a passage between it and the preceding variety.

This Cardium is generally of a small size in the brack-
ish waters of the Baltic, and often more elongated trans-
versely than individuals of the same species in the ocean.
This transverse form is seen in the fossils found at Solna
and other places near Stockholm mentioned in the me-
moir ; and Mr. Gray tells me that the same variety has
been observed elsewhere in brackish waters. But indivi-
duals of the more ordinary form, though of a dwarfish
size, are also found living in the Baltic, and fossil in the
localities above mentioned.

The variety of this shell, which occurs fossil at Solna,
Brankyrka, Sodertelje, Ulfva, &c., is small, about half an
inch long, like that now inhabiting the brackish waters
of the Baltic. It is almost always found in a state of de-
composition, and converted into a violet-coloured marl.

Found fossil at Solna, Brankyrka, Sodertelje, Sker-
plinge, and other places bordering the Baltic. I found va-
rieties of different ages, but never any which approached
the larger size which the same species often attains on
the borders of the ocean.

A young specimen of this occurred fossil with the for-
mer at Brankyrka ; also in the violet-coloured marl from
Nadendal in Finland, given me by Colonel Hallstrom
(see page 22).

I found specimens of this at Solna.

A great number of small univalves, of which I have
given figures, are found fossil with littoral shells at Solna,
Brankyrka, and Sodertelje, resembling those which occur
generally in the sands of the shores of the Baltic, as well
as on those of the ocean between Uddevalla and Gothen-
burg. The three principal varieties which are figured are

THE LAND IN CERTAIN PARTS OF SWEDEN.

35

Names.

8. Rissoa parva. {Turbo
parvus, Mont.)

9. Neritinajluviatilis.

10. BuUmus lubricus.

Observations.

selected from the different localities of fossils before men-
tioned near Stockholm. In var. a there are five volutions,
which are of a squarish form ; in var. b five, which are
rounded ; and in var. c six, which are rounded. On com-
paring a great number of individuals, there appeared to be
so many passages from one form to another as to render
it difficult, if not impossible, to establish distinct species.

I found at Brankyrka a few individuals which Mr. Gray
referred to this species.

A small black variety of this species was met with at
Brankyrka, which I also saw recent in abundance on the
shores of Moen, in Denmark. Dr. Beck, of Copenhagen,
regards it as a distinct species. It is smaller than the
same shell living in fresh water. I found some varieties
both fossil at Brankyrka and recent at Graso, near Gefle,
which had the ordinary colours of the N.JiuviatiUs.

Fossil at Brankyrka. (See page 6.)

List of Fossil Shells from Uddevalla, on the West Coast of Sweden.

Names.

1. Pholas crispata.

2. My a truncata.

3. Anatina my alts, Lam.
{My a pubescens, Turt.
Llgula pubescenSj Mont.)

4. Saxicava rugosa. {My-
tilus rugosus, Mont.)
PI. II. figs. 24—29.

Observations.

I met with one valve only of this species, at Capell-
backen, near Uddevalla.

Found in very great abundance around Uddevalla.

I met with one very perfect specimen, with its liga-
ment, fossil near Uddevalla.

The small individuals, figs. 28, 29., would be called by
some conchologists Hiatella arctica ; but many natural-
ists are now of opinion that the shells called Saxicava or
Hiatella rugosa {Mytilus rugosus, Linn.), and the Hia-
tella arctica, are not specifically distinct ; and the fossils
which I collected in great abundance at Uddevalla con-
firm me in this opinion. This shell is more abundant
perhaps than any other, and some individuals are of great
thickness, and must evidently have been very aged (see
fig. 27.)- I never found any of them lodged in cavities in
f2

36

MR. LYELL ON THE PROOFS OF A GRADUAL RISING OF

Names.

5. Tellina triangularis.

6. T. Baltica,

7. Astarte. Figs. 17, 18.

8. Astarte. Figs. 19^ 20.

9. Astarte. Figs. 21, 22,
23.

10. Cardium edule.

1 1 . Mytiius edulis.

12. Modiola barhata.

13. Pecten Islandicus.

14. Terebratula. PI. II.
figs. 32, 33.

15. Patella, allied to ^e^/w-
rfmaria,CHEMN. {P.Cle-
landijSow.) PI. II. figs.
30,31.

Observations.

rocks, and I presume that they must have lived in the
roots of fuci, in which situation they are sometimes met
with on our coast.

Common at Capellbacken.

I found one individual, which seems not distinguishable,
in size or shape, either from the fossil or recent T. bal-
tica of the neighbourhood of Stockholm.

Shell rather convex, transversely elliptical, thin; its sur-
face strongly furrowed ; furrows rounded, about sixteen.
Lunette deep, elliptical. Lateral tooth slender, elon-
gated, more transverse than the recent Astarte Garensis,
and with somewhat fewer furrows, but perhaps a variety
of the same?

Shell convex, transversely elongated, but less so than
the former ; both the anterior and posterior margins more
rounded than in the preceding ; rather thin ; its surface
strongly furrowed ; furrows deep, rounded, about sixteen.
Lunette deep, lanceolate, elongated. The lateral tooth
slender. Perhaps, like the former, a variety of A. Ga-
rensis, to which it approaches much nearer.

Shell compressed, suborbicular, slightly truncated on
the posterior margin ; thin ; its surface rugose, marked
with many transverse furrows when young. Lunette
deep, lanceolate, short, pointed. Lateral tooth small,
short. Fulcrum long.

In great abundance, and preserving a portion of its
colour ; about two inches in length.

From Kured.

In great abundance, often preserving its colour, and
covered with Balani.

A single perforated valve is all that I found of this
genus.

This Patella is referable to the genus Lottia, Gray,
(Philosophical Transactions, 1834.).

THE LAND IN CERTAIN PARTS OF SWEDEN.

37

Names.

1 6. Patella Noachina,
Chemn. (Puncturella,
Lowe.) Pl.II.figs. 13,14.

1 7. Margarita striata, Lowe .
(Trochus, Lam.)

1 S.Littorina littorea. {Tur-
bo littoreus, Linn.)

19. Littorina} Plate II.
fig. 10.

20. Turritella} Plate II.
figs. 11, 12.

21. Natica, allied to N.
clausa. PI. II. figs. 7,
8, 9.

22. Felutina, Gray. PI. II.
figs. 15, 16.

23. Fusus. {Murex rum-
phitis, Mont.)

24. Fusus corneus.

25. Buccinum undatum.

26. Balanus sulcatus.

27. Balanus tulipa. (Lepas
tulipa, MuLLER, Chem-
nitz, viii. t. 92. f. 832.)
PI. II. figs. 34, 35, 36,
37, 38, 39.

Observations.

Mr. G. SowERBY informs me that this species has been
lately found fossil with other recent shells, at a slight
elevation above the level of the sea near Glasgow.

Some young individuals at Uddevalla retain their co-
lour in great perfection.

The shell here figured has lost its outer coat, and may
perhaps belong to the genus Littorina.

This shell is very like a worn Scalaria, but perhaps
belongs to the genus Turritella.

This shell is common at Uddevalla, especially at Kured,
and differs decidedly from the N. glaucina, having a less
flattened spire, and being more ventricose, I presume that
it is the N. glaucina of Mr. Hisinger's list of Uddevalla
shells.

Probably Helix laevigata, Mont. An imperfect speci-
men.

Very common.

Abundant.

Very abundant, and of large size, and occurs both at-
tached to other shells and fixed to the rocks of gneiss,
(see p. 25.)

Mr. Gray informs me that this shell is not noticed by
Lamarck, and that it differs from other Balani in the
substance of the shells being solid, and the base being
only longitudinally grooved on the inner side; also in the
side edges of the valves being entire and not crenulated.
By the aid of these characters Mr. Gray has formed of
this and a few other species which are in the collection
of the British Museum, a particular section, to which he
has given the name of Chirona. This I presume is the
species called B. Uddevallensis in some of the Swedish
lists of Uddevalla fossils. It is of great size, frequently
three or four inches long. The supports, figs. 38 and 39,
were found adhering in great numbers to the' face of the

38 MR. LYELL ON THE RISING OF THE LAND IN SWEDEN,

Names. Observations.

rocks of gneiss, and they appeared to me, from their large
size, to belong to this species.

28. Echinus. {Echinome- Fragments of this Echinus were found at Capellbacken
tra.) PI. II. figs. 40,41. near Uddevalla, and they have been put together as re-
presented Plate II. figs. 40, 41.

This collection of Uddevalla fossils must be very incomplete, as they are only such
as I could obtain by diligent search, and with assistance, in one day. I did not meet
with Plleopsis Ungarica, but Mr. Hisinger showed me specimens of that shell which
he obtained there.

Description of the Plates.

Plate I.

Map of part of Sweden, to indicate the principal localities referred to in the pre-
ceding paper.

Plate II.

Figs. 1, 2. Tellina Baltica, var. a, from Solna, Brankyrka, and Sodertelje. (See
Appendix, p. 33.)

3, 4. The same, var. b, from Ulfva. (Appen. p. 34.)
Fig. 5. Paludina ulva}, three varieties, from Solna, Brankyrka, and Sodertelje.
(Appen. p. 34.)
6. Transverse variety of Cardium edule, from Solna. (Appen. p. 34.)
Figs. 7. 8, 9. Natica, allied to N. clausa, from Kured. (Appen. p. 37.)
Fig, 10. Littorina} of which the outer coat is lost. (Appen. p. 37.)
Figs. 11, 12. Turritella} (Appen. p. 37.)

13, 14. Patella, Lam. (Appen. p. 37.)

15, 16. Felutina. (Appen. p. 37.)

17, 18. Astarte. (Appen. p. 36.)

19, 20. Astarte. (Appen. p. 36.)

21, 22, 23. Astarte. (Appen. p. 36.)

24, 25, 26, 27, 28, 29. Saxicava rugosa, from Uddevalla. (Appen. p. 35.)

30, 31. Patella. (Appen. p. 36.)

32, 33. Terebratula. (Appen. p. 36.)

34, 35. Large valves of Balanus tulipa, from Uddevalla. (Appen. p. 37.)

36, 37. Opercular pieces of the same. (Appen. p. 37.)

38, 39. Supports of the same. ? (Appen. p. 37.)

40, 4L Echinus (Echinometra) , from Capellbacken. (Appen. p. 38.)

[ 39 ]

II. Note on the Electrical Relations of certain Metals and Metalliferous Minerals.
By R. W. Fox. Communicated by Davies Gilbert, Esq. F.R.S.

Received and read January 15th, 1835.

I HAVE ascertained that the crystallized grey oxide of manganese holds a much
higher place in the electro-negative scale than any other body with which I have com-
pared it, when immersed in various acids, and alkaline solutions ; and the other metals
and minerals which I have examined, appear to rank after it in the following order :
Manganese.

1

These five hold nearly the same place, varying in their mu-
tual relations according to the time of their remaining im-
^mersed, and the nature of the liquid.

The same may in some degree be said of the three other
bodies included in the larger bracket.

Rhodium.

Loadstone.

Platina. )>

Arsenical pyrites. |

Plumbago. J

Iron pyrites.

Arsenical cobalt.

Copper pyrites.

Purple copper.

Galena.

Standard gold.

Copper nickel.

Vitreous copper.

Silver.

Copper.

Pan brass.

Sheet iron.

I have also compared the action of different metalliferous combinations in various
diluted acids, &c. on the needle of the galvanometer, and some of the results are given
in the following Table, in which cases sea-water, and also muriatic acid diluted with
thirty-two parts of water, were employed. The figures show the angles of deflection
observed when the needle became stationary, which may serve to give some idea of
the relative effect of the combinations in question on the needle ; but I find that the
results are often considerably modified by the bodies being exposed for a longer or
shorter time to the action of the acids, &c. ; indeed this is so remarkable in the case
of copper with zinc, that the needle often moves back much more than ten degrees
from its maximum angle of deflection in one or two minutes after immersion;
whereas in the case of iron with zinc, for example, the immediate retrograde motion

40

NOTE ON THE ELECTRICAL RELATIONS, ETC.

of the needle is very inconsiderable, and it is still less, if anything, when some of the
ores are substituted for one or both these metals. May not these phenomena depend
on the relative degrees of tenacity with which the electric elements are retained by
different bodies, it being apparently greatest in the case of compound bodies ?

Manganese* (crystallized)

Loadstone

Platina

Plumbago

Iron pyrites

Copper pyrites

Purple copper ore

Galena

Gold

Vitreous copper ore

Silver

Sheet copper

Pan brass

Sheet iron

Zinc.

Sea
Water.

Diluted

Muriatic

Acid.

56
41
21
52
34
49
44
47
26
42
56
55
34
36

60
58
46
56
38
57
45
50
38
51
59
58
43
46

Copper.

Sea
Water,

35

21

1

23

7
36
14
19
11
16
22

Diluted

Muriatic

Acid.

45
29

5
31

8
31
10
27
14
24
21

Iron.

Sei
Water.

52
33
21
45
20
43
33
36
14
17
47
19
11

Diluted

Muriatic

Acid.

Lead.

Sea
Water.

Diluted

Muriatic

Acid.

54
48
23
45
29
44
40
41
30
25
45
37
17

50
32
15

42
20
45
32
37
25
24
44
40
11

56
47
21
45
19
43
38
37
24
32
42
38
30

If we regard the electrical relations of different metalliferous minerals in a geologi-
cal point of view, it is curious to observe how nearly many of those which are usually
associated in the same veins agree in this respect, their reciprocal voltaic action being
generally very small. Were it otherwise, it may be assumed that the evidences of
decomposition in situ would be much more decided and general than they now are.
There is, however, a sufficiently strong action in some cases to account for the electro-
magnetic phenomena which have been observed in copper and lead veins : thus, when
copper pyrites and vitreous copper form a voltaic combination in water taken from a
mine, or even in spring water, they are capable of producing considerable deflections
of the needle. It is not, therefore, surprising, that when two parallel veins, or two
portions of the same vein separated by imperfect conductors, are connected with the
galvanometer, the action on the needle should be very decided. The degree of in-
fluence on the needle does not seem to depend, in the case of metalliferous minerals,
upon extensive voltaic surfaces ; for only one or two inches of surface may produce
nearly the maximum effect in deflecting it, if the wire used in the galvanometer be
small. Hence, the considerable deflection, which has been sometimes observed when
two masses of ore were connected by the wires, proves that their reciprocal action,
taken in the aggregate, must be veiy great ; and it appears to be highly probable that
the metalliferous veins, and perhaps even the rocks themselves, impregnated as they
are with different mineral waters, and thereby rendered imperfect conductors, if not
exciters of electricity, may have an important influence in the economy of nature.

* The contact of the wire with the manganese and other minerals was produced by pressure only, and the •
deflections would doubtless have been greater if the contact had been more perfect.

t I have ascertained that the electro-magnetic action of mineral veins was the same whether copper or zinc
conductors were employed for making the contact with the ores.

[ 41 ]

III. Experimental Researches in Electricity. — Ninth Series. By Michael Faraday,
D.C.L. F.R.S. Fullerian Prof. Chem. Royal Institution, Corr. Memh. Royal and
Imp. Acadd. of Sciences, Paris, Petershurgh, Florence, Copenhagen, Berlin, 8§c. S^c,

Received December 18, 1834, — Read January 29, 1835.

§. 15. On the influence by induction of an Electric Current on itself: — and
on the inductive action of Electric Currents generally.

1048. XHE following investigations relate to a very remarkable inductive action
of electric currents, or of the different parts of the same current, and indicate an
immediate connexion between such inductive action and the direct transmission of
electricity through conducting bodies, or even that exhibited in the form of a spark.

1049. The inquiry arose out of a fact communicated to me by Mr. Jenkin, which
is as follows. If an ordinary wire of short length be used as the medium of commu-
nication between the two plates of an electromotor consisting of a single pair of
metals, no management will enable the experimenter to obtain an electric shock from
this wire ; but if the wire which surrounds an electro-magnet be used, a shock is
felt each time the contact with the electromotor is broken, provided the ends of the
wire be grasped one in each hand.

1050. Another effect is observed at the same time, which has long been known to
philosophers, namely, that a bright electric spark occurs at the place of disjunction.

1051. A brief account of these results, with some of a corresponding character
which I had observed in using long wires, was published in the Philosophical
Magazine for 1834*; and I added to them some observations on their nature.
Further investigations led me to perceive the inaccuracy of my first notions, and
ended in identifying these effects with the phenomena of induction which I had been
fortunate enough to develop in the First Series of these Experimental Researches -j-.
Notwithstanding this identity, the extension and the peculiarity of the views respect-
ing electric currents which the results supply, lead me to believe that they will be
found worthy of the attention of the Royal Society.

1052. The electromotor used consisted of a cylinder of zinc introduced between the
two parts of a double cylinder of copper, and preserved from metallic contact in the
usual way by corks. The zinc cylinder was eight inches high and four inches in
diameter. Both it and the copper cylinder were supplied with stiff wires, surmounted
by cups containing mercury ; and it was at these cups that the contacts of wires, he-

* Vol. V. p. 349. t Philosophical Transactions, 1832, p. 126.

MDCCCXXXV. G

42 DR. FARADAY'S EXPERIMENTAL RESEARCHES IN ELECTRICITY.

lices, or electro-magnets, used to complete the circuit, were made or broken. These
cups I will call G and E throughout the rest of this paper (1079.).

1053. Certain helices were constructed, some of which it will be necessary to de-
scribe. A pasteboard tube had four copper wires, one twenty-fourth of an inch in
thickness, wound round it, each forming a helix in the same direction from end to
end ; the convolutions of each wire were separated by string, and the superposed
helices prevented from touching by intervening calico. The lengths of the wires
forming the helices were 48, 49*5, 48, and 45 feet. The first and third wires were
united together so as to form one consistent helix of 96 feet in length ; and the se-
cond and fourth wires were similarly united to form a second helix, closely inter-
woven with the first, and 94*5 feet in length. These helices may be distinguished by
the numbers i and ii. They were carefully examined by a powerful current of electri-
city and a galvanometer, and found to have no communication with each other.

1054. Another helix was constructed upon a similar pasteboard tube, two lengths
of the same copper wire being used, each forty-six feet long. These were united into
one consistent helix of ninety-two feet, which therefore was nearly equal in value to
either of the former helices, but was not in close inductive association with them.
It may be distinguished by the number iii.

1055. A fourth helix was constructed of very thick copper wire, being one fifth of
an inch in diameter ; the length of wire used was seventy-nine feet, independently of
the straight terminal portions.

1056. The principal electro-magnet employed consisted of a cylindrical bar of soft
iron twenty-five inches long, and one inch and three quarters in diameter, bent into
a ring, so that the ends nearly touched, and surrounded by three coils of thick copper
wire, the similar ends of which were fastened together ; then each of these termina-
tions was soldered to a copper rod, serving as a conducting continuation of the wire.
Hence any electric current sent through the rods was divided in the helices surround-
ing the ring, into three parts, all of which, however, moved in the same direction. The
three wires may therefore be considered as representing one wire, of thrice the thick-
ness of the wire really used.

1057. Other electro- magnets could be made at pleasure by introducing a soft iron
rod into any of the helices described (1053. &c.).

1058. The galvanometer which I had occasion to use was rough in its construction,
having but one magnetic needle, and not at all delicate in its indications.

1059. The effects to be considered depend on the conductor employed to complete
the communication between the zinc and copper plates of the electromotor ; and I
shall have to consider this conductor under four different forms : as the helix of an
electro-magnet (1056.) ; as an ordinary helix (1053. &c.) ; as a long extended wire,
having its course such that the parts can exert no mutual infliuence ; and as a short
wire. In all cases the conductor was of copper.

1060. The effects are best shown by the electro-magnet (1056.). When it was

INDUCTIVE ACTION OF AN ELECTRIC CURRENT ON ITSELF. 43

used to complete the communication at the electromotor, there was no sensible
spark on making contact, but on breaJcmg contact there was a very large and bright
spark, with considerable combustion of the mercury. Then, again, with respect to
the shock : if the hands were moistened in salt and water, and good contact between
them and the wires retained, no shock could be felt upon making contact at the elec-
tromotor, but a powerful one on hreaMng contact.

1061. When the helix i or iii (1053. &c.) was used as the connecting conductor,
there was also a good spark on breaking contact, but none (sensibly) on making
contact. On trying to obtain the shock from these helices, I could not succeed at
first. By joining the similar ends of i and ii so as to make the two helices equivalent
to one helix, having wire of double thickness, I could just obtain the sensation. Using
the helix of thick wire (1055.) the shock was distinctly obtained. On placing the
tongue between two plates of silver connected by wires with the parts which the
hands had heretofore touched (1064.), there was a powerful shock on breaking con-
tact, but none on making contact.

1062. The power of producing these phenomena exists therefore in the simple helix,
as in the electro-magnet, although by no means in the same high degree.

1063. On putting a bar of soft iron into the helix, it became an electro-magnet
(1057.), and its power was instantly and greatly raised. On putting a bar of copper
into the helix, no change was produced, the action being that of the helix alone. The
two helices i and ii, made into one helix of twofold length of wire, produced a greater
effect than either i or ii alone.

1064. On descending from the helix to the mere long wire, the followmg effects
were obtained. A copper wire, 0*18 of an inch in diameter, and 132 feet in length,
was laid out upon the floor of the laboratory, and used as the connecting conductor
(1059.) ; it gave no sensible spark on making contact, but produced a bright one on
breaking contact, yet not so bright as that from the helix (1061.). On endeavouring
to obtain the electric shock at the moment contact was broken, I could not succeed
so as to make it pass through the hands ; but by using two silver plates fastened by
small wires to the extremity of the principal wire used, and introducing the tongue
between those plates, I succeeded in obtaining powerful shocks upon the parts of the
mouth, and could easily convulse a flounder, an eel, or a frog. None of these effects
could be obtained directly from the electromotor, i. e. when the tongue, frog, or fish
was in a similar, and therefore comparative manner, interposed in the course of the
communication between the zinc and copper plates, separated everywhere else by the
acid used to excite the combination. The bright spark and the shock, produced only
on breaking contact, are therefore effects of the same kind as those produced in a
higher degree by the helix, and in a still higher degree by the electro-magnet.

1065. In order to compare an extended wire with a helix, the helix i, containing
ninety-six feet, and ninety-six feet of the same- sized wire lying on the floor of the
laboratory, were used alternately as conductors : the former gave a much brighter

G 2

44 DR. FARADAY'S EXPERIMENTAL RESEARCHES IN ELECTRICITY.

spark at the moment of disjunction than the latter. Again, twenty-eight feet of cop-
per wire were made up into a helix, and being used gave a good spark on disjunction
with the electromotor ; being then suddenly pulled out and again employed, it gave a
much smaller spark than before, although nothing but its spiral arrangement had
been changed.

1066. As the superiority of a helix over a wire is important to the philosophy of
the effect, I took particular pains to ascertain the fact with certainty. A wire of cop-
per sixty-seven feet long was bent in the middle so as to form a double termination
which could be communicated with the electromotor ; one of the halves of this wire
w^as made into a helix and the other remained in its extended condition. When these
were used alternately as the connecting wire, the helix gave by much the strongest
spark. It even gave a stronger spark than when it and the extended wire were used
conjointly as a double conductor.

1067- When a shor^t wire is used, all these effects disappear. If it be only two or
three inches long, a spark can scarcely be perceived on breaking the junction. If it
be ten or twelve inches long and moderately thick, a small spark may be more easily
obtained. As the length is increased, the spark becomes proportionately brighter, until
from extreme length the resistance offered by the metal as a conductor begins to in-
terfere with the principal result.

1068. The effect of elongation was well shown thus : 114 feet of copper wire, one
eighteenth of an inch in diameter, were extended on the floor and used as a conduc-
tor ; it remained cold, but gave a bright spark on breaking contact. Being crossed so
that the two terminations were in contact near the extremities, it was again used as
a conductor, only twelve inches now being included in the circuit : the wire became
very hot from the greater quantity of electricity passing through it, and yet the spark
on breaking contact was scarcely visible. The experiment was repeated with a wire
one ninth of an inch in diameter and thirty-six feet long with the same results.

1069. That the effects, and also the action, in all these forms of the experiment are
identical; is evident from the manner in which the former can be gradually raised from
that produced by the shortest wire to that of the most powerful electro-magnet : and
this capability of examining what will happen by the most powerful apparatus, and
then experimenting for the same results, or reasoning from them, with the weaker ar-
rangements, is of great advantage in making out the true principles of the phenomena.

1070. The action is evidently dependent upon the wire which serves as a con-
ductor ; for it varies as that wire varies in its length or arrangement. The shortest
wire may be considered as exhibiting the full effect of spark or shock which the
electromotor can produce by its own direct power; all the additional force w^hich
the arrangements described can excite being due to some affection of the current,
either permanent or momentary, in the wire itself That it is a momentarij e^Qct, pro-
duced only at the instant of breaking contact, will be fully proved (1089. 1100.).

1071. No change takes place in the quantity or intensity of the current during the

THE CONSTANT CURRENT UNCHANGED IN ITS CHARACTERS. 45

time the latter is continued, from the moment after contact is made up to that pre-
vious to disunion, except what depends upon the increased obstruction offered to
the passage of the electricity by a long wire as compared to a short wire. To ascer^
tain this point with regard to quantity, the helix i (1053.) and the galvanometer
(1058.) were both made parts of the metallic circuit used to connect the plates of a
small electromotor, and the deflection at the galvanometer was observed ; then a soft
iron core was put into the helix, and as soon as the momentary effect was over, and
the needle had become stationary, it was again observed, and found to stand exactly
at tlie same division as before. Thus the quantity passing through the wire when
the current was continued was the same either with or without the soft iron, although
the peculiar effects occurring at the moment of disjunction were, very different in de-
gree under such variation of circumstances.

1072. That the quality of intensity belonging to the constant current did not vary
with the circumstances favouring the peculiar results under consideration, so as to
yield an explanation of those results, was ascertained in the following manner. The
current excited by an electromotor was passed through short wires, and its intensity
tried by subjecting different substances to its electrolyzing power (912. 966. &c.) ; it
was then passed through the wires of the powerful electro-magnet (1056.), and again
examined with respect to its intensity by the same means and found unchanged.
Again, the constancy of the quantity passed in the above experiment (IO71.) adds
further proof that the intensity could not have varied ; for had it been increased upon
the introduction of the soft iron, there is every reason to believe that the quantity
passed in a given time would also have increased.

1073. The fact is, that under many variations of the experiments, the permanent
current loses in force as the effects upon breaking contact become exalted. This is
abundantly evident in the comparative experiments with long and short wires (1068);
and is still more strikingly shown by the following variation. Solder an inch or two
in length of fine platina wire (about one hundredth of an inch in diameter) on to one
end of the long communicating wire, and also a similar length of the same platina
wire on to one end of the short communication ; then, in comparing the effects of these
two communications, make and break contact between the platina terminations and
the mercury of the cup G or E (1079.). When the short wire is used, the platina will
be igtiited by the constant current, because of the quantity of electricity, but the
spark on breaking contact will be hardly visible ; on using the longer communicating
wire, which by obstructing will diminish the current, the platina will remain cold
whilst the current passes, but give a bright spark at the moment it ceases : thus the
strange result is obtained of a diminished spark and shock from the strong current,
and increased effects from the weak one. Hence the spark and shock at the moment
of disjunction, although resulting from great intensity and quantity of the current at
that moment, are no direct indicators or measurers of the intensity or quantity of the
constant current previously passing, and by which they are ultimately produced.

46 DR. FARADAY'S EXPERIMENTAL RESEARCHES IN ELECTRICITY.

1074. It is highly important in using the spark as an indication, by its relative
brightness, of these effects, to bear in mind certain circumstances connected with its
production and appearance. An ordinary electric spark is understood to be the bright
appearance of electricity passing suddenly through an interval of air, or other badly
conducting matter. A voltaic spark is sometimes of the same nature, but, generally,
is due to the ignition and even combustion of a minute portion of a good conductor ;
and that is especially the case when the electromotor consists of but one or few pairs
of plates. This can be very well observed if either or both of the metallic surfaces
intended to touch be solid and pointed. The moment they come in contact the cur-
rent passes ; it heats, ignites, and even burns the touching points, and the appearance
is as if the spark passed on making contact, whereas it is only a case of ignition by
the current, contact being previously made, and is perfectly analogous to the ignition
of a fine platina wire connecting the extremities of a voltaic battery.

1075. When mercury constitutes one or both of the surfaces used, the brightness of
the spark is greatly increased. But as this effect is due to the action on, and probable
combustion of, the metal, such sparks must only be compared with other sparks also
taken from mercurial surfaces, and not with such as may be taken, for instance, be-
tween surfaces of platina or gold, for then the appearances are far less bright, though
the same quantity of electricity be passed. It is not at all unlikely that the com-
monly occurring circumstance of combustion may affect even the duration of the
light ; and that sparks taken between mercury, copper, or other combustible bodies,
will continue for a period sensibly longer than those passing between platina or gold.

1076. When the end of a short clean copper wire, attached to one plate of an
electromotor, is brought down carefully upon a surface of mercury connected with
the other plate, a spark, almost continuous, can be obtained. This I refer to a succes-
sion of effects of the following nature : first contact, — then ignition of the touching
points, — recession of the mercury from the mechanical results of the heat produced at
the place of contact, and the electro-magnetic condition of the parts at the moment*,
— breaking of the contact and the production of the peculiar intense effect dependent
thereon, — renewal of the contact by the returning surface of the undulating mercury,
— and then a repetition of the same series of effects, and that with such rapidity as to
present the appearance of a continued discharge. If a long wire or an electro-magnet
be used as the connecting conductor instead of a short wire, a similar appearance may
be produced by tapping the vessel containing the mercury and making it vibrate ; but
the sparks do not usually follow each other so rapidly as to produce an apparently
continuous spark, because of the time required when the long wire or electro-magnet
is used both for the full development of the current (1101. 1106.) and for its complete
cessation.

1077. Returning to the phenomena in question, the first thought that arises in the
mmd is, that the electricity circulates with something like momentum or inertia in

* Quarterly Journal of Science, vol. xii. p. 420.

INDUCTIVE ACTION OF A CURRENT UPON ITSELF. 47

the wire, and that thus a long wire produces effects at the instant the current is
stopped, which a short wire cannot produce. Such an explanation is, however, at
once set aside by the fact, that the same length of wire produces the effects in very
different degrees, according as it is simply extended, or made into a helix, or forms
the circuit of an electro-magnet (1069.). The experiments to be adduced (1089.)
will still more strikingly show that the idea of momentum cannot apply.

1078. The bright spark at the electromotor, and the shock in the arms, appeared
evidently to be due to one current in the long wire, divided into two parts by the
double channel afforded through the body and through the electromotor ; for that
the spark was evolved at the place of disjunction with the electromotor, not by any
direct action of the latter, but by a force immediately exerted in the wire of commu-
nication, seemed to be without doubt (IO7O.). It followed, therefore, that by using
a better conductor in place of the human body, the whole of this extra current might
be made to pass at that place ; and thus be separated from that which the electro-
motor could produce by its immediate action, and its direction be examined apart
from any interference of the original and originating current. This was found to be
true ; for on connecting the ends of the principal wire together by a cross wire two
or three feet in length, applied just where the hands had felt the shock, the whole of
the extra current passed by the new channel, and then no better spark than one
producible by a short wire was obtained on disjunction at the electromotor.

1079. The current thus separated was examined by galvanometers and decom-
posing apparatus introduced into the course of this wire. I will always speak of it
as the current in the cross wire or wires, so that no mistake, as to its place or ori-
gin, may occur. In the wood-cut, Z and C represent the zinc and / \

copper plates of the electromotor ; G and E the cups of mercury V V

where contact is made or broken (1052.) ; A and B the termina-
tions of D the long wire, the helix, or the electro-magnet, used to
complete the circuit ; N and P are the cross wires, which can
either be brought into contact at x, or else have a galvanometer
(1058.) or an electrolyzing apparatus (312. 316.) interposed there.

The production of the shock from the current in the cross wire,
whether D was a long extended wire, or a helix, or an electro-magnet, has been
already described (1064. 1061. 1060.).

1080. The spark of the cross-wire current could be produced at .2? in the following
manner : D was made an electro-magnet ; the metallic extremities at a; were held
close together, or rubbed lightly against each other, whilst contact was broken at
G or E. When the communication was perfect at x, little or no spark appeared at
G or E. When the condition of vicinity at x was favourable for the result required,
a bright spark would pass there at the moment of disjunction, none occurring at G
and E : this spark was the luminous passage of the extra current through the cross-
wires. When there was no contact or passage of current at x, then the spark ap-

48 DR. FARADAY'S EXPERIMENTAL RESEARCHES IN ELECTRICITY.

peared at G or E, the extra current forcing its way through the electromotor itself.
The same results were obtained by the use of the helix or the extended wire at D in
place of the electro-magnet.

1081. On introducing a fine platina wire at <r, and employing the electro-magnet
at D, no visible effects occurred as long as contact was continued ; but on breaking
contact at G or E, the fine wire was instantly ignited and fused. A longer or thicker
wire could be so adjusted at x as to show ignition, without fusion, every time the
contact was broken at G or E.

1082. It is rather difficult to obtain this effect with helices or wires, and for very
simple reasons : with the helices i, ii, or iii, there was such retardation of the elec-
tric current, from the length of wire used, that a full inch of platina wire one fiftieth
of an inch in diameter could be retained ignited at the cross wires during the con-
tinuance of contact, by the portion of electricity passing through it. Hence it was
impossible to distinguish the particular effects at the moments of making or breaking
contact from this constant eff^ect.

1083. On using the thick wire helix (1055.), the same results ensued. Proceeding,
however, upon the known fact that electric currents of great quantity but low inten-
sity, though able to ignite thick wires, cannot produce that effect upon thin ones, I
used a very fine platina wire at a?, reducing its diameter until a spark appeared at G
or E, when contact was broken there. A quarter of an inch of such wire might be
introduced at x without being ignited by the continuance of contact at G or E ; but
when contact was broken at either place, this wire became red hot ; proving, by this
method, the production of the induced current at that moment.

1084. Chemical decomposition was next eff'ected by the cross-wire current, an elec-
tro-magnet being used at D, and a decomposing apparatus, with solution of iodide of
potassium in paper (1079.), employed at .r. The conducting power of the connecting
system A B D was sufficient to carry all the primary current, and consequently no
chemical action took place at x during the continuance of contact at G and E ; but
when contact was broken, there was instantly decomposition at x. The iodine
appeared against the wire N, and not against the wire P ; thus demonstrating that
the current through the cross-wires, when contact was broken, was in the reverse
direction to that marked by the arrow, or that which the electromotor would have
sent through it.

1085. In this experiment a bright spark occurs at the place of disjunction, indi-
cating that only a small part of the extra current passed the apparatus at x, because
of the small conducting power of the latter.

1086. I found it difficult to obtain the chemical effects with the simple helices and
wires, in consequence of the diminished inductive power of these arrangements, and
because of the passage of a strong constant current at x whenever a very active
electromotor was used (1082.).

1087. The most instructive set of results was obtained, however, when the galvano-

INDUCTIVE ACTION OF AN ELECTRIC CURRENT. 49

meter was introduced at x. Using an electro- magnet at D, and continuing contact,
a current was then indicated by the deflection, proceeding from P to N, in the direc-
tion of the arrow ; the cross wire serving to carry one part of the electricity excited
by the electromotor, and the arrangement ABD, as indicated by the arrows, the
other and far greater part. The magnetic needle was then forced back, by pins
applied upon opposite sides of its two extremities, to its natural position when unin-
fluenced by a current ; after which, contact being broken at G or E, it was deflected
strongly in the opposite direction ; thus showing, in accordance with the chemical
effects (1084.), that the extra current followed a course in the cross wires contrary to
that indicated by the arrow, i. e. the one produced by the direct action of the elec-
tromotor *.

1088. With the helix only, these effects could scarcely be observed, in consequence
of the smaller inductive force of this arrangement, the opposed action from induc-
tion in the galvanometer wire itself, the mechanical condition and tension of the
needle from the eff'ect of blocking (1087.) whilst the current due to continuance of
contact was passing round it, and other causes. With the extended wire all these cir-
cumstances had still greater influence, and therefore allowed less chance of success.

1089. These experiments, establishing as they did, by the quantity, intensity, and
even direction, a distinction between the primary or generating current and the extra
current, led me to conclude that the latter was identical with the induced current
described (6. 26.) in the first series of these Researches ; and this opinion I was soon
able to bring to proof, and at the same times obtained not the partial (1078.) but
entire separation of one current from the other.

1090. The double helix (1053.) was arranged so that i should form the connecting
wire between the plates of the electromotor, ii being out of the current, and its ends
unconnected. In this condition i acted very well, and gave a good spark at the time
and place of disjunction. The opposite ends of ii were then connected together so as
to form an endless wire, i remaining unchanged : but now no spark, or one scarcely
sensible, could be obtained from the latter at the place of disjunction. Then, again,
the ends of ii were held so nearly together that any current running round that helix
should be rendered visible as a spark ; and in this manner a spark was obtained from
ii when the junction of i with the electromotor was broken, in place of appearing at
the disjoined extremity of i itself.

1091. By introducing a galvanometer or a decomposing apparatus into the circuit
formed by the helix ii, I could easily obtain the deflections and decomposition oc-
casioned by the induced current due to the breaking contact at helix i, or even to
that occasioned by making contact of that helix with the electromotor ; the results in
both cases indicating the contrary directions of the two induced currents thus pro-
duced (26.).

* It was ascertained experimentally, that if a strong current was passed through the galvanometer only, and
the needle restrained in one direction as above in its natural position, when the current was stopped, no viora-
tion of the needle in the opposite direction took place.
MDCCCXXXV. H

60 DR. FARADAY'S EXPERIMENTAL RESEARCHES IN ELECTRICITY.

1092. All these effects, except those of decomposition, were reproduced by two ex-
tended long wires, not having the form of helices, but placed close to each other ; and
thus it was proved that the extra current could be removed from the wire carrying
the original current to a neighbouring wire, and was at the same time identified, in
direction and every other respect, with the currents producible by induction (1089.).
The case, therefore, of the bright spark and shock on disj unction may now be stated
thus : If a current be established in a wire, and another wire, forming a complete cir-
cuit, be placed parallel to the first, at the moment the current in the first is stopped it
induces a current in the same direction in the second, the first exhibiting then but a
feeble spark ; but if the second wire be away, disjunction of the first wire induces a
current in itself in the same direction, producing a strong spark. The strong spark
in the single long wire or helix, at the moment of disjunction, is therefore the equiva-
lent of the current which would be produced in a neighbouring wire if such second
current were permitted.

1093. Viewing the phenomena as the results of the induction of electrical currents,
many of the principles of action, in the former experiments, become far more evident
and precise. Thus the different effects of short wires, long wires, helices, and elec-
tro-magnets (1069.) may be comprehended. If the inductive action of a wire a foot
long upon a collateral wire also a foot in length, be observed, it will be found very
small ; but if the same current be sent through a wire fifty feet long, it will induce in
a neighbouring wire of fifty feet a far more powerful current at the moment of making
or breaking contact, each successive foot of wire adding to the sum of action ; and
by parity of reasoning, a similar effect should take place when the conducting wire
is also that in which the induced current is formed : hence the reason why a long
wire gives a brighter spark on breaking contact than a short one (1068.), although
it carries much less electricity.

1094. If the long wire be made into a helix, it will then be still more effective in
producing sparks and shocks on breaking contact ; for by the mutual inductive action
of the convolutions each aids its neighbour, and will be aided in turn, and the sum
of effect will be very greatly increased.

1095. If an electro-magnet be employed, the effect will be still more highly ex-
alted ; because the iron, magnetized by the power of the continuing current, will
lose its magnetism at the moment the current ceases to pass, and in so doing will
tend to produce an electric current in the wire around it (37. 38.), in conformity with
that which the cessation of current in the helix itself also tends to produce.

1096. By applying the laws of the induction of electric currents formerly deve-
loped (6. &c.), various new conditions of the experiments could be devised, which by
their results should serve as tests of the accuracy of the view just given. Thus, if a
long wire be doubled, so that the current in the two halves shall have opposite actions,
it ought not to give a sensible spark at the moment of disjunction : and this proved
to be the case, for a wire forty feet long, covered with silk, being doubled and tied
closely together to within four inches of the extremities, when used in that state,

INDUCTIVE ACTION OF AN ELECTRIC CURRENT. 61

gave scarcely a perceptible spark ; but being opened out and the parts separated, it
gave a very good one. The two helices i and ii being joined at their similar ends,
and then used at their other extremities to connect the plates of the electromotor,
thus constituted one long helix, of which one half was opposed in direction to the
other half: under these circumstances it gave scarcely a sensible spark, even when
the soft iron core was within, although containing nearly two hundred feet of wire.
When it was made into one consistent helix of the same length of wire it gave a very
bright spark.

1097. Similar proofs can be drawn from the mutual inductive action of two sepa-
rate currents (1110.); and it is important for the general principles that the consist-
ent action of two such currents should be established. Thus, two currents going in
the same direction should, if simultaneously stopped, aid each other by their relative
influence ; or if proceeding in contrary directions, should oppose each other under
similar circumstances. I endeavoured at first to obtain two currents from two dif-
ferent electromotors, and passing them through the helices i and ii, tried to effect
the disjunctions mechanically at the same moment. But in this I could not suc-
ceed ; one was always separated before the other, and in that case produced little or
no spark, its inductive power being employed in throwing a current round the re-
maining complete circuit (1090.) : the current which was stopped last always gave a
bright spark. If it were ever to become needful to ascertain whether two junctions
were accurately broken at the same moment, these sparks would afford a test for the
purpose, having an infinite degree of perfection.

1098. I was able to prove the points by other expedients. Two short thick wires
were selected to serve as terminations, by which contact could be made or broken
with the electromotor. The compound helix, consisting of i and ii (1053.), was ad-
justed so that the extremities of the two helices could be placed in communication
with the two terminal wires, in such a manner that the current moving through the
thick wires should be divided into two equal portions in the two helices, these por-
tions travelling, according to the mode of connexion, either in the same direction
or in contrary directions at pleasure. In this manner two streams could be obtained,
both of which could be stopped simultaneously, because the disjunction could be
broken at G or F by removing a single wire. When the helices were in contrary
directions, there was scarcely a sensible spark at the place of disjunction; but when
they were in accordance there was a very bright one.

1099. The helix i was now used constantly, being sometimes associated, as above,
with helix ii in an according direction, and sometimes with helix iii, which was placed
at a little distance. The association i and ii, which presented two currents able to
affect each other by induction, because of their vicinity, gave a brighter spark than
the association i and iii, where the two streams could not exert their mutual in-
fluence ; but the difference was not so great as I expected.

. 1100. Thus all the phenomena tend to prove that the effects are due to an indue-.

h2

52 DR. FARADAY*S EXPERIMENTAL RESEARCHES IN ELECTRICITY.

tive action, occurring at the moment when the principal current is stopped. I at one
time thought they were due to an action continued during the continuance of the
current, and expected that a steel magnet would have an influence according to its
position in the helix, comparable to that of a soft iron bar, in assisting the effect.
This, however, is not the case ; for hard steel, or a magnet in the helix, is not so ef-
fectual as soft iron ; nor does it make any difference how the magnet is placed in the
helix, and for very simple reasons, namely, that the effect does not depend upon a
permanent state of the core, but a change of state, and that the magnet or hard steel
cannot sink through such a difference of state as soft iron, at the moment contact
ceases, and therefore cannot produce an equal effect in generating a current of elec-
tricity by induction (34. 37.).

1101. As an electric current acts by induction with equal energy at the moment
of its commencement as at the moment of its cessation (10. 26.), but in a contrary
direction, the reference of the effects under examination to an inductive action, would
lead to the conclusion that corresponding effects of an opposite nature must occur
in a long wire, a helix, or an electro-magnet, every time that contact is made with the
electromotor. These effects will tend to establish a resistance for the first moment
in the long conductor, producing a result equivalent to the reverse of a shock or a
spark. Now it is very difficult to devise means fit for the recognition of such nega-
tive results ; but as it is probable that some positive effect is produced at the time,
if we knew what to expect, I think the few facts bearing upon this subject with which
I am acquainted are worth recording.

1102. The electro-magnet was arranged with an electrolyzing apparatus at x, as
before described (1084.), except that the intensity of the chemical action at the elec-
tromotor was increased until the electric current was just able to produce the feeblest
signs of decomposition whilst contact was continued at G and E (1079.) ; (the iodine
of course appearing against the end of the cross wire P;) the wire N was also sepa-
rated from A at r, so that contact there could be made or broken at pleasure. Under
these circumstances the following set of actions was repeated several times : contact
was broken at r, then broken at G, next made at r, and lastly renewed at G ; thus
any current from N to P due to breahing of contact was avoided, but any additional
force to the current from P to N due to making contact could be observed. In this
way it was found, that' a much greater decomposing effect (causing the evolution of
iodine against P) could be obtained by a few completions of contact than by the cur-
rent which could pass in a much longer time if the contact was contifiued. This 1
attribute to the act of induction in the wire A B D at the moment of contact render-
mg that wire a worse conductor, or rather retarding the passage of the electricity
through it for the instant, and so throwing a greater quantity of the electricity which
the electromotor could produce, through the cross wire passage N P. The instant
the induction ceased, AB D resumed its full power of carrying a constant current of

INDUCTIVE EFFECT AT THE COMMENCEMENT OF A CURRENT. 53

electricity, and could have it highly increased, as we know by the former experi-
ments (1060.) by the opposite inductive action brought into activity at the moment
contact at Z or C was broken.

1103. A galvanometer was then introduced at a?, and the deflection of the needle
noted whilst contact was continued at G and E : the needle was then blocked as
before in one direction (1087.)? so that it should not return when the current ceased,
but remain in the position in which the current could retain it. Contact at G or E
was broken, producing of course no visible effect ; it was then renewed, and the nee-
dle was instantly deflected, passing from the blocking-pins to a position still further
from its natural place than that which the constant current could give, and thus
showing by the temporary excess of current in this cross communication, the tempo-
rary retardation in the circuit A B D.

1104. On adjusting a platina wire at x (1081.) so that it should not be ignited by
the current passing through it whilst contact at G and E was continued, and yet be-
come red hot by a current somewhat more powerful, I was readily able to produce
its ignition upon making contact, and again upon breaking contact. Thus the momen-
tary retardation in A B D on making contact was again shown by this result, as well
also as the opposite result upon breaking contact. The two ignitions of the wire at x
were of course produced by electric currents moving in opposite directions.

1105. Using the helix only, I could not obtain distinct deflections at x, due to the
extra effect on making contact, for the reasons already mentioned (1088.). By using
a very fine platina wire there (1083.), I did succeed in obtaining the igniting effect
for making contact in the same manner, though by no means to the same degree, as
with the electro-magnet (1104.).

1106. We may also consider and estimate the efffect on making contact, by trans-
ferring the force of induction from the wire carrying the original current to a lateral
wire, as in the cases described (1090.) ; and we then are sure, both by the chemi-
cal and galvanometrical results (1091.), that the forces upon making and breaking
contact, like action and reaction, are equal in their strength but contrary in their
direction. If, therefore, the effect on making contact resolves itself into a mere re-
tardation of the current at the first moment of its existence, it must be, in its degree,
equivalent to the high exaltation of that same current at the moment contact is broken.

1107. Thus the case, under the circumstances, is, that the intensity and quantity
of electricity moving in a current are smaller when the current commences or is
increased, and greater when it diminishes or ceases, than they would be if the in-
ductive action occurring at these moments did not take place; or than they are in the
original current wire if the inductive action be transferred from that wire to a colla-
teral one (1090.).

1108. From the facility of transference to neighbouring wires, and from the effbcts
generally, the inductive forces appear to be lateral, i. e. exerted in a direction per-
pendicular to the direction of the originating and produced currents : and they also

54 DR. FARADAY'S EXPERIMENTAL RESEARCHES IN ELECTRICITY.

appear to be accurately represented by the magnetic curves, and closely related to,
if not identical with, magnetic forces.

1109. There can be no doubt that the current in one part of a wire can act by in-
duction upon other parts of the same wire which are lateral to the first, i. e. in the
same section, or in the parts which are more or less oblique to it (1112.), just as it
can act in producing a current in a neighbouring wire. It is this which gives the
appearance of the current acting upon itself: but all the experiments and all analogy
tend to show that the elements (if I may so say) of the currents do not act upon them-
selves, and so cause the effect in question, but produce it by exciting currents in con-
ducting matter which is lateral to them.

1110. It is possible that some of the expressions I have used may seem to imply,
that the inductive action is essentially the action of one current upon another, or of
one element of a current upon another element of the same current. To avoid any
such conclusion I must explain more distinctly my meaning. If an endless wire be
taken, we have the means of generating a current in it which shall run round the
circuit without adding any electricity to what was previously in the wire. As far as
we can judge, the electricity which appears as a current is the same as that which
before was quiescent in the wire ; and though we cannot as yet point out the essential
condition of difference of the electricity at such times, we can easily recognise the two
states. Now when a current acts by induction upon conducting matter lateral to it,
it probably acts upon the electricity in that conducting matter whether it be in the
form of a current or quiescent, in the one case increasing or diminishing the current
according to its direction, in the other producing a current, and the amount of the
inductive action is probably the same in both cases. Hence, to say that the action
of induction depended upon the mutual relation of two or more currents, would, ac-
cording to the restricted sense in which the term current is understood at present
(283. 517. 667.), be an error.

1111. Several of the effects, as, for instances, those with helices (1066.), with accord-
ing or counter currents (1097. 1098.), and those on the production of lateral cur-
rents (1090.), appeared to indicate that a current could produce an effect of induction
in a neighbouring wire more readily than in its own carrying wire, in which case it
might be expected that some variation of result would be produced if a bundle of
wires were used as a conductor instead of a single wire. In consequence the follow-
ing experiments were made. A copper wire one twenty-third of an inch in diameter
was cut into lengths of five feet each, and six of these being laid side by side in one
bundle, had their opposite extremities soldered to two terminal pieces of copper.
This arrangement could be used as a discharging wire, but the general current could
be divided into six parallel streams, which might be brought close together, or, by
the separation of the wires, be taken more or less out of each other's influence. A
somewhat brighter spark was, I think, obtained on breaking contact when the six
wires were close together than when held asunder.

INDUCTIVE ACTION OF AN ELECTRIC CURRENT. 55

1112. Another bundle, containing twenty of these wires, was eighteen feet long:
the terminal pieces were one fifth of an inch in diameter, and each six inches long.
This was compared with nineteen feet in length of copper wire one fifth of an inch in
diameter. The bundle gave a smaller spark on breaking contact than the latter, even
when its strands were held together by string : when they were separated, it gave a
still smaller spark. Upon the whole, however, the diminution of effect was not such
as I expected ; and I doubt whether the results can be considered as any proof of
the truth of the supposition which gave rise to them.

1113. The inductive force by which two elements of one current (1109. 1110.) act
upon each other, appears to diminish as the line joining them becomes oblique to the
direction of the current, and to vanish entirely when it is parallel. I am led by some
results to suspect that it then even passes into the repulsive force noticed by Ampere*;
which is the cause of the elevations in mercury described by Sir Humphry Davy -f,
and which again is probably directly connected with the quality of intensity.

1114. Notwithstanding that the effects appear only at the making and breaking of
contact, (the current remaining unaffected, seemingly, in the interval,) I cannot resist
the impression that there is some connected and correspondent effect produced by
this lateral action of the elements of the electric stream during the time of its conti-
nuance (60. 242.). An action of this kind, in fact, is evident in the magnetic relations
of the parts of the current. But admitting (as we may do for the moment) the mag-
netic forces to constitute the power which produces such striking and different results
at the commencement and termination of a current, still there appears to be a link in
the chain of effects, a wheel in the physical mechanism of the action, as yet unrecog-
nised. If we endeavour to consider electricity and magnetism as the results of two
forces of a physical agent, or a peculiar condition of matter, exerted in determinate
directions perpendicular to each other, then, it appears to me, that we must consider
these two states or forces as convertible into each other in a greater or smaller degree ;
i. e. that an element of an electric current has not a determinate electric force and a
determinate magnetic force constantly existing in the same ratio, but that the two
forces are, to a certain degree, convertible by a process or change of condition at pre-
sent unknown to us. How else can a current of a given intensity and quantity be
able, by its direct action, to sustain a state which, when allowed to react, (at the ces-
sation of the original current,) shall produce a second current, having an intensity
and quantity far greater than the generating one ? This cannot result from a direct
reaction of the electric force ; and if it result from a change of electrical into mag-
netic force, and a reconversion back again, it will show that they differ in some-
thing more than mere direction, as regards that agent in the conducting wire which
constitutes their immediate cause.

1115. With reference to the appearance, at different tunes, of the contrary effects

* Recueil d' Observations Electro-Dynamiques, p. 285.
t Philosophical Transactions, 1823, p. 155.

56 DR. FARADAY'S EXPERIMENTAL RESEARCHES IN ELECTRICITY.

produced by the making and breaking contact, and their separation by an inter-
mediate and indifferent state, this separation is probably more apparent than real.
If the conduction of electricity be effected by vibrations, or by any other mode in
which opposite forces are successively and rapidly excited and neutralized, then we
might expect a peculiar and contrary development of force at the commencement and
termination of the periods during which the conducting action should last (somewhat
in analogy with the colours produced at the outside of an imperfectly developed solar
spectrum) : and the intermediate actions, although not sensible in the same way, may
constitute the very essence of conductibihty. It is by views and reasons such as these,
which seem to me connected with the fundamental laws and facts of electrical science,
that I have been induced to enter, more minutely than I otherwise should have done,
into the experimental examination of the phenomena described in this paper.

1116. Before concluding, I may briefly remark, that on using a voltaic battery of
fifty pairs of plates instead of a single pair (1052.), the effects were exactly of the
same kind. The spark on making contact, for the reasons before given, was very
small (1101. 1107.); that on breaking contact, very excellent and brilliant. The
continuous discharge did not seem altered in character, whether a short wire or the
powerful electro-magnet were used as a connecting discharger.

1117. The effects produced at the commencement and end of a current, (which are
separated by an interval of time when that current is supplied from a voltaic appara-
tus,) must occur at the same moment when a common electric discharge is passed
through a long wire. Whether, if happening accurately at the same moment, they
would entirely neutralize each other, or whether they would not still give some defi-
nite peculiarity to the discharge, is a matter remaining to be examined ; but it is
very probable that the peculiar character and pungency of sparks drawn from a long
wire depend in part upon the increased intensity given at the termination of the dis-
charge by the inductive action then occurring.

1118. In the wire of the helix of magneto-electric machines, (as, for instance, in
Mr. Saxton's beautiful arrangement,) an important influence of these principles of
action is evidently shown. From the construction of the apparatus the current is per-
mitted to move in a complete metallic circuit of great length during the first instants
of its formation : it gradually rises in strength, and is then suddenly stopped by the
breaking of the metallic circuit ; and thus great intensity is given by induction to the
electricity, which at that moment passes (1064. 1060.). This intensity is not only
shown by the brilliancy of the spark and the strength of the shock, but also by the
necessity which has been experienced of well insulating the convolutions of the helix,
in which the current is formed ; and it gives to the current a force at these moments
verj' far above that which the apparatus could produce if the principle which forms^
the subject of this paper were not called into play.

Royal Institution,
December 8th, 1834.

[ 57 ]

IV. On the Determination of the Terms in the Disturbing Function of the fourth order
as regards the Eccentricities and Inclinations which give rise to Secular Inequali-
ties. By J. W. Lubbock, V.P. and Treas. R.S.

Received October 16, — Read November 20, 1834.

Hitherto in the theory of the secular inequalities the terms in the disturbing
function of the fourth order as regards the inclinations have been neglected. As the
magnitude of these terms depends, in great measure, upon certain numerical co-
efficients, it is impossible to form any precise notion a priori with respect to their
amount, and as to the error which may arise from neglecting them. I have therefore
thought it desirable to ascertain their analytical expressions ; and the details of this
calculation form the subject of this paper. Some of the secular inequalities which
result from these terms are far within the limits of accuracy which Laplace appears
to have contemplated in the third volume of the M^canique Celeste.

The method which I have here adopted for developing the disturbing function rests
upon principles which I have already explained *. Very little trouble is requisite to
obtain certain analytical expressions for the terms upon which the secular inequalities
depend, or for any others, in the development of the disturbing function ; but it is not
so easy to put these expressions in the simplest form of which they are susceptible ;
and this is a point to which I think hitherto sufficient attention has not been paid.
It will be found that I have obtained, finally, expressions of very remarkable sim-
plicity : to accomplish this, however, I have been obliged to go through tedious pro-
cesses of reduction, the details of which are here subjoined, in order that my results
may be verified or corrected without difficulty. In order to give an additional example
of the great facility with which terms in the disturbing function are arrived at by my
method, I have calculated one of those given by Professor Airy, and which is required
in the determination of his inequality of Venus ; and I have arrived at the result which
he has given. The same method, with certain modifications, is applicable to the de-
velopment of the disturbing function in terms of the true longitudes. The terms in
the disturbing function which give rise to the secular inequalities of the elliptic con-
stants, when the terms of the order of the fourth powers of the eccentricities and
inclinations are retained, and higher powers of those quantities are neglected, are as
follows : and I propose, as they form, in fact, a system apart, to distinguish them by
the indices given in the left-hand column.

* Philosophical Transactions, 1832, Part II.
MDCCCXXXV. I

58 MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R.

0. 0

1. r-l + l,

II. 2 r - 2 ^ + 2 i,

III. r + I + I, - 2 ;;

IV. r — I — I, -\- 2 yji
V. ^ — ^, — *J + %

VI. I + It — ri — rj^

VII. 2r + 2|^ — 2;?

VIII. 21 — 2 n

IX. 2 r — 2 I + 2 ;;^

X. 2 I, - 2 ;;,

XI. r -^ n + rit

XII. r — 2| + ^ + ;j^

XIII. r -\- 2 1^ — 7} — ri,

XIV. 2 r — I + 1/ - ?7 + ?7,
XV. 2 r — 2 ;; 4- 2 ;?^.

After extensive reductions I find

, 9^/^% e2e24-m /--^^i . ^^' ^ 1.4

[o.]
+ {- •32^*5.1 - 3|-l7'*5,2} {y' +7/'} jee.cos (r - ^ + y

+ ^§"^5.1 e^, 7/' COS (r - i - I, + 2^^) + ^|^&5,ie e,yy,cos(i -l,-n + %)

[IV.] ' [v.]

9 m, a

T6^\l^e^yy,C0S ($ + ^, - ;; - ^j

[VI.]

MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R. 59

+ '^z { - TI^ hi + i&t h^ } '' ^' cos (2 r + 2 ?, - 2 ,)

[VII.]

+ ^/ { - ll^ hi + ^ ^5,2 } ^' y' cos (2 I - 2 »j)

[VIII.]

+ ^/ { - ll^^ ^5,1 + ^3 } ^' 7/' COS (2 r - 2 I + 2 ;?,)

[IX.]

+ '^z I - T6^ ^5.1 + 64^ *5,2 j ^z' 7/' COS (2 I, - 2 p?^)

[X.]

+ '^z { ""4^ *3,i - tI^ ^5,0 (e^ + ^/^) + il^ \o (y^ + r,^) }y y/cos (r-;j+»,,)

[XI.]

+ ^/ { 8T^ ^5,1 - si^ ^5,2 j e^ y yy COS (r - 2 g + ?7 + ;7^)

[XII.]

+ ^/ {l^«^5,0 - ^^5,2}^/Vy/COS (r 4- 2^, - P7 - Pjj

[XIII.]

32^3^1 + 32^^5,3 j^^y yy/ COS (2r - I + I, ~ ;? + ^J

[xiv.]
~ '^z 32^ *5,o y^ y/^ COS (2 r - 2 pj H- 2 ;?^)

[XV.]

The method which I propose to employ in order to arrive at the terms in the
disturbing function, independent of the inclinations, is sufficiently explained in the
Philosophical Transactions. The following are the equations employed :

dR _ adR dr dR d\

de de rde'drd^

[0] [2] [8]

17 71

— ^ e2 cos 3 1 — 2^ e3 cos 4 I

[20] [35]

^ = 2(l-2|!)sin| + |e(l-^e2)sin2| + T^'si^3H-^e2sin4|.

[2] [8] [20] [35]

i2

60 MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R.

Calculation of the Term in the non-periodical Portion of R multiplied hy e*.

If R'2 denote the term in the coefficient of cos i multiplied by €^,

Rs cos 2 1 .... e2,

JH non-periodical portion of R multiplied by e^,

» coefficient of cos | multiplied by e,

^ ^ 2 — 2 da ""Sda"" 4 da da ~*~ 8da

""^ z. I « J. z? _ _£L ^ j_ .1^ h

^2 = - 2^ ^3.0 + 2^^3.1 ^8 — - 2a3 ''3.0 i- 8a^3 »3,l

^2 -Rs 3 o D/ , 9 D __ ^«' J. 3fl , _9_

"2 2~ "" T^2 - ^0 H- y ^0 — 8 af ^3,0 — iQa,^ \l ~~ l6a, ^1.0

o r»/ ^«' A 3a , 9a /j^ , , \ ^ (a , , \

^^2 = 1^ ^3,0 - W^ ^^3,1 + j6 a 2 V fl; ^3,0 - 03,1; — y « 4 V ^^ ^5,0 - %lj

+ TF^ VT, ^5,1 - 2 ^5,0 - 2 ^5,2;

!>/ _- 7a^ , _a_ , £a4 9 a^ 3 a^ 3 q^

^2— idaj" ^3,0 — 4a^^ %,1 — Sfl^s ^5,0 H- i(j«4 »5,1 ~ 32 «^^ ^5,0 32 a/ %2

_ 7a^ ^ _«_, _3_a^7 , ^_^ ^ Sa^ , ^ a_ ,

— Idaf ^3,0 — 4a^a ^3,1 — y ^3 03,0 -r i(ja3 ^'s.o - ib^; ^5,1 + ]tja/ ^3,1

flg ^ 3a , 3ag Sa^

— 76^^3,0 — i6fl3 ^'s.i + 16 « 3 ^5,0 — 16 a/ V-

If R"q denote the term in the non-periodical portion of the disturbing function
multiplied by e*,

, _ ad 71^0 adigp ^ adR'^ QadR^ SadR^
4^0— 2da "^ 8da ~ 2da+ 16 da "" 4.da

. P„ 1_ , g /_^ 7 7 \ _1_ , a , , 9 a' ,

^^ h -J_ ^^ /"^ A 7. ^ L 3a^ /a - 1 1 7 \

~ 16 a^ '^s,! -r ida^ Va, ^5,0 — ^5,1 J + 30^3 \— 05,1 " "2 ^5,0 " "2" ^2)

15 a^ (a^, . \ , }±c^ (a ] 1 \

"" 32 a 4 V a, ^^7,0 — «'7,i; + 32 ^3 \^ ^^ ^7,1 — "2 ^7,0 — "2 ^7,2;

1 (a^ 4- g ' I, Q^, \ a { a ^ , \ 1 a

— 16 aA a,2 03,0"- ^ a^ f>i,i) - J^a V^ ^3,0 - ^'s.i; - Te^ <^3.0 - T6< ^3,1

_?1 ^ i_^ ^ 1 _?JL Z"^/. i.\.3a*/a, 1, l-\

Xag'^M"" I6fl2''5,l -r \Qaf\a^%^''%\) +32^3^-^ »5,1 ~ -q%0-'-q:%2)

9^

32

MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R. 61

"" 32 a^ \ af ^7,0 — ^ a^ ^7,1^ + 64 ^ 3 ^'/.o — 64^3 O7.2

— 8a/ V a/ ^5,1 — a^ %,0 — «^ «'5,2/ + 64 af %0 — s^ %l
~ 64 a 3 ^5,2 32 « 3 %o + 32 « 9 O5 1

— 64^^50—32^205^1 — 32^05,1 + 54-^3652

— ^ A I ^^ i j_ «^ 7 13a , «^ , 5«^

— 32 «/ ^5,1 -r 32 « 4 05,1 -h g4 ^3 05,2 — 32 a,^ ^5,1 — 32 a* %1 + 64^ ^5,2

_ 3a 7 I 3«' I

— ~ 8^ ^5,1 + 32^ 05,2-

Hence R contains the term

r J_a_ , 3«^ ")

^' )_ "" 32 < ^5,1 + 128 a^3 05,2 J «^-

Putting for 65 1, 65 2 their values in series, the first term is

~ 32 a,3-

This result agrees with what I have before arrived at in the Lunar theoiy. I have
neglected no similar opportunity of verifying the terms in the disturbing function
given in this paper ; these opportunities are however but few, as the terms multiplied
by y 2 may be dispensed with in the lunar theory.

Calculation of the Term in the non-periodical Portion of the disturbing Function mul-
tiplied by e^ ef.

If R^ now denote the term in the coefficient of cos | multiplied by e ef,

R'o non-periodical portion . . . e,^,

R\ e2e/,

jy ^ ^ Tfi "^-^^0 Jit

^2 — — 8a/ \a^ ^5,1 — 2 ''s.s — 2 ^5.2/ "T 8 «/ ^3,1

^^^ ~~ 2da ~~ 2da

T>< T>i « T g , , Sa^ - 3«« , 3a^ ,

i<0 — ^2 — - 8 «/ ^3,1 — 8 «/ ^3,1 -r 8 a4 05,1 — 16 a/ ''s.O - 16 «/ 05,2

rt r»,/ * t I 3ft^ / « , 1 , ^ 7. ^ I 9«^ ,

2 i« 0 = - 8^ 03,1 + 8^ V^ ^5,1 - -2 ^5,0 - 2 ^5,2; i- i6«4 O5.I

62 MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF /?.

+ 32^3 V^ bj,0 - h,l) + 32^2 V a, ^7,2 - 2 ^7,1 " 2 ^7,3;

« 7. I i^A £^7. ^"%

= ~ 8^ ^3,1 + le o 4 05,1 — 8 a/ ^5,0 4 « 3 »5,2

15 a,^ /«1+_«L J. ± /. ^ ;. ^ j_ ^^"^ ;. 1^«^ 7

"" W¥ \ af ^7,1 - a, ^7.0 - «^ 07,2; + 64 « 4 ^7,1 -" 64 a ^ ^l,^

— ■" 1^ ^5,0 + 16 a3 05,2 — 8 af ^5,0 -- 16 af ^5,2 — " 16 «/ ^5,0-
Hence the disturbing function contains the term

"■ sf^ ^5,0 ^ ^/'^ ; in the lunar theory — -j^ e2 e^2.

Calculation of the Term in the non-periodical Portion of R multiplied hy e^.

If ij'g denote the term in the coefficient of cos |^ multiplied by e^g,

i?i7 . cos 2 1^ . . . . e^,

«5 • cos I, . . . . e^,

Rq non-periodical portion of R multiplied by e^,

R'o . . .e>*,

p, a^dR^ a, d i?^ S a, d R^ a, d R'q 9 a d JJq

3 if 5 — -Q^ — 2 d a, Ada, da, "r" 8 da,

^5 = — 2^^ ^3,0 + 2< ^3,1 ^/7 = — "2^, ^3,0 + -8^ h,l R'o = — 8^« *3,1

W — -L /i ^ :?/Z. J. O R' _J_ -^ » — ^5 ^/7 Of I 9 o

'^o — — a^ «'i,o 2 "' 2 ""4^5 — ^o-Ts^o 4 2 ^o-r~8^o

— Qa, '^3,0 — 16 «/ ^3.1 — 16 ^1.0

•» »' — A A I _i£ ^|9, 9a { a , ,\

'^ «5 - - 8 a, ^3,0 -t- 8 «; %.l + 16 a, ^1.0 - 16^ V^ ^3,0 - %,i;

■^ 8 a2 \a^ f>5,o - ^5.1; - T6^3 ^^ 65 ^ - -^ 65 q - - 65,2/

- 8 a, ''3.0 - 16 af ^3.0 i" 16 af \\ + "16^, \~"<~ ^3,0 ~ -^^3,i;

__ 9« /'«^+< I ^. «A^|27a% 9a, 9a^,

16 a; V af %l - a, ^5.0 - a, ^^>V + 32^3 \o - 16^2 65,1 - ^^ ^5,

IV 1_ f Sa , 3a^ ,3a,

'^ 5 — 16 a, ^3,0 - 16 af ^3,1 "T 16 a,^ ^5,0 " 16^ %\

4i>/f 3_MjRj , a^Ro a,d/gs 9a,di?5 na^d/J;;
^*0 2da, "T" 8da, 2da, + l6d"7r 4d^7"

MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R. 63

2"'8~'2~'"6 5— 4 -"17

16< ^3,1 —Ida, ^1.0 "" 32 a, ^3,0 + 32 af ^3,1 - 32^ ^5,0

■T" 32 «/ ^5,1 — 32 a, ^3,0 "T" 32 a,^ ^3,1 + 8 a, ^3,0 — 32 a^2 »3,i

A nil — ^ A « /^ A A \ 1 A « / 9«^ /

^^ 0 — 16 a, ^1.0 ~" 16 a 2 V a^ ^3.0 — f^3,i/ — kj «^ %o — 16 «^3 ^3,1 + 32^3 ©5,0

3« , 3a /^ A ^ _l_ ^^^ /"^ A ^ -A ^ A ^

"" 16a/ ^5,1 -1- 16 «3 Va, ^5,0 — %ij -f" 32 «3 \^^ 05,1 — Y ^5,o — 2 ^5,2/ '

~ 32 a * \ a, ^7,0 — ^7,1^ + 32 «/ \ a, ^7.1 — 2 ^7.0 — 2 °7,2)

~ 16 a^ I ~^ ^3,0 — 2 — 63 1 1 - 16 a^ \^^ ^s.o - 03,1 j — -TF^^ ^3,0 - 16^2 03,1

9a^ , 3^ ,Ja(±i a\i ^^^ /^ A JL A -L A \

■^ 32a^a^5,0 — I6fl2«'5,l -t- 16 a/ \^fl^ ^5,0— 05,1; -r 32 «/ \^a^ »5,1 " 2 ^5,0 — 2 ^5,2/

"" 32^3 (^ ^^ 070 — 2 — 67 ij + g^3 67 0 - g^ 67 2

a /a^ 4- a/, a, '^'\_j_^^'^^A ^^ h

— " OIT^ \ af ^5.1 ■" ^ ^5,0 — "^ Ki) -r 64^ *5,0 — 8^ »5,1

JL^ A 15 a^ , 3a ,

"" 64^^ ^5,2 — 32^3 05,0 + 32 af ^5,1

13 a , a^ . . 5a^

64

af ^5.0 — 32 af *5,l " 32 a ^ \\ + 64 a/ *5,2

CL Cl €l 1 3 tt fl O ^

= 32^ *5,1 + 32^4 ^5,1 + 64^ ^5.2 - 32^ *5,1 — 32^ *5,1 + 64^ ^5,2
8Vf ^5,1 + 32 af ^5,2-

Hence the disturbing function contains the term

"^'{-MTf ki + 1^3 ^^5,2 } el" ; in the lunar theory - ^-J^

In the preceding instance, and in the case of terms depending either upon e^ or e*
solely, the term in the disturbing function can only be obtained irom "jj or jj; but
in obtaining those which depend both upon e and e,, they may be obtained indifFer-
ently either from the combinations which enter into the expression tor -^ or trom

, . , . 1 . ^ dR

those which enter into the expression for -^ .

64 MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R.

Calculation of the Coefficient of ^e^ cos (r — | + I) in the Development of R.

If R^ denote that part of the coefficient of cos {r — 21) which is multiplied by e^

jRj COST e^

i?! e2

R^ cos(r + |) e

i?3 cos (r + 1) e

^3 ^

•^^3 — "adT ~ 2d« ■^^s'T- 16 da "T- 8 ^1 "" 4 dfl ~ 4 ^4 — gda "" ^i

„ _3_fl ^ , c^ J « - J? _ _?_ g , ^ ?>

^3 — — 2^3 + 4 a,2 ^3,0 - 2 a^2 ©s,! — 4^2 ^3^2 ^9 — 8 af " Uu^^ ^3,0 " Jg^ h,2

I? — J?_ -^ ^ -^ A _J_ -i^ h R' — -^ _l_ -^ /; « 7

^4 — 2 a 3 4 a^3 »3,0 — 2 a 2 03,1 i- 4 ^^3 %,2 ^ 1 — ~ 2 a ^ i" 4 «^2 «'3,0 — 2 «/ ^3,2

^1 ""a; ~ a, 2 "" 2 ■*" l6^i ~ 4 ^4 — 2 " "" 8a/ "•" l6a/ ^3,0 i- g^^a O31 — ^^^2(^3^2

^ -I- 8 ^1 ~ 4 ^4 — ^1 — 8 a/ "■ 16< ^3,0 i- 8 a3 %i — jg ^^2 03,2
,5 /t3 — — 8 a/ ■*■ 16 a/ ^3,0 "t" 4 «/ ^3.1 — s a/ -^.2 — ] g ^^ \^a^ ^5 ^ — Or^-^J

■" ¥ {^ ("^ ^5,1 ~ 2" ^5,0 - "2 ^5,2) - ^3 (— *5,2 - "2 ^5,1 - "2 ^5.3) j

, 3a 3a , \_^ ^ h ^ ^ h

+ 8a/ ~ 16a/ ^3,0 + s^^s »3,l ~ Hj^^ ^3,2

— l^h 1^ h 1^ (^ k I. \

— 8 a/ ^3,1 - 16 a/ ^3,2 — 16 a 3 V"^ ^5,0 — %l)

3 f a^ /a^ + af a_ «. \ _^. , «' , , «" , «% 1

8 \ a/ V «/' ^'1 " «, ^5,0 - -^ 05,2; - 2 a/'^5,l + 2^^5,3 + 2^4^5,0 - 2^405,2 |

8 a/ ^3,1 16 «/ ^3.2 - 16^ ^5,0 + 16^3 05^1

«/ a_ . , 3a^ 3 a»

^3 — 16a/ O3.2 -r 16 a/ ©5,1 — J6^ 65,2.

If /2'i5 denote that part of the coefficient of cos (r-^ + y which is multiplied by e^e^,
^15 2da^ -^3

- 16 a/ ^^3,2 -1- 32 «^3 ^5,1 - 8 a/ ^5,2 + 32^3 (^ — ^'5,2 ~ -i" ^5.1 - "g ^5,3 J

"" 52 {.< (^ *7,1 - 2" *7.0 - "2 ^7,2) - ^5 (^ ^7,2 - 4" ^7,1 - i f'7,^ I

, _o , 3g« , 3 rt3

T" 16 a/ ''3.2 ~ 16^3 ^'s.i + 16 a/ *5,2

MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R. 65

— 64 a 3 ^5,1 - 32 a 3 05,2 — 54 ^3 05,3 - 32 | "" «/ V «/' ^'^ ~ "^ ^7,1 " "^ O7 3 j
"■ 2 a 4 07,0 -t- 2 a^4 07,2 i- 2 «/ ^7,1 - 2 a/ ^7,3 J

— 64 a 3 ^5,1 32 ap ^5.2 04 « ^ %3 + 32 «; ^5,2 + 32 ap ^5,1 — 1 g a* *5,2

___ 15 ff^ , 3 a

— 32ai^^^A — 1 6 a/* ^5,2-

Hence i? contains the term

r 15«3 , 3a , "1 _ , ^ . ^v

'^' \ 32^^ Ki - 16^^ h,2 j e^ e3 cos (r - 1 + ^ .

Calculation of the Coefficient of e ef cos (r — | + !/)•
If /?i9 denote that part of the coefficient of cos (r + 2 1^) which is multiplied by ef,

Ri COST e,o,

R'l . e,2,

^6 COS (r - I/) e^,

^7 cos(r + y e^,

iJ'_ . ... e^

"^^7 — 2da, ■" 2da, "*" ^19 "T 16 da, + 8 ^1 ~ 4 da, "" 4 ^6 "" 2da, ~^i

n __ 3a , ^ , g 7 P _ g fl^ 7 g 7

^7 — 4 a^3 03,0 — 2 a/ ^3,1 — 4 «^3 »3,2 ^19 — 8 af "" 16 a/ ^3,0 " 16 a,^ ^^3,2

ij __ 2a a -L 7. j_ ^^ A P' _ ^ I « r g 7

^6— a,^ ~" 4 0/^^^3,0 - 2 a, 3,1 "r 4 ^^2 »3,2 ^1" ""2a/2 "T" 4 a ^ ^3,0 "" 2 a^^ ^3,2

^1 = :$ - :^ *l.l
2 ~ 2 ■*" 16 "1 ■" 4 ^6 — 2 — — 4 a/ "T" l6a/ ^^3,0 T- 8 a^ ^3,1 — 8 a/ ^3,2

^19 -r g ^1 — 4 Itg — ^1 — — 2 a; ~ l6a/* ^3,0 i" 8 a^ '^3,1 — iQa,^ ^3,2

Q »' — '^^ 3a ^ 7. I « t , 9«^ M A 7, "^

•^ ^7 — 2a2 ~ 8^ ^3.0 - 8^^ »3,l + 4^ ^3,2 + Hf^ Va^ ^5,0 - ^S.l^

+ ¥ { < \:^ ^5,1 - -2 ^5,0 - -2 ^5,2) - ^ (^ ^5,2 - -2 ^5,1 - -2" hs) j
~ 2^ ~ 76^ ^3,0 + 8^ ^3,1 — W^f ^3,2

— — 16"^* ^3,0 -1- 2«/ ^3,1 - i6fl^2 ^3,2 + 8 I a/ V af ^^,2 - ^^ %\ «^ ^3,3;
a^ a* a a ") 9 a^ 9 a^

+ "2^ K\ "" 2^ ^5,3 — 2< ^5,0 + 2^" ^5,2 I + re'^^ ^5,0 " 16^ ^5,1
MDCCCXXXV. K

66 MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R.

9 o T I 1 i I « r 3« I 1 ^ i

= ~ 16^2 h^ + 2^, ^3,1 + l^f «'3,2 - 8^ ^3,2 i" 4 a,^ ^^3.2

" 87^ ^3,1 + 16 a4 «'5.o — 16 af ^5,1

3 , 3 a« , , 3 « A '^« , I _?_ / _L ^^^ A ^«^ /

= " 8^/3,1 - 8^ ^3,1 + I6< ^3,2 - i6a,^^3,2 + 80,^3,1-1- i6tf/^5,o i6«3^5,i

_ 9a» , _L_9f^ A
— ■"■ 16" a 3 ^5,1 -t- 16«4%2'

u 3 «9 _3«^ ,

If i?'i5 now denote that part of the coefl&cient of cos (r — ^ + |J which is multi-
plied by e ef,

— WJp ^5,1 — 32 fl 4 05,2 -t- 32 a/ ^5,2 -t- 32 a ^ O5 1 >

3o3 3tf^ 3a" ,

■""16^^5 2+ J6«f^5,i"" 16 < ^5,2

— 32 « 3 ^5,1 — i6a;^5,2
Hence R contains the term

^/ 1 32^ ^5,1 - T6 < ^0,2 j ^ ^/' cos (r - I + IJ.
I have found that the disturbing function contains the term

As I have given elsewhere the details of the calculation of this term, it is unneces-
sary to repeat them here.

In order to obtain the terms depending partly upon y^, y/^, &c., from the same
equation, the following transformations are necessary :

cos X' = cos (V — v + ") = cos {\' — v) COS V — sin (V — j*) sin v
tan (>C — v) = cos / tan (X — €)

,^y . 1 ' /^\ \ cos I tan (X — S)

^ '^ ^1 + cos«»tan2(x — 5) ^ ^ ^ 1 + cos^ 1 tan^ (A — §)

-, . cos^ — COS (A — ^ + v) + sin- — cos (\ — S — v)
,_ cos V — cos I tan (X — 6) sinv __ 2 ^ ^ 2 ^

"~ ^ I + cos* » tan^ (X - g) "" ^ 1 — sin^ j sin^ (X — f)

-. . cos^ -— sin (X — g + y) — sin^— sin (X — ^ — v)

. , cos I tan (X — b) cos v — siny 2 2

^^^ ~" ^l"+~cos«Ttan2{x^rg)~ — ^1 - sin^ sin2 (X - g)

r" = r ^i - sin« » sin« (X - g)

MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R. 67

^' r] {cos (X' — X^) + * *J = r r^ j cos^ y cos^ ^ cos (X — \ — g + g^ + ^ — ^j

+ Sill2 y cos Y cos (X -f X^ — g — g^ — »; -I- ,.^)

+ cos2 ~ sin2 -^ COS (?i + X^ — € + I' — i/^)

+ sin2 Y sin2 -|- cos (X — \ — g + €^ — v + j^^)

, tan * tan i, , <=, « .

+ — 2 — <=°^ (K - X, - € + g,)

cos

2

Iftan/ = y, cos2y = 1 - ^ + -^ / sm2y = ^--^/.

If ?2 ^ — w^ # + g — 2/ — g + g^ + " — ^ be called r,
and if ??^ + s — g = ^ w^ ^ + g^ —• g^ = p?^ since when the eccentricities

are neglected X = w ^ + g, X^ = w^ # + s^ r =. a, r^-= a^

r r/ {cos (V--X\) + ^^^} = a «^ j cos2 y cos^ y cos r + sin^ y cos^ y cos (r — 2 ??)

+ cos2y sin2 -^ COS (r+2 ri) + sin^y sin^ -^ cos (r~2??+2;j^)
+ ^' cos (;? — ^^) — ^' cos (?j + ;?^)

+ ^ 0 - ^') '=*'« ("^ - 2 ') + ^ 0 - t) ''"s (t H- 2 ,,)
+ 4r cos(r- 2, + 2;,,) +^(l - ^ - ^') cos(, - „)

In order to have the terms required depending upon the squares of the inclina-
tions, it is sufficient to take

R— — ^ |y ^1,0 + ^1,1 COST + ^i2COs2r -I-&C. j

+ l< { 2" ^3,0 + ^3,1 COS r + ^3^2 COS 2 r + &c. j

{ (^^"I-^) COS r - ^ COS (r - 2 ;?) ~ ^%os (r 4- 2 ;j,)

— 7 y^ COS (;? — rt) -\- 7 y, cos (?? + ?7^) >

k2

68 MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R.

= - ^ {t *i.o + \i COS r + *i,2 COS 2 r + &c. |

+ 1^ (7^ + y/') *3.i + 8^ (^3,0 + M (7' + r>^) COS r

m.a ^ „ , ^ X ^/«

- 1^ «3,o y^ cos (. - 2 ,) - ^ «3.o r,^ cos (r + 2 ,,)

- ^ *3,o 7 r, COS (, - ri,) + ^ A3.0 COS (, + ,,) - ^ b,^^ yf cos (2 r - 2 ,)

- 1^ *3,i y^ cos 2 , - ^ ^3., 7,^ cos (2 r + 2 ,,) - 1^ A,,, y,^ cos 2 ,,

"~ 4i?"^3,i yy/cos (r - ?j + J7,) + 4^ ^3.iyr/Cos (r + ;? + ?7j

+ 4^?" ^3,1 77/ COS (r - JJ - ^,) - 4^ ^3,277, COS (2r - ?? + ^^) + &c.

, , , di? d72dr , diidA
As before, "dl = d7 dl + 7u d7^

but in this form of development

dR __dR dR dR __ _dR dR

dA'~"dT'T'd»j dx^ dT'd>j/

Calculation of the Term in R multiplied hy e^ y^.

^ — d^ ^0 "" 8a2 %,l

^2 — — 8 af ^3,1 i- 8 a/ \«/ ^'^ "~ 2 ^^,0 — 2 ^5,2 j

"" "" 16 af ^5,0 + 16 af ^5,2 + 8 a/ ^5,1 " 16 a^^ 65 0 — ^g ^3 05,2

— "" 8fl3 ^5,0+ 8 a* V*
If the term in R^ multiplied by e^ y^ \^q called R\,

„ _ adRp adR^
"^^0— 2da "T 2da.

__ 3a^ , 3a» , _3_a^ _9^

— 16 a3 ^5,0 — 16 a/ ^5,1 + 8 a,^ %o " iq ^ 4 ^s.l

- tI { ^* (I; ^7.0 - ^7.1) - ^ (^ ^7.1 - i ^7,0 - Y ^7,2) }

— I6a8\0— 4a/%l - 16\~ a4\^ a,^ 67,1- a/7,0 — -^07.2 j +2^507,0-^6^7,2/

~ I6fl» ^5.0 — 4 a; ^5,1 + i6a/ ^5,1 "" 16 a/ ^3,1

_ 9a^ ,

— 16 a/ ^5.0-

MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R. 69

Hence R contains the term 32^ ^5,0 ^^ (7^ + yf)' Putting for fcg q its value in series

according to powers of — , neglecting yf, I find for the lunar theory ^^' 3 e^ 7^^
which agrees with the result I have arrived at elsewhere by other methods.

Calculation of the Term in Rq multiplied hy ef y^.
_ a,dRo _ a

a_ _a_ 3_^ 3j^ 3_a^ 3 a^ 3 a^

"- 4 a,2 ^^3,1 - 8 «/ ^3,1 + 16 «^2 05,0 — 16 «^3 05,2 — 8 a," ^5.1 + l6 «/ ^5,0 + j^ «^3 05,2

— Sl^ ^3.1 + 8^3 05,0 — 8^ 05,1-

If R"q denote the term in Rq multiplied e^^ y 2^

„ _a,dRo a,dR^
^^o— 2d a, — 2 da,

~ "" Tf^ ^3,1 — l6^3 05,0 +16^4 05,1 + 8 a 3 03,1 + iq}{s 05^0 — 4^ 05,1

3 g^ / a ^ 2. J_ A \ , 15 a^ 3 a^

"" 16a^^ Va/ ^'^ "" 2 ^5,0 — 2 ^25J + I6a/^5,i " i6a,4^5,i

_ 9a^

"~ 16 a 3 ^5,0-

9 m a^ 9 7W a^

Hence i? contains the term -3:7^ ^5,0 ^i^ (7^ + y/^)j ^^ ^^ t^^ lunar theory ^^^^3 ej^ y^

Calculation of the Term in R^^ or (Rj) multiplied hy y^,
^3 = - Tda - ^1 ^1 = 8^3 (&3,o + ^3,2)

^3 = - Fd^ (^3.0 + &3,2 + 16^3 I ^ 65,0 - &5,1 + ^ &5,2 ~ T &5,1 - ^ ^5.3 }

— 3 « /«' + «/^ , o_^ A \ a ^ I A^ 7. 3a^

— 16 a^ V ^i'' ^'^ «, ^'V "" 16 a/ ^3,2 + iq «4 05,0 — ig «^3 ^o,!

I J_^ 7, 3a^ 3a« 3a^ 3 a'

+ 1 6 a^* ^5,2 32 a 3 05,1 32 a 3 05^3 — 3^ ^^3 65 ^ + 3^ ^^3 05,3

^7. ^'^7>_l_^®^7.

— "~ 16^2 03,2 - YgT} ^5.0 + 167* ^5,2-

70 MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF B.

If the term in R^^ multiplied by y^ be called R\^,
2 da,

il 15 = TTj^ A

a . 3a 30^7. il^S^t—h h \

= "" 16^' ^2 - T6-a7 ^5,0 + 8-^4 ^5,2 H- 32 \ «,^ V «/ ^'^ ~ ^'^Z

~ ^ V^ ^7.2 - -2 ^7,1 - -J h,3) I + 16^3 ^3,2 + 16 «; %,0 - 16 « 4 %,2

3 o^ , 15 r a^ /«!_±_«L 7, -^7, ii 7, \

= T6< ^o,2 + 32 I "" ^^ V"~^?~ ^'^ " «/ ^'' "" «/ ^'V

a^ /a^ + a; . a . « 7, \ i «* 7, "^ 7, M

— 16 «/ ^^5,2 - 32 a/ ^^5,1 - 32 «; %2 + 16 «/ ^5,2

— l_5a^ , 3«3

— "" 32«/^5,i ~ 32a;^5,2•
Therefore R contains the terra

^/ { - i^3 &5,1 - i^4 &5,2} e e, (y2 + y^2) pos (r - | + g.

Calculation of jRj„, or #^e Coefficient of cos (r + I + 1/ — 2 ;j), 2W ^^e Development of R.

Distinguishing- at present the argument r -\- ^, ^ 2 rj hy the index 7, and the argu-
ment r — 2 ;j by the index 1,

_ a,dR, „ __ _c^

^7— - 2da, ~ ^i ^1 — — 8 «,2 03,0

jy ^ 7, _L ^ "^ / " 7> 7. \ J_ ^ A ^ 3 g^ ^ ^ "^ 7,

^7 — - 8^ ^3,0 + Y6"^3 [^ O5 0 - 05,1 j + 8 < ^3,0 — 16-^4 O5 0 — 16^ ^'o,!

^"i— "■ 2da ~ ^7

— l^h A.l^h a.i^/^/«7. 7. ^

— ~ 32 < ^5,0 -r 16 «3 05,1 "T 32 I a,^ \a^ %0 ~ f^7,l)

" «/ \a, ^7,1 - 2 ^0.0 -t- 2 ^7,2; J - 16 «/ ^5,0 -r 16 «^3 05,1

- i^^" 7. . 15 r«' /«' + g; 7. I o « 7. ^ «^ 7. • «' 7. 7 • 30%

- "" 32 a^ %0 "t" 32 I a/ V < ^'^ "^ ^ ^.ij - 2^ h,0 + 2^4 ^7,2 J + F^a t's,!

15 a^ 15 g^ 3g^ 7. 1 '"^ «% _ ^ < 7.

■~ 32 a* \o + 32 g4 ^5,0 + 32 ^3 05,1 + s g^ ^5,1 — 32^ h,\'

D tn a^
Hence R contains the term '^^^3 65 1 e e, y2 cos (r + ? + |^ — 2 ?;).

MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF B. 71

Calculation of R^y , or the Coefficient of cos (r ~ | — |^ + 2 j;^), in the Development of R.
Distinguishing at present the argument r — ^ -{■ 2 ri, by the index 3, and r -j- 2 p?^
by the index 1,

Tf — «^^ y? P — _f_7.

^3 — 16^2 ^3,0 - itia,^\a, Ko ~ hi) + 8 a,^ ^3.0
~ iTT^ ^3,0 — 16 «4 05,0 + le^s 05,1

a, d i^a
'27rflr7

— 16 «; ^3,0 — 8 a 4 ^5,0 + 3C2 a,^ »5,i — 32 ^3 \^^ 05,0 — »5,i;

15a3, 3a^ 3a 3 a^ 3 g^

+ 32^ ^5 0 — 32 a,^ ^5,1 — 16 fl/ ^3,0 H- 16^4 %0 — iQ a,^ ^5,1

— l^h

— 32 a/ '^S,!-

Hence R contains the term -32^ ^5,1 ^ ^y 7/^ cos (r — | — f ^ + 2 ?7y).

Calculation of i?^, or f Ae Coefficient of cos (| — i^ — ?; + ;jj, z/» ^^e Development of R.
Distinguishing the argument ?j — ?7^ -- i by the index 3, and ^ — ??^ by the index I,
odR, ^ ^. «

^■^ — ~ 2dfl, "~ ^1 ^1 — - 4< ^3,0

a, tl R3 n _ _9_^ 7,

2 da, ■" ^3 — I6a3%l

Q ?/2 fit

Hence i? contains the term -j(f^ h,i ^ ^i7 7, cos (| — |^ — ;? + ;?^).

Calculation of R^^, or the Coefficient of cos (| + f, — ?? — ;?^), in the Development of R.

Distinguishing the argument tj ~\- r,, — ^hy the index S, and ?? + >?/ by the index 1,

_ adi^i a_,

^3 — — 2da ~ ^1 ^1 — 4a/2 ©3,0

^vi — "" 2 d fly ^3 — — 16 a^3 05,1-

Q 771 CI

Hence R contains the term j^^ ^51 cos (| + |^ — ;? — ??^).

Calculation of R^^^, or the Coefficient o/* cos (2 r + 2 |^ - 2 v), in the Development of R.
Distinguishing the argument 2 r — 2 ?j + |^ by the index 7, and 2 t — 2 ?? by the
index 1,

72 MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF i?.

^7 = - ird^ - 2 /?i i?i = - — ^>3i

— 8^ ^3,1 + l() a 4 05,1 - 32 «,^ ^5,0 32 fl^ ^5.2

-" 16^ ^5,0 — ]ija* ^5,2 + 16 a 4 ^5,1 — 32 a^^ ^5,0 — 32 «/ ^5,2

3 a^ 3 a^ 9 o^

= "32^3 *5,0 + 16^* ^5,1 - 32^ h,2

= -j^— 3 in the lunar theory.

_ a,dll^ 3 a,dR, 5^

^^vii— -2da --^^7 4 d«, ■" 2 ^1

— 2 — 4 ^1 64 a^3 O5.0 — 32 «^4 O5J i- ^4 ^3 ^5 2 -\- ^4 ^3 05,0 - 64«? ^5.2

— A^^ 7, 3ff3 ,
"~ 32 o? ^5,0 — 32 a* ^5,1

o» At?— A^a 1^ ^ ^_9_^7. I '^«% l''^"^

- J /t7 - 2 ^1 — — 16 af- %0 - 8 a4 05,1 "r 16 «^3 ^5,2 + 32^3 ff^fi — 32^3 0.5,2

— 9»^ ;, 3«3 3^2

— 32 a 3 ^5,0 — 16 « 4 05,1 + 32 a} ^5,2

2 iC^„ - - 32 a 3 ^5.0 + 8 < ^5,1 + 32 | < \"^ ^7.0 " 07,1; " ^^ V "^ ^7,1 - -2 ^7,0 - -Qb;^,2) j
"T" 32 of ^50—8 «,4 ^^5,1 -T 32 ^^3 «»5,2

— 32 a3 05,2 -1- 32 I - < V < ^7,1 - ;^ ^,0 - -^ «'7,2; + 2:^ ^7.0 - -^5 *7,2 I

__ 3«^ 15 a3 3a3

— 32 « 3 ^5,2 - >2 « 4 %l + 32 «/ ^5,1

— A^ A I A^ 7.

— ■" 8 a 4 ^5.1 + 32 a 3 05,2-

Hence /2 contains the term m, | - ~ ^^51 + ^^5,2 1 e,^ y2 cos (2 r 4- 2 1^ - 2 ^).

Calculation of R^^^, or the Coefficient of cos (2^ — 2 jj), in the Development of R.

Distinguishing the argument ^ - 2 ;j by the index 65, and the argument 2 j? by the
index 62,

2 d a ~ ^ ^62 , -"62 = - Ya^ *3,i

MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R. 73

_ 3«^ 3a^ 3a^ ^ 3 a^ 3 a^ , a

~~ 32 a^ ^5,0 — 32 «3 05,2 — 16 a 4 %i + 32 « 3 ^5^0 + 32 a^ ^5,2 + 4 ^^2 »3,i

— ITf *3,i + iti af ^5,0 — r6^4 »5.1

9 c?
= g — 3 in the lunar theory.

^ ^viii — — 2da "• ^ ^65 — 4d« - — 2 ^62

~~ ■" 16 a7 ^5,0 -r 32 a 4 O5.1 + 32 af ^5,0 — 32 «* 05,1

a^Sa^^a 1, 1^\

- 8^" ^3,1 + 8^ V^ ^5,1 - -2 ^5,0 - -^ 05,2;

+ i { ^ (-^ ^7,0 - h,) - -^(^ ^7,1 - 4 ^7,0 -• 4- ^7,2) }

3a^ 3a3 ^A i_^^^

— 8^ ^5,0 + 8^ 05,1 — 2^ 03,1 + ^Q^ 03,1

~ 32 « 3 ^5,0 ~ 32 a 3 05,0 + 32 « a 05,2 + 4 « 4 ^5,1

"T- 32 1 ~ < V « 2 07^1 - — O7 0 - ^^ 072^ -h 2 ^6 Or.o — 2 «^5 ^7,2 J

— ~ 16 a,3 »5,0 + S2 af ^5,2 + 4 « 4 05,1 ~ 32 « 4 05,1 + 32 af ^^,1
"" ~" 16 a,3 05,0 H- 8^4 05,1 + 32 af ^5,2 — "" 8 « ^ %,i + 32 «^3 05,2

= — * 8 — 3 i^ the lunar theory.

{3a S a^ ")

~ \{r~' ^5.1 "^ 64*0^ ^5>2 f ^^ 7^ COS (21 — 2?;).

Calculation of R^^, or the Coefficient of cos (2r — 2f + 2 ;;^), z« #Ae Development of R.

Distinguishing the argument 2 r ~ | + 2 ;?/ by the index 3, and 2 r + 2 j?^ by the
index 1,

^2 ^ "-/a

^3 — T6^ ^3,1 — \Qaf U; ^5,1 - 2 ^5.0 — 2 ^5,2; + 4fl^2 *3,1

* -RvmCor iZ-,) = — — —, this agrees with the result I arrived at formerly, since confirmed by M. Poisson.
MDCCCXXXV. L

74 MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R.

Sa^ Sa^ 3^ 3 a^ 3 a^ _a_ ,

= 32^ ^5,0 — 3^3 05,2 — 16 « 4 %,i i- 3C2 a 3 «?5,o -h 32 « 3 05,2 "T 4 ^2 ^'s,!

_ a , 3 a' , 3a^ ,

— T^ *'3.1 + 32 a,^ ^5,0 — 3£ fl 3 ^5,2

2^ix— — 2da "^^^ 4 da 2^1

— 2" ^3 — T ^1 — ~ 3 a 2 »3,1 — 32 af ^5,0 "T 32 « 4 05,1 "T 32 « 2 ^'a.l

a . 3 a^ , 3 a^ ,

= ~ 32^ ^3,1 — i^3 05,0 + 32^ %,1

— ~ "8^ ^5.0 + 8 a^ ^5,1 — 16 af ^3,1
2 ^ix = — 32^2 03,1 + ig ^^3 05,3 -h 32 a/ ^5,1 "T 32 a^ V^^ %,l — 2 ^5,0 — 2 \y
+ i { $ (^ *7,0 - ^l) - -^ (^ *7,1 - T ^7,0 - i ^7,2) }

3 a', . 3 a

III i

"■ 8^ ^5,0 + 8^ ^5,1 - 7g^2 ^3,1

— 7a , 39 g^ 3a3 3a ,

— ~ 32^^ ^3,1 — ei4 ^3 05,0 + 4 a 4 ^5,1 — 5-4«^3 »5,2

15/ o^ /g" + af , ^ , ^ ;. ^ _L _fL 7. ^'^ a 1

+ 32 \ ~ a4 V a 2 ^7,1 " ^^ ^70 — ^^ 07^2; i" 2 a/ ^7,0 - 2 a/ ^7,2 J

— ^^"^ A _L IL^ A 39 a^ , 3a^ 3a , ]5_^ 3 a^

— ~6-4 a/ ^5.0 + 64 a^ ^5,2 — 64 a^ %0 + 4 a/ ^5,1 — 64 a/ ^5,2— 32 a^ ^5,i + 32a*^5,i

~ ~ 8 a,^ ^5.1 + 32^3 ^5,2-
Hence R contains the term | - jg-g b^^ + ^^3 b^^ \ e^ yf cos (2 r — 2 | + 2 ??^).

Calculation of R^, or the Coefficient of cos (2 f^ ~ 2 vi), in the Development of R.

Distinguishing the argument 2 ;?, — i, by the index 65, and the argument 2 ti^ by
the index 62,

-^— ~ 2da, ~^^62 /{62 = - 8^ <53 1

^65 - - 8 «^2 O3.I i- 15 ap \a, ^5,1 ~ ^g ^5,0 - Y 65,2^ + J^ ^3,1
— IG a* ^3,1 — 16 a 3 ©5,0 "i" i6^« %i

MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R. 75

— 16 a,2 03^1 — 32 «^3 ^5,0 + 8 < ^5.1 — 32 a^ \ a, %l "" 2 ^5,0 " 2 ^5,2^

15 g^ 3a« _3«_ _3a2 ^3^ ^^

~* 32 « 4 t'M + 32 a,* ^5,1 - 8«f ^3,1 + g « 3 05^0 — 8 « * V " l6«,^ ^3,1

+ 32^3 V«, ^5,1 — 2 ^5,0 — 2 ^5,2; -1- 16 «^2 ^3,1

^5,0— 16 a,^ ^3,1 — 8«4 V

~32«3'^5,0 16 a,^ ''3,1 8 a;
"" "" 8 a 4 ^5,1 + 32 « 3 05,2-
Hence i? contains the term j — j^^ b^ ^ + ^^^ J. 2 j ^i^ 7/^ cos (2 |, — 2 ^j,).

Calculation of the Term in R^^ multiplied by e^.

Distinguishing the argument r — ?j + ?j, by the index 1, r — ;? + ;?, — | by the index 3,
and r - ;? + P7, + I by the index 4,

_ a^R^ p __ «digi __ _ _a_

^3— --2dfl ^4--~2da~^3 ^1 — ~4«^2«3,l

n «_ , 3a^ /^ , 1 JL ^ ^

^3 — 8 af ^^3.1 ~ 8 a,A a^ ^5,1 — 2 O5 q — g O^^^J

— 16^^ ^5 0 — 16 «^s 05^2 — 8 a^ ^5,1 + i(j «3 05,0 + 16 af" ^^,2

_ 3«^ _3a^ ,

— 8 a 3 ^5,0 — 8 « 4 %\

adi^i adl^g adi?4 a6.R^ aAR^

^ ^xi ~ 2da 2da 2da ~ 2da da

3a^ , ,9a3 ,15 fa/a h \ ^(±h Lk ^h\\

= ~ 4^ ^5,0 + 8^ ^5,1 + T I ^4 V^ ^/,0 - bj^i) -^s \^^ ^7.1 - 2 ^7,0 - 2 ^7,2j J

■"■ 8 a/ ^3,1 ■+■ 8^ \a^ ^5,1 — 2 '^^o — 2 ^^^V

= - 4^ ^5,0 + 8^^5,1 +^ I - ^4 V"^;^ ^7,1 - ^^7.0 - «^ ^7,2; -I- 2 a,** ^7,0 - 2 ar7,2 j

3a^ , 3^ 3_a^ 3 g^ ^ o^^ ,

■" 16^3 ^5 0 + 16 «3 05,2 + 8 g4 ^5,1 — 16 «3 05,0 — 16 a3 ^5,2

3 «^ 7. I 9 g3 , 15g3 , 1^ 7. 3«^ 7

— "" 4^ ^5,0 + 8 g 4 ^5,1 - 8 a/ ^5,1 + 3 a,^ ^5,1 " 16 a^ ^^5,0

* For certain reductions which occur here, see the calculation of ^2^^^^.

l2l

76 MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R,

+ 16 «3 «'5,2 + 8 a,'* ^5,1 — It) a 3 ^^5,0 — i6 «3 05,2

Therefore iJ contains the term — jg-p ^5 0 ^^ y y^ cos (r — ;j -f ^j-

Calculation of the Term in jR^^ multiplied by e®.

Distinguishing the argument r — ;? + I; by the index 1, the argument r — ;? + ;;^ — ^^
by the index 6, and r — ;j + ??^ + i^ by the index 7,

_ <?/digi p _ «/ d -Ri _ „ „ _ _«_,

^6 = "" 4^ *3,1 + 5^ V:^ ^5,1 — Y *5,0 — 2" ^5,2;

— 3«^ 3«^ 3a3 3»a 3ftg _«_

■~ — iQaf ^5,0 + i6«3 05,2 + 8«4 05^1 — ig«3 05,0 — i6«3 05,2 — 8a/ ^3.1

— "~ 8 «/ ^3,1 — 8 « 3 ''s.o + 8 a 4 %i
a, d Ri a,d Rq a, d R^ a^ dR^ a^d Rq

XI Ida, 2 da, 9. da, 2 d «^ d a^

2^xx =

^ ^xi = — "8^ ^5.0 + y^ ^5,1 — 4^ ^3,1

u

8

+ ^ { ^4 (:^ ^^7,0 - h,^ - ^5 (^ &7,1 - i 2^7.0 - Y ^7,2) }

■*■ 8 a/ Va^ ^5,1 - 2 ^5,0 - 2 ^5,2j i- 4^ 03,1 - 8^ (^^ %,l " Y ^5,0 " -205,2;

- 8 a^ ^5,0 -i- 2 a * ^5,1 - 8 a'f ^5,0 + 8 «/ ^5,2 " 8 «/ ^5,1 4" s^ %,! + q^ %i

3 a" 3«^ il^A 3a2 3 a^ , 3 a^ Sa^

""16 a/ ^5,0 16 a/ %2 i" 8 a/ ^5,0 - 8 a/ ^5,2 - 8 a/ %i + le^a/ ^5,0 + ig"^ 05,2

— 9a^
8 a/ ^5,0'

9 a'
Therefore i? contains the term — —-3 65,0^/^ 7 7i cos (r — ;? + ;j^).

Calculation of R^^^ or the Coefficient o/" cos (r - 2 1 + ;? + jj^) in the Development of R .

Distinguishing the argument r + >? + ;j^ — | by the index 3, and r + ;; + n, by the
index 1,

P a d iJj Q

MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OP R. 77

o » _ ^^-^3 o » A «^-^i _ £ 7?
^ ^xii — ""2da~^^3— 4 da 2^1'

It is evident from the calculation of jRym that B contains the term

{^ ^5,1 - i^3 ^5,2} e2y y^cos (r - 2 i + ^ + ^;).
It is evident similarly, and from the calculation of R^, that R contains the term

{1^ \i - l^3^5,2}^/'yy;COs(r + 21,-- n + ;?,).

Calculation of Ry^^^ or the Coefficient of cos (2 r — | + |^ — ?? -|- ^7^).

Distinguishing the argument 2 r — >j + ^/ + 1/ by the index 7, and the argument
2 r — ;? + ^; by the index 1,

«;d.fii ^ «_

^-"-Td^~^i ^1- 4«;^3,2

^7—4^ 03,2 + 8^ V«y ^'2 " 2 ^5,1 - 2 ^5,3; -t- 4«^2 03,2
— 8 «2 03,2 - 16 «^4 05,2 + 16 a,^ ^5,2

R _ a^ R7 n

^xiv — ~~ 2da 7

— ~ 8«/ O3.2 - i6fl/^5,2 + 8fl^« ^5,3 — 8«/ Va, ^5,2 — 2 ''a,! ~ 2 V^j

+ T^ ^3,2 — s:^ »5,2 + 8^ O3 5

_ 21 a^ 15«2 j^

— ~" 16 «4 ^5,2 + 8 «; ^5.3 + 8 a^2 03,2

15r<r*/aM-<, a, «7,\ "^7.i_^7,_i__^7. ^'^ h \

+ 16 I ^* V «;^ ^7.2 - -^^7.1 - -7 ^7,3; -2«r7,2-t- 2a'4'^7,4 i" 2r;/^7.1 -- 2c/^7,3 j

_ 21 a\ 15a^ 9 a^ 9 a^ 15 a^ ^f^, , 3 a^

— "" 16 a;^5,2 + 8 a 3 05,3 + 32 aS^s,! — 32 ^305,3 + ig 0^*05 2 ig ^^305,3 + s a/ %2

__ 9a^ 33 a^

— 32a3^M + 32 a 3^5.3-

Therefore i? contains the term

{i$^i + HI ^3} ^^.rr^cos (2r - I + I, - ^ + ;j,)

78 MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OP R.

R = * terms independent of the quantities h

- f { T *'.« + ^' *=°' ' + *''^ *'°' ^ '■■'■' ^"^ }

- ^ { T *3.o + *3,i cos r + 43,2 cos 2 r +, &c. }

+ ^Vi - ^) cos (r + 2 >,,) + 2^'cos (r - 2 , + 2 »,,)

+ y^.(,_^_^')cos(,-,)-^'(i-^-^>oB (, + >/)}

- H^ { ¥ *5,o + *5,i COS r + «5,2 COS 2 r +, &c. }

o "12

|/^+^)cosr-^cos(r-2;?)-^cos(r + 2?7^)-yy,cos(;?-?j,)+7yyCOs(^ + ^/) j

= |^ + Z^V51^J^l+cos2r} +{-^-5:^'}{cos(2r-2,)+cos2,}

+ I _ y^' _ ^ j {cos (2 r + 2 pjj + cos 2 ;? J

+ I - "^ - ^'j {cos (r + ?j -»?,) + cos (r -;? + ^,)}

^ + ^ j {cos (r + »j 4- ^;) 4- cos (r - ;? - ;j^)}
+ ^ { 1 + cos (2 r - 2 ;?) } + ^' (cos (2 T - 2 ;j + 2 ;j^) + cos (2 pj - 2 ;? j }
H- ^ {cos (r - ;j - ^^) + cos (t - 3 ?7 + ;?j}

+ ^ {cos (r - ;? + ;?>+ cos (r - 3 ;?-;?,)}+ ^ {1 + cos (2 r - 2 ;7^)}
+ ^ {cos (r - »j + ;?^) + cos (r ~ ^ + 3 ;j,n + ^ { 1 + cos (2 ;j - 2 p? j }

3 2 2 2

-'^{cos2;j4-cos2;7,} + ^{1 + cos (2;j + 2 ??^)}.

* It is useless to consider these terms, because as 22 contains no term multiplied by — , if the other part is

«/-

found to contain any term multiplied by — it must be neglected, that is to say, got rid of by adding a simi-
lar term independent of the quantities h, and with a contrary sign.

MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R. 79

In order to obtain the term in R depending upon y^, y"^, yf and y *, it is sufficient to
take

^ = '^\k ^3,0 + «'3,iC0sr + ^32COs2r +,&c. j

I - (|- y2 + ^ + |- y/) COST + y 7^ (y2 ^- y2) COS (>j - n)
-5^'cos(r-2?? + 2^^) +, &c.|
"" "8^3" I ~2 ^5,0 + 05,1 COS r + <^5 2 COS 2 r + , &c. j

{ (^ + ^) ^^® '' ~ ^ ^^^ (r - 2 ;;) ~ ^'cos (r + 2^,)
— y y^ cos (>; - ??^) + y y< cos (;? + n) |
= ^ { Y ^3,0 + ^3,1 cos T + ^3^2 cos 2 r +, &c. j

{-(|/ + ^' + |y;')cosr + yy,(7" + y;^)cos(;j-0

-5^cos(r-2^4-2;?^)+,&c.j

- ^^ {4" *5,o + &5.1 cos r + \^^ cos 2 r +, &c. j

|^ + i4^ + ^-5^'(y2 + y^2)eos(r + ,-^,)-^'(y2 + y,2)eos(r-., + ,^)
+ (t +^' +^') cos r + 4y'y/' cos (2pj - 2;j,) + ^'cos (2r - 2H- 2;?,) j

~ I "■ 64 af ^5,0 + tj4 a 3 %.2 — 64 « 3 05,0 54 «^3 ^5,2 J y

r 3 a2 , 3a« , i >''> «^ , ' 15«^ j, 1 2 2

+ I "^ 64^3 05,0 + 64 af ^5,2 - (j4 «^^ ^5,0 " 64 af \'^ J ^ ^^

I I A^ A I ?-^ A Ai A -1^ 7, "I 4

"^ I ~ 64 a^^ ^5,0 + 64 a^3 ^5,2 " 64 af '^^.o "" 64 af ^5,2 J y/

+ { 1$ *5.o - ^3 ^^5.2 + 1^3 ^^5,0 + 1^3 ^5.2 } y y. (y^ + y.^) co^

+ {-^3^5,0 + ^s\2 - ^3^5,0 - 64f3*5,2}y'y;'cos(2r - 2 ;, + 2 ,^)
= (- T6^3 ^'s.oH- 32^3 &5,2J/ + |- 32^3*5.0- I6^3^'5.2|y y/

+ { " ll^^ ^5.0 + ^3 ^^5.2 } y/ ^^f hfs y y/ (y' + y?) cos (r - »; + ^,)

- ^3*5,0 y'y;'cos(2r~2pj + 2^,).

80

MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R.

In order to give another example of the employment of this method, I propose to
calculate the coefficient of

e / cos (13 r — i — 4 ri),
the argument of which occurs in Professor Airy's inequality of Venus, nt and n^t
being the mean motions of that planet and of the earth.

It is easily seen from the preceding pages that R contains the term

- ll -$- y" ^Mi c«« (13 r - 4 n).

If the coefficient of / cos (13 r — 4 ;?) be denoted by R^
e/cos(13r — I — 4?j) . . . R>,

adR^

R,=

2d«

-9iRi

3 C «2, 5a^ (a , \ , }_ . \ 9«_S \

= - 128 I "" ^ ^5,11 + -^ V^ ^7,11 - 2 ^7,10 - 2 ^7,12 ) - « 3 ^5,11 |

3 riOa«, 5a^(a, \_ , 1. h W

= 728 I "<" ^5,11 - -^ V^ ^7,11 - 2 ^7,10 - 2 ^7,12 ; I

And R contains the term

3 ri0a2 5aWa 1 1 h \\ a

128 I "^ ^5,11 - « 4 V a, ^7.11 - 2 ''7,10 - 2 «'7,12 J j ^ r-

Professor Airy has

{?(0>0) + ^(0,l)}c;'eA*

2

In Professor Airy's notation

2 2

and substituting my notation in Professor Airy's expression, that which I have found
results.

The method I have given of developing the disturbing function in terms of the
mean longitudes may also be employed with advantage in procuring tlie development
in terms of the true longitudes. In this problem

dR rdRdr adRdr

de drrde da;di

d r d , log. r
rde de

log. r = log. a 4- log. (1 — e2) ~ log. (1 + e cos (X — tsr)

= log. a - e2 —

ecos

(>^-^) + 2T2{l+2cos(2X-2m) I

* See p. 89 of Professor Aiky's paper.

MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R. 81

— -^—^ I 3 COS (X - ^3r) + COS (3 X — 3 tsr) 1

-f ^ 1 3 + COS (2 X - 2 w) 4- COS (4 X — 4 tir) j
= log.«- — -32^-^ V + 4'/^^^(^~"'^) + TV^ +-2JC0S(2X-2t!r)

— — COS (3 X — 3 tjj-) + Q^ COS (4 X — Am)

d_r Se

r d e 2

- y e3 - e (l + -| ^2^ COS (X _ Z57) + -^ (1 + e2) cos (2 X - 2 tjr)

J cos (3 X ■— 3 bt) + -g- COS (4 X ~ 4 z^).

It follows from the analysis of M. Poisson, in his Memoire sur le Mouvement de

la Lune autour de laTerre, that the coefficient of cos (2^—2 nr) in the development

of the quantity

r^ rf R

according to the true longitudes, is the same as that of cos {2m — 2 m) in the develop-
ment of R according to the mean longitudes.

dQ _ ad^Q rd_r dQ _ a,dQ r, d r,

de da de d Cj da, de, '

By means of these equations, and after reductions similar to those of which so
many examples have been given in the course of this paper, I find the coefficient of

cos (2 X — 2 \) in Q = — a"^ a, h^^

e^cos(2X - 2X^ + \ — m^) ="2^,^3,1+2^3,2

e e, cos (2 X — 2 X^ — X + t!T + \ — OT ) ~ "" T ^,2

15 a* 3 «^ % a^

ee2cos(2X-2\-X + r!7 + 2\-2T!r,) . . . =- 32^*5.0 +-i6" ^5,1+32^*5,2

9 a'

e^efQ,o^{2'k—2\—2\-\-2w\-2\—2m}Qxe^ef(io%{2m-2xs) = — 54^ *5,2-

MDCCCXXXV. M

[ 83 ]

V. On the Results of Tide Observations made in June 1834 at the Coast Guard Sta-
tions in Great Britain and Ireland. By the Rev. William Whewell, F.R.S.,
Fellow of Trinity College, Cambridge.

Received March 27, — Read April 2, 1835.

In the conclusion of " An Essay towards a first Approximation to a Map of Cotidal
Lines/' published in the Philosophical Transactions for 1833, I stated my opinion that
simultaneous tide observations, made at the stations of the Preventive Service, and
continued for a fortnight, would give us a clearer view of the progress of the tide
along the coasts of this country than we could acquire from any records then extant.
A representation to this effect being made to Captain Bowles, the Chief Commis-
sioner of that Service, and to Captain Beaufort, the Hydrographer of the Admiralty,
those gentlemen entered with great interest and activity into the proposal for pro-
moting this branch of science by such a series of observations ; and they undertook
to give orders for carrying the plan into effect, and directions for its execution. Such
observations were accordingly made at all the Preventive Service stations on the
coasts of England, Ireland, and Scotland, from June 7 to June 22 inclusive, and the
registers of the observations were sent to the Admiralty, where they now are.

I expected to be able to deduce from these returns the solution of several curious
and important questions respecting the tides, and probably to obtain some new laws
of their phenomena. For this purpose, however, it was necessary to perform a pre-
vious reduction of the registered observations, correcting the times as far as the
methods employed would allow, and subtracting from each time of tide the time of
the previous transit of the moon, in order to obtain the interval. Though this opera-
tion was very simple, the performance of it in so many cases (above 12,000) required
more time than I could devote to it. Captain Beaufort kindly allowed it to be exe-
cuted by Mr. Dessiou, of the Hydrographer's Office ; and it was my intention to defer
laying the account of the observations before the Society till the whole of them had
been reduced, and their results investigated. But Mr. Dessiou, having executed this
reduction for the whole of the south coast of England, has been prevented by illness
and by more pressing employments, from proceeding to the remaining coasts. In
the mean time, having examined the reduced observations, I have been led to some
conclusions which appear to me interesting and important ; and which, I think, con-
sidering the delay which may attend the reduction of the remaining returns, and the
intention which is entertained of repeating the observations in the ensuing June, it
may be worth while very briefly to announce. I shall defer the communication of

M 2

84 THE REV. W. WHEWELL'S RESULTS OF TIDE OBSERVATIONS.

the details by which these results are established till I am able to include in them
the east coast of England and the coasts of Ireland and Scotland.

1. In the first place I will observe, that I am convinced from the examination
which I have given to the subject, that observations made in this manner may be
depended upon for many extensive and important inferences. The returns of last
June are more consistent and accurate than I could have anticipated. I have reason
to believe that in much the greater part of the cases they were made with care and
fidelity, and in many instances with ingenious and suifable contrivances. It is im-
possible not to take the opportunity of saying that they reflect great credit both
upon the intelligence and the punctuality of the officers and men of the coast-guard
service.

2. One of the reasons for wishing to obtain such simultaneous tide observations,
was the hope of ascertaining by this means whether there are general irregularities
which affect the tides at all places along an extensive line of coast. Such irregu-
larities are beforehand very conceivable. The tide-wave which visits our coasts has
been propagated up the Atlantic, and influenced at least, if not produced, by the tide
of the Antarctic Ocean. If the causes which determine the velocity of this wave
could in any case so far vary as to make it an hour behind its time in the Atlantic,
that one tide would at all our ports take place an hour later than the regular time ;
and the existence of an influence of this kind would be detected by such an anomaly
appearing in the observations of the whole or a large portion of the British coast.

I think I may venture to say that no such general irregularity affected any of the
tides from the 7th to the 22nd of last June. Partial anomalies of greater or less
extent occur in the observations, but nothing which can be considered as being of a
general character, and indicating a distant origin, like what has been spoken of.

This result is, I conceive, important ; for it appears to render it probable that we
may, with care and perseverance, make our mathematical prediction of the tune of
the tide much more accurate than we might otherwise have hoped. Since the tide
is not affected by distant and general irregularities, it is irregular only so far as it is
influenced by causes which operate in the neighbourhood, and vary from one place
to another ; as, for instance, the eff'ect of the wind in connexion with the form of the
land. Now, not only will irregularities arising from such causes disappear in the means
of long series of observations, but where such mean results have been obtained, the
effiect of the disturbing causes (as, for instance, the wind blowing at and near the
place,) may be determined empirically. We should thus have a local meteorological
correction to apply to the prediction of the tide, in addition to the astronomical cor-
rections ; our tide tables would be much improved, and our knowledge of the tides
rendered more correct and complete.

3. My examination of the results of the observations of the time of high water has
been conducted for the most part by the method already so often employed by
Mr. Lubbock ; namely, by erecting a series of equidistant ordinates to represent the

THE REV. W. WHEWELL'S RESULTS OF TIDE OBSERVATIONS. 85

intervals of the moon's transit and high water, and drawing a continuous line through
the extremities of these ordinates. The curves present, in general, the form of that
deduced by Mr. Lubbock from the London Observations, though of course in the
rude observations of a single fortnight there are great irregularities. But the means
of several places, and even, in most instances, the tides of a single place, present the
features of agreement with theory, which Mr. Lubbock has shown to obtain with
such remarkable exactness in the London tides ; that is, the ordinate of the curve
has in the course of a fortnight a minimum and a maximum magnitude, so that the
curve assumes the form jt- Moreover, it is not symmetrical on the two sides of the
minimum and maximum, the slope being greater after the minimum than before it.
The curve descends from the 7th to about the 13th of June; it then ascends till the
18th or 19th, and ascends more rapidly than it had descended, and then descends
again less rapidly. All this agrees with the form given by theory.

4. But though the general course of the curves has this resemblance, the amount
of flexure is not the same at different places. This result had already been obtained
by the comparison of previous observations, especially those made at Brest, Ply-
mouth, and London ; it is confirmed so clearly by the observations here referred to,
that I think it may now be assumed to be a general fact.

The inferences from this fact are very important ; for in the first place it puts an
end to all attempts to deduce the mass of the moon from the phenomena of tides, or
to correct the tables of the tides by means of the mass of the moon. The approximate
agreement of the mass of the moon deduced by Laplace from the tides of Brest, with
the mass obtained from other phenomena, cannot be considered as otherwise than
accidental. If he had employed the tides of London, he would have obtained a mass
very different, as Mr. Lubbock has shown ; if he had taken those of Plymouth, or of
Brighton, the mass would have been again very different.

This evidence of the inapplicability of this part of the theory will not surprise any
one who recollects how remote the hypotheses of the theory are from the case of
nature. Such a theory may point out the general features of the phenomena, but
any assumption of the actual correctness of the magnitudes determined by means of
it is altogether gratuitous. The force of the moon determines the amount of the
semimenstrual inequality ; but probably we shall never be able to ascertain otherwise
than empirically, hy what rule this force, producing oscillations in an ocean of irre-
gular form and depth, as the actual ocean is, determines the semimenstrual inequality
at each point.

5. But since the semimenstrual inequality is thus determined in general by the
force of the moon, and has a common form at different places, and yet is different in
amount (and in other circumstances) at each place, we may represent it by resolving
it into two parts, one of which shall be common to the whole ocean, or to a large
portion of it, and the other part shall be a smaller and local correction, also following
a cycle of half a month.

86 THE REV. W. WHEWELL'S RESULTS OF TIDE OBSERVATIONS.

By the introduction of a local semimenstrual inequality, in addition to the general
semimenstrual inequality, we should be able to reconcile the discrepancies of the
curve which represents this inequality for different places, as London and Plymouth ;
discrepancies which have hitherto been a source of perplexity to those who have stu-
died the subject.

The existence of these discrepancies, and their general prevalence, which is shown
by our observations, make it clear that we cannot correctly use the tide table of one
place to determine the tides of another, by adding or subtracting a constant interval,
as is often done. For such a purpose the difference of the local semimenstrual in-
equalities of the two places requires also to be applied.

I have not attempted to determine the amount or form of the local semimenstrual
inequalities of different places, not thinking our present materials sufficient ; but a
comparison of the curve of the semimenstrual inequality of different places is the
way in which it must be obtained, and on this subject I have some remarks to make.

6. By what causes is the semimenstrual inequality at one place made to be dif-
ferent from that at another? There are some circumstances which we can readily
imagine may produce such an effect, though we should probably not succeed in
guessing what the effect would be ; as, for instance, the form of the coast, the di-
stance which the tide wave has travelled over, and the meeting of tides proceeding
different ways. I think I can discover in the observations of last June indications of
the effect of all these circumstances.

In the first place it appears that the curves (by which I mean here, and in what
follows, the curves of the semimenstrual inequality) are Jiatter when the observations
are made at promontories than they are for the general line of coast. I speak here of
the promontories of the first order, which divide the south coast of England into large
or primary bays, as the Lizard, the Rame Head, Prawle Point, Portland Bill, St. Al-
ban's Head, St. Catherine's Point, Beachy Head. At such places the amount of the
semimenstrual inequality appears from the observations to be less than it is in the
intervening bays.

7. In the next place it seems to follow from the observations that the curves are
flatter and flatter as the tide wave proceeds further and further. Thus the curve is
flatter in Brighton Bay than it is in Mount's Bay on the coast of Cornwall, the tide
having travelled further from west to east.

I do not consider this point as quite firmly established, because, though the curves
do exhibit such a modification in going eastward, when we get as far east as the Isle
of Wight we seem to perceive the influence of another cause which has been men-
tioned, the meeting of the two tides, which may produce this apparent modification.

8. This subject, the meeting of the tides, appears to be often misunderstood. For
instance, in a paper published in the Philosophical Transactions for 1819, it is taken
for granted, that when the two tides meet which come up the British Channel and
down the German Ocean there must be a visible and marked conflict of opposite cur-

THE REV. W. WHEWELL'S RESULTS OP TIDE OBSERVATIONS. 87

rents of the water. But this supposition is altogether gratuitous. The place of the meet-
ing of the two tide-waves, which come in opposite directions, is the part of the coast
where the tide is later than it is on either side of that part. For example, we know
that on the coast of Dorsetshire and Hampshire the tide-hours are VII. VIII. IX.
going eastward, and that on the coast of Norfolk the tide-hours are VII. VIII. IX.
proceeding southwards. The tide-waves, therefore, move in an opposite direction
along these coasts, and must meet at some intermediate point, as, for instance, on the
coast of Kent ; and at this point the tide is later than it is if we go along the coast
either to the east and north, or to the south and west. But these motions of the tide-
waves must be distinguished from the motions of the streams which bring the tide, as
will be obvious when it is recollected that the tide-wave travels from the Land's End
to the Isle of Wight in six hours. At the place where the tides meet there will not
necessarily be anything more marked in the stream of flood and ebb than at any
other point. The tendencies to opposite tide-streams may partially balance each other
during a part of the flow and of the ebb, and leave only the diff'erence of tendency in
actual operation. There may be strong and conflicting tide-streams produced under
certain circumstances ; but these results will depend much more upon the local con-
ditions of the ground than upon the general course of the tide-wave.

The meeting of the tides, however, will not be a single point ; for by the laws of
fluids the two opposite undulations, which we term the tide-waves, will be propagated
independently of each other, and the fluid will be affected by both. If they were thus
propagated without any loss of magnitude, we could easily trace the consequences.
Let the tide-wave on the south coast move eastward so as to bring high water to cer-
tain places,

A. B. C. D. E. F. G. H. K. L. M.,
at the hours

VI. VII. VIII. IX. X. XI. XII. I. II. III. IV.,

and let the tide coming from the north and east in the opposite direction arrive at the
same places at the hours

IV. III. II. I. XII. XI. X. IX. VIII. VII. VI.

It is then manifest that the tide at F. will still take place at XI. ; also the tides at
E. and D. will occur about XL, the hour intermediate between X. and XII., and be-
tween IX. and I. In the same way the tide at G. and H. will be about XL I do not
say exactly dit XL, because each tide may diminish in amount as it advances ; and for
this reason each tide may, at a certain distance after their meeting, less affect the
other. From these considerations we may expect the tide-hours along such a coast
to be as follows ;

A.

B.

C.

D.

E.

F.

G.

H.

K. L. M.

VI.

VII.

IX.

XI.

XL

XI.

XI.

XI.

IX. VII. VI

The question now remains to be answered. Do we find any such succession of
tide-hours as this on the coast of Britain ? And to this the coast-guard observations

88 THE REV. W. WHEWELL'S RESULTS OF TIDE OBSERVATIONS.

on the south coast enable us to reply, that the hours do follow an order of this kind.
Along a great extent of coast (from the Land's End to the Isle of Wight) the tide-
hours increase in order from 4^ 30™ to 1 1^ 30°^. But from the Isle of Wight eastward,
the tide-hour continues to be about 1 1^ 30™, with small and irregular changes only :
and this is true as far along the coast eastward as the observations have been reduced.
The examination of the eastern-coast observations will show how far this peculiarity
extends.

Thus " the tides meet," in reality, along the whole coast, from the Isle of Wight to
the Downs, and perhaps to the coast of Suffolk ; that is, along the whole of this tract
the water is affected by the tide-waves which arrive in the two opposite directions.

It may appear strange that the influence of the eastern tide should cease suddenly
when it reaches the Isle of Wight, not extending any further to the west. If, how-
ever, we look at the map, and observe the sudden widening^of the channel to the west
of Cape La Hogue, we shall be at no loss to conceive that the tide-wave may be ex-
tremely diminished by this rapid diffusion, as we know that the tides are greatly in-
creased by the gradual contraction of their beds in estuaries and rivers. But whether
or not this be the cause, the fact is indisputable in the observations, that to the east
of this point the tide-hour changes very little, while to the west it diminishes with
comparative rapidity.

If it were at all doubtful that this difference arises from the interference of the
eastern tide as far as this point, the question would, I conceive, be settled by the two
following articles.

9. The heights, as well as the times of high water, were observed ; these heights I
have hitherto examined for a particular purpose only, namely, to ascertain the ex-
istence of a diurnal difference of height, which follows from the theory, as I have ob-
served in a former paper *. From this examination it appears that this diurnal dif-
ference manifests itself with remarkable constancy along a large portion of the co^st
now under consideration. From the Scilly Islands to Portland Bill, most of the sta-
tions exhibit this inequality operating upon the greater part of the tides. The law is,
as is well known, that at a certain season of the year the morning tide is greater than
the afternoon tide, and at a certain other season it is less. In June the evening tide
was the greater; this appears clearly in the early part of the observations. As the
morning tide approaches noon, the difference diminishes ; and when the morning tide
is become the afternoon tide, the diurnal difference has skipped one tide, so as still to
be found conforming to the rule. The diurnal difference of height is variable, ranging
from two or three inches to one foot.

10. I have said that this diurnal difference may be traced as far as Portland Bill.
Eastward from this point the tides do not appear to be affected by it, the morning
and evening tide not having any steady relation of greater or less.

This change is remarkable, and the more so when we observe that it takes place

* Philosophical Transactions, 1833, p. 221.

THE REV. W. WHEWELL'S RESULTS OF TIDE OBSERVATIONS. 89

at the limit of the influence of the eastern tide, according to what was said in arti-
cle 8. Will the interference of the tides explain such a change ?

It obviously will do so ; for the two tides at their meeting differ by twelve hours in
the extent of their course, the one which has come round the northern extremity of
Scotland and down the east coast being so much older than the channel tide. If,
therefore, one of the two be a morning tide (when referred to its origin), the other
must be an afternoon tide ; and each compound tide being made up of such a pair,
will show no peculiar character of either one or the other. Thus we may expect
that, as far as the interference of the tides extends, the diurnal difference will dis-
appear.

Taking the two considerations of Article 8. and this article together, I think it
cannot be doubted that the sea, from the Isle of Wight to the Downs, and probably
further, is affected by both the western and the northern tide.

11. It is natural to inquire whether we can, from our observations, discover the
nature of the effect which the form of the coast produces on the time and height of
the tide. On this subject I can offer some reply, though a more complete discussion
of the existing returns, and of future observations, is desirable to confirm and extend
our views.

The principal feature which appears in the observations of June is, that the tide-
hour varies very rapidly in rounding the main promontories of the coast, and very
slowly in passing along the shores of the intervening bays. Thus, along the whole of
the great bay formed by the coast of Devonshire and Dorsetshire, from Prawle Point
to Portland Bill, the tide hour is nearly the same, ranging only from about 6^ 5™ to
6*^ 20™. But in passing round into Weymouth Bay the hour becomes 7^, and on
going round St. Alban's Head into Swanage Bay, it becomes suddenly 9^.

If we draw the cotidal lines so as to correspond with these conditions, it is clear
that the ends of these lines will be brought close together at the promontories, and
that the lines will run along nearly parallel to the shore. Thus, the extremity of the
6^ cotidal line is near Prawle Head, the line itself following nearly the coast of the
bay to Portland Bill. The 7^ cotidal line ends at Portland Bill, and the 8*" and 9^
lines end at St. Alban's Head. The 10^ and 11^ lines appear to meet the coast near
St. Catherine's Head in the Isle of Wight ; and, agreeably with what has already been
stated, the ll'' line runs at a little distance from the coast through the straits of
Dover. The cotidal lines drawn in my Essay printed in 1833 require to be modified
according to these remarks.

12. At points of the coast where the cotidal lines are brought near together, the place
of high water moves slowly ; so that it is high water at one point, while at another
point not far off, the water is still considerably deficient from its greatest height.
Hence there will be a difference of level and a rapid tide-stream in such cases. Thus
the peculiarity just noticed in the reference of cotidal lines to promontories is con-

MDCCCXXXV. N

90 THE REV. W. WHEWELL'S RESULTS OF TIDE OBSERVATIONS.

nected with the occurrence of strong currents governed by the tide, like the Race of
Portland and the similar current which is found off St. Alban's Head.

I abstain from making any further remarks till the reduction of the whole of the
returns of last June shall give me more complete materials. I am the more de-
sirous to draw attention to the results which such observations may supply, on ac-
count of its being intended to repeat the observations at the Coast Guard stations in
the ensuing June, from the 9th to the 27th. I am also glad to be able to state, that
the subject having been laid before the Lords of the Admiralty by Captain Beau-
fort, Their Lordships expressed their wish that application should be made to foreign
maritime states, with a view to induce them to make contemporaneous observations
on their coasts ; and that such applications are now in the course of being made.
The extension of such results as have been stated in the present paper to other coasts,
and the discovery of other similar laws, cannot but be looked upon as a valuable and,
interesting addition to our knowledge.

[ 91 ]

VI. On certain Peculiarities in the Double Refraction and Absorption of Light exhi-
bited in the Oxalate of Chromium and Potash. By Sir David Brewster, K.H.
LL.D. F.R.S,

Received January 27, — Read February 12, 1835.

This remarkable salt was put into my hands about the end of the year 1 832, by
Dr. William Gregory, of Edinburgh, to whom I have been indebted for much kind
assistance in carrying on my inquiries respecting the action of coloured bodies in ab-
sorbing definite rays of the spectrum. A very brief examination of its optical pro-
perties was sufficient to indicate its more obvious peculiarities, and a short notice of
these was published at the time. Having received, however, from Dr. Gregory a
very fine group of well formed crystals, and having had an opportunity in the spring
of 1833 of observing their action upon the spectrum, both in their solid state and in
the state of aqueous solution, I am now able to present to the Society a general view
of the results which I obtained.

The oxalate of chromium and potash occurs in flat, irregular, six-sided prisms. The
two broadest faces are inclined to each other like the faces of a wedge, whose sharp
edge is the summit of the crystal. These faces are considerably rounded, being pa-
rallel near the base, and inclined to each other about three degrees at the apex of the
prism. The incidence of the broad faces upon the adjacent faces of the prism is about
140°, and therefore these faces are inclined to one another at an angle of 180° — 148°
X 2 = 64°. The crystal is terminated by four minute planes equally inclined to the
broad face and the axis of the prism, but two of these faces often disappear, and the
crystal terminates in an oblique edge in place of a triangular apex.

If we call A A' the broad faces of the ciystal, m, m', m, m' the other four faces of
the prism, and o, o', p, p' the faces on the summit, the following are the angles which
they form with each other.

Incidence of A upon A in a line passing through the axis of the prism 5° 10'

A upon m, and A' upon m' 148 0

m upon m 64 0

— A upon 0, and A' upon o' 112 10

A upon 7?, and A' upon y 112 10

0 upon o', and 7?' upon y 50 10

A upon A' over o,o' or p,p' 4 36

The crystals of oxalate of chromium and potash are, generally speaking, opake ;
and at thicknesses not much greater than the twenty-fifth of an inch they are abso-

n2

92 SIR D. BREWSTER ON THE DOUBLE REFRACTION, ETC.

lutely impervious to the sun's rays. In this state their colour, seen by reflected light,
is nearly black ; but their powder is green in daylight, and of a French grey colour
by candlelight. In the smaller crystals, which are generally the best formed, the
colour both of reflected and transmitted daylight is blue, but that of candlelight is
jmrple. I have not been able to find any distinct traces of cleavage.

This salt possesses a powerful double refraction, which is no doubt related to two
axes. In reference to the axis of the prism the double refraction is negative, like
that of calcareous spar. The greatest refractive index is about 1*605, and the least
about 1*506, reckoning from a line near the boundary of the blue and green rays.

One of the most remarkable properties of this salt is the difference of colour in the
two images formed by double refraction. At a certain small thickness the least re-
fracted image is bright blue, and the most refracted image bright green, in daylight,
or bright pink in candlelight. The blue contains an admixture of green when ana-
lysed by the prism, and the green an admixture of red, the red predominating over
the green in candlelight. At greater thicknesses the blue becomes purer and fainter,
and the green passes into red ; and at a certain thickness the least refracted blue
image disappears altogether, and the most refracted image is olive green. At still
greater thicknesses this image disappears also, and absolute opacity ensues.

When the crystal is exposed to polarized light, with its axis in the plane of polari-
zation, the transmitted light is green ; but when the axis of the crystal is perpendi-
cular to that plane, the transmitted light i^ blue.

When the oxalate of chromium and potash is dissolved in water its double refrac-
tion disappears, in consequence of the particles being released from the force of ag-
gregation by which they are held together in the solid state, and by which double
refraction is produced. The solution, however, exhibits the same general action upon
light as the solid. At moderate thicknesses its colour is a dark blueish green by
daylight, and a bright blood red by candlelight ; but when we increase the thick-
ness of the fluid it becomes of a blueish pink by daylight, and of a deeper blood red
by candlelight, the red rays continuing to increase both in day- and candle-light, as
we lengthen the path of the ray through the solution.

The most remarkable property of the oxalate of chromium and potash, and the one
on account of which I have submitted this paper to the Royal Society, is its specific
action upon a definite red ray lying near the extremity of the red portion of the spec-
trum. This is a property which is not possessed by any solid or fluid body with
which I am acquainted, although I have submitted some hundreds of coloured bodies
to direct experiment. Like all coloured bodies, the oxalate under our consideration
exercises a general absorbent action on the spectrum. The smallest thickness of it,
in which colour is scarcely discernible, attacks the yellow rays of the spectrum on the
more refrangible side of the line D of Fraunhofer. As the thickness of colour of the
solution increases, the violet rays are absorbed, and also all the yellow, orange, and
less refrangible green, till the whole space D E, and part of the spaces on the other

OF THE OXALATE OF CHROMIUM AND POTASH. 93

side of the lines D, E, are wholly destroyed. In this state the prism gives two distinct
images of objects, viz. a red and a greenish blue image, which are considerably sepa-
rated. As the absorption advances, the green on the blue side of E, and the blue on
the violet side of F, gradually disappear, till a pure blue image about F alone remains,
and this too wholly vanishes by an increased thickness of the solution, leaving the red
rays unabsorbed.

While these changes are going on throughout the spectrum, a specific action is
exerted upon a red ray between A and B of Fraunhofer, and in that very part of the
spectrum over which the solution exercises no general absorptive action. The sharp
and narrow black band which is thus formed constitutes a Jixed line in all artificial
lights, and also in solar and day light, which will enable philosophers to measure the
refractive powers of all bodies in reference to this line with an accuracy which could
not otherwise be obtained, unless by the use of fine prisms of the refracting sub-
stances, which in most cases are unattainable.

In order to render this line or band of real use in practical optics, I have endea-
voured to fix its place with as great accuracy as possible. Between the lines A, B of
Fraunhofer there is a group of lines nearly bisecting the space A B, which he has
marked a in his map. The dark band lies in the space B a ; and if we designate it
by the letter X, its position is such that B X = J B a, or the index of refraction in the
Water spectrum, of the rays which are absorbed at the band X is almost exactly
r330701, the temperature of the water being 65° of Fahrenheit.

The relations of this salt to common and polarized light may be readily examined
and finely exhibited by placing upon a plate of glass a few drops of a saturated solu-
tion of it in water. If the crystals are slowly formed they will be found of various
thicknesses, each thickness exhibiting a different colour, varying from perfect trans-
parency, through all shades of pale yellow, green, and blue, in daylight, and through
all shades oi pale yellow, pale orange, red, and blue, in candlelight.

Belleville, by Kingussie,
March 2\st, 1835.

[ 95 ]

VII. Second Essay on a General Method in Dynamics. By William Rowan Hamilton,
Member of several Scientific Societies in Great Britain and in Foreign Countries,
Andrews Professor of Astronomy in the University of Dublin, and Royal Astro-
nomer of Ireland. Communicated by Captain Beaufort, R.N. F.R.S.

Received October 29, 1834,— Read January 15, 1835.

Introductory Remarks.
1 HE former Essay* contained a general method for reducing all the most important
problems of dynamics to the study of one characteristic function, one central or ra-
dical relation. It was remarked at the close of that Essay, that many eliminations
required by this method in its first conception, might be avoided by a general trans-
formation, introducing the time explicitly into a part S of the whole characteristic
function V ; and it is now proposed to fix the attention chiefly on this part S, and to
call it the Principal Function. The properties of this part or function S, which were
noticed briefly in the former Essay, are now more fully set forth ; and especially its
uses in questions of perturbation, in which it dispenses with many laborious and cir-
cuitous processes, and enables us to express accurately the disturbed configuration of
a system by the rules of undisturbed motion, if only the initial components of veloci-
ties be changed in a suitable manner. Another manner of extending rigorously to
disturbed motion the rules of undisturbed, by the gradual variation of elements, in
number double the number of the coordinates or other marks of position of the
system, which was first invented by Lagrange, and was afterwards improved by
PoissoN, is considered in this Second Essay under a form perhaps a little more ge-
neral ; and the general method of calculation which has already been applied to
other analogous questions in optics and in dynamics by the author of the present
Essay, is now applied to the integration of the equations which determine these ele-
ments. This general method is founded chiefly on a combination of the principles of
variations with those of partial diff*erentials, and may furnish, when it shall be ma-
tured by the labours of other analysts, a separate branch of algebra, which may be
called perhaps the Calculus of Principal Functions ; because, in all the chief applica-
tions of algebra to physics, and in a, very extensive class of purely mathematical
questions, it reduces the determination of many mutually connected functions to the
search and study of one principal or central relation. When applied to the integration
of the equations of varying elements, it suggests, as is now shown, the consideration

* Philosophical Transactions for the year 1834, Second Part.

96 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

of a certain Function of Elements, which may be variously chosen, and may either
be rigorously determined, or at least approached to, with an indefinite accuracy,
by a corollary of the general method. And to illustrate all these new general
processes, but especially those which are connected with problems of perturbation,
they are applied in this Essay to a very simple example, suggested by the motions of
projectiles, the parabolic path being treated as the undisturbed. As a more important
example, the problem of determining the motions of a ternary or multiple system,
with any laws of attraction or repulsion, and with one predominant mass, which was
touched upon in the former Essay, is here resumed in a new way, by forming and inte-
grating the differential equations of a new set of vaiying elements, entirely distinct
in theory (though little differing in practice) from the elements conceived by La-
grange, and having this advantage, that the differentials of all the new elements for
both the disturbed and disturbing masses may be expressed by the coefficients of one
disturbing function.

Transformations of the Differential Equations of Motion of an Attracting or Repelling

Si/stem.

1 . It is well known to mathematicians, that the differential equations of motion of
any system of free points, attracting or repelling one another according to any func-
tions of their distances, and not disturbed by any foreign force, may be comprised in
the following formula :

2.m{a^'^x+y"l7/ + z"^z)=z^V: . ......... (1.)

the sign of summation 2 extending to all the points of the system ; m being, for any
one such point, the constant called its mass, and a?7/z being its rectangular coordi-
nates ; while jc"i/"z" are the accelerations, or second differential coefficients taken
with respect to the time, and Ix, ly, I z are any arbitrary infinitesimal variations of
those coordinates, and U is a certain force-function, introduced into dynamics by La-
grange, and involving the masses and mutual distances of the several points of the
system. If the number of those points be w, the formula (1.) may be decomposed into
3 n ordinary differential equations of the second order, between the coordinates and
the time,

^»^» = FZ' '^yi = F^i ^i^i=^IT'' (2.)

and to integrate these differential equations of motion of an attracting or repelling
system, or some transformations of these, is the chief and perhaps ultimately the only
problem of mathematical dynamics.

2. To facilitate and generalize the solution of this problem, it is useful to express
previously the 3w rectangular coordinates j?y ^ as functions of 3w other and more
general marks of position ??i ^2 • • • ''s n 5 ^^^ ^^^n the differential equations of motion
take this more general form, discovered by Lagrange,

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

97

(3.)

d §T §T _ SU

in which

T=:i2.m(^2+y24.2'2) . (4,)

For, from the equations (2.) or (1.),

in which

82'

(5.)

(6.)

and

^•"^K^ dt8ri,+y rf^8>,, + ^ rf/8^J
■ / ,8^' , ,8y , ,8s!'\ 8T

(7.)

T being here considered as a function of the 6 n quantities of the forms ri' and 73, ob-
tained by introducing into its definition (4.), the values

of = t]

8 a;

1 8

♦Ji

+ ^'

8 a;

2S

»J2

+ ... + '?'

8 ^

3n Si

, &C.

'3n

(8.)

A different proof of this important transformation (3.) is given in the M^canique
Analytique.

3. The function T being homogeneous of the second dimension with respect to the
quantities f]', must satisfy the condition

8T

2T = 2 .??'

8V

(9.)

and since the variation of the same function T may evidently be expressed as follows,

^8T . . . ST

^

T=2(^^,' + ^S,), (10.)

we see that this variation may be expressed in this other way,

ST ST

8T=2(,'S^-^S,) ■ • • ■ ("•)

If then we put, for abridgement.

8T

8V,

8T

HT

1' • • • 8V,

= OT.

3w

3n'

(12.)

MDCCCXXXV.

98 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS,

and consider T (as we may) as a function of the following form,

we see that

I^, = ''i'"'f^ =^3„» (14.)

and

and therefore that the general equation (3.) may receive this new transformation,

^' = ^-fi^> (16.)

dt ^1i ^ ^

If then we introduce, for abridgement, the following expression H,

H = F - U = F (td-i, ^2, . . . TJTg^, ;?!, r]2, - ' '%J — '^ i^i, 'J2? • • • ^3„). • (17.)

we are conducted to this new manner of presenting the differential equations of
motion of a system of n points, attracting or repelling one another :

drii
dt "■

SH

dt ~"

—

8H -)

dt —

8H

dt "~
' dt

SH
8H

dt

8H

(A.)

In this view, the problem of mathematical dynamics, for a system of n points, is to
integrate a system (A.) of 6n ordinary differential equations of the first order, be-
tween the 6 n variables f]. rs. and the time t ; and the solution of the problem must
consist in assigning these 6 w variables as functions of the time, and of their own
initial values, which we may call e.p.. And all these Qn functions, or Qn relations
to determine them, may be expressed, with perfect generality and rigour, by the
method of the former Essay, or by the following simplified process.

Integration of the Equations of Motion, hy means of one Principal Function.
4. If we take the variation of the definite integral

«=X'(2-|^-H)'^' • • ■ • 08.).

without varying t or dt, we find, by the Calculus of Variations,

iS=f'lS'.dt, (19.)

c/o

in which

S' = 2.^|^-H, (20.)

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS. 99

and therefore

$S' = 2(^Sg^---g^^;;), (21.)

that is, by the equations of motion (A.),

SS' = 2(^4^ + ^S,) = ^2.^S,; (22.)

the variation of the integral S is therefore

hS=^{7^hn —p^e), (23.)

(p and e being still initial values,) and it decomposes itself into the following 6 n ex-
pressions, when S is considered as a function of the 6 ?i quantities fj. e., (involving also
the time,)

5S as

^1 - 8^ ; Pi = - fT,'

__ 8S __ SS

^^2 — 8,,^; ^2 — — 8^2 '

8S SS

(B.)

= 8« » Psn^— 8^^ '
'3n 3ra

which are evidently forms for the sought integrals of the 6 n differential equations of
motion (A.), containing only one unknown function S. The difficulty of mathema-
tical dynamics is therefore reduced to the search and study of this one function S,
which may for that reason be called the Principal Function of motion of a system.
This function S was introduced in the first Essay under the form

S=X'{T + V)dt,

the symbols T and U having in this form their recent meanings ; and it is worth
observing, that when S is expressed by this definite integral, the conditions for its
variation vanishing (if the final and initial coordinates and the time be given) are
precisely the differential equations of motion (3.), under the forms assigned by La-
grange. The variation of this definite integral S has therefore the double property,
of giving the differential equations of motion for any transformed coordinates when
the extreme positions are regarded as fixed, and of giving the integrals of those dif-
ferential equations when the extreme positions are treated as varying.

5. Although the function S seems to deserve the name here given it of Principal
Function, as serving to express, in what appears the simplest way, the integrals of the
equations of motion, and the differential equations themselves ; yet the same analy-
sis conducts to other functions, which also may be used to express the integrals of
the same equations. Thus, if we put

Q=/'(-2-W + H)'''' ^''-^

and take the variation of this integral Q without varying t ov dt, we find, by a simi-
lar process, , .

lQ = ^(ti^r!r'-elp); (25.)

o2

100 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

SO that if we consider Q as a function of the 6 n quantities w. p. and of the time, we
shall have 6 n expressions

. ^i = + 8^.' ^i = - 8^' (26.)

which are other forms for the integrals of the equations of motion (A.), involving the
function Q instead of S. We might also employ the integral

V=/'2.-|^<i< = 2/'t.rf,, . (27.)

which was called the Characteristic Function in the former Essay, and of which, when
considered as a function of the 6 w + 1 quantities ri. e. H, the variation is

lY,=:^{mlfi - pie) -\-tlli (28.)

And all these functions S, Q, V, are connected in such a way, that the forms aii^d
properties of any one may be deduced from those of any other.

Investigation of a Pair of Partial Differential Equations of the first Order, which the

Principal Function must satisfy.

6. In forming the variation (23.), or the partial differential coefficients (13.), of the
Principal Function S, the variation of the time was omitted ; but it is easy to calcu-

late the coefficient -^j corresponding to this variation, since the evident equation

dt — dt ^ -^ ^ri dt ' ' ' {^^')

gives, by (20.), and by (A.), (B.),

as ^, ^ 8H

lT = S'-2...z.g^= -H (30.)

It is evident also that this coefficient, or the quantity — H, is constant, so as not
to alter during the motion of the system ; because the differential equations of mo-
tion (A.) give

dt — ^ \^ri dt "^ '^'ST dt) — ^ W^-)

If, therefore, we attend to the equation (17.)> and observe that the function F is neces-
sarily rational and integer and homogeneous of the second dimension with respect to
the quantities w., we shall perceive that the principal function S must satisfy the two
following equations between its partial differential coefficients of the first order,
which offer the chief means of discovering its form :

as . ^/dS SS 8S \ TT/ si

^-F^^ ^ ^ e e e \--U(e e e ) ^^^'^

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

101

Reciprocally, if the form of S be known, the forms of these equations (C.) can be
deduced from it, by elimination of the quantities e or ;? between the expressions of its
partial differential coefficients ; and thus we can return from the principal function S
to the functions F and U, and consequently to the expression H, and the equations
of motion (A.).

Analogous remarks apply to the functions Q and V, which must satisfy the partial
differential equations,

"~ yr + * V^^l' "^25 • • • ^3n' bVi' Scr^' • • • 81:^3^ - ^ \8< 85T2' • • • B^^J'

SQ 8Q

3n

>(32.)

and

^ VH' ^' • * • S^' ''^' '''^'"' ''^"Z = W + ^ ('?P ^2» • • • ''Isn)^ I

^ \8^^ 8^' • • • 8^^ ^1' ^2. • • • ^3 J = H + U (ei, ^2, . . . egj.

. . (33.)

General Method of improving an approximate Expression for the Principal Function

in any Problem of Dynamics.

« 7. If we separate the principal function S into any two parts,

Si + 82 = 8, (34.)

and substitute their sum for S in the first equation (C), the function F, from its
rational and integer and homogeneous form and dimension, may be expressed in this
new way,

„/8Si 8S1 \ T./SS2 _8S2 \

, +^uJh + "- + ^u,3„;8,3„'

^^'(^:)=F'(lf)-F'(|5.), (36.)

because

and

and since, by (A.) and (B.),

102 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS,

F(if)=Fw=:-^^=i^, (3«-)

we easily transform the first equation (C.) to the following,
which gives rigorously

supposing only that the two parts S^, Sg, like the whole principal function S, are
chosen so as to vanish with the time.

This general and rigorous transformation offers a general method of improving an
approximate expression for the principal function S, in any problem of dynamics.
For if the part Si be such an approximate expression, then the remaining part 83 will
be small ; and the homogeneous function F involving the squares and products of the
coefficients of this small part, in the second definite integral (E.), will be in general
also small, and of a higher order of smallness ; we may therefore in general neglect
this second definite integral, in passing to a second approximation, and may in general
improve a first approximate expression Sj by adding to it the following correction,

^S.=/'{-^ + U(''.,--0-F(|J.--||t'''"--0}<''' (I^-)

in calculating which definite integral we may employ the following approximate forms
for the integrals of the equations of motion.

expressing first, by these, the variables jj^ as functions of the time and of the 6 n con-
stants €i Pi, and then eliminating, after the integration, the 3 n quantities p^, by the same
approximate forms. And when an improved expression, or second approximate value
Si + A Si, for the principal function S, has been thus obtained, it may be substituted
in like manner for the first approximate value S^, so as to obtain a still closer ap-
proximation, and the process may be repeated indefinitely.

An analogous process applies to the indefinite improvement of a first approximate
expression for the function Q or V.

Rigorous Theory of Perturbations, founded on the Properties of the Disturhing Part

of the whole Principal Function.
8. If we separate the expression H (17.) into any two parts of the same kind,

Hi + H2=H, (40.)

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS. 103

in which
and

H2 = F2 (sTi, «r25 • • • ^3»J »?1J '?2» • • ^^Sn) — ^2 ('^U '?2» • ' ^^sJ* • • • • • (42.)

the functions Fj Fg Ui Ug being such that

Fi + F2 = F, Ui-}-U2 = U; (43.)

the differential equations of motion (A.) will take this form,

l!! - !iL a. Hi f^' _ iiii ?ii

It '1 '»

and if the part H2 and its coefficients be small, they will not differ much from these
other differential equations,

dt "" 8«r.' rf^ — ~ 8,,. ' (H.)

so that the rigorous integrals of the latter system will be approximate integrals of
the former. Whenever then, by a proper choice of the predominant term H^, a
system of 6 n equations such as (H.) has been formed and rigorously integrated,
giving expressions for the 6 n variables rii ^i as functions of the time /, and of their
own initial values e^ jo„ which may be thus denoted :

^.- = Pi (t, ^1, e^,..e^^,p^,p2,'.p3n), (44.)

and

^i = '^i(t,e^,e2,'^€^n^Pl,P2^"Pzn)^ (45.)

the simpler motion thus defined by the rigorous integrals of (H.) may be called the
undisturbed motion of the proposed system of n points, and the more complex motion
expressed by the rigorous integials of (G.) may be called by contrast the disturbed
motion of that system ; and to pass from the one to the other, may be called a Pro-
blem of Perturbation.

9. To accomplish this passage, let us observe that the differential equations of un-
disturbed motion (H.), being of the same form as the original equations (A.), may
have their integrals similarly expressed, that is, as follows :

Sj being here thQ principal function of undisturbed motimi, or the definite integral

Si=/'(2--^-H,)'^<, (^6.)

considered as a function of the time and of the quantities tji a- In like manner if we
represent by Sj -}- S2 the whole principal function of disturbed motion, the rigorous
integrals of (G.) may be expressed by (B.), as follows :

8 S, . 8 Sa 8 S, 8 So /-gr \

104 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

Comparing the forms (44.) with the second set of equations (I.) for tlie integrals of
undisturbed motion, we find that the following relations between the functions ^, Sj
must be rigorously and identically true :

ni = (Pi\t,e^,e^,..e^^,-jj-^,-fj^,..-Y^J\ ....... (47.)

and therefore, by (K.), that the integrals of disturbed motion may be put under the
following forms,

^. ^u^2.--^3«'i'i + y;;'^2+ g^.-'i'sn + iT^/ (L.)

We may therefore calculate rigorously the disturbed variables r^ by the rules of un-
disturbed motion (44.), if without altering the time t, or the initial values e^ of those
variables, which determine the initial configuration, we alter (in general) the initial
velocities and directions, by adding to the elements p^ the following perturbational
terms,

A;>. = ||,Ap, = g,.. A;'3„ = ^„: (M.)

a remarkable result, which includes the whole theory of perturbation. We might
deduce from it the differential coefficients ??'i, or the connected quantities rar^, which
determine the disturbed directions and velocities of motion at any time t ; but a
similar reasoning gives at once the general expression,

^^£ = 87-+ "4^^ [ty ^1, ^2. • • ^3«./^l + 8^'-?^2 + 8^, . . • ;?3n + fj-)^ ' W

implying, that after altering the initial velocities and directions or the elements j9. as

before, by the perturbational terms (M.), we may then employ the rules of undisturbed
motion (45.) to calculate the velocities and directions at the time t, or the varying
quantities ts., if we finally apply to these quantities thus calculated the following new

corrections for perturbation :

A ^ ^2 A ^ ^2 A ^ ^2 /r\\

^^i = H' "^"^2 = 8^, ••^^3n = 8;5;; (O.)

Approximate expressions deduced from the foregoing rigorous Theory.

10. The foregoing theory gives indeed rigorous expressions for the perturbations,
in passing from the simpler motion (H.) or (I.) to the more complex motion (G.) or
(K.) : but it may seem that these expressions are of little use, because they involve an
unknown disturbing function S2, (namely, the perturbational part of the whole princi-
pal function S,) and also unknown or disturbed coordinates or marks of position ;?..
However, it was lately shown that whenever a first approximate form for the princi-
pal function S, such as here the principal function S^ of undisturbed motion, has been
found, the correction Sg can in general be assigned, with an indefinitely increasing

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS. 105

accuracy ; and since the perturbations (M.) and (O.) involve the disturbed coordi-
nates 9j. only as they enter into the coefficients of this small disturbing function S^, it
is evidently permitted to substitute for these coordinates, at first, their undisturbed
values, and then to correct the results by substituting more accurate expressions.

11. The function S^ of undisturbed motion must satisfy rigorously two partial dif-
ferential equations of the form (C), namely,

di "T- ^l \^ri^>" • 8^^ ^IJ . . • ^3n) = Ui (??i, . . . ;?3 J,

and therefore, by (D.), the disturbing function S2 must satisfy rigorously the following
other condition :

,,-=U,(,„. .,3.)- F,(g, ..^, ,,. . . ,3„)+F(g, . .^^,,,, ..,^„),(Q.)

and may, on account of the homogeneity and dimension of F, be approximately ex-
pressed as follows :

or thus, by (I.),

that is, by (42.),

^2=-f,'^2dt (T.)

In this expression, H2 is given immediately as a function of the varying quantities
??. OT^., but it may be considered in the same order of approximation as a known func-
tion of their initial values e. p. and of the time t, obtained by substituting for ;;. m.

their undisturbed values (44.) (45.) as functions of those quantities; its variation
may therefore be expressed in either of the two following ways :

^H2 = 2(^'S,+ ^n^), (48.)

or

in,= t(^-^le + '-^^p)+'-^lt.. . (49.)

Adopting the latter view, and effecting the integration (T.) with respect to the
time, by treating the elements e. jo. as constant, we are afterwards to substitute for

the quantities p. their undisturbed expressions (39.) or (I.), and then we find for the

variation of the disturbing function S2 the expression

MDCCCXXXV. P

106

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

which enables us to transform the perturbational terms (M.) (O.) into the following
approximate forms :

and

82 Sj /»< S Ho

(U.)

Arsr. = 2 .

8 ^ 8 )j .

I"-^'^^, (V-)

containing only functions and quantities which may be regarded as given, by the
theory of undisturbed motion.

12. In the same order of approximation, if the variation of the expression (44.) for
an undisturbed coordinate ri. be thus denoted,

i,^=.JlU+l{-^ie + ^ip), . (51.)

the perturbation of that coordinate niay be expressed as follows :

' bp

(W.)

that is, by (U.),

8pj»/o 0^1

Sn. M c 8«.

A«.

8

-«- VS;., 8.,2 "^ 8p, 8., 8^2 ^ • • • "^ a;>3„ ^e.de^JJo ^p, ^^

\ . (52.)

+

Besides, the identical equation (47.) gives

S').-

8^, 8p, 8.,8^, + 8^, 8.,S^, i- • • • -t- g^^^ g,^g,^^^ ;

(53.)

the expression (52.) may therefore be thus abridged.

^^i

« 8 7J, c/o

8H.

i)i-/o 8^,

6/^— . . . -

(X.)

and shows that instead of the rigorous perturbational terms (M.) we may approxi-
mately employ the following.

A^. = -X^''''>

(Y.)

in order to calculate the disturbed configuration at any time t by the rules of undis-

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS. 107

tiirbed motion, provided that besides thus altering the initial velocities and directions
we alter also the initial configuration, by the formula

^'i=Jo -f^/' (Z.)

It would not be difficult to calculate, in like manner, approximate expressions for the
disturbed directions and velocities at any time t ; but it is better to resume, in an-
other way, the rigorous problem of perturbation.

Other Rigorous Theory of Perturhation, founded on the properties of the disturbing
part of the constant of living force, and giving formulae for the Variation of Ele-
ments mot^e analogous to those already known.

13. Suppose that the theory of undisturbed motion has given the 6w constants
e. p. or any combinations of these, x^, x^, . . . x^^, as functions of the 6n variables
fj. w. and of the time /, which may be thus denoted :

^• = %ift'?i. '?2. • •^3n'^i'^2' • -^sJ' • ••.•.. (54.)
and which give reciprocally expressions for the variables ri. rs. in terms of these ele-
ments and of the time, analogous to (44.) and (45.), and capable of being denoted
similarly,

\ — ^i {*> ^U »2J • • • «6 J' ^i = "^i ft ^1' -^25 • • • ^6n) ' • • • • (^^'^

then, the total differential coefficient of every such element or function «., taken with

respect to the time, (both as it enters explicitly and implicitly into the expressions
(54.),) must vanish in the undisturbed motion ; so that, by the differential equations
of such motion (H.), the following general relation must be rigorously and identically
true :

o = -^ + 2(^ia_ -EJi) 56.

In passing to disturbed motion, if we retain the equation (54.) as a definition of the
quantity «., that quantity will no longer be constant, but it will continue to satisfy
the inverse relations (55.), and may be called, by analogy, a varying element of the
motion ; and its total differential coefficient, taken with respect to the time, may, by
the identical equation (56.), and by the differential equations of disturbed motion
(G.), be rigorously expressed as follows :

» -- 2 ( I ^ — i l±h) (A'.)

14. This result (A^.) contains the whole theoiy of the gradual variation of the ele-
ments of disturbed motion of a system ; but it may receive an advantageous trans-
formation, by the substitution of the expressions (55.) for the variables ri. -a. as func-
tions of the time and of the elements ; since it will thus conduct to a system of 6 w

p2

108 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

rig-orous and ordinary differential equations of the first order between those varying
elements and the time. Expressing, therefore, the quantity Hg as a function of these
latter variables, its variation I Hg takes this new form,

m,=^^.^-^^^ + ^-^u, (57.)

and gives, by comparison with the form (48.), and by (54.),

yi — ^ LMii-^ Uh—y I3il^ r-Q\

8« — ^ • 8x S>, ' Sot — ^ • Sx 8w ' \^^-)

'r 'r r r

and thus the general equation (A^.) is transformed to the following,

in which

(8x. 8x 8x. 8x\
j^j^~"fi~^i)'' (c^)

so that it only remains to eliminate the variables tj -us from the expressions of these
latter coefficients. Now it is remarkable that this elimination removes the symbol t
also, and leaves the coefficients a^ ^ expressed as functions of the elements « alone, not
explicitly involving the time. This general theorem of dynamics, which is, perhaps,
a little more extensive than the analogous results discovered by Lagrange and by
PoissoN, since it does not limit the disturbing terms in the differential equations of mo-
tion to depend on the configuration only, may be investigated in the following way.

15. The sign of summation 2 in (C^), like the same sign in those other analogous
equations in which it has already occurred without an index in this Essay, refers not
to the expressed indices, such as here f, .9, in the quantity to be summed, but to an
index which is not expressed, and which may be here called r ; so that if we intro-
duce for greater clearness this variable index and its limits, the expression (C^) be-
comes

3n /8x. 8x^ 8x. 8x\

and its total differential coefficient, taken with respect to the time, may be separated
into the two following parts.

> (60.)

which we shall proceed to calculate separately, and then to add them together. By
the definition (54.), and the differential equations of disturbed motion (G.),

dt 813- htivr

snrj^c^.gj^ 8j^. S^^• /S_Hi 8_H,.-)

^ (u)]l8i^8^^V8t3^-t- St^rJ ^^J^r\^\ ~^ ^\' r ^ ■^

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS,
in which, by the identical equation (56.),

S^x.

we have therefore

^♦J,. "^ Sw« S« §OT^ 8« Sot,. 8^ J'

8H,

Sot

S«x.
t

I BJ 6 •CT

109

(62.)

(63.)

and -r- ^ may be found from this, by merely changing / to ^ : so that

(r,u)i,il \8>j^S^„8^^ S,,^8t!r^8W S>,^ + VS ,,^ S>,J^^ ^'J, ^\ S^/"S^

■8 X. 8x

Sx
8 X 8 X.

Sx S X.

\ (64.)

and similarly,

(r)i\^'sr^dt 8>j^ 8c7^ f/^ 8>jy

8 X. 8^ X

^ 3n,Sn|/8x^ 8^x. _ 8x. S^^XgH,, / ^ '^j

8x 8^x.

Sta- 8« 8>j

8x 8XA g2fj^

■ST 8)j Sot d'UT 8>3 / 8>j

«< 'r r u 'r 'u

8x 8x. 8x. 8x

)

■ (65.)

/OX. 0X^._ OX^ OXA g-2H^ /l^_^__^i .^"jiULl

\8 -cr^ 8 M 8 CT 8 jj / Sot 8m \8 ■bt 8ct 8 •or Sot / 8 « 8 « f

r 'a r 'm u 'r r u r u 'u 'r •'

Adding, therefore, the two last expressions, and making the reductions which pre-
sent themselves, we find, by (60.),

dt h-f

3n / fi

2 (A

(«) 1 v /,

-f B ^

in which
A

i,s

^^3n,8x
r)l V

8^X.

8,,

8 X. 8*x

)'

(D>.)

8x. 8«x 8x S^x. X

dtff 8cr 8m Sw 8 ■cr 8m/'

(r)i\8M8i3"8'57 SmSctSw ' Gtff ocrOM

N ' 'r u r 'r u r r u 'r

,.W ^ 3n . 8x^ 8^x, 8x. 8^x 8x. S^^x 8x S^x. \

»,* (r)! \8cr^ 8rj^8>j^ 8ot^ 8)j^8rj^ Sj?^ 8»j^8w^ S)j^ 8>j^ 8^/ '

(66.)

and since this general form (D^) for t;«,,j contains no term independent of the dis-

8 H 8 H
turbing quantities -y- ^, -g^, it is easy to infer from it the important consequence

already mentioned, namely, that the coefficients a^^^, in the differentials (B'.) of the
elements, may be expressed as functions of those elements alone, not explicitly in-
volving the time.

110 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

It is evident also, that these coefficients «,^ , have the property

«,,£=-«,,5. (^^)

and

«,,, = 0; (68.)

S H d X.-

the term proportional to -~ disappears therefore from the expression (Bi.) for-—;

and the term

8 H2 SJIg . 8JI2 ^

destroys the term

8H2 8H2 . 8H2 ^«,

8 Xj * *> * * 8 x^- 8 X, dt '

when these terms are added together ; we have, therefore,

i Hg </ X

8 X ^^

2.'-^^r = 0, (E.)

or

' dt ~~ dt

tZ H.2 _ 8 H2

that is, in taking the first total differential coefficient of the disturbing expression H2
with respect to the time, the elements may be treated as constant.

Simplification of the differential equations which determine these gradually varying
elements f in any problem of Perturbation ; and Integration of the simplified equations
by means of certain Functions of Elements.

16. The most natural choice of these elements is that which makes them corre-
spond, in undisturbed motion, to the initial quantities e^ p^. These quantities, by the
differential equations (H.), may be expressed in undisturbed motion as follows,

and if we suppose them found, by elimination, under the forms

^i = ^i + ^i {t, ^1, yi2, . . . rjs^, T^i, STg, . . . Tffsn), 1

\ (70.)

Pi =^i-^% (t, yii, >l2, ' ■ - %„J ^1, ^25 • • • ^3n)j J

it is easy to see that the following equations must be rigorously and identically true,
for all values of ;?, rff-,

0 = '^. (0, ??j, ;?2J • • • ^3nJ ^1> ^2> • • • '^3 J- J

When, therefore, in passing to disturbed motion, we establish the equations of defi-
nition^

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS. Ill

Ki = rii + O. {t, 71^, V2, . . . ??3 n» ^IJ ^2J • • • ^3n). 1

introducing 6 n varying elements «,. \., of which the set X,. would have been represented
in our recent notation as follows :

^i = «3n + »; (73.)

5j c> tv * jv -

we see that all the partial differential coefficients of the forms —J, —J, *, f, vanish

5tj^ SsB-y drj^ Sxsr^

when ^ = 0, except the following* :

T^=''8^=" (74.)

and, therefore, that when t is made = 0, in the coefficients a^^^, (59.), all those coeffi-
cients vanish, except the following :

^r, 3n f r = 1^ ^3n + r,r = ~~ 1 (75.)

But it has been proved that these coefficients «,^ ,, when expressed as functions of
the elements, do not contain the time explicitly ; and the supposition t = 0 introduces
no relation between those 6 n elements x- X^, which still remain independent : the co-
efficients «^„ therefore, could not acquire the values 1,0, —1, by the supposition
/ = 0, unless they had those values constantly, and independently of that supposition.
The differential equations of the forms (B^), may therefore be expressed, for the pre-
sent system of varying elements, in the following simpler way ;

dt ^ ^\ ' U'^ 8«i ' ^^ '^

and an easy verification of these expressions is offered by the formula (E^), which
takes now this form,

^(^'^ + ^^)=0 .(H.,

17. The initial values of the varying elements «^ X^ are evidently e^pi, by the defi-
nitions (72.), and by the identical equations (71) ; the problem of integrating rigo-
rously the equations of disturbed motion (G.), between the variables rji ts^ and the
time, or of determining these variables as functions of the time and of their own
initial values e,- /?,., is therefore rigorously transformed into the problem of integrating
the equations (G^), or of determining the 6 n elements »^ X, as functions of the time
and of the same initial values. The chief advantage of this transformation is, that if
the perturbations be small, the new variables (namely, the elements,) alter but little :
and that, since the new differential equations are of the same form as the old, they
may be integrated by a similar method. Considering, therefore, the definite integral

112 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

as a function of the time and of the 6n quantities x^, ^g^ . . . x^^^, e^, eg, . . . 63^, and
observing that its variation, taken with respect to the latter quantities, may be shown
by a process similar to that of the fourth number of this Essay to be

lE = y.(Xhx-p^e), (P.)

we find that the rigorous integrals of the differential equations (G^) may be ex-
pressed in the following manner :

in which there enters only one unknown function of elements E, to the search and
study of which single function the problem of perturbation is reduced by this new
method.

We might also have put

c==y^(-2.«^' + H2)rf<, .(7/.)

and have considered this definite integral C as a function of the time and of the 6 n
quantities \ p^ ; and then we should have found the following other forms for the in-
tegrals of the differential equations of varying elements,

^^- = + -fiX.' ^' = - 87. (L •)

And each of t\\Q^Q functions of elements, C and E, must satisfy a certain partial differ-
ential equation, analogous to the first equation of each pair mentioned in the sixth
number of this Essay, and deduced on similar principles.

18. Thus, it is evident, by the form of the function E, and by the equations (K^),
(G^), and (76.), that the partial differential coefficient of this function, taken with
respect to the time, is

^ = ^!-2.|14^ = -H,. . . . .■■. . (M..)

and therefore that if we separate this function E into any two parts

El + Eg = E, . (N^)

and if, for greater clearness, we put the expression Hg under the form

H2 = H2 {t, «i, «2» • • • «3nJ ^1» >^25 • • • ^3n)j (^^ ')

we shall have rigorously the partial differential equation

8E1 8E2 / 8E1 , 8E2 8E1 , SE^x. ,_. •

\ 1 1 3 n 3 n/

which gives, approximately, by (G'.) and (K^), when the part Eg is small, and when
we neglect the squares and products of its partial differential coefficients,

^ |E, ^ ^X

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS. 113

Hence, in the same order of approximation, if the part Ej, like the whole function E,
be chosen so as to vanish with the time, we shall have

E. = -X'{4!^+H,(,«„....3.|A,...^)}= (R.,

^ ^ 3n J

and thus a first approximate expression Ej can be successively and indefinitely cor-
rected.
Again, by (L^) and (GK), and by the definition (77.),

the function C must therefore satisfy rigorously the partial differential equation,

17 = H2(^^,g^,...^,Xi,...X3„j: (T^)

and if we put

C = Ci + C2, (Ui.)

and suppose that the part Cg is small, then the rigorous equation

* * an 3m

becomes approximately, by (G^) and (L^),

and gives by integration,

C2=X'{-'# + H,0,g,...|g.,X„...O}'''. • • • • (X--)

the parts C^ and Cg being supposed to vanish separately when ^ = 0, like the whole
function of elements C.

And to obtain such a first approximation, Ej or C^, to either of these two functions
of elements E, C, we may change, in the definitions {7Q.) (77-), the varying elements
X, X, to their initial values e, p, and then eliminate one set of these initial values by
the corresponding set of the following approximate equations, deduced from the for-
mulae (G^) :

»<8H
fC; = e.

■i+rit'^*-' (Y.)

and

A

i=Pi-f!-JTd' (Z'-)

It is easy also to see that these two functions of elements C and E are connected
with each other, and with the disturbing function Sg, so that the form of any one
may be deduced from that of any other, when the function Si of undisturbed motion
is known.

MDCCCXXXV. Q

114 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

Analogous formulae for the motion of a Single Point.

19. Our general method in dynamics, though intended chiefly for the study of
attracting and repelling systems, is not confined to such, but may be used in all
questions to which the law of living forces applies. And all the analysis of this
Essay, but especially the theory of perturbations, may usefully be illustrated by the
following analogous reasonings and results respecting the motion of a single point.

Imagine then such a point, having for its three rectangular coordinates x y z, and
moving in an orbit determined by three ordinary differential equations of the second
order of forms analogous to the equations (2.), namely,

^=i75y' = y^' ^" = 17' (78.)

U being any given function of the coordinates not expressly involving the time : and
let us establish the following definition, analogous to (4.),

T = 4-(^'^+y2 + ^'2), (79.)

a^ i/ z' being the first, and jc" y" z" being the second differential coefficients of the
coordinates, considered as functions of the time t. If we express, for greater gene-
rality or facility, the rectangular coordinates x 7/ zas functions of three other marks of
position f}i f]2 ^3) ^ "^ill become a homogeneous function of the second dimension of
their first differential coefficients n'l ^\ ^'3 taken with respect to the time ; and if we
put, for abridgement,

8T ST ST

TO", — v^, "^o = ^r-r, ^

1 — g^M «'2~ Ir^^y "'3 — Irl^'

(80.)

T may be considered also as a function of the form

T = F (tjTi, rzTg, t;73, ;?1, ;j2J ^j)j (81.)

which will be homogeneous of the second dimension with respect to w^ wg ^^3. We
may also put, for abridgement,

F (tjTi, tJTg, ^3, ??i, J72J ^3) — U ini, ??25 ^73) = H ; (82.)

and then, instead of the three differential equations of the second order (78.), we may
employ the six following of the first order, analogous to the equations (A.), and ob-
tained by a similar reasoning.

rf^_ SH ^_ , SJI ^_ I ^ "^

(83.)

dt -^ "^ S^i' dt "^ "^ IvTc^' dt '^ '^ S^a' I
dt S>]j' dt ^1)2' dt ^»!3* J

20. The rigorous integrals of these six differential equations may be expressed
under the following forms, analogous to (B.),

__ 8S _ SS SS

1-8,1' "2-8^, ^3-8^. I

ss ss ss i •••(•)

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS. 115

in which e^ €2 e.^ p^ p^ p^ are the initial values, or values at the time 0, of vi^ fj^ %
^1 "^2 ^3 5 ^^^ S is the definite integral

pt / 8H , 8H , 8H ,,\ ,

^=Jo V^i8-^ + ^2 8^+^3 8:^3-HJrf/, (85.)

considered as a function of pjj 1^2 % ^1 ^2 ^3 ^^^ ^- l^e quantity H does not change
in the course of the motion, and the function S must satisfy the following pair of
partial differential equations of the first order, analogous to the pair (C),

8S , „/8S 8S 8S \ ^,. -

"87 + F (^g^, g^, g^, pji, yi2, n,) = U {n,, n-,, %) ;

, T./8S 8S 8S \ XT, s \

8S
8^

f

(86.)

This important function S, which may be called the principal function of the motion,
may hence be rigorously expressed under the following form, obtained by reasonings
analogous to those of the seventh number of this Essay :

S = ^1 +/o{- ^ + U (rj„^2,^^) - F (l|.^.||' ^1,^2,^3)} dt ]

^^l?f^^ ^Si SS 8S, 8S 8S1 \,^ I ^ .

■^Jo ^VH-H''H-8^'8^-8^''^1''^^'W^^' J

Si being any arbitrary function of the same quantities v^ ;?2 ^3 ^1 ^2 ^3 ^j so chosen as
to vanish with the time. And if this arbitrary function S^ be chosen so as to be a
first approximate value of the principal function S, we may neglect, in a second ap-
proximation, the second definite integral in (87.)-

21. A first approximation of this kind can be obtained, whenever, by separating
the expression H, (82.), into a predominant and a smaller part, H^ and Hg, and by
neglecting the part Hg, we have changed the differential equations (83.) to others,
namely,

1

yi r ^"-^

dt ~~ 8>ji' dt "^ 8»j2' dt ~~ SiJa'J

and have succeeded in integrating rigorously these simplified equations, belonging to
a simpler motion, which may be called the undisturbed motion of the point. For the
principal function of such undisturbed motion, namely, the definite integral

S.=X'(-iS+-2|5 + -3'|f-H,)'^^, (89-)

considered as a function of f^^ rj2 fj^ ^1 ^2 ^3 ^j will then be an approximate value for the
original function of disturbed motion S, which original function corresponds to the
more complex differential equations,

Q 2

f?r]i _ 8H1 rf>32 _ ^H,
rf^ ~ 8-57, ' df ~~ dnr^'

cZ>33 _8Hi
dt ~~ 8-573'

d'STi 8 Hj c? -Bj-g

8 Hj d W3

116

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

«?Wi 8 Hi 8 Hg f^^-sTa 8 Hi

dri
~dt

dt

8>3i

8*)i ' dt "~ 8)j2 8>j2» dt

8H2 <^^3____^Hj^_^ I

(90.)

The function Sj of undisturbed motion must satisfy a pair of partial differential
equations of the first order, analogous to the pair (86.) ; and the integrals of undis-
turbed motion may be represented thus,

SSi _ 8S1 1

(91.)

Pi

8 Si
1 djji

while the integrals of disturbed motion may be expressed with equal rigour under the
following analogous forms,

?_Si j_ 8_S2 1

__ 8S1 8^2
^"1 ~ 8);i "I 8>)i-

Pl

8 Si

_ 8S1 SS2
8 Si

0 Oi 8 Sg 8 Si 8 Sg 8 Sj 8 Sg 1

~ 8^ ~ 8^' P2— ~ f^'" 8^' Ps— - jy^ — f^y J

^3- g;; + 8,3.

^

(92.)

if S2 denote the rigorous correction of Sj, or the disturbing part of the whole principal
function S. And by the foregoing general theory of approximation, this disturbing
part or function 83 may be approximately represented by the definite integral (T.),

S2=-X^2^^' • (93.)

in calculating which definite integral the equations (91.) may be employed.
22. If the integrals of undisturbed motion (91.) have given
^1 = <Pi {t, €\y ^2, ^3, p^, P2, Pi), ^

^2 = ^2{ti^l^^2yHi PvP2^Pz)i > (94.)

^3 = <P3 (^J ^1> ^2> ^3> P\^ P2i Pz)i J

and

^1 = -^1 (^^ ^IJ ^2? ^3J /'IJ P2J P^)y'\

, «^2 = -+2 (^» ^1> «25 ^3* />1» ;?2J ;^3)j /^ (95.)

•^i = •^'S (^^ ^1> ^2J ^3J i^D ;'2J ?3)j J

then the integrals of disturbed motion (92.) may be rigorously transformed as follows,

^ t J. I ^ ^2 I ^ ^2 I ^ SoX

^1 = <Pl \ty ^1, e^, ^3, pi + g^, ;?2 + y^^, ;?3 + jfj,

^2 = <P2 (^. ^1, ^2. ^3,;^1 + g^f, P2 + -g^', i?3 + g^f). > . . . (96.)
^ / J. I ^ So , 8 So ,8 SgX

^73 = <Pz \U ei, e2, e3, p^ + -g^^ ^2 + i-e^ i^3 + f^).

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

117

and

1 = K "^ "^^ V' ''' ^2' ^^'^^ + J7,^P2 + 8^, Pz + nf ),
8 So , , / , I ^ So I ^ So , S SoX

2 = 8^' + ^2 (^. ^1, ^2, ^3./>l + fT,'P2-\' ff^, PZ + 87-)^ >

S So , , / , I ^ So I ^ So , S So\

3 = 8^ + ^3 (^. ^1, ^2. ^3,?l + 8^, 7^2 + 8^, ^^3 + 8^), ^

(97.)

Sg being here the rigorous disturbing function. And the perturbations of position, at
any time t, may be approximately expressed by the following formula,

together with two similar formulae for the perturbations of the two other coordinates,
or marks of position ;;2J '73- In these formulae, the coordinates and H2 are supposed
to be expressed, by the theory of undisturbed motion, as functions of the time t, and
of the constants e^ eg 63 pi p2 Ps-

23. Again, if the integrals of undisturbed motion have given, by elimination, ex-
pressions for these constants, of the forms

^1 = ^1 + ^1 {^3 ^13 ^23 ^3J ^15 ^2J ^3)3 1

^2 = ^2 + ^2 (*3 ^\3 ^23 ^33 ^1? «^2J ^^3)^ }- (99).

), J

and

^3 = ^3 + ^3 (^3 ^15 ^25 ^3> ^IJ ^23 ^3);

J»l = ^1 + "*"l {^3 '7l> ^2J '73> '^IJ ^2> ^3)^ 1

JO2 = ^2 + "^"2 i^3 ^IJ ??25 '?3J '^IJ ^^2? ^3)? )•
J»3 = ^3 + "^3 (^^ ^IJ '?2J ^33 "^13 ^25 ^3) ; J

and if, for disturbed motion, we establish the definitions

^1 = 'Jl + ^1 (^J ^^l^ ^2J ^3J '^IJ ^2J ^3)5 T
«2 = ^2 + ^2 (^> *?!» '^2? ^3J ^15 ^2J ^3)3
«3 = '^S + ^3 {^3 ^\3 %3 ^^SJ ^1> ^^2? ^3)5

(100.)

and

^1 = "^1 + "^1 (^3 ^13 ^2J ^33 ^^15 ^2J ^^3)3 1
^2 = ^2 + ^2 {^3 'Ju »?2> %> ^'li ^2? ^3)5 r*

^3); J

(101.)

(102.)

^3 = ^3 4- ^3 {^3 ^13 ^25 ^3> '^15 ^^2? ^^3^

we shall have, for such disturbed motion, the following rigorous equations, of the
forms (94.) and (95.),

^l = 'P\ {*3 «1) ^2> ^3J ^13 ^23 ^3)3

'?2 ^^ '^'2 (^3 ^13 ^23 *33 ^13 ^23 ^3)3

^3 = ^3 ('3 ^13 ^23 *33 ^13 ^23 ^-3)3 J

;:1

(103.)

118 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS,

and

^1 ^ '^'l (^> ^U ^2? *3J ^1> ^2j ^3)^ 1

^2 = "^2 (^^ «1J «2J «3J ^U ^^2J ^3)^ )• (104.)

^3 = '^'S (^5 ^15 ^2> *3J ^15 ^2' ^3) 5 J

and may call the quantities »i «2 ^3 ^1 ^2 ^3 ^be 6 varying elements of the motion. To
determine these six varying- elements, we may employ the six following- rigorous equa-
tions in ordinary differentials of the first order, in which H2 is supposed to have been
expressed by (103.) and (104.) as a function of the elements and of the time :

^ Hg -^

8A3V

y (105.)

dx^ 8 Ho I

dK^ _ 8 H2 dy.^ __l Hg
dt ""■ 8Ai ' dt ~~ 8A2'

dv.^
dt

d\ 8 Hg dXci _
dt 8x1 ' dt ~~ '^

8H,

8x2

dt ~~ 8x3 ' J

and the rigorous integrals of these 6 equations may be expressed in the following
manner,

_ 8^ __ 8_E _ 8^ 1

^1 — 8X1' ^— 8X2' ^3 — gxg' I

V\~ — le^' P2— — le^' P^ "~ "" 8^3' J

the constants e^ e^ e^p^ P2P3 retaining their recent meanings, and being therefore the
initial values of the elements «j «2 ^2 ^1 ^2 ^3 ? while the function E, which may be
called the function of elements, because its form determines the laws of their variations,
is the definite integral

E=/'(x,^ + K,^ + X3^^-H,)rf*,. ..... (.07.)

considered as depending on x^ n^ H ^1 ^2 ^3 ^iid/. The integrals of the equations (105.)
may also be expressed in this other way.

^1 ~ + 8 Ai' *2 — + g A2' ^3 — + 8 y^

> (108.)

_ _ 8C _ ic _ i^
C being the definite integral

^, /.</ 8H2 , 8H2 , 8H2 tt\,^ .,^^x

^^VoV^iT^ + ^^T^ + ^^Tlif-H^)^^, (109.)

regarded as a function of \ Xg ^.3 p^ p^ p^ and ^ : and it is easy to prove that each of
these two functions of elements, C and E, must satisfy a partial differential equation
of the first order, which can be previously assigned, and which may assist in disco-
vering the forms of these two functions, and especially in improving an approximate
expression for either. All these results for the motion of a single point, are analogous
to the results already deduced in this Essay, for an attracting or repelling system.

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

119

Mathematical Example, suggested hy the motion of Projectiles.

24. If the three marks of position ri^ 712 % ^^ the moving point are the rectangular
coordinates themselves, and if the function U has the form

g, (Jj, V, being constants ; then the expression

n = iir,,^ + ^2'-\-^3')+g'i3 + i{(^''(^i' + ^2')+^^^3'h • . (111.)

is that which must be substituted in the general forms (83.), in order to form the 6
differential equations of motion of the first order, namely,

dflx drjQ drjQ

o d tff^ o I

(112.)

dt — (" ''i' dt
These differential equations have for their rigorous integrals the six following,

and

7)

?jj = e^ cos /[A ^ + — sin |M; ^,
n^ = €2 cos (Ji>t -^ — - sin (ju t,
7]^ = e^ cos p t -\--^ sinvt — -^ vers v t, j

(113.)

(114.)

^1 ^^ Pi ^^^ ^t — i^j Ci sin |M< f , 1

73^2 ^ P2 cos (Jb t — (j^ 62 sin (Ji^t, i

tJ73 = /?3 cos V ^ — (i' eg + -7) sin f # ; I

ej 62 63 jOj /?2 Pa heing still the initial values of jjj ri2 Vs ^^i ^2 ^3*

Employing these rigorous integral equations to calculate the function S, that is, by
(85.) and (110.) (111.), the definite integral

we find

■BTc, + ■BTc

+ U)6f/,

(115.)

')=i{/^l' + i'2'+i>/ + ^'(^l' + ^2') + G^3 + f)'}|

- ^2 (ei2 + ^2')} cos2^^ - i^M, (^i;?i + eg/^a) sin2p^ >(116.;

+ i{;^3' - (veg^- f y}cos2.^ - ^(ve, + f )j?3sin2./,

and

U = ^ - i { Pi' + ^^2^ + i^3' + i^' (^1' + ^2') + G e'3 + f )' }

+ i {Pi' +P2' - i^^ (^1^ + ^2^)} cos2 (U, ^ - iit* (eijoi + e2;?2) sin 2^/ 5> (li;.)
■^\\vi- Oe3 + ^yjcos2vj?-i(ve3 + f)/?3sm2.^;

and therefore,

120 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

~r \m -r /'2 ~ r ^'^

sin 2 V ^

S = 0 + {p,'+p,^ - ^2 (,^2 + e^^)} '-^^^ - i (ei^^i + e^p^) vers 2^^P[

+ {;>3^-(-3 + fy}^^-4P3(e3 + f)vers2...

kll8.)

In order, however, to express this function S, as supposed by our general method, in
terms of the final and initial coordinates and of the time, we must employ the analo-
gous expressions for the constants p^ P2P3i deduced from the integrals (113.), namely,

the following :

jM, )ji — [x. e^ cos j«. t
Pi ~ sin ft i '

i"" >i2 — ft- gg COS ft t

P2— sin j* ^ •

Ps

V ijg + Jl — (ve^ + ^ j cos V ^

sin v^

and then we find

(119.)

k5 — ^ 2 -h « . tan jt* /

_4_ _L (^3 - ^sY
' 2 • tanv/

- jw/ (^1 6?! + ??2 ^2) tan "V "■ " V3 + -f ) (^3 + ^) tan

2

^ . . . (120.)

This principal function S satisfies the following pair of partial differential equations
of the first order, of the kind (86.),

— 0I

e

3 '

(121.)

J

and if its form had been previously found, by the help of this pair, or in any other
way, the integrals of the equations of motion might {hy our general method) have been
deduced from it, under the forms,

and

^^1 = g^ = /M. (;ji — ej cotan^ ^ - i^^i tan -^,
tsTg = g^ = I"* (>?2 — ^2) cotan !«. # — ^ ^2 tan -^,
^^3 = 8^ = K^3 - ^3) cotanv^ _ (^^gg + ^)
^1= — 87- = |^(»7i — ei)cotan/A^ + ^;jitan -^,
^2 = — 8l~ = i^ ('^2 — ^2) cotan ^ ^ + fA ??2 tan -g-,

tan

Li
2^

(122.)

8S

P3 = - g-

(^3 — ^3) cotan c ^ + (v ;j3 + ^) tan ^ : ,

(123.)

the last of these two sets of equations coinciding with the set (119.), or (113.), and
conducting, when combined with the first set, (122.), to the other former set of inte-
grals, (114.).

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

121

25. Suppose now, to illustrate the theory of perturbation, that the constants (ji,, v
are small, and that, after separating the expression (111.) for H into the two parts,

Hi = :|(V + ^2^ + «^3^) + §'>?3. (124.)

and

H2 = i{//'f(^i2 + pj2') + ''2^3n, (125.)

we suppress at first the small part Hg, and so form, by (88.), these other and simpler
differential equations of a motion which we shall call undisturbed:

^ _ ^ __

d%

IT — ^' IT — ^' IT —'~S-

(126.)

These new equations have for their rigorous integrals, of the forms (94.) and (95.)

and

^1 = ^1 + V\ *, ^2 = ^2+P2^> ^3 = ^3+P3^ — ig^» '

^1 = Pl> ^2 =P2> '^3=P3-- g^

(127.)
(128.)

and the principal function Sj of the same undisturbed motion is, by (89.),

=(

OT 2 + OT ■

g^3

)d.

p{'+pi +pi

Px + Vi + Vi

2

-^^3 - '^gP3t-\-g'^t'^)dt
— §^3)* - gP3^^ + ig'^^>

> ,

(129.)

or finally, by (127.),

^1 — 97 q g^VlS^ ^3) ^ QAg ^ '

(130.)

(131.)

This function satisfies, as it ought, the following pair of partial differential equa-
tions,

^+4{(ify+(a)V(g)l=-..>
^■+i{(sy+(ify+(it)7=-^^-

And if by the help of this pair, or in any other way, the form (130.) of this principal
function 3i had been found, the integral equations (127.) and (128.) might have been
deduced from it, by our general method, as follows :

ra*, =

_ S^i __ ^i — gi

8>)i

ar,

8S1

^^3-8,3

8 Si ___

MDCCCXXXV.

*i2 -- gg
t '

t 26 *5 ^

R

. . . . (132.)

122

and

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

P\-

— !^ _>?! -

Ze,

^2 — — g ^„ — t '

(133.)

^3 - - Si" - "I— + 2 ^ ^ . J

the latter of these two sets coinciding with (127), and the former set conducting to
(128.).

26. Returning now from this simpler motion to the more complex motion first
mentioned, and denoting by Sg the disturbing part or function which must be added
to Si in order to make up the whole principal function S of that more complex mo-
tion ; we have, by applying our general method, the following rigorous expression
for this disturbing function,

in which we may, approximately, neglect the second definite integral, and calculate
the first by the help of the equations of undisturbed motion. In this manner we find,
approximately, by (125.) (127-),

-H2= -^ ^(^e,-^ p,tY -^ {e^^ p^ty^ -^ '^ {e^-^rPzt - ig^Y, (135.)
and therefore, by integration,

So

- i {^' W+P2^) + "' {Pi-ge,)} ^+ 1,2^^^^ _ ^,2^2 t^,

(136.)

or, by (133.),

S2 = — ^ W + ^1 ^1 + ^1^ + 7}^ + ^2 ^2 + ^2)

iU^'t

- V{''3^ + ^3^3 + ^3^+T^('^3 + ^3)^^+^^^^} •• J

(137.)

the error being of the fourth order, with respect to the small quantities ^, v. And
neglecting this small error, we can deduce, by our general method, approximate forms
for the integrals of the equations of disturbed motion, from the corrected function
Sj + Sg, as follows :

""i ~ H + H - ~~t 3" V'^i + "2 ^1/'

2 - 8^ + S^ - ~~t 3" V''2 + 2" ^2)»

'^3 = H + s^ = "V-"-T^^-— ('^3+ 2-^3 + T^^V' .

(138.)

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

123

and

Pi

8S, 8S.

^2— - g^^' lei —

8 Si 8 So >jo — ^o . 1 . v^t t 1 1 \

or, in the same order of approximation,

^3 = ^3 + B ^ - Y ^ ^^ "" 4" '^ ^H^3 + 4 ^3 ^ - ]^ ^ ^^) ,

(139.)

(140.)

and

w,

TtTo

'CT'i

= P2-f^'^t{e2 + -QP2t),

(141.)

Accordingly, if we develope the rigorous integrals of disturbed motion, (113.) and
(114.), as far as the squares (inclusive) of the small quantities /-«< and v, we are con-
ducted to these approximate integrals ; and if we develope the rigorous expression
(120.) for the principal function of such motion, to the same degree of accuracy, we
obtain the sum of the two expressions (130.) and (137.)-

27. To illustrate still further, in the present example, our general method of suc-
cessive approximation, let S3 denote the small unknown correction of the approximate
expression (137.)? so that we shall now have, rigorously, for the present disturbed
motion,

S = Si + S2 + S3, (142.)

Sj and S2 being here determined rigorously by (130.) and (137-). Then, substituting
Si + S2 for Si in the general transformation (87.)? we find, rigorously, in the present
question.

«3=-/'i{(g)V(Sf+(||f}'^^

+/'i{(l|f+(IS)^+(g)7'^'=

(143.)

and if we neglect only terms of the eighth and higher dimensions with respect to
the small quantities {/j, v, we may confine ourselves to the first of these two definite
integrals, and may employ, in calculating it, the approximate expressions (140.) for

r2

124 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

the coordinates of disturbed motion. In this manner we obtain the very approximate
expression,

seio

(4 ??i2 + 7 p^j ei + 4 ei2 + 4 ;?22 4. 7 ^^ e^ ^ 4 ^2)

y (144.)

- 360 (^ ^3' + 7 ^73 ^3 + 4 ^32) - -2^ (p?3 + ^3) - -4032(p

- "^ Gl' + IB ^1 ^1 + ^1^ + ^^2' + IS ^^2 ^2 + ^2')

^^l?/" 2 j_ £i . I .2^ ^^^^gtH-^s + e^) 31vVi(^;
~ 945 \^3 -T 16 ^3 ^3 -r ^3 y 40320 725760

which is accordingly the sum of the terms of the fourth and sixth dimensions in the
development of the rigorous expression (120.), and gives, by our general method,
correspondingly approximate expressions for the integrals of disturbed motion, under
the forms

and

^l =

8S, ,

SS3

^2 =

8S,

8S,

8 S3

^3 =

8S,

5S, ,

8 S3

S)33'

i'l =

8S2

8 S3
6ei'

P2 =

■ 8Si
-he,-

8S2

8 S3
~ 8^2'

Pi-

-8.3-

8^3-

8 S3
-8.3-

(145.)

(146.)

28. To illustrate by the same example the theory of gradually varying elements,
let us establish the following definitions, for the present disturbed motion.

(147.)

»1 = J?! — ^1 t, »2 = ^2 - ^2 ^? «3 = 'JS — ^^3 ^ — Y ^ *^'
Xj = tSTj, Xg = ^2j ^3 = ^^3 + ^ ^i

and let us call these six quantities «i »2 *3 ^1 ^2 ^3 ^^^ varying elements of that motion,
by analogy to the six constant quantities e^ e^ e^ p^ p2 p^, which may, for the un-
disturbed motion, be represented in a similar way, namely, by (127.) and (128.),

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS,
ei = pji — TSTi t, 62 = ^12 — ^2 t> ^3

125

Pi

m

(148.)

V

P2 = ^^2^ /?3 = ^3 + ^ ^- J

We shall then have rigorously, for the six disturbed variables jj^ V2 % ^i ^2 ^-a ex-
pressions of the same forms as in the integrals (127.) and (128.) of undisturbed
motion, but with variable instead of constant elements, namely, the following :

;?! = »1 + Xi t, f}2 = ^2 + h*> ^3 = »3 + h^ — -Q g t^

ro-j = Xi,

TSTn

^2>

= h- g^'*

(149.)

and the rigorous determination of the six varying elements x^ »2 «3 ^1 ^2 ^3? as func-
tions of the time and of their own initial values e^ e^ e^ p^ p^ p^, depends on the in-
tegration of the 6 following equations, in ordinary differentials of the first order, of
the forms (105.):

^ = TIT = ^^ (*2 + 5^2 t),

and

dt

=

8H2

8A3 -

rfA,

8H2

dt

-"■

- 8x,

dh^
dt

=

8H2

dX..

SH,

(150.)

= — (0,2 («i -f- Xi /),
= — ^2 (;p^ _|, ^2 ^),

^l

(151.)

H2 being here the expression

H2 =^{K + ?^lO'+ (^2 + ^2 0^} + y(^3 + hf-^g^'Y^

(152.)

which is obtained from (125.) by substituting for the disturbed coordinates ri^ ri2 fj^
their values (149.), as functions of the varying elements and of the time. It is not
difficult to integrate rigorously this system of equations (150.) and (151.) ; and we
shall soon have occasion to state their complete and accurate integrals : but we shall
continue for a while to treat these rigorous integrals as unknown, that we may take
this opportunity to exemplify our general method of indefinite approximation, for all
such dynamical questions, founded on the properties of the functions of elements C
and E. Of these two functions either may be employed, and we shall use here the
function C.

29. This function, by (109.) and (152.), may rigorously be expressed as follows :

(153.)

126 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

C = ^f^ (V ^2 _ ^2 + y^l t2 _ ^2)dt

and has therefore the following for a first approximate value, obtained by treating
the elements k^ »2 «3 ^i ^2 ^3 ^^ constant and equal to their initial values e^ e^ e^ p^ p^ P-i->

C = - -I" 1^2 (e^2 + ei) + ^2 63^ I + I 1^2 (^^2 4. p2) J^ ,2^^2|

(154.)

In like manner we have, as first approximations, of the kind expressed by the ge-
neral formula (Z^), the following results deduced from the equations (151.),

^2=P2- f^^ (^2 ^ + "i P2 ^>
and therefore, as approximations of the same kind.

(155.)

e^ =

Pi*

^2 — ^ — Q P2*

>^\-Pl

^3 = ~^/>3^ + -6^^2--Vf.

(156.)

Substituting these values for the initial constants e^ 63 e^ in the approximate value
(154.) for the function of elements C, we obtain the following approximate expres-
sion Cj for that function, of the form supposed by our theory :

r _ ^ f (^1 -Pif + {\ -P^r , (^3 - Psf \

-^{{^^l- Pl)Pl-^ {^2-P2)P2 + {^3-P'6) (Pi- ^ g*)] > (157.)

The rigorous function C must satisfy, in the present question, by the principles of the
eighteenth number, the partial differential equation,

-I7 = |-{(u; + ^i0 +Wi + h')} + ^{^ + ht-^gfi) ;(158.)
and if it be put under the form (U^),

C = Ci -I- C2,
Ci being a first approximation, supposed to vanish with the time, then the correction
C2 must satisfy rigorously the condition

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

127

In passing to a second approximation we may neglect the second definite integral,
and may calculate the first by the help of the approximate equations (155.) ; which
give, in this manner,

+ iX'{h-TSt)(h-Ps)t'dt

= -T{{h- Pif + {\- p^Y + c^s - P3)n

+ 24 {i^'^Pi (^1 - Pi) + ^^^^2 (^2 - Pi) + "^i^a (^3 - Pz) }

240

-ix-c,^sp^ + — "''-''

240

945

(160.)

We might improve this second approximation in like manner, by calculating a new
definite integral C3, with the help of the following more approximate forms for the
relations between the varying elements Xj Xg X3 and the initial constants, deduced by
our general method :

^1 — ~ 8;?i ~ g;?! — ~" |x2/{ V^ ■*■ 6 "^ 24 / 2 \^ "^ 12 "•" 60 /'

^2— ~ 8j92 — gp^— — fj,it V "^ 6 "*" 24 / 2 V* "T" 12 ^ 60 /^

A^ —

y^t V^ "T 6 "*" 24/ ~ 2 \^ "*■ 12 "•" 60/

M161.)

. "^ 6 \^ "^ 60 "^ 40/ '
in which we can only depend on the terms as far as the second order, but which
acquire a correctness of the fourth order when cleared of the small divisors, and give
then

'^i=Pi-i^''t (^1 + 4 Pi*) + 4" ^' ^' (^1 + T^iO'

X2 = ;?2 - f*^ K^2 + -kp^ V + i" ^* ^^ (^2 + T^2 V'

X3 = ;?3-.2^(e3+-|p3^--F^^')+-B-'''^(^3+T^3<-^^^')-

(162.)

128

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

(163.)

But a little attention to the nature of this process shows that all the successive cor- -
rections to which it conducts can be only rational and integer and homogeneous
functions, of the second dimension, of the quantities Xj Xg X3 jt^ p2 Ps g, and that they
may all be put under the following form, which is therefore the form of their sum,
or of the whole sought function C ;

C = (^-' a^ (Xi - p,Y + h^p^ (Xi - pi) + ^2 c^p2

+ 1^"^ % {^2 - Vlf- + *^?2 (^2-^2) + ^^ <^f.V2

+ ""^ «. ^2. - 7^3)^ + ^.Vz ih - Ps) + ^'^ c, p.^

+ f.g (h - Ps) + "^ ^.gPs + "^ ig^
the coefficients a^ «, &c. being functions of the small quantities fju, v, and also of the
time, of which it remains to discover the forms. Denoting therefore their differen-
tials, taken with respect to the time, as follows,

da^-= a!^dt, da^=z cH^dt, &c., (164.)

and substituting the expression (163.) in the rigorous partial differential equation
(158.), we are conducted to the six following equations in ordinary differentials of
the first order :

^2a',= (2«, + .2^)2; h\= i2a,-\-vU){h, + t); c', = i (5, -f- 0'; 1

/',= (2«, + .2^) (/- i^2). h\=={h,+t){f,^^fi), z", =i(/ - J^2)2.|(165.)

along with the 6 following conditions, to determine the 6 arbitrary constants intro-
duced by integration.

t^

(166.)

''^O — "~ 2 / 5 Oo — 2 ' -^O — 6 ' ^0 — 24 ' ^0 — "■ 24 5 «o — go-

In this manner we find, without difficulty, observing that a^ h^ c^ may be formed
from «, h^ c^ by changing v to ^,

a, = — iv^ t — \v cotan v t, o^ = — 2 l"*^ ^ ~~ 4 i"* cotan il t.

&, = - / -h -;;- tan 2-,
/ = J #2 _ _|_ _ cotan V t,

b^= -t-\- — tQXi^,

^f-— " 2/x2 + ^.

1 ut

3- tan —

2 '

/8 I

V

2

i = 27 — g;? — 27 cotan f /.

(167.)

The form of the function C is therefore entirely known, and we have for this func-
tion of elements the following rigorous expression.

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

129

C = -

ih-PiY + (\ - P^^ (h - Psf

2 [I tan /x. t

2 V tan V ^

- ^ {i^l (^1 - Pi) + P2 (^2 - P2) + Ps (h - Pi) }

+ - {Pi (>^i - ^1) + P2 ih - P2)} tan -^ + - Pi (X3 - ^3) tan ^

> (168.)

- I iPi' + P2' + ?3^) + 7 (i^i^ + ^^2^) tan ^' + -j ;>/ tan ^

+ ("2 "• ^ + T ^^tan »' ^ ) g- (X3 - ?3) + (t ■" "7 ^^^ ^) ^i^3

+ (^ - -6 - fv cotai^ ^ 0 ^''

which may be variously transformed, and gives by our general method the following
systems of rigorous integrals of the differential equations of varying elements, (150.),
(151.):

= - — = — ^'^P' - ^ tan —
1 S^j jttsin/x^ H* 2 '

^2 — — g^2 ~" H^sinju,^ y. ^"^^ 2 '

>. . (169.)

and

^ _ L5 _ _ hzUb _ P3 tan - -^ -^ f-^ -"l

^3— 8^3 ~ vsinv^ V '' 2 ^ v Vsinv/ v /'

«i = 1^ = - (Xi - p^) {t + ^cotan^^) +;^i (- ^ + ^ tan ^),

^2 = 1^= - (>^2-;^2) (^ + ^cotan^^) + ;)2 (- ^ + ^ tan ^^),

^3 = |r= ~ (^3-?3) 0+ ycotani/j?) +i?3(--^ + -7ta^V)

MI70.)

+ ^(¥~"^ + "r^°*^^''V'

that is.

and

Xi = jOj cos jU» ^ — Cj |W/ sin ^ #,
X2 = P2 cos (jbt — 62(^1^ sin jfA /,
X3 = ^3 cos f # -- ^3 1' sin f ^ + ^ (^^ ;;- sin v tj, \

»j = ej (cos |a< ^ + jw, # sin ja» ^) + jo^ (^— sin p # — # cos ^ ^j,
X2 = 62 (cos |U» # + /M. ^ sin p #) + ;>2 ("j;: sin ^ # — # cos ^ t),

«3 = 63 (cos V t ■\- V t ^inv t) '\- pz \j ^va.v t — t cos V tj

(versvt t . ^ I ^\

(171.)

(172.)

MDCCCXXXV.

130 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

Accordingly, these rigorous expressions for the 6 varying elemen^ts, in the present
dynamical question, agree with the results obtained by the ordinary methods of inte-
gration from the 6 ordinary differential equations (150.) and (151.), and with those
obtained by elimination from the equations (113.) (114.) (147.).

Remarks on the foregoing Example.

30. The example which has occupied us in the last six numbers is not altogether
ideal, but is realised to some extent by the motion of a projectile in a void. For if
we consider the earth as a sphere, of radius R, and suppose the accelerating force of
gravity to vary inversely as the square of the distance r from its centre, and to be

= o- at the surface, this force will be represented generally by ^-^- ; and to adapt

the differential equations (78.) to the motion of a projectile in a void, it will be suffi-
cient to make

U=^R2(-^-^) (173.)

If we place the origin of rectangular coordinates at the earth's surface, and sup-
pose the semiaxis o^ -{• z to be directed vertically upwards, we shall have

r = ^(R + zY + ^2 + y2^ (174.)

and

V = -g.+S^-ii^, (.75.)

neglecting only those very small terms which have the square of the earth's radius
for a divisor : neglecting therefore such terms, the force-function U in this question
is of that form (110.) on which all the reasonings of the example have been founded ;

the small constants jca, v, being the real and imaginary quantities \/ ^i V ~r^'

respectively. We may therefore apply the results of the recent numbers to the
motions of projectiles in a void, by substituting these values for the constants, and
altering, where necessary, trigonometrical to exponential functions. But besides the
theoretical facility and the little practical importance of researches respecting such
projectiles, the results would only be accurate as far as the first negative power (in-
clusive) of the earth's radius, because the expression (110.) for the force-function U
is only accurate so far ; and therefore the rigorous and approximate investigations of
the six preceding numbers, founded on that expression, are offered only as mathe-
matical illustrations of a general method, extending to all problems of dynamics, at
least to all those to which the law of living forces applies.

Attracting Systems resumed : Differential Equations of intetmal or Relative Motion ;

Integration hy the Principal Function.

31. Returning now from this digression on the motion of a single point, to the
more important study of an attracting or repelling system, let us resume the differen-
tial equations (A.), which may be thus summed up :

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS. 131

dt^ll = ^{d^'^nT^ dvT^f}); (A2.)

and in order to separate the absolute motion of the whole system in space from
the motions of its points among themselves, let us choose the following marks of

position :

X .mx 'X.my X.mz ^

^ii~ ^m ' y^i ~ Xm ' ^11 ~ Xm ' (1/6.)

and

|,.=:a?,--^„, ;?. =3/. --3/„, ^. = ;5. -2;„; (177.)

that is, the 3 rectangular coordinates of the centre of gravity of the system, referred
to an origin fixed in space, and the 3 /i— 3 rectangular coordinates of the n— 1 masses
Wi m2 . . . m„ _ 1, referred to the nth. mass m„, as an internal and moveable origin, but
to axes parallel to the former. We then find, as in the former Essay,

T = i(a/,2-|-y7 + ;,7)2m

the sign of summation 2^ referring to the first w — 1 masses only ; and therefore.

. (178.)

^.Xm

+ 4 ^-i{(.W + 67)^ + 07 >

+^,{(^47+(^-w)^+(^'S)7-.

(179.)

If then we put for abridgement.

^1— m 8^'
, _ J_ ST

, _ 1 8T

Xm '

, X^.mrl
n —

Xm '
Xm '

>

(180.)

(B«.)

m 8 ^' "~ ^
we shall have the expression

H = 4 W + y / + «?) 2 m + i 2, . m (^ 2 + y,2 + a'/) -

+ 2^ «2, . m ^,)2 + (2, . my,)2 + (2, . m ^7} - U,

of which the variation is to be compared with the following form of (A^.),
dt^K = (da^i,lj[/„ — da/iilx^, + di/,fy',i — dy\^y^^ + c^z^^Sz'^, — dz'„hz,) 2 w
+ ^,.m(id^^a/, - dx',^^ + dTjli/, - dy\^7}-\- dZ,^z\ - dz',m
in order to form, by our general process, 6n diiferential equations of motion of the
first order, between the 6 n quantities x,^i/i, %,, j/^^ y,l z\, InZ, x' ,y\ z\ and the time t. In
thus taking the variation of H, we are to remember that the force- function U de-
pends only on the 3 w — 3 internal coordinates In^ being of the form

s 2

} . (C2.)

132

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

- 2 ^n - 1 /« - 2, n - 15 J

(D2.)

U = m„ (mi/i + 7W2/2 + • • • + wi„ _ i/„ _ 1)
+ mi mg/i^a + i^\ ^3/1,3 + . . • + ^r
in which /i is a function of the distance of m^ from m„, and/-^;^ is a function of the
distance of m^ from rtij^, such that their derived functions or first differential coeffi-
cients, taken with respect to the distances, express the laws of mutual repulsion, being
negative in the case of attraction ; and then we obtain, as we desired, two separate
groups of equations, for the motion of the whole system of points in space, and for
the motions of those points among themselves ; namely, first, the group

d x^i = x'li dt, d of II = 0, "^

dy„=y'„dt,d!/'„ = 0, I ........... (181.)

d Zii = z'li dt, d z'li = 0, J
and secondly the group

fi?|= {fi^i + -^^i.ma/i) dt,dj[/, = -j^dt,

dZ, = [z'l + -^ ^i.mz'i) dt, dz\ =

The six differential equations of the first order, (181.)? between Xnyn Zn ^'ni/'n z',,
and t, contain the law of rectiUnear and uniform motion of the centre of gravity of the
system ; and the 6n^ 6 equations of the same order, (182.), between the 6 w — 6
variables I ?? ^ ^r'^ 3/'^ z'l and the time, are forms for the differential equations of internal
or relative motion. We might eliminate the 3 n—3 auxiliary variables a?',y^ z'l between
these last equations, and so obtain the following other group of 3 ^^ — 3 equations of
the second order, involving only the relative coordinates and the time,

>

m 8^

dt.

(182.)

/ = 1 ^ .

^ — w s? "*" w„ ^/

. ru

su

y

(183.)

but it is better for many purposes to retain them under the forms (182.), omitting,
however, for simplicity, the lower accents of the auxiliary variables .r'^y, z\, because it
is easy to prove that these auxiliary variables (180.) are the components of centrobaric
velocity, and because, in investigating the properties of internal or relative motion,
we are at liberty to suppose that the centre of gravity of the system is fixed in space,
at the origin oi xy z. We may also, for simplicity, omit the lower accent of 2^, un-^
derstanding that the summations are to fall only on the first ^^ — 1 masses, and de-
noting for greater distinctness the nila. mass by a separate symbol M ; and then we

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

133

may comprise the differential equations of relative motion in the following simplified
formula,

in which

And the integrals of these equations of relative motion are contained (by our gene-
ral method) in the formula

in which a^ y a V d denote the initial values of | ;j ^ ^ y' %', and S is the principal

function of relative motion of the system ; that is, the former function S, simplified by

the omission of the part which vanishes when the centre of gravity is fixed, and which

gives in general the laws of motion of that centre, or the integrals of the equations (181 .).

Second Example : Case of a Ternary or Multiple System with one Predominant Mass ;
Equations of the undisturbed motions of the other masses about this, in their seve-
ral Binary Systems ; Differentials of all their Elements, expressed by the coeffi-
cients of one Disturbing Function.

32. Let us now suppose that the w — 1 masses m are small in comparison with the
wth mass M ; and let us separate the expression (F^.) for H into the two following parts,

H,=

+

M
mi mi,

{W.)

of which the latter is small in comparison with the former, and may be neglected in
a first approximation. Suppressing it accordingly, we are conducted to the following
6w — 6 differential equations of the 1st order, belonging to a simpler motion, which
may be called the undisturbed :

d^_±in,_( m\ d^__ l^Hi^ivi^-

dt — m S^ — V^ "T" M/^ ' dt —~ m 8^ —^^^d^
rf>, _ 1 SHi/, , m\ , dl_ 1 g Hi _ ^^ df

^llMl- (i ill),/. !1Z.___1.1^_M

^_ 1 ^H,_ 8/

=:M

(P.)

di — m ^z' —V '^ U)^ '' dt—~~m S? — "'"8^ J
These equations arrange themselves in w — 1 groups, corresponding to the w — 1
binary systems (m, M) ; and it is easy to integrate the equations of each group sepa-
rately. We may suppose, then, these integrals found, under the forms,

^ = x^'^ (t, I ^, K, ^, y\ ^'), " = x^'^ {t, I, n, Z, ^', y. ^X

X = x^^) {t, I, ,, ^, of, y\ ^\ r = x^^) (t, |, n, ^, ^, y\ z% V . . (K^.)

^ = %(3) {t, I, n, ?, a!, y\ %^\ « = >:(«) {t, I v, ^, a!, y, ^') J

134 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

the six quantities zX (jij v r m being constant for the undisturbed motion of any one
binary system ; and therefore the six functions x^^\ X^^\ X^^\ X^'^\ %^^\ X^^\ or «, K, ^^
V, r, u, being such as to satisfy identically the following equation,

8x SxSHi Sj^SHi SxSHi l!i LMl I !^ ?ii liiilL n2\

O — mg^ + g^-g^-g^ g^ +g^ ^j^i - y 8, +8? 8z' ""8 2' 8? ^ ' ^^ ■>

with five other equations analogous, for the five other elements K, yij, v, r, a, in any one
binary system (m, M).

33. Returning now to the original multiple system, we may retain as definitions
the equations (K^.), but then we can no longer consider the elements «. X. uj. v. r. u. of

the binary system (m., M) as constant, because this system is now disturbed by the
other masses w^ ; however, the Qn — Q equations of disturbed relative motion, when
put under the forms

SH.

d^
^ dt

8Hi 8H2

— 8j^ + 8^ '

da}
"^ dt =

8 Hi

8?

dr}
"^ dt

8 Hi 8 H2

— 8y + 8y '

dj/
"^ dt =

8 Hi

- 8,,

dK
'''-dt

_ 8 H 8 H,

— 83' "^" 82' '

d^
"^ dt =

8 Hi

8?

^

8^ '

8^,

8,, ^

8H.

(M2.)

8?

and combined with the identical equations of the kind (L^.), give the following simple
expression for the differential of the element », in its disturbed and variable state,

'^ dt~- l^ Sy 8^ 8^ + 8>j 8y 8y 8>, + 8?' 82' 82' 8? ^ * ^^ 'f

together with analogous expressions for the differentials of the other elements. And
if we express | ;? ^ a?' t/' ;s', and therefore H2 itself, as depending on the time and on
these varjring elements, we may transform the ^n^^ differential equations of the
1st order, (M^.), between ^yiZ^x' y' z' t, into the same number of equations of the
same order between the varying elements and the time ; which will be of the forms

^x f , , 8 H2 , _ 8 H^ , , . 8 H2 , ^ 8 H2 , ^ , 8 H2 1

:^= K ?^} -gX + ^*^^>-87- + ^*' "> "87" + ^^^ '■>~87" + ^^^ "^T^'

d^ ,, , 8 H, . ,. , 8 H2 , . 8 H2 , .^ . 8 H2 . ,. . 8 Ho

m

^^ r . 8 H2 , ^ , 8 H2 , ^ 8 Hg . ^ , 8 H. . , 8 Ho

'^-df = i'> *> 17-+ (^ ^} -87- + ^"^ ^> -8^+ ^^ ^> -87- + ^^ ^> T^'

r» ^'' / 1 ^ ^2 , . . , 8 H2 , ^ 8 H2 , ^ 8 H2 , , , 8 H2

>(02.)

Wl

<i« _ , S H2 . . , 1 S H2 , , . 8 H2 , , , 8 H2 , ^ 8 Hi

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

135

if we put, for abridgement.

8x 8a _ Sx 8X 8x Sa SxSa SxSx 8x8a
{«,A} — g^g^ g_^(g^ + 8>jSy "" gy 8,, + 8^8^ ~ 8^'8^»

(Ps.)

and form the other symbols {x,(ji^}, {\x}, &c., from this, by interchanging the letters.
It is evident that these symbols have the properties,

{X,»} = - {«,X}, {»,«} = 0; (184.)

and it results from the principles of the 15th number, that these combinations {«, X},
&c., when expressed as functions of the elements, do not contain the time explicitly.
There are in general, by (184.), only 15 such distinct combinations for each of the
n— I binary systems ; but there would thus be, in all, 15 w — 15, if they admitted
of no further reductions : however, it results from the principles of the 16th number,
that 12 /i — 12 of these combinations may be made to vanish by a suitable choice of
the elements. The following is another way of effecting as great a simplification, at
least for that extensive class of cases in which the undisturbed distance between the
two points of each binary system (m, M) admits of a minimum value.

Simplification of the Differential Expressions hy a suitable choice of the Elements.

34. When the undisturbed distance r of m from M admits of such a minimum q,
corresponding to a time r, and satisfying at that time the conditions

r' = 0, r">0, (185.)

then the integrals of the group (P.), or the known rules of the undisturbed motion of
m about M, may be presented in the following manner :

V = tan

-1 »}2'-?y

-X

M + m* \/dr^

dr ,

rz=. dr

> ■ (Q^O

a; = V -|- sm

^{2^ + 2M/(r)-(l + ^)^}'

/W+m dr
V "~M

-/QAx — A^

-X

Vdr^'r

-^ . dr

y/{2..+ 2M/(r)-(l+^)^}'

the minimum distance q being a function of the two elements «, f^, whicl must satisfy
the conditions

2f. + 2M/(?)-(n-|)^ = 0,M/(y) + (n-H)J>0; ■ (186.)
and sin" ' s, tan" '<, being used (according to Sir John Herschel's notation) to ex-

136 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

press, not the cosecant and cotangent, but the inverse functions corresponding to sine
and cosine, or the arcs which are more commonly called arc (sin = s), arc (tan = t),

dr
It must also be observed that the factor ^^/^j which we have introduced under the

signs of integration, is not superfluous, but is designed to be taken as equal to posi-
tive or negative unity, according as c? r is positive or negative ; that is, according as
r is increasing or diminishing, so as to make the element under each integral sign
constantly positive. In general, it appears to be a useful rule, though not always
followed by analysts, to employ the real radical symbol ^R only for positive quan-

T

titles, unless the negative sign be expressly prefixed ; and then -j= will denote posi-
tive or negative unity, according as r is positive or negative. The arc given by its
sine, in the expression of the element a, is supposed to be so chosen as to increase
continually with the time.

35. After these remarks on the notation, let us apply the formula (P^.) to calculate
the values of the 15 combinations such as {», ?i},of the 6 constants or elements (Q^.)-

Since

r= v(i2 + ^2 + ^2), (187.)

it is easy to perceive that the six combinations of the 4 first elements are as follows :
{k,\} = 0, {k,il} = 0, {k,v} =0, {\l^} = ^, {X,v} = l, {;a.,^} = 0. . (188.)
To form the 4 combinations of these 4 first elements with r, we may observe, that
this 5th element r, as expressed in (Q^.), involves explicitly (besides the time) the
distance r, and the two elements x, (Jj ; but the combinations already determined
show that these two elements may be treated as constant in forming the four combi-
nations now sought ; we need only attend, therefore, to the variation of r, and if we
interpret by the rule (P^.) the symbols {», r} {X,r} {[Jij,r} {v,r}, and attend to the
equations (P.), we see that

dT

{;s,r} = 0, {X,r} = 0, {|U.,r} = -^^, {v,r} = 0, (189.)

dv

-^^ being the total differential coefficient of r in the undisturbed motion, as determined

by the equations (I^.) ; and, therefore, that

{«,r} = 0, {X,r}=0, {»',r}=:0, (190.)

and

r 1 ^T dr dtdr rim \

i(^>''} = -fT-d-t= + Trrt = ^'' (1^1-),

observing that in differentiating the expressions of the elements (Q^.), we may treat
those elements as constant, if we change the differentials of | ;j ^ a?' 3/' z' to their undis-
turbed values. It remains to calculate the 5 combinations of these 5 elements with
the last element a ; which is given by (Q^.) as a function of the distance r, the coor-
dinate ^, and the 4 elements «, \{J(*, v; so that we may employ this formula,

{^.«}=TFK^} + |f{^,0 + |^{e,«}+|^{e,X}+|^Kit.}+|^{e,.}, (192.)

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS. 137

in which, if e be any of the first five elements, or the distance r,

{e,^} = --7Vlg^ + ^8y +?87;,{e,?} = ~ jy,{e,;c}=0, . (193.)

and

-1

8 CO /^\ li!i <?? Sctt Sett

T? °" W/ ' 8r~""^T?^ "87—^' 094.)

the formula (192.) may therefore be thus written:

0 CO 8 ctf I

+ K''} +-8x^^^^>+8]:^^^^>- J

We easily find, by this formula, that

{;.,.,} = - 1; {X,«}=0; {fi,^} = 0; {r,^}=-^|^; . . . (196.)
and

8 V 8ctt 8a)
{".«> = -8i'r?-"8l. = ^ (197.)

The formula (195.) extends to the combination {r, u) also; but in calculating this
last combination we are to remember that r is given by (Q^.) as a function of », jm», r,
such that

87 = -^r' — • • 098.)

and thus we see, with the help of the combinations (196.) already determined, that

8t 8ett 8 /»»• 8 /»»•
{r.-) = -r.-l^ = r.J,®rdr + ^^J^€l^dr, (199.)

if we represent for abridgement by 0^ and CL^ the coefficients of ^ r under the integral
signs in (Q^.), namely,

M + m x^ ■) -* 1

^ / M dr C . ^,, ^,, M + m xn-4 ]

^ X / M. + m dr C y ^y,„ p, k M + w x« •)
"' = F\/Tr-7dl3{V + 2M/(r) M-'FJ

These coefficients are evidently connected by the relation

8e 8/2

^ + Tir = 0' (201.)

which gives

■hX®rdr-\-~:Xn,dr = i>, (202.)

r, being any quantity which does not vary with the elements » and ^ ; we might
therefore at once conclude by (199.) that the combination {r, »} vanishes, if a diffi

MDCCCXXXV. T

138 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

culty were not occasioned by the necessity of varying the lower limit q, which de-
pends on those two elements, and by the circumstance that at this lower limit the
coefficients 0^ Cl^ become infinite. However, the relation (202.) shows that we may
express this combination {r, u} as follows :

{'">''} =J^fJ' ^rdr + ^fj' n^dr, (203.)

r, being an auxiliary and arbitrary quantity, which cannot really affect the result,
but may be made to facilitate the calculation ; or in other words, we may assign to
the distance r any arbitrary value, not varying for infinitesimal variations of », (^,
which may assist in calculating the value of the expression (199.). We may there-
fore suppose that the increase of distance r — ^ is small, and corresponds to a small
positive interval of time t — r, during which the distance r and its differential coeffi-
cient r' are constantly increasing; and then after the first moment r, the quantity

e. = ^ (204.)

will be constantly finite, positive, and decreasing, during the same interval, so that
its integral must be greater than if it had constantly its final value ; that is,

t^r=^JJ ©^dr>(r-q)(d, (205.)

Hence, although 0^ tends to infinity, yet (r — q) 0^ tends to zero, when by dimi-
nishing the interval we make r tend to q ; and therefore the following difference

J, ^rdr--^^jj^ e,dr = -y^J^ [^-j,)Q,dr, . . (206.)

will also tend to 0, and so will also its partial differential coefficient of the first order,
taken with respect to /a. We find therefore the following formula for {r, u}, (re-
membering that this combination has been shown to be independent of r,)

{r,«}=,^j|j-^7^ e,rfr + -^y5^7; e,rfrj; . . . (207.)

the sign ^ _ ^ implying that the limit is to be taken to which the expression tends
when r tends to q. In this last formula, as in (199.), the integral / Q^ dr may be

considered as a known function of r, q, x, ^, or simply of r, q, z, if |U/ be eliminated
by the first condition (186.) ; and since it vanishes independently of « when r = ^, it
may be thus denoted :

J^ &rdr = (p{r,q,K) - <p{q,q,K), (208.)

the form of the function p depending on the law of attraction or repulsion. This
integral therefore, when considered as depending on » and jM/, by depending on k
and y, need not be varied with respect to «, in calculating {r, u\ by (207.), because

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

139

its partial differential coefficient \f^J S^^r), obtained by treating q as constant,
vanishes at the limit r = 9- ; nor need it be varied with respect to q, because, by (186.),

r. + srfi = ^-- • • ■ (209-)

it may therefore be treated as constant, and we find at last

{r,c,}=0, (210.)

the two terms (199.) or (203.) both tending to infinity when r tends to q, but always
destroying each other.

36. Collecting now our results, and presenting for greater clearness each combi-
nation under the two forms in which it occurs when the order of the elements is
changed, we have, for each binary system, the following thirty expressions :
{K,K} = 0, {k,(ju} = 0, {K,u} = 0, {»,r} = 0, {»,*;} = - 1, ^
{X, «} = 0, {X, fA} = 0, {X, V} = 1, {X, r} = 0, {X, cj} =z 0,
(it*, k} = 0, {[Jt,, X} = 0, {fju, v} = 0, {^, r} = 1, {|M., 6f} = 0,
{v, k} = 0, {v, X} = - 1, {V, (I.} = 0, {u, r} = 0, {V, CO} = 0,
{t,k} = 0, {r,X} = 0, {T,(^} = - 1, {r,v} = 0, {r,<w} = 0,
{«, x} = 1, {ft;, X} = 0, {a;, /a} = 0, {*;, *'} = 0, {a;, r} = 0 ;
so that the three combinations

{/*,r} {&>,x} {X,v}
are each equal to positive unity ; the three inverse combinations

{r,^} {»,&>} {v,X}
are each equal to negative unity ; and all the others vanish. The six differential
equations of the first order, for the 6 varying elements of any one binary system
{m, M), are therefore, by (O^.),

(R2.)

m

m

d fA 8 Hg

dr

dt

S. 5 '1'' J i.

It ' dt

dta

dt

8H2 d)c

=" ^x' "^ dt

dK

8H, dv

8H, 1
8 Ho

dt

8(0
8H«

>

(S2.)

£/^ ~ 8a '

and, if we still omit the variation of /, they may all be summed up in this form for
the variation of Hg,

lU2=^.m([J^'^T-T'^(j^'}-aj'^»-»'^c^-{-X'^V'-v'hK), . . (T2.)

which single formula enables us to derive all the 6 t? — 6 differential equations of the
first order, for all the varying elements of all the binary systems, from the variation
or from the partial differential coefficients of a single quantity Hg, expressed as a
function of those elements.

t2

140 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

If we choose to introduce into the expression (T2.), for $ Hg, the variation of the
time t, we have only to change Ir to Ir — lt, because, by (Q^.), 1 1 enters only so
accompanied ; that is, t enters only under the form t — r^, in the expressions of
l- J}. ^. ^. 7/'. z'. as functions of the time and of the elements ; we have, therefore,

?^=_2!^'=-2.mp'; (211.)

and since, by (H^.), (Q^.),

Hi = 2.mp, (212.)

we find finally,

dt —"^ dt ^^^ '^

This remarkable form for the differential of H^, considered as a varying element,
is general for all problems of dynamics. It may be deduced by the general method
from the formulae of the 13th and 14th numbers, which give

dt 5x, \ dri Sty 8«r 8)} / "^ " * ~^ Sxg^ V Sij Sot Sot Sij / I

r (213.)

Sxi S^ "*" Sxg 8^ "• * * * "*" Sxgn S^ S^ ' J

«i »2 • • *6 » heing any 6 n elements of a system expressed as functions of the time and
of the quantities ;? tsr ; or more concisely by this special consideration, that Hj + Hg is
constant in the disturbed motion, and that in taking the first total differential coeffi-
cient of Hg with respect to the time, the elements may by (F^) be treated as constant.
It is also a remarkable corollary of the general principles just referred to, but one not

Sx
difficult to verify, that the first partial differential coefficient ~ of any element «„

taken with respect to the time, may be expressed as a function of the elements alone,
not involving the time explicitly.

On the essential distinction between the Si/stems of Varying Eleynents considered in this
Essay and those hitherto employed hy mathematicians.

37. When we shall have integrated the differential equations of varying elements
(S2.), we can then calculate the varying relative coordinates i p? ^, for any binary sy-
stem (m, M), by the rules of undisturbed motion, as expressed by the equations (P.),
(Q2.), or by the following connected formulae :

I = r (cos ^ 4- ~ sin (^ — v) sin v\
r}=:r (sin ^ — — sin (^ ~ v) cos i'),
? = ^ V2X» — X2 sin (^ - f) :

(V2.)

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS. 141

in which the distance r is determined as a function of the time t and of the elements
T, », ^, by the 5th equation (Q^.)^ J^^d in which

dr X .
-irdr

y/\2{^ + 2 M/(r) - -^^ .^}

q being still the minimum of r, when the orbit is treated as constant, and being still
connected with the elements z, ^m,, by the first equation of condition (186.). In astro-
nomical language, M is the sun, m a planet, | ?? ^ are the heliocentric rectangular co-
ordinates, r is the radius vector, & the longitude in the orbit, u the longitude of the
perihelion, v of the node, & ^ u is the true anomaly, ^ — v the argument of latitude,
yij the constant part of the half square of undisturbed heliocentric velocity, diminished
in the ratio of the sun's mass (M) to the sum (M -|- m) of masses of sun and planet,

X is the double of the areal velocity diminished in the same ratio, — is the versed sine

of the inclination of the orbit, q the perihelion distance, and r the time of perihelion
passage. The law of attraction or repulsion is here left undetermined ; for Newton's
law, /!/» is the sun's mass divided by the axis major of the orbit taken negatively, and
X, is the square root of the semiparameter, multiplied by the sun's mass, and divided
by the square root of the sum of the masses of sun and planet. But the varying
ellipse or other orbit, which the foregoing formulae require, differs essentially (though
little) from that hitherto employed by astronomers : because it gives correctly the
heliocentric coordinates, but not the heliocentric components of velocity, without dif-
ferentiating the elements in the calculation ; and therefore does not touch, but cuts,
(though under a very small angle,) the actual heliocentric orbit, described under the
influence of all the disturbing forces.

38. For it results from the foregoing theory, that if we differentiate the expressions
(V^.) for the heliocentric coordinates, without differentiating the elements, and then
assign to those new varying elements their values as functions of the time, obtained
from the equations (S^.), and deduce the centrobaric components of velocity by the
formulae (P.), or by the following:

then these centrobaric components will be the same functions of the time and of the
new varying elements which might be otherwise deduced by elimination from the in-
tegrals (Q^.), and will represent rigorously (by the extension given in the theory to
those last-mentioned integrals) the components of velocity of the disturbed planet w,
relatively to the centre of gravity of the whole solar system. We chose, as more
suitable to the general course of our method, that these centrobaric components of
velocity should be the auxiliary variables to be combined with the heliocentric co-
ordinates, and to have their disturbed values rigorously expressed by the formulae

142 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

of undisturbed motion ; but in making this choice it became necessary to modify
these latter formulae, and to determine a varying orbit essentially distinct in theory
(though little differing in practice) from that conceived so beautifully by Lagrange.
The orbit which he imagined was more simply connected with the heliocentric mo-
tion of a single planet, since it gave, for such heliocentric motion, the velocity as well
as the position ; the orbit which we have chosen is perhaps more closely combined
with the conception of a multiple system, moving about its common centre of gravity,
and influenced in every part by the actions of all the rest. Whichever orbit shall be
hereafter adopted by astronomers, they will remember that both are equally fit to
represent the celestial appearances, if the numeric elements of either set be suitably
determined by observation, and the elements of the other set of orbits be deduced
from these by calculation. Meantime mathematicians will judge, whether in sacri-
ficing a part of the simplicity of that geometrical conception on which the theories of
Lagrange and Poisson are founded, a simplicity of another kind has not been intro-
duced, which was wanting in those admirable theories ; by our having succeeded in
expressing rigorously the differentials of all our own new varying elements through
the coefficients of a single function : whereas it has seemed necessary hitherto to em-
ploy one function for the Earth disturbed by Venus, and another function for Venus
disturbed by the Earth.

Integration of the Simplified Equations, which determine the new varying Elements.

39. The simplified differential equations of varying elements, (S^.), are of the same
form as the equations (A.), and may be integrated in a similar manner. If we put,
for abridgement,

and interpret similarly the symbols (^, u, X), &c., we can easily assign the variations
of the following 8 combinations, (r, x, v) {^, u, X) {^, k, v) (r, u, X) (r, u, v) (jm., k, X)
(r, », X) (^, a, v) ; namely,

^ (r, «, v) = 2 . w (r S jU; — Tq S |!^Q -|- » 5 <w — «o ^ *'o "f" " ^ ^ ""■ ''o ^ ^) — ^2 ^ ^5
S (jU;,ft;,X) = 2 . m (jU^o ^''o — \h\r •\- ca^^it^ — u\k -\-\^v^ — \hv) — Hg S t,

^ (r, fi;,X) = 2 . w (r ^ |M» — Tq ^ jO/Q -j- ft/Q ^ *o ~" ^ ^ * + ^0 ^ "o ~ ^ ^ ") "~ Hg S ^, I ,^2 \

^ (r, a>, v) = 2 . wi (r S jU; — Tq § ^O/Q -f- ft>o ^ *o "~ ** ^ ^ ~l" ** ^ ^ "" "o ^ ^o) ""■ ^2 ^ ^3
^ (fjtj,K,X) =2 .m(^Q^rQ — (jijIt -\- x^&f — Xq^ ofQ -{• Xq'6 Vq — Xlv) — Hg^^,

^ (r,«,X) =: 2 . m (tI fjb — Tq^ (jbQ -^^ x^ ej — Xq^ Uq -{■ Xq'6 Vq — X S f) — Hg ^ #,

I {[^,6f, V) = 2 . m{(Jl,QlTQ-^ (Jt.'^T -^ UqIxq— Cj'^X -\- »^X — VqIXq) — H.^^t,

*o ^0 (^0 "o ''o ^0 being the initial values of the varying elements x X (ji, u r co. If, then,
we consider, for example, the first of these 8 combinations (r, x, v), as a function of

PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

143

all the 3 ?z — 3 elements jM/^ co^ X^, and of their initial values (juq^ ^q t \) i> involving also
in general the time explicitly, we shall have the following forms for the 6 n — 6
rigorous integrals of the 6 n-^ 6 equations (S^.) :

^i''i= dj. (^'*'*'); ^t''o,t

^i'^i = Y^,(r''^>'')'^ ^t«o.t =

_8_

-§-;r-(''^«''');

0,1

'^i^i — fx. ^''^ *' ^^ 5 wz,. Vo^j = - g— (r, », J') ;

i 0,t

(Z'.)

and in like manner we can deduce forms for the same rigorous integrals, from any
one of the eight combinations (Y^.). The determination* of all the varying elements
would therefore be fully accomplished, if we could find the complete expression for
any one of these 8 combinations.

40. A first approximate expression for any one of them can be found from the form
under which we have supposed Hg to be put, namely, as a function of the elements
and of the time, which may be thus denoted :

Hg — H2 {t, ;Ci, Xi, ^1, Vj, Tj, <yi, . . . «„_!, X„_i, ^„_i, Vn-\, '^n-li '"n-l)

(A3.)

by changing in this function the varying elements to their initial values, and em-
ploying the following approximate integrals of the equations (S^.),

(B3.)

For if we denote, for example, the first of the 8 combinations (Y^.) by G, so that

G = {r, ;., .}, (C3.)

we shall have, as a first approximate value,

and after thus expressing Gi as a function of the time, and of the initial elements, we
can eliminate the initial quantities of the forms Tq xq vq, and introduce in their stead
the final quantities [ju cj X, so as to obtain an expression for Gj of the kind supposed
in (Z2.), namely, a function of the time t, the varying elements (/juX, and their initial
values (JbQ uq Xq. An approximate expression thus found may be corrected by a pro-
cess of that kind, which has often been employed in this Essay for other similar pur-
poses. For the function G, or the combination (r, «, v), must satisfy rigorously, by
(Y2.) (A^.), the following partial differential equation :

144 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS.

^ ^G , „ / 1 SG , 1 8G 1 8G 1 8G \ ,_,, .

and each of the other analogous functions or combinations (Y^.) must satisfy an
analogous equation : if then we change G to Gj + Gg, and neglect the squares and
products of the coefficients of the small correction Gg, Gj being a first approximation
such as that already found, we are conducted, as a second approximation, on prin-
ciples already explained, to the following expression for this correction Gg :

which may be continually and indefinitely improved by a repetition of the same pro-
cess of correction. We may therefore, theoretically, consider the problem as solved ;
but it must remain for future consideration, and perhaps for actual trial, to determine
which of all these various processes of successive and indefinite approximation, de-
duced in the present Essay and in the former, as corollaries of one general Method,
and as consequences of one central Idea, is best adapted for numeric application, and
for the mathematical study of phenomena.

[ 145 ]

VIII. Continuation of a former Paper on the Twenty-five Feet Zenith Telescope lately
erected at the Royal Observatory. By John Pond, Esq. A.R. F.R.S.

Received March 11,— Read March 12, 1835.

During the last summer I had the honour of submitting to this Society a short
paper on the subject of the large zenith telescope lately erected at this Observatory.

It is now nearly twenty years since the erection of such an instrument was first
suggested to the President and Council of this Society ; at that time the Royal Ob-
servatory was in a very inefficient state compared to what it is at present. We had
only one circle ; and there existed doubts as to the excellence of this instrument,
though not any were ever entertained by me. The erection of a second circle put this
question at rest ; it has been abundantly shown in various volumes Of the Greenwich
Observations, by a series of more rigorous investigations than any instrument was
ever submitted to before, that both the circles may be considered as perfect, their
errors being less than their respective makers themselves assigned.

This circumstance, though satisfactory to myself, a little diminished the importance
of the new zenith telescope. It was hardly to be expected that any new instrument
could throw light upon errors already reduced within such small limits ; this, how-
ever, has been done, and the object of this paper is to explain the process I have em-
ployed for the purpose.

Whoever is acquainted with the method of constructing the Greenwich Catalogue,
must have perceived that the places of those stars which are observed by reflection
are, according to all probability, more exactly determined than those which have
been observed only by direct vision, y Draconis, a star which since the time of
Bradley has been of first-rate importance in the Greenwich Observations, cannot
be observed by reflection. The probability of error was therefore greater in the
place of this star than in that of any other. The new instrument has shown that this
error does not exceed a quarter of a second ; a degree of accuracy scarcely credible,
and no doubt requiring to be confirmed by future observations.

The nature of the question to be determined in this case has happily produced a
competition for excellence among the observers with the different instruments, which
gives me an opportunity of showing the present state of practical astronomy at
Greenwich.

The new instrument has been employed during the last summer under very un-
favourable circumstances, both the building and the instrument having been almost
constantly under repair. It is not requisite on this occasion to enter into the details

MDCCCXXXV. u

146 MR. POND ON THE NEW ZENITH TELESCOPE

of these difficulties ; I only wish to explain the nature of the experiments, the results
of which I am no^v about to lay before the Society.

We have now three distinct methods of determining the place of any star passing
the meridian near the zenith. First, by means of the mural circles ; secondly, by
the zenith telescope used alternately east and west, as is usually done with similar
instruments ; and lastly, by means of a small subsidiary star, as described by me
last year in a paper laid before this Society, and which I am inclined to think more
exact than any other method. By the following computations it will be seen that
the three methods give results nearly identical; and that when the observations with
the two circles are numerous and made with sufficient care, a quarter of a second
is the greatest error to be apprehended.

Royal Observatory, March 10, 1835.

Results of Obset^vations on y Draconis and Bode 170 Draconis.
Zenith distance of y Draconis determined by three different methods.

Zenith distance,
First, — Result by 324 observations with the Mural Circles reduced toi ^^^^'

the latitude of the Zenith Telescope room, the difference between |> 2 1-36 North.

which and the Circle room being 0"*65 North J

By Zenith Telescope employed in the unsual manner by alternate ob- "^

}

aper of
last year, and which result I prefer to either of the others .

serrations East and West ; 28 results

}

By means of the subsidiary angle as described in my former paper of'.

Zenith distance of Bode 170 Draconis determined by three different methods.

Zenith distance,
First,— Result by 132 observations with the Mural Circles reduced toT '^•^^•

the latitude of the Zenith Telescope room, the difference between \ 1 0-45 South:

which and the Circle room heing 0"-65 North J

By Zenith Telescope employed in the usual manner by alternate ob- 1

servations East and West ; 14 results J

By means of the subsidiary angle as described in my former paper of 1

last year, and which result I prefer to either of the others J

1 0-61

1 0-74

LATELY ERECTED AT THE ROYAL OBSERVATORY.
Table I.

147

Containing 60 successive observations of the small auxiliary star, Bode 170Draconis

divided into series of 10 each.

1833.

Bode 170 Draconis, by Joni

ss's circle.

1834,

Bode 170 Draconis, by Jones's Circle. 1

N. P. D.

DifF. of each
Obs. from

DifF. between
the Mean of 10

N. P. D.

Diff. of each

Diff. between
the Mean of 10

Jan. 1, 1834.

Mean of 60.

and the Mean
of 60.

Jan. 1, 1834.

Mean of 60.

and the Mean
of 60.

July 22.

3°8 32 20-68

0-40

July 8.

3°8 32 21-40

0-32

23.

21-62

0-54

9.

21-00

0-08

25.

20-83

0-25

. 10.

20-68

0-40

26.

21-70

0-62

11.

21-08

0-00

27.

21-25

0-17

12.

21-39

0-31

29.

21-87

0-79

14.

20-99

0-09

31.

21-73

0-65

15.

20-48

0-60

Aug. 1.

21-79

0-71

16.

20-97

0-11

3.

22-17

1-09

17.

20-77

0-31

4.

21-81

0-73

21.

20-39

0-69

Mean of 1 0 obs.

38 32 21-55

0-47

Mean of 10 obs.

38 32 20-92

0-16

6.

21-70

0-62

22.

21-07

0-01

9.

21-57

0-49

24.

21-84

0-76

11.

21-09

0-01

25.

20-11

0-97

13.

20-91

0-17

30.

20-92

0-16

14.

20-50

0-58

Aug. 1.

20-42

0-66

16.

20-65

0-43

2.

21-68

0-60

23.

20-79

0-29

6.

21-24

0-16

25.

21-20

0-12

11.

21-02

0-06

26.

20-85

0-23

12.

20-14

0-94

27.

20-43

0-65

16.

20-86

0-22

Mean of 10 obs.

38 32 20-97

0-11

Mean of 10 obs.

38 32 20-93

0-15

28.

21-07

0-01

19.

20-63

0-45

Sept. 1.

20-82

0-26

22.

21-57

0-49

3.

20-86

0-22

23.

21-36

0-28

4.

20-86

0-22

25.

20-76

0-32

5.

21-13

0-05

27.

21-18

0-10

6.

21-36

0-28

Sept. 4.

20-89

0-19

12.

21-31

0-23

5.

21-19

0-11

18.

21-07

0-01

12.

21-21

0-13

20.

20-95

0-13

13.

21-38

0-30

23.

20-92

0-16

15.

20-58

0-50

Mean of 10 obs.

38 32 21-04

0-04

Mean of 10 obs.

38 32 21-08

0-00

M

ean of 60 obs.

38 32 21-08

0-357

0-155

From this it appears that the mean error of 10 observations = 0"'155, and that the mean error of 30 obser-
vations, as deduced from the next page, = 0"-067.

The zenith distance from this result =1 0-078 South. (Assumed co-latitude = 38° 31' 21"*.)

Difference of latitude for zenith telescope r= +0'65

Zenith distance for the latitude of zenith"! __ ^ 0*7 28
telescope J

By zenith telescope by means of the sub-"l _ ^ ^.^^ ^j^j^j^ ^^ quantities are identical,
sidiary angle from the preceding page . . J

* The accuracy of this quantity is of no importance, as the circles, according to our present mode of employ-
ing them, give, in fact, zenith distances, which are afterwards converted into polar distances by the application
of the above co-latitude, and as such are registered in the Greenwich Catalogues.

u2

148

MR. POND ON THE NEW ZENITH TELESCOPE

Table II.
The same observations of Bode 170 Draconis arranged alternately in two columns of

30 observations each.

N. P. D.
Jan. 1, 1834.

N. P. D.
Jan. 1, 1834.

1833. July 22.

38 32 20-68

1833. July 23.

38 32 21-62

25.

20-83

26.

21-70

27.

21-25

29.

21-87

31.

21-73

Aug. 1.

21-79

Aug. 3.

22-17

4.

21-81

6.

21-70

9.

21-57

11.

21-09

13.

20-91

14.

20-50

16.

20-65

23.

20-79

25.

21-20

26.

20-85

27.

20-43

Meanof lOobs.

38 32 21-159

Meanof 10 obs.

38 32 21-355

Aug. 28.

38 32 21-07

Sept. 1.

38 32 20-82

Sept. 3.

20-86 .

4.

20-86

5.

21-13

6.

21-36

12.

21-31

18.

21-07

20.

20-95

23.

20-92

1834. July 8.

21-40

1834. July 9.

21-00

10.

20-68

11.

21-08

12.

21-39

14.

20-99

15.

20-48

16.

20-97

17.

20-77

21.

20-39

Meanof 10 obs.

38 32 21-004

Meanof 10 obs.

38 32 20-946

July 22.

38 32 21-07

July 24.

38 32 21-84

25.

20-11

30.

20-92

Aug. 1.

20-42

Aug. 2.

21-68

6.

21-24

11.

21-02

12.

20-14

16.

20-86

19.

20-63

22.

21-57

23.

21-36

25.

20-76

27.

21-18

Sept. 4.

20-89

Sept. 6.

21-19

12.

21-21

13.

22-38

15.

20-58

Meanof 10 obs.

38 32 20-872

Meanof 10 obs.

38 32 21-133

Mean of 30 =

= 38 32 21-012

Mean of 30 =

= 38 32 21-145

Mean of 60 =

38° 32' 21"-08.

LATELY ERECTED AT THE ROYAL OBSERVATORY.

149

Table III.

Difference of North Polar Distance of y Draconis

Difference of North Polar Distance of y Draconis 1

and Bode 170 Draconis

1833.

and Bode 170 Draconis, 1834.

Observed Difference.

Differ.

Difference,

Observed Difference.

Differ-

Difference,

1833.

ence of
Equa-

January

J, 18.<}3.

1834.

ence of
liqua-

January 1, 1834.

Tboughton. Jones.

tions.

Trol'ghton.

Jones.

Troughton.

Jones.

tions.

Troughton.

Jones.

/ //

/ //

II

/ //

/ //

/ //

' " „

II

/ //

July 5.

3 6-2

3 5-4

— 1-36

3 4-84

3 4-04

July 8.

3 1-4

3 3-6

-1-31

3 0-09

3 2-29

6.

5-3

6-7

— 1-35

3-95

5-35

9.

3-6

4-2

-1-30

2-30

2-90

9.

6-0

4-9

-1-31

4-69

3-59

10.

3-5

3-3

-1-28

2-22

2-02

15.

5-5

5-5

-1-18

4-32

4-32

11.

3-7

3-0

-1-27

2-43

1-76

16.

5-9

5-7

-M5

4-75

4-55

12.

3-1

3-0

-1-24

1-86

1-76

22.

4-8

5-3

— 1-04

3-76

4-26

14.

2-7

2-4

-1-21

1-49

1-19

23.

4-5

5-9

-1-01

3-49

4-89

15.

3-3

3-0

-1-20

2-10

1-80

25.

5-1

5-4

-0-98

4-12

4-42

16.

1-9

3-8

-1-19

0-71

2-61

26.

6-0

5-6

-0-95

5-05

4-65

17.

3-8

2-4

-1-17

2-63

1-23

27.

5-7

5-6

-0-94

4-76

4-66

21.

2-7

2-1

-1-08

1-62

1-02

29.

4-9

5-9

-0-89

4-01

5-01

22.

4-3

3-0

-1-04

3-26

1-96

31.

4-6

4-0

-0-84

3-76

3-16

24.

3-3

3-6

-1-01

2-29

2-59

August 1.

3-8

4-7

-0-81

2-99

3-89

25.

3-2

2-6

-0-98

2-22

1-62

3.

4-8

4-9

-0-77

4-03

4-13

30.

3-2

3-1

-0-86

2-34

2-24

4.

6-0

5-2

-0-74

5-26

4-46

August 2.

2-3

3-4

— 0-84

1-46

1-96

6.

4-8

4-0

-0-69

4-11

3-31

6.

2-3

1-8

-0-71

1-59

0-21

9.

5-1

4-8

-0-61

4-49

4-19

11.

3-6

2-6

-0-55

3-05

2-05

11.

2-9

4-7

-0-56

2-34

4-14

12.

2-4

1-3

-0-52

1-88

0-78

13.

3-6

5-4

-0-50

3-10

4-90

16.

2-5

1-0

-0-43

2-07

0-57

14.

4-1

4-6

-0-47

3-63

4-13

19.

3-1

1-6

-0-32

2-78

1-28

16.

3-0

4-3

-0-42

2-58

3-88

22.

2-0

2-3

-0-24

1-76

2-06

2?.

3-7

4-6

-0-19

3-51

4-41

23.

2-0

3-0

-0-21

1-79

2-79

25.

3-6

3-9

-0-13

3-47

3-77

25.

1-4

2-0

-0-15

1-25

1-86

26.

3-9

4-2

-0-09

3-81

4-11

27.

2-3

2-1

-0-08

2-22

2-02

27.

4-5

4-4

-0-06

4-44

4-34

Sept. 5.

1-0

1-9

+ 0-24

1-24

2-14

28.

4-7

4-7

-0-04

4-66

4-66

12.

1-4

1-7

+ 0-45

1-85

2-15

Sept. 1.

3-0

3-6

+ 0-10

3-10

3-70

13.

1-1

2-7

4-0-49

1-59

3-19

3.

1-6

3-7

+ 0-16

1-76

3-86

15.

1-3

0-4

+ 0-57

1-87

1-97

4.

3-6

3-9

+ 0-19

3-79

4-09

16.

0-8

1-2

+ 0-60

1-40

1-80

5.

2-8

3-7

+ 0-23

3-03

3-93

6.

3-5

4-3

+ 0-26

3-76

4-56

12.

2-7

3-9

+ 0-43

3-13

4-33

18.

2-8

3-0

+ 0-67

3-47

3-67

20.

2-6

3-7

+ 0-75

3-35

4-45

23.

3-1

3-3

+ 0-86

3-96

4-16

Mean of 35 obs. =

3 3-807

3 4-228

Mear

of 29 obs. =

3 1-901

3 1-854

Mean of 70 c

)bs ^

3' 4"-0]

8

Mea

n of 58 ot

s

= 3' l"-877

Mean of 70 obs. (= 35 x 2) v

i^ith both c

circles for

the epoch

Jan. 1, IJ

333, as above = 3 401 8

Sum of Annual Variations of I
Difference of North Polar Dist

>oth stars
ance reduc

= — 2-240

ed to Jar

1.1,1834,

by 70 obs

. in 1833 . . =

= 3 1-778

Mean of 58 obs. (=29 X 2) f<

Mpar> r\f fr>fol 1 9« nha .Tfin 1

yc Jan. 1,
1834 . . .

1834, by

58 obs. in

1834 .. .

= 3 1-877

= 3 1-823

iviccti

1

150

MR. POND ON THE NEW ZENITH TELESCOPE

Table IV.
Fundamental determinations of the Zenith Distances of y Draconis.

Epochs.

State of
lunar
nuta-
tion.

Observed
zenith dist.
reduced
to tlie be-
ginning of
each year.

Side

of

zen.

Zenith distance deduced from M. Bessel's
Formula (Tabula REGioMONTANiE, p. 46.).

Difference
of formula

and ob-
served zen.
dist.

Epochs.
1800.

1st term. 2nd term.

Resulting
Z. D.

1753.
1768.
1802.
1813.
1833.

-6-87
4- 3-83
+ 9-52
-7-64
—4-30

/ //
3 2-05

2 SO-30

2 25-30

2 17-40

2 2-47

N.

2 <ili-^^^
2 26-669
2 26-669
2 26-669
2 26-669

+ 33-555
+ 22-899

- 1-428

- 9-281

- 23-560

+ 2-233
+ 1-035
+ 0-004
+ 0-171
+ 1-101

/ //
3 2-457

2 50-603

2 25-245

2 17-559

2 4-210

+ 0-407
+ 0-303
— 0-055
+ 0-159
+ 1-740

By Bradley with Zen. Sector.
Maskelyke Ditto.
Ditto. Ditto.
Pond Ditto.
Ditto New Zen. Telescope.

The above results (column 3rd) are those that have been obtained with the greatest
care during their respective periods ; and having been deduced from observations with
the zenith sector, they are quite independent of the latitude of the Observatory.

M. Bessel's formula is deduced from the observations for the first sixty years,
and therefore agree very well ; but when we attempt to predict from the observations
of these sixty years the place of the stars for twenty years to come, we find a differ-
ence of l"-74 between the predicted and observed zenith distance, the observed place
being this quantity south of it.

Explanation of the foregoing Tables.

Table I. contains the results of 60 observations of the small star Bode 170 Draco-
nis, made with Jones's circle, and is intended to show what degree of accuracy may
be obtained by extreme care. The mean difference 0"-357, column 3, between the
mean of the whole and each result, (and which is nearly the probable error of a
single observation from this series,) demonstrates with what care they have been
made. The same may be said with respect to the mean difference of column 4,
namely, 0""155, which is similarly obtained from the mean of the whole and the
mean of each ten (a quantity which represents nearly the probable error of the mean
of ten observations). However, it may be remarked, that the exact coincidence ex-
hibited throughout this series does not prove the truth of the final north polar
distance of the star here assigned, since some omissions or errors in the process of
reduction would affect it. That no instrumental error exists is demonstrated by the
identity of the result with that obtained with the new instrument.

Table II. contains the same observations arranged in a different manner.

This is the arrangement I have advantageously followed in investigating the differ-
ence of parallax ; the object being to distinguish the effect arising from accidental
error of observation from that which is due to any permanent astronomical cause.

LATELY ERECTED AT THE ROYAL OBSERVATORY. 151

This method should be employed when the object is to judge of the consistency of
observations, without any reference to the astronomical result.

Table III. shows the manner in which the difference in zenith distance between
the two stars is obtained by means of the circles ; a quantity, as I have shown, of
the highest importance in the investigation.

This quantity, having been determined by the microscopes of the respective circles,
might be erroneous if the runs of the microscopes were not exact, although the error
here must be very small, twelve microscopes being constantly used. But as they
have lately been taken down, examined, and replaced, without any sensible alteration,
it may be presumed that the error from this source is sufficiently corrected.

Table IV. This Table contains in a very compressed form the result of an immense
number of observations of y Draconis during a period of eighty years ; and it will be
seen that if from M. Bessel's formula*, deduced from the first sixty years of these
observations, we attempt to predict or assign the place of the star for the present
time or twenty years in advance, the star will be found 1"75 south of its computed
place.

* By this formula the zenith distance of the star north for 1800, + t = 2' 26"-669 - t . 0"-71394 + t"- .
0"-001011. Where t is the number of years before or after 1800, if before, the sign of t is minus.

[ 153 ]

IX. Some account of the Eruption of Fesuvius, which occurred in the month of August
1834, extracted from the Manuscript Notes of the Cavaliere Monticelli, Foreign
Member of the Geological Society, and from other sources; together with a State-
ment of the Products of the Eruption, and of the condition of the Volcano sub-
sequently to it. By Charles Daubeny, M.D. F.R.S. F.G.S. ^c, Professor of
Chemistry and Botany in the University of Oxford.

Received February 25, — Read March 19, 1835.

A HE eruption of Vesuvius which occurred in the month of August of last year,
excited on the spot an unusual share of interest, from the largeness of the volume
of lava at the time discharged, and the extent of the damage it occasioned in its
progress down the mountain ; whilst in a scientific point of view it attracted the
greater attention, since it was regarded by many as the concluding link in a series of
volcanic operations, which had been going on up to that period with only occasional
intermissions from the year 1831.

It was therefore natural, that on my arrival at Naples shortly after the mountain
had subsided into a state of comparative repose, I should seize upon the opportunity
which appeared to offer of increasing my acquaintance with volcanic phenomena;
first, by collecting on the spot such information as could be best relied on, with
respect to the leading features of the past eruption ; and secondly, by ascertaining
from personal examination the actual condition of the volcano, and the products re-
sulting either from its late operations, or from those in actual progress.

With a view to the former object, I solicited and obtained from the Cavahere
MoNTiCELLi (one of the Foreign Members of the Geological Society) a written account
of the eruption, from which he has permitted me to extract such particulars as I might
deem likely to interest the Members of the Royal Society ; whilst in the hope of ac-
complishing the latter object, a considerable portion of the time I spent at Naples
was taken up in visiting the several parts of Vesuvius, and in collecting the solid as
well as aeriform substances, ejected from its crater, and from the recently erupted
lava.

In the former part, therefore, of the present communication, I can claim no further
share, than as the compiler of facts observed and reported to me by others ; and all
that I conceive myself personally responsible for is the latter portion, in which I
have stated the several products and actual condition of the volcano at the time I
visited it.

MDCCCXXXV. X

154 DR. DAUBENY ON THE ERUPTION OF VESUVIUS.

It would appear that for a considerable time previous to the eruption in question,
the crater of the volcano had continued to throw up stones and scoriae, which falling
down for the most part almost perpendicularly round the point of their emission, had
by degrees accumulated into two conical masses, which rose up in the midst of the
g-reat crater. The largest of these cones is calculated to have been more than 200
feet in height, and possessed at one time a regular pyramidal form, with an appear-
ance of stability.

It is stated, however, by Monticelli, that in May last, from the 20th of which
month up to the 20th of July, the volcano had continued to throw up stones and
ashes, and even to emit lava, both these conical hillocks were observed to be broken
away, and to sink towards the south ; whence, in a memoir read by him to the Aca-
demy of Sciences at Naples on the 5th of August, he predicted their speedy disap-
pearance.

These anticipations were realized at no long period subsequently. On the 22nd
of August, after the volcano had continued for a month in a state of apparent repose,
volumes of black smoke began to show themselves on the summit of the more recent
of the two hillocks above noticed ; and after a smart shock of an earthquake, this
was succeeded by ejections of red-hot stones and scoriae, which continued to be shot
forth all the night with fresh quakings and rumblings of the soil.

Early on the 23rd, a current of lava was seen to issue from the foot of the great
cone which encompasses the crater on its western side, and this bending in the direc-
tion of the point called Crocelle, reached the flanks of the rising ground denominated
Contaroni, whence, moving continually forwards at the rate of about six feet per
minute, and reinforced by a second stream of lava which had burst forth from an ad-
jacent point, it reached about nightfall the path generally taken from the Hermitage
to the summit of the mountain, which it completely blocked up.

During the 24th, lava continued to flow from the same points, and to advance
down the western declivity of the mountain ; and during the night a violent shaking
of the volcano, which agitated the whole adjacent country, was apparently coin-
cident with the falling in of both the conical hillocks described as existing in the
interior of the crater, ho traces of which were visible in the morning. Thus we
have here a decided instance of two considerable pyramidal masses of volcanic ma-
terials, not blown into the air, as some might suppose to be the case, but actually
swallowed up within the cavities of the mountain in the course of a single night.

Up to this time the western side of the volcano had been the point that yielded to
the internal pressure, and the inhabitants of Portici and Resina had imagined them-
selves to be chiefly menaced. But on the evening of the 24th a fresh vent was
established on the eastern side of the mountain near the Grotta del Mauro, whence
the lava of 1817 had issued; and after this had taken place, no more lava was ob-
served to flow from the western side of the cone. On the other hand, the current
from the eastern side was reinforced on the morning of the 25th by a second stream.

DR. DAUBENY ON THE ERUPTION OF VESUVIUS. 155

which issuing forth from the foot of the great cone on the spot called Coutrel, flowed
over the preceding one.

On the morning of the 26th, an immense column of black and dense smoke served
as the prelude to the bursting forth of a new current of lava from the same point as
before, as well as from several others in the neighbourhood ; and the whole of this
molten mass poured down the mountain in a single narrow stream, circumscribed
within the boundaries of a hollow way or water-course. Here, its progress being
favoured by the rapid slope of the declivity, it very soon reached Mauro, and took
possession of the road leading from Bosco-tre-case to Ottayano.

On the 27th it was augmented by two fresh currents emitted from points not far
distant ; but now, instead of flowing on in a single stream as before, it became di-
vided into three. The largest of these currents, going straight in the direction of
Mauro, spread over some lands belonging to the hamlet of Torcigno ; the second
covered the cultivated fields above Bosco-reale ; and the third invaded the upper part
of the village of Bosco-tre-case.

It was the first, however, of these currents which effected the greatest damage.
Widening as it descended, it had acquired, by the time it reached the base of the
mountain, a breadth of nearly half a mile, retaining even there a depth which aver-
aged from fifteen to eighteen feet.

At Mauro, the Casino of the Prince of Ottayano formed its precise boundary to
the north, and one wall of that mansion was swept away by it, whilst all the rest of
the building stood uninjured. From this point the lava proceeded to the road which
leads from Torre del Annunziata to. Ottayano, which it completely blocked up, and
moving still further to the eastward, swept away in its course several detached ham-
lets included in the Commune.

It is calculated, that 180 houses, the abode of about 800 persons, were destroyed
by the current, and that 500 acres (moggie) of land were covered over and reduced
to sterility by it.

Among the remains of the houses overthrown by the lava, which I was able to exa-
mine, no traces of fusion were visible, and the lava seemed to have acted merely as
so much dead weight pressing upon them from without. These, however, it is to be
remarked, were on the verge of the stream, where the lava was least hot ; for in the
interior of the current I was unable to discover any vestiges of the houses that had
been destroyed.

At the time that the eruption occurred, the villages in the neighbourhood were
covered, to the depth, it is said, of two inches, by a shower of capilli ; and from one
account which I have seen, it would appear that torrents of hot water were poured
down from the crater on the 28th.

The flow of lava from the crater continued all the 29th ; but subsequently to that
date no further eruption was perceived, and the principal current already described,
being no longer urged forwards or augmented by fresh streams from above, gradually

x2

156 DR. DAUBENY ON THE ERUPTION OF VESUVIUS.

slackened in its progress, and stopped at a distance of about a quarter of a mile be-
yond the road from Torre to Ottayano.

The lava is said to have been accompanied throughout its progress by a cloud of
black sand, which hovered over its path, and from this cloud emanated frequent
flashings of very vivid lightning, sometimes, but not always, followed by thunder.

These flashings Monticelli refers to the particles of sand being in an opposite
state of electricity to that of the air, and consequently, when diff'used through it by
the wind, producing a discharge of electrical light. The same phenomenon was re-
marked by him in the preceding month of May, at which time the volcano, as has
been stated, emitted a cloud of light volcanic sand. This was diffused by the wind
over the whole of the circumambient atmosphere, and from the edges of this cloud,
where the lightest and finest particles only of the sand were present, frequent corus-
cations of lightning appeared to emanate, whilst in its denser and blacker portion
none such were discernible.

Towards the close of this eruption there occurred a phenomenon, which may per-
haps be attributable to the volcanic action going on under Vesuvius. In a pond be-
longing to a private individual at Puzzuoli, all the fish suddenly died. In the lake
of Fusaro, at this time, from twelve to thirteen hundred weight of fish were calcu-
lated to have perished ; and it was remarked, that the victims principally belonged
to those species which congregated at the bottom of pools, such as eels. Thus, too,
a vast number of oysters at the bottom of this lake were found dead, whereas those
which had attached themselves to the stones or the reeds on its sides are said to
have escaped. In the neighbouring lake of Licola, also, several of the same species
of fish were found to have perished.

After the 29th of August no further signs of internal commotion were exhibited by
the mountain during the past year, except that disengagement of aqueous and aeri-
form vapours from the crater which is scarcely ever entirely absent.

So tranquil a condition of the volcano, although to a general observer it might
appear deficient in that lively interest which belonged to the state of things that had
preceded it, was at least favourable to a detailed examination of the several parts of
the mountain, and allowed of my descending twice into the interior of the crater, which,
owing to the falling in of the two conical hillocks alluded to, presented at that time a
comparatively level surface. There were, indeed, three depressions or pits of con-
siderable depth in the midst of it, which, though without any visible communication
with the interior, were so charged with the noxious vapours evolved from an infinity
of minute and scarcely visible spiracles, that it was judged unsafe to venture down into
them. The rest of the crater, however, was a concavity of no great depth, which was
traversed by my guide and myself with comparative facility, after we had remained
within its precincts time enough, to collect the various sublimations that lined its
walls, and to condense some of the vapours still copiously exhaled from its crevices.
The sides of the crater consisted of strata which might be traced for a considerable

DR. DAUBENY ON THE ERUPTION OF VESUVIUS. 157

way round its brim in a direction nearly horizontal, except in one part, where, from
some shock or fracture, they had sunk abruptly downwards. These strata consisted
of loose volcanic sand and rapilli, coated with saline incrustations of common salt,
coloured red and yellow by peroxide of iron, and presenting a beautiful and brilliant
appearance. I could perceive no dykes intersecting these strata, as at the Monte
Somma.

In order to collect the vapours, I caused to be constructed an apparatus, consisting
of the head of a large alembic, fitted on to a cylindrical vessel of tinned iron with
riveted joints, which, being open at bottom, and introduced a little way into the
ground, served to conduct the exhalations into the receiver connected with it above.
By this contrivance I succeeded in the course of an hour or two in condensing a suf-
ficient quantity of the vapour for chemical examination at Naples. In the liquid
collected I could detect no saline ingredient, and there appeared only a slight trace
of sulphurous or sulphuric acids. The principal body condensed along with the steam
was muriatic acid, which was uncombined with any base.

Whether carbonic acid might be disengaged from the crater I could devise no un-
exceptionable method of determining ; yet by comparing the quantity of carbonate
of barytes precipitated, by exposing a given quantity of barytic water for five minutes
in the vapour of one of the Fumaroles, with what was obtained from the same quan-
tity in equal times exposed to the open air out of the Fumaroles, I am led to con-
clude that this gas was exhaled.

Of nitrogen, the air of the Fumarole appeared to contain the same proportion, as
atmospheric air does in general.

No sulphuretted hydrogen was emitted from the crater, neither could I discover,
either in the condensed vapour or in the sublimations lining its walls, any trace of
muriate of ammonia.

Muriatic salts principally were detected among the latter, but sulphates of lime,
alumina, and iron were likewise present.

The next point in the volcano which arrested my attention was the vent on the
eastern side of the great cone, from which issued one of the principal streams of lava
that burst from the mountain in August last.

The vapours here collected appeared to agree in composition entirely with those
from the interior of the crater ; and the sublimations were of the same nature, with
the addition of much specular iron ore and some muriate of copper.

The lava, which had been emitted in August, continued, when I visited it in Novem-
ber, to give out throughout the whole of its course white vapours ; and even after the
copious rains which fell subsequently, many of the spiracles, so late as the end of De-
cember, continued to emit the same. The interior of the current appeared also at both
these periods to retain a considerable proportion of its original temperature. After
removing about six feet of loose scoriae, I at length reached the upper surface of the
bed of lava itself, into which it would have been impossible to penetrate without the

158 DR. DAUBENY ON THE ERUPTION OF VESUVIUS.

assistance of mining implements. The surface temperature of the lava was indeed not
high enough to melt lead, but one of Daniell's pyrometers, with an iron rod, left in
contact with it for a few minutes, rose more than one degree. It is probable, however,
that I had failed in this instance in obtaining the full temperature of the superficies ;
for nearly a month afterwards, that is, late in December, after much rain had fallen,
I removed the scoriae from another contiguous portion of the bed, and found that a
thermometer placed upon it, and merely covered over with a little sand, rose to 390°
of Fahrenheit. From the cracks and cavities of this lava much aqueous vapour was
still exhaling, and this I succeeded in condensing by means of the same apparatus
which I had employed within the crater.

The condensed steam on examination was found to be impregnated, not only with
free muriatic acid, but also with muriate of ammonia ; and as the vapours were col-
lected at the very point of their escape from the lava, it can hardly be doubted, that
the latter salt is actually present ready formed within the cavities of the stone,
having been emitted from the volcano along with the lava itself. The scoriae which
cover the surface of the bed are in some places quite incrusted over with beautiful
crystals of this sort, some of which are perfectly white, whilst others are of an orange-
yellow colour. The latter appears to be owing to the presence of oxide of iron. The
quantity of sal ammoniac was large enough to repay the trouble of collecting, and
much of it was carried away by the peasants to Naples to be sold to the workers in
brass and jewellery. Muriate of soda was also common amongst the substances in-
crusting the scoriae, but none could be detected in the vapour emitted at the period
of my examination.

The very same substances I found to be exhaled, during my stay at Naples, from
the crater of the Solfatara of Puzzuoli, which differed however in one respect, namely,
in that of emitting much sulphuretted hydrogen, from which the vapours of Vesuvius
were entirely free. Hence the film of minute crystals of sulphur which forms on the
surface of the rock of the Solfatara in the immediate neighbourhood in the Fuma-
roles ; whilst from the Vesuvian lava no sulphur in any form was given out at the
time of my visit, although amongst the sublimations produced at an earlier stage of
the operations, crystals of this body were not uncommon.

The disengagement of such principles, as water, muriatic acid, and sal ammoniac
from a semi-extinct volcano like the Solfatara, is much more intelligible, than its escape
from the substance of a bed of lava which has already undergone consolidation.

In the latter instance, what is the condition in which we are to imagine such bo-
dies to exist in the heart of the mass ? Not certainly in a state of chemical union
with its constituents, for we cannot conceive any affinity inherent in salts of ammonia
or soda for the earthy ingredients of a bed of lava; neither, if in combination with
them, would they be separated, as the latter parted with its heat.

It seems necessary to suppose, that these bodies, being thrown up at the time of
the eruption from the interior of the volcano, became entangled within the interstices

DR. DAUBENY ON THE ERUPTION OF VESUVIUS. 159

of the lava at the same time disengaged ; that a portion of what was originally ejected
still continues in a compressed state within the cavities of the rock, especially in its
interior ; and that it is only by slow degrees that they find means of escape through
chinks and crevices to the surface.

We know that many trap rocks contain a portion of water and of muriatic acid,
and that the latter body has even been detected in the domite of Auvergne, a vol-
canic production, which, comparatively speaking, must be regarded as of extreme
antiquity* ; so that we may more readily conceive, in what manner lavas of recent
origin retain larger quantities of the same volatile principles, and even certain saline
substances, diffused through their pores and fissures.

Perhaps indeed, although chemical attraction in these cases is out of the question,
a certain degree of adhesive affinity may have been exerted, between the substances
exhaled, and the walls of the cavities that had contained them. Dr. Faraday, in the
Sixth Series of his Researches on Electricity, published in our Transactions, has in-
troduced some pertinent remarks on this kind of influence, referring to it, amongst
other phenomena, the operation of platina in determining the union of oxygen and
hydrogen in Dobereiner's experiment. Nor indeed does it seem improbable, that, as
heat exercises a repulsive power, not only between the particles of bodies, but like-
wise between masses of them-}-, so likewise a species of aflinity may exist between
masses of matter even where their particles are not mutually attractive ; and that this
may retard the operation of heat upon bodies possessing intrinsically a considerable
degree of volatility, and prevent their entire disengagement all at once from the cavi-
ties of the substance which entangled them.

Be that as it may, it seems certain from the above observations, that ammonia is
one of the original products of volcanic action in the case of Vesuvius ; and it
would be easy to extend the same inference to other volcanos, — a fact, I am aware, by
no means new, but still one, the circumstances of which seem to deserve investiga-
tion, especially, as from the readiness with which nascent hydrogen enters into com-
bination with azote, it might be imagined, that the ammonia was somehow or other
generated in the open air, owing to a disengagement of hydrogen from the lava.

I trust, that the having traced it to the vapour directly issuing from the mass effec-
tually dispels such a suspicion, and will serve as an additional argument in support of
an opinion I have long entertained, that atmospheric air and water both find their way
to the seat of volcanic operations, and are alike deprived of their oxygen by certain
principles there existing ; whilst the residuary nitrogen and hydrogen are evolved, in
in some cases separately, in others united, in the form of ammonia.

* I might likewise refer to the existence of carburetted hydrogen in a condensed state in cavities of rock-
salt at Wielitzka, and that of sal ammoniac in that of the Tyrol, as facts of the same description. The latter
might lead to some speculations with regard to the origin of sea-salt, to which I may perhaps on some future

occasion recur.

t See Professor Powell's Paper in the Philosophical Transactions for 1834, Part II.

[ 161 ]

X. On the Atmospheric Tides and Meteorology of Dukhun (Deccan), East Indies. By
Lieutenant-Colonel W. H. Sykes, F.R.S. L.S. G.S. Z.S. rice-President of the
Statistical and Entomological Societies.

Received May 14,— Read June 19, 1834.

1 HE value of the following meteorological observations depending on the goodness
of my instruments, on certain precautions in the use of them, and on the care with
which atmospheric changes were recorded, I shall preface my notices on the me-
teorology of Dukhun with an account of the instruments I had in use, and of my
method to insure correct results. In determining atmospheric pressure, for the first
two years I was confined to two of Thomas Jones's barometers : they required to be
filled when employed, and were destitute of an adjustment for the change of level of
the mercury in their cisterns, unless the position of the cistern had been altered at
each observation ; a measure attended with insuperable inconvenience. At first I
experienced a good deal of vexation in expelling the moisture from the tubes ; but
by previously rubbing the inside with a tuft of floss silk tied to the end of an iron
wire, I dried them so effectually (unless in the monsoon months) as to excite power-
ful electricity : and I have frequently had shocks in my right thumb, running up to
my shoulder, in pouring the mercury into the tube, accompanied with cracking
noises, until the approach of the mercury to within two inches of my thumb, when
the electricity was discharged as described. I experienced these shocks at Salseh,
near Purranda, on the 3rd of February ; at Pairgaon, on the Beema River, on the
14th of February; at Kundallah, in the hilly tracts, on the 14th of March, 1828;
and at many other places. Jones's barometers were each provided with a thermo-
meter let into one of the legs of the tripod on which the barometer was suspended.
The scale of this thermometer was of thin ivory, and the tube excessively slender.
During the heat of the day in the dry season, the scale was contracted, by parting
with its moisture, into the segment of a circle, bending the tube of the thermometer.
At night the ivory scale relaxed from its curvature, and at sunrise it had returned to
a right line. This operation continued daily for more than three weeks ; but on the
15th of February 1827, the contraction of the scale was too great for the flexibility
of the glass, and the tube of thermometer No. 1. broke. The thermometer attached
to barometer No. 2. subsequently shared the same fate, from a similar cause. Thomas
Jones's barometers pack well, carry easily, and are certainly very useful as checks
upon permanently filled barometers, which frequently give false indications, from the
unknown escape of the mercury, or the admission of air, which could not be detected

MDCCCXXXV. Y

162 LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

without the aid of a second barometer : but they are very troublesome to fill ; are
destitute of a thermometer near the cistern, to determine the temperature of the
mercury; and want the means of adjusting the lower level of the barometric
column ; the tubes are frequently breaking, from the pressure of the iron screw
which fixes the cistern to the tube, (I have broken seven tubes from this cause,)
and in case of not being tightly screwed on, the cistern falls off from the weight of
the mercury in it, and the mercury is lost ; and from the uncertainty of expelling
air and moisture from the tubes, particularly in the moist months, the indications of
the instrument can only be looked upon as approximations to the truth.

On the 12th of April 1827, I had the gratification to receive three barometers
from England : they were made by Gary on the Englefield construction, which
admits of a most delicate adjustment of the lower level of the barometric column
in the reservoir. They were beautifully finished, but unluckily had reservoirs of
ivory ; and I instantly foresaw the inconvenience to which such selection of ma-
terial would subject me. In the dry weather the ivory contracted, and permitted
the escape of the mercury by the screws (male and female) which joined the two
portions of the reservoir. Subsequently the reservoirs cracked at the spots where
the metallic screws attached the reservoir to the brass cylinder surrounding the tube
of the barometer. I was finally compelled from these disasters, within a twelve-
month, to send two barometers back to England to have glass or iron reservoirs put
to them. From the ease, accuracy, and delicacy with which the contrivance in these
instruments permits the mercury to be adjusted at its lower level, they require only
an iron cistern to render them quite eflficient ; and they are peculiarly suited to
measure minute changes in the atmospheric tides. Mr. Newman of Regent-street
has acted upon my suggestion, and has constructed two Englefield barometers with
iron cisterns, to which he has applied an excellent improvement of his own to pre-
vent the oscillation of the mercury in the tube en route.

Having broken the seventh and last tube belonging to Jones's barometers, to pre-
vent my observations being confined to a solitary instrument I had recourse to one
of the India Company's barometers made by Gilbert: it was very heavy, and clum-
sily constructed, had air in the tube, and I ascertained the mercury not to be of
the specific gravity engraved on the reservoir. The instrument had a glass reservoir,
and the manner of fixing it to the tube was sufficiently ingenious ; but it wanted an
accurate and efficient method of adjusting the lower level of the mercury. This
operation was to be effected by looking through the glass reservoir and screwing up
the mercury to a line marked on it ; but the oxidation of the mercury usually
dimmed the glass, and made it no easy task ; even had it been readily practicable,
the occurrence of the tube exactly in the centre of the convex surface of the mer-
cury prevented its outline being fully seen, and the reading off could never be rigidly
accurate. These causes combined to render unsatisfactory, observations taken with
the instrument to fix the exact time of the flux and reflux of the diurnal and noc-

AND METEOROLOGY OF DUKHUN. 1^

turnal atmospheric tides ; but it answered sufficiently well as a check upon my other
barometers. Several others by Gilbert, used by myself and my friends, were found
to be similarly defective.

Auxiliary to the barometers, I had in use Adie's sympiesometer. This instrument,
so ingenious in its construction, I soon found to be utterly inadequate to measure
the pressure of the atmosphere with the correction given to it for the expansion from
heat of the hydrogen gas in the tube. An inspection of my meteorological register
will show by a glance the inefficiency of the instrument as a substitute for the baro-
meter within the range of my observations. In fact, it constantly sunk with increase
of heat, and gradually rose with the return of cold. In very few instances in a whole
year was it found to have stood higher at 9| a.m., the period of the maximum atmo-
spheric pressure, than at sunrise ; and in these trifling approximations to truth it
evidently deteriorated since the first record of its indications. A sympiesometer
in possession of the Assay Master at Bombay was subject to the same defects. I
nevertheless continued my observations with the instrument simultaneously with the
barometers, to supply the inventor with the necessary elements for its correction,
should he desire to make use of them. I was further induced to keep the instru-
ment on my register, from the advantages I derived from the attached elegant and
accurate thermometer, which had its degrees divided into fifths.

The temperature of the air was determined by two excellent Dollond's Fahren-
heit thermometers, one of which had been in my possession twenty-two years. One
had a brass scale, the other a stout ivory scale sufficiently robust to prevent the
dry air warping it materially. These thermometers never differed from each other
more than half a degree, and I had great confidence in their indications. No. 1. with
the brass scale was used for several years to determine the temperature of boiling
water at different levels. In this process small particles of mercury rose from the
surface, and fixed themselves at the apex of the tube ; but this was easily remedied
by driving the mercury by heat up to the apex, and in retiring it always carried with
it the particles which had risen.

For the determination of the moisture in the atmosphere, two of Leslie's and one
of Daniell's hygrometers were sent to me from Calcutta. The former were kept in
use from the 21st of March 1826 until the 7th of April 1827, when, finding them
destitute of uniform indications with respect to each other and to Daniell's hygro-
meter, I was induced to give up employing them further. Daniell's hygrometer
was continued in use from the 21st of March 1826 until the 30th of September 1827,
when it was unfortunately broken. There not being an instrument of the kind for
sale in India, Colonel Goodfellow, Chief Engineer at Bombay, was good enough to
assist we with one, which was brought into use on the 25th of October following.
This continued in use, with occasional interruptions from the want of aether, until
the 28th of March 1828, when it shared the fate of the former. From this period
until the Uth of June 1829, I was disabled from making hygrometric observa-

y2

164 LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

tions, when the arrival of other hygrometers from Europe permitted me to resume
them.

Daniell's hygrometer I found to be an admirable instrument, ingenious in its con-
struction, definite and uniform in its indications, simple in its use, and satisfactory in
its results. But it is not without a drawback upon its utility. Independently of the
demand for a constant supply of aether, there are periods of the year in Dukhun
when the high temperature and extreme dryness render the dew-point only obtain-
able at such an expense of aether as to render it an object of pecuniary considera-
tion ; and with the very best aether I have never been able to reduce the tempera-
ture more than 61° of Fahrenheit's scale, that is to say, from 90° to 29°, on the 16th
of February 1828, at 4 p.m.; and at that hour the attempt in the months of March and
April 1827 proved fruitless, and I was obliged to give up a register of the dewing-
point in the afternoon. In the month of January, at sunrise, on the 4th and 6th
respectively, I got the dewing-point at three degrees below that of congelation of
_water, namely at 29°, the temperature of the air being 62° ; and on the 3rd of Febru-
ary 1828, the dewing-point was at 28° Fahr., the air 56°, at sunrise. On the
17th of February the lowest dewing-point ever registered was obtained, namely 27°
Fahr., temperature of air 57°'50 at sunrise. The objections, therefore, to this
instrument are, the great expense of aether in the dry months, and the occasional in-
ability to obtain the dewing-point when the temperature is very high and the day
very dry. I never had any difficulty in Bombay or in the Konkun in obtaining the
dewing-point, even at a temperature of the air of 91°'50 Fahr., nor will the effi-
ciency of the instrument ever be doubtful within the tropics near to the sea shore. It
is necessary to mention that the temperature of the air in Dukhun sometimes exceeds
the boiling-point of good aether.

The measure of the quantity of rain which fell was taken with two instruments,
one of which was sent to me from Calcutta under the apposite name of ombrometer,
and the other was obtained from the medical stores at Bombay with the hybrid ap-
pellation of pluviometer attached to it. A hollow cylinder closed at one end had a
metallic float with gage-rod, resting on the bottom. The rain was received into a
round funnel fixed to the top of the cylinder: the diameter of the mouth of the funnel
was in a certain ratio to that of the cylinder, and this ratio regulates the length of
the inches on the gage-rod. The ombrometer was made of brass, neatly finished.
The pluviometer, of lackered iron, large, rudely finished, and unwieldy ; and it had
further the disadvantage (unlike the ombrometer) of its funnel-shaped mouth not
closing round the gage-rod, an improvement preventing the evaporation of the water
that falls into the instrument. Both rain-gages stood more than three feet high,
but their cylinders were of diff'erent diameters. In both, the inches on the gage-rod
were so large as to admit of hundredths (and even thousandths if it were required) of
an inch of water being read off with ease. They always worked very well together,
the only discrepancy being in the larger instrument indicating two or three hun-

AND METEOROLOGY OF DUKHUN. ]65

dredths of an inch of water less than the smaller in the first tenth of an inch of rain.
Subsequently they coincided in their indications even to the hundredth of an inch.

With Gary's Englefield barometers, I received three thermometrical barometers,
for determining heights by the difference in temperature of boiling water at different
levels. Owing to faultiness in their construction, they proved complete failures, and
were sent back to England. I satisfied myself there was a good deal superfluous in
the apparatus accompanying them, which made them moreover expensive, and I effi-
ciently supplied the place of these barometrical thermometers by two good common
thermometers with metaUic scales and a tin shaving-pot with a slit in the Hd, in which
the thermometer was placed, being moveable in a collar of cork. Pure water and
dry sticks were always found, an attendant carried a light, and my boiling-operation
was concluded in a quarter of an hour without the aid of tallow, lamp, sulphuric
acid, phosphoric matches, trimming-scissors, tweezers, hanging-screw to fix into
trees, water-bottle, &c. &c., involving the outlay of several pounds. Accuracy in the
indications of the instrument also was risked, owing to three fourths of the stem of
the thermometer being exposed to the wind or cold air during the time of the im-
mersion of the bulb in the boiling water, which checked the rise of the mercury.

Having for several years practised the barometrical and thermometrical methods
to determine heights, I have no hesitation in expressing my opinion, that a good
thermometer and a boiling-pot may efficiently supply the place of the expensive and
delicate barometer where great accuracy is not required. In many instances I found
the results by the two processes almost identical.

My electrometers consisted of two balls of pith suspended in small glass jars capped
with brass, having an elevated point on the plane of one cap, and a wire projj^cting
from the apex of the other, which was bell-shaped. They were in fact Cavallo's
pith ball bottle electrometers, with Saussure's addition of pointed wires, but without
a graduated scale on the bottle to measure the divergence of the balls. Owing to
some peculiarity in the instruments, they feebly indicated the presence of electricity
in the atmosphere, although at certain seasons it was so rife as to be painful to the
feelings. When first received, they were sensible to artificial electricity, but latterly,
without having been injured, they lost all susceptibility. I never could make a record
of their indications. Even had they been available, the want of a scale rendered it im-
possible to give any positive idea of the extent of the electric state of the atmosphere
at any time. A scale, in case it did not measure definite quantities, would neverthe-
less be highly useful to determine the electricity of any particular period relatively to
that of any other period.

In placing the instruments for measuring the pressure and heat of the atmosphere,.
I was particularly careful to secure them from the operation of causes capable of
producing partial and unsatisfactory results. They were always in the shade, and
always guarded from direct or reflected heat, but with a free admission of the external
air. Annually, from October until May inclusive, they stood, for the most part,

166 LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

just within the inner doors of a field officer's tent, having a third canopy or extra fly
to it ; and during the hot months commonly pitched under the shade of lofty trees.
For the remaining, or monsoon months of the year, the instruments were kept in a
room at Hay Cottage, Poona, through which there was a constant draft of air by two
windows opposite to each other in the line east and west. In using the hygrometers,
they were always taken to the door of the tent or to an open window. Whether in
determining ordinary pressure, atmospheric tides, temperature, moisture, or heights,
by the barometer or boiling-water process, I have invariably deemed it necessary to
guard my observations from error by the employment of instruments in pairs. I have
been thus minute in the description of my instruments and my manner of using
them, not less to supply the means for a just estimate of the value of my meteorolo-
gical observations, than to enable meteorologists who may tread in my steps to benefit
by my experience and disasters.

The barometrical means have been reduced to32°FAHR. by Professor Schumacher's
tables, with corrections for the expansion of the brass scale ; and the monthly means
for 1830 were obtained by the ingenious process recommended by Professor Forbes.

In regard to the following barometrical observations, I must premise, that my
three best barometers, although precisely of the same construction and placed under
precisely similar circumstances, would occasionally differ slightly from each other,
not only in the amount of the oscillations, but in the period at which the several tides
turned ; and this fact is of some importance to those who may be disposed to rely
too confidently upon the indications of a single instrument.

My erratic life necessarily disabled me from determining the mean absolute height
of the barometer at any one place for a period exceeding five or six consecutive
months, excepting for the year 1830. I cannot, therefore, state the annual range of
the barometer for several years successively ; but repeated returns to Poona in vari-
ous months of the year would have supplied the materials for tolerably just estimates,
even had I not one entire year's observations made at Poona. The monthly range is
recorded for many complete months, and the diurnal range for six years with few
omissions ; but I propose to confine my deductions to my observations for the last
four years, as the instruments I had in use at first (Jones's) did not admit of a
delicate adjustment of the lower level of the mercury.

The great features in the barometrical indications are the diurnal and nocturnal
tides, embracing two maxima and two minima in the twenty-four hours ; the former
occurring with occasional exceptions between 9 and 10 a.m. and 10 and 11 p.m., and
the latter between 4 and 5 p.m. and 4 and 5 a.m. The same hours obtain at Calcutta
and Madras at the level of the sea ; at Kotgheriy on the Neelgherry mountains at
6407 feet; in South America at 12,000 feet; and in London and Edinburgh, and
other places in Europe where careful observations have been made. Hitherto little
has been known respecting the nocturnal atmospheric tides, but the existence of the
diurnal tides is now established beyond doubt in most parts of the world. Hum-

AND METEOROLOGY OF DUKHUN. 167

BOLDT, on the authority of Horsburgh, has been led into the expression of a belief
that they are masked or suspended on the western coast of India during the pre-
valence of the south-west monsoon. I am, however, enabled to state that this is
quite unfounded with respect to Dukhun, as they were never interrupted, even for a
single day, during six monsoons ; and the same fact was observed at Kotgherry on
the Neelgherry mountains at 6407 feet above the sea during part of the monsoon of
1828. Of their occurrence on the coast I am also enabled to offer some evidence
from registers kept at the Engineer Institution in Bombay, and regularly transmitted
to me ; but the hours selected for observation, 9 noon and 3 p.m., were not exactly
adapted to fix the full amount of the tide ; but on the whole the fact of their oc-
currence during the monsoon of 1829 in Bombay is undeniable; and they were
similarly remarked at Calcutta in 1822 by General Hardwicke, and by Mr. Prinsep
in 1829, 1830, and 1831. This fact will relieve Humboldt from some of his diffi-
culties in his reasoning on the tides.

With respect to the tides in general, I have to state that in many thousand obser-
vations made by myself there was not a solitary instance in which the barometer
was not higher at 9 — 10 a.m. than at sunrise, lower at 4 — 5 p.m. than at 9 — 10 a.m.,
whatever the indication of the thermometer or hygrometer might be : nor was there
a solitary instance in the year 1830 in which the maximum night tide was not higher
than the 4 — 5 o'clock day tide, although it rarely, if ever, rose so high as the 9 — 10
a.m. day tide. The nocturnal minimum tide occurring at 4 — 5 a.m., from three to
four hours after my usual time of retiring to rest, my observations of it were very
limited in number; nevertheless the accompanying Tables will furnish some direct,
and ample indirect, testimony of its existence, since the fact of the rapid, constant,
and considerable rise of the barometer from sunrise until 9 — 10 a.m. justifies the
inference that there must have been a considerable previous fall to have admitted of
such rise : the commencement of such fall was necessarily observed by me in my
labours during 1830 to determine the limit hours of the tides, as I was obliged to
continue observing in each case until the tide had turned. Moreover, at different pe-
riods I devoted forty-nine nights to the investigation of the minimum a.m. tide.
Dr. Walker at Mahabuleshwar, at 4500 feet above the sea, bestowed eight months'
labour upon the tides ; and Mr. Dalmahoy, on the Neelgherry mountains, was simi-
larly employed for four or five months. Humboldt in his narrative mentions the
determination of the extent of the diurnal oscillations, the duration of the stationary
state of the barometer at its maxima and minima, and the exact periods at which it
becomes stationary and is in action again, as desiderata. I shall take these subjects
in order as I proceed.

The extreme oscillation of the barometer in the same day never amounted to two
tenths of an inch, in fact to '1950, with a difference of the attached thermometer
during this range of -h7°'6, and the hygrometer 15° from the point of saturation.
Wind light and variable. This took place on the 19th of April 1830. There were

168 LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

great masses of clouds, and distant thunder and lightning ; a storm threatened, but
did not take place. The same appearances continued daily until the 21st, on which
day there was a hail storm, whilst the thermometer stood at 86°'3. On the 23rd
there was another hail storm and thunder : this weather continued to the end of the
month, and the daily oscillations were so great as to make the mean exceed that of
any other month in the year. Here there could be little doubt of the oscillations
being affected by the state of the weather. In 1827 the maximum oscillation of '1892,
(difference of thermometer attached +10°, dewing-point 37° from saturation, wind
none,) took place on the 7th of March, and the weather was free from any of the
indications before noticed ; but on the 9th of March there was a little lightning
and some drops of rain. In 1828 the maximum oscillation of •1856, (difference of
thermometer attached +10° 8', no wind, and clear sky,) took place on the 2nd of
January. In 1829 the maximum oscillation was on the 26th of February, and amounted
only to "1648, difference of thermometer +11° 5', wind light east, and clear sky.

In 1827 the minimum oscillation of the year occurred on the 7th of August, between
9 A.M. and 4 p.m., amounting to '0150; difference of attached thermometer — 0°'8, light
west wind, sky quite overcast, but no rain, although the dewing-point was only 3°
from the point of saturation. A nearly similar oscillation, *0153, thermometer +5°*2,
took place on the 29th of the preceding May, with a violent west wind and clear sky,
and no dew-point obtainable at 4 p.m. In 1828 the smallest diurnal oscillation of
•0155, thermometer +2°*3, took place on the 19th of October during a gentle rain
and light S.W. wind. In 1829 the smallest oscillation was '0281, thermometer +0°*9,
on the 2nd of July, with a partially clouded sky and fresh W.S.W. wind, the hygro-
meter being 6° from the point of saturation. On the 21st of March the next smallest
oscillation of the year took place, with a misty sky, light west wind, and air very dry.
In 1830 the minimum of the year was also in July, amounting to '0327, the thermo-
meter being half a degree lower at the minimum than at the maximum hour ; sky
overcast, no rain, wind light west, hygrometer 8° from the point of saturation. On
the 20th of March there is also a small oscillation of -0493, thermometer +9°'9, sky
clear, fresh west wind, and hygrometer 29° from the point of saturation. I have been
particular in noticing the state of the weather and the winds, &c., at the periods of
these extreme oscillations, as Mr. Snow Harris of Plymouth suggests that the atmo-
spheric tides may be influenced by the force of the wind, whilst others refer them to
hygrometric causes.

The mean of the diurnal oscillation of the barometer in Dukhun from 9 — 10 a.m.
to 4 — 5 P.M. for 1827 was '1025, mean range of attached thermometer between the
two periods +5°-99. In 1828 it was ^1093, thermometer +6°'36. In 1829 it was '0991,
thermometer +3°-92. The smallness of the range both of barometer and thermometer
in this year is attributable to three months' observations having been taken at an
elevation of nearly 4000 feet above the sea. In 1830 the barometers were stationary
for the whole time at Poona, and I look upon these observations as affording the

AND METEOROLOGY OF DUKHUN. 169

best types of the meteorological phenomena of Dukhun. The fall of the tide from
9 — 10 A.M. to 4 — 5 P.M. was -1 166, thermometer +4°'9. Comparing this tide with the
same tide observed in other places, we find that at Madras, lat. 13° 5', from observations
taken at the Observatory every tenth day in 1823, the mean oscillation was '079,
mean range of attached thermometer +8°'5. At Calcutta, latitude 22° 35', the means
of the years 1829, 1830, and 1831, make the oscillation amount to '110, thermometer
range + 12°'2. At Saharunpoor in Hindoostan, 1000 feet above the sea, latitude 3 1°N.,
by Mr. Royle's registers, the tide was '120, mean range of thermometer 4-24°-2. At
Ava, latitude 21° 51', Major Burney's observations in 1830 make the tide amount
to '126, mean diurnal range of thermometer +10°-6. Agreeably to Mr. Prinsep, at
Benares, latitude 25° 30', it is "105, range of thermometer attached + 16°'6. Professor
Forbes in Edinburgh found the oscillation to be '0114, mean range of thermometer
attached for three years — 0°*57. And Mr. Hudson, at the Royal Society in London
in 1831, determined the oscillation to be '0289, therm. 4-l°73.

Humboldt and Bonpland in equatorial America, at Cumana, La Guayra, Payta,
Lima, and Rio Janeiro, found the mean extent of the oscillation at most from "0945
to -1 181 *. At Lima, latitude 12° 26', it was a little less (-0669 to '0905 f) than nearer
to the equator, where it was from '1023 to '1291 J. Boussingault and Rivero in
1823-4, at Santa F6 de Bogota (latitude 4° 35' N.), height 8196 feet, found it to be
•0905, approaching my mean for 1829. At La Guayra (latitude 10° 36' N.), at the
level of the sea, it was '0960 ; but as the preceding observations in America, with the
exception of those at Bogota, were for a few days only, they are valueless as indi-
cative of the mean diurnal oscillations, much less the monthly and annual means.
The extent of the diurnal oscillation from 9 a.m. until 4 p.m. on the table land of
Bogota was from -0248 to -1433 §. In Dukhun in 1827 it was from -0150 to -1892 ;
in 1828 from -0155 to "1856; in 1829 from '0281 to '1648; and in 1830 from -0327
to "1950. The mean of the monthly variations at Bogota are from '0580 to -106211.
Mine for 1827 were from "0489 in July to -1616 in December; in 1828 from -0471 in
July to -1505 in February; in 1829 from "0654 in July to '1358 in January; and in
1830 from '0750 in July to -1430 in April. Considering that my observations were
made on a level more than 6000 feet lower than that of Messrs. Boussingault and
Rivero, the above data exhibit curious approximations, and prove that diurnal varia-
tions in the pressure of the atmosphere at great differences of level may have consi-
derable uniformity. But to this we find an immediate exception, for Dr. Walker at
Mahabuleshwur, at 4500 feet above the sea, and a few miles south of the latitude of
Poona, found the mean fall for ten months, from 9 — 10 a.m. to 4—5 p.m., to be '0694,
difference of thermometer attached +2°-61, which is infinitely less than M. Boussin-
gault's mean at 8000 feet.

The monthly means of the diurnal oscillations in consecutive years, although not
uniform, have marked approximations. The five monsoon months in each year ex-

* 2«''«-4 to Z^^'O. t l»°»-7 to a^'^-a. X 2'°'"-6 to 3'""'-3. § 0°>'"'63 to 3«"»-64. !l I'^'^'S to 2'»°"7.
MDCCCXXXV. Z

170

LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

hibit comparatively a low range, in fact the month of July has the lowest mean di
nrnal oscillation in each year; and it may be broadly stated, that with two or three
exceptions the monthly mean diurnal oscillation increases from July to December or
January, and decreases from these months to July. How far the monthly mean oscil-
lations of the barometer and the monthly mean range of the thermometer coincide,
will be seen by the following Table. The monthly mean temperature and the monthly
mean diurnal oscillations of the barometer have little coincidence.

Mean range of the Thermometer attached to Englefield's Barometer between sun-
rise and 4 — 5 p.m. at Poona and Mahabuleshwur.

Poona. 1827. 1823 feet.

and between lat. 17<»25'

and 19027'N.

Poona. 1828.

and between lat. 1 7° 40'

and]9«>ll'N.

Poona. 1829.

and between lat. 18" IC

and 19° 23' N.

Mahabuleshwur. 1828-29.
4500 feet.

Barom.

Monthly
mean osc.

Thermometer.
Mean range.

Barom.
Monthly
mean osc.

Thermometer.
Mean range.

Barom.
Monthly
mean osc.

Thermometer.
Mean range.

Barom.
Monthly
mean osc.

Thermometer.
Mean range.

January . .
February. .
March. . . ,

April

May ....
June ....

July

August . .
September
October . .
November
December

•1134
•1257
•1248
•0836
•0624
•0902
•0489
•0600
•0813
•1147
•1444
•1616

14

23

21

*10

13

6

4

4

6

7

21
26

4

1

6

1

1

35

36

33

47

21

4

7

•1483
•1505
•1123
•1334
•0836
•1007
•0471
•O7O6
•0910
•1106
•1277
•1141

25

27

*17

17

19

7

3

3

5

5

8

*16

7

1
68
89
82
34

6
88
38
58

5
28

•1358
•1083
•1024
•0981
•0903
•0734
•0654
•0866
•0772
•1116
•1067
•1338

20

21

tl3

tl4

tl2

4

3

3

6

9

11

il4

81
88
82
51
96
29
26
87
18
67
23
46

•0735

•0666
•0827
•0835
•0757
•0528
•0556
•0503

•0801
•0738

8

15

9

7
4

4
6

75
40
09

84

89
80
85
64

68
70

In 1827 the greatest monthly mean diurnal oscillation and the maximum mean range
of attached thermometer were coincident in December ; but the next greatest mean
oscillation was in November, whilst the greatest mean range was in February. No-
vember and March have nearly the same mean thermometric range, but differ 0*196
in mean barometric oscillation. In 1828 the greatest mean oscillation and range of
thermometer are coincident in February. January accords in a similar manner ;
but May is quite anomalous, having a mean barometric oscillation of the monsoon
month of September, range of thermometer +5°-88, whilst its own range is -|-19°'82.
In 1 829 the movements of the barometer and thermometer are not coincident ; the
maximum of the former being in January, that of the latter in February. In Decem-
ber we find the oscillation of the barometer nearly identical with that of January
preceding, whilst the mean range of the thermometer is nearly seven degrees less.
At Mahabuleshwur the monthly mean maximum oscillation of the barometer is in
April, whilst the maximum mean range of the thermometer is in February, and
nearly doubles the range of April.

* The observation for those months with the * were taken in Bombay, with the f at Hurreechundurghur,
ftnd with + at Chamblee.

AND METEOROLOGY OF DUKHUN. 171

Of the rise of the barometer from sunrise to 9 — 10 a.m. I shall say only a few
words, as the period embraces but four sixths of the time occupied by the flux of
the atmospheric tide, and the figures in consequence are of little further value than
as affording presumptive evidence that the rise, without the exception of a single day
for six years, must have been preceded by a nocturnal ebb. Although the annual
means, -0473, difference of thermometer attached +7°-27, for 1827 ; -0481, thermome-
ter -j-6°71,for 1828 ; and '0382, thermometer +7°*48, for 1829,agree tolerably well, yet
the monthly means for successive years do not manifest the same accordance ; as in
the tide just noticed the smallest mean oscillation is in the monsoon months, and it
increases until December — January, and then decreases to June — July. In 1828, how-
ever, June is a remarkable exception, the oscillation being greater than in any month
of the year excepting January, and nearly double that of June 1827. Dr. Walker
at Mahabuleshwur, at 4500 feet, found the rise from sunrise to 9— 10 a.m. to be nearly
identical ('0476, thermometer +4°- 18) with my rise at less than 2000 feet. Mr. Dal -
MAHoy at Kotagherry, at 6407 feet, found the rise from sunrise to noon to be -0490,
thermometer 4-10°-4 ; and had his observations been taken at the hour of the maxi-
mum diurnal tide (9 — 10 a.m.), the oscillation would no doubt have exceeded those
recorded by Dr. Walker and myself at infinitely lower levels. Mr. Goldingham at
the Observatory at Madras, a little above the level of the sea, makes this tide amount
to '0470 ; so that, in fact, it is less at the level of the sea than at 6407 feet !

The nocturnal rising tide from 4 — 5 p.m. to 10 — 11 p.m. I observed with great care
for eleven months continuously in 1830. It amounted to -0884, thermometer — 7°-2.
The indications of monsoon influence in this tide are scarcely perceptible. Indeed,
the smallest monthly mean oscillation occurs in December, "0450, thermometer — 6°*3 ;
and the greatest in May, '1140, thermometer — 9°*0. Unlike the preceding tides, we
cannot trace a maximum in the coldest months, and a minimum in the most rainy.
Dr. Walker found it to amount to '0439, thermometer — 5°*58 ; the monthly mean
maximum oscillation, '0632, thermometer — 3°*21, being in November, and the mini-
mum, *029 1 , thermometer — 6°'74, in January. Mr. Dalmahoy, at 6407 feet, found it to
be '0430, the minimum, "0280, being in June, and the maximum, '0560, in April ; but
as he did not determine the exact period of the time of the tide between 9 — 12 p.m.,
the real extent of the tide is unknown. In my own observations I watched for the
turn of the tide. Mr. Goldingham, at Madras, makes the value of this oscillation
•0630 ; whilst M. Duperrey, at Payta in America, latitude 5° 5' S., makes it -1259.

I now pass to the fourth tide, the fall between 10 — 11 p.m. and 4 — 5 a.m. Here
the data are defective, as observers have only, for very short intervals of time, en-
deavoured to fix its limit hours ; and I have no reliance whatever upon occasional
observations as types of a whole year, or even a month or week. For myself, I am
not an exception, as my observations between 4 — 5 a.m. are very limited in number.
The maximum night tide, I have before stated, was observed by me for eleven
months, and the a.m. tide at sunrise for several years. Dr. Walker, at Mahabu-

z 2

172 LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

leshwur, observed at both these periods for eight months ; and Mr. Dalmahoy, at
Kotagherry, between 9 — 12 p.m. and a little before sunrise, observed for five months.
On the 30th of November 1828, at Poona, the a.m. minimum tide turned at 4^" 30°*
A.M., and the maximum nocturnal tide at 10^ 30™ p.m.; the fall between these periods
being '0150, and the difference of attached thermometer — 7°'6. The other tides of
this day were a rise of -0572, thermometer +9°-0, from 4^^ SO'" a.m. to 9^ 30™ a.m. ;
fall from 9^' 30™ to 4 p.m. -1330, thermometer +3°*4, and a rise of -0908, thermome-
ter — 11°'0, from the last hour to 10^ 30™ p.m. The mean of eighteen days in Sep-
tember at Poona, in 1827, gave a rise of -0753, thermometer — 5°'l, from 4 — 5 p.m.
to 10 — 11 P.M., and a fall of '0254, thermometer ^l°-37) from 10 — 11 p.m. to sun-
rise. The rise from the latter hour to 9 — 10 a.m. was '0352, thermometer -|-3°*65,
and the fall from 9 — 10 a.m. to 4 — 5 p.m. was '0844, thermometer +2°'82. For
twenty-one nights in October the fall from 10—11 p.m. to sunrise was only "0010,
thermometer — 2^*39 ; the rise from 4 — 5 p.m. to 10 — 11 p.m. '0745, thermometer
— 4°*76. But for nine nights in November the nocturnal a.m. tide occurred with a
contrary sign, the barometer being -0052 less, thermometer — 10°-2, at sunrise than
at 10 — 11 P.M. The maximum night tide, however, appears with the proper sign, the
rise being -0801, thermometer — 1 ]°65. On the 3rd of November of the following year
the A.M. minimum tide appears with the proper sign, the fall being '0040, thermome-
ter — 4°*0; and the rise from 4 — 5 p.m. to 10 — 11 p.m. was '0714, thermometer — 6°-5.
In the above, although we find great discrepancies in the fall from 10 — 11 p.m. to
sunrise, we yet observe great uniformity in the nocturnal rise from 4 — 5 p.m. to
10 — 11 P.M. with a falling thermometer. Dr. Walker found the mean nocturnal a.m.
tide for eight months to be -0180, thermometer — 1°'68 ; and the rise from 4 — 5 p.m.
to 10 — 11 P.M. to be '0439, thermometer --5°*58. Mr. Dalmahoy, at Kotagherry,
from 9 — 12 p.m. to a little before sunrise, for four months, found the mean fall to
amount to '0433, and the rise from sunset to 9 — 12 p.m to be '0430. Mr. Prinsep,
F.R.S., in a voyage from Calcutta to Bombay, during thirty-two days found the ba-
rometer fall '0220 from 10 p.m. to sunrise, and rise '0440 from sunrise to 10 a.m. ; fall
•102 from 10 a.m. to 4 pm., and rise '0800 from the last hour to 10 p.m. Observa-
tions taken hourly at the Madras Observatoiy, every tenth day and night, make the
night tide from 10 p.m. to 4 a.m. to amount to '035, and the 4 a.m. to 10 a.m. tide to
be '047 ; the other two tides being respectively '079 and '063. The smallness of this
maximum diurnal tide appears very anomalous, considering that Madras is in a low
latitude and at the level of the sea.

In opposition to the above facts. Dr. Russell, at Boorhanpoor, gives a nocturnal
minimum tide with a contrary sign, or a n^e instead of a, fall of 0200, between 10 p.m.
and 5 a.m.; and in observations of Dr. Royle, at Saharunpoor in India, at 1000
feet above the sea, and of Fray Juan, at Vera Cruz, the nocturnal tide appears
in the monthly means so often with a plus instead of a minus sign, that the annual
mean establishes this tide only by '001 at Saharunpoor, and by -002 at Vera Cruz.

AND METEOROLOGY OF DUKHUN. 173

Mr. Hudson however, at the Royal Society, in his careful hourly observations even
in the high latitude of London, found it amount to "0120 ; and I feel assured that
further observations will establish its existence at those places rendered doubtful by
the data just quoted.

With respect to the exact periods of the diurnal flux and reflux, and the duration
of the quiescent state of the atmospheric tides, the subject has been wholly over-
looked, as far as I can learn, in Western India ; but even had it not escaped atten-
tion, there have not been, I believe, instruments in use sufficiently delicate in their
construction to read off" very small quantities. Dr. Walker at Mahabuleshwur, Cap-
tain Jervis in Bombay, at the Engineer Institution, and myself, are the only persons
who have made observations on the tides. For myself, my multitudinous avocations
deprived me of the necessary leisure for some years to enable me to enter systemati-
cally into the inquiry. Occasionally, at the admitted limit hours of the diurnal oscil-
lations of the barometer, I made a few observations ; but they were of little further
value than to show that the maxima and minima, on consecutive days, did not occur
at the same exact period of time. In 1830, however, with two of Englefield's baro-
meters, which admitted of the adjustment of the lower level of the mercury to the
1000th of an inch, I made observations every quarter of an hour, and sometimes every
five minutes, during the whole of the year at the limit hours of the diurnal maximum
and minimum a.m. and p.m. and maximum p.m. tides. Messrs. Walker and Jervis
had in use Gilbert's barometers, and did not observe for the exact limit hours.

Messrs. Boussingault and Rivero, in addressing Humboldt from South America,
state that their labours had verified the fact established by Humboldt, that the mer-
cury between the tropics attains its maximum between 8 and 1 0 a.m., then descends
till near 4 p.m., and is at the minimum between 3 and 5 p.m. : then it ascends till 1 1
at night, without reaching however the same height at which it was at 9 in the morn-
ing, and finally re-descends till 4 in the morning. It will be seen how closely these
limit hours hold good in Dukhun as well as in America ; and Mr. Hudson has de-
termined that they hold good in London : but I have on record instances of the
barometer rising until 10^ 45™ a.m., falling until 6 p.m., and rising until 12 at night ;
but the instances are rare : and even the tremendous storms preceding and closing
the monsoons in India only modify and do not interrupt the tides *. Humboldt ob-
serves, that in Macao, in 1814, there were frequent tempests, and twenty-six stormy
days, and yet there was not a single instance of the tides being interverted. He says
also, that in reviewing the whole of his observations made at different heights, and

* The variations appear to be independent of those of temperature and the seasons. If the mercury was
descending from 2'' till 4'', or rising from 4'' till IP, a violent storm, an earthquake, showers, and the most
impetuous winds, would not alter its movement, which nothing appears to determine but the real time or the
position of the sun. — Humboldt, Personal Narrative, vol. vi. part ii. p. 701.

Humboldt further remarks that the hurricanes (in the West Indies) are not in general accompanied by such
an extraordinary lowering of the barometer as is imagined in Europe. Captain Don Thomas de Ugartb, on

174 LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

in latitudes more or less near the equator, it seemed to him that the extent of the
variations diminished very little with the elevation of the spot. Mr. Colebrooke re-
marks, that in the interior of India the periodicity of the tides is manifest, and inde-
pendent of the variations of the temperature and the seasons of the year. My obser-
vations, on the whole, tend to strengthen the opinions of Messrs. Humboldt and
Colebrooke.

I found the stationary/ period of the tides to vary from nil to one hour and a half.
With respect to the maximum diurnal tide, it appears by the accompanying Table
that it never turned before 9 a.m. or after 10^ 20™ a.m. during the whole of
the year 1830; the seasons therefore were inoperative; and this is confirmatory of
Mr. Goldingham's observations at Madras in 1823, although no great reliance can
be placed upon them, from their having been made onli/ every tenth day : confirmatory
also of Margue Victor's observations made for years at Toulouse. I found the maxi-
mum diurnal tide (indeed all the tides) to oscillate in its time of turning, and in its
stationary period between the hours stated, without relation to any change in the
attached thermometer. On the 5th of February the tide turned before 10 a.m. ; on
the 14th it turned at 10^^ 20™ ; on the 11th of March at 9'' 15™ ; on the 19th not be-
fore 10 A.M.; April 11th at 9^ 30™; April 17th at 9^ 45™; on the I4th of June it
turned at 9 o'clock ; on the 10th of June at 10 o'clock ; and similar anomalies occur
in the following months. The stationary periods of the maximum a.m. tide range
from 0 to 45 minutes, and the Table shows several instances of the latter. The fall
of the barometer in equal periods of time after the turn of the tide presents irregu-
larities. On the 1 1th of March the fall was '010 in 30 minutes : on the 1 1th of April
in 30 minutes it was only "001.

The afternoon tide has the same irregularities as the preceding. It never turned
before 4 p.m., and in a few instances only after 5 p.m. On the 5th of February the
tide turned at 4 p.m. ; on the 8th at 4^ 30™ ; on the 20th of August at 5 p.m. ; on the
4th of October at 4 p.m., &c.

The stationary period was from 0 to 45 minutes ; but of the latter there is only one
instance in the Table, although there may be more in the registers, as the extracts
were taken at random. On the 9th of February there is a curious instance of the tide
turning at 4*^ 15™ p.m. ; then rising -004 to 4** 30™, continuing stationary until 5 p.m.,
and then resuming its rise. As in the morning tide, the movements of the barometer
were not equal in equal times. On the 5th of February the tide rose only -002 in

board ship in the terrible hurricane of the 27th and 28th of August 1794, found that the column of mercury-
fell only '4448 (11"""*3). — Personal Narrative, vol. vi. part ii. page 794.

I am enabled to strengthen this assertion by the following extract from the log-book of the Duke of Buccleuch,
Captain Henning, from Calcutta to London, in January 1833, during a frightful tempest of two days' duration
off the Isle of France : —

" 21st. Lat. 24° 31'. Long. 61° 49'. Bar. max. 30°00. Bar. min. 29°-60. Temp. 80|°.

22nd. Lat. 25° 39'. Long. 57° 32'. Bar. max. 29°-76. Bar. min. 28°-94. Temp. 82°."

The whole fall, therefore, amounted to no more than one inch and six hundredths in the two days.

AND METEOROLOGY OP DUKHUN. * 175

ninety minutes ; on the 6th it rose '008 in seventy-five minutes ; and on the 8th it
rose -005 in fifteen minutes ; and on the 11th of April -001 only in forty-five minutes.

In the maximum nocturnal tide (10 — 11 p.m.) there was rarely any difference in the
thermometer during the oscillations of the mercury ; nevertheless the turn of the tide
ranged from 9^ SO'" to 1 1^ SO"*, and in two remarkable instances even beyond these
hours. On the 12th of October it turned at 9 p.m., and on the 9th of June at 12 p.m.;
both of these anomalies may have been produced by the state of the weather, there
having been a heavy thunder storm from 7^ to 8^ 30™ on the 9th of June, and several
thunder storms round the horizon on the J 2th of October, although not immediately
at Poona. The stationary period ranged from 0 to 60 minutes, but of the latter there
is only one instance in the Table. As in the preceding tides, the movement of the
mercury in equal periods of time manifested occasional irregularities, although the
thermometer remained stationary, or nearly so. On the 6th of February the night
fall was '008 in 15 minutes, and on the 8th it was only -001 in 15 minutes ; in neither
instance was there any movement of the thermometer, whilst on the 10th of June,
between 10^ 45™ and 11 p.m., the barometric fall amounted to '010. From the above
facts, and they could be infinitely multiplied, it is clear there is not any positive uni-
formity in the oscillations of the mercurial column, nor in the duration of the sta-
tionary periods ; nevertheless as the irregularities are bounded by comparatively
narrow limits, the movements may be considered subject to a general law, the
rationale of which remains to be explained.

Experiments have determined that the diurnal atmospheric tides (the nocturnal
tides have been less attended to) extend from the equator to high parallels of lati-
tude, but that the oscillation decreases as the latitude increases. It is further pre-
sumed that the oscillation gradually diminishes in ascending from the level of the sea
to great heights. Professor James For3es of Edinburgh has laid down an assumed
curve, in which the diurnal oscillation amounts to -1190 at the equator, and nil at
latitude 64° 8' N. ; and beyond that latitude the tide occurs with a contrary sign,
the maximum hour becoming the minimum. More extended and careful observations
in different parts of the earth will probably confirm the empirical law sought to be
established by Professor Forbes, but our present meteorological data offer many ex-
ceptions to it. In the valuable table given by Professor Forbes in his paper*, there
are exceptions to his law in the observations of Russell at Boorhanpoor, and Prinsep
at Benares, each for three years. The mean diurnal oscillation, agreeably to the
former, in latitude 24° 4', being less ('0877), mean temperature 75°'2, than that at
Benares (-1059), mean temperature 78°'8, in latitude 25° 30'. Mr. Goldingham in
1823, at the Madras Observatory, latitude 13° 5', observing every tenth day, found
the diurnal oscillation amount only to -0790, mean temperature 81°-69. At Ava in
the Birman empire, latitude 21° 51', agreeably to Major Burney, the oscillation
amounted to -1260, mean temperature 78°-39, being greater than in any other series
* Transactions of the Royal Society of Edinburgh, vol. xii. Part I. p, 170.

176 LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

of observations made in India. My own observations are also exceptions to the law.
In latitude 18° 30', at 1823 feet, with a mean temperature of 78°, the mean diurnal
oscillation for one year, at the limit hour of the tide, was -1166, whilst in Calcutta,
latitude 22° 33', mean temperature 78°* 13, the mean of three years' oscillations (1829,
1830, and 1831,) give only "1100; and as the observer was Mr. Prinsep, his name
is a guarantee for his accuracy.

But the exceptions are not confined to the tropics, for we find that the mean of
five years' observations at Marseilles, latitude 43° 16', mean temperature 60°*8, gives
a less oscillation (-0326*) at a few toises above the sea than at Berne, latitude 46° 57',
mean temperature 53°'6, at 532 toises above the sea, where the mean of ten years'
observations gives an oscillation of •0354-}-. Here, therefore, the oscillation unques-
tionably should have been less, because the latitude is higher, the temperature lower,
and the height above the sea greater. But these discrepancies may be attributed to
the observations not having been taken at the exact limit hours of the tides, and do
not therefore give the true oscillation ; nor will satisfactory light be thrown upon
the irregularities of the tides until hourly observations are made for lengthened pe-
riods in various parts of the earth.

On the subject of decrement in oscillation, consequent on elevation above the sea,
I have collected such data as were available, and have thrown them into the form of
a table. Humboldt found that at the Caraccas, at 936 toises above the sea, the
oscillation was greater ('1063 J, mean temperature 69°*8,) than at Cumana at 10 toises
above the sea, where it was '1004, mean temperature 78°'8. My own careful obser-
vations at Poona furnish a similar anomaly. At 1823 feet above the sea the mean
oscillation for a year was greater ("1166) than at Bombay, where for nine months the
mean was -0765 at the Engineer Institution ; and in my occasional visits I found it
respectively -0836 in April 1827, '1123 in March 1828, and '1141 in December 1828.
At Madras, in a lower latitude than Poona, at the level of the sea, I have shown it
to be only '0790 ; whilst at Calcutta, in a higher latitude than Poona, the means of
three years make it '1100. Proceeding to higher levels, however, we find a marked
diminution in the extent of the diurnal tide. At Mahabuleshwur, at 4500 feet, the
means of eight months reduce the oscillation to '0694 ; at Hurreechundurghur, at
3900 feet, the oscillation for the three hottest months was "0969 ; whilst at Kota-
gherry, at 6407 feet, it was for five months from noon to sunset only '0498. The oscil-
lation at Mahabuleshwur, at 4500 feet, was in fact less than Humboldt's oscillation
at Mexico of -0708 at nearly 7000 feet.

When we pass to the other tides we find the same puzzling anomalies. The mean
rise from sunrise to 9 — 10 a.m., whether at Hurreechundurghur, at Mahabuleshwur,
or Kotagherry, instead of being less than at Poona, is in fact greater. The mean of
three years on the level of Poona gives -0445, whilst the first place gives -0488, the
second place -0476, and the last '0490. The maximum night tide, on the contrary,
* 0™°»'83, t 0""n-90. X 2«"°'7o.

AND METEOROLOGY OF DUKHUN.

177

is infinitely greater at Poona than at Mahabuleshwiir or Kotagherry (it was not de-
termined at Hurreechundurghur), being -0884 at Poona, '0439 at Mahabuleshwur,
and '0430 at Kotagherry. The fourth or minimum nocturnal tide occurring in the
dead of night, has been rarely observed at the exact a.m. limit hour ; but the obser-
vations have been taken at sunrise, which is from one and a half to two hours after
the turn of the tide. I have previously shown that at different times I found this
tide to amount to —'0150, —'0254, -'0010, and +'0053, and —'0040; taking the
mean of these, after deducting the plus sign, we have '0134 as an approximation to
the amount of the oscillation in this tide ; and this corrected for a presumed propor-
tional increase from 4 a.m. to sunrise, would make its value '0181. During eight
months at Mahabuleshwur Dr. Walker found the mean fall from 10 — 11 p.m. to
sunrise to be -0180, thermometer — 1°'68 ; corrected to 4 a.m. it would be about '0240.
Mr. Dalmahoy at Kotagherry, at 6407 feet, found the fall from 9 — 12 p.m. to a little
before sunrise, amount to -0350 ; and as it is probable he took his observations as often
after the tide had turned at 10 — 11 p.m. as he took them after the limit hours of the
4 — 5 A.M. tide, the errors may be considered as compensating each other, and the
oscillation may be left uncorrected.

Mr. Prinsep, in a voyage of thirty two days from Calcutta to Bombay, found the
fall of the barometer from 10 p.m. to sunrise, amount to -022, which corrected to 4 a.m.
would be about -0293. Correcting the rise of the tide from sunrise to 9 — 10 a.m.
in the same rough way, the following will be the amount of the mean oscillation
of the barometer in the different tides.

Nocturnal/aZ/mg

Diurnal rising

Diurnal max-

Nocturnal max-

minimum tide

tide from

\m\imfaUing tide

imum rising tide

from 10—11 P.M.

4 5 A.M. to

from 9—10 a.m.

from 4 — 5 p.m.

to 4—5 A.M.

9 10 A.M.

to 4 — 5 P.M.

to 10—11 P.M.

Mr. Prinsep, 32 days, level of!
the sea J

-•0293

+ •0587

-•1020

+ •0800

M. DuFERREY, Ship Coquille, "1

—•0669

+ •0629

-•1417

+ •1259*

Payta, lat. 5° 5' S., two days/

Mr. GoLDiNGHAM, Madras Ob- 1

—•0350

+ •0470

-•0790

+ •0630

servatory, every tenth day. . /

Mr. Hudson, Royal Society, ^
London J

—•0162

+ •0185

-•0289

+ •0272

Colonel Sykes, 1800 to 2000"!
feet, Poona, one year /

—•0181

+ •0445

-•1166

+ •0884

Dr. Walker, 4500 feet, Maha- 1
buleshwur, ten months . . . . j

—•0240

+•0636

-•0694

+•0439

Mr. Dalmahoy, 6407 feet, Ko- \
tagherry, five months j

— •0433

+ •0490

-•0498

+ •0430

1

The observations of Duperrey, Goldingham, and Hudson were made during the
limit hours of the several tides, and have not in consequence any correction applied
by myself. Prinsep's, Dr. Walker's and my own observations are corrected from
sunrise back to 4 a.m. ; but the other tides are as they were observed. Mr, Dalma.

MDCCCXXXV.

* Humboldt, Personal Narrative, vol. vi. part ii. page 703.
2 A

178 LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

HOY*s hours of observations have been previously noticed. M. Duperrey's observa-
tions were made every fifteen minutes, but continued only for two days ; and it is
remarkable, although the first day gave a diurnal maximum falling tide of • 1417, the
next day gave only '0984 : any deductions, therefore, from observations for short pe-
riods of time even in the tropics must be fallacious. The above data unquestionably
prove the existence oi nocturnal tides, of which doubts exist, or did exist, in Europe ;
although Humboldt says they were observed in Dutch Guiana as far back as 1 722
by a naturalist whose name is unknown.

Unhappily, during 1 830, whilst observing the exact time of the turn of three tides,
I was so harassed by public duties, that I omitted to record the barometer at sim-
rise, and therefore want the data to assist in determining for any lengthened conti-
nuous period the amount of the tide between 10 — 11 p.m. and 4 — 5 a.m. or sunrise.
But as there is a remarkable accordance in the absolute height of the barometer at
Poona during the monsoons of 1829 and 1830, if I were to adopt the mean height of
the barometer at sunrise in 1829 for 1830, and then deduct this amount from the
mean height at 10 — 11 p.m. in 1830, we shall have '0332 as the value of the oscilla-
tions, which, corrected to 4 a.m., will give '0442 as the value of the falling tide between
10 — 11 P.M. and 4 — 5 a.m.; and this amount I have little doubt would be infinitely
nearer the truth than my forty or fifty nights' observations taken at different periods.

From the above short table it will appear that in my observations for four years,
the maximum oscillation was between 9 — 10 a.m. and 4 — 5 p.m. ; the next greatest
was that between 4 — 5 p.m. and 10 — 11 p.m., amounting to a little more than 75f
per cent, of the preceding fall : then follows the rising tide between 4 — 5 a.m. and
9 — 10 A.M., amounting to nearly 40 per cent, of the diurnal tide ; and finally comes
the falling tide between 10 — 11 p.m. and 4 — 5 a.m., which by the few direct observa-
tions I made would not be more than 15 J per cent, of the great tide, but which by
the process above noticed, I suppose would be about 38 per cent. ; and this would
accord tolerably well with Mr. Prinsep's proportion, which is nearly 28| per cent.
I shall not remark upon the discrepancies between the ratio thus eliminated, and that
deducible from the observations of the other gentlemen quoted in the Table. One fact,
however, appears established by all the observers, that the greatest oscillation is du-
ring the day, the least during the night ; the second greatest from 4 — 5 to 10 — 1 1 p.m.,
and the second least from 4 — 5 to 9 — 10 a.m. ; and that all the irregularities occur
within comparatively narrow limit hours.

My barometrical observations were taken on various levels, excepting for the yearly
residence of five or six months at Poona during the monsoon, and for the entire year
1830: the statements of the absolute height of the barometer and the annual and
monthly changes of pressure of the atmosphere will therefore be comparatively limited;
and it may be as well to confine my remarks almost entirely to the year 1830. The
maximum height of the barometer, and the mean monthly maximum in that year,
both occurred in January, the former being 28*242 inches, thermometer 73°-6, and the

AND METEOROLOGY OF DUKHUN. 179

latter 28087 inches, thermometer 75°4. The minimum height in the year and the
mean monthly minimum, in like manner, both occur in the same month, July, the
former being- 27'570 inches, thermometer 75°, and the latter 277666, thermometer
76°'95. The annual range of the barometer, therefore, amounted only to "6720 ;
and the difference of the thermometer at the extreme periods was l°-4 ; the greatest
monthly range, -3710, was in November ; the difference of the attached thermometer
at the extreme periods was 10°'2 ; the smallest monthly range of -2170 was in Au-
gust ; the difference of the attached thermometer at the extreme periods being 0°'5.
In 1827 the barometer ranged during six months whilst I was stationary, only -5103.
In seven months in 1828 it was -3656, and for seven months in 1829 it was -4867;
and in no instance did a range of eight tenths of an inch come under my observa-
tion, even in comparing the maximum of one year with the minimum of another.
Whilst in England, at Edmonton and Cheltenham, in 1827, the extreme range of the
barometer was respectively 1*88 inch and 175 inch. In 1828, at Edmonton, Chel-
tenham, and Weycomb, the range was 1*44 inch, 1*41 inch, and 1-61 inch respectively.
An inspection of my tables will show that in four years, in the five monsoon montJis,
from the maximum height 28' 1343 inches, thermometer 76°'4 in October 1827, to the
minimum height of 27'570, thermometer 75° in July 1830, the range amounted only
to "5643, difference of thermometer attached 1°'4. In looking over Mr. Goldingham's
tables for twenty-one years at Madras, the greatest annual range (with a solitary ex-
ception of 1-430 inch in a terrific hurricane in May 1820,) amounted to '9640 in 1818,
and the greatest monthly range was in October of the same year 7940 ; the smallest
annual range was '4620 in 1814; in fact, the annual range very rarely exceeded
six tenths of an inch.

I found the mean monthly pressure of the atmosphere at its maximum in the
coldest months, December and January ; it gradually diminished until July or Au-
gust, the most damp months ; and gradually increased again until the cold months.
Mr. Goldingham's means of twenty-one years give nearly the same results ; the maxi-
mum pressure 30*085 inches, thermometer 75°' 1 68, being in December or January;
it then diminishes until May, June, and July, the mean height of the barometer,
29*860, thermometer 86°*907, being nearly the same in those months. But it is to
be remarked, that two of these months, which atPoona are the most damp, at Madras
are the hottest of the year : the minimum pressure, therefore, was as independent of
moisture at Madras, as it was independent of extreme heat at Poona. From July the
pressure gradually increases as at Poona, until December or January. Three years'
observations at Calcutta indicate the same alternations. The barometer is highest in
January, 30*0225 inches, and lowest in June, 29*5155 inches. At the Havannah the
mean of three years gives a maximum pressure in January and a minimum in Sep-
tember. Opposed to these indications of uniformity of atmospheric action over a
wide range of latitude and longitude, M. Boussingault found the maximum height
of the barometer at Bogota for one year greatest in June and July, and least in Decem-

2 a2

180 LIEUT-COLONEL SYKES ON THE ATMOSPHERIC TIDES

ber and January *. The means of four years' observations, from 1827 to 1830 inclu-
sive, made by Mr. Hudson at the Royal Society, give two maxima and two minima
in the year, the former occurring in February and October, and the latter in April
and September. Professor Forbes's observations in the same years at Edinburgh give
a mean maximum in the winter months, December, January, and February, of 29-442
inches, and a mean minimum in spring, March, April, and May, of 29*0359 inches.

The annual mean height of the barometer at Poona was 27*9254 inches ; at Ma-
dras for twenty-one years it was 29*958 inches ; at Calcutta the means of three years
make it 29*764 ; M. Arago, at Paris, by nine years' observations, reduced to the level
of the sea, makes the mean height 29*9546 inches, almost identical with the mean
height at Madras.

The climate of Dukhun is subject to very considerable variations of temperature,
more, however, in the diurnal than in the monthly or annual ranges ; indeed, less so in
the last particular than in Europe. In 1827, the extreme range of the thermometer
at Edmonton was 75° Fahr. (83° highest, 8° lowest) ; at Cheltenham it was 64°*5
(80°*5 highest, 16° lowest) ; in 1828 at Edmonton it was 61° (83° highest, 22° lowest).
These extremes are even exceeded on the continent of Europe. In St. Petersburgh
the thermometer has been as low as 35°*7 below zero, and as high as 91°* 4, the range
therefore 127°' 1. At Berne in Switzerland the range has been from 24° below zero
to 95°*25 Fahr. The extreme range of my thermometer in 1 826 was from 93°*9 to
40°*50 or 53°*4 ; the former occurring on the 12th of March at 4 p.m., and the latter
on the 15th of January at sunrise. In 1827 the extreme range was from 96°-8 to 48°,
exhibiting a difference of 48°*8, the maximum being on the 28th of March at 4 p.m.,
and the minimum on the 12th of December at sunrise. In 1828 the maximum
occurred on the 7th of May at 4 p.m., being 101°, and the minimum 56° on the 16th
of February and 4th of December at sunrise, the range not exceeding 45°. I have to
remark, however, that for a short time on the 7th of May, the thermometer rose to
105° (this was at the source of the Beema river, at a height of 3090 feet above the
sea), the highest record of the instrument I have ever had in Dukhun, in the shade, in
very many years' observations. These occasional manifestations of extreme heat would
appear not to be confined to the equatorial regions, there being many similar in-
stances in the temperate zones. At Montpelier in France, in 1823, the thermometer
stood for some days at 100° Fahr. In Paris, in 1793, it was at 99°*6 ) and Humboldt,
in his Personal Narrative, mentions, on the authority of Arago, it being even 101°* 12
Fahr. at Paris. The range of the thermometer in Paris, between 1793 and 1795 in-
clusive, was from 8°*6 below the freezing-point of Fahr. to 99°*6 or 81°.

The monthly means do not differ much from each other in Dukhun. In 1826 the
difference between the means of the hottest month, May (83°*28), and the coldest, Ja-

* January, 0""»-56045 ; Temperature 15°-7. June, 0'"'"-56124; Temperature 15°-1.
December, 0""»-56013; Temperature 15°-0. July, 0"""-56134; Temperature 14°-2.

Humboldt, Personal Narrative, vol. vi. part ii. page 743.

AND METEOROLOGY OF DUKHUN. 181

nuary (65°-90), was only 17°-38. In 1827 January was the coldest month, and the hot-
test was April, their mean difference being 1 4°'06. In 1828 the coldest month was De-
cember and the hottest May, their difference 15°'41. In 1829 March was the hottest
and November the coldest, their difference 13°'66. The greatest diurnal range in 1826
was 37°-30, on the 5th of March, from 50°*5 to 87°-8. In 1827 it was 39°-5, on the 12th
of December, from 49°-5 to 89°. In 1828 it was 34°-8, on the 16th of February, from
56° to 90°*8. In 1829 the maximum diurnal range was 37°'5, in December. The least
diurnal range in 1826 was on the 22nd of August, amounting only to 0*60. In 1827
it also occurred in August (9th), being only 0°-40. In 1828 the minimum range was
on the 18th of October, amounting to 0°'40 ; an unprecedented circumstance in that
month. In 1829 the minimum range was 0°-60, in August. In 1830 it was 0°'5, in
July.

With respect to the greatest diurnal and the greatest monthly range, of the ther-
mometer, the winter months have a range nearly in a quadruple ratio to the monsoon
months, June, July, August, and September. The latter have mostly their temperature
very equable, the difference of the monthly means rarely exceeding 3°, and the greatest
diurnal range in five years only once amounted to 13°*6. The latter end of March,
and April and May are the hottest months in the year, from the position of a nearly
vertical sun, the intensity of whose influence is but slightly modified by the occasion-
ally cloudy weather in May preceding the monsoon. The temperature falls in June,
and continues nearly stationary until the end of September ; it then rises in October,
but falls at the end of the month until its annual minimum in December or January.
It is low the early part of March, but rises suddenly after the middle of the month,
occasioning a difference of 6° or 8° between the means of February and March, which
is more than double that of other consecutive months in the year. The rise in
October is also sudden, but does not occasion so great a difference of means as be-
tween February and March. It will thus be remarked that the temperature does not
follow the sun's declination, owing to the interference of the monsoon.

My thermometrical observations in Dukhun were made upon levels ranging from
1400 feet above the sea to 4500. At the latter height, however, they were very limit-
ed in number, and beyond the levels of 1600 and 2200 feet they may be considered
to have scarcely any sensible influence upon a mean temperature struck for tracts
traversed between 1900 and 2000 feet. For instance, the mean temperature of Ah-
mednuggur in 1828 (1900 feet). Dr. Walker determined to be 78° Fahr., and
my mean temperature for the country I traversed in that year was 77°'93. In 1827
it was 77*25 ; and in 1826, when my researches were a good deal confined to the
hilly tracts, the mean temperature was 76°-46 ; and in 1829 the mean temperature was
reduced to 74°*8, three months' observations of the year having been taken at 3943
feet above the sea, and one month's observations at 2416 feet. One fact is very re-
markable ; the observed mean temperature of places on the table land of India is
much higher than the calculated mean temperature of the same places agreeably to

182 LIEUT.- COLONEL SYKES ON THE ATMOSPHERIC TIDES

Mayer's formula. Ahmednuggur is 1900 feet above the sea with a mean temperature
of 78° : the calculated mean temperature is 72°*27. Mhow in Malwa, at 2000 feet,
observed mean temperature 74° ; calculated 69°'86. A spring in the hill fort of Hur-
reechundurghur I found to be 69°'5 : the calculated mean temperature for the lati-
tude of that fort, at an elevation of 3900 feet, is 65°' 45. The calculated mean tempe-
rature of Poona is 72°'78 ; the observed IT'I - But I purpose enlarging on this sub-
ject in a future paper on the mensuration of heights in Dukhun, determined barome-
trically and thermometrically.

An inspection of my tables of temperature will show that the mean temperature of
9^' 30™ A.M. is almost identical with the annual mean temperature deduced from the
maxima and the minima. Professor Forbes observes that the same holds good at
Edinburgh. To show the importance of position in placing instruments for observa-
tions of temperature, in November 1828, I put thermometer No. 2 under a grass roof
adjoining the eastern wall of my house, but within twelve feet of thermometer No. 1,
which remained in its usual place. The instrument was secure from direct or re-
flected heat. At sunrise the mean for the month of No. 2 was 7°' 42 lower than the
mean of No. 1 ; at O'' 30™ it was 1°76 higher ; and at 4 p.m. it was 2°-71 higher-, but
its mean for the whole month was 2°*35 less than the mean of the thermometer kept
in the house near the open window.

To ascertain the numerical cooling effect of shutting out the external diurnal air
from acting upon the thermometer in the hot months, I hung thermometer No. 2, in
the month of April 1827, in my drawing-room, communicating by double doors with
a large dining-room surrounded by an inclosed and glazed verandah. I had all the
external windows and doors carefully shut at 7 a.m. daily, and opened again at sun-
set. Thermometer No. 1 was in its usual place in my library, with a free circulation
of air. Thermometer No. 2 was 1°*73 higher than No. 1 at sunrise ; at 9^ 30™ a.m. it
was 0°-63 Icrwer ; and at 4 p.m. it was 5°'5 loiver ; and the difference of the monthly
means was 3°'62 minus in favour of thermometer No. 2. There cannot be a doubt,
therefore, of the advantage of closing a room in the tropics during the heat of the day.

My hygrometric observations with Daniell's hygrometer for forty-three months,
from April 1826 until March 1828, and from June 1829 until January 1831, were
very complete and satisfactory. The first great feature was the annual mean dewing-
point being higher at 9 J a.m. than at sunrise or 4 p.m., excepting in 1829 — 1830 ; but
it did not uniformly hold good in each month of the year. In 1826 the mean dewing-
points in Dukhun at sunrise and 9j a.m. were respectively 66°'58 and 67°*56 ; tem-
perature of air 73°'66 and 77°'53, containing 7*473 and 7*634 grains of water in a
cubic foot of air ; but in the monthly means, October had a higher dewing-point at
sunrise than at 9 J a.m. : October, however, was the only month in which this occurred.
In the mean for 4 p.m., September had a higher dewing-point at 4 p.m. than at 9\ a.m.
On the whole, it may be asserted that the mean dewing-points of the three periods of
the day were tolerably uniform, although at 4 p.m. there was a much less absolute

AND METEOROLOGY OF DUKHUN. 183

weight of moisture in the air, allowing for the correction for increased temperature,
than at sunrise or 9 J a.m. From June to December, inclusive, the mean dewing-point
was 66°75, mean temperature 77°'23, a cubic foot of air containing 7*455 grains of
water.

The highest dewing-point recorded in Dukhun in 1826, occurred at 4 o'clock on
the 2 1st of October, being 76° ; temperature of air 84°*50 ; a cubic foot of air con-
taining 9-945 grains of water. The lowest dewing-point occurred at sunrise on the
4th of December, being 44° ; a cubic foot of air containing 3 '673 grains of aqueous
vapour at a temperature of air of 56°. But the lowest dewing-point did not indicate
the driest state of the atmosphere, as a dewing-point of 45° in November, with a tem-
perature of 87°, at 4 P.M. gave only 3*587 grains of water in a cubic foot of air. The
most moist month was July, the mean weight of water in the atmosphere in a cubic
foot of air being 8*775 grains, and the point of saturation 4°*85 from the dewing-point.

The greatest monthly range of the dewing-point was in October (30°), and the
smallest range in July and August (7°). An inspection of the monthly ranges will
show that they conform to a limited extent only with the ranges of the barometer
and thermometer. From June to December inclusive, the extreme dewing-points
differed 32°.

In 1827 my hygrometric observations are complete for the whole year. The fol-
lowing are the results. In the means for the months, as in 1826, with the exception
of part of April and the months of May and October, the 9 J a.m. means give a greater
quantity of moisture in the atmosphere than at sunrise ; the mean for the year at half-
past nine having a dewing-point of 60°*74, temperature of air 78°'50, the cubic foot of air
containing 6*140 grains of moisture ; and the yearly mean at sunrise having a dewing-
point of 59°*26, temperature 71°'20, and the cubic foot of air containing 5*940 grains
of aqueous vapour. In part of April and in the month of August only does the mean
at 4 P.M. give a higher dewing-point and a greater quantity of vapour in the air than
at 9j A.M. and at sunrise. In August we find a cubic foot of air at 4 p.m. containing
8*692 grains of aqueous vapour.

The quantity, however, is only great in relation to the quantity contained in the
air at other hours of observation in the same month, and it will not bear comparison
with the mean quantity held suspended at other periods during the monsoon ; for
we see by the Table, that in June, at 4 p.m., a cubic foot of air held 8*883 grains of
water, and the other hours of observation had still larger quantities: nevertheless the
monthly mean indicates August being the most moist month in 1827; for although
a cubic foot of air contained only 8*574 grains, and June held 8*931 grains of
water in a cubic foot of air, yet the difference between the dewing-point and the tem-
perature of the air in August was only 5°*18, while in June those points were 7°'51
from each other : the air in August, therefore, was nearest to saturation ; but the re-
maining months of the monsoon differ very slightly from these results. The highest
dewing-point in Dukhun, in 1827, occurred at 4 p.m., on the 13th of June, being 76°,

184 LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

temperature 79°; a cubic foot of air containing 10-049 grains of aqueous vapour.
This may be looked upon as great, the temperature of the air at Poona being rarely
7&° Fahr. when it absolutely rains.

A very dry state of the atmosphere occurred in January, the dewing-point on the
4th of the month at sunrise being obtained three degrees below the congelation of
water, temperature 62°. A cubic foot of air at this observation contained 2*146 grains
of water ; but this did not indicate the driest state of the atmosphere, the dewing-
point from the point of saturation being 33°, while on the 5th of December it diifered
46°, the dewing-point being 37°, and temperature of air 83°.

As in the preceding year, the smallest range of the hygrometer is found in July and
August. From these months there is a rapid increase in the range until January,
when the greatest monthly range occurs, namely 38°. December has also a very high
range of 32°. The extreme range in the year amounts to 47° ; that is to say, from a
dewing-point of 29°, temperature 62°, in January, to 7^"", temperature 79°, in June.

In 1827, as in the preceding year, there is a limited conformity in the range of the
hygrometer to that of the thermometer. The monsoon months have the smallest
range, the cold months the greatest, and the remaining months a range between
those already noticed.

In 1828 my hygrometric observations in Dukhun extend through three months
only. In these months, as in the preceding years, there was more aqueous vapour in
the atmosphere at 9J a.m. than at sunrise or at 4 p.m. In February of this year the
lowest dewing-point ever recorded on the general level of the country took place,
being 5° below the freezing-point, namely, 27° Fahr., the temperature of the air being
57°'50, and a cubic foot supporting 2*032 grains of aqueous vapour. Even this is not
the lowest degree of absolute dryness remarked in the Dukhun, as on the hill fort
of Loghur, on the 12th of March, the dewing-point, although 27° Fahr., took place
when the temperature of the air was Q7° Fahr. : consequently, a cubic foot of air
contained only 1*995 grains of aqueous vapour instead of 2*032 grains. A yet further
degree of dryness occurred on the 1 6th of February at 4 p.m., at Downd, near Pair-
gaon, on the.Beema river, when the dewing-point was 61° from the point of satura-
tion, the former being 29°, and the temperature of the air 90°. The highest dewing-
point in the three months of winter occurred at 9 J a.m. in January, namely, 69° Fahr.,
the weight of moisture being 7*988 grains; a state of the atmosphere which may be
looked upon as very unusual in that dry month. The range of the dewing-point in
January (37°) approximates very closely to that of the same month in the preceding
year. The same observation applies to the month of March ; but there is a discre-
pancy with respect to February.

In 1 829 my observations extend from June to December, inclusive : the mean of
the three periods of the day is nearly identical for the monsoon months, viz. 69°*03,
69°*77 and 70°*06 : the maxima, 77°, occurred in June and October at 4 p.m. ; the
minima all in October, 58° at sunrise, 50° at 9j a.m., and 44° at 4 p.m. The mean

AND METEOROLOGY OF DUKHUN. ']8o

dewing-point for the monsoon was 69°-62, temperature of the air 75°-83, the cubic
foot of air containing 8* 191 grains of water; the maximum diurnal range 6° in Sep-
tember, and the maximum monthly range 8° in June and September. In October
the mean dewing-point fell to 65°*83, temperature 78°' 13. The maximum diurnal
range increased to 26°, and the extreme monthly range was 33°. In 1830 the ob-
servations are only complete for 9 — 10 a.m. : the mean dewing-point was 61°-9, mean
temperature 78°'4, and a cubic foot of air contained 6*351 grains of water : the ex-
treme range of the hygrometer was 47°, and the lowest dewing-point 31°, tempera-
ture 50°, in December. An inspection of the tables Nos. 17 — 21 will show the gradual
increase of moisture in a cubic foot of air from the most dry month, February, until
June or July. Hence the moistness remains nearly stationary until the beginning of
October, when it diminishes, somewhat rapidly and regularly, until February.

It might be supposed that the hottest months in the year, March, April, and May,
would also be the driest ; but such is not the fact. The powerful action of the sun
on the ocean in the middle of March raises a large quantity of aqueous vapour, which
continues to increase in the ratio of the sun's progress north. The westerly winds
waft this aqueous vapour inco Dukhun : much of it is arrested by the Ghats and
hilly tracts eastward of those hills ; accounting for the sensible moistness of the air,
the frequent night-fogs, and deposition of dew on this line in the end of March and
in all April and May. The supply of moisture diminishes in proportion to the
distance eastward from the sea to the limits of the Coromandel coast monsoon : we
in consequence find the Ghats, Poona, Ahmednuggur, and the Bala Ghat, all with
very different dewing-points in the hot months.

My visits to Bombay on public duty in successive years, in the hot and cold
months, enabled me to determine, in the most satisfactory manner, with the aid of
I Daniell's hygrometer, the usual surcharged state of the air of the coast with mois-
ture, and its ample means of supplying the interior table land with aqueous vapour.

In April and May 1826, in Bombay, the monthly mean dewing-points were respec-
tively 72°'84 and 75°'59, temperature 83°-48 and 84°-52, a cubic foot of air holding
8*988 grains, and 9*748 grains of water suspended ; whilst July, the most rainy
month during the monsoon at Poona, had only a mean of 8*775 grains of water
suspended. In 1827 the mean of ten days' dewing-points in Bombay in April gave
10*243 grains. The greatest mean quantity at Poona during the monsoon in June
was only 8*931 grains of water in a cubic foot of air. In 1828 I was enabled, in the
month of March, to establish comparisons, derived from observations on consecutive
days, between Bombay, the top of the Ghats, the hill fort of Loghur, and Poona.
At' 4 P.M. in Bombay, on the 10th of March, a cubic foot of air held 11*205 grains of
water. At Poona, at the same hour on the 14th of March, a cubic foot of air con-
tained only 2*273 grains of water. At Bombay, on the 10th, at sunrise and at
9i A.M., the dewing-points were respectively 72° and 71°, temperature 75° and 81°*50;
a cubic foot of air containing 8*873 grains at the former hour, and 8*487 grains of

MDCCCXXXV. 2 B

186 LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

water at the latter hour. The following morning, at Kundallah, on the top of the
Gh^ts, 1744 feet above the sea, at the same hours, the dewing-points were 36° and
40°, temperature 72° and 78°, equivalent only to 2*690 grains and 3*004 grains of
water in a cubic foot of air. In the afternoon of the same day, at Karleh, 2015 feet
above the sea, seven miles east of Kundallah, a cubic foot of air held 2954 grains,
and on the 12th, at 4 p.m., 2'61 1 grains of aqueous vapour. On the summit of Loghur,
3381 feet above the level of the sea, and 1366 feet above Karleh, the dewing-point
at sunrise the next day was 5° Fahr. below the freezing-point, temperature of air 67° ;
and a cubic foot of air held only 1 -995 grains of water in a state of vapour.

These facts fully establish the remarkable discrepancies between the hygrometric
state of the air in Bombay and Dukhun, and that too within a difference of a few
miles of latitude and longitude. A comparison of the absolute fall of rain in Bombay
and in Poona for the years 1826, 1827, and 1828, shows an agreement (to a certain
extent) in their ratio to the relative hygrometric state of the air at Poona and Bombay
above noticed*. The occasional extreme dryness of the air in the months of Decem-
ber, January, February, and part of March, is productive of some inconvenience; new
furniture cracks, planks separate from each other, doors shrink so much that the
locks will not catch ; the leaves of card-tables warp, and manifest a disposition to
curl up, and are only kept level by the constant application of brackets ; ink disap-
pears as if by magic, and the nibs of pens, by their recession from each other, mani-
fest a provoking mutual antipathy.

I will confine my observations on the fall of rain in Dukhun within a narrow com-
pass, as a glance of the eye over the Tables, Nos. 23 — 28, will afford every infor^
mation. The rains are light, uncertain, and in all years barely sufficient for the
wants of the husbandman, and a slight failure occasions much distress. They usually
commence at the end of May, with some heavy thunder showers from the E. to the
S.E., the lightning being terrific, and frequently dangerous. They set in regularly
within the first ten days in June, and continue until the end of September from the
W. to the S.W., and break up with thunder storms from the E. to S.E. before the
middle of October. During the remaining months of the year an accidental shower
or two may fall from the Coromandel monsoon ; and the further the distance east-
ward from Poona, the greater the chance of showers in the cold months. The
monsoon temperature is equable and agreeable, and the rain occurs almost always
in showers, rarely continuing uninterruptedly for a day or more, as is common on
the coast and in the Konkun. There does not appear to be any uniformity in the

* The mean annual fall of rain in Bombay for those years was 93" 62 inches, and the mean fall at Poona
26' 926 inches, or 28|- per cent, only of the fall in Bombay. The absolute weight of aqueous vapour at
Poona in March 1828, was 4\^ per cent, of the quantity suspended in the air in Bombay in the same month.
The comparison of the means of the annual fall of rain in Bombay for twelve years, from 1817 to 1828 in-
clusive, viz. 82-01 inches, and of the fall of rain at Poona, 23-43 inches, from 1826 to 1830 inclusive, gives
the same result.

AND METEOROLOGY OF DUKHUN. ' 187

fall of rain in the same months in consecutive years. In 1826, July was the most
rainy month, and August the driest. In 1827, June had the most rain, and July the
least. In 1828, July was the most rainy, and, unlike the two preceding years, June
the least so. In 1829 and 1830, June had the most rain, and September less than
any monsoon month for many years previously. In five years' observations in Dukhun,
the greatest quantity of rain fell in the months of June and July. October, the month
in which the monsoon breaks up, is the next most rainy, but the rain falls in a few
heavy squalls, and the greatest part of the month is quite fair and bright. September,
August, and May follow in the order of their aggregate supply of water. In those
five years no rain whatever fell in February, twice only in December, and only once
in January, March, and April respectively. The mean annual fall was 23j inches,
while the mean fall for twelve years in Bombay, only 80 or 90 miles to the westward,
was 82 inches. The clouds supplying the monsoon torrents would appear to have a
low elevation, as I have frequently seen through breaks, as they were passing rapidly
from the west to the east, a superior stratum, apparently stationary, or moving slowly
in a contrary direction, and gilded by the sun's rays. The greatest fall of rain in any
one day was 2*58 inches, on the 6th of July 1826 ; and in the whole five years there
were only six other instances of the diurnal fall having exceeded 2 inches, namely,
on the 15th of January, 2*17 inches; on the 29th of June, 2*57 inches; on the 26th
of September 1827, 2*54 inches; on the 30th of August 1828, 2-24 inches; on the
24th of June 1830, 2*31 inches; and 25th of July, 2*4 1 inches.

At Hurnee, on the coast of the southern Konkun, on the 15th of June 1829, there
is a record of 8*133 inches of rain in the 24 hours. In the year 1828, in Bombay,
there is an instance of a similar diurnal fall of rain on the 24th of June, viz. 8*67
inches ; and in July of the same year, on the 12th and 18th, there fell respectively
7*40 and 7'45 inches of rain.

The mean annual fall of rain for all England, from many years' observations, is
32*2 inches ; but the means of difl:erent counties vary from 67 in Cumberland to 19
in Essex.

The direction of the wind was carefully recorded three times daily for the years
1826, 1827, 1828, 1829, and 1830. The great features in these observations are the
prevalence of winds from the west and westerly quarters, east and easterly points,
and the extreme rareness of winds from the north and south, and the points ap-
proximating to them, and these features appear to be constant in the several years.
In 5229 observations, the wind blew from the west or points adjoining 2409 times ;
and in this number the south-west (305) and north-west winds (122) amount only to
427, including the record of south-west winds (159) in May, June, and July 1826,
which in truth were so westerly, that in the succeeding years in the same months
they were classed as westerly winds, their inclination in general being more to the
west than to the south of west-south-west, thus leaving 2141 observations of the wind
almost exclusively from the west. The records of the easterly winds, including south.

2 b2

188 LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

east (103) and north-east (143), in five years, amount to 949 : of this number 246 are
from the points north-east and south-east, leaving 703 from the east. There is a re-
markable paucity of northerly and southerly winds, there being records of the wind
blowing from the north only 1 15 times, and from the south but 36 times. Another
remarkable feature is the frequent absence of wind, particularly at sunrise ; and more
so in the months of January, February, March, October, and November, than in other
months of the year. The cessation of wind from the month of May to September in-
clusive, is comparatively rare ; and generally throughout tlie year the absence of wind
at 4 P.M. may be looked upon as unusual. In five years there are 1720 observations
of "No wind," and 847 of these belong to sunrise, 452 to 9 — 10 a.m., and 304 only to
4 P.M., and 117 to 10 — 11 p.m. in 1830. An inspection of the Tables will show that
there is very considerable uniformity in the direction of the wind in the same months
in consecutive years. The westerly winds begin to prevail in March, alternating with
the easterly winds, which blow during the latter part of the night, and up to 7 or 8 a.m.
At first they are to the northward of west, but they gradually come round to the west,
and for the few last days in May and first week in June they are from the south-west ;
but when the rains fairly set in, they are limited to west and west-south-west until the
beginning of October. In this month they are variable, and the records of " No wind*'
increase suddenly and rapidly. A few easterly winds, however, indicate the change
which is about to take place ; they gradually increase, and with those from the north-
east and south-east, almost entirely supersede the winds from the westerly points. In
March, from the sun's approach, the interior land during the day gets heated ; an
influx of air from the sea-coast commences after 10 a.m. ; but as the earth at this
period cools more rapidly than the sea at night, the interior is cooler than the coasts,
and there is a reflux of air towards the ocean ; the easterly and westerly winds thus
alternate day and night. This alternation, however, diminishes in the ratio of the
sun's increasing power ; and when the earth gets so thoroughly heated that it cannot
reduce its temperature by radiation below that of the sea, the consequence is the
prevalence of winds from the westerly points to the almost entire exclusion of those
from easterly points. In June the west-south-west wind sets in as previously stated.

The winds are rarely remarkable for blowing with very great violence, unless in
the terrific but short thunder storms preceding the monsoon. At these periods trees
are blown down, thatched houses unroofed, great damage is done by lightning, and
the rain falls in a deluge. At Dholpoor in Hindoostan, in May 1805, I saw Lord
Lake's camp levelled (except where partially sheltered) in one of these squalls as if
by the wand of a magician ; and trees which had stood two hundred years were torn
up by the roots. Dense clouds of dust always precede the rain and darken the air;
and it is amidst this imposing gloom that the lightnings flash with fatal eff'ect.

The principal period of the year in which the wind is marked by its force, is in the
latter end of March, all April, and part of May. During these months it is mostly
a fresh west, sometimes strong ; and I find by a reference to my registers that there

AND METEOROLOGY OF DUKHUN. 189

are many instances of its being violent. At these times it is exceedingly exhausting
to the frame ; and few old Indians are robust enough to bear to sit exposed to its
direct action for any continuance. The easterly winds are characterized by their
extreme dryness ; the lips chap, the exposed parts of the skin are cut, and become
harsh and scaly ; windows, doors, and joiner's work shrink, and present numerous
interstices ; and to sleep exposed to the night easterly wind is to risk the loss of a
limb or a whole side. With these exceptions the winds are usually agreeable to the
feelings and of moderate force.

The hot winds (that is to say, a wind blowing over a heated extensive surface), so
well known and complained of in the interior of the Indian Peninsula and in Hin-
doostan, are of limited duration within my range of observation. They are from the
north-north-west to west, and occur in March and April. It is to be observed, that
the same westerly wind which on the Ghats may be passably cool and agreeable, will
at Ahmednuggur, and at places more to the eastward, become a hot wind. The in-
habitants of Poona and its neighbourhood are little incommoded by hot winds ; and
in my registers the records of their occurrence, even on my eastern boundary, are too
limited to constitute a marked feature.

I must not omit to notice, that in these very months of the hot winds for five years
a most unaccountable wind blew for a day or two from the north-north-west to the
west-north-west so severely cold as to be injurious to vegetation, and intense enough
to benumb the hands and feet. At Yagrah, near the source of the Mota river, on the
nth of March 1825, at sunrise, the young shoots of plants were nipped as if by a
frost, although the thermometer was down only to 42°* 10 Fahr. On the 9th of
March 1826, the thermometer was at 58° at sunrise ; the cold intense, no wind, but
a westerly wind at 4 p.m. On the 13th of March 1827, atTacklee near Ahmednuggur,
a fresh west-north-west wind was so cold at sunrise, that I could not extend the
fingers of my bridle hand, and my people had not been able to sleep during the night
from the want of warm covering. In 1828 intense cold occurred on the 2nd of Fe-
bruary at Barlonee, on the Seena river, but without wind. On the 29th of February,
whilst driving from Poona to Karleh before daylight, my limbs were positively stiff-
ened by a cold north-west wind. In 1829, at Hurreechundurghur, on the 4th of
April, in the midst of the hot season, the cold was so great, with a west-north-west
wind blowing, that a sheet, blanket, and counterpane were insufficient protection, and

I was necessitated to rise in the night and put on a flannel dressing-gown to ensure
comfortable feelings. In 1830 this wind occurred on the 2nd of March at Poona, at

I I P.M., and continued all night. It is difficult to assign a cause for these transitory
cold winds at the commencement or in the midst of the hot season.

Those curious whirlwinds, noticed by all travellers in Africa, and which in the
deserts are not only inconvenient but dangerous, are of common occurrence in Duk-
hun in the hot months. A score or more columns of dust, in the form of a speaking
trumpet or water spout, may be seen at one time chasing over the treeless plains.

190 LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

marking that vortex of heated air, which in its whirl carries up dust, sand, straw,
baskets, clothes, and other light matters, to a height of one or two hundred yards or
more. They are not dangerous, but particularly troublesome in a camp, striking the
tents, and scattering about all light loose matters on the surface ; and the rushing
noise with which they come terrifies horses, and induces them to break from their
pickets. They are sufficiently powerful also to lift oflf the grass roof of a hut ; and I
have known instances of officers' houses having shared the same fate. They appear
and disappear with great suddenness ; and I have been frequently startled by hearing
a loud sound of air rushing from all parts to a central axis, round which it furiously
whirls, and on the instant finding myself enveloped in one of these " devils," as they
are called by Europeans in India.

During the dry months of December, January, February, and even during March
and part of April, electricity is occasionally so prevalent in the air, that removing
flannels with quickness from the body in the dark is accompanied with flashes of
light ; the hair crackles under the comb and emits sparks ; suddenly shaking lino-
musquito bed-curtains has been known to produce a flash ; and stripping down bed-
clothes has done the same. From the 8th of March until the 23rd of April 1829,
while in tents in the hill fort of Hurreechundurghur, at 3943 feet above the sea, in
stripping down the bed-clothes to get into bed I have frequently found my hand in
contact with the clothes enveloped in a flame of blue light. On the last date men-
tioned, at 1 1 o'clock at night, the flash was so broad, vivid, and repeated at every
movement of the bed-clothes, as to excite more than ordinary attention and surprise.
I had not the means to determine the hygrometric state of the air at the time; the
thermometer at 4 p.m. had stood at 90°'80 ; no change had taken place in the usual
movements of the barometer ; the wind up to 9^ 30™ a.m. had been east-north-east,
and from that hour until past midnight had continued at west-north west in gusts :
the night had not felt particularly dry; indeed the night of the 21st of April had
been so moist as to wet the tents. Electric shocks in filling Jones's barometer in
different parts of the country, and the terrific lightning of the storms in May, have
been already noticed.

Hail sometimes falls in the hot months of March, April, and May, in those thunder
storms to which I have alluded. The hail, which in many instances is found to con-
sist of masses of transparent ice, is of considerable magnitude. In the storms of the
21st and 22nd of April 1830 at Poona, the hail-stones were larger than marbles ; and
they were of a similar size in a hail-storm in the fort of Hurreechundurghur, at
3943 feet above the sea, in the preceding April. I have known a mass of clear ice
fall exceeding an inch in diameter, and I have been assured that much larger pieces
have been picked up. On one occasion at Poona the hail-stones consisted of globular
masses of clear ice, in which was imbedded a star of many points, of diaphanous ice
like ground glass ; and I deemed the fact sufficiently curious to induce me to make
drawings of some of the stones.

AND METEOROLOGY OF DUKHUN. 191

Dews first appear towards the close of the monsoon, on the last mornings of Sep-
tember after cloudless nights. A precipitation of moisture takes place on similar
nights in October and November. In December dews usually become somewhat
constant and copious ; and they are seen in January and February ; but they occur
under very anomalous circumstances, the causes of which I cannot explain. In con-
secutive nights of similar temperature, and similarly cloudless, dew will be found to
have been deposited one night and not the following. In September 1827, the
journal records " Heavy dew" on the nights of the 23rd, 24th, 25th, 26th, 27th, 28th,
29th, and 30th ; they then cease until the 5th of October, on the morning of which
there was a little dew ; on the 6th there was not any, and on the 7th there was a little.
They do not occur again until the 26th ; hence to the 1st of November " Dew :" sub-
sequently none until the 1st of December; hence no dew until the 6th of January
1828, when dew was met with on garden land, but not on Jield land; such continued
to be the case during the whole of January. At Marheh, Pergunnah Mohol, garden
produce was covered with a copious dew every morning ; the lands bordering the
gardens for forty or fifty yards around were slightly sprinkled with it ; but there was
not a vestige of it on the fields constituting the rising ground north and south of the
tract of garden land. I had daily experience of these facts from my habits of quail
shooting. In the young wheats I observed that the quantity of dew on the plants was
in ratio to the proximity of the time at which they had been irrigated. Plants on
land, irrigated the day previously, wetted my shoes and cloth pantaloons thoroughly
in a few minutes. Plants on land watered two days previously were plentifully
covered with dew, but I could walk through two or three fields ere my clothes were
fully saturated. Wheat irrigated three or four days previously, and bordering the
fields above noticed, had dew on it, but not sufficient to wet me through. Such rela-
tive states of moisture in adjoining fields seem to establish the fact of the local charac-
ter of dews. Aqueous vapour would appear to have been taken up by the action of
the sun during the day, suspended over the spot, and deposited at night as dew on
the land in proportion to the supply yielded by day, or the diflferent lands radiated
their heat in a different manner. My tents were within 200 yards of the fields where
I observed these phenomena ; but from the 1 1th to the 30th of January there was not
any deposition of dew about them, excepting on the 13th of January only, and the
dewing-point was but once within 4°-5 of the point of saturation. In consequence of
these observations I was induced to remark particularly the localities of dew at Poona
and in its neighbourhood. In September and October I found that when there was
not a trace of dew in the cantonment, there would be a deposition on the fields of
standing grain half a mile distant ; and when there was not any dew either in the
cantonment or in the Jields, it would yet be found on the banks of running rivulets,
and on the banks of the Mota Mola river : but with respect to the rivulets, fifteen or
twenty feet from the water were the limits of the deposition.

The local character of dew is further attested by the following facts. On the night

192 LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

of the 28th of February 1828, there was not any deposition of dew at Poona or in its
neighbourhood. Before daylight I rode thirty-four miles west-north-west to Karleh,
in the hilly tracts, and to my surprise found my baggage, which had been left exposed
during the night, dripping wet with a copious deposition. On the 1st of March I
reached Bombay at sunrise, and observed all the tents pitched on the esplanade satu-
rated with dew ; and they were nightly in this state during the period of my stay in
Bombay up to the 10th of March. On the 11th, at sunrise, on my return to Poona,
I was at Kundallah, at the top of the Bore Ghat, thirty-one miles inland from the
margin of Bombay Harbour, and at ] 700 to 1 800 feet above the sea. Dew had not
been deposited during the night of the 1 1th. On the 12th there was not any on the
summit of the hill fort of Loghur, near Karleh; none at Poona on the 13th of
March ; nor have I a record of dew again on the plains of Dukhun, unless near to
irrigated lands, until September, although in marching north in April and May, upon
the meridian of Poona, there is occasional mention of a moist soft air at sunrise ;
and when encamped in May on the Ghats, at Beema Shunkur, 3090 feet above the
sea, I was sometimes enveloped in mists rising during the night from the low land of
the Konkun, at the level of the sea, passing rapidly to the eastward, but entirely dis-
appearing by 8 o'clock a.m. The first mention of dew on the register after the mon-
soon of 1828 is on the 23rd of September, and it was very heavy. There was not any
on the 24th, 25th, and 26th. On the 27th it fell again copiously, and continued to
do so until the 6th of October. It then ceased until the 21st, reappeared, and
was deposited with occasional interruptions as in the preceding year. On the 14th
of February 1829 there was a remarkable fall of dew at Pait, on the meridian of
Poona, and thirty-two miles north of the city : with this exception there is scarcely
a record of dew in the whole of that month. From the 10th of December 1828 until
the 5th of January 1829, I was in Bombay on the esplanade ; there was a nightly
deposition of dew, not so copious as I had found it in April and May, but sufficiently
abundant on several occasions to drip from the tents in the morning. In 1829 and
1 830 the first dew appeared on the 6th of September in both years, and at intervals
afterwards as in the preceding years. These notices are sufficient to show the want
of uniformity in the appearance of dew. Its occurrence with an absolutely overcast
sky is rare ; but such was the case on the 23rd of September 1828. There are many
instances of its being met with under a misty sky, also under a sky chequered with
masses of clouds. For the most part it has been found to form most copiously in
clear nights ; but an inspection of my registers will show that in two consecutive
nights equally clear, and with trifling difference in the thermometer, one night will
be characterized by a fall of dew, the other not.

I have thought these details necessary, as a knowledge of the local deposition of
dew, and its anomalous occurrence, is of some importance in applying the correction
to the specific gravity of air in determining heights barometrically ; for in the square
of a mile the dewing-points at Marheh on the same morning at sunrise ranged from

AND METEOROLOGV OF DUKHUN. 193

30° to 65* ! ! There are some circumstances in the appearance of dew in Dukhun
militating against Dr. Wells's theory of its formation ; but more extended and care-
ful observations may possibly show that they resulted from peculiar combinations
not affecting his broad principles ; and some of the anomalies may be traced to the
different power of radiation of heat in different soils.

Fogs are certainly of rare occurrence in the Desh or open country within the limits
of my researches, although along the Ghats they prevail for six months in the year.
In the Desh they are only seen in the months of October, November, December, Ja-
nuary and February, and then only for a few mornings. By 9^ a.m. they are uniformly
dissipated. In 1826 the first record of a fog was on the 8th of October, which was
confined to the banks of the river at Poona. The same occurred on the 15th, 21st,
and 31st. On the 18th of November of the same year there was a thick fog at Beh-
loondeh, on the meridian of Ahmednuggur. On the 17th of January 1827 a thick
fog occurred at Poona, which continued until 9 J a.m. On the 31st of the same month,
and on the 1st of February, there was a partial fog until 9^ a.m. At Pairgaon, on the
Beema river, on the 29th of November 1827, there was a partial fog until 9^ a.m.
On the 31st of December, at the junction of the Beema and Seena rivers, and ex-
tending to Wangee, ten miles up the Seena, there was a remarkable fog in a stratum
a few feet thick, lying close to the ground, its upper surface being quite fiat, and not
corresponding to the inequalities of the country. In consequence it frequently oc-
curred, that in passing over slight rises on horseback, I had my head above the fog,
while my body was enveloped in it. My view ranged over a sea of mist, and trees
and houses appeared to spring from a sheet of water, the surface of which reflected
prismatic colours. On the 3rd of October 1828, at Poona, a slight fog occurred; a
heavy fog on the 6th, and the same on the 21st. On the 23rd and 24th of November
also, at Poona, there was a thick fog. It was during one of these fogs at Poona that
I witnessed a white rainbow. I had mounted my horse shortly after daybreak in pro-
secution of my accustomed ride, and galloped a few miles towards the east. Suddenly
I found myself emerge from the fog, which terminated abruptly in a wall some hun-
dred feet high. Shortly after sunrise I turned my horse's head homewards, and was
surprised to discover, in the mural termination of the fog-bank, a perfect rainbow,
defined in its outline, but destitute of prismatic colours. As the sun rose, the bow
and fog-bank disappeared. Niebuhr, in his Voyage to Africa, describes a white rain-
bow ; and Mr. St, John, in his Lives of Celebrated Travellers, mentions having seen
one, on the 21st of May 1830, in Normandy, on " the morning mist*."

At Poona, on the 12th and 22nd of October 1829, fog until 7 a.m. and 8 a.m. ; 23rd
of October, partial fog. In 1830 there is not any notice of fog. — Such are my
records of fogs in five years in the Desh, amounting only to nineteen times occur-
rence.

In the hilly tracts, and along the line of the Ghats, they have been much more

* Vol. iii. p. 121,
MDCCCXXXV. 2 C

194 LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

frequent. In March, April, and May, for several years, I was encamped for a week
or more on the crest of the Ghats. About the middle of March fogs commence to
rise, at uncertain intervals, from the Konkun. As the heat increases, the intervals
become shorter ; and from the first ten days in May I usually found myself enveloped
in a thick fog, three or four times a-week, from dark until 9 or 10 o'clock the next
day, by which time the heat of the sun had always redissolved the partially con-
densed moisture, and cleared the air. These fogs, when they were accompanied by
westerly winds, rose rapidly from the Konkun, and flew with great swiftness east-
ward. At sunset there would not be a speck upon the sky ; and within two hours,
by a fall in the temperature of the air, the aqueous vapour from the sea, suspended
over the Konkun, would be condensed, become visible, and shut out objects from view
at a few yards' distance. When there was a want of wind from the west, or light
easterly winds prevailed, the condensed vapour did not rise from the Konkun to the
Ghats, but appeared at daybreak lying upon the former, 1000 or 2000 feet below
the level of the crest of the latter, like a sea of milk in repose, on which the prismatic
colours of the rainbow were occasionally visible after the sun rose. All above would
be perfectly bright and clear, and the sky a fine blue. The tops of mountains rose
from this singular sea like islands, and the stupendous barriers of the Ghats looked
like a magnificent rocky shore. As the sun got high, the fog would be seen to creep
up the chasms of the Ghats and midway along the slopes of the ranges bounding
the valleys, at the top of the Ghats, and the Konkun would gradually reappear.

It was during such periods that I had several opportunities of witnessing that sin-
gular phenomenon the circular rainbow, which from its rareness is spoken of as of
possible occurrence only. The stratum of fog from the Konkun on some occasions
rose somewhat above the level of the top of a precipice forming the north-west scarp
of the hill fort of Hurreechundurghur, from 2000 to 3000 feet perpendicular, without
coming over upon the table land : I was placed at the edge of the precipice just
without the limits of the fog, and with a cloudless sun at my back at a very low
elevation.

Under such a combination of favourable circumstances, the circular rainbow ap-
peared quite perfect, of the most vivid colours, one half above the level on which I
stood, the other half below it. Shadows in distinct outline of myself, my horse, and
people appeared in the centre of the circle as in a picture, to which the bow formed
a resplendent frame. My attendants were incredulous that the figures they saw un-
der such extraordinary circumstances could be their own shadows, and they tossed
their arms and legs about, and put their bodies into various postures, to be as-
sured of the fact by the corresponding movements of the objects within the circle ;
and it was some little time ere the superstitious feeling with which the spectacle
was viewed wore off. From our proximity to the fog, I believe the diameter of the
circle at no time exceeded fifty or sixty feet. The brilliant circle was accompanied
with the usual outer bow in fainter colours. I witnessed these phenomena on the

AND METEOROLOGY OF DUKHUN. 195

29th of April, the 9th, 11th, and 12th of May 1829, on the hill fort of Hurreechun-
durghur.

I made some observations on solar and terrestrial radiation in 1828 and 1829,
and had purposed extending them through several months ; but unfortunately the
severe labour of my statistical duties in those years did not admit of my devoting
the necessary time to the interesting inquiry. In 1830, however, I persisted in in-
vestigating the subject day and night during the whole year, but as this paper is
already too voluminous, I must reserve the details for a future communication. I
will simply remark, that a thermometer on the grass covered with black wool at
2 P.M. on the 25th of November 1828, at Poona, rose to 164° Fahr., whilst a thermo-
meter in my library stood at 7Q°'Q\ the force of the solar power, therefore, was 87°-4,
far exceeding the maximum of any observations that have come under my notice :
and I find that grass was frequently exposed to a range of more than 111° Fahr. be-
tween sunrise and 2^ 30™ p.m.

The opacity of the atmosphere in the hot months is very remarkable. In looking
from the crest of the Ghats over the Konkun at sunrise, the sky would be free from
a cloud, and every object in the Konkun 3000 or 4000 feet below the spectator di-
stinctly visible in the intervals of the fogs previously noticed : as the day advanced
and the heat increased, the air would get misty, but without a cloud in the sky, and
by 1 or 2 o'clock objects of great magnitude only would be visible in the Konkun,
seen as through a diaphanous medium. The upper surface of this stratum of hot air
was horizontal and quite defined. I found it very rarely reach to the height of 4000
feet, and I could invariably foretell the temperature of the coming afternoon above the
Ghats, by observing at 9 or 10 a.m. the height of the upper line of the heated atmo-
sphere of the Konkun. If very high at those hours, compared with the preceding
day, the temperature would be high ; and vice versa. In the Desh or open country
above the Ghats, the heated air rises for a few feet from the ground in wavy lines ;
and objects seen through the atmosphere in this state have an undulatory flickering
motion.

Humboldt most truly says, that in judging of temperature, nothing is more deceit-
ful than the testimony of the senses : we can judge of the diff*erence of climates only
by numerical calculations. Having felt the full force of this dictum, I have thought
it necessary to expatiate fully on the meteorology of Dukhun ; and it now only re-
mains for me to show how far the preceding numerical indications are coincident
with salubrity of climate. This point I shall illustrate by a few facts equally brief
and satisfactory. I was six years and one month in Dukhun employed in my sta-
tistical labours : my followers in the field, with their famihes, always exceeded one
hundred persons, and in monsoon quarters the number was rarely below forty.
During the whole period, and amongst such a number of persons, there was not a
single casualty of an adult, and only one of an infant shortly after its birth ; and but
one case of disease that I could not cure myself without professional aid, — a degree
of healthiness which probably few other countries can equal. Dr. Walker, long civil-

2 c 2

196 LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

surgeon in the city of Abmednuggur, (exclusive of losses from spasmodic cholera,)
found the casualties in that city to be only 1*82 per cent., or 1 in 55*1 persons ; and
including cholera, 2'48 per cent., or 1 in 40*2 persons. Dr. Lawrence, in charge of
a regiment of natives 1000 strong, lost only 0*85 parts of an integer per cent., or
about 5 men in every 600 per annum during the years the regiment was in Dukhun !
In conclusion, it may be desirable to give an abstract of the facts established, and
the principal matters noticed in the preceding paper, viz. the entire removal of Hum-
boldt's doubts, founded on the authority of Horsburgh, of the suspension of the at-
mospheric tides during the monsoon in Western India : the existence of four atmo-
spheric tides in the twenty-four hours, two diurnal and two nocturnal, each consist-
ing of a maximum and a minimum tide : the occurrence of these tides within the same
limit hours as in America and Europe : the greatest mean diurnal oscillations taking
place in the coldest months, and the smallest tides in the damp months, of the mon-
soon in Dukhun ; whilst at Madras, the smallest oscillations are in the hottest
months, and in Europe it is supposed the smallest oscillations are in the coldest
months : the regular diurnal and nocturnal occurrence of the tides without a single
case of intervention, whatever the thermometric or hygrometric indications might
be, or whatever the state of the weather, storms and hurricanes even only modifying
and not interrupting them : the anomalous fact of the mean diurnal oscillations be-
ing greater at Poona at 1823 feet, than at the level of the sea in a lower latitude at
Madras : the fact of the diurnal tides at a higher elevation than Poona being less,
whilst the nocturnal tides were greater than at Poona : the seasons apparently not
affecting the limit hours of the tides : the maximum mean pressure of the atmosphere
being greatest in December or January, then gradually diminishing until July or Au-
gust, and subsequently increasing to the coldest months : the very trifling diurnal and
annual oscillations compared with those of extra-tropical climates : the annual range
of the thermometer less in Dukhun than in Europe, but the diurnal range much
greater : the maximum mean temperature in April or May, gradually declining until
December or January : the observed mean temperature of places on the continent of
India much higher than the calculated mean temperature agreeably to Meyer's for-
mula: annual mean dewing-point higher at 9^ SO"" than at sunrise or 4 p.m. : highest
dewing-points in the monsoon, and lowest in the cold months : considerable differ-
ence in the dewing-points within very short distances : remarkable contrast between
the dewing-points in Bombay and Dukhun : dew frequently local and occurring under
anomalous circumstances : rain in Dukhun only 28 per cent, of the fall in Bombay,
ninety or a hundred miles to the westward r winds principally from the westerly and
easterly points, rarely from the northerly or southerly points, and the absence of
wind frequent : electricity very abundant under certain circumstances : fogs rare, and
always dissipated by 9 — 10 a.m. : very remarkable circular and also white rainbows :
solar radiation very great : and finally, I must not omit to notice the singular opa-
city of the atmosphere in the hot weather, and the occurrence of the mirage.

AND METEOROLOGY OF DUKHUN.

197

Table I.

Oscillations of the Barometer in Dukhun, East Indies, between the parallels of lati-
tude 17° 25' and 19° 27' N., and longitude 73° 30' and 75° 53' E., at a mean eleva-
tion of 1800 feet above the sea ; the whole reduced to 32° Fahr., with correction
for the brass scale.

1827.

1828. 1

Rise of Barometer

1

Rise of Barometer

from sunrise to

Fall of Barometer from 9—10 A.M. to 4—5 P.M.

from sunrise to

Fall of Barometer from 9—10 A.M. to 4—5 P.M. 1

9—10 A.M.

9—10 A.M.

Monthly

Therm.

Max.

Therm.

Min. 1 Therm.

Monthly

Therm.

Monthly , Therm.

Max Therm, t m!„

Therm.

Monthly

Therm.

Mean.

attached.

attached.

' attached.

Mean.

attached.

Mean. attached.

i attached.

attached.

Mean.

attached.

in.

9. -

in.

o

in. 1 o

in.

in. o

in.

in.

in.

Jan.

+ •0483

+ 8-5

-1442

+ 7-5

--0664 + 5-0

-1134

+ 5^9

+ 0713 +121

-•1856

+ 10-8

-•0753

+ 8^5

-•1483

+ 13^6

Feb.

+ •0483

+ 14-4

-•1709

+ 5-5

-•0891 i + 7-

-1257

+ 8-7

+•0658 +13^07

-1791

+ 17-9

-•1048

+10-8

-•1505

+ 14-04

March.

+•0562

+ 12-9

-•1892

+ 10-0

-•0722+100

-•1248

g.r +^0439;+ 8^13
+ O'\ ++.0360 + 8-92

-1575
-1302

+ 8-5
+ 5-6

-•1038
-•0938

+ 8-5
+ 6-1

-•1386
-1123

+ 9-55
+ 7-6

April.

•+•0645

+ 10-05

-•1282

+10-0

-•0218+ 1^5

-•0836

- 005

+•0585 !+ 7^92

-•1642

+ 7-2 --1093

+ 8-5

-•1334

+ 9-97

May.

+•0408

+ 5-7

-•1180

+ 7-4

-•0153 + 5-2

-•0624

+ 7-4

+•0500 + 9-27

^-•1270

+13-8

-0441

+ 5^5

-•0836

+10-55

June.

+•0334

+ 2-94

-•1591

+113

-•0316 - 15

-•0902

+ 3^41

+-0658 + 4-84

U-1229

+ 6-2

-•0252

+ 3-8

-•1007

+ 2-5

July.

+ 0331

+ 2-72

-•0930

+ 5^4

-•0195 + 3-5

-•0489

+ 1^64

+•0133 + 3-04

-0862

+ 0-2

-•0220

- 11

—0471

+ 0-56

Aug.

+•0323

+ 3-02

-•0827

+ 2-5

-•0150 - 0-8

-•0600

+ 131

+•0162 + 2-67

-1249

+ 4-2

-•0381

+ 0-5

-•0706

+ 1-21

Sept.

+•0327

+ 3-65

-•1259

- 14

-•0368 + 2^8

-•0813

+- 2^82

+-0419 + 3-15

-•1178

+ 3-0

-•0672

+ 0^7

-•0910

+ 2-23

Oct.

+•0412

+ 4-63

-1472

+ \2

-•0567 - 36

-1147

+ 2-52

+-0530 + 3-12

[-•1366

+ 2-5

-•0155

+ 2-3

-1106

+ 2-46

Nov.

+•0590

+lbO

--1695

+ 4^5

-•0956 +103

-1444

+10-4

+-0448 + 5-19

-•1627

+ 5-0

-0562

+ 1-0

-1277

+ 3-31

Dec.

+•0775

+131

--1835

+1M

-•1161+140 —•1616

+13-6

:+-0530 + 7-8

-1533

+ 8-9

-0945

+ 8^6

-1141

+ 8-48

Year.

+•0473

+ 7-27

-•1892

+10^0

-•0150 _ 0-8

-•1025

+ 5-99

+-0481 + 6-71

-•1856+10-8 -0155 + 23

-•1093

+ 6-36

1829.

1830.

Rise of Barometer

1

Rise of Barometer

from sunrise to

Fall of Barometer from 9—10 A.M. to 4—5 P.M.

Fall of Barometer from 9-10 A.M. to 4— 5 P.M. 1

from 4—0 P.M. to

9—10 A.M.

1

10—11 P.M.

Monthly Therm.

Therm.

Min. Therm.

Monthly

Therm.

M.ix.

Therm.

Min. \ Therm.

Monthly

Therm.

Monthly

Therm.

Mean, j attached.

attached.

j attached.

Mean.

attached.

attached.

attached.

Mean.

attached.

Mean.

attached.

in. 1 o

in.

in. 1 o

in.

in.

in. 1 o

in.

o

in.

Jan.
Feb.

+•0401 1+11-34
+•0422 +13-56

•1606

+ 14^5
+ 115

-•0934 + 2^7
-0765 + 7-6

-1358

+ 9-47
+ 8-32

-1643

+ 5^5 ;

+ ?2

--1211 + 8-2
--0692 + 3-7

- ^136

+ 5^8

-•1648

--1083

--1781

- •HO

+ 6^5

+ -088

- 81

March.

+•0437 ■+ 9-57

-•1641

+ 10^7

-•0343 +11

--1024

+ 4-25

-1663

+100

--0493 + 9-9

- 133

+ 9^8

+ -097

-12-7

April.

+•0514 +10-91

-1371

+ 6-0

-•0607 + 9-5

-•0981

+ 3-6

-•19.50

+ 7-6

-•0887 + 8-7

•143

+ 7-7

+ ^108

-11-1

May.

+•0514 +10-54

-•1192;- 4^8

--0523 + 3-7

-•0903

+ 2-42

--1799

+ 6-0

-0622 - 0-2

- 132

+ 5^8

+ -114

- 9-0

June.

+•0234 + 2^74

-•1366 i+ 3^7

--0351 + 0-7

-•0734

+ 1^55

-•1583

+ 5-3 i

--0544 + 1-5

- -106 + 3-7 1

+ ^105

- 7-4

July.

+•0363 + 251

-•1091

- 10

--0281 + 0-9

-•0654

+ 0^75

-•1117

+ 3^3

-0327,- 0-5

- -075

+ !•!

+ ^094

- 30

Aug.

+•0251 + 3-07

-•1045

+ 2^8

--0521 - 1-0

-•0866

+ 0-8

-1224

+ 21

--0463 + 1-0

- -085

+ 2^3

+ ^082

- 4-5

Sept.

+•0330 + 4-75

-•1073 j-i- 3-5

_-0460 + 0-0

-0772

+ 1-43

-•1480

+ 5^5

-•0519 + 2-2

- -090

+ 21

+ ^074

- 4-7

Oct.

+-0350 + 5-56

-•14461+ 5^0

-•0594 + 3-5

-1116

+ 4-01

-•1478

+ 3^0

-0966 + 40

- 125

+ 2-9

+ -084

- 4-1

Nov.

+-0364 + 6-53

-1403 + 40

--0680 + 4-5

-•1067

+ 4-7

-•1561

+ 60

-•0624 + 6-7

- 125

+ 6-5

+ ^082

- 8-2

Dec.

+-0399 + 8-72

-•1435 j + 60

--0659 + 5-0

-•1338

+ 5-74

-•1372

+ 5^5

-•0740 + 4-5

- 110

+ 4-9

+ 045

- 6-3 i

Year.

+•0382

+ 7-48

--1648 +11-5

-•0281 + 0^9

-•0991

+ 3^92

-•1950

+ 7-6 1

-•0327 - 0-5

-•1166

+ 4-9

+•0884

- 7-2

The mean rise of the barometer from sunrise to 9 — 10 a.m. for 3 years is -0445, thermometer + 7°-15.
The mean fall of the barometer from 9 — 10 a.m. to 4 — 5 p.m. for 4 years is '1066, thermometer +5°-21.
The mean rise of the barometer from 4 — 5 p.m. to 10 — 11 p.m. for 1 year is -0884, thermometer — 7°-2.

• 1827, April, in Bombay, not included in the means.

+ 1828, March, ten days, in Bombay, not included in the means. , „-„, r , v .u

•^ 1828, December, in Bombay, not included in the means. 1829, February, sixteen days, at Pait, at 2531 feet above the sea.
1829. March, April, and May, at 3943 feet above the sea. 1829, December, nineteen days, at Chamblee, at 2416 feet above the sea..

198

LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

Table II. — Mean diurnal and nocturnal oscillations of the barometer, and difference
tioned places within the Northern Tropic on the Continent of India ; reduced

Calcutta,
1829, 1830, 1831.

Fall from 9h. 40m,
to 4 P.M.

Barom.

Therm,
attached.

Madras, maximum and minimum
every tenth day, 1823.

Fall from 9—10
A.M. to 4—5 P.M

Barom. Therm,
attached

FaU from 10 P.M.
to 5 A.M.

Barom.

Therm,
attached.

Bombay, 1829.

Fall from 9 A.M.
to 3 P.M.

Barom. 'i?^^j
attached.

Poona, 1830. 1823 feet above the level of the sea.

Hill Fort of Hurreechundurghur, 1829.

3900 feet above the level

of the sea.

Fall from 9— 10 A.M.
to 4—5 P.M.

Barom.

Therm,
attached

Rise from 4—5 P.M.
to 10—11 P.M.

Rise from sunrise
to 9— 10 A.M.

Barom.

Therm,
attached

Barom.

Therm,
attached.

Rise from sunrise
to 9—10 A.M.

Barom.

Therm,
attached.

Fall from 9-10 A.M
to 4—5 P.M.

Barom.

Therm,
attached.

-123
—117

-•125

-•124

-•115
-•095
-•090
-•099
-•101
-110
-•107
-•114

-•110

+20-7
+18-5

-I- 14-0
+ 14^6

+13^7
+ 7-6
+ 61
+ 5^9
+ 62
+ 8-4
+134
+17^1

+122

072
-•070

—076

1—081

-•081

-•092

-•097

-•105

-•094

068

071

071

+ 11^0
+10-0

+ 7^0

+ 9-0

+ 9-0

+ 9-0

+ 7-0

+ 7-0

+ 6^0

+ 8^0

+ 8-0

+ 9-0

-•079 + 8-5

-•004
•029

•026

-•027

-•014
-•026
-•009
-•028
-•024
-033
010
019

•021

-•099

-•091

-•1123
-•102

+5-4
+3-7

t-

•0836
•089

•071

•054

•046

•063

•074

^-•1141

-•075

+7-6

+4

•"}

+0-51

+3-1 ;

+23

+2^2
+ 12

+ 1^4
+2-1

+8^48

+2-82

-•136
-140

-133

-143

-132
-•106
-•075
-•085
-•090
-125
-•125
-•110

-•1166

+ 5^8

+ 6-5

+ 9^8

+ 7-7

+ 5^8

+ 3-7

+ M

■f- 2-3

+ 2^1

+ 2-9

+ 6^5

+ 4^9

+•088
+•097

+•108

+•114
+•105
+•094

+•082
+•074
+•084
+•082
+•045

+ 4^9 +^0884

- 8-1
-12-7

-IM

- 9-0

- 74

- 30
4-5

- 47

- 4^1

- 8-2

- 6-3

72

•0234
•0363
•0251
•0330
•0350
•0364
•0399

2-74
251
307
475
5-56
6-53
8-72

•0437

•0514
•0514

9-57

10-91
10^54

•1024

•0981
•0903

4-25

3-68
2-42

•0488

10-34

•0969

3-45

The Calcutta observations were made in the Surveyor- General's office ; those at Madras, by Mr. Golding-
HAM, at the Observatory ; in Bombay, by Captain George Jervis, at the Engineer Institution ; at Poona and

• Ten days' observations in Bombaj, in 1828, made by Colonel Stkes from 9 — 10 a.m. to 4 — 5 p.m.: Rise from sunrise to
9—10 A.M. •0360; Therm. +8°^92.

t April 1827, in Bombay. — Observations made by Colonel Stkes, in tents, from 9 — 10 a.m. to 4 — 5 p.m. : Rise from sunrise to
9— 10a.m.^0645; Therm. +100^05.

f Observations made in Bombay, 1828, by Colonel Svkes, from 9— 10 a.m. to 4 — 5 p.m.: Rise from sunrise to 9— 10 a.m. •0530 j
Therm. +7°-8, intents.

AND METEOROLOGY OF DUKHUN.

199

of thermometer attached, at different levels above the sea, at the undermen-
to 32° Fahr.

Mahabuleshwur, the source of the Kristna River, 1828, 1829,
at iSOO feet above the level of the sea.

Kotagherry on the Nielgherry Mountains, 1826,
at 6407 feet above the level of the sea.

Rise from sunrise
to 9—10 A.M.

FaU from 9—10 A.M.
to 4 P.M.

Rise from 4 P.M.
to 10 P.M.

Fall from 10 P.M.
to sunrise.

Rise from sunrise
to noon .

Fall from noon to
sunset.

Rise from sunset
to 9—12 P.M.

Fall from 9— 12 P.M.
to sunrise.

+ •0498

+•0478

+-•0456

+•0627

+•0536
+•0392

+•0357
+•0468

+ •0476

Therm,
attached.

+3^99
+8^90

+6^86

+5^26

+ 3-56
+ -31

in.

-•0735
-•0666

-•0827

-•0835

•0757

•0528
•0556
•0503

+ 1^46
+-3^15

•0801
•0738

+4^18

-•0694

Therm,
attached.

Barom.

-+4^76
+6-5

+2-23

+2-58

+ 1-33

+ -49
+ ^85
+ ^64

+322
+3-55

+•0291
+ 0362

+•0534

+•0443

+•0445
+•0365

+•0632
+•0443

+2^61

+•0439

Therm,
attached.

Barom.

- ^-n

-12^92

- 679

- 5^96

- 402

- -33

m.
-•0054

-•0174
-•0163

-•0235

-0224
-•0229

321
4^64

•0188
•0173

5^58

-•0180

Therm,
attached.

-201

-2^48

-23

-1^84

- •s;

- ^47

+•033
+•073

+ 031

+•033

+•075

-139
.2-06

-1^68

+•0490

Therm,
attached.

Barom.

+ 11-8
+14^5

+105

+10^9
+ 4-3

-•037
-•044

-•042

-•046
-•080

+10-4

•0498

Therm,
attached.

Barom.

-32
-55

-4^6

-4^8
-2-5

•045

•056

•043

•028

-4-0

•0430

Therm,
attached.

•074

•045

•030
•023

■0433

Therm,
attached.

Hurreechundurghiir, by Colonel Sykes ; at Mahabuleshwur, at the convalescent station, by Dr. Walker ; and
at Kotagherry by Mr. Dalmahoy. The whole are unpublished, with the exception of those taken at Madras
and Calcutta. From the hours at which Captain Jekvis observed, and the small oscillation of the thermome-
ter, I have not thought it worth while to reduce his observations to 32'' Fahr. My own observations in Bom-
bay are reduced.

200

LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

Table III.

Table of some of the Anomalies in the period of the ebb and flow of the atmospheric
tides in Dukhun, together with their Stationary Periods during 1830 at Poona.

Date.
1830.

Feb. 5.
6.

8.

9.
14.

20.

March 11.
19.

April 11.

17.

May 10.

June 9.

10.
14.

July 30.

August 5.

20.

30.
Sept. 5.

11.
October 4.

12.

13.

14.
3.

6.
15.

Nov.
Dec.

Maximum diurnal tide 9—10 a.m.

Exact hour at which the tide turned,
together with the stationary period.

Turned before lOi" am.

/Turned at lO*" 15'"; station-"!
\ ary 35"'. J

9'" 45"" to lO** 15"" ; quite stationary
9''30'"tolO''A.M.; quite stationary

gh 45m tolO*" 20°' ; quite stationary

9'' 30"" to lO*" A.M ; quite sta-
tionary; fall to ll*" A.M.,
= •008.
9i'15'"; fall to9i'45'° = -010.
9'' SO"" to lO*- ; quite stationary

9'' SO-" ; fall to 10" = -001.

9" 45'" ; fall to 10" = -002.

9" SO" to lO" 15

stationary.

lOh A.M.

9I' SO™ to lO" ; stationary.
9'' ; fall to 10" = -017.

9" SO*" to lO" IS"" ; stationary.

10" 15>" A.M.

r9" 30™ to 10''; stationary ;\
I fall to 10" 30"' = -003. /

9" 45™; fall to 10" 15"' = '004.
9" 30™ to 10" ; stationary.
9" 30™ to 10" 15™ ; stationary.
9" 30™ ; fall to 10" = -002.
9" 30™; fall to 10" 10™ = -002.

9" 30™ ; fall to 10" = -003.

9" 30™; fall to 10" --001.
10"; fall to 10" 15™ =-003.
9" 45™ to 10" 10™ ; stationary.
9" 45™ : fall to 10" 15™ = -004.

Differ.

of
attached
Therm.

-I-0-5
+0-5

-I-0-4

+ 10

+ 1-5

+2-0
+0-5

-I-2-5

+0-5

+ 1-0

f2-0

+ 1-0
+1-5

+1-0

00

+0-5

4-10
+0-5
+0-5
+ 10
+ 1-0

+0-2

+1-0

+0-5

00

+M

Minimum diurnal tide 4 — 5 p.m.

Exact hour at which the tide turned,
together with the stationary period.

Differ.

of

attached

Therm.

r Turned at 4" p.m. ; rise of -002 "1
\ only in 90™. J

4" P.M.; rise of -008 in 75™.

/ Turned at 4" 30™ ; rise of -005 1
1 in 15™. ;

{Turn at 4" 15™; rise to 430 1
= "004 ; then quite stationary y
till 5" P.M. J

{ Turn at 4" 45™ ; rise to 5*45 1
I =-005. J

Turn at 4"; rise to 5-30 = -008.

4" to 4" 30™ ; quite stationary.
4" ; rise to 4-40 = -024.

4" ; rise to 4" 45™ = '001.

4" 30™; rise to 5" p.m. = -002.

4" 30™ ; rise to 4" 45™ = -005.

4" P.M. ; rise to 4" 15™ = '004.

'}

4" 15™ ; rise to 4" 30™* = -008,
4" 30™ ; rise to 4" 45™ = -004.
J 4" 15™ to 4" 40™ ; stationary
\ rise to 5" = -002.
4" 15™ ; rise to 5" = -003.

4" 30™ to 5" ; stationary.

4" 45™ ; rise to 5" 30™ = -013.
4" 30™ to 4" 45™ ; rise of -001 only.
4" 15™ ; rise to 4" 30™ = -003.
4" ; rise to 4" 30™ = -001.
4" 15™; rise to 4" 30™ =-004.

4" 30™ P.M.

4" 30™ P.M.; rise to 5" = -003,
4" to 4" 15™ ; stationary.

4" P.M.

4" 15™ to 5" P.M.; stationary.

+0-5

+0-2

0-0

-0-5

-0-3

-0-5

00
-20

-1-2

-0-2

-0-5

00

0-0
00

0-0

00

-0-5

-0-5
00
-0-3
-0-5
-0-5

00

0-0
0-0
00
00

Maximum nocturnal tide 10 — 11 p.m.

Exact hour at which the tide turned,
together with the stationary period.

Differ.

of

attached

fherm.

/ 10" to 10" 30™ ; quite station- 1
I ary ; fall of -002 in 15™. /

r Turned at 10" 30™ ; fall to 10" "1
I 45™ = -008. /

/Turned at 10" 45™; fall tol
\ 11" P.M. = -001. /

/ Turn at 10" 15™ ; fall to 10" 1
\ 45™ = -004. /

Turn at 11" p.m.

10" 30™; fall to 10" 45™ = -006.

'}

10" 30™ ; fall to 10" 45™ = -003,
10" ; fall to 10" 30™ = -001.
/ 10" to 10" 45™; stationary
1 fall to 11" =-006.
10" 30™ to 11" p.m. ; stationary.
/ 10" 15™ to 10" 45™ ; stationary; ]
t fall to 11" 15™ =-005. /

12" p.m., after heavy storm from
N E. at 7" 0™ and 8" 30™ ; tide
not suspended during storm,
10" 45™; fall to 11" =-010.
10" 30™ to 11"; stationary.

10" ; fall to 10" 30™ = -001.

10" 15™; fall to 11" = -003.

11" P.M. ; fall to 11" 15™ = -001.

10" 45™.

11" 20™; fall to 11" 30™ = -001.
10" 45™; fall to 11" 15™ = -003.
11" to 11" 30™; stationary.
t9" P.M. ; fall to 11" P.M. = -012.
r9" 30™ to 10"; stationary; falll
1 to 10" 30™ = -002. /

10" to 11"; stationary,
11" P.M. ; rise to 11" 30™ = -001.
11" P.M.; fall to 11" 45™ = -003.
11" 30™ : fall to 11" 45™ = -001.

-10
00
00

00

00

00

0-0
00

-0-3

00

0-0

+0-3

+0-5
00

00

+0-2

00

00

00

-01

-0-5

-0-5

00

-0-8
00
00
00

I have no instance of a stationary period of 5** 30™, nor of two hours even, as observed by Dr. Balfouk in
Calcutta in 1795 ; and I strongly suspect that these lengthened periods would not have been on record had
Pr. Balfour's barometer read off to thousandths of an inch instead of hundredths.

* Storm at 4 p.m.

t Storms round the horizon at 4" 30™.

AND METEOROLOGY OF DUKHUN.

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208

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Table XVI.

Showing the maximum, minimum, and mean temperature, the maximum, minimum,
and mean diurnal range, and the extreme monthly and annual range of the ther-
mometer for the year 1829 in Dukhun, between the parallels of latitude 18° 10'
and 19° 23' North, and longitude 73° 20' and 74° 30' East.

1829.
Months.

Place of observation.

Height in

feet above

the sea.

Extreme tempera-
tures.

Maximum. Minimum

Monthly
mean
tempera-
ture.

Maximum
diurnal
range.

Minimum
diurnal
range.

Mean
diurnal
range.

Extreme
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range.

January.
February.

March.
April.

May.

June.

July.

August.

September.

October.

November.
December.

En route ,....

En route

f Tents in Hill Fort of Hur-")
\ reechunderghur J

r Tents in Hill Fort of Hur- "|
\ reechunderghur J

r Tents in Hill Fort of Hur- ]
\ reechunderghur J

Hay Cottage, Poona

Hay Cottage, Poona

Hay Cottage, Poona

Hay Cottage, Poona

Hay Cottage, Poona

r Hay Cottage, Poona

L Sasswur Government House

r Chamblee, in tents

L Hay Cottage, Poona

3943

1823

2416
2416
1823

82
88-90

88-80
94-20

87-30

86

81-50

79

85

89-50

83-50

80

84

85

45-10
47-30

68-80
60

64-80

71-50

70-50

70-50

69

66-50

68

49-50

43

55

67-70
70-60

78-31

78-07

76-11

76-80
75-50
73-80
75-43
78-40
75-67
64-65
66-71
71-20

30-90
32-40

17-90

20-80

19-50

8-50

7

8

12-50
17
15

26-50
37-50
30

9
10-40

8-70

4-50

4
-60

2-30

6-50
10
10

8
16

20-80
21-40

14-01
14-72

13-35

6-33

5-62

4-31

6-48

12-74

12-50

21-62

24-92

22-26

36-90
41-60

20
34-20

22-50

14-50
11

8-50
16
23

15-50
30-50
41
30

Year.

94-20

43

74-80

37-50

-60

12-90 51-20

The mean temperature of the year was reduced several degrees from former years, in consequence of the
whole of the observations for the hot months having been made in the Hill Fort of Hurreechunderghur in the
Western Ghats, at an elevation of 3943 feet above the level of the sea. The weather also during the Mon-
soon was cooler than usual.

AND METEOROLOGY OF DUKHUN.

209

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LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

Table XXIII.
Register of the Ombrometer from December 1825 to December 1826.

Dates.

1826.

Dec.

January.

Feb.

March.

April.

May.

June.

July.

August. S

ept.

0

ctober. Nov.

1.

....

•10

•34 ....

2.

....

•10

12

•02

3.

....

•03

02

•42 ....

4.

....

•11

04

•12

5.

....

•06 ,

•01

6.

•01

2^58

•07

7.

•14

•10

•08

03

8.

•09

•18

•05

14

9.

•21

•06

•03 .

. .

10.

•01

....

01

•20

11.

....

•22

....

49

•01

12.

•02

•24

....

03

13.

•53

•11

. .

14.

•06

....

02

•04

15.

•01

•07

•02

07

• • • ....

16.

....

•02

....

02

•10

17.

•06

•04

. . .

... ^70

18.

....

•16

. . .

19.

....

•52

....

03

20.

....

•23

03

... ^76

21.

•03

•48

....

•12

•33

22.

1-05

•74

•15

11

'96 '16

23.

....

•87

•09

14

•02 •OS

24.

•45

•03

•07

•06

08

25.

....

1^01

1-32

•08 .

26.

•27

•10

•28

•01 ....

27.

•02

....

28.

•37

29

•17

....

•05

....

04

30.

1-43

....

•03

31.

•70

Total

3-41

3-30

8-43

1^03 1

54

[•90 2-33

T

ot

Edfal

lof

rain

21

•94 inc]

les.

The Register, during the Monsoon, was kept at Poona every year.

AND METEOROLOGY OF DUKHUN.

213

Table XXIV.
Register of the Ombrometer from December 1826 to December 182/^ in Dukhun.

Dates.

1827.

Dec.

January.

Feb.

March.

April.

May.

June.

July. Ai

gust.

Sept.

October.

Nov.

1.

^ ^

J ,

> > • «

....

•22

01

•06

2.

•03

....

•01

04

•05 .

3.

•04

•17

•01

23

•11

4.

•39

•02

03

•08

....

5.

•60

•01

22

•06

....

6.

....

....

•06

02

7.

•39

•17

•03

07

•03

•03 .

8.

•15

•01

24

•48

9.

•05

40

•31

10.

.01

•01

•74

•02

11

•27

•09

11.

1^32

•03

•10

•07

12.

1^51

•03

•09

•60

•38

13.

1-68

•22

•37

14.

•09

•10

•03

•04

....

•28

15.

2^17

....

•13

•04

•02

16.

•02

•18

•16

•22

•10

•33

17.

•02

•07

07

•13

....

18.

•15

•02

03

....

1-81

19.

•31

•01

•17

20.

•04

•07 .

•04

....

21.

•01

1^23

•08

•01

22.

•15

•01

•01

....

23.

•34

•01

24.

•07

•20 .

....

25.

•28

•02 .

26.

•04

•11

2^54

•09

27..

•51

•05

•13

•07

•06

28.

•34

•01

....

....

29.

2-57

•01

30.

•75

31.

Total

•40

2^29

••

•04

•04

13^47

1-79 2

•01

4-51

4^33

•15

Total fall of rain 29*03 inches.

214

LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

Table XXV.
Register of the Ombrometer from December 1827 to December 1828, in Dukhun.

Dates.

1828.

Dec.

January.

Feb.

March.

April.

May.

June.

July.

August. S

ept.

October.

Nov.

1.

•15

•29

•11

2.

•03

•02 1

•17

....

3.

•17

•13

1

•53

....

4.

....

•57

•03

....

•15

....

5.

•12

....

•32

•71

6.

• . • •

....

•02

•02

....

7.

•06

•12 .

. . .

....

8.

•04 .

• . .

....

9.

....

•02

06

•21

10.

....

•28

•03

•68

11.

•08

...»

•20

....

12.

•03

....

•01

....

13.

....

•15

14.

....

....

•01

1^47

15.

•04

•12

•07 .

•08

16.

•07

....

•01

•03

17.

•17

•43

....

•03

1^96

18.

•06

....

•31

•03

19.

•01

M6

•05 1

•48

•69

•23

20.

1-50

•93

•01 1

15

•22

1-81

21.

•30

....

06

22.

•31

. . • •

23.

•52

•70

• • • •

04

24.

•04

• • • •

04

25.

•45

•08

• • • • '

01

26.

• • • > •

27.

•19

• • • • • •

28.

•02 .

29.

•06

•28 .

30.

M7

2^24 .

31.

....

.

1^48

•18 ..

.

Total

...

1-95

1^63

7^58

3^35 6^

92

6-34

2^04 1

Total fall of rain 29-81 inches.

AND METEOROLOGY OP DUKHUN.

215

Table XXVI.
Register of the Ombrometer in Dukhun during the year 1829.

Dates. J
1829.

anuary.

Feb.

March.

April.

May.

June.

July. Au

gust.

Sept. Oct*

jber.

Nov.

Dec.

1.

10 .

2.

03 .

3.

18

4.

31

05

. .

5.

•02 ..

6.

.

03

....

i9

7.

•

64

•07

8.

09

12

•04 ..

9.

•05

....

09 .

•07 •

37

10.

•53

08

10

•11

07

•50

11.

....

... 1

09

09

•70

12.

•12

07

13.

•04

1^30

10

11

14.

03

13

•02 ..

15.

07

03

16.

•05

04

08

17.

•12

16

18.

....

19.

. . .

20.

•19

.

36

64

21.

•05

M9

•70 .

04

22.

•35

•15

•05

23.

1-90

•11

•08

24.

•10

•14

12

25.

•50

•24 .

26.

•40

•65 .

. . .

27.

•25

....

1

•16 .

28.

•02

•17

04

29-

•17

•02

■18

30.

•01

•02

31.

•04 .

Total

...

2^74

4^86

4

•38 3

•21

•33 1^

81

1-20

Total

18-53 i

acl

les.

216

LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

Table XXVII.
Register of the Ombrometer at Poona during the year 1830.

Dates.
1830. '

Fanuary.

Feb.

March.

Ap

ril. May.

June.

July. Ai

igust.

Sept.

October.

Nov.

Dec.

1.

•39

•03

•40

2.

•02 .

•04

3.

....

. . .

4.

.02

•40

•02

5.

....

....

•10

....

6.

•02

....

•10

7.

•04

•02

•06

8.

•04

•12

•08

•17

9.

•03

•50

•11

10.

•20

•24

11.

•10

•05

•23

12.

M9

•01

1^81

13.

•06

•04

•07

•01

14.

15.

•01

1-81

16.

....

•07

17.

•08

18.

■02

19.

20.

21.

•4

3 -28

•32

22.

•47

04

23.

•3

0 -33

•33

....

24.

•1

9 ....

2-31

17

25.

•0

9 ....

2^41

04

26.

•16

27.

•0

3

•52 .

28.

•03

•02

•02

29.

01

•10

30.

. . .

....

31.

•41

Total

1-0

4 ^79

5^57

5-35 1-

61

•29

3^07

AND METEOROLOGY OF DUKHUN.

217

Table XXVIII.
Tabular view of the fall of rain in Dukhun from 1826 to 1830, both inclusive.

Months.

1826.

1827.

1828.

1829.

1830.

Total in
five years.

January.

February.

March.

April.

May.

June.

July.

August.

September.

October.

November.

December.

inches.

3-41
3-30
8-43
1-03
1-54
1-90
2-33
•40

inches.

2-29
-04

-04
13-47
1-79
2-01
4-51
4^33

•15

inches,

1-95
1-63
7-58
3-35
6-92
6-34
2-04

inches.

2-74
4-86
4-38
3-21
-33
1-81

1-20

inches.

1-04
•79
5-57
5-35
1-72
•29
3-07

inches.

2-29

•04

1^04

8^93

28^83

27-53

11-32

13-59

17-45

4-52

1-60

Total

22-34

28-63

29-81

18-53

17-83

117-14

23"43 inches mean annual fall.

Table XXIX.

Tabular view of the fall of rain in Bombay from 1817 to 1829, inclusive, in the

monsoon.

Months.

1817.

1818.

1819.

1820.

1821.

1822.

1823.

1824.

1825.

1826.

1827.

1828.

1829.

Total.

Jan.

inches.

inches.

inches.

inches.

inches.

inches.

inches.

inches.

inches.

inches.

inches.

inches.

inches.

inches.

Feb.

....

....

....

....

....

....

....

....

....

....

Mar.

....

....

....

....

....

....

....

....

....

....

....

....

....

April.

....

....

....

....

....

....

....

May.

....

....

....

....

June.

45-72

22^54

15^95

18-82

15-18

29-21

21-76

3-89

24-25

17-75

49-15

23-53

27-86

July.

23-67

17-69

30-66

28-37

20-60

26-39

15-96

8-07

25^17

26-97

10-29

52-75

19-78

Aug.

9-34

28^45

20-24

19-49

28-52

33-83

19-70

17-86

12-94

8-40

10-51

17-22

12-40

Sept.

24-87

10-39

,10-11

10-66

18-29

22-16

4-28

1-78

9-68

23-50

10-16

22-08

4-95

Oct.

-19

2-07

-14

....

•40

-82

....

2-37

....

1-23

-92

6-40

Nov.

....

....

....

. . . ,

....

Dec,

....

Total

103^79

81-14

77-10

77-34

82^99

112-61

61-70

34-33

72-24

77-85

81-03

121-98

64-99

MDCCCXXXV.

80-69 inches mean annual fall in the monsoon.
2 F

218

LIEUT.-COLONEL SYKES ON THE ATMOSPHERIC TIDES

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[ 221 ]

XI. Geometrical Investigations concerning the Phenomena of Terrestrial Mafrnetism.
iBy Thomas Stephens Davies, Esq. F.R.S. Lond. and Ed. F.R.A.S. Royal Military
Academy, Woolwich.

Received December 18th, 1834, — Read February 5th and 12th, 1835.

X HOUGH the experiments of Michel and Coulomb have satisfactorily determined
the law according to which magnetic forces vary as the distance of the needle acted
on is made to vary, yet, so far as I know, no one has attempted to deduce from that
law any method of accounting for the phenomena of terrestrial magnetism. Till that
is done, however, we cannot assure ourselves whether the poles (I use the term to
designate the centres from which the forces emanate,) be two or more ; nor even
whether it be necessary to consider them infinite in number and distributed over the
whole surface or through the whole mass of the magnet. The agreement of the re-
sults as to quantity with the actual phenomena would be decisive in favour of any
hypothesis. The necessary consequences have not, however, yet been deduced from
any one hypothesis whatever : and even had it been otherwise, there is so much un-
certainty attached to magnetical observations, and so many anomalous and unac-
countable discrepancies and disturbances continually mingling in the registered
results, that it is not possible, in the present state of the mimerical data, to bring any
hypothesis fairly to the trial, however complete the mathematical development of its
consequences may be.

Notwithstanding the great difficulty of conducting a series of observations in a per-
fectly unexceptionable manner, and the utter impossibility, with our present know-
ledge, of properly determining the correction to be made at any given place and
period with any given instrument, there are yet several features in the phenomena
which are of too decided a character to be overlooked in comparing the results of
any theory with observation. We may not, indeed, be able to avoid considerable
discrepancies in our comparison, but still there should at least be a general tendency
towards agreement, and in no case a direct reversal of the phenomena presenting
itself as the result of any hypothesis which prefers its claims to our adoption. In
respect to terrestrial magnetism, no direct attempt has, however, been made to em-
body the results of any hypothesis in a series of appropriate formulae ; and hence the
conjectures which have been made respecting such agreements have been made from
extremely vague and inconclusive considerations.

The duality of the terrestrial magnetic poles is the oldest hypothesis, and perhaps
that whose consequences will be found most easy to examine. The hasty comparisons

222 MR. DAVIES'S GEOMETRICAL INVESTIGATIONS

that have been made between its supposed results and the observations made on the
needle at certain places, and especially respecting the Halleyan lines, and Hansteen's
poles of greatest intensity, have caused the hypothesis to be rejected by many persons,
who, if they had looked more closely into the question, could not have failed to dis-
cover that their conclusions were altogether premature, and probably erroneous. I
speak now of the broad features of the phenomena compared with a popular rather
than a calculated series of deductions from the hypothesis. Whether, however, when
the results come to be more closely tested by an appeal to the numerical values of
the quantities in question, the same accordance would be found, is a question alto-
gether different : and it is one which we are not at present in a condition, for want of
numerical data, upon which to offer a distinct opinion, much less are we entitled to
express a positive decision concerning it.

The present series of papers is chiefly intended to deduce the mathematical conse-
quences of the theory of two poles situated arbitrarily within the earth, and especially
to investigate the singular points and lines which result from the intersection of the
earth's surface with other surfaces related to the magnetic poles. Amongst these are
the magnetic equator, the points at which the needle is vertical, the lines of equal
dip, the Halleyan lines, the isodynamic lines, and the Hansteen poles. If it shall
appear in the course of these developments that the general features of all these are
roughly represented by the hypothesis of two poles, then it will be a strong argument
in favour of that simple theory ; but should a result, in any one of these cases,
follow from that hypothesis which is very decidedly opposed to the corresponding-
observed phenomena, we shall be compelled, if our observations are authentic and to
be depended on as unaffected by an extreme degree of foreign influence, to abandon
it altogether.

Our hope of being able to separate the disturbing from the primary forces must
depend altogether upon their relative quantities. The success of astronomical re-
search has hinged wholly on the relative smallness of the disturbances in comparison
with the primary forces that govern the motions of a planet : and if the same order
of magnitude should exist in the magnetic forces in question, the same success will,
there is every reason to hope, follow in due time. If not, the research should be
placed at once amongst the desperata. However, till some method is discovered of
ascertaining whether such is the case or not, we should leave no effort untried either
to accomplish the proposed object, or to render manifest its impracticability. With
that view the present investigations, which are conducted in a manner altogether un-
tried before by any one, are offered to the attention of geometers, as being calculated,
besides exhibiting the general consequences of the dual hypothesis, in some degree to
point out where we should look for the influence of foreign forces, and especially
showing that in reference to one great circle, the want of symmetry in the results at
positions taken symmetrically with respect to it, gives us great cause to suspect the
action of such foreign forces.

CONCERNING TERRESTRIAL MAGNETISM.

223

The nature of this paper does not allow of much numerical experiment upon the
observation-data ; but still, in illustration of the method of determining the position
of the magnetic axis, I have entered into a little. The results are not very favourable
to the hypothesis ; but when it is considered that the observations were selected almost
at hazard, all made with different instruments, by various persons, and in geological
regions extremely dissimilar, we could hardly, in the confessedly imperfect state of the
art of observation, expect to obtain satisfactory results. Taking all things into
account, the results are, unfavourable though they be, as satisfactory as we could
expect. However, whatever conclusion may be drawn from them, they furnish at
least a pattern for calculating any better and more consistent observations we may at
any future time be able to procure ; and if any that are beyond question can be ob-
tained, it will enable us to bring the linearity of the magnetic axis to an indisputable
test. The duality, should the linearity be established, can be at once put to the test
by means of the process in Section III.

Now that this method of investigation is proposed, it will doubtless occur to some
of my readers that a more direct course would have been to assume the undetermined
coordinates a^ b^ c^, a,, b^ c,,, of the two poles, and express the equation of the sphere in
reference to the same axes, and hence the directive effect of the two poles upon a
needle placed at a point xy z on the spherical surface. Such a method, they will
believe, must also have occurred to me as the most natural ; but if they will take
the trouble to form the equations of condition that this method will require, they will
see the utter impracticability of effecting the reductions under the mere motive of
making an experiment upon the results of an hypothesis when no confidence was felt
in the numerical data which entered into the formula. The reason for adopting the
less direct, but incomparably more simple, preliminary test illustrated by Sections XI.
and XII. will then be suflicientlv obvious.

I. — Given the dip and variation of the magnetic needle and the geographical coordi-
nates of the place of observation, to find the geographical coordinates of the
place where the needle, sufficiently prolonged, will intersect the surface of the
earth again.

We assume, for reasons too well known to need spe-
cification here, that the orthogonal projection of the dip-
ping-needle upon the horizontal plane gives the position
of the horizontal needle ; or, which comes to the same,
that the dipping-needle and the horizontal needle are in
the same vertical plane. This plane cuts the sphere in
a great circle, which we shall for the present suppose to
coincide with the plane of the paper, and to be repre-
sented in the annexed figure by C K B. Let E C be the

224

MR. DAVIES'S GEOMETRICAL INVESTIGATIONS

Fig. 2.

intersection of the plane B K C with the horizontal plane, and let C B be the line
along which the dipping-needle disposes itself.

Join CO, OB, (O being the centre of the circle and, of consequence, of the sphere) :
then the arc C K B measures the angle COB, which is twice the angle E C B, or twice
the dip of the free needle. This arc, then, is known from observations at several
particular places on the earth's surface.

Next, let the spherical triangle ABC denote that whose vertex
A is the geographical pole of the earth ; C the place of observation ;
and the angle B that determined as above from observations
made at C : and let the angle A C B denote the observed variation
of the horizontal needle at C. Then we have the sides A C, C B,
and included angle A C B, from which to determine the colatitude
A B and polar angle B A C.

We have therefore the polar spherical coordinates of the point B,
the polar distance A B at once, and the polar angle by adding BAG
to the longitude of C with its proper sign.

I shall designate the coordinates of C and B by a^ /3y and a^^ jS^^ respectively, as is
done in my paper on Spherical Geometry in the twelfth volume of the Edinburgh
Transactions ; a denoting the polar distance and j8 the longitude of the point.

II. — Given the dip, variation, and geographical coordinates of the place of observation,
to express the equations of the line in which the dipping-needle disposes itself.

Let a, b, c, and a^, h,, c^, denote the coordinates of two points in space : then the equa-
tions of the straight line through them are

X =

a„ c, — a,c

/"/i

hn — If,
y = —

•7 r.. — r.

Z —

Cii c,

Cn — Cl

But in the present case the points a^ b, c, and a^^ b,, c,, are on the surface of the
sphere ; and if we consider the axis of the sphere to be the axis of z, the intersection
of the meridian with the equator to be the axis of «/, and that of the meridian at right
angles to it with the equator to be the axis of tr, then a^ (3^ and a,^ |3^, being, as before
stated, the coordinates of the extremities of the chord in which the dipping-needle
disposes itself, we shall have, for determining the equations of the needle, the follow-
ing values of the constants :

Ci = r cos a^

6^ = r sin a^ cos 3,

a^ = r sin u, sin ^,

:^i = r cos ocii

bji = r sin a^, cos /3^^
a^i = r sin a^^ sin fi„.

Hence the equations of the needle take the following forms :

CONCERNING TERRESTRIAL MAGNETISM.

^ sin Ui, sin ^„ — sin «y sin /S^ sin a^^ sin fi„ cos a^ — sin u, sin /S^ cos Un

cos «yy — COS a-i cos ay^ — cos a,

sin «yy cos j8yy — sin ay cos /3y sin «yy cos /3y, COS a, — sin ay cos fi, cos ayy

•^ cos «yy — cos ay COS ayy — cos ay

223

• (1.)

• (2.)

III. — Let M, N, P be the centres of three
dipping-needles at known positions on the
surface of the earth, and denote the poles by
T and U. Then the needles will arrange
themselves so as that each shall be in a plane
passing through T U ; and hence each needle
prolonged will cut the magnetic axis T U in
some point, as A, B, C, respectively.

Take any point, O, in T U, and refer all the
points to this origin ; denote the several distances O U, O T, O C, O B, O A, by m, t,
c, h, a respectively ; the angles MAO, N B O, and P C O, by A, B, C ; and the di-
stances M A, N B, P C, by/, g, h.

Then we have

MT2=(a- #)2~ 2/(a- OcosA+/2

M U2= (a - w)2 _ 2/ (a - u) cos A -\-f^

'NT^=z{b—ty--2g{b-t) cos B -f- ^2

NU2= (b — uy — 2g{b-u)cosB+g^

P T2 = (c - ^)2 ~ 2 A (c - t) cos C + ¥

P U2 = (c — 2^)2 — 2 A (c — w) cos C 4- h\
Again, by the properties of a needle subjected to the action of the magnetic poles
T and U, we have (those needles being small in comparison with its distance from
those poles,) the following proportions :

TA : AU : : TM^ : M U^ ^

TB : BU :: TN3 : NU3 !> (4.)

T C : C U : : T P3 : P U3. J

Inserting in (4.) the values of the lines T A, &c. given in (3.), we get the three

equations

a- t _ r (g -if -2 f{a - t) cos A +/' ")
a — u (^ (a — «)^ — '2,J\a — u) cos A +J^j

h — t {{b -ty-Qg{b - t)co?iB + g^

>

(3.)

b-

{b — uy — 2g{b
{c-tf-Q.h{c

\

u) cos B + g^ J

t) cos C 4- A'

(c _ m)8 _ 2 A (c - u) cos C -I- A*

}'

(5.)
(6.)
(7.)

MDCCCXXXV.

2 G

226 MR. DAVIES'S GEOMETRICAL INVESTIGATIONS

IV. — Given the equations of the dipping-needle at three given places on the surface

of the earth to find the magnetic poles.

Let M, Nj P be the places on the surface of the earth, and denote the needles as
follows, viz.

MA by x=^ a' z + a' and y = Vz-\-^' (8.)

NB by a: = «"2; + a" and i/ = ft"% + /3" (9.)

P C by a: = «'" z + a'" and y = V" z + (3'", (10.)

and denote the magnetic axis itself (T U) by

0? = as; + a and 3/ = ft ;s -j- |8. . (11.)

Then, since the line (11.) intersects the lines (8.), (9.), (10.), we have the three
equations of condition

(a'~a) (fe'-I) = (i3'-^) (a'-a) (12.)

(a" -a) (fe" - I) = (i3" - ^) (a" - a) ........ (13.)

(a'" -a) (5'" - «0 = (l3"' - ^) («'" - «) (14.)

Taking now as the unknown coordinates of the magnetic poles, T and U, the sym-
bols a^ h, c, and a^^ b^ c^, we have a b, a p, given functions of a, b, c, and a^^ b,, c^^ ; and
hence we have in the equations just given three equations for the discovery of these
six quantities which determine the poles. The three other requisite equations are
thus derived ;

By means of (11.) combined separately and successively with (8.), (9.), (10.), we
can find the coordinates of the points A, B, C in terms of a, b, c, and a^, b,, c^^ and given
quantities a! a' V |3', &c. ; and the coordinates of T and U are themselves a^ b^ c, and
^// ^11 ^ir ^^ hence have the several quantities a—^t,b~t,c—t,a — u, b — Uj and
c — urn terms of a^ b, c, and a^^ b,, c,,. Also the distances M A, N B, PC, that is,y,^, h,
are also given in terms of the coordinates of M and A, N and B, P and C respec-
tively, and hence in terms of a, b^ c^ and a,, b,, c,, and given quantities. And lastly, the
equations of the lines T U and MA, N B, PC being given in terms of a^ b^ c^ and
a^i b^j c^f and known quantities, the cosine of the inclinations of T U to each of them,
that is, of the angles A, B, C, are given so as to involve no quantities but known ones
and the coordinates of the magnetic poles. It hence follows, that all the terms which
enter into the composition of the equations (5.), (6.), (7.), are functions of the coor-
dinates of the poles and of given quantities. The three remaining requisite equations
for the actual determination of the magnetic poles are furnished, then, by those equa-
tions marked (5.), (6.), and (7.) ; the whole six equations which we have laid down
being each, obviously, independent of the others under every combination.

V. — ^The preceding processes show that the determination of the magnetic poles,
their duality being admitted, as well as the equality of their intensity, can be effected
from three observations of the magnetic needle as to dip and azimuth ; and hence

CONCERNING TERRESTRIAL MAGNETISM. 227

that the problem is now reduced to a purely arithmetical state, requiring only the
application of known processes, and perfectly capable of execution, for the actual
assignment of the positions of the poles themselves. A very slight attention to the
processes themselves must, however, convince us that the operations will be very
laborious ; but at the same time, the symmetrical forms in which the two triads of
equations are presented, might induce us to hope that a gi-eater degree of simplifi-
cation would result in the final formulae than our passage through so many operations
could at first sight lead us to expect. Such, indeed, proves to be the case ; and the
results are not altogether destitute of elegance, as well as simplification. Fortunately,
however, there is no necessity to even attempt the solution under the present aspect
of the problem ; and having learnt from it, in its present state, the number of obser-
vations necessary for the determination of the poles, we shall exchange it for another,
which is in some degree different as to general plan, and considerably more simple
in its requisite calculations.

VI. — A necessary consequence of the hypothesis upon which we are proceeding,
is, — that all the needles must intersect the magnetic axis. If, then, we assume the
coordinates of the two poles a^ b, c, and a^^ b,, c^^ we have the equation of the magnetic
axis as before,

a„— a, a„c, -^ a,c„ -\

(15.)

X = -r — . z

I _ "II "I — '*/'"//

C/i Ci

And if we take the equations of four magnetic needles, as

X = a' z -{- (x! and^ = b' z -\- p' ^

x = a" z + a" andy = b"z + Q" I

^ ^ > (16—19.)

x = a"'z + a"'axidi/=zb"'z + ^" | ^

X =z a^"^ z -{- u^ and y =^b^^ z -{- 13^^, J
the intersections of (15.) with (16 — 19.) give four equations, of condition similar to
those of (12.), (13.), (14.), from which to determine o, b^ c, and a^^ b^, c^^ viz.

(«' - "-^^') (*' - 1^;) = (^' - ^t^) («' - ^;)- • • (20-24.)

//»

These four equations will determine four of the coordinates, as a^ b, and a^, b
leaving the two others indeterminate. But still the law of force furnishes four other
equations from which to determine the two quantities c, and c^^ ; that is, a redundancy
of equations, from which redundancy the remaining number may be taken as checks
of accurate calculation if the principle be admitted, or as tests of the truth of the
principle when we are assured of the accuracy of calculation and of observation.

By this method a greater uniformity of process, and a perfect symmetry in respect
to the quantities involved, are obtained ; but still the process is very laborious, and it

2g2

228 MR. DAVIES'S GEOMETRICAL INVESTIGATIONS

is probable that the resulting equation will be of a higher degree than really belongs
to the problem in its direct form. If so, it will contain foreign factors, which it may-
be difficult to detect and peculiarize, so as to separate them from the proper solutions
ol the problem. The method, besides, is not essentially different from the last.

Another difficulty also presents itself here ; nor is it the only one. The mere in-
tersection of the magnetic axis with the magnetic needle is not a test of the duality
in point of number, nor of the equality of intensity in point of force, nor is it confined
to any law of variation of force whatever ; and hence the mere intersection is not of
itself sufficient for the determination of the question respecting the duality or the
relative intensity of the poles. Still it is one of the necessary conditions, though not
the only one, by which the hypothesis is to be tested ; since the poles, being of any
number, and of any intensities whatever, if situated in the same straight line, will cause
the needle to intersect that line, and hence render that phenomenon incapable of de-
termining the number, intensity, or position of the poles ; yet wherever this intersec-
tion is not fulfilled the duality of the poles cannot be admitted, nor yet the position
of the poles, however many they may be, be in one straight line. The determination
of a^ b, Cj ttii b„ Cji from the equations (20 — 24.) cannot then be effected completely.

We shall hence proceed in the following manner. A straight line, which constantly
touches three given straight lines, but undergoing all the changes compatible with
that triple contact, describes the hyperboloid of one sheet. This surface being of the
second order, will be cut by a fourth given line in two points ; and hence there are
two positions which a line resting upon four other lines can take. If, then, we ima-
gine these four lines to be four different positions of the magnetic needle, and the
line which rests upon them to be the magnetic axis, we shall perceive at once that in
case of any number of poles of any variety of intensity, and acting under any law of
variation of force depending upon distance, the magnetic axis can be determined in
position from four observations of the magnetic needle ; and, therefore, of course, in
the case which we are examining, where the poles are two, the intensities equal, and
the law of force that determined by Michel and Coulomb.

Let us take as the equations of the magnetic axis and four of the needles, respec-
tively, the following :

0? = a 2 -f- a andy = b 2 + |8

X =z a' « + a' andi/ = b' z -\- (i'

x = a" z-\-u". eiudy=:b" z + ^" ^ (25—29.)

X = a'" z + a'" andy = b'" z + ^'"

X =z a^" z -\- co" and y ^h" z -{■ ^^ .

Then the condition, that the first of these intersects each of the others simultaneously,
gives the four equations,

(a'-a)(6'-F) = ((3'-^)(a'-a) . (30.)

CONCERNING TERRESTRIAL MAGNETISM. 229

(cc" ^-^) (b" -J) ={(i"-^p)ia"--a) (31.)

(u'"-a){b"'-b) = {p"'-J){a"'-^a) (32.)

(«-_.^)(r_F) = (p'^-^)(«--a) (33.)

This reduction is easily effected by subtracting the first from each of the others, in
which case we obtain equations of the first degree, giving each of the other three
the quantities a & a /3 in terms of the fourth, as of u. These substituted in any one
of the four equations give a quadratic equation involving a-, and hence we obtain
two values of a, and hence again of ^ of a^ and of ^. We should then obtain, by a
simple and direct process, the equations of the magnetic axis.

The next inquiry is into the signification of this double result. Are there two mag-
netic axes which fulfill the condition ? If so, are they both occupied by magnets ? Or
if not, why is one to be selected in preference to the other ? Can they both belong to
even/ quadruple combination of the magnetic needle ?

The last question may be answered at once. If they both belonged to all the com-
binations of the needles, then they must form two of the directrices of a rule surface,
to which the needles themselves were always tangents. The third directrix not being
yet fixed, there is no inconsistency in the conclusion thus derived ; for the needles
are at liberty to rest upon any magnetic surface, whatever be the number or intensity
of the poles, or whatever be the parameter which determines the particular stratum
of surface which corresponds to the place of observation on the sphere. There is
hence nothing to prevent their belonging to every position of the magnetic needle,
so far as we at present can discover from the conditions in their arbitrary form.
How far this is consistent with the particular data is another question, and will be
presently discussed.

There is no necessity that they should be both occupied by magnets ; and it is at
once giving up the duality of the poles, and even their being situated in a right line,
to make such an hypothesis. They are both, it is true, solutions of the algebraical
problem which we have proposed ; but as the algebraical rarely includes all the con-
ditions of the physical problem, it is easy to suppose that one of these solutions may
be foreign to the inquiry, without violating our knowledge of the nature of the re-
lations subsisting between the algebraical and physical problem. To prove that it
actually is a foreign result must be subsequent to the determination of the particular
values of the coefficients of the quantities involved in the inquiry. All we can say at
present is, that there are two axes which fulfill the algebraical condition ; but as there
is only one which enters into the physical h5rpotheses, one of these two algebraical
axes must be rejected. We cannot, however, ascertain which, except by other con-
ditions than have yet been taken into the formula. For the present, then, we can
only compute them both, and take that which best answers to those other physical
conditions of which the algebraical problem has taken no account.

230 MR. DAVIES'S GEOMETRICAL INVESTIGATIONS

VII. — Having obtained the equations of the magnetic axis by the determination of
ab a ^, we may put the rectilinearity of the positions of the poles to the test at once.
For if we take a fifth needle

x = a"" z -{- ct' and 1/ = b"" z -\- P'' (34.)

and combine it with (29.), viz.

:t; = a z -\- oc, and 1/ =: b z -\- fi,
so as to ascertain whether they intersect or not, by means of the equation of condition

(a^ -'^) (J^ -1) = (j3^ -"^) (a^ - «) ...... (35.)

The approximation to a fulfilment of this condition for a^ a"", i^ j8% derived from all the
other observations upon which reliance can be placed, and to the extent of the probable
accuracy of those observations, will establish this hypothesis to the same extent.

In order to estimate the real amount of the error in the application of this equation
of condition, we must recollect that the formula itself is derived from that which
gives the shortest distance between two given lines, viz.

D (dist.) = + (-: - "-^ ^^' - ^) - ^^' - ^^ ^^' - ^^ (36.)

y (flv _ af + (6^ — bf + (a 6^ - a- bf

Hence, in order to estimate the number of miles which the needle would be from
fulfilling the condition, we must calculate the denominator of the fraction (36.), and
divide the result of (35.) by it. By then calculating the angle which D would sub-
tend at the place of observation, we shall be in some degree prepared to judge
whether such an error might possibly have arisen from unskilful observation, the im-
perfect structure of the instrument, from any probable geological or meteorological
causes, or from any temporary local disturbance. Or, conversely, were this line satis-
factorily determined by a great number of tests, and the instrument and observer
well prepared for the task, then we should be able in some degree to estimate the
amount of the disturbing forces that climate, geological structure, and local attrac-
tion do actually exert at that place, and perhaps in some cases also to form a pro-
bable conjecture respecting the separate contribution of each of these causes to the
total amount of the disturbance.

VIII. — Let us now suppose the magnetic axis satisfactorily determined and tested ;
and proceed to inquire whether the poles be two or more, and whether equal or un-
equal in the intensity of their action : and in the first place we shall suppose the
intensities equal.

Recurring to the figure in (III.) and the conditions that are tabulated, as (5.), (6.),
(7.), we have the quantities designated as a, b, c, A, B, C,f, g, h, and the correspond-
ing ones for any number of points M^ N^ P^ Q^, &c. from actual observation and the
calculated equation of the magnetic axis. From any two of these, as (5.), (6.), we
then shall be able to compute t and u. The remaining equations, whatever be their

CONCERNING TERRESTRIAL MAGNETISM. 231

number, will serve as tests of the truth of the dual hypothesis with the poles of
equal intensity.

It will be the most convenient method of taking the point O, to assume for it the
intersection of the magnetic axis by the perpendicular from the centre of the sphere.
Having, then, the distances of the poles from this point, and the equations of the line
in which they lie, we can easily determine their coordinates, the great object of our
inquiry.

It can be no objection to this process that it necessarily requires the solution of
equations of a high order, since it is only the solution of it in the case of given nu-
meral coefficients, and not with literal coefficients. The method of effigcting these
solutions with rapidity and precision is now well known, and need not here be dwelt
upon. We shall have occasion hereafter to employ them in the numerical solution of
this special problem*.

IX. — If we suppose the intensities unequal, we can assume their ratios to be that
of F, to F^;, or R. The relation upon which (5.), (6.), (70? ... are founded no longer holds
good in this case. Nevertheless, by reference to (XIV.) we see that the difference is
only in the numeral coefficients of the equations, and not in the form or the number of
terms, or in any circumstance that alters in the slightest degree the labour or the dif-
ficulty of the actual solution. We have however, in consequence of the new quantity
R which is thus introduced, to employ one equation more derived from observation-)-,
and one only. Hence still in this case, too, four observations are sufficient, not only
for the determination of the actual position of the poles, but also to furnish a test of
the accuracy of the hypothesis. As a method, then, this also is complete, and the
problem is fully brought within the reach of known and familiar operations.

X. — As a specimen of the method of computing the equations of the magnetic
needle, I have given calculations for Chamisso Island, Valparaiso, Paramatta, Port
Bowen, Paris, and Boat Island ; and that the whole process may be distinctly seen,
I have also given the equations of the magnetic axis itself as deduced from the equa-
tions of the first four needles, and a comparison of the result with the Paris needle.
That result is not very favourable to the theory, provided the observations themselves
are considered trustworthy. But since those philosophers who have had most ex-
perience in the use of magnetical instruments, and especially of the dipping-needle,
are most strongly convinced that there are errors attached to all our present instru^
merits and modes of observation whose amount vitiates any result obtained by them,

* I refer, of course, to Mr. Horner's method, published in the Philosophical Transactions for 1819, and in
the fifth volume of Professor Leybourn's Mathematical Repository. It is unnecessary to add, that all the
f^ective methods of solution of algebraical equations that have since appeared have been but imitations of

Ax. Horner's, however much the notation and /orm of the reasoning employed in them may differ from his.

t Or if we seek to determine the actual value of F^ and F^^ we shall want all the four complete observations.

232 MR. DAVIES'S GEOMETRICAL INVESTIGATIONS

I have not thought it necessary to add any further discussion of the question in the
present stage of my investigations, in as much as till the results can be ensured as un-
affected by extraneous sources of error, all methods must alike be useless, since they
are alike dependent upon data that are at least unsatisfactory if not erroneous. There
is some reason, however, to hope, since the attention of the scientific world is now so
intensely turned to researches of this nature, that there will at length be discovered
some methods of observing which shall be free from this class of errors. However,
till this is done, it would be useless to attempt the discussion of the present or any
other method of mathematical investigation into its numerical details : and the ut-
most we can now perform is to lay down methods of investigation by which, when
satisfactory experimental data are obtained, the question may be brought to a deci-
sive test at once.

I should also state here, that in consequence of the great labour attending the cal-
culations of the axes, I have been led to examine the method of construction by de-
scriptive geometry, (especially on account of the facility and the considerable degree
of certainty which may be attached to its solutions,) of the problem of describing a
line which shall rest upon four given lines. In any case where the data are so uncer-
tain as the present, such a method is sufficiently accurate, since in very few cases will
the errors of construction be probably near so great as the errors in the data them-
selves. The geometrical problem itself is not in practice so simple as could be desired,
at least by any method yet made public, but still it offers far greater facilities than
the algebraical one. It has, moreover, one important advantage which the algebra-
ical has not, viz. the ready and visual exhibition of those cases which are unfit for
this method, or those in which a small error in the data will greatly increase in the
result. It should hence be always used before the algebraical. No doubt the alge-
braical method may be rendered subservient to the same purpose, but then the me-
thod is intolerably operose, and hence, practically, almost useless.

By employing such constructions, I find that there is a greater degree of approxi-
mation in the few magnetic axes which I have determined by them from existing data
than appears compatible with any other theory of the constitution of the terrestrial
magnet than that which considers the magnetic force situated in two isolated centres
or poles. By this I would not be understood to say that the approximation is close,
but simply that, in comparison with all the positions which lines may take, there
seems to be one region of space, in reference to the coordinate planes or planes of
projection, into which they dispose themselves, but dispose themselves very irregu-
larly in it.

As I expect to be favoured, by the kindness of my distinguished colleague Mr.
Christie, with the results of the observations of the late lamented Captain Foster,
I shall probably resume this branch of the subject at an early period ; and hence any
further details respecting these constructions which may appear necessary will be
with more propriety included in a future than in the present paper.

CONCERNING TERRESTRIAL MAGNETISM.

233

The equations of the magnetic needle for different places, in reference to rectangular
coordinates, when the geographical coordinates, dip, and variation are given.

Let A O A' be the meridian of Greenwich,
E O Q the equator, C the position of a place
where a magnetic observation is made, A C B
the variation, and B C equal to twice the dip
of the needle. Then B is the point on the
surface of the earth towards which the dipping-
needle is directed, and that in which the straight
line which coincides with the needle intersects
the earth a second time.

Estimating (as is done in my paper on Sphe-
rical Loci before referred to) the positions of
places on the surface of the earth by means of
the polar angle C A O and radius -vector C A, we
have the coordinates of C directly from observation ; and by means of the triangle
A C B, whose sides B C, C A, and included angle A C B are given, we can compute
the coordinates of B. Denote the polar distance and polar angle of C by a^ j3^, and
those of B by a^, 1^^.

In the next place, by the employment of equations (1.), (2.) of IL, we may obtain
the equations of the needle, referred to three rectangular axes, the coordinate planes
of which are the meridian of Greenwich, the meridian of 4; 90°, and the equator.
The results for the six different places before mentioned are given in the last column
of the following Table. The construction of the Table itself is indicated at the head
of each column, in a way that renders further explanation unnecessary.

Place, Date, Observer, and
Authority.

Port BoAven. 1824.
Capt' Parrt & Foster.
Phil. Trans. 1826.

Boat Island, 1821.
Captain Pahry.
Voyage, I.

Chamisso Island. 1827.
Captain Beechet.
Voyage, A pp. p. 732.

Paris. 1829.
M. Arago.
Annuaire, 1830.

Valparaiso. 1821.
Captain Bash- Haix.
"Magnetism," Enc.Met

Paramatta. 1823.
Sir Thomas Brisbane.
Phil. Trans. 1829, pt. 3.

Geographical coordinates
of the place.

Lat. 730 14' 0"N
Long. 88 54 0 W.

Lat. 68° 59' 13" N
Long. 53 12 56 W

Lat. 66° 12' 0"N,
Long.161 46 0 W.

Lat. 48° 50' 0"N.
Long. 2 20 0 E.

Lat. 33° 1' 0"S.
Long.288 29 0 E,

Lat. 33° 48' 50" S.
Long.151 1 34 E.

Ob

served position of
tlie needle.

Dip.
Var.

81°
124

1'24"N.
0 0 W

Spherical coordinates of
the place of observation.

Dip. 82° 53' 40" N
Var. 72 2 0 W.

Dip. 77° 39' 0"N.
Var, 32 0 30 W,

Dip. 67° 41' 18" N.
Var. 22 12 5 W,

Dip. 38° 46' 0"S.
Var. 14 43 0 E.

Dip. 62° 57' 0"S.
Var. 8 47 41 E-

=

16=

— 88

46'
54

0"
0

«/

^

=

21°
- 53

0'47"
12 56

/3.

=

23°
-161

48'
46

0"
0

Spherical coordinates of
the second intersection.

cc„= 165° 25' 32"
li„ = - 256 3 55

a, = 41° 10' 0"

;3, = 2 20 0

a, = 123° 1' 0"

/3, = 288 29 0

«, = 123° 48' 50"
/3, = 151 1 34

«„= 151° 5' 36"
a,, = = 204 45 57

a„= 133° 34' 36"
/3„ = 0 27 25

Rectangular equations of the needle.

X = _ -278746 z - -023702 r
y= -0346112- -027756 r

x= - •270U7z- -034011 r
y= -122598 2- -122598 r

«„= 96° 10' 34"
li„ = - 1C2 10 56

156°58'2r
85 20 23

«,, = 109° 46' 44"
li„ = - 21 23 25

»= - -081565 2- -051635 r
y= - -690471 z + -248470 r

x= -384722 2- -262819 r
y= 1-8645002- -745899 r

T = - 3-159630 2 - 2-518180 r
y- -621395 2+ -206769 r

= - 3-418875 2 - 1-500120 r
y = 7-349865 z + 3-363313 r

MDCCCXXXV.

2 H

234 MR. DAVIES'S GEOMETRICAL INVESTIGATIONS

XII. — We may now proceed to compute the equations of that straight line (or lines,
for there are two, but determined by the same series of processes,) which rests upon
any four of lines determined as those in the last section were found. Thus we shall
take as an instance Chamisso, Valparaiso, Paramatta, and Port Bowen, the equations
of which are given in the Table.

Assume as the equations of the magnetic axis the two following :

X =: az-\- a,

and denote the several equations of the needles by equations of the same form, but
with the constants accented, viz. a' b', oc' |3' : then the conditions of intersection will,
in each case, be expressed by the equation

(«' - a) (b' -b)- (,G' - (B) {a' - a) r= 0.

The insertions of the actual values in the four cases mentioned above being made,
and the vincula thrown open, we obtain

•055920 + -690471 a — '081565 (5 + '248470 a + '051635 b + ub — a(i = 0,

— •911471 — -621395 05 —3'1 59630 f3 + '206769 a +2^518180 ^> + a Z> — rtj8 = 0,
•473095 —7-349865 a —3-418875 |3 +3-363313 a -\-l'500l20 b -\- ub — a|3 = 0,

— •008188— •034611a- •278746(3- -027756 a + ^023702 6 + afe — a(3 = 0.

Subtracting each of the last three of these from the first, we obtain

b = -391938 + •531872 a +1-247954/3 + -017024 a,
b= - -288008 + 3-550860 a +2-304000 13 - 2^150420 «,
b = —2^295058 -25-957900 a —7*059053 13 —9*888800 a.

Subtract the two latter from the former of these, then there result

«= —-271254 — 2-674164a — -838603/3, and
a = — -313706 +1-392881 a +-487231 (3.

From equating which values of a we obtain (3 = -032019 —3-067660 a.
Insert this value of j8 in that of a, and we find a = — -298105 — '101755 a.
In a similar manner, from the proper substitutions, 6 = '426822 —3-288083 a.
And inserting all these values in the first of the four equations, that of the Cha
misso needle, we obtain

a2 —'071009a = '003821, and hence a = '035505 +'071274.

The two pairs of equations which result from this calculation, then, as those of the
magnetic axis, are

x=: --308970 5J +-106779r,
1^ = -075732 2 —•295538 r ;

and X = —•294465 z —•035769 r,
y— •544430 5; +^141744r;

according as the + or — sign is taken in the valuation of a.

In the same way we may proceed to find the magnetic axis which would accord
with any other four observations, and by a comparison of these ascertain whether the

CONCERNING TERRESTRIAL MAGNETISM. 235

discrepancies were such as to admit of account from the errors of observation and
the imperfection of instruments. However, it is much simpler to ascertain whether
the axis thus determined agrees with the observation made at a fifth or a sixth place.
Let us take the Parisian needle as an instance.

By recurring to equation (36.), and putting the values o^ ah and a |3 just deter-
mined and those of a7 b^ and a^ |3^ found in the table of section XI. for Paris, we have
the least distance between the Parisian needle and the magnetic axis either •173341 r
or '189540 r, according as the + or — sign above mentioned is employed.

These are between a fifth and a sixth part of the terrestrial radius. We may now,
were it necessary, seek the coordinates of the points in which the line of shortest
distance intersects the two different magnetic axes and the Paris needle, and thence
the equations of the lines drawn from those points to Paris, and thence again the
angle formed by the Paris needle, and each of the other lines : that is, we should find
the error of observation in the Paris needle if we suppose the magnetic axis correctly
determined from the other four needles. But it is unnecessary to go through the
computations, as it is easy to see that this angle will not be very different from (but its

difference, whatever it be, will be greater than it,) tan"" '173341, and tan"^ '189540,
that is, about 10° or 11°. The discrepancies in every other case that I have tried are
as great as, and in most of them still greater than, in that just examined. The further
prosecution of this branch of the inquiry, with our present data, must therefore be
abandoned.

XIII. — So far as method is concerned, the previous processes are perfectly adapted
to decide the question of the duality and the equality of intensity of the magnetic
poles. In the absence, however, of data upon which full reliance can be placed, we
are not at present able to apply that method to the actual circumstances of the earth.
It hence becomes desirable to examine certain other phenomena, to ascertain whether,
in their general bearings and character, they also are compatible with the hypothesis
of two such centres of force. These are : — the^points at which the needle becomes ho-
rizontal, constituting the magnetic equator ; the points at which the needle becomes
vertical ; the curves of equal dip ; the Halleyan lines, or curves of equal variation ;
the lines of equal magnetic intensity, or isodynamic lines of Hansteen ; and those
particular cases where the isodynamic line is reduced to a point, which constitutes
the "pole" in the language of Hansteen and a considerable number of modem writers.
The first two of these I shall examine in the present, and the remaining ones in a
subsequent paper. I then propose to enter into a minute numerical discussion of
such observations as I may be able to obtain in the interim ; and of course attempt
to ascertain how far any one may be vitiated by instrumental or local circumstances,
and how far the geometrical peculiarity of the observation itself may render it unfit
for our present method of investigation.

I do not propose this course without being fully sensible of the difficulty and
labour it entails upon me ; but at the same time I feel perfectly assured that any

2 H 2

236

MR. DAVIES'S GEOMETRICAL INVESTIGATIONS

assistance which it is in the power of men of science to afford will be freely offered
me ; and especially in furnishing such observations as they themselves place most
reliance on, together with the circumstances under which the observations were made.

XIV. — On the Magnetic Curve.

Let F^ and F^^ denote the intensities of the forces
situated in the two poles T, U ; and /3 the angle
which the needle, subjected to the action of those
forces and situated in a given point N {xy), would
make with the axis of (x) the magnet itself. Let also
r 2 = 3/2 _j_ (^ + af

r,^=y'^-\- {oc - af.
Then the usual considerations give us

F,(;t- + «) .).F,(.

f7J^ = »«»'^ (37.)

But if we represent tan /3 by ^, we shall have the differential equation of the curve

to whicii the needle will be a tangent, and which passes through that point, xy. To
find the equation of the curve itself it only remains then to integrate

rf r^f

_ ^y

dx

(38.)

u 'It

Multiply the numerators of all the terms of the first side by y, and also multiply
out the denominators ; then there will result

F,fdx- F,2/{a; + a)dy Y^^y^dx - F„y{x - a)dy

In the former of these numerators add and subtract F^ (x + a)^ dx, and in the latter
F,^ {x — ay dx\ then we shall obtain another form, which is immediately integrable.

It is

F/ {y + (^ + of} dx - F^ (^ + a) {y dy ^ [x^ dfdx}

rf

I Fy<{y + (^ — of} dx — F;,(:r — a){ydy + {x — fl)<^^}_n.

"T" r^ ^»

the integral of which is

F/(^ + «) , F;,(.r-g) __c_

r^ I" Tt, ""a' ^^^-^

in which — is the arbitrary constant which particularizes the individual curve we

CONCERNING TERRESTRIAL MAGNETISM. 237

may have occasion to consider. It is determinable from any one condition; as
passing through a given point, touching a given line, &c.

But — - — and — - — are the cosines of the angles which the directions of the com-

ponent forces make with the axis of x^ that is, with the magnetic axis; and hence, de-
noting these by ^^, &^^, (being estimated from the same branch of the axis,) we shall
have

F^ cos &^ + F^^ cos ^^^ = 2 cos |3', (40.)

where /B' = cos" ^ -x—.
' 2 a

This equation having the values of r^, r^^ and )3 restored, becomes
F/ (-y + a) , F,^ {x - a) _ c

>/y^ + (^ + «)3 "^ -/y + (^- - a)2 2a^ C41-;

which, when deprived of its radicals and denominators, is of the eighth degree.

We might, however, obtain this property in a different manner ; and as it also fa-
cilitates the investigation of one or two other theorems which we shall require here-
after, it may with propriety be added here.

Let T and U be the poles, N the centre of
the needle. Let, as before, the forces be F,
and F/, ; let T N S and U N S, the angles made
by each of the component forces and the re-
sultant one, be called A^ and A^^ respectively.
Let r^ and r^^ be the distances T N, N U, and
^^, &^^ the angles N T S, N U S ; and take N h ;

F F
N ^ : : -| : -f, and complete the parallelogram 'S kng. Then N n is the position

of the needle. Produce it to meet the axis T U in S ; and draw the perpendiculars
T K and U L upon N S. Then by the composition of forces

In
sin 4 p_ sinj?Nw"| _ N;j _ J^ __ F/, r/

sin Jy

Denote now the angle N S T by 2, and TS, U S by # and u respectively. Then

t

i/yL~singNwJ "Ny" F, "" Y^'r,f ^^ '*

sm JS"
sin A^ r^ t Vi,

^^i'^if-sin^-""^

r,,

(43.)

or by comparing (42.) and (43.), we obtain,

— — ?m!± ...... ^44 )

a relation which, when F^ ± F/, = 0, is already known*.

* Vide Leslie's Geometrical Analysis, art. " Magnetic Curves" ; or Mr. Baklow's Treatise on Magnetism
in the Encyclopaedia Metropolitana, p. 794.

238 MR. DAVIES'S GEOMETRICAL INVESTIGATIONS

Represent now the perpendiculars by p, and p^^, and then, by the common formula
for the inclination of the tangent to the radius-vector, we have

Hence

or

^ - _ ^^'^^/ -A - ImtI

or again, since ^ = -^^', it becomes finally

F^ sin d,d0,-{- F,i sin ^^ d d„ = 0,

the integral of which, as before, is

F^ cos 0, + F^, cos d^i = 2 cos |3'.

If now we take F, + F^^ = 0, or F^ = — F^^, we shall have our formula simplified,
at the same time that we adopt the hypothesis which seems best to accord with all
we yet know of the disposition of the forces in the artificial and also in a natural
magnet ; and hence it is the most appropriate assumption we can make respecting
the constitution of the terrestrial magnet itself. We shall thus have

cos 0, — cos 0^1 = 2 cos |3,
where cos |3 = F^ cos j3 ; or, since one of these angles is external to the triangle N T U
formed by the magnet and its polar distances from N, we may substitute instead of 0^,
its supplement, and then the last equation will take the form

cos 0, -\- COS dif = 2 cos (3 (45.)

This property was originally given by Professor Playfair in Professor Robison's
article "Magnetism," published in the First Supplement to the Encyclopaedia Britan-
nica. See also Robison's Mechanical Philosophy, vol. iv. p. 350. Professor Robison,
from one or two passages in his writings, seems to have entertained some idea that
these curves could be rendered available to an explanation of the phenomena of ter-
restrial magnetism ; but I do not recollect that either he or any one else has sug-
gested how this was to be accomplished, nor, much less, attempted to actually ac-
complish it by such means.

XV. — If, still considering the axis of the magnet as the axis of cT, we conceive the
magnetic curve to revolve about that axis so as to describe a surface of revolution,
its equation obviously is obtained by putting 3/^ ^ z^ instead of y^ in the equation of
the generating curve. That is, the magnetic surface is expressed by the equation
a + a X — a c_ .

vy T^^TT^-T^)^ ^i/^ + z^ + {^- af ~" a V •;

In this equation of the magnetic surface, a, or half the length of the magnet, is
constant, and c is arbitrary, giving different curves according as the value of that
parameter is varied.

CONCERNING TERRESTRIAL MAGNETISM. 239

Again, since we can refer this surface, or any one of its meridional sections, to any
new system of coordinates, we may conceive the last equation (46.) to be so trans-
formed as to represent the same geometrical surface that it now does whilst it is re-
ferred to the centre of the earth as the origin, and to the mutual intersections of the
equator and two rectangular meridians as axes of coordinates. This transformation,
however, by the usual processes, would be extremely difficult — perhaps impracticable
— on account of the labour it would require ; but this labour may be almost wholly
avoided by means of the property (Playfair's) of the curve referred to the polar
angles expressed in equation (45.).

Let the coordinates of the poles T and U referred to the above-named axes be
a^ b, Ci and a^^ b,, c^ respectively ; and the individual curve defined by the parameter ^.
Then viewing d^ and O^i as the two internal angles, we shall have

^{a;^a;)^ + (^-b;)' + {z-c;)' + (a,^a,;)^ + {b,-b,;)^ + {c,-c,;}'-(a;-a,;)'-{:y-b,^^^^
2^ {(«,~«,)^ + (^',-6/ + (c,-c/} X {G^-«/ + (y-*/ + (^-c/}

__ (a,-^) (a,-a,>) + (br-^) {b,-b,^ + {c,-z) {c,-c,^

and

From (4.), (12.), and (13.), we have at once the equation of the surface, viz.

(x - a,) {a, - g„) + (y - b,) (b, - b„) + {z - c,) (c, - c,;}
^(a;^a,y+{t/-b,)^+{z-c,f

_ (^ - a,) (a, - a,i) + ( j/ - &//) {b, - b,;) + (z - c,,) {c, - c,,)

= ±2cos/3^/(a^-aJ2+(^_y2^(e«c,)2=:-f4«cosf3.

This equation, deprived of its radicals and denominators, like the equation of the
generating curve, is of the eighth order.

Now by varying the parameter j8 (which defines the particular surface upon which
the point we are considering is situated,) by minute increments, we shall have a series
of thin strata, each of which is isolated and independent, and which, collectively, ex-
tend through all space. If, therefore, we conceive these strata to be infinitesimally
thin, we may consider the magnetic influence extended over a series of surfaces,
eaeh of which has the property of being touched by a small needle placed at any point
in that surface. If, moreover, we conceive the sphere arid each of these surfaces to
be cut by a series of meridian planes passing through the magnetic axis, we shall
always find some one magnetic curve on each side of the magnetic axis which will
touch the two segments into which the magnetic axis (prolonged if necessary) divides
the circle lying in that magnetic meridian plane. At these points the needle will
touch the sphere, or, which is the same thing, it will be horizontal to the earth ; and

> (49.)

240

MR. DAVIES'S GEOMETRICAL INVESTIGATIONS

as there will be such points in each of the consecutive meridional sections, there will
be a series of consecutive points on the surface of the earth at which the needle will
be horizontal. These points lie in a continuous curve, which has been called the mag-
netic equator ; and we proceed to inquire into the character of that curve.

XVI. — On the Magnetic Equator.

Let T U, as before, be the poles
of the terrestrial magnet, and TNU
that one of the magnetic curves
which touches the corresponding
magnetic meridian of the earth
QNRinN.

Put for the moment the equation
of the circle Q N R under the gene-
ral form

{x - cf + (y - hf = r2 ;

(50.)

and denoting by ^^0 and g^,0 the
coordinates of Q and R respectively,
we shall find

c = €^', andr2 = i2 + (fi^'y (51.)

Inserting (51.) in (50.), and reducing the equation, the circle is finally expressed by

^[-gi + g,^-\-g^S,i^y'' - 2 % = 0 . (52.)

This involves the arbitrary quantity b, which is the parameter upon which the iden-
tical circle depends.

d y

Since this circle is to touch the magnetic curve at some point N, the values of -^

derived from the equations of the circle and magnetic curve at their common point
{xy) must be equal ; and as the arbitrary constant in the equation of the magnetic
curve vanishes by differentiation, we shall have three equations between which to

eliminate the indeterminate quantities -^ and h. This elimination will leave one

equation between w and y, which will designate the locus of the point N.
By differentiating (52.) we obtain

dy_ _
dx

(53.)

And the differential equation of the magnetic curve is, from (38.) and F^ -|- F^^ = 0,

^y

dx

y y

3

x-'ra x—a'

(54.)

'H

CONCERNING TERRESTRIAL MAGNETISM. 241

Also, from (52.),

2(^^b)=^^^^^±^i^^^^I^ (,,,)

y

Insert (55.) in (53.) ; then there results, after combining (53.) and (54.) and slightly
reducing

{x + a)r,^-{x-a)rf^ f - ^^ + g, + g,,^ - g,g^,' • • • • K^^-)

which is a rectangular equation to the curve which is traced out by N. It separates
at once into the two components

3/ = 0 (57.)

^/ - ^/^ _ y,±gu-^^ . .

{x + a)r^^-{x-a)r'^ f - oe^ + g, + g,,^ - g,gi,' ^ '^

which last is readily reduced to

{y^ +(x + ay^a-{-g,.a-{-g,} r/ = {3^2 -{. (^ - a)'^ - a ■-- g,.a- g,,} rf. (59.)

Squaring both sides, and restoring the values of r, and r^^ it becomes an equation

of the ninth order ; in which, arranging according to powers of x or 3/, the coeflScients

become very complex, and altogether unmanageable by any of the usual methods.

It is of the form

(^-^, + ^.)3/' + A^« + By + C3/2 + D=:0, .... (60.)

where A, B, C, D are functions of x, which in all cases render the terms not
higher than of the ninth degree.

XVII. — Though we cannot completely discuss the course of the curve and the
character of its singular points by means of this equation, we may yet learn some
particulars of its general features with considerable facility ; and as they will be of
great use to us in our future inquiries, we shall insert them here.

1 . Since y appears only in even powers, the curve is composed of pairs of branches,
such that the branches in each pair are equal and symmetrically disposed with respect
to the axis oi x.

2. Since x appears of an odd degree, there will be at least one real value of x for
every value of y, whether y be positive or negative. There will at least be one pair
of equal and symmetrical branches, and these branches will be infinite ones.

3. Since (y"^) appears of th^ fourth degree, there may possibly be four values of y"^
for every specific value of <r ; but there cannot possibly be an odd number. Of these
four possible roots any number may be minus, and the corresponding values of y
itself be still impossible or imaginary. But by art. 2, there must be at least one pair
of real values of y, there must be at least two real values of y-, one of which must
be -f-j for every value whatever of <r.

4. Also four is the greatest number of pairs of symmetrical branches that can exist.

5. If the system be made to revolve round the axis of symmetry (that of x), it will

MDCCCXXXV. 2 I

242 MR. DAVIES'S GEOMETRICAL INVESTIGATIONS

generate as many sheets of surface as there are branches in the curve ; but as the
symmetrical branches of the curve generate superposed sheets of surface, or sheets
which are geometrically identical, the number actually described is only half as great
as the number of branches. There may hence be one, two, three, or four sheets of
surface generated, according as one, two, three, or four of the values oi'if- are real and
positive ; and upon any point in one of these a minute needle being placed, and a
circle described through that point and the points Q R, the needle will find its re-
pose in that plane, and be a tangent to the circle at that point.

6. The intersection of these four sheets of surface with the earth's surface would
give four separate and continuous lines upon the surface of our globe, upon any point
of which the needle being placed, it would be horizontal. In other words, there may
be four such lines as that which has been denominated the magnetic equator.

7. Observation, however, seems to indicate only one single branch of this inter-
section ; though it must be confessed that the greater part of the observations, and
the mode of determination of the position of the equator, are far from satisfactory,
llie great difficulty of procuring good instruments, and the almost equally great
difficulty in making a correct observation with any instrument whatever, at places
which would give results free from suspicion of foreign and local sources of error ;
the extremely small number of observations actually attempted, and the very hypo-
thetical character of the formula by which the equator is determined from observations
made on either side at the distance of a few degrees ; all these reasons, and others,
render the delineation of this line, as laid down by M. Morlet, very far from satis-
factory. The four branches may indeed be easily conceived to lie so near to one an-
other, that of points which have been actually observed or inferred from observation
and theoretical reductions, some might be in one and others in other branches of the
fourfold system of lines ; and hence that the spherical polygon traced through these
might not be in reality composed of chords of any one single branch of the system.

8. It therefore becomes necessary to examine the curve more minutely as to the
number and circumstances of the branches of which it is actually composed on any
hypothesis which is consistent with the other phenomena to be accounted for. Since,
however, the general equation in terms of x and y is altogether unfitted for our pur-
pose, and the equation between the radius vector and polar angle offers no simplifi-
cation in the form of the expression, I was led to attempt it by examining the relation
which subsists between the angles made by radiants from the poles to points in the
curve, with the line joining the poles. This also proved almost equally useless in
respect to the purpose I had in view ; but upon trying the radiants themselves the
object was completely attained.

Resuming equation (59.), and recollecting that

y^ + (« + «)^ = rf
y2 + (^ - of- = r/,

CONCERNING TERRESTRIAL MAGNETISM. 243

and putting also for abbreviation (and at the same time retaining the homogeneity
of the equations into which these terms enter,)

a+g,-a + g„ = k'^

we have (59.) converted into

(r;^- h^)r,^-(r,;^-¥)r^ = 0; (61)

or, arranging them in reference to r^^ it is

"^if — r^ L h^ ' ^if — — rf -h^ (62.)

For r,, write r + s(r^'-^h^Y ^^^ ^^^ equation (62.) becomes

which is a cubic equation wanting the second term, and which for accommodation
to the usual notation may be written for the moment thus :

r3 — 3 c r = 2 </. x

Then we have

^^"^ ""~ Ax%r{rl-h^f V64.)

Now in the case before us, putting g^= — (a-\- a) and^^^ = (a + ««), which, since
the poles of the terrestrial magnet being either within or upon the surface of the earth
is always the case in nature, we have

h'' = a- g,.a-g,==-a,{2a-{- fl,)l

A:2 = a-\-g, .a-\-g^,= —a,{2a-\- ajj'

and which equations, since a, a^, and a^ are essentially -j-, are themselves essen-
tially —. These values of A^ and k'^ inserted in (30.) render the whole value of
(^ -\- d"^ essentially +, whatever the value of r, may be. There is hence one pair of
symmetrical branches indicated by this method also, as in the former. But in addi-
tion to this we learn at once that there is ow/y one such pair ; since when the root is
given by Cardan's formula, (which is the case here,) that root is the only real one*.

9. The conclusion is now established, that there is only one sheet of the tangential
surface compatible with the actual condition of the terrestrial magnet, and hence only
one line of intersection between it and the earth's surface ; or, in other words, the
magnetic equator is one isolated and continuous line on the surface of the earth.

10. Also, since from other considerations it can be shown that the two poles are

* Lagrange's test might have been employed instead of this ; but as that appears to be something more
laborious, I have preferred the present one.

2 I 2

244 MR. DAVIES'S GEOMETRICAL INVESTIGATIONS

not in the same diameter of the earth, nor equally distant from the centre in any
chord of the earth, the two axes of revolution of the sphere and tangential surface do
not coincide ; and hence their common intersection is not a plane, nor its trace on
the sphere, that is, the magnetic equator, a circle of any magnitude whatever. It is
therefore a curve of double curvature. The conclusion, therefore, deduced by Biot
from Humboldt's observations, and the conclusion deduced by Morlet from the
discussion of all the observations he could collect from authentic sources, are quite
consistent in this respect with the hypothesis of the duality of the poles.

11. The discussion of any further cases of this problem need not be given here. In
a geometrical point of view the discussion would be interesting, and under that aspect
this paper would be incomplete without them ; but as they have no bearing upon the
main object of the present research, and are moreover so perfectly analogous to those
we have just given as to offer not the slightest ditficulty by the same method which
has been here employed, any further notice of them would be altogether superfluous,
and irrelevant to the purpose we have in view.

12. It is to be remarked, however, that these results are true only on the hypothesis
of the forces in the poles being related by the equation F^ 4: P,, = 0. Under any
other condition than this the highest power of x would not disappear from equation
(59.) ; and hence the equation would be of an even order, and hence the branches of
the magnetic equator would be tivo at least, and always an even number. The ap-
parent singleness of branches furnished by observation is a strong argument in favour
of the duality of the poles and equality of their intensities ; but as the method by
which the magnetic equator has been laid down is far from satisfactory, too much
reliance should not be placed on this argument, decisive as it otherwise would
certainly be.

13. The equation of the tangential surface and the equation of the sphere would
completely define that line considered in reference to rectangular coordinates ; that
is, in the usual manner of considering the equations of lines situated in space. In
the form of the equation of the locus of N on a meridian plane marked (60.), we
have only to write i/^ _j_ ^2 instead of y^^ and the result is the equation of the surface
referred to the axis of x and any other two axes at right angles to it and to one an-
other. The coordinates of the centre of the sphere referred to these axes, and the
radius of the sphere, being also given, we have its equation in the usual form, viz.
r2 = {x — a^)2 ^ (a^ — h,)^ + (2. — c^. By the transformation of coordinates we
can change the axes of reference to any given axes, as, for instance, to the polar
axis and the intersection of the equator by two rectangular meridians. In the next
place, to adapt the expression to the usual mode of denoting spherical position,
(latitude and longitude,) we must transform this into a polar equation, and put the
radius vector of the resulting equation constant and equal to the terrestrial radius.
The equation thus obtained will be one between the latitude and longitude of the
points which constitute the magnetic equator.

CONCERNING TERRESTRIAL MAGNETISM.

245

The state of the physical problem is not at present such as to render any further
mathematical details respecting this curve necessary in this place.

XVIII. — On the Points of the Earth's Surface at which the Needle takes a position

vertical to the Horizon.

As our hypothesis is that of two poles, or resultant centres of force, the freely-
suspended magnetic needle will always lie in the plane which passes through its own
centre and the centres of magnetic force. The dipping-needle lies, therefore, wholly
in the plane passing through the place of observation and the true magnetic poles.
But when the needle is vertical to the horizon, it passes through the centre of the
earth ; and hence the plane of the magnetic meridian also passes through the centre,
and makes with the sphere a section, which is a great circle. Also, as this plane then
passes through three points not in a right line, it is unique ; or, in other words, there
is only one circle of the sphere in which the needle can be placed to be capable of
taking a vertical direction, and that is a great circle.

It is also obvious, from the expressions already given for the inclination of the tan-
gent to the radiants from the poles to points in the magnetic curve, that there are
only isolated points in that circumference in which the phenomenon of verticity can
take place ; and it is our business in this section to inquire into their possible num-
ber, and the method of determining their actual number and their respective po-
sitions.

XIX. — Let O be the centre of the
great circle in which we have just
shown all the possible vertical nee-
dles must lie, and T U the magnetic
poles, and N one of these points.
Take the centre of the circle as ori-
gin of coordinates.

Let T U be denoted by the coor-
dinates a^ h^ and a^^ b^ respectively ;
then the equation of the magnetic
axis is

{x-a){b„^b)=:{y-b;)ia„-a)i66.)
Also the equation of O N is

^y-^'i/ = 0, . . . (67.)
where jc'y' are the coordinates of N.

The intersection of these gives the coordinates of R, the point where the tangent to
the magnetic curve at N, and whose poles are T and U, intersects the magnetic axis.

From (66.) we have

246 MR. DAVIES'S GEOMETRICAL INVESTIGATIONS

y = ?/Lzl/^_VLzA^/ (68.)

and from (69.) we have

y = f^^,. . . • • • • (69.)

which two equations, (68.) (69.), equated, give, after simple reduction,

and hence also ^ (70.)

Again, we have,

1 K - j «, - ^^^^ - ^) ^ - (a, - «,)y J '^V' ib, - ^.,)^ - (a, - a,)y / I

_ {(«, - a;f + {b„ - b,n {b,x' - a,yr \^^^'^

{(5,~z.,)y-(«,-ar)yr * -^

And in the same manner we obtain

R TT2 — {(^„ - «y)^ + {b„ - b,y} {b,,x'-' a,it/) .^^ .

{{bu-b,)a:>-{a„-a,)yr ^ ^^

Also

TN2=(«^-^)2+(5^-y)2 . (73.)

UN2 = (a,-a^)2 + (^^^-y)2 (74.)

But by the property of the magnetic curve, expressed in equation (44.), we have

RUUN^
R T — T N3'

or

b.^- a,I/' _ r (a, - ^r + {b, -1/y I i-
b„:^-a,^-\{a,-a:'r + {b„-2/rS ^^^'^

This is the equation of the curve of contact of the tangent from O to the magnetic
curve, whose poles are T and U, with the curve ; and in rectangular coordinates is,
like the magnetic curve itself, of the eighth order when freed from fractions and ra^
dicals.

Having now eliminated x^ from the preceding equations in which they appeared,
we may drop the distinguishing accents from o/y in (75.) and reduce the fractions
and radicals. We thus obtain

(b, X - a,yf{(% - xY + {b, - yY)^ = (^, x - a,yf {{a, - xf + {b, - yf}^ . (76.)

And, as the intersection of this curve with the circle gives the points concerning
which this inquiry is instituted, we may write the circle at once, its radius being r,

x^ + y^=:r^ (77^)

CONCERNING TERRESTRIAL MAGNETISM. 247

The determination of .r and y from these two equations will require the solution of
an equation of the tenth degree. For putting (76.) under the form

(*/ ^ - f^iV? W + V + ^2 _|. ^2 _ 2 («^^ X + h^^yf
= (*/i ^ - «/;y) W + ^,2 4. ^2 + ^2 _ 2 [a^ X + h^y)'Yy

we have it converted at once, by means of {77-), into

{b^ x-a,yY [V 4. b2 + r2 - 2 (a, a: + A, y)^ 1 .

= (i,x-a,3/)h2 + ^^2 4^2_2(a,a. + ^.3/)P. J ^ '^

Hence by means of (77-), which is of the second, and (78.), which is of the fifth,
degree, we obtain an equation of the tenth, from which to determine x or y, and hence
to find the points at which the needle will be vertical. Still the reduction is ex-
tremely laborious, and hence, also, our means of determining how many of the roots
are real, and how many are imaginary ; that is to say, how many of its roots are
compatible, simultaneously or separately, with the values to which a^ b^ and a^ b,, are
limited by the physical which must be appended to the algebraical conditions from
which the equations (77-) and (78.) were formed. Those conditions are r^ > aj^ + b^,
and r^ > a^j^ + b^j^, that is, of the poles being within the earth ; but whether the per-
pendicular from the centre of the earth upon the magnetic axis intersects that axis
between the poles or not, cannot be, a priori, nor yet from any knowledge furnished
by experiment, at present determined. As, however, all the cases that can arise
from all possible positions of the two poles are included in the above formulae, and
as they evidently cannot simultaneously exist, we are entitled to infer that all the
roots are not simultaneously real. In the absence, however, of these considerations,
we learn that there are not more than ten points on the surface of the earth at which
the needle can be vertical ; and that whatever may be the number of them, it is at
all events even, viz. 2, 4, 6, 8, or 10. We also learn that how many soever of these
be real, they are all in one plane passing through the centre of the earth ; and with
respect to the great circle in which it cuts the terrestrial surface, taken as the axis
of spherical coordinates, all magnetic phenomena on the surface of the earth are sym-
metrically disposed. How far this is verified, within the limits of errors of observation
and of local interference with the full development of the effects of the magnetic
force, has not yet been inquired into. Indeed, till this plane has been determined it
would be impossible to conduct the inquiry in a direct manner; and as only one of
these points is yet actually assigned with any close degree of approximation, we
are not yet in a condition to enter upon the inquiry. Still, these facts combined with
observations relative to other phenomena, especially respecting dip and intensity,
(the variation for obvious geometrical reasons included,) accurately made, might
furnish important aid in a tentative determination of the plane itself; the method of
proceeding in which must be sufficiently obvious to those inquirers to whose minds
the geometry of coordinates is familiar.

248 MR. DAVIES ON TERRESTRIAL MAGNETISM.

In conclusion of the present paper I shall, though I have not been able to decom-
pose the equation which results from {77-) and (78.) into factors, yet hazard the con-
jecture of its being even in its literal form capable of such a resolution ; so that the
component equations are, when viewed simultaneously, the one essentially imaginary
with the values which render the other real. Of course these must be into factors of
even degrees, — probably two of the fourth and one of the second. Several instances
of this kind are well known to geometers ; a very remarkable one of which is the
expression given by M.Bret for the determination of the foci of a line of the second
order, in Gergonne's Annales des Math4matiques, tom. viii. I offer it, however, only
as a conjecture, which future researches may show, after all, to be too hastily made.

Royal Military Academy, Woolwich,
December 16, 1834.

[ 249 ]

XII. Researches towards establishing a Theory of the Dispersion of Light. By the
Rev, Baden Powell, M.A. F.R.S. Savilian Professor of Geometry in the Uni-
versity of Oxford.

Received February 19, — Read March 12, 1835.

Introductory Remarks.
JL HE phenomena of prismatic dispersion, as originally discovered by Newton, and
since examined throughout a vast range of transparent bodies by succeeding philo-
sophers, especially Sir David Brewster, were principally considered with reference
only to successive parts, or spaces, of the coloured spectrum, designated generally as
the red, or violet, or mean rays.

The increasing precision of modern science has been evinced in the elaborate and
justly celebrated researches of M. Fraunhofer, who, availing himself of the dark and
bright lines to mark and designate distinct points of the spectrum, by prismatic ob-
servations for ten different media, solid and liquid, has determined in each the re-
fractive indices for seven principal rays, thus always absolutely identifiable. We will
use the term "definite rays" to signify the specific parts of the spectrum thus defined.
As to the law of the phenomena, the first notion of a simple proportionality was soon
disproved. The refrangibility was seen to vary considerably and irregularly for each
ray and each medium ; and when Fraunhofer had assigned serieses of numbers as
the accurate expressions of the varying refractive powers throughout the several
spectra, the apparent absence of any law connecting these numbers was only ren-
dered more palpable. All that could be said was, that the numbers increased from
the red to the blue end of the scale, and in a different way in each medium.
' The first object of inquiry in the search after such a law, would be some other cha-
racteristic of the same definite rays, equally well determined ; between which and
the refractive index some connexion might possibly be found to subsist.

The only such characteristic, perhaps, is the length of the interval for each ray,
the Newtonian fit, or the undulatory wave, which (by whatever name it be called,)
has demonstrably a real existence in the nature of light ; and the value of which, for
each of the definite rays, has also been determined by Fraunhofer, with his usual
accuracy, from phenomena totally independent of refraction, viz., his very remark-
able experiments, in which a spectrum absolutely pure and perfect is obtained with-
out the intervention of any prism, from the interferences produced by a fine grating
of parallel wires covering an object-glass. The positions assumed by the successive

MDCCCXXXV. 2 K

250 PROFESSOR POWELL'S RESEARCHES TOWARDS ESTABLISHING

rays, here depend on nothing but the lengths of their periods or waves simply as
such ; and the intervals between them are precisely proportional to the differences of
these lengths. These lengths decrease from the red to the blue end of the spectrum.

We might search for some empirical law which should connect these two serieses
of data, the one being some inverse function of the other ; but it would be more
satisfactory should such a formula be supplied by any theory of light.

I shall not I trust be considered as assuming a controversial tone, if I observe that
no researches directly suggesting any such formula have been published except those
of M. Cauchy, on the hypothesis of undulations. In these, indeed, such a formula is
not actually developed. But in a paper in the London and Edinburgh Journal of
Science*, in the former part of which I have offered a brief abstract of M. Cauchy's
peculiar theory of undulations, some remarks upon it are given, including the de-
duction of a formula in which the relation between the length of a wave and the velo-
city of its propagation is precisely expressed ; this last quantity being in fact the
same as the reciprocal of the refractive index.

Without entering any further into theoretical considerations, it will be admitted
that such a formula, (from whatever source derived,) if found to supply anything like
a representation of the law of nature, or a clue to guide us through the seeming dis-
order which prevails among the experimental results, would be entitled to attention.

It has therefore been my object, without reference to the support of a theory, to
examine by means of this formula the relation between the index of refraction and the
length of the period or wave for each definite ray throughout the whole series of nume-
rical results which we at present possess. And it will become a matter of increasing
interest to pursue observations on the indices of definite rays for a greater range of
transparent media.

The present paper will be occupied with the discussion of the data already known;
and before proceeding to that discussion I will merely add, that whatever degree of
interest may attach to the inquiry, the merit is due to Professor Airy, in whose sug-
gestion it originated.

General Observations on the Formula.

In the investigations in the paper above referred to, on substituting for the velocity

s I

of a wave expressed by -r its equivalent — , the formula at once presents the relation

between the index ^ and the length of a wave X. H, r, and 71 are quantities depen-
dent on the nature of the medium ; r, by hypothesis, always being a sensible fraction
of "K : thus the formula becomes

^ = n

sm

(^")

* Nos. 31 et seq.

A THEORY OF THE DISPERSION OP LIGHT. 251

Here the value of ^ will evidently vary with a change in the value of X, or from one
rai/ to another ; it will also vary with a change in the constants H, r, or n, that is,
from one medium to another.

The mere inspection of the formula will suffice to show that it exhibits at least a
general accordance with the obvious constitution of the prismatic spectrum in the
greater dispersion of the blue end.

For, in general, as X is diminislied, the arc (-y-j is increased, and consequently

the ratio of the arc to its sine increases, or (jb increases. And the variation in the
value of this ratio, and consequently in that of [ju, for a given variation in X, is greater
when the arc is greater, that is, when X is less.

Thus, towards the blue end of the spectrum, where X is least, the dispersion or ex-
pansion of the rays is greatest.

But we must proceed from these very general remarks to the more precise compa-
rison of numerical values.

Comparison of Numerical Results.

In proceeding to apply the formula to actual calculation, we are met by several
difficulties arising out of the peculiar form of the function. The process is, in fact,
reduced to finding arcs which shall fulfill the twofold condition of being themselves
in the ratio of the values of X, while they are to their sines in the ratio of the values
of (/J. For this I have not been able to make any direct method available.

By indirect and tentative methods, however, and the assumption of arcs which
were seen (from a table of the lengths of arcs,) to be nearly in the required ratio to
their sines, I advanced by successive trials of greater or less arcs to more exact
values. Those for the two extreme rays were usually assumed in the first instance,
and their ratios to their sines compared with the ratios of the refractive indices;
and these once brought to a sufficiently near accordance, a fundamental arc was
obtained, from which those for the other rays were deduced on dividing by the
corresponding value of X\ and the product of a constant coefficient multiplying
the ratio of the arc and sine, which in theory ought to give the value of the refrac-
tive index, was compared with the index deduced from observation. This will
sufficiently explain the meaning of the several columns in the tabular statement of
the results.

It must be borne in mind that the values finally adopted are still only approxima-
tive, and are open to further correction by repeating the process ; so that in all the
cases here considered a still closer coincidence might probably be obtained were it
thought desirable.

The fundamental data of these comparisons are (as already said) those very precise
determinations of the value of X for the several definite rays named by the letters B,
C, D, &c., obtained by Fraunhofer from the interference-spectrum ; and which

2 K 2

252

PROFESSOR POWELL'S RESEARCHES TOWARDS ESTABLISHING

Sir J. Herschel has justly characterized as data of the utmost value in the theory
of light*. These values are as follows :

Ray.

Value of A.

B

•00002541

C

•00002422

D

-00002175

E

-00001945

F

•00001794

G

•00001587

H

•00001464

With these values I have gone through every case of a refractive index for a defi-
nite ray at present known, that is, for every one of these seven definite rays in each
of the ten substances whose refractive energy for the different rays was examined by
Fraunhofer.

The following tabular statement gives the comparison between the refractive index
for each ray in each medium, as given by Fraunhofer's observations in the first
column, and as resulting from the formula of theory (adopting his independent de-
terminations of the values of X,) in the last ; whilst in the intermediate columns the
elements of the calculation are exhibited.

Flint Glass, No. 13.

Fraunhofer.

Assumed values

Calculated va-

Ray.

Observed values
of /«.

of .

Ratio ('"'^'^Y
\sine /

lues of ft

-constxO'-'^).
\sme /

B

1-6277

1^ 10

1-0134

1-6275

C

1-6297

16 41

1-0143

1-6299

D

1-6350

18 35

1-0178

1-6355

E

1-6420

20 44

1-0222

1-6426

F

1-6483

22 31

1-0261

1-6486

G

1-6603

25 29

1-0356

1-6609

H

1-6711

27 39

1-0399
const =1-607

1-6711

Flint Glass

3, No. 23. I

Fraunhofer

•

B

1-6265

1^ 6

1-0131

1-6269

C

1-6285

16 17

1-0135

1-6278

D

1-6337

18 15

1-0172

1-6335

E

1-6405

20 22

1-0214

1-6403

F

1-6467

22 8

1-0252

1^6464

G

1-6588

25 2

1-0325

1^6582

H

1-6697

27 9

1-0393
const = 1-606

1-6697

See Treatise on Light, art. 751. 756.

A THEORY OF THE DISPERSION OF LIGHT.

253

Flint glass. No. 30. Fraunhofer.

Assumed values

Calculated va-

Ray.

Observed values „vrrn
of^. of ^ .

Ratio (^"^Y
\sine/

lue of (A

= const. x/'^^Y
\sine/

B

1-6236

16 0

1-0131

1-6239

C

1-6255

16 17

1-0135

1-6246

D

1-6306

18 15

1-0172

1-6305

£

1-6373

20 22

1-0214

1-6373

F

1-6435

22 8

1-0252

1-6434

G

1-6554

25 2

1-0325

1-6551

H

1-6660

27 9

1-0393

1-6660

1

const. = 1-6033

Flint glass. No. 3. Fraunhofer.

B

1-6020

o /

15 20

1-0120

1-6000

C

1-6038

16 5

1-0133

1-6039

D

1-6085

17 55

1-0164

1-6079

E

1-6145

19 59

1-0206

1-6145

F

1-6200

21 42

1-0243

1-6204

G

1-6308

24 33

1-0312

1-6313

H

1-6404

26 39

1-0369

1-6404 1

const. = 1-582

Crown glass, M. Fraunhofer.

B

1-5548

o /

12 19

1-0077

1-5548

C

1-5559

12 55

1-0085

1-5561

D

1-5591

14 23

1-0106

1-5593

E

1-5632

16 5

1-0133

1-5634

F

1-5667

17 ^^

1-0156

1-5671

G

1-5735

19 42

1-0199

1-5738

H

1-5795

21 22

1-0235
const. = 1-543

1-5792

Crown glass, No. 13. Fraunhofer.

B

1-5243

o /

11 18

1-0065

1-5243

C

1-5253

11 51

1-0071

1-5252

D

1-5280

13 12

1-0089

1-5279

E

1-5314

14 46

1-0112

1-5314

F

1-5343

16 0

1-0131

1-5343

G

1-5399

18 5

1-0168

1-5399

H

1-5447

19 37

1-0198
const. = 1-5145

1-5444

Crown glass. No. 9. Fraunhofer.

B

1-5258

o /

11 18

1-0065

1-5259

C

1-5269

11 51

1-0071

1-5269

D

1-5296

13 12

1-0089

1-529^

E

1-5330

14 46

1-0112

1-5332

F

1-5360

16 0

1-0131

1-5360

G

1-5416

18 5

1-0168

1-5416

H

1-5466

19 37

1-0198

1-5462

(

3onst.= 1-5162

254

PROFESSOR POWELL ON THE DISPERSION OF LIGHT.

Oil of turpentine. Fraunhofer.

Assumed values

Calculated values

Ray.

Observed values
of (t*.

of

X

Ratio ( ^'^ \
\ sine /

of ft

= const. xr^-\
vsiney

B

1-4.705

0 '
12 25

1-0078

1-4703

c

1-4715

13 1

1-0086

1-4715

D

1-4744

14 30

1-0107

1-4746

E

1-4783

16 13

1-0135

1-4786

F

1-4817

17 35

1-0159

1-4821

G

1-4882

19 51

1-0203

1-4886

H

1-4939

21 32

1-0239
const. = 1-459

1-4938

Solution of potash. Fraunhofer.

B

1-3996

10 34

1-0056

1-3999

C

1-4005

11 5

1-0062

1-4008

D

1-4028

12 20

1-0077

1-4029 ■'

E

1-4056

13 10

1-0088

1-4044

F

1-4081

14 57

1-0114

1-4080

G

1-4126

16 55

1-0147

1-4126

H

1-4164

18 20

1-0173
const. = 1-3922

1-4162

Water. Fraunhofer (two experiments).

B

1-3309

9 54

1-0050

1-3309

C

1-3317

10 25

1-0055

1-3315

D

1-3336

11 36

1-0068

1-3333

E

1-3358

12 57

1-0085

1-3355

F

1-3378

14 3

1-0101

1-3376

G

1-3413 i 15 51

1-0129

1-3413

H

1-3442 17 11

1-0151
const. = 1-3243

1-3443

Conclusion.

Upon comparing the numbers above given as resulting from theory and from ob-
servation, and bearing in mind that the assumptions of the constants on which the
calculation depends are but tentative and approximative, and open to farther cor-
rection, it will, I think, be allowed that the coincidences are quite sufficient to permit
us to regard the formula as a very close representation of the law of nature.

We are thus, I think, justified in concluding, that for all the substances examined
by Fraunhofer, viz. for four kinds of flint glass, three of crown glass, for water,
solution of potash, and oil of turpentine, the refractive indices observed for each of
the seven definite rays are related to the lengths of waves for the same rays, a^ nearly
as possible according to the formula above deduced from M. Cauchy's theory.

Thus, then, for all the media as yet accurately examined, the theory of undulations
(as modified by that distinguished analyst,) supplies at once both the law and the ex-
planation of the phenomena of dispersion.

Oxford,
February 17, 1835.

HiU. Tnuis. MIX ■( Y "XHW /"/»/.

TMLOS.7-/CUU . MP C C CXXXV. rirUr U.jf.JJ.

TOSS'II, SHELLS' from. UDLI] VAI^LA in SWXIH:^.

J. J), as.

ROYAL MEDALS.

HIS MAJESTY KING WILLIAM THE FOURTH, in restoring the
Foundation of the Royal Medals, graciously Commanded a Letter, of
which the following is an extract, to be addressed to the Royal Society,
through His Royal Highness the Duke of Sussex, K.G., President :

" Windsor Castle, March 25, 1833.

" It is His Majesty's wish, —

" First, That the Two Gold Medals, value of Fifty Guineas each, shall
" henceforth be awarded on the day of the Anniversary Meeting of the
" Royal Society, on each ensuing year, for the most important discoveries
" in any one principal subject or branch of knowledge.

" Secondly, That the subject matter of inquiry shall be previously settled
" and propounded by the Council of the Royal Society, three years pre-
" ceding the day of such award.

" Thirdly, That Literary Men of all nations shall be invited to afford the
" aid of their talents and research : and,

" Fourthly, That for the ensuing three successive years, the said Two
" Medals shall be awarded to such important discoveries, or series of in-
" vestigations, as shall be sufficiently established, or completed to the
" satisfaction of the Council, within the last five years of the days of award,
" for the years 1834 and 1835, including the present year, and for which
" the Author shall not have previously received an honorary reward.

(Signed) " H. Taylor."

The Council propose to give one of the Royal Medals in the year 1836, to the most
important unpublished paper in Astronomy, communicated to the Royal Society for

VI

insertion in their Transactions, after the present date (May 13th, 1833,) and prior to
the month of June in the year 1836.

The Council also propose to give one of the Royal Medals in the year 1836 to the
most important unpublished paper in Animal Physiology, communicated to the Royal
Society for insertion in their Transactions, after the present date (May 13th, 1833,)
and prior to the month of June in the year 1836.

The Royal Medals for the year 1833 were awarded lo

Sir JOHN FREDERICK WILLIAM HERSCHEL, K.H. F.R.S.,

for his Paper on the Investigation of the Orbits of Revolving Double Stars ; and to

Professor AUGUSTE PYRAME DE CANDOLLE, of Geneva, Foreign Member

of the Royal Society,

for his Discoveries and Investigations in Vegetable Physiology.

Those for 1 834 were awarded to

JOHN WILLIAM LUBBOCK, Esq., V.P. & Treas. R.S.,
for his Papers on the Tides published in the Philosophical Transactions ; and to

CHARLES LYELL, Esq.,
for his Work entitled " Principles of Geology."

The Council propose to give one of the Royal Medals in the year 1837 to the most
important unpublished paper in Physics, communicated to the Royal Society for
insertion in their Transactions, after the present date (November 27th, 1834,) and
prior to the month of June in that year.

The Council also propose to give one of the Royal Medals in the year 1837 to the
author of the best paper, to be entitled " Contributions towards a System of Geo-
logical Chronology founded on an examination of fossil remains, and their attendant
phenomena," such paper to be communicated to the Royal Society after the present
date (December 1st, 1834,) and prior to the mouth of June 1837.

METEOROLOGICAL JOURNAL,

KEPT BY THE ASSISTANT SECRETARY,

AT THE APARTMENTS OF THE

ROYAL SOCIETY,

BY ORDER OF

THE PRESIDENT AND COUNCIL.

OBSERVANDA.

Height of the Cistern of the Barometer above a Fixed Mark on Waterloo Bridge =83 feet 2| in,

above the mean level of the Sea (presumed about) ... .=95 feet.

The External Thermometer is 2 feet higher than the Barometer Cistern.

Height of the Receiver of the Rain Gauge above the Court of Somerset House =79 feet.

The hours of observation are of Mean Time, the day beginning at Midnight.
The Thermometers are graduated by Fahrenheit's Scale.
The Barometer is divided into inches and decimals.

METEOROLOGICAL JOURNAL FOR JULY AND AUGUST, 1834.

9 o'clock, A.M.

3 o'clock, P.M.

Dew

External Thermometer.

1834.

Point at
9 A.M.

in de-
grees of

Fahr.

Rain, in
inches.
Read off
at9A.M.

Direction
of the

Wind at
9 A.M.

REMARKS.

Barom.

Attach.

Barom.

Attach.

Fahrenheit,

Self-registering.

Therm.

Therm.

9 A.M.

3 P.M.

Lowest.

Highest.

T 1

30.319

71.2

30.220

69.8

55

63.2

67.0

51.4

67.6

NE

Lightly cloudy and overcast. — Evening, lowerlntf.

W 2

30.080

65.3

30.033

69.2

56

61.7

71.2

55.8

71.8

NNE

f Lifflit wind.— A.M. Slightly lowering. .P.M. Fine— light clouds.
X Evening clear.

T 3

30.089

64.7

30.059

68.7

55

59.8

73.2

55.7

73.7

N

A.M. Overcast. P.M. Fine— light clouds.

f LiKlit wind.— A.M. Lightly cloudy. P.M. Fine and cloudless.

\ Evening, fine— light high clouds.

F 4

30.172

65.4

30.132

69.3

56

62.7

75.8

55.4

76.4

NE

S 5

30.107

65.9

30.030

71.0

58

62.7

74.2

56.7

77.1

N

f A.M. Overcast-light wind.— P.M. Fair— lightly cloudy. Night,
\ heavy rain.

• 0 6
. M 7

29.988
29.994

68.2
71.2

29.983
29.954

70.7
72.6

63
61

65.2
67.8

66.3
73.3

62.7
61.8

70.1

75.7

.389
.083

E
WSW

f A.M. Overcast. Noon, coDtioued thunder with light rain.

I P.M. Clear— lowering.

Clear — cloudy. — Evening, light rain.

T 8

29.893

71.3

29.909

72.8

65

66.8

73.7

61.7

75.3

.011

SSE

A.M. Rain. P.M. Fine— light clouds.

W 9

30.134

71.7

30.156

71.8

55

64.2

68.5

57.8

71.2

.111

NW

JA.M. Lowering— light haze. P.M. Lightly overcast. E»en-
X ing, clear.

T 10

30.105

75.2

30.057

72.4

56

69.1

69.5

58.2

73.4

SSE

Lightly cloudy.— Evening, fine and clear — light breeze.

F 11

30.132

74.7

30.057

73.2

55

68.2

73.9

56.2

76.3

WSW

C Fine — nearly cloudless.— A.M. Light clouds, and cloudiness.
X P.M. Clear.

S 12

29.887

77.4

29.823

73.6

60

73.9

75.8

56.7

78.2

ssw

Fine and clear — nearly cloudless.— Light wind, a.m.

©13

29.920

75.8

29.908

74.4

55

68.2

74.2

62.4

75.8

WSW

A.M. Cloudy. , P.M. Fine and clear— a few light clouds.

^ M14

30.045

71.8

30.071

74.3

54

68.7

75.4

60.7

77.0

WSW

fFine. — A.M. Clear— cloudy. P.M. Light clouds. Evening,
X cloudless.

S T15

30.263

77.3

30.239

74.8

57

70.8

77.6

59.3

79.7

ssw

Clear and cloudless.

S W16

30.282

73.6

30.220

75.4

61

71.6

80.6

62.1

81.6

WSW

Fine and cloudless.— Evening, clear.

T 17

30.186

79.3

30.089

77.8

60

74.7

85.2

64.0

86.7

WSW

f Fine and cloudless— haze.— Evening, clear. Night, light un-
X steady breeze.

F 18

29.809

78.4

29.724

74.8

67

74.7

68.0

64.8

85.2

E

f Lieht brisli unsteady wind.— A.M. Fine— light soft clouds.
X P.M. Dark— continued rain : thunder-storm at 71 h.

S 19

29.508

72.3

29.595

71.3

63

63.2

60.6

63.2

65.4

.944

WSW

Continued rain.

O02O

29.747

73.5

29.748

72.7

59

62.9

66.2

56.4

68.7

.203

SW

fFine — showery.— A.M. Cloudy. P.M. Clear — broken clouds
t —light wind.

M21

29.760

70.1

29.784

69.6

58

62.7

65.7

58.8

68.4

.056

SE

Lowerini— light rain.— Evening, fine— cloudy: distant thunder.

T 22

29.944

67.8

29.994

71.3

61

65.5

66.7

57.0

73.7

.014

ESE

f A.M. Fine— light clouds and haze. P.M. Cloudyand overcast
X — occasional light showers : distant thunder at 3^ h.

W23

30.076

72.2

30.031

71.7

60

67.9

73.4

59.1

75.8

E

Fine.- A.M. Cloudless— haze. P.M. Liglitly cloudy.

T24

30.067

70.3

30.043

72.2

61

66.8

70.3

61.3

73.7

NNE

A.M. Fair — lightly cloudy. P.M. Fine and clear— light clouds.

F25

30.059

68.6

30.031

71.9

60

63.8

73.8

59.8

74.7

W

A.M. Overcast. P.M. Fine and clear— light clouds.

S 26

29.936

71.4

29.816

72.9

57

65.4

70.3

58.7

74.5

.056

WSW

Lightly overcast.— Fine, a.m.

©27

29.677

66.3

29.791

69.8

60

60.7

65.5

55.7

69.0

E

A.M. Overcast.— P.M. Fair— lightly cloudy. Evening, clear.

M28

30.027

72.3

30.030

72.4

57

68.5

73.2

57.2

74.5

E

/Fine.— A.M. Cloudless— streaked cloudiness. P.M. Light
X clouds. Midnight, thunder storm.

T29

30.019

70.0

29.996

73.3

69

69.2

79.2

62.9

80.3

.339

E

Lowering- liaiht wind.— ijh. to 3h. p.m. distant thunder.
/A.M. Continued rain. Noon, heavy clouds. P.M. Fine and
X very clear— light clouds and breeze.

W30

29.871

70.4

29.907

74.5

65

65.7

73.5

63.7

75.2

.958

E

T31

29.829

69.4

29.819

70.6

63

64.4

67.0

62.0

69.6

.200

NNE

/A.M. Broken clouds: light rain from 7 h. to 10 h. P.M.Over-
X cast and foggy : rain from 12^ h. to 2 h.

Means . .

29.998

71.4

29.976

72.3

59.4

66.5

71.9

59.3

74.7

Sum.
3.364

Mean of Barometer, corrected for Capil- ) 9 A.M. 3 P.M.
larity and reduced to 32° Fahr J 29.876 29.853

F 1

29.878

70.7

29.863

73.4

65

69.2

75.0

63.8

78.2

.319

WSW

Fine— lightly cloudy— light haze.— Evening, clear.

/A.M. Lightly cloudy— unsteady air. P.M. Fine and clear—

1 light clouds and breeze. Evening, cloudless.

S 2

29.911

71.4

29.899

74.2

63

67.7

74.9

63.8

75.6

NNE

© 3

29.918

70.7

29.877

72.3

53

64.2

72.8

56.4

73.3

N

/Fine.— A.M. Lightly cloudy. P.M.CIoudless-lightcloudiness:
X at 8ih. heavy clouds in the N.W. with frequent lightning.

M 4

29.933

70.0

29.938

73.2

64

65.1

73.2

61.6

74.3

WSW

/A.M. Overcast. P.M. Fine and clear— cloudj— light breeze.
1 Evening, cloudy. [a.m.
Fine and lowering, alternately— light breeze.— Light rain, eaily

• T 5

29.899

72.7

29.889

73.7

64

70.0

71.4

61.9

74.2

SSE *"•

W 6

29.894

73.7

29.879

73.2

61

67.7

71.6

62.2

73.8

w

/Clear.— A.M. Heavy clouds: atllj h. heavy shower. P.M. Fine
1 — cloudv- light breeze : shower about 5 h.

T 7

29.984

70.2

29.983

70.7

62

65.6

67.9

58.3

68.8

.211

s

/Overcast— broken clouds— light wind— showery.— Evening, con-
X tinned rain.

F 8

29.805

69.8

29.810

72.7

67

67.9

70.4

63.5

74.3

.181

ssw

/A.M. Lowering— light brisk wind. P.M. Soft broken clouds :

X shower at 3 n.

A.M. Lightly cloudy. P.M. Fine— high clouds.

S 9

30.114

70 3

30.138

71.7

60

65.7

70.3

55.7

72.2

.161

NNE

©10

30.181

71.7

30.130

72.6

59

67.3

76.8

58.3

78.2

.011

N

Fine.— A.M. Overcast. P.M. Fine and clear— light clouds.

Mil

30.067

71.7

30 068

72.8

62

69.6

75.2

60.3

78.6

S

/A.M. Fine and cloudless— light cloudiness. P.M. Fair— lightly
X cloudy. Evening, cloudless— sultry.

T 12

30.128

72.3

30,095

73.4

64

71.7

78.6

61.3

797

WSW

/Fine.- A.M. Lightly cloudy. P.M. Clear and cloudless— light

X airs. Evening, very clear.

/Fine.— A.M. Cloudless. P.M. Lightly cloudy. Evening, clear.

X Night, lightly cloudy. _ „ „ ^

A.M. Fine-light clouds-light unsteady air. P.M. Overcast.

W13

30.001

75.7

30.037

75.7

63

75.2

77.8

64.2

83.3

SSE

^ T 14

30.104

70.8

30.081

73.9

60

65.3

70.2

59.7

72.7

N

g F15

30.119

68.2

30.122

72.8

62

63.8

73.5

58.2

73.7

N

Fair— light mingled clouds— light unsteady breeze.

o S 16

30.213

70.7

30.172

73.0

65

66.7

74.6

61.8

76.3

NNE

A.M. Cloudy— light wind. P.M. Fine— light clouds.

< ©17

30.188

73.0

30.095

73.3

63

66.9

74.6

58.8

76.2

NE

Fine-light clouds.-A.M. Light wind, P.M, clear.

M18

29.978

70.9

29.924

73.2

63

67.8

74.8

62.5

76.0

E

Fine— light clouds and wind.

OT 19

29.980

70.6

29.938

73.6

62

66.9

72.7

60.0

73.7

NNE

Light wind.— A.M. Fine— light clouds. P.M. Lightly overcast.

W20

29.812

70.2

29.728

72.7

62

64.8

73.0

62.0

74.7

SSW

Fine— light broken clouds.— Evening, light rain at 8i h.

T 21

29.784

72.0

29.726

72.6

56

65.0

70.5

58.6

72.6

SW

Fine.— A.M. Clear— light clouds. P.M. Nearly cloudless.

F 22

29.821

71.0

29.772

71.4

52

64.2

67.7

53.7

70.8

S

i A.M. Fine and cloudless. P.M. Cloudy— light brisk wind :
X light shower at 3i h. ...,.,..

S 23

29.962

69.7

29.944

69.7

50

62.3

66.9

52.0

69.6

s

/Fine.— A.M. Nearly cloudless— light wind. P.M. Light showers
X and clouds.

©24

29.814

66.7

29.728

67.0

54

61.0

58.6

51.8

67.9

.063

E

Cloudy and overcast— light wind.— Light rain, p.m.

M25

29.685

64.8

29.746

66.0

49

59.0

62.7

47.5

65.2

.152

ssw

Fine— lightcloud8.-A.M.CIear. P.M. Lightwind : ihoweratajb.
/A.M. Fogand light drizzling rain. P.M. Cloudy— light wind :
X at 4 h. thunder-storm.

T 26

29.821

62.0

29.768

65.6

52

58.2

63.9

50.2

66.7

s

W27

29.808

62.7

29.798

65.4

52

54.8

64.0

49.3

65.2

.122

g

Fine— light clouds.— Clear— light wind, a.m.

T 28

29.946

62.7

29.905

64.9

50

56.8

62.5

46.2

65.2

SW

/Light brisk wind.— A.M. Fine— nearly cloudless. P.M. Over-
X cast: heavy shower at lOi h.

F 29

29.748

64.0

29.655

66.0

57

62.2

64.5

56.4

68.0

.205

ESE

Overcast.— Light shower at Ijh. p.m.— light brisk wind.

S 30

29.677

66.7

29.695

67.0

57

63.7

65.9

57.0

67.9

SE var.

/A.M. Overcast— light rain and wind. P.M. Fine and clear—
t light clouds. At night, heavy rain.

©31

29.744

67.2

29.784

68.0

59

64.5

65.9

57.2

67.4

.263

SSW

Fine— light clouds and wind.— Showery, p.m.

Means ..

29.933

69.5

29.909

71.2

59.1

65.2

70.4

57.9

72.8

Sum.

1.688

Mean of Barometer, corrected for Capil- \ 9 A.M. 3 P.M.
larity and reduced to 32° Fahr ) 29.819 29.789

METEOROLOGICAL JOURNAL FOR SEPTEMBER AND OCTOBER, 1834.

1834.

M
T

T
F

S

0

M

T

WIO

g Til

M F 12

I S 13

£014

g M15

T 16

OW17

T 18

F 19

S20

021

M22

T 23

W24

T25

F 26

S 27

028

M29

T30

Meaks ..

9 o'clock, A.M.

Barom.

I Attach,
i Therm.

3 o'clock, P.M.

Barom.

Attach,
Therm,

29.942

30.041

30.164

30.095

29.930

30.044

30.208

29.685

29.406

29.812

29.808

30.138

30.499

30.536

30.380

30.047

30.037

30.218

30.261

30.382

30.362

30.245

30.235

30.204

30.212

30.095

29.876

30.093

30.285

30.190

30.114

W

#T

F

S
0

M
T
W 8
T 9
F 10
S 11
rt 0 12
g Ml3
g T 14
§W15
T 16
OF 17
S 18
0 19
M 20
T 21
W 22
T 23
F 24
S 25
0 26
M 27
T 28
W29
T 30
F 31

30.174
30.104
30.190
30.219
30.192
30.259
30.230
30.178
29.982
29.999
30.116
30.146
30.120
29.768
29.770
29.707
29.307
29.590
30.036
29.774
29.987
29.943
29.615
29.757
30.080
30.344
30.404
30.485
30.665
30.480
30.215

64.5
65.2
63.6
66.2
66.6
66.8
64.0
62.2
63.2
62.8
62.4
62.6
60.9
59.6
58.3
59.7
62.8
65.7
66.2
68.6
66.2
64.9
61.2
59.6
59.0
59.9
62.2
61.9
60.2
58.2

62.9

29.950
30.061
30.122
29.998
29.942
30.069
30.093
29.584
29.491
29.792
29.806
30.210
30.491
30.479
30.267
30.008
30.063
30.225
30.243
30.356
30.305
30.190
30.208
30.111
30.162
30.029
29.920
30.130
30.229
30.128

67.0
66.0
67.2
68.0
70.3
69.3
673
66.0
65.9
65.0
65.7
65.9
63.6
62.3
61.7
62.4
66.5
67.9
68.7
70.6
67.5
67.8
63.9
62.5
62.0
64.4
64.7
65.2
63.3
61.6

Dew
Point at

9A.M.

ill de-
grees of

Fahr.

56
53
56
58
63
56
54
57
57
55
60
54
50
49
52
53
59
60
60
64
62
59
48
47
50
55
60
57
56
53

External Thermometer.

Fahrenheit. Self-registering.

9 A.M. 3 P.M. Lowest. Highest.

30.089

65.7

55.8

63.2
61.3
61.2
67.7
65,4
62.4
58.5
57.4
59.7
59.6
60.6
57.1
57.2
55.9
53.7
58.9
65.6
64.6
62.6
67.9
60.2
60.0
54.3
55.3
55.9
58.8
62.3
58.2
55.3
54.2

63.5
66.2
66.0
71.8
69.8
67.0
66.2
64.4
66.3
61.7
65.2
65.9
63.2
62.7
63.4
68.2
72.0
70.2
72.0
72.4
68.0
64.6
59.8
60.3
62.9
65.0
65.8
66.2
63.4
61.3

59.8 65.8 54.1

56.9
55.6
53.7
59.9
60.9
56.7
53.0
53.6
53.7
51.7
58,0
53.2
48.0
46.8
46,2
49,9
58.5
60,7
59.0
60.2
58.9
57.5
47.2
50.3
48.8
54.7
58.8
54.0
51.0
46.9

Rain in
inchefi.
Read off
at9A.M.

67.7
67.5
68.4
72.8
72.6
68.7
67.3
66.2
66 9
65.2
66,8
66,7
64.6
63.6
64.2
68.4
73.3
71.6
72 7
74.8
68.6
67.3
61,8
62.4
63.4
65.3
66.9
67.0
63.8
62.3

,158

,092
.144

Direction
of the
Wind at
9 A.M,

REMARKS,

,041

,055
.092

57.4

30.119

56.5

30.064

55.3

30.181

55.6

30.185

57.7

30.180

60.3

30.200

62.9

30.193

63.0

30.108

63.2

29.901

61.4

30.010

55.3

30.069

55.7

30.142

57.2

30.003

57.6

29.691

56.7

29.723

54.4

29.430

55.8

29.445

52.3

29.715

49.7

29.938

53.8

29.749

54.7

30.188

51.4

29.820

53.9

29,576

46.3

29,796

45.7

30.131

43.7

30.412

45.3

30.419

49.0

30.523

50.2

30.618

49.8

30.371

50.1

30.151

60.4
59.7
58.3
60.2
61.7
63.2
65.3
64.8
65.7
62.0
58.6
58.4
59.2
60.7
59.2
57.6
57.7
54.4
53.3
55.7
55.2
.53.7
55.5
48.2
48.6
47.3
48.4
50.7
50.7
52.7
53,4

50

51

47

52

51

56

60

58

60

49

45

47

54

57

48

49

48

43

42

53

53

48

52

26

38

38

46

49

45

47

49

54.1

52.6

48.6

52.3

54.4

56.4

60.4

58.9

61.7

55.9

47.4

50.8

54.9

58.3

51.7

50.0

53.6

47.6

45.4

56.8

53.3

49.4

53.8

38.5

42.3

41.1

46.8

51.6

48.2

47.5

49.8

61.2

62.6

60.6

66.7

68.4

68.8

67.6

63.3

65.7

57.7

57.6

58.3

60.3

62.4

55.9

57.9

51.2

51.3

54,2

59.0

51.3

55.3

54.3

43.4

47.5

48.2

53.3

52.5

49.2

52.2

56.3

47.4

45.3

44.3

46.7

49.3

53.8

55.9

56.5

58.3

54.8

42.4

46.6

49.5

50.3

49.3

42,3

49.4

42.2

38.3

44.6

50.3

39.8

48.7

34.4

37.4

35.9

37.3

45.7

46.8

45.7

43.3

67.3

Sum.
.582

S

sww

S var.

S

ssvv
sw
sw

ENE

ssw

sw

s

sw

E
ESE

E

E

E

SE

S

N
NE
NE
ENE

N
ENE

E
SSW
SW
ENE

E

A.M. Cloudy. P.M. Light continued rain.

Fine and clear— liglit clouds.

{^"■ht''wi'i;J."'*^''""""'" ""' ''*"• •••"• LiKlnly overca.1-

Fine.— A.M. Light broken clouds. P.M. Cloudless.

A.M. Overcast. P.M. Fair-cloudy— light wind.

A.M, Falr-cloudy-light wind. P.M. Fine andcloudleM.

A.M. Hazy. P.M. Fine— nearly cloudless.

Overcast — Light continued rain, a.m.

l^'"'nl7.T"^i" "'"''.--A.M. Overcast. P,M, Fine and clear
l — lignt broken clouds.

Overcast— light showers.

Overcast— light showers.— Light brisk wind, p.m.

Fine— light haze.

Fine-light brisk wind.— A.M. Cloudless. P.M. Light clouds.

Fine.— A.M. Light haze. P.M. Clear-light clouds.

A.M. Foggy. P.M. Fine and cloudless— light wind.

Fine and cloudless— light wind and haze.

A.M. Light fog. P.M. Fine— nearly cloudless.

Lightly overcast- light rain.

A.M. Foggy. P.M. Cloudy.

Fine and cloudless— light haze and wind.

Lightly overcast and hazy— light wind.

Heavy clouds— light wind.

Fine.— A.M. Cloudless— light haze and wind. P.M. Liebllv
cloudy. " '

Overcast and foggy.

Fine— light wind.— A.M. Light clouds. P.M. Cloudless.

Lighily overcast and cloudy.- Light rain and wind, a.m.

Overcast.— Light rain, p.m.

Lightly cloudy.— Fine, p.m.

A.M. Foggy— light wind. P.M. Fine— nearly cloudless.

Fine and cloudless.

Mean of Barometer, corrected for Capil-
larity and reduced to 32° Fahr

\ 9 A.M.
f 30.026

3 P.M.

026 29.992

61.4

62.6

60.7

66.7

70.2

70.2

68.3

64.3

66.4

59.4

57.7

58.7

61.6

63.6

56.7

58.3

57.3

51.7

56.6

59.4

56.3

55.3

55.7

43.4

47.7

48.2

53.3

53.3

49.3

52.3

56.6

.058

.025
.094

.008

N

E

E

E

SE
SSW
WNW
WSW
SSW
- N

N

N

SW

SSW

WSW

s

WNW
WNW
WSW

S

WSW

sw var.

WSW

NW var.

NNWvar

N

NWvar.

N

N

SW

WSW

Fine and cloudless.— A.M. Light haze. P.M. Light wind.

Fine andcloudless. A.M. Light haze and wind. P.M. Very clear.

A.M. Slrong haze— cloudless. P.M. Fine— hazy.

A.M. Strong fog. P.M. Clear and cloudless.

fA.M. Strong haze— cloudless. P.M. Fine and clondless— light

I cloudiness.

Fine and cloudless — hazy.

Fine andcloudless — light streaked cloudiness.— F.vening, clear.

{A.M. Litrhtty cloudy— light wind. P.M. Fine and clear— light
breeze amt clouds.
Light wind.— A.M. Lightly cloudy. P.M. Fioe-iightsoft clouds.
Fine — light clouds and wind. — Clear, p.m.

{Fine.— A.M. Cloudless. P.M. Clear — thin flocculons clouds,
and light wind.
Hazy.— Fine— light cloudiness, p.ni. Evening, local haze — clear
Fine and cloudless.— A few light clouds and cloudiness, a.m.

{Fine— soft floating clouds. — Clear, p.m. — Showers, noon and
evening.
Fine- light flocculons clouds. — Clear— light wind, p.m.
("Unsteady wind.— A.M. Fair & clear-light elds. P.M. Cloudy—
1 It. rain. Ev., fine & clear— light elds. — light unsteady treeze.

{Strong unsteady breeze.— A.M. Fine and clear. P.M. Heavy
rain— dark.
Fine— light elds. & cloudiness — lightbriskwind. — Evening, clear.

{Lightly cloudy.— A.M. Light haze. P.M. Light breeze and
deposition.
(Lightclnudsandbreeze.- A.M. Lightly cloudy, NooD,ghowers,
P.M. Fair and clear.
fA.M. Fine and clondless— light haze, P.M. Fair- lightly
I cloud) — light wind.

Lightly overcast &cldy.— light unsteady breeze.- Ev. light rain,
ighl brisk unsteady wind. — A.M. Lowering^^eposition.
P.M. Fair and clear— lightly cloudy.
/ Light fresh breeze.— A.M. Fine and 'cloudless. P.M. Lightly
I cloudy. Evening, clear.
Fine — light thin clouds— light brisk wind.
Fine — nearly cloudless- light wind.
Lightly overcast and cloudy— light haze.
Lightly overcast— light wind.
Overcast — haze.

Lightly clondy— light haze and wind.
Fine — lightly cloudy— light cloudiness, haze, and wind.

Means..

30.059

54.3 30.034 56.8 48.7

51,4 57.2 46.2

58.2

Sum.
,185

Mean of Barometer, corrected for Capil- I 9 A.M. 3 P.M.
larity and reduced to 32° Fahr I 29.996 29.964

METEOROLOGICAL JOURNAL FOR NOVEMBER AND DECEMBER, 1834.

9 o'clock, A.M.

3 o'clock, P.M.

Dew

External Thermometer.

1834.

Point at
9A.M.
in de-
grees of

Rain, in
inches.
Read off
at9A.M.

Direction
of the

Wind at
9 A.M.

KEMARKS.

BaTom.

Attach.

Barom.

Attach.

Fahrenheit. 1

Self-registering.

Therm.

Thprm.

Fahr.

9 A.M.

3 P.M.

Lowest.

Highest.

• S 1

30.117

53.3

30.101

55.3

51

52.6

55.7

48.7

56.3

WSW

Fine— thin flocculous clouds— liglit liaze and wind.

© 2

30.130

53.4

30.082

55.4

50

50.9

54.6

48.3

55.3

WSW

Fair— liglitly cloudy.

M 3

30.059

53.3

30.019

55.3

50

52.1

55.6

48.8

55.6

sw

Fine and cloudless — light cloudiness.

T 4

30.139

53.0

30.045

56.3

48

48.2

56.9

44.8

58.2

WSW

fA.M. Fine— lighlly cloudy— light fog and deposition. P.M.

I Fair— cloudy. Night, brislt wind.

Cloudy and lowering — strong deposition— brisk unsteady wind.

W 5

29.721

56.9

29.617

58.8

58

58.4

60.4

47.3

60.7

ssw

T 6

29.665

58.8

29.687

60.8

57

58.2

60.7

56.5

61.5

.008

ssw

Fair— lightly cloudy.— Evening, light rain. Night, brisk wind.

F 7

29.497

59.7

29.478

61.4

58

59.6

57.7

54.4

61.3

.019

SSE

r Light brisk wind.— A.M. Broken clouds. P.M. Fine and

\ clear. Evening, very light rain.

Fine and clear.— A.M. Light clouds. P.M. Nearly cloudless.

S 8

29.463

56.6

29.458

57.7

50

50.1

51.7

47.5

61.3

.008

ssw

© 9

29.454

55.3

29.531

56.3

51

51.8

52.3

47.4

53.6

ESE

Fog and light rain.

MlO

29.854

52.3

29.939

51.7

46

46.5

46.3

45.2

46.5

NNE

Overcast — light wind. — Light rain, a.m.

g Til

30.184

47.6

30.218

50.5

39

44.3

49.3

39.2

49.3

N

Fair — lighlly cloudy — light unsteady wind.

m Wi2
1 T 13

30.303

46.3

30.264

46.4

35

42.1

42.7

40.5

42.7

NNE

Lighlly cloudy and overcast— light unsteady wind.

30.272

43.8

30.275

45.3

35

39.2

42.0

37.7

42.3

NNE

Fair— lightly cloudy — light wind.

^ F14

30.400

43.3

30.387

46.7

40

40.0

46.2

34.8

46.4

N

Fine— light clouds— liglit brisk wind.

S'^ S 15

30.409

43.4

30.386

46.7

41

41.5

47.2

35.6

47.2

NNE

Fair— lighlly cloudy— light wind.

0©16

30.372

46.3

30.318

47.8

43

44.2

47.7

40.4

47.7

WNW

Overcast — liaze.

M17

30.188

46.3

30.090

48.7

43

45.0

49.8

40.7

49.8

WSW

A.M. Overcast. P.M. Fair— light clouds.

T 18

30.146

48.3

30.162

49.7

45

45.3

48.1

43.8

48.1

N

Fair— lightly cloudy.— Light brisk wind, p.m.

W19

30.275

46.3

30.228

46.3

38

39.5

41.3

37.5

41.4

NNE

Cloudless — light wind and haze.

T20

29.998

40.7

29.839

43.0

35

36.7

40.2

33.2

40.5

NE

Fine and nearly cloudless— light wind.

F21

29.768

41.3

29.738

43.3

34

37.6

41.8

34.6

43.6

E

Overcast.— Light rain and wind, p.m.

S 22

29.728

44.3

29.715

47.2

44

44.8

47.4

36.7

47.4

E

Overcast— light haze— A.M. Deposition. P.M. Light wind.

©23

30.008

46.3

30.071

46.7

39

44.7

45.6

36.7

45.6

NNE

Lightly overcast— light fog— light unsteady wind.

M24

30.124

43.7

30.063

46.3

42

42.8

45.9

36.8

45.9

NE

Fair— soft clouds— light breeze.

T25

29.903

44.7

29.849

44.7

38

41.7

40.7

40.3

41.7

E

Overcast.— A.M. Haze. P.M. Light breeze.

W26

29.843

43.3

29.852

43.9

36

38.8

40.0

37.0

40.0

NNW

Overcast- light wind.

T27

29.953

41.4

29.928

44.3

36

36.2

45.7

33.3

45.7

WSW

Fine and cloudless — haze and cloudiness.

F28

29.751

45.4

29.588

46.7

43

46.0

42.9

34.8

46.2

ssw

/Lightly cloudy.— A.M. Fine and clear. P.M. Light wind.—
I. Evening, light rain.

S 29

29.187

45.4

29.253

47.7

42

42.3

48.8

39.6

48.8

ssw

fA.M. Fine— thin streaked clouds- deposition. P.M. Cloudy—

1 light wind.

Fair— liglitly cloudy— light liaze.

©030

29.556

46.3

29.703

48.0

42

44.6

46.2

40.8

52.3

WNW

Meaks ..

29.949

48.2

29.929

50.0

43.6

45.5

48.4

41.4

49.4

Sum.
.035

Mean of Barometer, corrected for Capil- 1 9 A.M. 3 P.M. 1
larity and reduced to 32" Fahr j 29.904 29.879 1

M 1

29.268

47.7

29.383

49.4

48

50.3

49.3

40.7

49.7

WSW

(A.M. Light rain— light brisk unsteady wind. P.M. Fine—

(. light clouds.

Fair— light clouds, haze, and wind.

T 2

29.572

47.7

29.744

49.8

44

47.3

51.3

42.8

51.3

.017

WSW

W 3

30115

47.5

30.131

49.7

44

44.9

49.2

38.7

49.2

WSW

Lightly cloudy— fog and deposition.

T 4

30.187

50.0

30.156

51.2

48

48.7

50.3

43.7

50.7

SSW

Light haze.— A.M. Lightly cloudy. P.M. Fine.

F 5

30.202

47.7

30.164

49.6

43

43.4

47.5

39.4

47.5

SSW

A.M. Fog— deposition. P.M. Clear and cloudless.

S 6

30.204

47.8

30.188

50.0

46

46.7

49.2

40.4

50.7

SSW

Lightly cloudy- light fog and deposition.

© 7

30.181

50.9

30.091

52.3

50

51.4

53.4

45.3

53.5

S

A.M. Fair— lightly cloudy. P.M. Rain. Evening, clear.

M 8

30.263

49.8

30.346

50.1

39

43.8

44.8

42.6

44.8

WNW

Fine and cloudless— light haze.

T 9

30.555

46.4

30.499

47.8

39

39.0

44.6

37.3

44.6

SW

Cloudless — haze.

rt wio

30.294

47.6

30.356

47.3

42

48.1

44.3

37.7

44.3

.097

N

Cloudless— light wind and cloudiness.

g Til

30.602

43.3

30.620

43.7

37

37.3

38.2

34.8

38.2

N

Cloudless— haze and cloudiness.

S F 12

30.503

42.5

30.427

43.7

36

36.8

42.3

34.8

43.3

WSW

Lightly cloudy — haze.

8 S13

30.487

45.4

30.473

46.0

42

42.2

43.1

35.7

43.5

NE

Fair— lightly cloudy— light wind and haze.

g ©14

30.519

41.8

30.530

42.8

37

37.7

40.7

35.3

40.7

N

Overcast— light haze.— Light wind, p.m. Evening, clear.

M15

30.595

42.0

30.588

43.5

40

40.4

42.6

35.5

44.2

N

Overcast— light fog and deposition.

Ot 16

30.608

45.3

30.542

46.8

44

45.1

45.7

39.3

45.7

N

Lightly cloudy— light wind and haze.

W17

30.150

45.3

30.134

46.4

42

43.9

44.7

40.8

44.7

NNE

Light wind.— A.M. Nearly cloudless. P.M. Cloudy— light rain.

T 18

30.297

44.2

30.342

45.7

40

40.8

43.6

39.3

43.7

N

f Fair— light wind.— A.M. Cloudle^8— light fog and deposition.
I P.M.ligblclouds.

F 19

30.433

44.4

30.412

45.5

42

42.4

44.7

36.5

44.7

N

Overcast.— A.M. Fog — deposition. P.M. Light wind.

S 20

30.391

44.2

30.358

45.9

42

42.3

43.7

40.4

43.7

NNE

Lightly overcast— light haze and wind.

©21

30.382

45.5

30.373

46.7

39

42.3

46.3

39.8

46.3

W

Overcast— haze— light wind.

M22

30.528

45.1

30.533

44.7

38

40.0

40.4

39.4

40.4

NNE

( Light haze — A.M. Light soft clouds- light wind. P.M. Fine
t and cloudless.

T 23

30.507

41.3

30.503

42.7

34

34.0

38.9

31.7

39.0

NW

f Light haze.— A.M. Lightly overcast— light wind and hoar
\ frost. P.M. Fair— cloudless.

W24

30.503

39.2

30.434

40.3

33

33.2

36.2

29.2

39.7

W

A.M. Fog— hoar frost. P.M. Fair— cloudless— haze.

T25

30.358

41.3

30.370

43.3

41

41.3

45.8

32.3

45.8

W

A.M. Overcast— haze. P.M. Fair— nearly cloudless— light wind.

F 26

30.539

42.6

30.562

43.8

39

39.8

43.7

39.0

43.7

N

A.M. Fair— lightly cloudy. P.M. Overcast— liglit wind.

S 27

30.584

43.5

30.554

43.6

39

39.8

39.2

37.8

43.0

E

Overcast- light fog.

©28

30.460

41.7

30.372

42.3

36

36.3

39.0

33.8

39.0

£

Fine— nearly cloudless.

M29

30.204

40.3

30.100

42.3

38

38.3

43.6

32.6

48.7

SE

Fair- lightly cloudy— light fog and hoar frost.

• T 30

29.980

45.3

29.950

47.3

46

49.4

50.7

36.5

53.2

S

Overcast— light fog and deposition. — Light wind, p.m.

W31

29.841

49.8

29.816

51.6

53

53.4

53.3

48.3

54.5

SSWvar.

Lowering— deposition— light fog.— Showery— light wind, p.m.

Means.. 30.300

45.1

30.292

46.3

41.3

42.4

44.8

38.1

45.6

Sum.
.114

Mean of Barometer, corrected for Capil- ) 9 A.M. 3 P.M.
larity and reduced to 32° Fahr j" 30.265 30.253

PHILOSOPHICAL

TRANSACTIONS

OF THE

ROYAL SOCIETY

OF

LONDON.

FOR THE YEAR MDCCCXXXV.

PART II.

LONDON:

PRINTED BY RICHARD TAYLOR, RED LION COURT, FLEET STREET.

MDCCCXXXV.

CONTENTS.

XIII. Continuation of the Paper on the Relations between the Nerves of Motion and
of Sensation, and the Brain ; more particularly on the Structure of the Medulla
oblongata and the Spinal Marrow. By Sir Charles Bell, F.R.S. ^c. page 255

XIV. Experimental Researches in Electricity. — Tenth Series. By Michael Faraday,

D.C.L. F.R.S. Fullerian Prof. Chem. Royal Institution, Cmr. Memh. Royal
and Imp. Acadd. of Sciences, Paris, Petersburgh, Florence, Copenhagen,
Berlin, 8^c. ^c 263

XV. Discussion of Tide Observations made at Liverpool. By John William Lubbock,

Esq. V.P. and Treas. R.S. 275

XVI. Remarks on the difficulty of distinguishing certain Genera of Testaceous
MoUusca by their Shells alone, and on the Anomalies in regard to Habitation
observed in certain Species. By John Edward Gray, Esq. F.R.S. 8^c. . 301

XVII. On the supposed existence of Metamorphoses in the Crustacea. By J. O. West-
wood, F.L.S. 8^ Sec. Ent. Soc. Communicated by J. G. Children, Esq.
Sec. R.S. 311

XVIII. On the Ice formed, under peculiar circumstances, at the bottom of running
Water. By the Rev. James Farqvharson, of Alf or d, F.R.S. .... 329

XIX. Observations on the Theory of Respiration. By William Stevens, M.D. D.C.L.
Fellow of the Royal College of Physicians in Copenhagen, Fellow of the Royal
College of Surgeons in London, 8^c. ^c. Communicated by W. T. Brande, Esq.
V.P.R.S. 345

XX. Discovery of the Metamorphosis in the second type of the Cirripedes, viz. the

Lepades, completing the Natural History of these singular Animals, and con-
firming their affinity with the Crustacea. By J. V. Thompson, F.L.S. Deputy
Inspector-General of Hospitals. Communicated by Sir James Macgrigor, Bart.
M.D.F.R.S. , 355

[ viii ]

XXI. On the Double Metamorphosis in the Decapodous Crustacea, exemplified in
Cancer Msenas, Linn. By J. V. Thompson, F.L.S. Deputy Inspector- General
of Hospitals. Communicated by Sir James Macgrigor, Bart. M.D. F.R.S. 359

Index 365

Appendix.

Meteorological Journal kept at the Apartments of the Royal Society, by order of the

President and Council.

ERRATA.
Page 37, line 12. For allied to N. clausa, read allied to N. clausa, Zool. Journal.
Page 37, line 19. For Murex Rnmphius, Mont., read Murex Bamfius, Donov.
Page 37, line 21. For Fusus corneus read Fusus antiquus, Linn.

PHILOSOPHICAL TRANSACTIONS.

XIII. Continuation of the Paper on the Relations between the Nerves of Motion and of
Sensation^ and the Brain ; more particularly on the Structure of the Medulla oblon-
gata and the Spinal Marrow. By Sir Charles Bell, F.R.S. Sgc. §c. 8sc.

Received March 25, — Read April 30, 1835.

In this paper it will be necessary to enter on minute details of the anatomy ; but
they regard a subject hitherto untouched, although essential to the comprehension of
the nervous system, without which, indeed, it could not be said that we had a know-
ledge of the nerves as a system.

The author has advanced, by slow and laborious researches, from observing the
general arrangement of the nerves as they lie in the body, to the investigation of par-
ticular nerves and their endowments ; and, finally, to the examination of these parts
in the centre of the system, the brain and spinal marrow, which enables him to assign
the reason of that perfect symmetry which reigns through the whole.

The subjects of his last paper have been examined again and again by dissection,
and reviewed in every aspect. They have been found correct in every particular.
But they necessarily lead to further investigation : they point more especially to a
minute inquiry into the structure of the spinal marrow, and its relations to the en-
cephalon on the one hand, and to the origin of the nerves on the other.

It might be imagined that the author of this paper had, in these inquiries, fol-
lowed his preconceived notions ; but it has not been so. On the contrary, when
in search of the explanation of certain phenomena, he discovered a fact in the
structure which diverted him from his design, and carried him in a new course of
inquiry ^,

In an anatomical investigation of so much delicacy, it is necessary, in order to un-
derstand the descriptions, that he who follows it by dissection should have the parts
presented exactly in the same aspect, and trace them in a prescribed manner. When

* The paper on the Voice was undertaken as a preface to the investigation of the accessory respiratory nerves.
In following that subject, the author found it indispensable to deviate into this inquiry, which proves to be the
more important of the two.

MDCCCXXXV. 2 L

256 SIR CHARLES BELL ON THE RELATIONS BETWEEN

the anatomist has recognised the parts, and verified the descriptions of the author,
he will of course vary his mode of proceeding to satisfy himself.

Lay a portion of the spinal marrow, of two or three inches, on the dissecting board,
and pin it so as to look upon the posterior surface of that cord. Begin by making
a clean transverse section of it near one extremity, and inspect the newly-divided sur-
face (see Plate III. fig. 1.). The first thing which we distinguish is the cineritious
matter in the centre of the medullary. If we introduce the curette into the softer
cineritious matter, we can separate the medullary columns (as in figg. 2. & 3.), and
we distinguish these parts: the posterior columns, deeply divided by their sulcus;
the lateral columns ; and the anterior columns.

In making these divisions, directed by the natural sulci and by the cineritious
matter, we may soon satisfy ourselves that there is but one absolute bond of union
by nervous matter. We find the anterior columns tied together by a sort of commis-
sure, and to that commissure is attached the anterior portion of the posterior columns
at two points (fig. 3. d.).

Having contemplated the section of the spinal marrow, we proceed to the dissec-
tion by splitting up these columns. We raise the posterior columns together, in one
piece ; to do which we must divide them at the point of union with the anterior
columns (fig. 4. b.). But except at this angle, the whole tract is raised without the
slightest breach of its proper surface. When the columns are thus separated, the
surfaces are found to be covered with cineritious matter. We have split the cine-
ritious substance, and some of it lies on the lower surface of the part raised, and some
on the upper surface of that which is below.

If we now clear away the cineritious substance from the columns below, we shall
first discover the two lateral tracts or columns. We see them in their course, regular
as nerves. These columns or cords, in this aspect and condition, take a rounded
form, although they are of a different shape when packed together in their natural
state.

And now may be observed a structure which is not without interest. If we make
a slight breach upon the surface of the columns when divested of their cineritious
covering, and insinuate the point of the curette, we raise a thin pellicle, like a distinct
coat, and which we may separate all round. Having done this, and the remaining
surface being smooth, we may pierce it again, and in a similar manner separate a
third and a fourth layer, which, smooth and delicate themselves, leave the part below
as regular as the natural or exterior surface. It appears that the superficial layers
furnish the roots of the higher nerves, and that the lower layers go off into the roots
of the nerves as they successively arise.

If we now follow the sensitive or posterior roots of the spinal nerves towards their
origins, we find them entering and dispersing in the substance of these lateral
columns. Some authors describe these roots as derived from the cineritious matter.
This is quite at variance with my dissections. The cineritious matter is not of a con-

THE NERVES OF MOTION AND OF SENSATION, AND THE BRAIN. 257

sistence or structure into which nerves can be traced : and through the whole column
of the spinal marrow, up to the fifth and portio mollis of the seventh nerves of the
head, the cineritious matter is superimposed on the columns and nerves *.

Between the lateral columns, the cineritious matter lies deep. Upon raising it, the
anterior or motor columns are seen (fig. 4. d, d.). In essential circumstances they
resemble the lateral columns, and they are distinct from them. The cineritious
matter occupies a portion of the space between them ; and as to the remaining part,
the line of separation is distinct, and the surfaces are unbroken.

By the manner in which the dissection has been made, the posterior portion of the
spinal marrow being raised, as it were, out of the heart of the cord, the remaining
parts fall flat, and the lateral and anterior columns separate.

Having distinguished the columns which form the spinal marrow, their natural
sulci, their proper connexions, and the distribution of the cineritious substance be-
tween them, we have in the next place to observe how these columns are arranged,
and what change they undergo in the upper portion of the cord, called medulla ob-
longata. We approach from below the same parts which we looked upon in their
relations with the brain in the last paper.

We must now have before us a portion of the spinal marrow with the medulla ob-
longata attached to it, and proceed with the dissection.

The parts being presented in the same aspect as before, we raise the two posterior
columns, separating them from the others at the intervening cineritious matter. At
the back of the medulla oblongata we find the posterior columns diverging, and
forming the triangular space of the fourth ventricle; this space is laid open on
tearing up the pia mater, which connects the cerebellum with the medulla oblongata.
Each of these columns is now seen to consist of two, the outermost the larger, and
that towards the central line the smaller, and in shape pyramidal -(-. Following up
these diverging columns, we recognise them to be the processus cerebelli ad medul-
1am oblongatam. These great tracts, which form a large portion of the spinal mar-
row, are now seen to bear relation to the cerebellum.

The posterior tracts or columns being raised, we have only the lateral and anterior
columns, which belong to the cerebrum, to attend to. And here is the interesting
part of this communication.

Once more observing the layer of cineritious matter, we brush it off from the

* It is easy to trace the roots of the sensitive portion of the spinal nerve into the lateral column. It should
be observed at the same time, that in raising the posterior columns, by insinuating an instrument into the cine-
ritious intermediate substance, there is a more intimate attachment of the medullary substance of the posterior
column at its outer edge and in the line of the origins of the nerves. It is not impossible, therefore, that the
posterior column may be connected with the sensitive root of the spinal nerves, though hitherto I have not
traced the fibres.

t This subdivision of what I have called the posterior column of the spinal marrow is to be traced in the
whole length of the spinal marrow.

2l2

258 SIR CHARLES BELL ON THE RELATIONS BETWEEN

lateral columns. This grey matter may be traced into the fourth ventricle, ex-
tending over the parts to be presently described, and over part of the roots of the
fifth pair of nerves. It constitutes one sheet of matter from the cauda equina to
the roots of the auditory nerves, and forms a grand septum between the anterior
and lateral part of the spinal marrow which belongs to the cerebrum, and the pos-
terior columns which are related to the cerebellum.

Union of the lateral Columns in the Medulla Oblongata.

On brushing away the cineritious matter from the cerebral portion of the spinal
marrow, we recognise the two lateral columns. Upwards, or towards the brain,
each of these columns has a double termination ; first, in the root of the fifth nerve ;
and secondly, in the union of the columns, or, in other words, in their decussation.

These columns lie separate in the spinal marrow ; but having ascended to the
medulla oblongata, they fall together, and form one round column something less
than half an inch in length. On tracing this united column upwards they are dis-
entangled, but do not separate, for they now constitute those processes of the cere-
brum which, in a former paper, we traced down from the back of the crura cerebri
(fig. 5. E, E; fig. 6. A, A.).

On observing the portion of the united columns, the appearance is very much that
which is presented by the union of the optic nerves ; that is, however, rather when
the part is thoroughly hardened in spirit : when it is somewhat more pliant, we can
trace the filaments of one side into the column on the other side*. The decussation
is the most perfect of any to be demonstrated in the brain and nerves.

Reverting to the statement in the former paper, that a septum divides the right
and left sensitive tracts where they are seen in the fourth ventricle, and that in
tracing that septum downwards it terminates at the point of decussation of these
tracts : I have now to add, that the septum does not absolutely terminate, that it
splits to permit the oblique course and decussation of the filaments of these columns.
Thus separated at the union of the columns, the septa unite again below, and may
be followed downwards into that connexion which binds the posterior portion of the
spinal marrow to the anterior columns.

It remains a desideratum to know what is the nature of those fibrous septa which
intervene and divide the longitudinal tracts of nervous matter. But whatever may
be determined on this point, it is obvious that they form a perfect link or bond of
union and mechanical strength, extending from the pons to the cauda equina. Around
the commissures the fibres of these bands are especially interwoven -}-.

* Much of the anatomy, as I have here described it, may be made out in the recent parts. But it will be
easier and more satisfactory, when the parts are soft, to drop them into spirits, so that the surfaces as they are
exposed may be hsirdened and prepared for further dissection on a succeeding day.

t The true distinctions between the columns in the spinal marrow may be made, as we did those of the
medulla oblongata, by observing the splitting of the septa. From the circumstance of the columns scaHng off

THE NERVES OF MOTION AND OF SENSATION, AND THE BRAIN. 259

When the two tracts or columns which descend from the posterior portions of the
crura cerebri are transversely divided, where they form the slit of the calamus scrip-
torius, and when they are dissected down (fig-. 4. a, a, b.), we obtain a very interesting
view of the back part of the anterior columns (fig. 4. d, d.), or rather of the pyramidal
bodies, and their decussation. We see the union and decussation of these bodies before
they separate and descend to form the motor columns of the spinal marrow. The
motor and sensitive columns, — which were close together in tJie crura cerebri, and
which in their descent were separated in the pons, and by the septum which is con-
tinued down from the posterior transverse septum of the pons, — come here again into
contact at the point of union and decussation*. The motor columns approach the
sensitive columns, but no union takes place; the columns keep their respective
courses down the spinal marrow. When we dissect these parts carefully at the
back of the medulla oblongata, we may feel, and with sharp eyes we may see, very
minute and yet uncommonly strong filaments which run among these parts. We
may consider such filaments as a further proof how carefully these textures are
g-uarded against laceration.

When the dissection is carefully made, we have thus a view of the posterior part
of the decussation of the pyramidal bodies ; and after their decussation we see them
separate and descend in the two anterior or motor columns.

Concluding view of the Sensitive and Motor System of Nerves.

If it could be said hitherto that the distribution of the nervous system, more than
any other part of the animal structure, evinces design, the conclusion is irresistible,
when we perceive that the parts which minister to sensation and motion are arranged
with a symmetry beyond what we expect to see in architectural plans or ornaments,
where every part is balanced, and each has its counterpart.

It could not be well imagined that sensation and motion belonged to parts sepa-
rate and dissimilar. Formerly I believed that the nerves of sensation, that is to say,
the posterior roots of the spinal nerves, came from the posterior columns of the spinal
marrow, and consequently from the cerebellum. Whilst entertaining this belief I
found my progress barred, for it appeared to me incomprehensible that motion
could result from an organ like the cerebrum, and sensation from the cerebellum,
for there was no agreement between them. They conformed neither in size, shape,
nor subdivisions. Sensation and volition are necessarily combined in every action
of the frame -f. Although these influences, of whatever nature they be, are pro-

in regular pellicles, we may else be deceived. On separating, for example, the posterior and lateral columns
at the true sulcus of separation, we shall see the minute transverse fibres : which appearance is produced by the
splitting of the septum. See the former paper.

* The motor and sensitive columns do not mix or decussate, but only the motor columns with each other,
and the sensitive columns with each other.

t This has been illustrated in former papers, and particularly in treating of the actions of the lips.

260 SIR CHARLES BELL ON THE RELATIONS BETWEEN

jected in different directions, and belong to distinct filaments*, they must be finally
conjoined and in union. The anatomy conforms to this idea ; the cords of com-
munication between the seat of volition and the organs of the body proceed from
a centre, run parallel, undergo similar changes, and are blended in their ultimate
distribution, as in their central or cerebral relations.

It is pleasing to see that through the labours of members of this Society the prin-
ciples which have directed the author in the investigation of the human anatomy
are likely to be extended in their application, by a correspondence being observed in
the arrangement of the nervous tracts through every class of animals possessing
volition. It has long appeared to the author that the system does not differ, even in
the different classes of animals, although there is much apparent variety in the
distribution of the nerves.

When it became a question whether or not Crustacea possessed the organ of
hearing, the celebrated Scarpa undertook the investigation. With this purpose he
did not pry about to discover the external organ of the sense. He looked to the brain,
or cerebral ganglion, — recognised the part from which the acoustic nerve should
come, according to the analogy of other animals. He found the nerve, and traced it
to its destination ; that simple rather than imperfect organ, which, but for the cir-
cumstance of the auditory nerve in its cavity, might have been supposed too defective
in its organization to be capable of receiving the impulse of sounds.

In this manner is the nervous system to be studied ; for there is an internal change,
in accordance with outward organization, whilst the system or great plan does not
vary. There is an endowment in each particular column ; it is one through its whole
course. An animal, or a class of animals, may have a particular organ developed,
and with the external apparatus there is a corresponding or an adjusted condition of
the appropriated nerve. Another class may be deficient in the external organization,
when we shall in vain look for the accompanying nerve ; it is contracted, or hardly
visible ; but with all this the system is unchanged.

From a more cursory view of the comparative anatomy than others may have taken,
this is my conclusion ; but my time for such investigations has been given almost
exclusively to the human anatomy ; and in it I hope it will be granted that the
system, as it regards sensation and motion, has been displayed so as to increase the
interest of these pursuits, and to direct the studies of the pathologist to beneficial
results ; much advantage could hardly have been expected by dissection of the brain,
even from the utmost ingenuity of research, whilst the very elements of the subject,
as regards the natural anatomy, were unknown.

* See the paper on the Nervous Circle.

THE NERVES OF MOTION AND OF SENSATION, AND THE BRAIN. 261

Ejoplanation of the Plate.
Plate III.

Fig. 1. A transverse section of the spinal marrow, showing the distinctions of the
medullary and cineritious substance.

Fig. 2. Shows the section with the medullary columns parted at their natural
divisions, viz. by insinuating the curette into the cineritious substance,
and opening the sulci.

A. The posterior column.
B, B. The lateral columns.

c. The anterior columns.

Fig. 3. The same parts still further separated, so as to exhibit the connexion be-
tween the posterior columns of the spinal marrow and the motor columns.
The letters refer to the same parts as in the last figure.
D. The connexion between the posterior and anterior columns.

Fig. 4. In this view the posterior part of the spinal marrow, that which belongs to
the cerebellum, is taken away, leaving those columns only which belong
to the cerebrum. As the posterior portions (figg. 2. & 3. a.) enter deeply
into the spinal marrow, when they are taken away the remaining columns
fall flat on the board, and permit an easy separation.
a, a. The cineritious matter which intervenes between the columns belonging
to the cerebrum, and those belonging to the cerebellum.

B. Projecting lines where the posterior columns of the spinal marrow were

connected with the anterior. (See fig. 3. d.)
c, c. The lateral columns, or sensitive columns, after raising the cineritious

substance. Into these the sensitive roots of the spinal nerves are traced.
D, D. A deeper dissection of the cineritious substance exposes here the posterior

surface of the anterior or motor columns.

Fig. 5. This figure represents a posterior view of the upper part of the spinal mar-
row, and the medulla oblongata.

A. The two posterior columns of the spinal marrow being dissected up, they

are here represented diverging towards the cerebellum at g.

B. The cineritious matter left on the remaining part of the spinal marrow, after

raising the column (a.). The separation of the columns having been made
at the intervening cineritious matter, both surfaces have that matter
attached to them — both a and b.

262 SIR CHARLES BELL ON THE NERVES OF MOTION, ETC.

c, c. The lateral columns of the spinal marrow (figg. 2. & 3. b, b.), displayed on
their posterior surface. They are discovered on raising the cineritious
matter b. Into these columns the posterior root of the spinal nerves are
traced : they are the columns of sensation.
D. The short column formed by the union of the columns c, c. On dissecting
this portion, the decussation of the columns will be seen.

E, E. The same columns which were lateral in the spinal marrow, now continued
upwards, and visible in the fourth ventricle without dissection. They
ascend under the valvula cerebri and under the corpora quadrigemina,
and fall into the crura cerebri. So that, tracing them from above, each
of these columns descends from that part of the crus cerebri which is
posterior to the corpus nigrum.

F. The origin of the sensitive root of the fifth nerve of the encephalon.

G. The processus cerebelli ad medullam oblongatam.

Fig. 6. This figure represents the further dissection of the parts seen in fig. 5.
A, A. The columns marked e in the former plate. They are divided transversely,
and the lower portion folded down, being separated from the parts below
by a delicate dissection.
B. These columns folded down.
c, c. The lateral columns of the spinal marrow continued up into b.

D. The union of the anterior columns seen in their posterior aspect. The late-
ral or sensitive columns, and the anterior or motor columns, are held
together at this point. But it appears more for security than reunion.
A fine dissection exhibits them quite distinct ; and the parts above con-
tinuous into the columns of the spinal marrow ; each separately.
E, E. The sensitive roots of the fifth pair of nerves.

[ 263 ]

XIV. Experimental Researches in Electricity . — Tenth Series. By Michael Faraday
D.C.L. F.R.S. Fullerian Prof. Chem. Royal Institution, Corr. Memh. Royal and
Imp. Acadd. of Sciences, Paris, Petershurgh, Florence, Copenhagen, Berlin, S^c. 8sc.

Received June 16, — Read June 18, 1835.

§ 16. On an improved form of the Voltaic Battery. § 17. Some practical
results respecting the construction and use of the Foltaic Battery.

1119. X HAVE lately had occasion to examine the voltaic trough practically, with
a view to improvements in its construction and use ; and though I do not pretend
that the results have anything like the importance which attaches to the discovery
of a new law or principle, I still think they are valuable, and may therefore, if briefly
told, and in connexion with former papers, be worthy the approbation of the Royal
Society.

§ 16. On an improved form of the Voltaic Battery.

1 120. In a simple voltaic circuit (and the same is true of the battery) the chemical
forces which, during their activity, give power to the instrument, are generally divided
into two portions ; the one of these is exerted locally, whilst the other is transferred
round the circle (947- 996.) ; the latter constitutes the electric current of the instru-
ment, whilst the former is altogether lost or wasted. The ratio of these two portions
of power may be varied to a great extent by the influence of circumstances : thus, in a
battery not closed, all the action is local ; in one of the ordinary construction, much
is in circulation when the extremities are in communication ; and in the perfect one,
which I have described (1001.), all the chemical power circulates and becomes elec-
tricity. By referring to the quantity of zinc dissolved from the plates (865. 1126.),
and the quantity of decomposition effected in the volta-electrometer (711. 1126.) or
elsewhere, the proportions of the local and transferred actions under any particular
circumstances can be ascertained, and the efficacy of the voltaic arrangement, or the
waste of chemical power at its zinc plates, be accurately determined.

1121. If a voltaic battery were constructed of zinc and platina, the latter metal
surrounding the former, as in the double copper arrangement, and the whole being
excited by dilute sulphuric acid, then no insulating divisions of glass, porcelain, or
air would be required between the contiguous platina surfaces ; and, provided these
did not touch metallically, the same acid which, being between the zinc and platina,
would excite the battery ijito powerful action, would, between the two surfaces of

MDCCCXXXV. 2 M

264

DR. FARADAY'S EXPERIMENTAL RESEARCHES IN ELECTRICITY.

platina, produce no discharge of the electricity, nor cause any diminution of the
power of the trough. This is a necessary consequence of the resistance to the passage
of the current which I have shown occurs at the place of decomposition (1007. 1011.);
for that resistance is fully able to stop the current, and therefore act as insulation to
the electricity of the contiguous plates, inasmuch as the current which tends to pass
between them never has a higher intensity than that due to the action of a single pair.

1 122. If the metal surrounding the zinc be copper (1045.), and if the acid be nitro-
sulphuric acid (1020.), then a slight discharge between the two contiguous coppers
does take place, provided there be no other channel open by which the forces may
circulate ; but when such a channel is permitted, the return discharge of which I
speak is exceedingly diminished, in accordance with the principles laid down in the
eighth series of these Researches.

1123. Guided by these principles I was led to the construction of a voltaic trough,
in which the coppers, passing round both surfaces of the zincS;, as in Wollaston's
construction, should not be separated from each other except by an intervening thick-
ness of paper, or in some other way, so as to prevent metallic contact, and should thus
constitute an instrument compact, powerful, economical, and easy of use. On ex-
amining, however, what had been done before, I found that the new trough was in
all essential respects the same as that invented and described by Dr. Hare, Professor
in the University of Pennsylvania, to whom I have great pleasure in referring it.

1124. Dr. Hare has fully described his trough*. In it the contiguous copper
plates are separated by thin veneers of wood, and the acid is poured on to, or off,
the plates by a quarter revolution of an axis, to which both the trough containing
the plates, and another trough to collect and hold the liquid, are fixed. This arrange-
ment I have found the most convenient of any, and have therefore adopted it. My
zinc plates were cut from rolled metal, and when soldered to the copper plates had
the form delineated, fig. 1 . These were then bent over a gauge into the form fig. 2,
and when packed in the wooden box constructed to receive them, were arranged as
in fig. S-f-, little plugs of cork being used to keep the zinc plates from touching the

Fig. 2. Fig. 3.

/i

'

copper plates, and a single or double thickness of cartridge paper being interposed

* Philosophical Magazine, 1824, vol. Ixiii. p. 241 ; or Silliman's Journal, vol. vii. See also a previous
paper by Dr. Hare, Annals of Philosophy, 1821, vol. i. p. 329, in which he speaks of the non-necessity of in-
sulation between the coppers.

t The papers between the coppers are, for the sake of distinctness, omitted in the figure.

ESTIMATION OF VOLTAIC ENERGY BY EQUIVALENTS OF ACTION AND EFFECT. 265

between the contiguous surfaces of copper to prevent them from coming in contact.
Such was the facility afforded by this arrangement, that a trough of forty pairs of
plates could be unpacked in five minutes, and repacked again in half an hour ; and
the whole series was not more than fifteen inches in length.

1125. This trough, of forty pairs of plates three inches square, was compared, as to
the ignition of a platina wire, the discharge between points of charcoal, the shock on
the human frame, &c., with forty pairs of four-inch plates having double coppers, and
used in porcelain troughs divided into insulating cells, the strength of the acid em-
ployed to excite both being the same. In all these effects the former appeared quite
equal to the latter. On comparing a second trough of the new construction, contain-
ing twenty pairs of four-inch plates, with twenty pairs of four-inch plates in porce-
lain troughs, excited by acid of the same strength, the new trough appeared to sur-
pass the old one in producing these effects, especially in the ignition of wire.

1126. In these experiments the new trough diminished in its energy much more
rapidly than the one on the old construction, and this was a necessary consequence of
the smaller quantity of acid used to excite it, which in the case of the forty pairs new
construction was only one seventh part of that used for the forty pairs in the porcelain
troughs. To compare, therefore, both forms of the voltaic trough in their decom-
posing powers, and to obtain accurate data as to their relative values, experiments of
the following kind were made. The troughs were charged with a known quantity
of acid of a known strength ; the electric current was passed through a volta-
electrometer (711-) having electrodes 4 inches long and 2'3 inches in width, so as
to oppose as little obstruction as possible to the current ; the gases evolved were
collected and measured, and gave the quantity of water decomposed. Then the
whole of the charge used was mixed together, and a known part of it analysed, by
being precipitated and boiled with excess of carbonate of soda, and the precipitate
well washed, dried, ignited, and weighed. In this way the quantity of metal oxidized
and dissolved by the acid was ascertained ; and the part removed from each zinc
plate, or from all the plates, could be estimated and compared with the water de-
composed in the volta-electrometer. To bring these to one standard of comparison,
I have reduced the results so as to express the loss at the plates in equivalents of
zinc for the equivalent of water decomposed at the volta-electrometer : I have taken
the equivalent number of water as 9, and of zinc as 32*5, and have considered 100
cubic inches of the mixed oxygen and hydrogen, as they were collected over a pneu-
matic trough, to result from the decomposition of 12-68 grains of water.

1127. The acids used in these experiments were three, — sulphuric, nitric, and mu-
riatic. The sulphuric acid was strong oil of vitriol ; one cubical inch of it was equi-
valent to 486 grains of marble. The nitric acid was very nearly pure ; one cubical
inch dissolved 150 grains of marble. The muriatic acid was also nearly pure, and
one cubical inch dissolved 108 grains of marble. These were always mixed with
water by volumes, the standard of volume being a cubical inch.

2 M 2

266 DR. FARADAY'S EXPERIMENTAL RESEARCHES IN ELECTRICITY.

1128. An acid was prepared consisting of 200 parts water, 4J parts sulphuric acid^,
and 4 parts nitric acid ; and with this both my trough, containing forty pairs of three-
inch plates, and four porcelain troughs, arranged in succession, each containing ten
pairs of plates with double coppers four inches square, were charged. These two bat-
teries were then used in succession, and the action of each was allowed to continue
for twenty or thirty minutes, until the charge was nearly exhausted, the connexion
with the volta-electrometer being carefully preserved during the whole time, and the
acid in the troughs occasionally mixed together. In this way the former trough
acted so well, that for each equivalent of water decomposed in the volta-electrometer
only from 2 to 2*5 equivalents of zinc were dissolved from each plate. In four ex-
periments the average was 2*21 equivalents for each plate, or 88*4 for the whole
battery. In the experiments with the porcelain troughs, the equivalents of con-
sumption at each plate were 3*54, or 141*6 for the whole battery. In a perfect vol-
taic battery of forty pairs of plates (991. 1001.) the consumption would have been
one equivalent for each zinc plate, or forty for the whole.

1129. Similar experiments were made with two voltaic batteries, one containing
twenty pairs of four-inch plates, arranged as I have described (1124.), and the other
twenty pairs of four-inch plates in porcelain troughs. The average of five experiments
with the former was a consumption of 3'7 equivalents of zinc from each plate, or 74
from the whole : the average of three experiments with the latter was 5*5 equivalents
from each plate, or 1 10 from the whole : to obtain this conclusion, two experiments
were struck out, which were much against the porcelain troughs, and in which some
unknown deteriorating influence was supposed to be accidentally active. In all the
experiments, care was taken not to compare new and old plates together, as that
would have introduced serious errors into the conclusions (1146.).

1 130. When ten pairs of the new arrangement were used, the consumption of zinc
at each plate was 6*76 equivalents, or 67'6 for the whole. With ten pairs of the com-
mon construction, in a porcelain trough, the zinc oxidized was, upon an average,^
15*5 equivalents each plate, or 155 for the entire trough.

1 131 . No doubt, therefore, can remain of the equality or even the great superiority
of this form of voltaic battery over the best previously in use, namely, that with
double coppers, in which the cells are insulated. The insulation of the coppers may
therefore be dispensed with ; and it is that circumstance which principally permits of
such other alterations in the construction of the trough as gives it its practical ad-
vantages.

1132. The advantages of this form of trough are very numerous and great, i. It
is exceedingly compact, for 100 pairs of plates need not occupy a trough of more
than three feet in length, ii. By Dr. Hare's plan of making the trough turn upon
copper pivots which rest upon copper bearings, the latter afford fixed terminations ;
and these I have found it very convenient to connect with two cups of mercury,
fastened in the front of the stand of the instrument. These fixed terminations give

ADVANTAGES OF HARE'S TROUGH. 267

the great advantage of arranging an apparatus to be used in connexion with the bat-
tery before the latter is put into action, iii. The trough is put into readiness for use
in an instant, a single jug of dilute acid being sufficient for the charge of 100 pairs of
four-inch plates, iv. On making the trough pass through a quarter of a revolution,
it becomes active, and the great advantage is obtained of procuring for the experi-
ment the effect of the Jirst contact of the zinc and acid, which is twice or sometimes
even thrice that which the battery can produce a minute or two after (1036. 1150.).
v. When the experiment is completed, the acid can be at once poured from between
the plates, so that the battery is never left to waste during an unconnected state of
its extremities ; the acid is not unnecessarily exhausted ; the zinc is not uselessly
consumed ; and, besides avoiding these evils, the charge is mixed and rendered uni-
form, which produces a great and good result (1039.) ; and, upon proceeding to a
second experiment, the important effect oi Jirst contact is again obtained, vi. The
saving of zinc is very great. It is not merely that, whilst in action, the zinc performs
more voltaic duty (1128. 1129.), but all the destruction which takes place with the
ordinary forms of battery between the experiments is prevented. This saving is of
such extent, that I estimate the zinc in the new form of battery to be thrice as
effective as that in the ordinary form. vii. The importance of this saving of metal is
not merely that the value of the zinc is saved, but that the battery is much lighter
and more manageable ; and also that the surfaces of the zinc and copper plates may
be brought much nearer to each other when the battery is constructed, and remain
so until it is worn out : the latter is a very important advantage (1 148.). viii. Again,
as, in consequence of the saving, thinner plates will perform the duty of thick ones,
rolled zinc may be used ; and I have found rolled zinc superior to cast zinc in action ;
a superiority which I incline to attribute to its greater purity (1144.). ix. Another
advantage is obtained in the economy of the acid used, which is proportionate to the
diminution of the zinc dissolved, x. The acid also is more easily exhausted, and is
in such small quantity that there is never any occasion to return an old charge into
use. Such old acid, whilst out of use, often dissolves portions of copper from the black
fiocculi usually mingled with it, which are derived from the zinc ; now any portion of
copper in solution in the charge does great harm, because, by the local action of the
acid and zinc, it tends to precipitate upon the latter, and diminish its voltaic efficacy
(1 145.). xi. By using a due mixture of nitric and sulphuric acid for the charge (1 139.),
no gas is evolved from the troughs ; so that a battery of several hundred pairs of plates
may, without inconvenience, be close to the experimenter, xii. If, during a series of
experiments, the acid becomes exhausted, it can be withdrawn, and replaced by other
acid with the utmost facihty ; and after the experiments are concluded, the great
advantage of easily washing the plates is at command. And it appears to me, that
in place of making, under different circumstances, mutual sacrifices of comfort, power,
and economy, to obtain a desired end, all are at once obtained by Dr. Hare's form
of trough.

268 DR. FARADAY'S EXPERIMENTAL RESEARCHES IN ELECTRICITY.

1133. But there are some disadvantag-es which I have not yet had time to over-
come, though I trust they will finally be conquered. One is the extreme difficulty of
making a wooden trough constantly water-tight under the alternations of wet and
dry to which the voltaic instrument is subject. To remedy this evil, Mr. Newman is
now engaged in obtaining porcelain troughs. The other disadvantage is a precipi-
tation of copper on the zinc plates. It appears to me to depend mainly on the cir-
cumstance that the papers between the coppers retain acid when the trough is
emptied ; and that this acid slowly acting on the copper, forms a salt, which gradually
mingles with the next charge, and is reduced on the zinc plate by the local action
(1120.): the power of the whole battery is then reduced. I expect that by using
slips of glass to separate the coppers at their edges, their contact can be sufficiently
prevented, and the space between them be left so open that the acid of a charge can
be poured and washed out, and so be removed from every part of the trough when
the experiments in which it is used are completed.

1134. The actual superiority of the troughs which I have constructed on this plan,
I believe to depend, first and principally, on the closer approximation of the zinc and
copper surfaces; — in my troughs they are only one tenth of an inch apart (1148.) ; —
and, next, on the superior quality of the rolled zinc above the cast zinc used in the
construction of the ordinary pile. It cannot be that insulation between the conti-
guous coppers is a disadvantage, but I do not find that it is any advantage ; for
when, with both the forty pairs of three-inch plates and the twenty pairs of four-inch
plates, I used papers well imbibed with wax*, these being so large that when folded
at the edges they wrapped over each other, so as to make cells as insulating as
those of the porcelain troughs, still no sensible advantage in the chemical action
was obtained.

1135. As, upon principle, there must be a discharge of part of the electricity from
the edges of the zinc and copper plates at the sides of the trough, I should prefer,
and intend having, troughs constructed with a plate or plates of crown glass at the
sides of the trough : the bottom will need none, though to glaze that and the ends
would be no disadvantage. The plates need not be fastened in, but only set in their
places ; nor need they be in large single pieces.

§ 17. Some practical results respecting the construction and use of the Voltaic

Battery.

1136. The electro-chemical philosopher is well acquainted with some practical re-
sults obtained from the voltaic battery by MM. Gay-Lussac and Thenard, and given
in the first forty-five pages of their 'Recherches Physico-Chimiques'. Although
the following results are generally of the same nature, yet the advancement made in
this branch of science of late years, the knowledge of the definite action of electricity,

* A single paper thus prepared could insulate the electricity of a trough of forty pairs of plates.

NATURE AND STRENGTH OF THE BATTERY ACID. 269

and the more accurate and philosophical mode of estimating the results by the equi-
valents of zinc consumed, will be their sufficient justification.

1137. Nature and strength of the acid. — My battery of forty pairs of three-inch
plates was charged with acid consisting of 200 parts water and 9 oil of vitriol. Each
plate lost, in the average of the experiments, 4-66 equivalents, or the whole battery
186-4 equivalents, of zinc, for the equivalent of water decomposed in the volta-elec-
trometer. Being charged with a mixture of 200 water and 16 of the muriatic acid,
each plate lost 3'8, or the whole battery 152, equivalents of zinc for the water de-
composed. Being charged with a mixture of 200 water and 8 nitric acid, each plate
lost 1-85, or the whole battery 74*16, equivalents of zinc for one equivalent of water
decomposed. The sulphuric and muriatic acids evolved much hydrogen at the plates
in the trough ; the nitric acid no gas whatever. The relative strengths of the original
acids have already been given (11 27.); but a difference in that respect makes no
important difference in the results when thus expressed by equivalents (1140.).

1138. Thus nitric acid proves to be the best for this purpose : its superiority ap-
pears to depend upon its favouring the electrolization of the liquid in the cells of the
trough upon the principles already explained (905. 973. 1022.), and consequently
favouring the transmission of the electricity, and therefore the production of transfer-
able power (1120.).

1139. The addition of nitric acid might, consequently, be expected to improve sul-
phuric and muriatic acids. Accordingly, when the same trough was charged with a
mixture of 200 water, 9 oil of vitriol, and 4 nitric acid, the consumption of zinc was
at each plate 2786, and for the whole battery 111-5, equivalents. When the charge
was 200 water, 9 oil of vitriol, and 8 nitric acid, the loss per plate was 2-26, or for the
whole battery 90-4, equivalents. When the trough was charged with a mixture of
200 water, 16 muriatic acid, and 6 nitric acid, the loss per plate was 2-11, or for the
whole battery 84-4, equivalents. Similar results were obtained with my battei-y of
twenty pairs of four-inch plates (1129.). Hence it is evident that the nitric acid was
of great service when mingled with the sulphuric acid ; and the charge generally
used after this time for ordinary experiments consisted of 200 water, 4 J oil of vitriol,
and 4 nitric acid.

1140. It is not to be supposed that the different strengths of the acids produced
the differences above ; for within certain limits I found the electrolytic effects to be
nearly as the strengths of the acids, so as to leave the expression of force, when given
m equivalents, nearly constant. Thus, when the trough was charged with a mixture
of 200 water and 8 nitric acid, each plate lost 1-854 equivalent of zinc. When the
charge was 200 water and 16 nitric acid, the loss per plate was 1-82 equivalent.
When it was 200 water and 32 nitric acid, the loss was 2-1 equivalents. The differ-
ences here are not greater than happen from unavoidable irregularities, depending 01^
other causes than the strength of acid. ..;

1141. Again, when a charge consisting of 200 water, 4 J oil of vitriol, and 4 nit/i^

270 DR. FARADAY'S EXPERIMENTAL RESEARCHES IN ELECTRICITY.

acid was used, each zinc plate lost 2- 16 equivalents ; when the charge with the same
battery was 200 water, 9 oil of vitriol, and 8 nitric acid, each zinc plate lost 2*26
equivalents.

1142. I need hardly say that no copper is dissolved during the regular action of
the voltaic trough. I have found that much ammonia is formed in the cells when
nitric acid, either pure or mixed with sulphuric acid, is used. It is produced in part
as a secondary result at the cathodes (663.) of the different portions of fluid con-
stituting the necessary electrolyte, in the cells.

1143. Uniformity of the charge. — This is a most important point, as I have already
shown experimentally (1042. &c.). Hence one great advantage of Dr. Hare's mecha-
nical arrangement of his trough.

1144. Purity of the zinc. — If pure zinc could be obtained, it would be very advan-
tageous in the construction of the voltaic apparatus (998.). Most zincs, when put
into dilute sulphuric acid, leave more or less of an insoluble matter upon the surface
in the form of a crust, which contains various metals, as copper, lead, zinc, iron, cad-
mium, &c., in the metallic state. Such particles, by discharging part of the transfer-
able power, render it, as to the whole battery, local ; and so diminish the effect. As
an indication connected with the more or less perfect action of the battery, I may
mention that no gas ought to rise from the zinc plates. The more gas which is ge-
nerated upon these surfaces, the greater is the local action and the less the transfer-
able force. The investing crust is also inconvenient, by preventing the displacement
and renewal of the charge upon the surface of the zinc. Such zinc as, dissolving in
the cleanest manner in a dilute acid, dissolves also the slowest, is the best ; zinc
which contains much copper should especially be avoided. I have generally found
rolled Liege or Mosselman's zinc the purest ; and to that circumstance attribute in
part the advantage of the new battery (1134.).

1145. Foulness of the zinc plates. — After use, the plates of a battery should be
cleaned from the metallic powder upon their surfaces, especially if they are employed
to obtain the laws of action of the battery itself. This precaution was always attend-
ed to with the porcelain trough batteries in the experiments described (1125., &c.). If
a few foul plates are mingled with many clean ones, they make the action in the dif-
ferent cells irregular, and the transferable power is accordingly diminished, whilst the
local and wasted power is increased. No old charge containing copper should be
used to excite a battery.

1146. New and old plates. — I have found voltaic batteries far more powerful when
the plates were new than when they have been used two or three times ; so that a new
and a used battery cannot be compared together, or even a battery with itself on the
first and after times of use. My trough of twenty pairs of four-inch plates, charged
with acid consisting of 200 water, 4^ oil of vitriol, and 4 nitric acid, lost, upon the first
time of being used, 2*32 equivalents per plate. When used after the fourth time with
the same charge, the loss was from 3*26 to 4*47 equivalents per plate ; the average

EFFECT OF VICINITY OF THE PLATES— FIRST IMMERSION— NUMBER. 271

being 37 equivalents. The first time the forty pair of plates (1124.) were used, the
loss at each plate was only 1-65 equivalent; but afterwards it became 2-16, 217,
2-52. The first time twenty pair of four-inch plates in porcelain troughs were used,
they lost, per plate, only 3*7 equivalents ; but after that, the loss was 5'25, 5-36, 5-9
equivalents. Yet in all these cases the zincs had been well cleaned from adhering
copper, &c., before each trial of power.

1 147. With the rolled zinc the fall in force soon appeared to become constant, i. e. to
proceed no further. But with the cast zinc plates belonging to the porcelain troughs,
it appeared to continue, until at last, with the same charge, each plate lost above twice
as much zinc for a given amount of action as at first. These troughs were, however,
so irregular that I could not always determine the circumstances affecting the amount
of electrolytic action.

1148. Ficinity of the copper and zinc. — The importance of this point in the con-
struction of voltaic arrangements, and the greater power, as to immediate action,
which is obtained when the zinc and copper surfaces are near to each other than
when removed further apart, are well known. I find that the power is not only
greater on the instant, but also that the sum of transferable power, in relation to the
whole sum of chemical action at the plates, is much increased. The cause of this
gain is very evident. Whatever tends to retard the circulation of the transferable
force, (i. e. the electricity,) diminishes the proportion of such force, and increases the
proportion of that which is local (996. 1120.). Now the liquid in the cells possesses
this retarding power, and therefore acts injuriously, in greater or less proportion, ac-
cording to the quantity of it between the zinc and copper plates, i. e. according to the
distances between their surfaces. A trough, therefore, in which the plates are only
half the distance asunder at which they are placed in another, will produce more
transferable, and less local, force than the latter ; and thus, because the electrolyte
in the cells can transmit the current more readily, both the intensity and quantity of
electricity is increased for a given consumption of zinc. To this circumstance mainly
I attribute the superiority of the trough I have described (1134.).

1149. The superiority oi double co/?/?er^ over single plates also depends in part upon
diminishing the resistance offered by the electrolyte between the metals. For, in fact,
with double coppers the sectional area of the interposed acid becomes nearly double
that with single coppers, and therefore it more freely transfers the electricity. Double
coppers are, however, effective, mainly because they virtually double the acting sur-
face of the zinc, or nearly so ; for in a trough with single copper plates and the usual
construction of cells, that surface of zinc which is not opposed to a copper surface is
thrown almost entirely out of voltaic action, yet the acid continues to act upon it and
the metal is dissolved, producing very little more than local effect (947. 996.). But
when by doubling the copper, that metal is opposed to the second surface of the zinc
plate, then a great part of the action upon the latter is converted into transferable
force, and thus the power of the trough as to quantity of electricity is highly exalted.

MDCCCXXXV. 2 N

272 DR. FARADAY'S EXPERLMENTAL RESEARCHES IN ELECTRICITY.

1150. First immersion of the plates. — The great effect produced at the first im-
mersion of the plates, (apart from their being new or used (1146.),) I have attributed
elsewhere to the unchanged condition of the acid in contact with the zinc plate
(1003. 1037.) : as the acid becomes neutralized, its exciting power is proportionably
diminished. Hare's form of trough secures much advantage of this kind, by mingling
the liquid, and bringing what may be considered as a fresh surface of acid against
the plates every time it is used immediately after a rest.

1151. Number of plates*. — The most advantageous number of plates in a battery
used for chemical decomposition, depends almost entirely upon the resistance to be
overcome at the place of action ; but whatever that resistance may be, there is a cer-
tain number which is more economical than either a greater or a less. Ten pairs of
four-inch plates in a porcelain trough of the ordinary construction, acting in the
volta-electrometer (1126.) upon dilute sulphuric acid of spec. grav. 1*314, gave an
average consumption of 15*4 equivalents per plate, or 154 equivalents on the whole.
Twenty pairs of the same plates, with the same acid, gave only a consumption of 5*5
per plate, or 110 equivalents upon the whole. When forty pairs of the same plates
were used, the consumption was 3*54 equivalents per plate, or 14 1*6 upon the whole
battery. Thus the consumption of zinc arranged as twenty plates was more advan-
tageous than if arranged either as ten or as forty.

1152. Again, ten pairs of my four-inch plates (1129.) lost Q'JQ each, or the whole
ten 67 '6 equivalents of zinc, in effecting decomposition ; whilst twenty pairs of the
same plates, excited by the same acid, lost 3*7 equivalents each, or on the whole 74
equivalents. In other comparative experiments of numbers, ten pairs of the three-
inch plates (1 125.) lost 3*725, or 37*25 equivalents upon the whole ; whilst twenty pairs
lost 2*53 each, or 50*6 in all ; and forty pairs lost on an average 2*21, or 88*4 alto-
gether. In both these cases, therefore, increase of numbers had not been advan-
tageous as to the effective production of transferable chemical power from the whole
quantity of chemical force active at the surfaces of excitation (1120.).

1153. But if I had used a weaker acid or a worse conductor in the volta-electro-
meter, then the number of plates which would produce the most advantageous effect
would have risen ; or if I had used a better conductor than that really employed in
the volta-electrometer, I might have reduced the number even to one ; as, for in-
stance, when a thick wire is used to complete the circuit (865., &c.). And the cause
of these variations is very evident, when it is considered that each successive plate in
the voltaic apparatus does not add anything to the quantity of transferable power or
electricity which the first plate can put into motion, provided a good conductor be
present, but tends only to exalt the intensity of that quantity, so as to make it more
able to overcome the obstruction of bad conductors (994. 1158.).

1154. Large or small plates-^-. — The advantageous use of large or small plates for
electrolyzations will evidently depend upon the facility with which the transferable

* Gat-Ltjssac and Thenard, Recherches Physico-Chimiques, torn. i. p. 29. f Ibid.

EFFECT OF LARGE AND SMALL PLATES—SLMULTANEOUS DECOMPOSITIONS. 273

power or electricity can pass. If in a particular case the most effectual number of
plates is known (1 151.), then the addition of more zinc would be most advantage-
ously made in increasing the size of the plates, and not their number. At the same
time, large increase in the size of the plates would raise in a small degree the most
favourable number.

1155. Large and small plates should not be used together in the same battery : the
small ones occasion a loss of the power of the large ones, unless they be excited by
an acid proportionably more powerful ; for with a certain acid they cannot transmit
the same portion of electricity in a given time which the same acid can evolve by
action on the larger plates.

1156. Simultaneous decompositions. — When the number of plates in a battery much
surpasses the most favourable proportion (1151 — 1153.), two or more decompositions
maybe eifected simultaneously with advantage. Thus my forty pairs of plates (1124.)
produced in one volta-electrometer 22*8 cubic inches of gas. Being recharged exactly
in the same manner, they produced in each of two volta-electrometers 21 cubical
inches. In the first experiment the whole consumption of zinc was 88*4 equivalents,
and in the second only 48*28 equivalents, for the whole of the water decomposed in
both volta-electrometers.

1157. But when the twenty pairs of four-inch plates (1129.) were tried in a similar
manner, the results were in the opposite direction. With one volta-electrometer 52
cubic inches of gas were obtained ; with two, only 14-6 cubic inches from each. The
quantity of charge was not the same in both cases, though it was of the same
strength ; but on rendering the results comparative by reducing them to equivalents
(1126.), it was found that the consumption of metal in the first case was 74, and in
the second case 97, equivalents for the whole of the water decomposed. These results
of course depend upon the same circumstances of retardation, &c., which have been
referred to in speaking of the proper number of plates (1151.).

1158. That the transferring, or, as it is usually called, conducting, power of an elec-
trolyte which is to be decomposed, or other interposed body, should be rendered as
good as possible*, is very evident (1020. 1120.). With a perfectly good conductor
and a good battery, nearly all the electricity is passed, i. e. nearly all the chemical ^
power becomes transferable, even with a single pair of plates (867.) • With an inter-^
posed non-conductor none of the chemical power becomes transferable. With an
imperfect conductor more or less of the chemical power becomes transferable as the
circumstances favouring the transfer of forces across the imperfect conductor are ex-
alted or diminished : these circumstances are, actual increase or improvement of the
conducting power, enlargement of the electrodes, approximation of the electrodes,
and increased intensity of the passing current.

1159. The introduction of common spring water in place of one of the volta-elec-
trometers used with twenty pairs of four-inch plates (1156.) caused such obstruction

* Gay-Lussac and Thenard, Recherclies Physico-Chimiques, torn. i. pp. 13, 15, 22.

2 n2

274 DR. FARADAY'S EXPERIMENTAL RESEARCHES IN ELECTRICITY.

as not to allow one fifteenth of the transferable force to pass which would have cir
culated without it. Thus fourteen fifteenths of the available force of the battery were
destroyed, being converted into local force, (which was rendered evident by the evo-
lution of gas from the zincs,) and yet the platina electrodes in the water were three
inches long, nearly an inch wide, and not a quarter of an inch apart.

1160. These points, i. e. the increase of conducting power, the enlargement of the
electrodes, and their approximation, should be especially attended to in volta-electro-
meters. The principles upon which their utility depend are so evident that there can
be no occasion for further development of them here.

Royal Institution,
October n, 1834,

[ 275 ]

XV. Discussion of Tide Observations made at Liverpool. By John William Lubbock

Esq. V.P. and Treas. R.S.

Received and Read June 18, 1835.

JlJY permission of the British Association for the Advancement of Science, I am
enabled to present to the Society a discussion by M. Dessiou * of 13,327 observa-
tions of the tides made at Liverpool between the 1st of January 1774 and the 31st of
December 1792. These observations, which were made by Mr. Hutchinson, Dock-
master at that place, belong to the Lyceum at Liverpool, and they were granted
with the greatest readiness and liberality by the Committee of that Institution, upon
the application of Mr. Whewell and myself, for the purposes of the present inquiry.

Mr. Hutchinson recorded the solar time of high water, and the height of the tide in
feet and inches, at the Custom-House Dock gates, together with the direction and
strength of the wind, and the state of the weather ; also, during a great portion of the
time, the height of the barometer and thermometer.

The following note is prefixed to the first book of these valuable observations :
"I'hese five years' observations upon the tides were made from solar time, and the
winds from the true meridian, and their velocity judged according to Mr. Smeaton's
rule, our great storms going at the rate of sixty miles an hour ; the thermometer kept
in doors, at the head of a staircase four stories high ; by William Hutchinson, at
the Old Dock gates, Liverpool."

'f he following note is appended at the conclusion : "These observations, made
from the beginning of 1768 to August 10, 1793, make twenty-five years, seven months
and ten days, which I have given to our Library, exclusive of the 3000 observations
given to Messrs. Holdens, to make their tide tables, as mentioned in their preface
to them. I could not continue any longer to make observations, for want of the com-
mand of our dock gate men and gauge rod to take the night tides. Having resigned
my place as Dockmaster, this journal ceases by me, William Hutchinson."

These notes contain the only information with respect to the manner in which the
observations were made which the books afford. The observations appear to have
been carefully conducted, but no precautions are stated to have been taken to ensure
the accuracy of the time ; and it is difficult to fix whether by solar time is meant
apparent solar or mean solar time : this point ought not to have been left in doubt.
This point of uncertainty does not however, in any sensible degree, affect the Tables
VI., Vn., VIII., and IX., which have reference to the variations of the moon's parallax,

* M. Dessiou has received from the British Association more than £100 for this work.

276

MR. LUBBOCK ON TIDE OBSERVATIONS.

or those which have reference to the height of high water ; but the equation of time
is mixed up with the changes in the interval between the moon's transit and the
time of high water due to changes in the moon's declination ; and any uncertainty
with respect to the manner in which the clock has been regulated is therefore much
to be regretted.

The plan pursued is the same as that which I adopted with respect to the London
Dock observations, and which seems to me to be the only one, in the present state of
the subject, which can be resorted to with advantage. If the theory were complete,
and the laws or analytical expressions of the phenomena had been made out satisfac-
torily, it would be possible to proceed at once to determine the constants, which might
be done by means of fewer observations, and those might be selected which appeared
entitled to the greatest confidence : at present, however, I do not think that this
course can be safely pursued.

I trust that this laborious work, which M. Dessiou has accomplished at my insti-
gation, and by the liberal support of the British Association, will not be without uti-
lity, and will afford data upon which mathematicians who may hereafter improve
the theory of the tides may safely rest their conclusions.

The tides in this port continue to be observed at the London and St. Katherine
Docks. These Docks are contiguous, so that the places at which the observations
are made are not distant from each other more than 900 yards, as appears from the
diagram underneath.

/

500

River Thames

Scale of Feet.
1000 1500

2000

2500

We may therefore, I think, safely conclude, that whatever cause affects the tide at
one place will equally affect it at the other ; and hence, if we find the difference
in the registers of the times and heights of high water much greater than the average
difference, suspicion arises that the observation at one or the other place must be
erroneous. The observations at the London Docks are made (at the place of the
letter d) by a person who notes the time when the water has begun to fall, that is,
has made its mark. Those at the St. Katherine Docks are made by noting upon a
slate (ruled for the purpose) the height of the water every minute for a short time

MR. LUBBOCK ON TIDE OBSERVATIONS. 277

before high water is expected, all which is afterwards copied into a book ruled in
the same manner, and the time of high water, with the height, is easily inferred.
The height is ascertained by means of a rod or tide-gauge, connected with a float,
which is placed in a chamber, into which the water enters through a culvert, so that
the ripple or agitation of the water in the river is avoided as much as possible. A
clock, carefully regulated, stands close at hand. This plan has been adopted at
my suggestion, and, if the observer and the transcriber of the observation do their
duty, it does not seem to me to be susceptible of any improvement.

I find by examining the registers of the observations at the London and the St. Ka-
therine Docks, that the tide is on the average about five minutes later there than at
the former place, and the difference in height between the lines or zero points, from
which the rise is measured, is about five feet. Hence I formed Tables A. and B. by
first adding five minutes to the time of high water, and five feet to the height of high
water given in the London Dock books, and then comparing the times so altered
with those of the St. Katherine Docks. The discrepancies exhibited by these Tables
may be attributed to the carelessness of the observers at one or both places, or to
the inevitable difficulty of measuring with precision the quantities sought. I next
formed Tables C. and D. by adding five minutes to the time of high water given in
the St. Katherine Docks register, and five feet to the predicted heights in the British
Almanac, in order to compare the observations with the predictions given in the
British Almanac, and which are founded upon the Tables, the construction of which
I have explained in the Philosophical Transactions, excluding only those observations
which, by discordance with the cotemporary observations at the London Docks and
with the prediction, appear doubtful. It results from this comparison, that the average
error of the predictions of the time of high water contained in the British Almanac
is about ten minutes, that is, when the plus and minus errors are not allowed to
counteract each other. The average error of Mr. Bulpit's Table is about the same.
The tide predictions of Mr. Epps are evidently founded upon the same Tables and the
same methods with those in White's Ephemeris, and do not agree quite so well with
observation. Those of Mr. Innis are more inaccurate.

When the plus and minus errors are allowed to counteract each other, the average
error of the predictions in the British Almanac being, from the observations of the first
six months of this year, —9 minutes, leads me to suspect that a change in the establish-
ment has taken place owing to the removal of the old London Bridge. If I am right
in this conjecture, it is worthy of remark how sensibly the phenomena of the tides
are affected by any slight alteration of local circumstances. Moreover, the height of
high water appears to be less by 2 inches than formerly. If the predicted times be
increased by 9 minutes and the heights be diminished by 2 inches, the predictions
will then agree with observation, nearly as well as the observations at the London
and St. Katherine Docks agree with each other.

278

MR. LUBBOCK ON TIDE OBSERVATIONS.

Table A.

Showing a comparison of the observations of the Times of Hig-h Water made at the
London Docks, increased by five minutes, and those at the St. Katherine Docks.
The observations marked with an * appear doubtful.

Date.

January.

February.

March.

April.

May.

June.

London

St.Kath.

Differ-

London

St.Kath.

Differ-

London

St.Kath.

Differ-

London

StKath.

Differ-

London

St.Kath.

Differ-

London

St.Kath.

Differ.

Docks.
+5min.

Docks.

ence.

Docks.
+5min.

Docks.

ence.

Docks.
+5min.

Docks.

ence.

Docks.
+5min.

Docks.

ence.

Docks.
4-5min.

Docks.

ence.

Docks.
-(-5min.

Docks.

ence.

h m

h m

m

h m

h m

m

h m

h m

m

h m

h m

m

h m

h m

m

h m

h m

m

1.

3 5

3 12

- 7

4 20

4 17

+ 3

3 15

3 6

+ 9

3 50

3 52

- 2

3 55

3 49

+ 6

4 45

4 42

+ 3

3 35

3 47

-12

4 30

4 47

- 17

3 45

3 45

0

4 15

4 16

- 1

4 10

4 5

+ 5

4 10*

4 53

-43

2.

3 55

3 51

+ 4

4 55

4 57

- 2

3 50

3 41

+ 9

4 25

4 2Q

- 1

4 20

4 22

- 2

5 25

5 25

0

4 25

4 32

- 7

5 20

5 28

- 8

4 15

4 22

- 7

4 45

4 42

+ 3

4 35

4 36

- 1

5 35

5 43

- 8

3.

4 45

4 38

+ 7

5 15

5 13

-i- 2

4 20

4 24

- 4

4 45

4 44

+ 1

4 50

4 46

+ 4

6 25

6 20

+ 5

5 10

5 9

+ 1

6 5

6 2

+ 3

4 25

4 28

- 3

5 5

5 3

+ 2

5 0

5 8

- 8

6 35

6 34

+ 1

4.

5 25

5 27

- 2

6 5

6 3

+ 2

4 50

4 51

- 1

5 20

5 18

+ 2

5 35

5 26

+ 9

7 5

7 17

-12

6 5

5 56

+ 9

6 25

6 27

- 2

5 10

5 16

- 6

5 35

5 41

- 6

5 50

5 47

+ 3

7 25

5.

6 20

5 56

+24

6 45

6 37

+ 8

5 20

5 25

- 5

5 50

5 49

+ 1

6 15

6 6

+ 9

8 20

8 12

+ 8

6 50

6 45

+ 5

7 15

7 17

- 2

5 35

5 37

- 2

6 10

6 12

- 2

6 35

6 37

- 2

8 55

8 57

- 2

6.

7 5

6 47

+ 18

7 25

7 23

+ 2

5 45

5 41

+ 4

6 35

6 32

+ 3

7 10

7 17

- 7

9 45

9 43

+ 2

7 30

7 31

- 1

6 15*

8 6*

-111

6 15

6 16

- 1

7 5

7 2

+ 3

7 45

7 56

-11

10 5

10 6

- 1

7.

7 35

7 22

+ 13

7 50

7 42

+ H

6 15

6 16

- 1

7 35

7 31

+ 4

8 25

8 20

+ 5

10 40

10 47

- 7

8 20

8 12

+ 8

8 35

8 45

- 10

6 45

6 46

- 1

8 5

8 1

+ 4

9 5

9 10

- 5

11 20

11 3

+ 17

8.

8 20

8 11

+ 9

8 45

9 7

- 22

7 15

7 15

0

8 50

9 1

-11

10 10

10 7

+ 3

11 45

11 49

- 4

9 10

9 8

+ ^

9 35

9 39

- 4

7 15

7 17

- 2

9 55

9 51

+ 4

10 45

10 44

+ 1

12 5

12 3

+ 2

9.

9 20

9 15

+ 5

10 15*

10 47

- 32

7 50

7 45

+ 5

10 35

10 42

- 7

11 15

11 16

- 1

10 20

10 22

- 2

9 50*

10 25*

- 35

8 55

9 5

-10

11 25

11 28

- 3

11 45

11 50

- 5

12 45

12 43

+ 2

10.

9 15*

10 17

-62

9 5

9 0

+ 5

11 55

12 8

-13

12 55

12 58

- 3

11 5

11 9

- 4

12 20*

10 42*

+ 98

9 35

10 0

-25

12 15

12 20

- 5

1 35

1 31

+ 4

11.

11 10

11 21

-11

12 35

12 27

+ 8

10 35

10 55

-20

12 20

12 18

+ 2

12 35

12 38

- 3

1 55

1 49

+ 6

12 5

12 12

- 7

12 55

12 35

+ 20

12 0

11 58

+ 2

1 5

12 57

+ 8

12 55

1 3

- 8

2 15

2 19

- 4

12.

1 20

1 2

+ 18

12 0

12 6

- 6

1 20

1 12

+ 8

1 20

1 15

+ 5

2 35

2 43

- 8

12 15

12 22

- 7

1 35

1 43

- 8

1 40

1 44

- 4

1 45

1 52

- 7

3 10

3 7

+ 3

13.

1 5

1 2

+ 3

1 55

2 2

— 7

12 50

12 57

- 7

1 55

1 45

+ 10

2 5

2 3

+ 3

3 25

3 33

- 8

I 25

1 22

+ 3

2 30

2 28

+ 2

1 20

1 14

+ «

2 20

2 25

- 5

2 35

2 43

- 8

3 45

3 51

- 6

14.

1 35

1 37

- 2

2 45

2 44

+ 1

1 45

1 47

- 2

2 40

2 35

+ 5

2 55

2 53

+ 2

4 20

4 18

+ 2

1 55

2 2

- 7

3 15

3 17

- 2

2 5

2 7

- 2

3 5

3 7

- 2

3 20

3 27

- 7

4 35

4 37

- 2

15.

2 20

2 22

- 2

3 35

3 35

0

2 20

2 23

- 3

3 20

3 23

- 3

3 30

3 37

- 7

5 10

5 13

- 3

2 35

2 36

- 1

3 50

3 48

+ 2

2 35

2 38

- 3

3 45

3 42

+ 3

4 0

4 2

- 2

5 25

5 23

+ 2

16.

2 55

3 1

- 6

4 0

4 3

- 3

2 55

2 57

- 2

4 5

3 57

+ 8

4 25

4 25

0

.5 55

6 2

- 7

3 0

3 1

- 1

4 25

4 33

- 8

3 25

3 27

- 2

4 25

4 22

+ 3

4 55

4 33

+22

6 10

6 8

+ 2

17.

3 30

3 36

- 6

4 45

4 53

- 8

3 45

3 31

+ 14

4 45

4 38

+ 7

5 15

5 18

- 3

6 50

6 54

- 4

3 45

3 53

- 8

5 20

5 18

+ 2

4 5

4 16

-11

5 10

5 7

+ 3

5 35

5 32

+ 3

6 55

6 58

- 3

18,

4 10

4 2

+ 8

5 25

5 25

0

4 25

4 19

+ «

5 25

5 27

- 2

6 10

6 12

- 2

7 50

7 42

+ 8

4 40

4 46

- 6

6 0

6 12

- 12

4 50

4 56

- 6

5 50

5 57

- 7

6 20

6 27

- 7

7 55

7 55

0

19.

5 0

4 52

+ «

6 10

6 7

+ 3

5 15

5 7

+ 8

6 10

6 17

- 7

7 10

7 12

— 2

8 50

8 50

0

5 30

5 33

- 3

6 35

6 37

- 2

5 35

5 30

+ 5

6 40

6 43

- 3

7 20

7 17

+ •3

9 0

8 56

+ 4

20.

5 50

5 48

+ 5J

7 5

•6 47

+ 18

5 50

5 41

+ 9

7 25

7 22

+ 3

8 15

8 21

- 6

10 5

9 58

+ 7

6 10

6 13

- 3

7 30

7 27

+ 3

6 20

6 17

+ 3

7 50

7 50

0

8 40

8 37

+ 3

10 10

10 7

+ 3

21.

6 35

6 33

+ 2

7 45

7 43

+ 2

6 35

6 31

+ 4

8 30

8 37

- 7

9 35

9 33

+ 2

10 40

10 52

-12

7 10

7 11

- 1

8 25

8 30

- 5

7 5

7 37*

-32

8 55

9 7

-12

9 55

9 47

4- 8

11 5

10 57

+ 8

22.

7 25

7 25

0

8 55

8 52

+ 3

7 25

7 22

+ 3

10 5

10 13

- 8

10 45

10 44

+ 1

11 40

11 52

-12

7 55

7 57

- 2

9 35

9 28

+ 7

8 10

8 16

- 6

10 30

10 27

+ 3

11 20

10 57

+23

11 55

11 54

+ 1

23.

8 25

8 16

+ 9

10 35

10 35

0

9 10

9 1

+ 9

11 35

11 37

- 2

11 50

11 45

+ 5

9 5

9 7

- 2

11 5

U 2

+ 3

9 50

9 57

- 7

11 50

11 46

+ 4

11 50

11 59

- 9

12 20

12 22

- 2

24.

9 35

9 29

+ 6

11 25

11 23

+ 2

10 35

10 37

- 2

12 40

12 37

+ 3

10 10

9 56

+14

11 20

11 22

- 2

12 25

12 26

- i

12 35

12 36

- i

1 10

1 3

+ 7

25.

10 35

10 41

- 6

12 15

12 15

b

12 0

12 7

- 7

12 45

12 37

+ 8

12 50

1 16

^26

1 25

1 12

+ 13

U 25

11 27

- 2

12 50

12 52

- 2

1 15

1 15

1 33

-18

1 45

1 42

+ 3

26.

1 30

1 33

^ 3

12 25

12 27

_ 2

1 20

1 17

+ 3

1 20

1 12

+ 8

2 5

2 0

+ 5

12 10

11 57

+13

1 35

1 32

+ 3

12 55

1 3

- 8

1 45

1 53

- 8

1 45

1 44

+ 1

2 20

2 15

+ 5

27.

12 45

12 42

+ 3

1 50

1 52

- 2

I 10

1 4

+ 6

1 55

1 54

+ 1

1 50

1 53

3

2 35

2 35

0

1 5

1 7

^ 2

2 25

2 28

- 3

1 45

1 47

- 2

2 15

2 22

- 7

2 15

2 17

- 2

2 55

2 53

f 2

28.

1 40

1 31

+ 9

2 35

2 30

+ 5

2 10

1 52

+ 18

2 35

2 37

- 2

2 25

2 28

- 3

3 5

3 13

- 8

2 0

2 10

-10

3 0

3 6

- 6

2 25

2 28

- 3

2 50

2 53

- 3

2 50

2 53

- 3

3 35

3 37

- 2

29.

2 25

2 25

0

2 30

2 27

+ 3

3 5

3 8

- 3

3 5

3 4

+ 1

3 55

3 57

- 2

2 45

2 47

- 2

••••••

2 50

2 58

- 8

3 25

3 32

- 7

3 25

3 28

- 3

4 10

4 13

- 3

30.

3 10

3 2

+ «

3 5

3 3

+ 2

3 30

3 26

+ 4

3 35

3 37

- 2

4 40

4 42

- 2

3 25

3 32

- 7

3 20

3 22

- 2

3 40

3 35

+ 5

3 55

3 58

- 3

4 55

4 57

- 2

31.

3 45

4 5

3 44

4 13

+ 1
- 8

3 25
3 40

3 28
3 48

- 3

- 8

4 15
4 25

4 12
4 23

+ 3
+ 2

MR. LUBBOCK ON TIDE OBSERVATIONS.

279

Table B.

Showing a comparison of the observations of the Heights of High Water made at the
London Docks, increased by five feet, and those at the St. Katherine Docks.
The observations marked with an * appear doubtful.

Date.

January.

February.

March.

April.

May,

June.

1835.

London

St.Kath.

Differ-

London

St.Kath.

Differ-

London

St.Kath.

Differ-

London

St.Kath.

Differ-

London

St.Kath.

Differ.

London

St.Kath.

Differ.

Docks.

Docks.

ence.

Docks.

Docks.

ence.

Docks.

Docks.

ence.

Docks.

Docks.

ence.

Docks.

Docks.

ence.

Docks.

Docks.

+ 5 ft.

+ 5 ft.

+ 5 ft.

+ 5 ft.

+ 5 ft.

+ 5 ft.

ft. in.

ft. in.

in.

ft.

in.

ft.

in.

in.

ft.

in.

ft.

in.

in.

ft.

in.

ft. in.

in.

ft.

in.

ft. in.

in.

ft.

in.

ft.

in.

in

1.

28 0

28 0

0

27

0

27

0

0

27

11

27

9

+ 2

26

9

26 10

- 1

27

4

27 2

+ 2

26

6

26

6

U'

29 6

29 6

0

26

4

26

3

+ 1

27

8

27

8

0

26

7

26 7

0

27

0

26 11

+ 1

25

10

25

10

0

2.

27 4

27 3

+ 1

25

10

25

11

- 1

28

4

28

2

+ 2

26

3

26 3

0

27

0

27 0

0

26

0

25

7

+ 5

27 2

27 3

- 1

26

11

26

11

0

26

0

25

10

+ 2

26

9

26 3

+ 6

26

10

26 9

+ 1

25

5

25

4

+ 1

3.

26 9

26 9

0

26

8

26

8

0

27

0

26

11

+ 1

27

4

27 3

+ 1

26

9

26 8

+ 1

25

7

25

8

- 1

26 11

26 10

+ 1

26

11

26

11

0

26 11

26

11

0

26

5

26 5

0

26

1

26 1

0

24

10

24

9

+ 1

4.

26 3

26 2

+ 1

25

9

25

10

- 1

29

1

29

1

0

26

6

26 4

4-2

25

11

25 9

-1- 2

25

5

25

4

+ 1

26 0

26 0

0

25

11

25

11

0

25

7

25

6

+ 1

25

8

25 8

0

25

1

25 11

-10

24

6

a.

25 10

25 10

0

24

0

24

5

- 5

26

8

26

7

+ 1

25

7

25 7

0

25

3

25 3

0

25

4

23

0*

+28

25 6

25 10

- 4

23

2*

23

1*

+ 1

26

3

26

4

- 1

24

7

24 1 4

+ 3

23

3

23 5

- 2

24

5

24

4

+ 1

6.

24 6

24 4

+ 2

24

8

24

9

- 1

22

5

22

3

+ 2

23

11

23 11

0

23

8

23. 8

0

25

7

25

7

0

24 7

24 8

- 1

24

6

24

6

0

25

3

25

3

0

23

3

23 3

0

23

6

23 6

0

25

0

25

1

- 1

7.

24 2

24 2

0

21

2

21

1

+ 1

24

5

24

4

+ 1

23

6

26 4*

-34

24

3

24 2

+ 1

26

0

26

2

- 2

24 4

24 5

- 1

22

10

22

9

+ 1

22

8

22

7

+ 1

22

8

23 4

- 8

23

11

23 9

+ 2

25

10

25

11

- 1

8.

23 9

25 10*

-25

24

3

24

4

- 1

24

3

24

4

- 1

23

4

23 3

+ 1

24

10

24 10

0

27

0

26

11

+ 1

23 7

23 8

- 1

23

0

23

0

0

23

2

23

2

0

23

8

23 8

0

24

7

24 9

- 2

26 10

26

6

+ 4

9.

22 6

22 6

0

25

1

25

1

0

21

9

21

7

+ 2

23

11

23 10

+ 1

25

11

26 0

- 1

23 2

23 1

+ 1

21

5

21

0

+ 5

21

4

21

3

+ 1

24

9

24 9

0

25

6

25 5

+ 1

27

*4

27

4

6

10.

25 9

25 8

+ 1

...

22

0

21

9

+ 3

27

3

27 4

- 1

27

5

27

6

- 1

23 10

23 10

0

25

0

25

1

- 1

23

7

23

6

+ 1

••

...

26

8

26 8

0

27 10

27 11

- 1

11.

24 6

24 5

+ 1

23

7*

25

0

-17

21

2

21

1

+ 1

25

10

26 0

- 2

27

0

26 9

+ 3

28

0

27 10

+ 2

25 3

25 3

0

24

2

23

8

+ 6

24

10

24

10

0

27 11

28 0

- 1

27

10

28 0

- 2

28

0

28

0

0

12,

24

3*

25

3

-12

25

7

25

8

- 1

26

8

26 7

+ 1

27

4

27 4

0

28

2

28

2

0

25 4

25 3

+ 1

27

7

27

7

0

,,

27

8

27 7

+ 1

28

5

28 6

- 1

28

1

28

0

+ 1

13

24 6

24 7

- 1

26

3

26

8

- 5

26

8

26

8

0

27

5

27 1

+ 4

29

0

28 10

+ 2

28

4

28

4

0

25 5

25 5

0

27

3

27

3

0

27

10

27

10

0

28

7

28 8

- 1

28

8

28 3

+ 5

27

11

27

10

-\- 1

14.

26 3

26 3

0

27

6

27

7

- 1

26

8

26

9

- 1

28

3

28 3

0

30

2

30 3

- 1

28

2

28

2

0

27 0

27 0

0

27

2

27

1

+ 1

26

3

26

3

0

28

9

28 9

0

29

10

29 10

0

27

3

27

3

0

15.

27 4

27 4

0

27

8

27

3

+ 5

28

3

28

4

- 1

29

1

29 1

0

29

6

29 6

0

27

6

27

7

- 1

26 11

26 10

+ 1

27

7

27

7

0

28

11

29

0

- 1

29

9

29 8

+ 1

28

9

28 10

— 1

27

4

27

1

+ 3

IR

27 8

27 7

+ 1

27

4

27

4

0

28

5

28

6

- 1

29

11

29 10

+ 1

28

6

28 7

- 1

27

0

26

11

+ 1

25 6

25 3

+ 3

28

3

27

4

+ 11

29

1

29

0

+ 1

29

0

29 1

- 1

27

3

28 1

-10

26

3

26

1

+ 2

17

27 11

28 0

- 1

27

7

27

7

0

28

9

28

9

0

28

10

28 10

0

27

2

27 8

- 6

26

4

26

5

- 1

28 3

28 0

+ 3

27

9

27 10

- 1

29

0

29

1

- 1

28

0

28 0

0

26

4

26 4

0

25

6

25

6

0

18

27 11

27 10

+ 1

27

3

27

2

+ 1

29

0

29

0

0

27

4

27 5

- 1

26

11

27 0

- 1

25

4

25

S

+ 1

27 3

27 4

- 1

25

8

25

7

+ 1

29

1

29

2

- 1

26

1

26 0

+ 1

26

0

25 11

+ 1

24

8

24

2

+ 6

19

27 7

27 3

+ 4

27

4

27

4

0

28

4

28

4

0

25

7

27 6*

-23

26

1

26 0

+ 1

26

0*

23

11

+25

27 5

27 6

- 1

25

10

25

9

+ 1

27

7

27

6

+ 1

25

1

25 1

0

24

6

24 5

+ 1

24

7

24

7

0

?,0

29 0*

26 11

+25

24

3

24

4

- 1

27

7

27

7

0

25

0

25 1

- 1

25

3

25 2

+ 1

24

0

24

0

0

27 9

27 6

+ 3

25

11

25

11

0

26

8

26

6

-f- 2

24

2

24 1

+ 1

24

3

24 0

+ 3

24

9

24

8

+ 1

21

25 5

25 5

0

26

0

26

1

— 1

26

7

26

6

+ 1

24

6

24 6

0

24

11

24 10

+ 1

25

0

24

11

+ 1

25 6

25 7

- 1

25

3

25

3

0

25

7

25

7

0

23

3

23 2

+ 1

24

3

24 3

0

24

0

24

2

— 2

99

25 10

26 0

2

25

0

24

11

+ 1

25

6

25

6

0

25

2

25 1

+ 1

25

1

25 0

+ 1

25

3

25

2

+ 1

25 9

25 10

- 1

24

1

24

1

0

25

2

25

3

- 1

23

10

23 10

0

24

6

24 7

— 1

24

3*

26

1

-22

23

24 10

25 0

- 2

20 10*

26

10

-72

24

2

24

4

- 2

23

8*

24 8

-12

25

8

25 9

— 1

25 2

25 3

- 1

25

4

25

3

+ 1

23

8

23

7

+ 1

24

10

24 9

+ 1

25

3

25 1

+ 2

26

3

26

2

+ i

24.

24 3

24 5

- 2

26

2

26

2

0

25

0

25

1

- 1

• ••

>••

25

10

25

11

- 1

26 6

26 6

0

23

9

23

9

0

25

9

25 10

- i

26

3

2*6 2

+ .1

26

0

25

11

+ 1

25.

23 11

23 11

0.

25

3

25

4

- 1

25

4

25

4

0

25

1

25 1

0

25

0

25 11

-11

24

0

23

9

+ 3

26 2

26 3

- 1

24

3

24

3

0

....

••

26

6

25

10

25 8

+ 2

25

6

25

6

0

26.

25

11

24

11

+12

24

6

24

6

0

25

7

25 7

0

25

6

26 6

-12

28

0

27 10

+ 2

25 4

25 4

0

■?6

7

27

7

-12

25

11

26

0

- 1

27

0

27 4

- 4

26

9

26 9

0

26

10

26

10

0

27

26 3

26 4

- 1

26

3

26

3

0

26

3

26

3

0

26

6

26 5

+ 1

27

0

26 10

+ 2

28

6

28

6

0

26 7

26 8

- 1

26

6

26

7

- 1

27

0

26

11

+ 1

26

8

26 8

0

27

5

27 6

- 1

26

9

2;

9

-12

28

26 7

26 7

0

26

11

26

9

+ 2

27

3

26

6

+ 9

26

7

26 7

0

27

3

27 2

-I- J

27

b

2;

3

+ 2

26 9

26 8

+1

28

8

28

9

- 1

27

0

27

2

- 2

27

3

27 2

+ 1

27

3

27 4

- 1

27

1

2;

0

+ 1

29.

26 11

26 11

27

1

27

0

+ 1

28

0

27 11

+ 1

27

3

27 3

0

27

2

2'J

1

+ I

27 8

27 9

- 1

27

1

27

1

0

28

10

28 11

- 1

27

8

27 7

+ 1

26

9

26

10

— I

30.

27 3

27 3

0

27

0

27

0

0

28

1

28 1

0

27

4

27 4

0

26

8

26

8

0

27 10

27 10

0

...

27

6

27

6

0

27

4

27 5

- 1

27

1

27 1

0

26

6

26

;

— 1

31.

27 1
27 6

27 1
27 4

0

+ 2

...

...

27
27

3
5

27
27

8
5

- 5
0

...

...

26
26

9
3

26 8
26 3

+ 1

0

...

...

...

...

aiDcccxxxv.

2 o

280

MR. LUBBOCK ON TIDE OBSERVATIONS.

Table C.

Showing a comparison of the observed Times of High Water at the St. Katherine
Docks, increased by five minutes, with the predicted Times given in the British
Almanac. The observations marked with an * appear doubtful.

Date.

January.

February.

March.

April.

May.

June,

British StKath.

Error

St.Kath.

Error

British

St.Kath.

Error

St.Kath.

Error

St.Kath.

Error

St.Kath.

Error

1835.

Alman. ^ocks.

of Pre-

Docks.

of Pre-

Docks.

of Pre-

Docks.

of Pre-

Docks.

of Pre-

Docks.

of Pre-

+5 mm.

diction.

+5min.

diction.

+5min.

diction.

+5min.

diction.

+Smin.

diction.

+5min.

diction.

h m

h m

m

h m

h m

m

h m

h m

m

h m

h m

m

h m

h m

m

h m

h m

m

1,

3 14

3 17

- 3

4 20

4 22

- 2

3 24

3 11

+ 13

3 56

3 57

- 1

3 55

3 54

+ 1

4 41

4 47

- 6

3 33

3 52

-19

4 38

4 52

-14

3 42

3 50

- 8

4 11

4 21

-10

4 11

4 10

+ 1

5 1

4 58

+ 3

2.

3 56

3 56

0

4 55

5 2

- 7

3 58

3 46

+ 12

4 23

4 31

- 8

4 25

4 27

- 2

5 22

5 30

- 8

4 20

4 37

-17

5 12

5 33

-21

4 11

4 27

-16

4 36

4 47

-11

4 40

4 41

- 1

5 46

5 48

- 2

3.

4 40

4 43

- 3

5 30

5 18

+ 12

4 26

4 29

- 3

4 50

4 49

+ 1

4 56

4 51

+ 5

6 13

6 25

-12

5 1

5 14

-13

5 45

6 7

-22

4 41

4 33

+ 8

5 3

5 8

- 5

5 14

5 13

+ 1

6 40

6 39

+ 1

4.

5 20

5 32

-12

6 2

6 8

- 6

4 56

4 56

0

5 20

5 23

- 3

5 33

5 31

+ 2

7 6

7 22

-16

5 43

6 1

-18

6 20

6 32

-12

5 9

5 21

-12

5 37

5 46

- 9

5 55

5 52

+ 3

7 39

5.

6 2

6 1

+ 1

6 36

6 42

- 6

5 25

5 30

- 5

5 56

5 54

+ 2

6 20

6 11

+ 9

8 14

8 17

- 3

6 25

6 50

-25

6 55

7 22

-27

5 42

5 42

0

6 14

6 17

- 3

6 46

6 42

+ 4

8 51

9 2

-11

6.

6 47

6 52

- 5

7 14

7 28

-14

5 58

5 46

+ 12

6 36

6 37

- 1

7 18

7 22

- 4

9 27

9 48

-21

7 11

7 36

-25

7 35

8 11*

6 13

6 21

- 8

7 4

7 7

- 3

7 55

8 1

- 6

9 59

10 11

-12

7.

7 34

7 'i.l

+ 7

8 0

7 47

+ 13

6 32

6 21

+11

7 33

7 36

- 3

8 36

8 25

411

10 30

10 52

-22

7 55

8 17

-22

8 25

8 50

-25

6 50

6 51

- 1

8 14

8 6

+ 8

9 18

9 15

+ 3

11 3

11 8

- 5

8.

8 18

8 16

4- a

9 3

9 12

- 9

7 10

7 20

-10

9 0

9 6

- 6

9 59

10 12

-13

11 34

11 54

-20

8 46

9 13

-27

9 39

9 44

- 5

7 36

7 22

+ 14

9 45

9 56

-11

10 40

10 49

- 9

12 4

12 8

- 4

y.

9 15

9 20

- 5

10 17

10 52

-35

8 4

7 50

+ 14

10 30

10 47

-17

11 15

11 21

- 6

9 46

10 27

-41

11 1

10 30*

8 49

9 10

-21

11 12

11 33

-21

11 48

11 55

- 7

12 31

12 48

-17

10.

10 19

10 22

- 3

9 32

9 5

+27

11 45

12 13

-28

12 57

1 3

- 6

10 53

11 14

-21

li 36

10 47*

10 20

10 5

+ 15

12 15

12 25

-10

1 21

1 36

-15

11.

11 24

11 26

- 2

12 8

12 32

-24

11 4

11 0

+ 4

12 15

12 23

- 8

12 37

12 43

- 6

1 46

1 54

- 8

U 50

12 17

-27

12 28

12 40

-12

11 39

12 3

-24

12 43

1 2

-19

12 59

1 8

- 9

2 10

2 24

-14

12.

1 8

1 7

+ 1

12 4

12 11

- 7

1 10

1 17

- 7

1 20

1 20

0

2 36

2 48

-12

12 18

12 27

- 9

1 33

1 48

-15

1 35

1 49

-14

1 43

1 57

-14

3 2

3 12

-10

13.

12 42

1 7

-25

1 56

2 7

-11

12 43

1 2

-19

1 53

1 50

+ 3

2 5

2 8

- 3

3 27

3 38

-11

1 6

1 27

-21

2 21

2 33

-12

1 11

1 19

- 8

2 11

2 30

-19

2 27

2 48

-21

3 53

3 56

- 3

14.

1 29

1 42

-13

2 41

2 49

- 8

1 34

1 52

-18

2 31

2 40

- 9

2 51

2 58

- 7

4 19

4 23

- 4

1 52

2 7

-15

3 1

3 22

-21

1 57

2 12

-15

2 53

3 12

-19

3 13

3 32

-19

4 37

4 42

- 5

15.

2 13

2 27

-14

3 21

3 40

-19

2 18

2 28

-10

3 16

3 28

-12

3 37

3 42

- 5

5 0

5 18

-18

2 33

2 41

- 8

3 40

3 53

-13

2 38

2 43

- 5

3 38

3 47

- 9

4 1

4 7

- 6

5 23

5 28

- 5

16.

2 54

3 6

-12

4 0

4 8

- 8

3 0

3 2

- 2

3 58

4 2

- 4

4 24

4 30

- 6

5 44

6 7

-23

3 9

3 6

+ 3

4 22

4 38

-16

3 20

3 32

-12

4 20

4 27

- 7

4 46

4 38

+ 8

6 9

6 13

- 4

17.

3 33

3 41

- 8

4 41

4 58

-17

3 39

3 36

+ 3

4 39

4 43

- 4

5 11

5 23

-12

6 36

6 59

-23

3 53

3 58

- 5

5 1

5 23

-22

3 58

4 21

-23

5 1

5 12

-11

5 36

5 37

- 1

7 3

7 3

0

18.

4 16

4 7

+ 9

5 24

5 30

- 6

4 20

4 24

- 4

5 22

5 32

-10

6 2

6 17

-15

7 28

7 47

-19

4 38

4 51

-13

5 46

6 17

-31

4 39

5 1

-22

5 46

6 2

-16

6 27

6 32

- 5

8 1

8 0

+ 1

19.

5 1

4 57

+ 4

6 7

6 12

- 5

5 0

5 12

-12

6 8

6 22

-14

6 55

7 17

-22

8 32

8 55

-23

5 24

5 38

-14

6 30

6 42

-12

5 22

5 35

-13

6 35

6 48

-13

7 28

7 22

+ 6

9 1

9 1

0

20.

5 51

5 53

- 2

6 53

6 52

+ 1

5 44

5 46

- 2

7 4

7 27

-23

8 1

8 26

-25

9 31

10 3

-32

6 17

6 18

- 1

7 15

7 32

-17

6 5

6 22

-17

7 38

7 55

-17

8 41

8 42

- 1

10 1

10 12

-11

21.

6 39

6 38

+ 1

7 40

7 48

- 8

6 28

6 36

- 8

8 25

8 42

-17

9 20

9 38

-18

10 30

10 57

-27

7 1

7 16

-15

8 13

8 35

-22

6 52

7 42*

9 12

9 12

0

9 59

9 52

+ 7

11 0

11 2

- 2

22.

7 25

7 30

- 5

8 54

8 57

- 3

7 19

7 27

- 8

9 58

10 18

-20

10 38

10 49

-11

11 31

11 57

-26

7 48

8 2

-14

9 41

9 33

+ 8

7 52

8 21

-29

10 42

10 32

+10

11 15

11 2

+13

11 56

11 59

- 3

23.

8 18

8 21

- 3

10 28

10 40

-12

8 39

9 6

-27

11 21

11 42

-21

11 44

11 50

- 6

8 49

9 12

-23

11 11

11 7

+ 4

9 27

10 2

-35

11 55

11 51

+ 4

12 6

12 4

+ 2

12 18

12 27

- 9

24.

9 23

9 34

-11

11 50

11 28

+22

10 )7

10 42

-25

12 41

12 42

- 1

10 1

10 1

0

11 5

11 27

-22

12 22

12 31

- 9

12 25

12 41

-16

1 3

1 8

- 5

2a.

10 43

10 46

- 3

12 25

12 20

+ 5

11 45

12 12

-27

12 46

12 42

+ 4

12 44

1 21

•-37

1 23

1 17

+ 6

11 21

11 32

-11

12 57

12 57

0

1 8

1 1

1 38

-37

1 42

1 47

- 5

26.

1 25

1 38

-13

12 16

12 32

-16

1 28

1 22

+ 6

1 20

1 17

+ 3

2 0

2 5

- 5

11 58

12 2

- 4

1 52

1 37

+15

12 44

1 8

-24

1 44

1 58

-14

1 37

1 49

-12

2 18

2 20

- 2

2V.

12 31

12 47

-16

2 10

1 57

+13

1 10

1 9

+ 1

1 55

1 59

- 4

1 52

1 58

- 6

2 38

2 40

- 2

1 5

1 12

- 7

2 31

2 33

- 2

1 33

1 52

-19

2 10

2 27

-17

2 8

2 22

-14

2 57

2 58

- 1

28.

1 31

1 36

- 5

2 49

2 35

+ 14

1 50

1 57

- 7

2 25

2 42

-17

2 23

2 33

-10

3 15

3 18

- 3

1 58

2 15

-17

3 7

3 11

- 4

2 8

2 33

-25

2 40

2 58

-18

2 40

2 58

-18

3 33

3 42

- 9

29.

2 19

2 30

-11

2 27

2 32

- 5

2 54

3 13

-19

2 57

3 9

-12

3 52

4 2

-10

2 42

2 52

-10

2 44

3 3

-19

3 8

3 37

-29

3 14

3 33

-19

4 12

4 18

- 6

30.

3 4

3 7

- 3

2 59

3 8

- 9

3 24

3 31

- 7

3 30

3 42

-12

4 32

4 47

-15

3 25

3 37

-12

3 13

3 27

-14

3 39

3 40

- 1

3 47

4 3

-16

4 53

5 2

- 9

31.

3 43

4 2

3 49

4 18

- 6
-16

3 27
3 43

3 33
3 53

- 6
-10

4 7
4 26

4 17

4 28

-10
- 2

MR. LUBBOCK ON TIDE OBSERVATIONS.

281

Table D.
Showing a comparison of the observed Heights of High Water at the St. Katherine
Docks, with the predicted Heights given in the British Almanac, increased by
five feet. The observations marked with an * appear doubtful.

Date

1835

January.

February.

March.

April.

May.

June.

British
Alman
+ 5 ft.

St.Kath
Docks.

Error
■ of Pre-
diction.

British
Alman
+ 5 ft.

St.Kath
Docks.

Error
of Pre-
diction.

British
Alman.
+ bft.

St.Kath
Docks.

Error
of Pre-
diction.

British
Alman.
+ 5 ft.

St.Kath
Docks.

Error
of Pre-
diction.

British
Alman.
+ 5 ft.

St.Kath
Docks.

Error

■ of Pre.

diction.

British
Alman
+ 5 ft.

St.Kath
Docks.

Error
of Pre-
diction.

1.

ft.

27

in.
10

ft. in.
28 0

in.
- 2

ft. in.

27 5

ft.

27

in.
0

in.
+ 5

ft.

27

in.
6

ft. in.
27 9

in
- 3

ft. in.

27 3

ft. in.
26 10

in.
+ 5

ft.

27

in.
2

ft. in

27 2

in.
0

ft.
26

in
11

ft. in
26 6

in.
+ 5

+11

+ 9

2;

9

29 6

-21

27 3

26

3

+ 12

27

6

27 8

- 2

27 2

26 7

+ 7

27

1

26 11

+ 2

26

9

25 10

2.

2;

8

27 3

+ i>

27 1

25

11

+ 14

27

6

28 2

- 8

27 0

26 3

+ 9

26

11

27 0

- 1

26

4

25 7

2;

6

27 3

+ y

26 10

26

11

- 1

27

5

25 10

+ 19

26 10

26 3

+ 7

26

9

26 9

0

26

2

25 4

+10
+ 3
+ 11
+ 1

3.

2;

3

26 9

+ b

26 6

26

8

- 2

27

2

26 11

+ 3

26 8

27 3

- 7

26

6

26 8

- 2

25

11

25 8

2;

0

26 10

+ 2

26 3

26

11

- 8

27

0

26 11

+ 1

26 6

26 5

+ 1

26

3

26 1

+ 2

25

8

24 9

4,

26

V

26 2

+ iJ

25 11

25

9

+ 2

26

10

29 1

-27

26 3

26 4

- 1

26

0

25 9

+ 3

25

5

25 4

2b

2

26 0

+ 2

25 7

25

11

- 4

26

8

25 6

+ 14

25 11

25 8

+ 3

25

8

25 11

- 3

25

9.

b.

)io

11

25 10

+ 1

25 4

24

5

+11

26

5

26 7

- 2

25 7

25 7

0

25

4

25 3

+ 1

25

9,

23 0»

'2a

V

25 10

- 3

25 1

23

1*

26

2

26 4

- 2

25 3

24 4

+11

25

0

23 5

+19

25

3

24 4

+ 11

6.

25

3

24 4

+11

24 9

24

9

0

25

10

22 3

+43

24 11

23 11

+12

24

9

23 8

+ 13

25

5

25 7

- 2

25

0

24 8

+ 4

24 5

24

6

- 1

25

5

25 3

+ 2

24 7

23 3

+ 16

24

8

23 6

+14

25

8

25 1

+ 7

v.

24

8

24 2

+ ^

24 2

21

1

+37

25

3

24 4

+ 11

24 4

26 4*

24

8

24 2

+ 6

25

10

26 2

- 4

24

b

24 5

0

23 11

22

9

+ 14

24

11

22 7

+28

24 3

23 4

+ 11

24

10

23 9

+13

26

1

25 11

+ 2

8.

24

2

25 10*

23 10

24

4

- 6

24

7

24 4

+ 3

24 3

23 3

+12

25

3

24 10

+ 5

26

5

26 11

- 6

24

0

23 8

+ 4

23 10

23

0

+ 10

24

3

23 2

+13

24 7

23 8

+11

25

9

24 9

+12

26

9

26 6

+ 3

9.

2-6

11

22 6

+ 1/

24 1

25

1

-12

24

1

21 7

+30

25 1

23 10

+15

26

3

26 0

+ 3

23

U

23 1

+ 10

24 7

21

0

+43

23

11

21 3

+32

25 8

24 9

+ 11

26

9

25 5

+ 16

27

0

27 4

- 4

10.

24

0

25 8

-20

24

1

21 9

+28

26 2

27 4

-14

27

4

27 6

- 2

24

3

23 10

+ &

25 "1

25

i

0

24

6

23 6

+ 12

27

0

26 8

+ 4

27

7

27 11

- 4

11.

24

7

24 5

+ 2

25 6

25

0

+ 6

24

11

21 1

+46

26 8

26 0

+ 8

27

4

26 9

+ 7

27 10

27 10

0

26

1

25 3

- 2

26 0

23

8

+28

25

6

24 10

+ 8

27 2

28 0

-10

27

7

28 0

- 5

28

0

28 0

0

12.

26 7

25

3

+ 16

26

0

25 8

+ 4

27 8

26 7

+13

27

9

27 4

+ 5

28

1

28 2

- 1

'Jb

"3

25 3

6

27 0

27

7

- 7

27 11

27 7

+ 4

28

0

28 6

- 6

28

2

28 0

+ 2

13.

25

10

24 7

4-15

27 5

26

8

+ 9

26

8

26 8

0

28 1

27 1

+ 12

28

2

28 10

- 8

28

2

28 4

- 2

26

4

25 5

+ 11

27 9

27

3

+ 6

27

2

27 10

- 8

28 3

28 8

- 5

28

3

28 3

0

28

1

27 10

+ 3

14.

26

8

26 3

+ 5

27 11

27

7

+ 4

27

6

26 9

+ 9

28 4

28 3

+ 1

28

4

30 3

-23

27

10

28 2

- 4

27

0

27 0

0

28 1

27

1

+ 12

27 10

26 3

+ 19

28 5

28 9

- 4

28

4

29 10

-18

27

7

27 3

+ 4

15.

27

5

27 4

+ 1

28 3

27

3

+ 12

28

2

28 4

- 2

28 6

29 1

- 7

28

4

29 6

-14

27

2

27 7

- 5

27

7

26 10

+ 9

28 4

27

7

+ 9

28

4

29 0

- 8

28 6

29 8

-14

28

2

28 10

- 8

26

9

27 1

- 4

16.

27

9

27 7

+ 2

28 5

27

4

+ 13

28

5

28 6

- 1

28 5

29 10

-17

27 11

28 7

- 8

26

4

26 11

- 7

27 10

25 3

+31

28 4

27

4

+ 12

28

6

29 0

- 6

28 3

29 1

-10

27

5

28 1

- 8

25

11

26 1

- 2

17.

28

0

28 0

0

28 2

27

7

+ 7

28

6

28 9

- 3

27 11

28 10

-11

27

0

27 8

- 8

25

6

26 5

-11

28

0

28 0

0

28 0

27 10

+ 2

28

6

29 1

- 7

27 6

28 0

- 6

26

6

26 4

+ 2

25

1

25 6

- 5

18.

28

0

27 10

+ 2

27 9

27

2

+ 7

28

4

29 0

- 8

27 0

27 5

- 5

26

1

27 0

-11

24

9

25 3

- 6

27 11

27 4

+ 7

27 5

25

7

+22

28

2

29 2

-12

26 6

26 0

+ 6

25

6

25 11

- 5

24

6

24 2

+ 4

19.

27

9

27 3

+ 6

27 0

27

4

- 4

27 11

28 4

- 5

25 11

27 6*

25

0

26 0

-12

24

3

23 11

+ 4

27

6

27 6

0

26 7

25

9

+ 10

27

7

27 6

+ 1

25 3

25 1

+ 2

24

7

24 5

+ 2

24

2

24 7

- 5

20.

27

3

26 11

+ 4

26 0

24

4

+20

27

1

27 7

- 6

24 9

25 1

- 4

24

3

25 2

-11

24

1

24 0

+ 1

27

0

27 6

- 6

25 5

25

11

- 6

26

6

26 6

0

24 4

24 1

+ 3

24

2

24 0

+ 2

24

1

24 8

- 7

21.

26

8

25 5

+15

25 0

26

1

-11

25

11

26 6

- 7

24 2

24 6

- 4

24

2

24 10

- 8

24

2

24 11

- 9

26

3

25 7

+ «

24 7

25

3

- 8

25

4

25 7

- 3

24 1

23 2

+11

24

4

24 3

+ 1

24

4

24 2

+ 2

22.

25

10

26 0

- 2

24 4

24

11

- 7

24

10

25 6

- 8

24 3

25 1

-10

24

7

25 0

- 5

24

7

25 2

- 7

25

5

25 10

- 5

24 4

24

1

+ 3

24

5

25 3

-10

24 6

23 10

+ 8

24

11

24 7

+ 4

24

10

26 1

-15

23.

25

1

25 0

+ 1

24 7

26

10

-27

24

2

24 4

- 2

24 11

24 8

+ 3

25

1

25 9

- 8

• ■•■

24

9

25 3

- 6

24 11

25

3

- 4

24

2

23 7

+ 7

25 3

24 9

+ 6

25

3

25 1

+ 2

25

2

26 2

-12

24.

24

8

24 5

+ 3

25 4

26

2

-10

24

5

25 1

- 8

25

5

25 11

- 6

24

9

26 6

-21

■ ••

24

9

23 9

+ 12

25 7

25 10

- 3

25

6

26 2

- 8

25

10

25 11

- 1

25.

25

0

23 11

+ 13

^5 "9

25

4

+ 5

25

2

25 4

- 2

25 11

25 1

+ 10

25

8

25 11

- 3

26

3

23 9

+30

25

4

26 3

-11

26 3

24

3

+24

....

••

26 3

26

0

25 8

+ 4

26

6

25 6

+ 12

26.

..

26 7

24

11

+20

25

6

24 6

+12

26 7

25 7

+ 12

26

3

26 6

- 3

26 10 1

27 10

-12

25

'9

25 4

+ 5

26 10

27

7

- 9

25

10

26 0

- 2

26 9

27 4

- 7

26

6

26 9

- 3

27

1

26 10

+ 3

27.

26

2

26 4

- 2

26 1

26

3

- 2

26

1

26 3

- 2

26 10

26 5

+ 5

26

8

26 10

- 2

27

4

28 6

-14

27

7

26 8

+ 11

27 4

26

7

+ 9

26

7

26 11

- 4

26 11 i

26 8

+ 3

26 111

27 6

- 7

27

5

27 9

- 4

28.

26

11

26 7

+ 4

27 6

26

9

+ 9

26

10

26 6

+ 4

27 1 i

}6 7

+ 6

27

1

27 2

- 1

27

6

27 3

+ 3

27

2

26 8

+ 6

27 6

28

9

-15

27

1

27 2

- 1

27 2 i

?7 2

0

27

2

27 4

- 2

27

7

27 0

+ 7

29.

27

5

26 11

+ 6

• •••

,,

27

4

27 0

+ 4

27 3 :

J7 11

- 8

27

3

27 3

0

27

6

27 1

+ 5

27

7

27 9

- 2

..

27

5

27 1

+ 4

27 3 2

}8 11

-20

27

4

27 7

- 3

27

6

26 10

+ 8

30.

27

8

27 3

+ 5

,.

27

5

27 0

+ 5

27 3 i

IS 1

-10

27

4

27 4

0

27

5

26 8

+ 9

27

8

27 10

- 2

....

••

27

5

27 6

- 1

27 3 5

17 5

- 2

27

3

27 1

+ 2

27

3 .

26 7

+ 8

31.

27

7

27 1

+ 6

27

4

27 8

- 4

27

2

26 8

+ 6

.

27

6

27 4

+ 2

••

27

3

27 5

- 2

27

1

26 3

+ 10

2o2

282

MR. LUBBOCK ON TIDE OBSERVATIONS.

Table I.

Showing the Interval between the Apparent Solar Time of the Moon's Transit and
the Time of High Water, and the Height of High Water at the Liverpool Old
Docks (as recorded by Mr. Hutchinson), corresponding to the Apparent Solar
Time of the Moon's Transit, in each month of the year. (If Mr. Hutchinson's
clock was regulated according to mean solar time, the interval must be diminished
by the equation of time given at foot of each month.)

^ i

t'zt

= Si

January.

1 1
S"o >

February.

S3 .1

I'sl

March. 1

Mean

Mean

Mean

Moon's

Interval.

Height of

of

5 s

Moon's

Interval.

Height of

of

s o >■

Moon's

Interval.

Height of

of

'^ 1

Transit.

Tide.

Moon's

■^ »

Transit.

Tide.

Moon's

^ 1

Transit.

Tide.

Moon's

o

Decl.

S

Decl.

o

Decl.

h m

h m

ft. in.

o

h m

h m

ft. in.

o

h m

h m

ft. in.

o

90

31-2

11 13-3

17 5-6

18

89

31-9

11 17-9

18 0-6

10

105

30-0

11 19-1

18 4-7

5

Q7

1 31-6

10 591

17 9-0

15

92

1 31-4

11 8-0

18 0-5

5

99

1 30-9

11 3-7

18 5-9

8

93

2 31-3

10 46-8

17 61

10

90

2 30-9

10 49-4

17 8-4

5

101

2 31-9

10 49-0

17 7-3

13

103

3 30- 1

10 371

16 1-0

5

90

3 29-3

10 37-4

16 8-9

8

92

3 31-2

10 330

16 3-4

16

100

4 28-5

10 31-2

15 2-2

5

92

4 29-1

10 27-3

15 2-5

14

89

4 30-2

10 20-3

14 5-8

21

105

5 30-6

10 33-9

13 8-3

8

86

5 29-2

10 26-2

13 4-7

18

89

5 30-4

10 16-2

13 0-0

22

96

6 29-7

10 49-2

12 7-3

14

86

6 29-7

10 37-8

11 11.5

21

88

6 31-6

10 30-5

11 4-6

22

95

7 30-5

11 16-3

12 4-3

19

84

7 30-8

11 8-3

11 9-3

21

85

7 30-4

11 5-9

11 3-7

22

93

8 30-8

11 38-1

13 6-7

19

79

8 30-4

11 37-6

12 9-4

23

94

8 310

11 41-3

12 8-5

20

84

9 30-6

11 45-1

14 11-5

28

82

9 29-8

11 51-1

14 5-7

22

98

9 31-8

11 50-6

14 81

15

89

10 311

11 38-4

16 0-0

22

79

10 3M

11 43-8

15 11-6

19

97

10 31-2

11 44-8

16 Q-9

10

84

11 31-6

11 34-1

16 8-9

22

84

11 30-2

11 31-5

17 4-8

15

92

11 29-7

11 33-5

17 8-1

6

Equat. of Time to 6e1 ijn
added to app. time. ..}'

...

+ 15

+9

...

April.

May.

June.

90

29-9

11 19-4

18 0-1

12

86

29-1

11 16-5

17 41

20

79

30-3

11 13-4

16 8-8

23

91

1 30-5

11 1-0

17 10-6

17

89

1 30- 1

10 57-9

17 1-9

22

85

1 30-0

10 55-5

16 10-1

22

87

2 30-0

10 43-4

17 01

20

85

2 31-4

10 38-3

16 6-6

23

85

2 30-0

10 39-8

16 7-9

20

87

3 309

10 30-2

15 11-6

22

82

3 30-3

10 25-1

15 91

22

92

3 30-0

10 29-6

15 9-8

16

87

4 31-0

10 14-0

14 5-1

23

93

4 29-2

10 16-0

14 6-0

20

98

4 30-3

10 24-9

14 8-3

11

85

5 30-7

10 12-9

12 10-6

22

97

5 30-4

10 18-8

13 3-9

16

96

5 29-6

10 31-5

13 9-0

6

90

6 30-5

10 31-9

11 5-2

20

99

6 29-3

10 41-6

12 4-2

12

107

6 29-6

10 52-8

13 0-8

5

92

7 30-4

11 14-5

11 8-6

16

105

7 29-7

11 20-6

12 7-0

7

98

7 30-4

11 24-7

13 11

8

93

8 29-6

11 43-9

13 3-2

11

103

8 30-0

11 46-9

13 90

5

97

8 30-2

11 44-0

13 10-4

12

96

9 28-4

11 54-2

15 0-3

6

102

9 30-5

11 52-6

15 11-2

7

92

9 3M

11 491

14 11-4

17

104

10 291

11 48-3

16 7-2

5

97

10 31-2

11 46-8

16 3-2

12

85

10 30-3

11 41-8

15 110

20

94

11 291

11 36-1

17 7-2

7

89

11 30-0

11 31-2

17 0-1

17

83

11 311

11 28-7

16 7-0

22

Equat. of Time to be\ q
added to app. time... i

1

— 4.

0

...

...

Tt ...

• ••

July.

August.

September.

88

320

11 131

17 1-2

19

95

31-2

11 17-2

17 8-4

11

m

311

11 201

18 3-8

4

89

1 31.1

10 57-6

17 1-8

16

99

1 29-5

11 4-6

17 11-6

6

96

1 31-3

11 2-6

18 4-8

7

100

2 30-6

10 45-2

16 101

11

105

2 29-0

10 51-8

17 4-6

5

97

2 30-4

10 48-7

17 10-8

12

101

3 31-5

10 37-4

16 3-4

6

102

3 29-3

10 35-5

16 5-5

7

93

3 30-3

10 34-9

16 6-0

17

101

4 311

10 33-1

14 11-3

5

97

4 29-6

10 30-2

15 0-4

13

88

4 30-2

10 21-3

14 11-3

20

99

5 29-7

10 34-2

13 10-0

8

96

5 30-0

10 28-7

13 5-6

17

82

5 290

10 16-9

13 2-7

22

101

6 29-5

10 51-5

12 10-6

13

89

6 29-7

10 38-3

12 0-0

21

92

6 29-7

10 321

11 7-5

23

QQ

7 30-4

11 12-3

12 8-8

18

85

7 29-2

11 8-2

11 9-5

22

82

7 30-7

11 5-2

11 9-3

22

91

8 30-7

11 39-2

13 4-9

21

90

8 29-8

11 37-4

12 9-9

25

89

8 30-0

11 39-3

12 10-3

20

86

9 29-7

11 48-5

14 7-8

22

86

9 30-8

11 470

14 4-3

22

92

9 31-4

11 50-5

14 9-9

16

91

10 30-5

11 39-5

15 7-3

23

91

10 30-9

11 42-3

15 10-3

19

91

10 30-7

11 46-3

16 4-9

11

89

11 32-6

11 26-7

16 6-5

22

91

11 30-4

11 30-1

17 0-0

16

101

11 32-2

11 34-8

17 8-5

6

Equat. of Time to be\, k
added to app. time. . . J'

...

+4

...

-5

...

...

October.

November.

December. j

93

291

11 19-3

18 6-3

11

85

32-6

11 17-8

17 11-6

20

80

31-3

11 12-6

17 31

23

95

1 29-3

11 1-9

18 3-5

16

81

1 31-5

10 58-2

17 8-8

22

85

1 30-4

10 54-7

17 3-4

21

89

2 28-1

10 42-9

17 7-7

20

83

2 30-5

10 390

17 0-0

23

86

2 29-9

10 40-8

16 9-Q

19

93

3 29- 1

10 26-9

16 6-0

22

84

3 29-6

10 24-2

16 00

22

97

3 29-3

10 28-8

15 10-9

16

95

4 30-8

10 14-6

14 9-0

23

94

4 30-0

10 14-7

14 6-0

20

102

4 31-1

10 23-9

14 11-3

11

86

5 31-3

10 12-2

13 1-3

22

89

5 321

10 17-3

13 3-6

16

103

5 30-9

10 30-7

13 9-7

8

91

6 31-2

10 29-4

11 8-2

20

99

6 300

10 40-4

12 3'3

13

109

6 31-5

10 530

13 0-6

5

97

7 31-2

11 11-8

11 11-6

17

99

7 30- 1

11 21-3

12 7-5

7

100

7 31-2

11 24-0

13 2-7

7

27

8 31-6

11 46-0

13 4-9

13

99

8 29-4

11 47-6

13 11-3

5

100

8 29-1

11 45-5

14 0-8

12

97

9 30-9

11 541

15 20

7

99

9 29-5

11 53-8

15 7-3

6

90

9 28-5

11 48-3

15 3-9

17

98

10 28-7

11 48-9

16 9-7

4

93

10 29-0

11 46-8

16 8-6

12

95

10 28-9

11 42-5

16 4-6

20

96

11 29-8

11 35-3

17 IM

7

96

11 30-8

11 32-7

17 61

17

84

11 30-6

11 27-6

17 1-7

21

Equat. of Time t
1 added to app. tir

ne...i

...

-15

...

1 I
-4

...

MR. LUBBOCK ON TIDE OBSERVATIONS.

283

The argument of all the Tables is the time of the Moon's transit at Greenwich,
taken immediately from the Nautical Almanac, which only amounts to neglecting
the Moon's proper motion during twelve minutes.

Table II. (Interpolated from Table I.)

Showing the Interval between the Apparent Solar Time of the Moon's Transit and
the Time of High Water at Liverpool Old Dock, for each month in the year.

Moon's
Transit.

January.

February,

March.

April.

May.

June.

July.

August.

Sept.

Oct.

Nov.

Dec. Mean. J

h m

h m

h m

h m

h m j h m

h m

h m

h m

h m

h m

h m

h m

h m

30

11 137

11 18-3

11 191

11 19-4 11 16-3

11 13-4

11 13-5

11 17-5

11 20-4

11 191

11 18-4

11 12-9

11 171

1 30

10 59-5

11 8-2

11 3-9

11 M 10 57-9

10 55-5

10 57-8

11 4-5

11 30

11 1-7

10 58-7

10 54-8

11 0-7

2 30

10 470

10 49-7

10 49-4

10 43-4 llO 38-6

10 39-8

10 45-2

10 51-6

10 48-8

10 42-3

10 391

10 40-8

10 43-9

3 30

10 3M

10 37-3

10 33-3

10 30-4 ilO 251

10 29-6

10 37-6

10 35-4

10 34-0

i0 26-7

10 24-1

10 28-7

10 31-5

4 30

10 31-1

10 27-3

10 20-3

10 14-2

10 16-0

10 24-9

10 331

10 30-2

10 21-3

10 14-7

10 14-7

10 23-9

10 22-7

5 30

10 33-8

10 26-3

10 16-2

10 12-8

10 18-8

10 31-6

10 34-2

10 28-7

10 16-9

10 12-2

10 17-1

10 30-6

10 23-3

6 30

10 49-3

10 37-9

10 30-2

10 31-8

10 41-9

10 52-9

10 51-6

10 38-4

10 32- 1

10 291

10 40-4

10 52-5

10 41-0

7 30

11 161

11 8-0

11 5-8

11 8-5

11 20-6

11 24-6

11 12-2

11 8-6

11 4-8

11 110

11 21-3

11 23-4

11 14-4

8 30

11 37-8

11 37-4

11 40-7

11 44-0

11 46-9

11 440

11 38-9

11 37-4

11 39-3

11 451

11 47-9

11 45-7

11 42-2

9 30

11 450

11 510

11 50-3

11 54-3

11 52-5

11 49-2

11 48-5

11 46-9

11 50-3

11 54-0

11 53-8

11 48-2

11 50-4

10 30

11 38-5

11 44-0

11 44-9

11 48-2

11 46-9

11 41-8

11 39-6

11 42-4

11 46-4

11 48-7

11 46-7

11 42-2

11 44-2

11 30

11 34-2

11 31-5

11 33-4

11 36-0

11 31-2

11 28-9

11 27-2

11 301

11 35-2

11 35-3

11 32-9

11 27-7

11 320

Table III. (Interpolated from Table I.)

Showing the Height of High Water at Liverpool Old Docks, corresponding to the
Apparent Solar Time of the Moon's Transit, in each month of the year.

Moon's
Transit.

January.

February.

March.

April.

May.

June.

July.

August.

Sept.

Oct.

Nov.

Dec.

Mean.

h m

feet.

feet.

feet.

feet.

feet.

feet.

feet.

feet.

feet

feet.

feet.

feet.

feet.

30

17-47

18-05

18-38

18-01

17-33

16-73

17-08

17-68

18-30

18-52

17-95

17-25

17-73

1 30

17-74

18-04

18-49

17-88

17-15

16-84

17-14

17-96

18-39

18-28

17-73

17-28

17-78

2 30

17-52

17-69

17-63

17-01

16-56

16-74

16-84

17-37

17-89

17-62

16-99

16-80

17-22

3 30

16-08

16-73

16-31

15-98

15-75

15-81

16-29

16-46

16-50

16-48

1601

15-89

16-19

4 30

15-14

15-20

14-47

14-44

14-48

14-69

14-96

15-03

14-94

14-76

14-50

14-95

14-96

5 30

13-69

13-39

13-01

12-89

13-33

13-75

13-83

13-46

13-19

13-15

13-33

13-82

13-40

6 30

12-61

11-96

11-42

11-44

12-35

13-07

12-87

12-00

11-63

11-70

12-28

13-06

12-20

7 30

12-38

11-78

11-31

11-71

12-58

13-09

12-72

11-80

11-78

11-95

12-62

13-21

12-24

8 30

13-56

12-79

12-68

13-28

13-75

13-86

13-39

12-82

12-86

13-37

13-95

14-07

13-36

9 30

14-95

14-47

14-62

15-07

15-91

14-93

14-64

14-34

14-78

1513

15-61

15-35

14-98

10 30

15-98

15-96

16-54

16-61

16-28

15-91

15-61

15-84

16-38

16-83

16-73

16-38

16-25

11 30

16-73

17-39

17-67

17-60

17-01

16-57

16-52

16-99

17-69

17-92

17-50

1714

17-23

284

MR. LUBBOCK ON TIDE OBSERVATIONS.

Table IV.

Showing the Difference in the Interval between the Apparent Solar Time of the
Moon's Transit and the Time of High Water, and the Mean Interval, for every
month in the year.

Moon's

January.

February.

March.

April.

May.

June.

July. August.

Sept.

October.

Nov.

Dec.

Transit.

h m

m

m

m

m

m

m

m

m

m

m

m

m

30

— 3-4

+

1-2

+ 2-0

+ 2-3

- 0-8

- 3^7

- 3-6

+

0-4

+

3^3

+ 2-0

+

1^3

- 4-2

1 30

- 1-2

+

8-2

+ 3^2

+ 1-6

- 2-8

— 5-2

- 2-9

4-

3-8

+

2-3

+ 1-0

—

2-0

- 5-9

3 30

+ 3^1

+

5-8

+ 5-5

— 0-5

— 5-3

— 4-1

+ 1-3

+

7-7

+

4-9

- 1-6

—

4-8

— 3-1

3 30

+ 5-6

+

5-8

+ 1^8

— 1-1

- 6-4

- 1-9

+ 6^1

+

3-9

+

2-5

- 4^8

—

7.4

- 8-4

4 30

+ 8^4

+

4^6

- 2-4

- 8-5

- 6-7

+ 2-2

+ 10-4

+

7-5

—

1^4

- 8-0

—

8-0

- 7-2

5 30

+ 10^5

+

3-0

- 7-1

-10-5

- 4-5

+ 8-3

+ 10-9

+

5-4

—

6-4

— IM

—

6-2

+ 7-3

6 30

+ 8-3

3-1

— 10^8

— 9-2

+ 0-9

+ 11-9

+ 10-6

—

2-6

—

8-9

-11-9

—

0-6

+ 11-5

7 30

+ 1-7

—

6^4

- 8-6

- 5^9

+ 6^2

+ 10-2

- 3^9

—

5-8

—

9-3

+ 3-4

+

6^9

+ 7-3

8 30

— 4^4

—

4-8

— 1-5

+ 1-8

+ 4-7

+ 1-8

— 3-3

—

0-4

—

1^5

4- 7-3

+

6'7

+ 7-9

9 30

- 5-4

+

0-6

- 0^1

+ 3^9

+ 2-1

- 1^2

- 1-9

+

1^9

+

5-3

+ 3^6

+

8^8

— 2-2

10 30

- 5^7

0^2

+ 0^7

+ 4-0

+ 2-7

- 2-4

- 4-6

+

3-9

+

2^2

+ 4-5

+

2-5

— 2^0

11 30

+ 2-2

—

0^5

+ 1^4

+ 4-0

- 0^8

— 5-3

- 4-8

—

1-9

+

3^2

+ 3-3

+

0^9

- 4-3

Table V.

Showing the Difference in the Height of High Water and the Mean Height for every

month in the year.

Moon's
Transit.

January.

February.

March.

April.

May.

June.

July.

August.

Sept.

October.

Nov.

Dec.

h m

feet.

feet.

feet.

feet.

feet.

feet. 1 feet.

feet.

feet.

feet.

feet.

feet.

30

-•26

+ •32

+ •65

+ •28

-•40

-1^00 —-65

—•05

+•57

+ •79

+ •22

-•48

1 30

—•04

+ •26

+ •71

+ •10

-•63

- -94

—64

+ •18

+ •61

+ •50

-•05

-•50

2 30

+ •30

+•47

+ •41

-•21

-•66

— ^48

—•38

+ •15

+ •67

+ •40

-•23

—42

3 30

-•11

+ •54

+ •12

-•21

-•44

- ^38

+ •10

+ •27

+ •31

+ •29

-•18

-•30

4 30

+•18

+ •24

—49

-•52

-•48

- ^27

00

+ •07

-•02

-•20

-•46

-•01

5 30

+ •29

-•01

—39

— •51

-•07

+ ^35

+ •43

+ •06

-•21

-•25

-•07

+ •42

6 30

+ •41

-•24

-•78

—76

+ •15

+ ^87

+•67

—•20

—57

-•50

+ •08

+•86

7 30

+ •14

-•46

-•93

-•53

+ •34

+ ^85

+ •48

—•44

-•46

—•29

+•38

+ •97

8 30

+ •20

-•57

—68

-•08

+ •19

+ •50' +^03

—•54

-•50

+ •01

+ •59

+ •71

9 30

-•03

-•51

-•36

+ •09

+ •93

_ .05- — •S^

-•64

-•20

+ •15

+ •63

+ •37

10 30

-•27

— •29

+ •29

+ •36

+ •03

- ^34

-•64

-•41

+ •13

+ •58

+ •48

+ •13

11 30

-•50

+ •16

+ •44

+ •37

-•22

- ^66

-•71

-•24

+ •46

+ •69

+•27

-•09

The quantities in this and the preceding Table are chiejly owing to the correction
far the Moon's Declination.

MR. LUBBOCK ON TIDE OBSERVATIONS.

285

Table VI.
Showing the Interval between the Apparent Solar Time of the Moon's Transit and
the Time of High Water, and the Height of High Water, at the Liverpool Old
Docks, corresponding to the Apparent Solar Time of the Moon's Transit, for every
minute of her Horizontal Parallax.

Hor. Par. 54'.

1 1

Hor. Par. 55'. 1

Moon's

Height

Moon's

Moon's

Height

Moon's

% 1

Transit.

Interval.

of

Decli-

^ 1

Transit.

Interval.

of

DecU-

o

Tide.

nation.

o

Tide.

nation.

h m

h m

ft.

in.

o

h m

h m

ft. in.

199

30-3

11 26-4

16

7-0

15

156

30-2

11 231

16 10-6

u

194

1 30-6

11 7-2

16

5-8

15

169

1 311

11 5-3

16 7-8

15

189

2 29-9

10 49-5

15

9-9

15

181

2 311

10 48-9

16 0-2

15

165

3 29-5

10 32-1

14

8-4

15

199

3 300

10 34-8

15 1-3

15

149

4 29- 1

10 23-6

13

7-3

16

234

4 31-0

10 23-5

13 10-0

16

119

5 29-5

10 24-8

12

3-4

16

246

5 30-6

10 25-8

12 5-8

15

124

6 31-5

10 46-5

11

0-5

17

255

' 6 29-8

10 44-9

11 4-3

15

140

7 30-4

11 27-5

11

4-8

15

223

7 29-7

11 24-6

11 5-4

15

181

8 30-4

11 57-7

12

8-3

15

204

8 29-5

11 53-0

12 9-4

15

180

9 30-3

12 3-6

14

1-8

15

181

9 30-3

12 0-9

14 4-1

15

197

10 29-7

11 55-3

15

4-5

15

173

10 30-0

11 53-3

15 6-9

15

187

11 29-5

11 41-4

16

3-6

15

164

11 29-5

11 39-8

16 4-6

14

Hor. Par. 56'.

Hor. Par. 57'. 1

119

30-7

11 16-0

17

3-5

14

95

31-9

11 171

17 6-4

14

119

1 31-0

11 1-3

17

11

14

109

1 31-5

11 1-9

17 1-Q

14

113

2 300

10 46-3

16

8-1

14

108

2 30-3

10 45-6

17 0-4

14

145

3 29-8

10 33-7

15

7-0

15

117

3 30-6

10 33-3

16 2-0

14

144

4 31-3

10 24-0

14

21

15

131

4 30-7

10 24-6

14 10-6

14

139

5 30-9

10 24-7

12

10-8

15

148

5 29-8

10 23-3

13 4-8

15

162

6 29-3

10 43-2

11

8-5

15

136

6 30-4

10 411

12 6-3

15

143

7 29-7

11 19-9

12

1-2

15

132

7 30-3

11 16-0

12 40

14

140

8 30-3

11 4M

13

1-9

14

115

8 29-7

11 43-7

13 4-2

15

129

9 30-7

11 56-5

14

8-1

14

111

9 29-9

11 51-5

14 9-5

14

121

10 31-0

11 49-4

15

11-9

14

108

10 29-7

11 46-7

16 0-3

14

114

11 32-7

11 36-3

16

9-9

15

105

11 30-2

11 33-1

17 00

14

Hor. Par. 58'.

Hor. Par. 59'.

91

30-4

11 15-7

17

11'6

13

99

30-1

11 13-2

18 4-5

14

97

1 28-4

10 59-2

18

1-4

14

99

1 32- 1

10 56-5

18 5-6

14

105

2 30-2

10 45-2

17

6-4

14

111

2 30-8

10 42-5

18 0-4

15

128

3 31-2

10 31-2

16

7-0

14

136

3 30-6

10 30-8

17 2-3

14

131

4 32-2

10 230

15

4-3

15

200

4 32-4

10 21-8

15 10-5

15

148

5 31-4

10 24-5

14

0-0

15

290

5 31-4

10 21-8

14 5-9

15

150

6 30-6

10 38-5

12

10-0

14

299

6 290

10 34-8

13 3-4

15

138

7 30-5

11 10-7

12

8-0

15

194

7 28-8

11 0-8

12 11-6

15

119

8 29-0

11 37-2

13

91

14

140

8 29-4

11 31-0

13 11-2

15

107

9 29-4

11 46-7

15

1-0

14

108

9 29-2

11 41-8

15 51

15

101

10 30-6

11 42-2

16

5-2

13

100

10 29-0

11 38-5

16 7-4

14

88

11 29-9

11 29-3

17

3-1

14

103

11 30-3

11 25-9

17 8-0

14

Hor. Par. SC/. j

Hor. Par. 61'. J

105

32-6

11 10-6

18

7-7

15

212

30-6

11 60

19 2-2

15

111

1 32-3

10 54-9

19

0-9

15

200

1 29-3

10 520

19 4-7

15

161

2 34- 1

10 401

18

8-8

15 1

133

2 25-8

10 39-3

18 10-9

16

226

3 29 7

10 28-2

17

8-7

16

147

4 27-0

10 20-5

16

3-4

16

23

5 16-7

10 14-7

15

0-4

15

21

6 45-7

10 431

13

0-8

16 '

148

7 24-4

11 4-6

13

3-4

16

226

8 320

11 25-8

14

1-7

16 i

163

9 28-0

11 37-9

15

7-6

15 !

125

9 35-5

11 33-7

15 11-4

15

114

10 30-7

11 34-3

17

0-6

15

196

10 30-9

11 301

17 3-9

15

110

11 31-3

11 231

18

11

14 i

212

11 30-7

11 19-7

18 5-6

15

Mean of the preceding.

Moon's

Interval.

Height of

Transit.

Tide.

h m

h m

ft. in.

0 30-8

11 16-0

17 .9-7

1 30-8

11 00

17 10-2

2 30-3

10 44-7

17 40

3 30-2

10 320

16 20

4 30-5

10 230

14 10-3

5 27-6

10 22-8

13 6-2

6 32-3

10 41-7

12 30

7 291

11 14-9

12 3-8

8 30-0

11 41-3

13 5-0

9 30-4

11 49-0

15 0-0

10 30-2

11 43-7

16 3-4

11 30-5

11 310

17 3-0

286

MR. LUBBOCK ON TIDE OBSERVATIONS.

Table VII

. (Interpolated from Table VI.)

.

H. P. 54'.

H. P. 55'.

H. P. 56'.

H. P. 57'.

H. P. 58'.

H. P. 59'.

H. P. 60'.

H. P.61'. 1

Height

Height

Height

Height

Height

Height

Height

Height

Transit.

Interval.

of

Interval.

of Interval.

of Interval.

of

Interval.

of

Interval.

of

Interval.

of

Interval.

of

Tide.

Tide.

Tide,

Tide.

Tide.

Tide.

Tide.

Tide.

h m

h m

ft.

h m

ft. h m

ft. 1 h m

ft.

h m

ft.

h m

ft.

h m

ft.

h m

ft.

30

11 26-4

16-58

11 231

16-88 11 16-3

17-29 11 18-1

17-53

11 15-9

17-96

11 13-2

18-37

11 11-8

18-62

11 6-3

19-17

1 30

11 7-5

16-46

11 4-7

16-64 11 1-8

17-09 11 2-6

17-63

10 58-4

18-12

10 57-5

18-45

10 56-0

19-09

10 51-7

19-39

2 30

10 49-5

15-82

10 49-5

16-02 10 46-3

16-67 10 45-7

17-04

10 45-1

17-54

10 42-8

18-04

10 41-9

18-75

10 38-4

18-87

3 30

10 31-3

14-69

10 34-8

15-11 10 33-6

15-58 ilO 33-5

16-17

10 31-6

16-58

10 31-0

17-19

10 28-1

17-70

4 30

10 23-7

13-59

10 23-7

13-86 1 10 24-3

14-20110 24-7

14-89

10 23-3

15-36

10 21-9

15-87

10 19-8

17-72

5 30

10 25-0

12-28

10 25-8

12-49

10 24-7

12-91 ilO 23-3

13-39

10 24-3

14-01

10 21-8

14-49

6 30

10 45-3

11-07

10 45-1

11-36

10 43-8

11-70

10 40-8

12-53

10 38-1

12-84

10 35-5

13-29

7 30

11 270

11-39

11 24-9

11-45

11 20-2

12-10

11 15-7

12-33

11 10-2

12-66

11 1-9

12-96

11 8-5

13-29

8 30

11 57-5

12-68

11 53-3

12-79

11 48-4

1315

11 43-9

13-36

11 S7-8

13-77

11 31-4

13-93

11 24-7

14-10

9 30

12 3-6

14-14

12 0-8

14-33

11 56-2

14-66

11 51-5

14-79

11 47-8

15-09

11 41-9

15-42

11 38-3

15-68

11 33-5

16-06

10 30

11 55-2

15-38

11 53-3

15-57

11 49-6

15-97

11 46-6

16-04

11 42-3

16-43

11 38-3

16-62

11 34-6

17-04

11 30-3

17-31

11 30

11 41-2

16-30

11 39-6 16-39

11 34-9

16-79

11 32-2

1700

11 29-3

17-26

11 26-0

17-66

11 22-9

18-08

11 19-9

18-45

Table VIII.

Showing the Difference in the Interval between the Time of the Moon's Transit and
the Time of High Water, and the Interval corresponding to fifty-seven minutes of
the Moon's Horizontal Parallax.

Moon's
Transit.

H. P. 54'.

H. P. 55'.

H. P. 56'.

H. P. 57'.

H. p. 58'.

H. P. 59'.

H. P. 60'.

H. P. 61'.

h m

m

m

m

m

m

m

m

m

30

+ 8-3

+5-0

-1-8

0

-2-2

- 4-9

- 6-3

-11-8

1 30

+ 4-9

+2-1

+0-8

0

-4-2

- 5-1

- 6-6

-10-9

2 30

+ 3-8

+3-8

+0-6

0

-0-6

- 2-9

- 3-8

- 7-3

3 30

- 2-2

+ 1-3

+0-1

0

-1-9

- 2-5

- 5-4

4 30

- 1-0

-1-0

-0-4

0

-1-4

- 2-8

- 4-9

5 30

+ 1-7

+2-5

+1-4

0

+ 1-0

- 1-5

6 30

+ 4-5

+4-3

+3-0

0

-27

- 5-3

7 30

+11-3

+9-2

+4-5

0

-5-5

-13-8

- 72

8 30

+13-6

+9-4

+4-5

0

-6-1

-12-5

-19-2

9 30

+12-1

+9-3

+4-7

0

-3-7

- 9-6

-13-2

-18-0

10 30

+ 8-6

+6-7

+3-0

0

-4-3

- 8-3

-120

-16-3

11 30

+ 8-0

+6-4

+ 1-7

0

-3-9

- 7-2

-10-3

-13-3

Table IX.

Showing the Difference between the Height of High Water and the Height corre-
sponding to fifty-seven minutes of the Moon's Horizontal Parallax.

Moon's
Transit.

H. P. 54'.

H. P. 55'.

H. P. 56'.

H. P. 57'.

H. p. 58'.

H. P. 59'.

H. P. 60',

H, P. 61'.

h m

feet.

feet.

feet.

feet.

feet.

feet.

feet.

feet.

30

- -95

- -65

-•24

0

+•46

+ ^84

+1^09

+ b64

1 30

-1-17

- -99

--54

0

+•49

+ ^82

+1-46

+ 1-76

2 30

-1-22

-1-02

--37

0

+•50

+1-00

+1-71

+ 1-83

3 30

-1-48

-1-06

-•59

0

+•41

+1-02

+ 1^53

4 30

-1-30

-1-03

-•69

0

+-47

+ ^98

+2^83

5 30

-1-11

- -90

-•48

0

+-62

+1-10

6 30

-1-46

-M7

--83

0

+-31

+ '76

7 30

- -94

- -88

--23

0

+•33

+ ^63

+ -96

8 30

- -68

- -57

-•21

0

+•41

+ ^57

+■•74

9 30

- -65

- -46

-13

0

+•30

+ -63

+ ^89

+1-27

10 30

- -66

- -47

-•07

0

+•39

+ ^58

+ 1-00

+ 1-27

11 30

- -70

- -61

-•21

0

+•26

+ -66

+ 1-08

+1-45

MR. LUBBOCK ON TIDE OBSERVATIONS.

287

Table X.
Showing- the Interval between the Apparent Solar Time of the Moon's Transit and
the Time of High Water, and the Height of High Water, at the Liverpool Old
Docks, corresponding to the Apparent Solar Time of the Moon's Transit, for every
three degrees of her Declination north and south. The Equation of Time to be
added to Apparent Time.

1° 30' N, to 1° SC South Declination.

Is
-1

1° 30' to 4° .SO' North Declination,

IS.

II

4° 30' to 7° 30' North Declination. 1

Moon's
Transit.

Equation
of Time.

Interval

Height

of
Tide.

Hor.
Par.

Moon's
Transit.

Equation
of Time.

Interval

Height Hor.
Til ^-

Moon's
Transit.

Equation
of Time.

Interval.

Height

of
Tide.

Hor.
Par.

h m

m

h m

ft.

in.

1

h m

m

h m

ft. in. /

h m

in

h m

ft in

48

29-3

4- 2-5

11 22-2

18

40

57-0

54

27-3

+ 2-2

11 211

18 3-5 57-2

55

31-3

+ 1-6

11 19-6

18 2-0

57-3

45

1 29-5

+ 6-0

11 5-0

18

3-3

57-4

52

1 30-0

+ 6-3

11 5-7

18 3-7 57-1

47

1 30-0

+ 6-5

11 5-7

18 5-9

57-2

52

2 28-7

+ 9-2

10 51-6

17

60

570

45

2 29-2

+ 8-2

10 51-4

17 11 57-5

48

2 30-9

+ 6-8

10 50-4

17 8-5

57-1

51 1 3 28-2

+ 8-8

10 39-3

16

9-5

57-1

54

3 33-2

+ 8-6

10 37-5

16 4-5 57-0

48

3 29-1

-f- 7-8

10 38-6

16 4-7

56-8

46

4 31-3

+ 6-1

10 31-4

15

01

56-8

50

4 30-2

+ 6-1

10 28-1

15 21 56-9

46

4 31-8

+ 5-5

10 310

15 0-0

57-0

44

5 30-9

+ 2-8

10 34-5

14

1-3

57-0

42

5 310

+ 2-6

10 35-4

13 7-4 56-7

42

5 31-3

+ 2-3

10 42-4

13 9-1

56-7

39

6 30-6

- 2-3

10 54-8

13

0-9

o6-8

49

6 29-5

+ 2-1

10 54-0

13 1-6 56-9

45

6 31-8

- 2-8

10 52-6

12 8-2

57-3

46

7 29-7

- 5-8

11 23-3

12

110

56-8

43

7 290

- 6-6

11 23-6

13 2-9 571

45

7 30-0

- 5-2

11 24-2

13 2-4

58-2

47

8 28-5

- 91

11 46-8

14

1-3

570

47

8 27-3

- 7-9

11 470

13 100 57-0

44

8 31-1

- 7-2

11 49-9

13 5-9

56-4

46

9 28-6

- 9-3

11 53-8

15

1-6

57-1

43

9 21-&

- 8-9

11 501

15 5-6 57-4

53

9 28-2

- 7-7

11 53-8

15 2-0

57-1

55

10 33-3

- 6-5

11 47-8

16

10-5

57-3

50

10 27-5

- 6-4

11 44-2

16 8-4 57-0

46

10 33-8

- 5-2

11 46-7

16 8-6

57-3

40

11 341

- 2-2

11 33-5

16

10-3

57-9

45

11 25-3

- 2-7

11 374

17 7-6 57-3

50

11 310

- 1-7

11 34-3

17 2-9

57-5

1° 30' to 4" 30' South Declination,

4° 30' to 7° 30' South Declination. 1

52

30-4

+ 3-0

11 18-3

18 6-6

57-7

53

29-8

+ 2-5

11 20-4 118 0-0

57-3

41

1 30-5

+ 7-0

11 3-6

18 3-5

58-0

43

1 31-3

+ 6-0

11 5-2:18 6-0

57-6

48

2 30-9

+ 8-1

10 49-8

17 71

57-5

46

2 31-3

-f- 8-0

10 50-4 117 8-7

57-6

41

3 31-9

+ 8-3

10 39-9 |16 6-2

56-7

44

2 320

+ 7-9

10 38-3 i 16 6-4

57-3

41

4 29-3

+ &•&

10 31-6 15 5-3

57-2

45

4 300

+ 5-0

10 29-6 i 15 5-2

56-8

45

5 29-0

-\- 2-3

10 34-5 [13 9-1

56-6

47

5 27-0

+ 3-1

10 32-7 14 1-4

57-0

49

6 30- 1

+ M

10 53-5:12 11-4

57-0

51

6 29-4

- 2-1

10 51-0 12 10-3

57-0

44

7 33-1

- 6-5

11 271 |13 01

57-0

50

7 30-4

- 51

11 21-6,12 11-5

57-0

45

8 32-4

- 8-1

11 41-3 jl3 1-6

57-3

40

8 29-0

- 6-8

11 47-0 ! 13 100

56-9

54

9 300

- 8-6

11 54-4 !l5 3-8

56-7

48

9 31-9

- 7o

11 54-5

15 6-3

57-2

47

10 28-5

- 60

11 41-8 16 80

57-3

46

10 30-3

- 5-6

11 44-9

16 11-5

57-8

54

11 311

- 4-6

11 34-8 17 90

57-4

52

11 30-2

- 1-9

11 320 18 00

57-7

7o SO* to 10° SC North Declination,

10° 30' to 13° SC North Declination.

1.3° 30' to 16° 30' North Declination.

h m

m

h m

ft.

in.

^

h m

m

h m

ft. in.

/

h m

m

h m

ft. in.

52

30-1

+ 1-3

11 20-3

18

11

57-1

54

30-8

+ 1-2

11 19-3

18 0-1

57-3

58

31-6

+ 0-1

11 18-8

17 9-6

56-7

54

1 30-7

+ 4-3

11 4-7

18

21

57-2

64

1 32-3

-1- 2-3

11 3-4

17 10-2

56-2

54

1 280

00

11 3-1

17 7-8

56-7

50

2 28-7

+ 6-0

10 49-2

17

51

57-3

45

2 31-7

+ 3-8

10 48-8

17 4-5

570

66

2 28-9

+ 1-5

10 47-3

16 10-8

55-8

55

3 27-8

+ 5-9

10 41-5

16

5-2

56-6

53

3 29-9

+ 3-9

10 35-3

16 0-4

56-8

Q1

3 27-6

+ 0-1

10 33-2

16 1-7

56-5

54

4 29-7

+ 5-1

10 30-3

14

11-3

56-7

51

4 30-7

+ 2-6

10 28-0

14 10-4

56-7

n

4 28-8

+ 0-1

10 25-2

14 8-1

56-4

45

5 28-9

+ 1-2

10 32-1

13

9-4

56-4

57

5 30-4

+ 1-3

10 27-4

13 6-3

56-7

75

5 290

+ 10

10 27-1

13 21

56-2

51

6 27-5

- 1-5

10 49-7

12

8-3

56-6

54

6 30-4

- 1-2

10 48-0

12 4-6

56-5

72

6 30-6

0-0

10 44-7

12 31

56-4

48

7 27-8

- 4-3

U 22-5

12

7-2

56-5

60

7 27-4

- 2-3

11 20-1

12 6-5

56-5

69

7 32-2

- 10

11 20-8

12 1-6

56-3

48

8 31-7

- 6-6

11 45-2

14

1-7

571

59

8 30-0

- 4-2

11 48-5

13 1-1

56-5

63

8 31-4

- 0-3

11 46-0

13 4-3

56-7

58

9 30-2

- 6-2

11 54-8

15

1-3

56-7

59

9 30-5

- 2-4

11 520

14 11-2

57-0

64

9 31-3

- 0-4

11 52-6

14 11-3

56-0

51 10 33-3

- 4-5

11 46-4

16

Q-7

57-3

60

10 291

- 2-6

11 48-5

16 ^-Q

o6-9

71

10 29-4

- 0-8

11 46-6

16 6-1

56-8

47 11 30-8

- 11

11 35-6

17

.7-9

56-9

61

11 27-0

- 1-4

11 36-6

17 2-5

56-8

70

11 32-5 00

11 34-1

17 1-1

56-8

7° 30' to 10° 30' South Declination,

10° 30' to 13° 30' South Declination.

13° 30' to 16° 30' South Declination. |

42

29-9

+ 1-2

11 18-7

18

4-9

57-8

54

30-6

+ 1-4

11 16-3

18 4-7

57-9

61

31-2

00

11 15-2

18 2-5

58-0

53

1 290

+ 4-8

11 3-9

18

50

57-7

57

1 30-3

+ 2-7

11 1-8

18 5-4

57-8

61

1 31-2

- 01

11 0-3

18 2-6

58-5

52

2 30-5

-f 5-2

10 49-1

17

8-2

57-3

59

2 30-5

-h 4-0

10 46-8

17 81

57-7

60

2 29-2

+ 0-6

10 45-0

17 6-6

57-6

51

3 27-3

+ 5-8

10 37-0

1&

9-9

57-4

48

3 30-3

+ 4-1

10 35-5

16 7-8

57-4

62

3 30-6

-f- 0-4

10 32-6

16 4-8 .

>7-5

49

4 32-3

+ 5-6

10 29-5

15

1-8

57-4

59

4 28-9

+ 3-1

10 27-3

15 1-9

571

60

4 30-5

+ 0-7

10 23-5

15 1-7 .

>7-3

46

5 32-7

+ 1-1

10 321

13

8-7

56-9

57

5 30-8

+ 1-4

10 290

13 10-7

57-3

64

5 29-0

+ 0-3

10 25-0

14 10 .

)71

44

6 32-6

- 1-2

10 49-3

13

0-0

57-2

59

6 28-7

- 1-9

10 45 0

12 6-6

57-0

58

6 30-6

00

0 42-6

12 7-5 .

^7-3

46

7 31-0

- 5-7

11 22-0

12

6-4

56-9

49

7 300

- 3-6

11 16-6

12 7-5

57-5

64

7 30-2

- 0-8

11 14-9

12 7-9 i

)7-5

54

8 28-5

- 5-5

11 43-4

13

10-3

57-5

53

8 28-4

- 4-0

11 42-4

13 7-8

57-3

73

8 31-0

- 0-9

11 40-6

13 6-3 :

.7-4

50

9 300

- 4-8

11 52-2

15

8-3

57-3

55

9 306

- 3-2

11 49-2

15 1-4

57-7

63

9 31-5

- 11

11 47-9 ]

5 1-6 .'

.7-8

53

10 29-4

- 4-9

11 46-0

16

7-5

57-6

53

10 30-5

- 1-5

11 45-3

16 90

57-7

67

10 30-7

- 0-3

11 42-2 ]

6 7-0.'

7-9

51

11 30-3

- 2-5

11 330

18

1-9

57-8

65

11 31-5

- 1-2

11 31-6

17 7-2

57-8

54

11 30-7

+ 0-2

11 29-5 17 4-6 p

8-0

MDCCCXXXV.

2 P

288

MR. LUBBOCK ON TIDE OBSERVATIONS.

Table X. (Continued.)

Ill

16°30'to 19° 30'

North Declination.

Hi

19° 30' to 22° 30'

North Declination.

Moon's

Equation

Interval.

Height of

Hor.

Moon's

Equation

Interval.

Height of

Hor.

'^'z>

Transit

of Time.

Tide.

Par.

!2;'S>

Transit.

of Time.

Tide.

Par.

h m

m

h m

ft. in.

/

h m

m

h m

ft. in.

/

92

32-6

- 0-4

11 18-4

17 1-0

56-3

62

310

- 1-7

11 11-4

17 9-7

58-4

95

1 31-6

- 3-0

11 10

17 2-1

56-5

61

1 33- 1

- 3-6

10 55-7

17 51

58-0

97

2 31-3

- 40

10 45-0

16 8-7

56-5

56

2 31-0

~ 4-1

10 39-4

17 20

58-1

93

3 30-8

- 3-8

10 310

15 10-9

561

72

3 311

- 41

10 28-0

16 1-5

57-5

100

4 31-6

- 2-6

10 21-7

14 4-3

561

64

4 29-9

- 2-6

10 17-7

14 110

57-8

94

5 30-7

- 1-5

10 21-6

12 9-5

56-0

67

5 28-0

- 0-3

10 17-8

13 50

57-4

95

6 29-5

+ 0-9

10 41-5

11 10-5

55-8

70

6 30-1

+ 0-8

10 33-6

12 27

57-6

106

7 31-0

+ 2-7

11 16-8

12 00

56-2

63

7 320

+ 3-4

11 7-2

12 2-5

57-8

89

8 311

+ 3-2

11 44-8

13 30

56-2

62

8 28-8

+ 4-3

11 36-7

13 3-6

57-7

102

9 28-8

+ 4-2

11 52-8

14 70

56-2

65

9 29-8

+ 3-7

11 45-7

14 6-4

57-2

95

10 30-6

+ 1-9

11 451

15 110

56-5

62

10 28-8

+ 3-6

11 39-2

16 21

58-1

91

11 32-3

+ 1-2

11 33-3

16 9-9

56-4

62

11 30-6

+ 1-0

11 26-2

17 01

58-3

16° 3C

•' to 19° 30'

South Decli

nation.

19° 30' to 22° SC South Declination. 1

83

29-9

- 0-9

11 2-4

17 11-2

58-2

65

30-3

- 0-8

11 15-4

17 1-2

56-9

84

1 30-1

- 20

10 56-6

18 2-5

58-7

67

1 27-8

- 4-0

11 0-2

17 0-4

56-5

87

2 28-6

- 3-3

10 42-3

17 9-9

58-2

71

2 29-0

- 5-2

10 41-4

16 5-6

56-7

93

3 29-0

- 41

10 35-2

16 91

58-4

70

3 28-8

- 3-6

10 28-6

15 9-9

56-6

^Q

4 30-3

_ 3-2

10 21-4

14 10-5

57-8

74

4 30-7

- 3-4

10 18-1

14 4-5

56-3

98

5 30-5

- 0-7

10 18-8

13 7-5

57-5

64

5 32-5

0-8

10 181

12 8-2

56-2

100

6 31-7

+ 1-0

10 35-5

12 9-9

57-5

75

6 30-7

+ 1-3

10 35-3

11 5-2

56-1

92

7 3M

+ 3-0

11 8-6

12 7-9

57-9

65

7 28-5

+ 30

11 21

11 7-4

56-4

91

8 31-6

+ 3-1

11 36-4

13 80

57-9

68

8 29-7

+ 4-5

11 44-7

12 7-5

56-1

80

9 31-2

+ 4-4

11 42-8

15 2-5

58-0

67

9 28-7

+ 4-5

11 48-8

14 5-7

57-2

88

10 290

+ 2-8

11 39-1

16 5-7

58-3

67

10 31-8

+ 3-4

11 450

15 8-5

56-6

83

11 31-9

+ 0-9

11 26-3

17 5-8

58-7

63

11 31-3

+ 1-2

11 320

16 71

56-9

22° SCy to 25° SC North. Declination.

Above 25° SO' North Declination.

h m

m

h m

ft in.

t

h m

m

h m

ft in.

/

48

30-8

- 1-3

11 1-Q

17 5-3

58-7

42

31-4

- 2-9

11 11-5

16 4-2

56-8

57

1 33-3

- 4-7

10 51-8

17 8-9

58-8

45

1 28-7

- 5-8

10 55 0

16 1-4

56-3

45

2 320

- 6-6

10 35-4

17 4-4

58-5

49

2 31-8

- 7-7

10 35-5

15 11-5

56-3

54

3 29-5

- 60

10 23-5

16 5-5

58-2

51

3 31 0

- 7-5

10 22-6

15 1-0

56-3

51

4 300

- 5-5

10 13-5

15 0-5

58-2

59

4 32-5

- 5-9

10 9-8

13 7-9

561

56

5 29-2

- 0-4

10 14-0

13 5-7

57-7

53

5 331

- 1-7

10 9-7

12 3-7

56-2

54

6 31-9

+ 1-2

10 29-9

12 1-7

57-7

58

6 29-8

+ 1-9

10 25-4

10 90

561

52

7 27-4

+ 4-2

11 2-5

11 11-4

58-0

54

. 7 31-4

+ 5-2

11 6-0

10 100

56-5

61

8 34-6

+ 5-1

11 29-8

13 21

58-1

51

8 30-5

+ 8-5

11 44-3

12 1-6

55-9

50

9 30-2

+ 7-2

11 38-5

14 111

58-8

44

9 30-2

+ 7-6

11 510

13 8-3

56-3

52

10 30-5

+ 4-4

11 35-3

15 11-7

58-5

47

10 28-9

+ 6-0

11 43-2

15 00

56-2

58

11 30-3

+ 1-4

11 25-6

16 9-0

58-0

41

11 30-4

4- 2-2

11 30-0

15 6-2

56-4

22° 30

' to 25° 30'

South Declii

lation.

Above 25° 30' South Declination. 1

57

31-9

- 1-8

11 161

16 5-1

561

42

28-5

- 20

11 6-9

17 2-5

58-3

52

1 30-8

- 4-6

10 57-4

16 5-6

561

41

1 30-0

- 5-4

10 50-0

17 5-6

58-4

61

2 321

- 6-2

10 40-2

16 0-8

56-0

43

2 28-6

- 7-5

10 34-3

17 01

58-4

50

3 28-9

- 5-7

10 261

15 5-7

55-7

49

3 30-7

- 7-9

10 20-9

16 10

58-0

65

4 30-0

- 3-6

10 15-4

13 11-9

55-9

50

4 31-8

- 6-7

10 9-5

14 8-2

57-7

50

5 30-6

- 1-9

10 12-6

12 6-4

55-8

52

5 28-8

- 1-9

10 81

13 2-8

57-7

63

6 28-5

+ 0-7

10 301

11 2Q

57-2

59

6 29-2

+ 1-5

10 22-2

11 6-5

57-4

60

7 32-3

+ 3-9

11 130

11 3-9

56-2

47

7 29- 1

+ 6-0

10 54-3

11 6-8

58-0

62

8 30-8

+ 6-3

11 441

12 6-9

560

52

8 30-0

+ 7-3

11 30-0

12 10-9

57-8

57

9 32-4

+ 6-1

11 52-7

14 2-3

56-0

42

9 29-7

+ 8-6

11 400

14 3-6

58-2

52

10 290

+ 5-3

11 46-8

15 1-3

56-2

44

10 32-7

+ 6-1

11 35-0

15 60

58-2

51

11 32-4

+ 1-4

11 30-2

16 40

56-8

37

11 30-4

+ 2-9

11 200

16 5-6

58-7

In forming this Table, it has been assumed that Mr. Hutchinson's clock was
regulated according to apparent solar time ; if it was regulated according to mean
solar time, the interval must be diminished by the equation of time given in the
third column.

MR. LUBBOCK ON TIDE OBSERVATIONS.

289

Table XI. (Interpolated from Table X.)
Showing the Interval between the Apparent Time of the Moon's Transit and the Time
of High Water at the Liverpool Old Docks for every three degrees of her Decli-
nation north and south.

Moon's
Transit.

0^

Dec.

3° N. Dec.

63 N. Dec.

9= N. Dec. 12° N. Dec.

150 N. Dec. 180 N. Dec.

210 N. Dec.

240 N. Dec.

270

N. Dec.

Mean.

h m

h

m

h m

h m

h

m h m

h m

h

m

h m

h

m

h

m

h m

30

11

22-1

11 20-4

11 19-9

11

20-3 111 19-3

11 19-2

11

19-0

11 11-7

11

7-8

11

11-9

11 17-2

1 30

11

5-0

11 5-7

11 3-7

11

4-9 ill 4-0

11 2-3

11

1-4

10 36-3

11

52-7

10

34-6

11 1-3

2 30

10

51-4

10 51-2

10 50-6

10

49-4 10 49-2

10 47-0

10

43-3

10 39-6

10

33-9

10

36-0

10 45-6

3 30

10

39-1

10 38-1

10 38-3

10

37-0 10 33-3

10 32-8

10

31-2

10 28-2

10

23-4

10

22-8

10 32-6

4 30

10

31-6

10 28-1

10 31-2

10

30-3 10 28-1

10 25-0

10

21-8

10 17-7

10

13-5

10

10-0

10 23-8

5 30

10

34-5

10 35-3

10 33-3

10

32-2 10 27-4

10 27-1

10

21-6

10 17-3

10

14-1

10

9-7

10 23-3

6 30

10

34-7

10 54-0

10 32-2

10

50-7 10 48-0

10 44-3

10

41-6

10 33-6

10

29-4

10

23-4

10 43-4

7 30

11

23-4

11 24-0

11 24-2

11

23-2 11 20-2

11 19-7

11

16-3

11 6-2

11

3-7

11

5-0

11 16-6

8 30

11

47-1

11 47-4

11 49-5

11

43-6 11 48-5

11 43-6

11

44-0

11 37-1

11

30-7

11

43-0

11 43-6

9 30

11

53-8

11 50-0

11 33-7

11

34-8 11 32-0

11 32-3

11

32-8

11 43-7

11

38-3

11

31-0

11 30-3

10 30

11

48-1

11 44-0

11 47-0

11

47-0 11 48-6

11 46-3

11

45-2

11 39-1

11

33-4

11

43-1

11 44-4

11 30

11

34-4

11 36-5

11 34-4

11

33-7

11 36-0

11 34-7

11

33-9

11 26-4

11

23-6

11

30-1

11 32-8

3° S. Dec.

6° S. Dec.

9° S. Dec.

120 s. Dec.

150 s. Dec.

180 S. Dec.

210 s. Dec.

240 s. Dec.

270 S. Dec.

Mean.

30

11 18-4

11 20-4

11

18-7

11 16-4

11 13-5

11

12-4

11 13-4

11

16-6

11

&'&

11 13-6

1 30

11 3-7

11 3-7

11

3-7

11 1-8

11 0-0

10

36-6

10 59-6

10 37-6

10

30-0

10 39-9

2 30

10 50-0

10 30-9

10

49-2

10 46-9

10 44-9

10

42-0

10 4M

10

40-3

10

34-0

10 44-3

3 30

10 40-2

10 38-7

10

36-6

10 33-3

10 32-7

10

33-1

10 28-3

10

25-9

10

21-0

10 32-6

4 30

10 31-5

10 29-6

10

29-9

10 27-2

10 23-6

10

21-4

10 18-2

10

15-4

10

9-8

10 22-9

5 30

10 34-7

10 33-0

10

32-0

10 29-0

10 23-1

10

18-8

10 18-0

10

12-6

10

8-2

10 23-4

6 30

10 33-5

10 31-2

10

48-7

10 44-4

10 42-4

10

33-0

10 33-1

10

31-8

10

22-4

10 41-0

7 30

11 25-9

11 21-4

11

21-6

11 16-6

11 14-9

11

8-1

11 2-9

11

13-0

10

34-8

11 13-2

8 30

11 40-7

11 47-4

11

43-7

11 42-8

11 40-2

11

36-4

11 44-7

11

44-1

11

30-0

11 41-0

9 30

11 54-4

11 34-4

11

32-2

11 49-1

11 47-8

11

42-7

11 48-8

11

52-7

11

40-0

11 49-1

10 30

11 41-6

11 44-9

11

43-9

11 43-3

11 42-3

11

39-0

11 43-1

11

46-8

11

33-2

11 42-9

11 30

11 34-7

11 32-0

11

33-0

11 32-0

11 29-6

11

26-6

11 32-4

11

30-2

11

20-1

11 30-1

Table XII.

Showing the Interval between the Apparent Time of the Moon's Transit and the Time
of High Water at the Liverpool Old Docks for every three degrees of her Decli-
nation north or south.

Moon's
Transit.

00 Dec.

30 Dec.

60 Dec.

90 Dec.

120 Dec.

150 Dec.

180 Dec.

21=

Dec.

240 Dec.

270 Dec.

Mean.

h m

h

m

h

m

h

m

h

m

h m

h

m

h

m

h

m

h

m

h m

h m

30

11

22-1

11

19-4

11

20-1

11

19-3

11 17-9

11

17-3

11

13-7

11

13-3

11

12-2

11 9-2

11 16-7

1 30

11

3-0

11

4-7

11

3-7

11

4-3

11 2-9

11

1-2

10

39-0

10

38-0

10

53-2

10 52-3

11 0-8

2 30

10

31-4

10

30-6

10

30-8

10

49-3

10 48-0

10

46-0

10

43-6

10

40-4

10

38-2

10 33-0

10 43-3

3 30

10

39-1

10

39-1

10

38-6

10

38-9

10 35-4

10

32-8

10

33-2

10

28-2

10

24-6

10 21-9

10 33-2

4 30

10

31-6

10

29-8

10

30-4

10

30-1

10 27-3

10

24-3

10

21-6

10

17-9

10

14-4

10 9-9

10 23-7

5 30

10

34-3

10

33-0

10

34-1

10

32-1

10 28-2

10

26-1

10

20-2

10

17-7

10

13-3

10 9-0

10 23-0

6 30

10

34-7

10

33-8

10

51-7

10

49.7

10 46-2

10

43-4

10

38-3

10

34-3

10

30-6

10 23-9

10 42-6

7 30

11

23-4

11

23-0

11

22-8

11

22-4

11 18-4

11

17-9

11

12-2

11

4-6

11

8-3

10 39-9

11 13-3

8 30

11

47-1

11

44-0

11

48-4

11

44-7

11 43-6

11

42-9

11

40-1

11

40-9

11

36-3

11 36-5

11 42-7

9 30

11

33-8

11

52-2

11

54-0

11

33-3

11 30-6

11

50-1

11

47-7

11

47-2

11

45-6

11 45-5

11 30-0

10 30

11

48-1

11

42-8

11

46-0

11

46-4

11 46-9

11

44.4

11

42-1

11

42-1

11

4M

11 39-2

11 43-9

11 30

11

34-4

11

33-6

11

33-2

11

34-3

11 34-0

11

32-1

11

30-2

11

29-4

11

27-9

11 23-1

11 31-6

2 p2

290

MR. LUBBOCK ON TIDE OBSERVATIONS.

Table XIII.

Showing the Difference in the Interval between the Apparent Solar Time of the Moon's
Transit and the Time of High Water, and the Interval corresponding to fifteen de-
grees Declination, for every three degrees of her Declination north and south.

Moon's

0

3° N. Dec.

6° N. Dec,

9° N. Dec.

12° N. Dec.

15° K. Dec.

18° N.Dec.

21° N. Dec.

24° N, Dec.

27° N. Dec,

Transit.

h m

m

m

in

m

m

m

m

m

m

m

30

+

2-9

+ 1-2

+ 0-7

+ 1-1

+ 0-3

0

— 0-2

- 7-5

-11-4

- 7-3

1 30

+

2-5

+ 3-2

+ 3-2

+ 2-4

+ 1-5.

0

— M

- 6-0

- 9-8

- 7-9

2 30

-1-

4-4

+ 4-2

+ 3-6

+ 2-4

4- 2-2

0

- 1-7

- 7-4

-IM

-11-0

3 30

+

6-3

+ 5-3

+ 5-7

+ 8-4

+ 2-5

0

- 1-6

- 4-6

- 9-4

-10-0

4 30

+

&'Q

+ 3-1

+ 6-2

+ 5-3

+ 3-1

0

— 3-2

- 7-3

-11-5

-15-0

5 30

+

7-4

+ 8-2

+ 8-2

+ 5-1

+ 0-3

0

— 5-5

- 9'^

— 13-0

-17-4

6 30

+ 10-2

+ 9-5

+ 7-7

+ 6-2

+ 3-5

0

- 2-9

-10-9

-15-1

-19-1

7 30

+

3-7

+ 4-3

+ 4-5

+ 3-5

+ 0-5

0

— 3-4

— 13-5

-16-0

-14-7

8 30

+

1-5

+ 1-8

+ 3-9

0-0

+ 2-9

0

- 1-6

- 8-5

-17-0

- 2-6

9 30

+

1-3

- 2-5

+ 1-2

+ 2-3

- 0-5

0

+ 0-3

- 6-8

-14-0

— 1-5

10 30

+

1-6

- 2-5

+ 0-5

+ 0-5

+ 2-1

0

— 1-3

- 7-4

— IM

- 2-4

11 30

—

0-3

+ 1-8

- 0-3

+ 1-0

+ 1-3

0

- 0-8

— 8-3

- 9-1

- 4-6

3° S. Dec.

6° S. Dec.

9° S. Dec.

12° S. Dec.

15° S. Dec.

18= S. Dec.

210 S. Dec.

24° S. Dec.

27° S. Dec.

30

+ 2-9

+ 4-9

+ 3-2

+ 0-9

0

— 3-1

- 0-1

+ M

- 8-9

1 30

+ 3-7

+ 5-7

+ 3-7

+ 1-8

0

- 3-4

- 0-4

— 2-4

-10-0

2 30

+ 5-1

+ 5-1

+ 4-3

+ 2-0

0

— 2-9

— 3-8

— 4-4

-10-9

8 30

+ 7-5

+ 7-5

+ 3-9

+ 2-8

0

+ 2-4

— 4-4

- 6-8

-11-7

4 30

+ 7-9

+ 5-9

+ 6-3

+ 3-6

0

— 2-2

- 5-4

— 8-2

-33-8

6 30

+ 9-6

+ 7-9

+ 6-9

+ 3-9

0

- 6-3

- 7-1

-12-5

-16-9

6 30

+ 1M

+ 8-8

+ 6-3

+ 2-0

0

- 7-4

- 7-3

— 10-6

-20-0

7 30

+ 11-0

H- 6-5

+ 6-7

+ 1-7

0

- 6-8

-12-0

- 1-9

-20-1

8 30

+ 0-5

+ 7-2

+ 3-5

+ 2-6

0

— 4-1

+ 4-7

+ 3-9

— 10-2

9 30

+ 6-6

+ ^-^

+ 4-4

+ 1-3

0

— 5-1

+ 1-0

+ 4-9

- 7-8

10 30

- 0-7

+ 2-6

+ 3-6

+ 3-0

0

- 3-3

+ 2-8

+ 4-5

- 7-1

11 30

+ 5-1

+ 2-4

+ 3-4

+ 2-4

0

- 3-0

+ 2-8

+ 0-6

- 9-5

Table XIV.

Showing the Difference in the Interval between the Apparent Solar Time of the Moon's
Transit and the Time of High Water, and the Interval corresponding to fifteen de
grees Declination, for every three degrees of her Declination north or south.

Moon's

0

3° Dec.

6° Dec.

9° Dec.

12° Dec.

15° Dec.

18° Dec.

21° Dec,

24° Dec.

27° Dec.

Transit.

h m

va

ra

m

m

m

m

m

m

m

m

30

+ 4-8

+ 2-1

+ 2-8

+ 2-2

+ 0-6

0

- 1-6

— 3-8

— 5-1

— 8-1

1 30

+ 3-8

+ 3-5

+ 4-3

+ 3-1

+ 1-7

0

- 2-2

- 3-2

- 6-0

- 8-9

2 30

+ 5-4

+ 4-6

+ 4-8

+ 3-3

+ 2-0

0

- 2-4

- 5-6

- 7-8

-11-0

3 30

+ 6-3

+ 6-3

+ 5-8

+ 6-1

+ 2-6

0

+ 0-4

- 4-6

- 8-2

-10-9

4 30

+ 7-3

4- 6-5

+ 6-1

+ 5-8

+ 3-0

0

— 2-7

- 6-4

- 9-9

— 14-4

5 30

+ 8-4

+ 8-9

+ 8-0

+ 6-0

+ 2-1

0

- 6-9

- 8-4

-12-8

-17-1

6 30

+ 11-3

+ 10-4

+ 8-3

+ 6-3

+ 2-8

0

— 6-1

- 9-1

-12-8

-19-5

7 30

+ 5-5

+ 7-1

+ 4-9

+ 4-5

+ 0-5

0

- 5-7

-13-3

- 9'Q

— 18-0

8 30

+ 4-2

+ M

+ 5-5

+ 1-8

+ 2-7

0

- 2-8

- 2-0

- ^'Q

- 6-4

9 30

+ 3-7

+ 2-1

+ 3-9

+ 3-4

+ 0-5

0

— 2-4

— 2-9

— 4-5

- 4-6

10 30

+ 3-7

- 1-6

+ 1-6

+ 2-0

+ ;^-5

0

- 2-3

- 2-3

— 1-0

— 5-2

11 30

+ 2-3

+ 3-5

+ M

+ 2-2

+ 1-9

0

- 1-9

- 2-7

— 4-2

- 7-0

MR. LUBBOCK ON TIDE OBSERVATIONS.

291

Table XV. (Interpolated from Table X.)

Showing the Height of High Water at the Liverpool Docks for every three degrees
of the Moon's Declination north and south.

Moon's
Transit.

0° Dec.

3° N. Dec.

6° N. Dec.

9° N. Dec.

123 N. Dec.

15° N. Dec.

18° N. Dec. 21° N. Dec.

24° N. Dec.

27° N. Dec.

Mean.

h m

30

1 30

2 30

3 30

4 30

5 30

6 30

7 30

8 30

9 30

10 30

11 30

feet.

18-33
18-27
17-49
16-75
15-04
14-12
13-08
12-91
14-13
15-14
16-86
16-83

feet.

18-30
18-31
17-90
16-38
15-17
13-61
13-13
13-24
13-86
15-52
16-71
17-69

feet.

18-14
18-49
17-71
16-40
15-05
13-78
12-69
13-19
13-48
15-21
16-64
17-23

feet.

18-09
18-17
17-40
16-38
14-94
13-77
12-68
12-71
14-11
15-11
16-49
17-56

feet.

18-00
17-86
17-39
16-04
14-87
13-53
12-38
12-56
13-63
14-92
16-22
17-25

feet.

17-79
17-63
16-89
16-10
14-64
13-15
12-27
12-13
13-33
14-90
16-51
17-07

feet.

17-08

17-17
16-72
15-91
14-39
12-80
11-87
12-00
13-01
14-67
15-95
16-81

feet.

17-80
17-44
17-16
16-14
14-91
13-37
12-21
12-19
13-32
14-53
16-19
17-00

feet.

17-43
17-72
17-38
16-44
15-04
13-45
12-16
11-97
13-07
14-92
15-97
16-75

feet.

16-34
16-11
15-97
15-10
13-70
12-37
10-75
10-82
12-12
13-69
15-02
15-52

feet

17-73

17-72
17-20
16-14
14-77
13-40
12-32
12-97
13-41
14-86
16-26
16-97

3° S. Dec.

6° S. Dec.

9° S. Dec.

12° S. Dec.

15° S. Dec.

18° S. Dec.

21° S. Dec.

24° S. Dec.

27° S. Dec.

30

1 30

2 30

3 30

4 30

5 30

6 30

7 30

8 30

9 30

10 30

11 30

18-54
18-28
17-60
16-55
15-43
13-75
12-94
13-00
13-13
15-31
16-69
17-73

18-00
18-50
17-73
16-68
15-43
14-06
12-86
12-95
13-85
15-48
16-95
18-00

18-40
18-41
17-68
16-81
15-20
13-76
13-03
12-54
13-88
15-69
16-63
18-15

18-38
18-44
17-67
16-64
15-13
13-89
12-55
12-62
13-67
15-11
16-75
17-58

18-19
18-21
17-54
16-40
15-14
14-06
12-64
12-65
13-51
15-09
16-56
17-37

17-93
18-20
17-80
16-74
14-87
13-64
12-83
12-65
13-64
15-18
16-49
17-45

17-10
17-04
16-41
15-80
14-39
12-74
11-43
11-63
12-62
14-51
15-67
16-57

16-41
16-45
16-08
15-45
13-99
12-53
11-22
11-31
12-56
14-14
15-12
16-30

17-21
17-46
16-99
16-09
14-64
13-20
11-54
11-57
12-90
14-30
15-45
16-46

17-80
17-89
17-03
16-35
14-91
13-51
12-34
12-33
13-31
14-96
16-26
17-29

Table XVI.

Showing the Height of High Water at the Liverpool Docks for every three degrees

of the Moon's Declination north or south.

Moon's
Transit

0° Dec.

3° Dec.

6° Dec.

9° Dec.

12= Dec.

15° Dec.

18° Dec.

21° Dec.

24° Dec.

27° Dec.

Mean.

feet

feet

feet.

feet

feet.

feet.

feet

feet.

feet

feet.

feet.

30

18-33

18-42

18-07

18-24

18-19

17-99

17-50

17-45

16-92

16-77

17-79

1 30

. 18-27

18-30

18-50

18-29

18-15

17-92

17-69

17-24

17-08

16-79

17-82

2 30

17-49

17-75

17-72

17-54

17-53

17-22

17-26

16-78

16-73

16-49

17-25

3 30

16-75

16-47

16-54

16-60

16-34

16-25

16-33

15-97

15-95

15-60

16-28

4 30

15-04

15-30

15-24

14-98

15-00

14-89

14-53

14-65

14-52

14-17

14-83

5 30

14-12

13-68

13-92

13-76

13-71

13-60

13-22

13-06

12-99

12-78

13-48

6 30

13-08

13-04

12-77

12-86

12-46

12-45

12-35

11-80

11-69

11-15

12-36

7 30

12-91

13-12

13-07

12-62

12-59

12-39

12-32

11-91

11-64

11-19

12-38

8 30

14-13

13-50

13-66

14-00

13-65

13-42

13-33

12-97

12-80

12-51

13-40

9 30

15-14

15-41

15-35

15-40

15-01

15-00

14-93

14-52

14-53

14-00

14-93

10 30

16-86

16-70

16-80

16-56

16-49

16-53

16-22

15-93

15-54

15-24

16-29

11 30

16-83

17-71

17-61

17-86

17-41

17-22

17-13

16-79

16-52

15-99

17-71

292

MR. LUBBOCK ON TIDE OBSERVATIONS.

Table XVII.

Showing the Difference between the Height of High Water and the Height corre-
sponding to fifteen degrees of the Moon's Declination, for every three degrees of
her Declination north and south.

Moon's

0^ Dec.

3° N. Dec.

6° N. Dec.

9° N. Dec.

12° N. Dec.

15° N. Dec.

18° N. Dec.

21° N. Dec.

24° N. Dec.

27° N. Dec.

Transit.

h m

feet.

feet.

feet.

feet.

feet.

feet.

feet.

feet.

feet.

feet.

30

+ •54

+ -51

+ •35

+ •30

+ •21

0

—71

+ •09

-•36

— 1-45

1 30

+ •64

+ ^68

+ •86

+ •54

+ •23

0

-•46

—19

+ •09

-1^52

2 30

+ •60

+ 1^01

+ •82

+ •51

+ •50

0

-•17

+ •27

+ •49

— ^92

3 30

+ •65

+ ^28

+ •30

+ •28

—06

0

— 19

+ •04

+ •34

-1^00

4 30

+ •40

+ -53

+ •41

+ •30

+ •23

0

— •25

+ •27

+ •40

- ^94

5 30

+ •97

+ ^46

+ •63

+ •62

+ •38

0

-•35

+ •22

+ •22

- ^78

6 30

+ •81

+ ^86

+ •42

+ •41

+ •11

0

— •40

—06

-•11

-2-52

7 30

+•78

+ -11

+ •06

+•58

+ •47

0

-•13

+ •06

—16

-1^31

8 30

+ •80

+ -53

-•15

+ •78

+ •30

0

-•32

-•01

-•26

-1-21

9 30

+ •24

+ ^62

+ •31

+ •21

+ •02

0

— •23

-•37

+ •02

-1^21

10 30

+ •35

+ ^20

+ •13

— •02

-•29

0

—56

— •32

-•54

-P49

11 30

-•24

+ ^62

— •02

+ •49

+ •18

0

-•26

-•07

-•32

— 1^29

j 3^ S.Dec.

6° S. Dec.

9° S. Dec.

12° S. Dec.

15° S. Dec.

18° S. Dec.

21° S. Dec.

24° S. Dec.

27° S. Dec.

30

+ •35

-•19

+ •21

+ •19

0

-•26

-1-09

-1^78

- ^98

1 30

+•07

—16

+ •20

+ •23

0

-•01

-M7

-1^76

- -75

2 30

+ •06

+ •19

+ •14

+ •13

0

+ •26

— M3

— 1^46

— ^55

3 30

+ •15

+ •28

+ •41

+ •24

0

+ •34

- -60

- -90

- •SI

4 30

+ •29

+ •29

+ •06

—•01

0

-•27

- ^75

-M5

— ^50

5 30

—•31

00

—•30

—17

0

— •42

-2-32

— 1^53

- -86

6 30

+ •30

+ •22

+ •39

-•10

0

+ •19

-1^21

— 1^42

-MO

7 30

+ •35

+ •30

— 11

— •03

0

00

-1^02

-1^34

— 1-08

8 30

-•38

+ •34

+ •37

+ •16

0

+ •13

- ^89

- -95

- ^61

9 30

+ •22

+ •30

+ •60

+ •02

0

+ •09

- -60

- -95

- ^79

10 30

+ •13

+ •39

+ •07

+ •19

0

-•07

- -89

-1^44

-Ml

11 30

+ •36

+ •63

+ •78

+ •21

0

+ •08

— -80

-1^07

- -99

Table XVIII.

Showing the Difference between the Height of High Water and the Height corre-
sponding to fifteen degrees of the Moon's Declination, for every three degrees of
her Declination north or south.

Moon's

O^Dec.

3° Dec.

6° Dec.

9= Dec.

12° Dec,

15^ Dec.

180 Dec.

2P Dec.

24^ Dec.

27° Dec.

Tiansit.

h m

feet.

feet.

feet.

feet.

feet.

feet.

feet.

feet.

feet.

feet.

30

+ •44

+ •43

+ •08

+ •25

+ •20

0

—49

— •54

-1^07

— 1^22

1 30

+•35

+ •38

+ •58

+•37

+ •23

0

-•23

-•68

- ^84

-M3

2 30

+•27

+ •53

+ •50

+ •32

+ •31

0

+ •04

—•44

- ^49

- ^73

3 30

+ •50

+ •22

+ •29

+ •35

+ •09

0

+ •08

— •28

- r30

- ^65

4 30

+ •15

+ •41

+ •35

+ •09

+ •11

0

-•36

-•24

- ^37

- ^72

5 30

+ •52

+ •08

+ •32

+ •16

+ •11

0

—•38

—•54

- ^61

— ^82

6 30

+ •63

+ •59

+ •32

+ •41

+ •01

0

-•10

-•65

- -76

-1^30

7 30

+ •52

+ •73

+ •68

+ •23

+ •20

0

-•07

—•48

- ^75

-1^20

8 30

+•71

+ •08

+ •24

+ •58

+ •23

0

-•09

-•45

- -62

- -91

9 30

+ •14

+ •41

+ •35

+ •40

+ •01

0

-•07

-•48

- ^47

— 1^00

10 30

+ •33

+ •17

+ •23

+ •03

-•04

0

-•31

-•60

- ^99

-1-29

11 30

—39

+ •49

+ •39

+ •64

+ •19

0

—09

—•43

- ^70

— 1^23

MR. LUBBOCK ON TIDE OBSERVATIONS.

293

Table IV. has been formed on the supposition that Mr. Hutchinson's clock was
regulated according to Apparent Solar Time. The following

Table XIX.
Results from Table I., if Mr. Hutchinson's clock was regulated according to Mean
Solar Time, showing the Difference in the Interval between the Mean Solar Time
of the Moon's Transit and the Time of High Water, and the Mean Interval, for
every month in the year.

Moon's
Transit.

January.

February.

March.

April.

May.

June.

July.

August.

Sept.

October.

Nov.

Dec.

h m

m

m

m

m

m

m

m

m

m

m

m

m

30

-13-3

-13-7

- 6-5

+ 2-8

+ 3-9

— 3-2

- 8-5

- 3-4

+ 8-5

+ 16-7

+ 16-2

0-0

1 30

-11-2

- 7-3

- 5-6

+ 0-7

+ 1-6

- 4-8

- 7-7

+ 0-3

+ 7-3

+ 15-6

+ 12-9

- 1-6

2 30

- 7-7

-10-1

— 4-5

— M

— 2-2

- 4-7

- 4-3

+ 3-3

+ 9-2

+ 12-4

+ 9-5

+ 0-3

3 30

— 4-5

- 9-2

- 7-6

— 1-4

— 2-5

— 2-0

+ 0-8

- 0-1

+ 8-3

+ 9-3

+ 7-6

+ 1-2

4 30

— 1-3

— 10-2

-11-2

-8-5

- 2-5

+ 2-4

-f 5-6

+ 3-7

+ 3-8

+ 6-1

+ 7-2

+ 5-4

5 30

+ 1-2

— 11-5

— 15-5

-9-8

+ 0-1

+ 8-8

+ 6-5

+ 2-0

-0-8

+ 3-5

+ 9'^

+ 12-0

6 30

- 1-4

-17-8

-19-1

-8-7

+ 5-0

+ 12-2

+ 5-9

- 6-3

-3-5

+ 2-8

+ 14-8

+ 16-4

7 30

- 8-0

— 21-0

-17-4

+ 0-2

4-10-3

+ 10-4

- 7-0

-10-1

-4-1

+ 11-5

+ 22-0

+ 13-7

8 30

— 14-0

-19-5

- 9-8

+ 1-8

+ 8-8

+ 1-9

- 7-9

- 8-7

+ 2-2

+ 17-9

+ 20-5

+ 7-4

9 30

-15-5

— 14-5

- 9-0

-I-3-6

+ 6-0

~ 1-5

- 7-1

- 7-6

+ 4-9

+ 17-5

+ 18-2

+ 1-7

10 30

-15-7

-15-3

— 8-3

+ 4-2

+ 6-7

— 2-3

- 9'^

- 5-8

+ 7-2

+ 18-8

+ 17-7

+ 2-4

11 30

- 7-6

-15-2

- 7-2

+ 4-4

-1- 3-5

- 3-0

-10-0

- 5-6

+ 8-1

+ 17-6

+ 16-0

- 0-1

Table XIII. has been formed upon the supposition that Mr. Hutchinson's clock was
regulated according to Apparent Solar Time. The following

Table XX.

Results from Table X., if Mr. Hutchinson's clock was regulated according to Mean
Solar Time, showing the Difference in the Interval between the Mean So lar Time
of the Moon's Transit and the Time of High Water, and the Interval correspond-
ing to fifteen degrees Declination, for every three degrees of her Declination north
and south.

Moon's

0

3° N. Dec.

6° N. Dec.

9° N. Dec.

12° N. Dec.

153 N. Dec.

18° N. Dec.

! 21° N. Dec.

24° N. Dec.

27° N. Dec.

Transit.

!

h m

m

m

m

m

m

m

m

m

m

m

30

+ 0-5

- 0-9

- 0-8

— 0-1

- 0-8

0

4- 0-3

- 5-7

-10-0

— 4-3

1 30

— 3-5

— 3-1

— 3-3

- 1-9

- 0-8

0

4- 1-9

— 2-4

— 5-1

— 2-1

2 30

- 3-3

— 25

- 1-7

- 2-1

— 0-1

0

4- 3-8

— 1-8

- 3-0

- 1-8

3 30

- 2-4

- 3-2

— 2-0

- 1-6

— 1-3

0

4- 2-3

— 0-4

— 3-3

— 2-4

4 30

+ 0-6

- 2-9

+ 0-8

4- 1-2

4- 0-6

0

— 0-5

- 4-6

- 5-9

- 9-0

5 30

+ 5-6

+ 6-6

+ 6-9

4- 4-9

0

0

- 3-0

— 5-3

-11-6

-14-7

6 30

+ 12-5

+ 7-4

4-10-5

4- 7-7

4- 4-7

0

— 3-8

-11-7

-16-3

-21-0

7 30

+ 8-5

+ 9-9

4- 8-7

-f 6-8

+ 1-3

0

- 7-1

-10-8

-21-2

-20-9

8 30

+ 10-3

+ 9-4

4-10-8

4- 6-3

4- 6-8

0

- 5-1

-13-1

-20-3

— 11-4

9 30

+ 10-2

+ 6-0

4- 8-5

4- 8-1

4- 2-0

0

- 4-3

-10-9

-21-6

- 9-5

10 30

+ 7-3

+ 3-1

4- 4-9

4- 4-2

4- 3-9

0

- 4-0

-11-8

-16-2

-10-2

11 30

+ 1-9

+ 4-3

4- 1-4

4- 2-1

4- 2-7

0

- 2-0

- 9-3

-10-5

- 6-8

3° S. Dec.

6° S. Dec.

9° S. Dec.

12° S. Dec.

15° S. Dec.

13° S. Dec.

21° S. Dec.

24° S. Dec.

27° S. Dec.

30

— 0-1

4- 2-4

+ 2-0

- 0-5

0

-^ 2-2

4- 0-7

+ 2-9

- 6-9

1 30

— 4-1

— 0-4

— 1-2

- 1-0

0

- 1-5

+ 3 5

4- 2-1

- 4-7

2 30

— 2-4

- 1-4

— 0-3

— 1-4

0

4- 1-0

4- 2-0

+ 2-4

~ 3-8

3 30

- 0-4

- 1-5

— 1-5

- 0-9

0

4- ^-9

— 0-4

- 0-7

-10-3

4 30

+ 0-8

4- 1-7

4- 1-4

4- 1-2

0

4- 1-7

- 1-3

- 3-9 :

- 6-4

5 30

+ 7-6

4- 5-1

+ 7-1

4- 2-8

0

— 5-3

- 6-0

-10-3 i

-14-7

6 30

+ 10-0

4-10-9

4- 7-5

4- 3-9

0

- 8-4

- 8-6

-11-3 !

-13-5

7 30

+ 16-7

4-10-8

4-11-6

4- 4-5

0

-10-6

— 15-8

- 6-6

-26-9

8 30

+ 7-8

+13-1

+ 8-1

4- 5-7

0

- 7-8

- -9

- 3-3

— 10-4

9 30

+ 14-1

4-13-0

4- 8-1

4- 3-4

0

-10-6

- 4-6

- 2-3

- 6-9

10 30

+ 5-0

4- 7-9

4- 8-2

4- 4-2

0

- 6-4

- 0-9

— 1-1

-13-5

11 30

+ 9-3

4- 4-5

4- 6-1

4- 3-8

0

4- 3-7

4- 1-8

- 0-6

-12-2

294

MR. LUBBOCK ON TIDE OBSERVATIONS.

Tables to he used in predicting the Time of High JVater at Liverpool,

Table XXI.

Showing the Semimenstrual Inequality + a constant, or the Interval between the
Moon's Transit and the Time of High Water, her Parallax being 57', and her De-
clination 15°. (This Table has been formed by interpolation from the column
corresponding to Parallax 57' in Table VII.)

Moon's

Interval.

Moon's

Interval.

Moon's

Interval.

Moon's

Interval.

Moon's

Transit.

Transit.

Transit.

Transit.

Transit.

h m

h m

h m

h m

h m

h m

h m

h m

h m

h m

0 0

11 25

2 30

10 45

5 0

10 23

7 30

11 16

10 0

11 50

0 10

11 23

2 40

10 43

5 10

10 23

7 40

11 20

10 10

11 49

0 20

11 21

2 50

10 41

5 20

10 23

7 50

11 25

10 20

11 48

0 30

11 18

3 0

10 39

5 30

10 23

8 0

11 30

10 30

11 47

0 40

11 16

3 10

10 37

5 40

10 24

8 10

11 34

10 40

11 44

0 50

11 13

3 20

10 35

5 50

10 26

8 20

11 39

10 50

11 41

1 0

11 10

3 30

10 33

6 0

10 28

8 30

11 44

11 0

11 39

1 10

11 8

3 40

10 32

6 10

10 32

8 40

11 46

11 10

11 37

1 20

11 5

3 50

10 31

6 20

10 36

8 50

11 48

11 20

11 35

1 30

11 2

4 0

10 30

6 30

10 40

9 0

11 50

11 30

11 32

1 40

11 0

4 10

10 28

6 40

10 46

9 10

11 51

11 40

11 30

1 50

10 57

4 20

10 26

6 50

10 52

9 20

11 51

11 50

11 28

2 0

10 54

4 30

10 25

7 0

10 58

9 30

11 52

2 10

10 51

4 40

10 24

7 10

11 4

9 40

11 52

2 20

10 48

4 50

10 24

7 20

11 10

9 50

11 51

Table XXII.

Showing the Semimenstrual Inequality -\- a constant, or the Height of High Water
at Liverpool, the Moon's Parallax being b7', and her Declination 15°, from the
Sill of the Old Dock Gates.

Moon's

Height of

Moon's

Height of

Moon's

Height of

Moon's

Height of

Moon's

Height of

Transit.

High Water.

Transit.

High Water.

Transit.

High Water.

Transit.

High Water.

Transit.

High Water.

h m

feet.'

h m

feet.

h m

feet.

h m

feet.

h m

feet.

0 0

17-25

2 30

17-04

5 0

14-12

7 30

12-33

10 0

15-40

0 10

17-35

2 40

16-90

5 10

13-90

7 40

12-40

10 10

15-60

0 20

17-45

.2 50

16-75

5 20

13-65

7 50

12-55

10 20

15-80

0 30

17-53

3 0

16-60

5 30

13-39

8 0

12-70

10 30

16-00

0 40

17-55

3 10

16-45

5 40

13-21

8 10

12-90

10 40

16-20

0 50

17-57

3 20

16-30

5 50

13-05

8 20

13-10

10 50

16-35

1 0

17-59

3 30

16-17

6 0

12-90

8 30

13-36

11 0

16-50

1 10

17-61

3 40

15-95

6 10

12-77

8 40

13-60

11 10

16-68

1 20

17-62

3 50

15-73

6 20

12-65

8 50

13-80

11 20

16-85

1 30

17-63

4 0

15-51

6 30

12-53

9 0

14-10

11 30

17-00

1 40

17-59

4 10

15-30

6 40

12-44

9 10

14-30

11 40

17-10

1 50

17-50

4 20

15-10

6 50

12-40

9 20

14-55

11 50

17-20

2 0

17-40

4 30

14-89

7 0

12-37

9 30

14-79

2 10

17-30

4 40

14-60

7 10

12-34 1

9 40

15-00

2 20

17-17

4 50

14-37

7 20

12-32

9 50

15-20

MR. LUBBOCK ON TIDE OBSERVATIONS.

295

The two following Tables have been made by arbitrary alterations in Tables VIII.
and XI., in order to get rid of the irregularities, and may, I think, be considered a^
showing the effect of changes in the Moon's parallax upon the tides at Liverpool.

Table XXIII.

Showings the Correction for the Moon's Parallax in the Time of High Water at

Liverpool.

Moon's
Transit.

H. P. 54'.

H. P. 55'.

H. P. 56'.

H. P. 57'.

H. p. 58'.

H. p. 59'.

H. P. 6(y.

m

m

m

m

m

m

m

m

0

+ 8

+ 5

+ 2

0

— 2

— 5

- 8

1

+ 7

+ 4

+ 2

0

- 2

— 4

- 7

2

+ 5

+ 3

+ 1

0

— 1

— 3

- 5

3

+ 3

+ 2

+ 1

0

— 1

— 2

— 3

4

+ 2

+ 1

+ 0

0

0

— 1

- 2

5

+ 2

+ 1

+ 0

0

0

— 1

- 2

6

+ 4

+ 2

+ 1

0

— 1

- 2

- 4

7

-f 10

+ 6

+ 3

0

— 3

- 6

- 10

8

+ 15

+ 10

+ 5

0

— 5

- 10

- 15

9

+ 15

+ 10

+ 5

0

- 5

- 10

— 15

10

+ 12

+ 8

+ 4

0

— 4

- 8

— 12

11

+ 10

+ 6

+ 3

0

— 3

- 6

-:o

Table XXIV.

Showing the Correction for the Moon's Parallax in the Height of High Water at

Liverpool.

Moon's
Transit.

H, P. 54'.

H. P. 55'.

H. P. 56'.

H. P. 57'.

H. p. 58'.

H. P. 59'.

H. P. 60'.

h

feet.

feet.

feet.

feet.

feet.

feet.

feet.

0

-M5

- -76

-•38

0

+ •38

+ -76

+ M5

1

— 1-25

- -82

— •41

0

+ •41

+ ^82

+ 1^25

2

-1-40

- -92

-•46

0

+ •46

+ -92

+ 1^40

3

— 1-50

— 1-00

-•50

0

+ •50

+ 1^00

+ 1-50

4

— 1-50

— 1-00

-•50

0

+ •50

+ 1-00

+ 1^50

5

— 1-50

-1-00

-•50

0

+ •50

+ 1^00

+ 1^50

6

— 1-50

— 1-00

-•50

0

+ •50

+ 1^00

+ 1^50

7

— 1-45

- -98

-•48

0

+ •48

+ -96

+ 1-45

8

— 1-35

- -90

—•45

0

+ •45

+ -90

+ 1-35

9

-1-30

- -86

-•43

0

+ •43

+ ^86

+ 1^30

10

— 1-25

- -82

— •41

0

+ •41

+ •SS

+ 1^25

11

— 1-20

- -80

— •40

0

+ •40

+ ^80

+ 1^20

MDCCCXXXV.

2Q

296

MR. LUBBOCK ON TIDE OBSERVATIONS.

The following Table has heen formed from Table XIV.

Table XXV.

Showing the Correction for the Moon's Declination in the Time of High Water at
Liverpool, if Mr, Hutchinson's Clock was regulated according to Apparent Solar
Time.

Moon's

QODec,

3° Dec.

6° Dec.

9° Dec.

12° Dec.

15° Dec.

18° Dec.

21° Dec.

24° Dec.

27° Dec.

Iransit.

h

m

m

m

m

m

m

m

m

m

m

0

+ 4

+ 3

+ 2

+ 1

+ 1

0

— 1

- 3

- 5

- 7

1

+ 5

+ 4

+ 2

+ 2

+ 1

0

- 2

— 4

- 6

- 8

2

+ 6

+ 4

+ 3

+ 2

+ 1

0

— 2

- 4

- 6

- 9

3

+ 7

+ 5

+ 3

+ 2

+ 1

0

- 2

— 4

- 7

-10

4

+ 9

+ 7

+ 5

+ 3

+ 1

0

- 3

- 6

- 9

— 13

5

+ 11

+ 8

+ 6

+ 4

+ 2

0

- 4

- 8

— 12

-16

6

+ 13

+ 10

+ 7

+ 4

+ 2

0

- 4

— 8

-13

-18

7

+ 9

+ 7

+ 5

+ 3

+ 1

0

— 4

- 8

-13

-18

8

+ 6

+ 4

+ 3

+ 2

+ 1

0

— 4

- 8

-12

-17

9

+ 4

+ 3

+ 2

+ 1

+ 1

0

— 1

- 3

- 5

- 7

10

+ 3

+ 2

+ 1

+ 1

+ 1

0

— 1

- 2

— 3

— 4

11

+ 3

+ 2

+ 1

+ 1

+ 1

0

— 1

- 2

- 3

— 4

The following Table has been formed from Table XVIII. Although it would seem
from Table XVII. that a difference does exist in the correction for north and south de-
clination, yet the numbers in the latter Table are so irregular as almost to defy any at-
tempt to reduce them to uniformity.

Table XXVI.

Showing the Correction for the Moon's Declination in the Height of High Water at

Liverpool.

Moon's
Transit.

OODec.

3° Dec.

6' Dec.

9° Dec.

12° Dec.

15° Dec.

18° Dec.

21° Dec.

24° Dec.

29° Dec.

h

feet.

feet.

feet.

feet.

feet.

feet.

feet.

feet.

feet.

feet.

0

+ •40

+ •32

+ •24

+•16

+ •08

0

—25

-•50

-•75

-1-00

1

+ •55

+ •44

+ •33

+ •22

+ •11

0

— •25

-•50

—75

— 1-00

2

+•64

+ •52

+ •39

+ •26

+ •13

0

-•19

-•37

—56

- ^75

3

+ •60

+ •48

+ •36

+ •24

+ •12

0

-•12

—•25

—37

- -50

4

+ •40

+ •32

+ •24

+ •16

+ •08

0

-•10

-•20

-•30

- ^40

5

+ •38

+ •29

+ •21

+ •14

+ •07

0

-•16

— •32

—•48

- ^65

6

+ •50

+ •40

+ •30

+ •20

+ •10

0

-•21

-•42

—63

— ^85

7

+ •70

+ •56

+ •42

+•28

+ •14

0

— •22

—•44

-•66

- •go

8

+ •60

+ •48

+ •36

+ •24

+ •12

0

-•20

-•40

—60

- -80

9

+ •50

+ •40

+ •30

+ •20

+ •10

0

—•14

— •28

— •42

- ^55

10

+ •40

+ •32

+ •24

+ •16

+ •08

0

-•14

-•28

-•42

- -55

11

+ •30

+ •24

+ •18

+ •12

+ •06

0

-•17

-•34

-•51

- -70

MR. LUBBOCK ON TIDE OBSERVATIONS. 297

Index to the Tables formed from Mr. Hutchinson's Observations,

In forming these Tables it has been assumed that the Observations were recorded in
Apparent Solar Time. The Time of the Moons Transit at Greenwich, which constitutes
the principal argument of the Tables, is always given in Apparent Solar Time.

Table I., showing the Interval between the Apparent Solar Time of the Moon's
Transit and the Time of High Water, and the Height of High Water at the Liver-
pool Old Docks (as recorded by Mr. Hutchinson), corresponding to the Apparent
Solar Time of the Moon's Transit, in each month of the year. (If Mr. Hutchinson's
clock was regulated according to mean solar time, the interval must be diminished
by the equation of time given at foot of each month.)

Table II. (Interpolated from Table I.), showing the Interval between the Apparent
Solar Time of the Moon's Transit and the Time of High Water at Liverpool Old
Docks, for each month in the year.

Table III. (Interpolated from Table I.), showing the Height of High Water at
Liverpool Old Docks, corresponding to the Apparent Solar Time of the Moon's
Transit, in each month of the year.

Table IV., showing the Difference in the Interval between the Apparent Solar
Time of the Moon's Transit and the Time of High Water, and the Mean Interval,
for every month in the year.

Table V., showing the Difference in the Height of High Water and the Mean
Height for every month in the year.

Table VI., showing the Interval between the Apparent Solar Time of the Moon's
Transit and the Time of High Water, and the Height of High Water at the Liver-
pool Old Docks, corresponding to the Apparent Solar Time of the Moon's Transit,
for every minute of her Horizontal Parallax.

Table VII. (Interpolated from Table VI.)

Table VIII., showing the Difference in the Interval between the Time of the Moon's
Transit and the Time of High Water, and the Interval corresponding to fifty-seven
minutes of the Moon's Horizontal Parallax.

Table IX., showing the Difference between the Height of High Water and the
Height corresponding to fifty-seven minutes of the Moon's Horizontal Parallax.

Table X., showing the Interval between the Apparent Solar Time of the Moon's
Transit and the Time of High Water, and the Height of High Water at the
Liverpool Old Docks, corresponding to the Apparent Solar Time of the Moon's
Transit, for every three degrees of her Declination north and south. The Equation
of Time to be added to Apparent Time. (In forming this Table, it has been assumed
that Mr. Hutchinson's clock was regulated according to apparent solar time ; if it
was regulated according to mean solar time, the interval must be diminished by the
equation of time given in the third column.)

2 q2

298 MR. LUBBOCK ON TIDE OBSERVATIONS.

Table XI. (Interpolated from Table X.), showing the Interval between the Apparent
Time of the Moon's Transit and the Time of High Water at the Liverpool Old Docks
for every three degrees of her Declination north and south.

Table XII., showing the Interval between the Apparent Time of the Moon's Transit
and the Time of High Water at the Liverpool Old Docks for every three degrees of
her Declination north or south.

Table XIII., showing the Difference in the Interval between the Apparent Solar
Time of the Moon's Transit and the Time of High Water, and the Interval corre-
sponding to 15° Declination, for every three degrees of her Declination north and south.

Table XIV., showing the Difference in the Interval between the Apparent Solar
Time of the Moon's Transit and the Time of High Water, and the Interval corre-
sponding to 15° Declination, for every three degrees of her Declination north or south.

Table XV. (Interpolated from Table X.), showing the Height of High Water at
the Liverpool Docks for every three degrees of the Moon's Declination north and
south.

Table XVI., showing the Height of High Water at the Liverpool Docks for every
three degrees of the Moon's Declination north or south.

Table XVII., showing the Difference between the Height of High Water and the
Height corresponding to fifteen degrees of the Moon's Declination, for every three
degrees of her Declination north and south.

Table XVIII., showing the Difference between the Height of High Water and the
Height corresponding to fifteen degrees of the Moon's Declination, for every three
degrees of her Declination north or south.

Table XIX. results from Table I., if Mr. Hutchinson's Clock was regulated ac-
cording to Mean Solar Time, showing the Difference in the Interval between the
Mean Solar Time of the Moon's Transit and the Time of High Water, and the Mean
Interval, for every month in the year.

Table XX. results from Table X., if Mr. Hutchinson's Clock was regulated ac-
cording to Mean Solar Time, showing the Difference in the Interval between the
Mean Solar Time of the Moon's Transit and the Time of High Water, and the In-
terval corresponding to 15° Declination, for every three degrees of her Declination
north and south.

Table XXL, showing the Semimenstrual Inequality -j- a constant, or the Interval
between the Moon's Transit and the Time of High Water, her Parallax being 57',
and her Declination 15°. (This Table has been formed by interpolation from the
column corresponding to Parallax 57' in Table VII.)

Table XXII., showing the Semimenstrual Inequality -f a constant, or the Height
of High Water at Liverpool, the Moon's Parallax being 57', and her Declination 1^°,
from the Sill of the Old Dock Gates.

Table XXIII., showing the correction for the Moon's Parallax in the Time of
High Water at Liverpool.

MR. LUBBOCK ON TIDE OBSERVATIONS. 299

Table XXIV., showing the Correction for the Moon's Parallax in the Height of
High Water at Liverpool.

Table XXV., showing the Correction for the Moon's Declination in the Time of
High Water at Liverpool, if Mr. Hutchinson's Clock was regulated according to
Apparent Solar Time.

Table XXVI., showing the Correction for the Moon's Declination in the Height of
High Water at Liverpool.

[ 301 ]

XVI. Remarks on the difficulty of distinguishing certain Genera of Testaceous
Mollusca by their Shells alone, and on the Anomalies in regard to Habitation
observed in certain Species. By John Edward Gray, Esq. F.R.S. S^c.

Received June 11, — Read June 18, 1835.

It has been a very common error, both among conchologists and geologists, to re-
gard all shells in which no remarkable difference of form and character can be distin-
guished as inhabited by one and the same genus of animals ; and not less usual to
assume that all the species of the same genus inhabit similar localities. Many geo-
logists have still further enlarged the boundaries of error, by taking for granted that
all the fossil species of shells which are referrible by the characters of the shell to
recent genera, must have been formed by animals which, in their recent state, pos-
sessed the same habits as the most commonly observed species of the genus to which
they appear to belong. These theories were, indeed, quite consistent with our former
ignorance of the habits of the animals of this class ; but since the works of Poli,
MiJLLER, Montagu, Lamarck, and Cuvier have induced zoologists again to turn
their attention, as was the practice among the older writers, to the animals of shells,
and their habits, and no longer to confine themselves, as was too often the case with
the followers of the Linnean system of conchology, to the study of the shells as mere
pieces of ornament, classed without reference to their inhabitants, the acknowledged
importance of the subject is daily bringing to our knowledge some animal unknown
before, and adding to our stock of information facts which prove the fallacy of the
opinions so hastily taken up. Thus, although even at the present day the animals of
less than one twentieth part of the well-known species of shells have been observed,
— and of those which are known the greater part have been very imperfectly de-
scribed,— numerous exceptions to the theories in question have been brought to
light, which deserve to be collected into one point of view, and made the subject of
serious consideration.

The exceptions which it is the object of the present paper to notice may be ar-
ranged under the two following heads :

1. Shells having every appearance of belonging to the same natural genus, but in-
habited by animals of a very different character.

2. Species of testaceous Mollusca living in very different situations from the majo-
rity of the known species of the genus to which they belong, or having the faculty of
maintaining their existence in several different situations.

These two classes of exceptions I shall proceed to notice in detail.

302 MR. GRAY ON TESTACEOUS MOLLUSCA.

1 . Of Shells apparently similar, hut belonging, on a comparison of their Animals, to

very different Genera.

In a note on my former paper on the structure of shells *, I pointed out the per-
plexity in which the extreme similarity of the shells belonging to the genera Patella
and Lottia must involve the geologist and the conchologist, intending at some future
time to pursue the subject further, and to show that similar difficulties existed in re-
gard to several other genera. The two genera above referred to are probably, how-
ever, the most remarkable example of this complete resemblance, on account of the
extreme dissimilarity of their animals, which are referrible to two very different
orders of Mollusca, while the shells are so perfectly alike, that after a long-continued
study of numerous species of each genus, I cannot find any character by which they
can be distinguished with any degree of certainty. Both genera present a striking
discrepancy from all other univalve shells, in having the apex of the shell turned to-
wards the head of the animal, the genera to which they are immediately related in
both the orders to which they belong offering no variation in this respect from the
usual structure of the class. The agreement in the internal structure of their shells
is equally complete ; yet the animal of Patella has the branchiae in the form of a
series of small plates disposed in a circle round the inner edge of the mantle, while
that of Lottia has a triangular pectinated gill seated in a proper cavity formed over
the back of the neck within the mantle, agreeing in this respect with the inhabitants
of the Trochi, Monodontoe, and Turbines, from which it differs so remarkably in the
simple conical form of its shell. This difference in the respiratory organs of animals
inhabiting shells so strikingly similar is the more anomalous, inasmuch as those
organs commonly exercise great influence on the general form of shells ; a circum-
stance readily accounted for when we reflect that a principal object of the shell is to
afford protection to those delicate and highly important parts.

To the practical conchologist it will be sufficient to mention Pupa and Vertigo,
Vitrina and Nanina, Rissoa and Truncatella, as affording numerous and perplexing
instances of the difficulty of distinguishing between genera of shells, inhabited by
very different animals.

A similar difficulty exists with regard to Siphonaria and Ancylus, genera belonging
to two different families, one inhabiting the sea-shores, while the other lives in rivers
and brooks. The only distinction between the shells of these two genera consists in
the Ancyli being generally of a thinner substance than the Siphonarice ; but this is
by no means an adequate character, some species of Siphonaria {S. Tristensis, for
example,) being quite as thin in texture as any Ancylus. Both have the muscular
impression interrupted by the canal through which the air passes to the respiratory
organs ; yet the animal of Ancylus has long tentacles, and eyes placed as in the
Lymncece, to which it is closely allied, while Siphonaria has no distinct tentacles, and

* Philosophical Transactions, 1834, p. 800.

MR. GRAY ON TESTACEOUS MOLLUSCA. 303

in these respects agrees with the equally marine genus Amphihola, confounded by
Lamarck with the Ampullariw.

About fifteen years since, I first observed, in the marshes near the banks of the
Thames between Greenwich and Woolwich, in company with species of Valvata,
Bithynia, and Pisidium, a small univalve shell, agreeing with the smaller species of the
littoral genus Littorina in every character both of shell and operculum ; yet this very
peculiar and apparently local species has an animal which at once distinguishes it
from the animal of that genus, and from all other Ctenobranchous Mollusca. Its
tentacles are very short and thick, and have the eyes placed at their tips ; while the
Littorince, and all the other animals of the order to which they belong, have their
eyes placed on small tubercles on the outer side of the base of the tentacles, which
are generally more oi* less elongated. The shell in question and its animal were
described and figured by Dr. Leach, in his hitherto unpublished work on British
Mollusca, under the name oi Assiminia Qrayana ; and as this name has been referred
to by Mr. Jeffries and other conchologists, it may be regarded as established, and
that of Syncera hepatica, proposed by myself in the Medical Repository, vol. x, p. 239,
will take the rank of a synonym. A second species of this genus, has lately been
made known by Mr. Benson, by whom it was found in ponds in India. Its shell is
banded like that of Littorina A-fasciata and several others of the smaller Littorince,
and had been figured in the Supplement to Wood's Catalogue, t. 6. f. 28, under the
name of Turbo Francesice.

Taking this in conjunction with the preceding, we have here two instances of uni-
valve shells apparently belonging to the same genus, the one found in fresh and the
other in salt water, but proving, when their animals are examined, to belong to genera
essentially distinct. My next illustration will show that a similar fact has been ob-
served among the bivalves.

The Mytilus polymorphus of Chemnitz is truly a freshwater species, having been
first observed in the Wolga by the illustrious Pallas. It has recently been intro-
duced, doubtless with the Russian timber, (for this species, in common with the Am-
pullarice, Paludince, and Neritince of fresh water, and the Littorince, Monodontce, and
Cerithia of salt, has the faculty of living for a very long time out of water,) into the
Lake of Haarlem and the Commercial Docks at Rotherhithe ; in both of which it
appears to increase with great rapidity. I am aware that Mr. Lyell has given an-
other explanation of the mode of introduction of this remarkable species ; but from
experiments which I have myself made on the animal's power of living out of water,
I cannot hesitate in giving the preference to the suggestion advanced above, rather
than supposing it to have made its passage from one river to the other, across the sea,
attached to the bottom of a vessel. The shell in question differs from the shells of
other Mytili in no character of more than specific importance ; but the animal is
essentially distinct. In the genus Mytilus the lobes of the mantle are free throughout
nearly their whole circumference, as in Unio, Cardita, Pecten, Ostrea, &c. ; while in

MDCCCXXXV. 2 R

304 MR. GRAY ON TESTACEOUS MOLLUSCA.

the animal of Mytilus polymorphus they are united through nearly their whole extent,
leaving only three small apertures, one for the passage of the foot and beard, and the
other two for the reception and rejection of the water, from the contents of which the
animal derives its sustenance. This shell must consequently form a new genus, to
which the name of Dreissena has been appropriated by Van Beneden *. As a proof
of the importance attached to this character, it may be observed that Cuvier con-
sidered the adherence or non-adherence of the lobes of the mantle so essential a
distinction as to found on it his division of the bivalves into families. In his system,
therefore, the genus Dreissena would be placed with the family of Chamacdes, while
the genus Mytilus forms the type of the preceding family of Mytilacdes. The genus
Iridina, however, and one or two others, show that this character cannot be implicitly
relied on for the natural classification of animals of this class, although it forms a
very good generic mark of distinction.

The genus Iridina^ above referred to affords a second instance of this anomaly;
for though the animals of the Iridina and Anodontcp. differ in the adhesion and non-
adhesion of the lobes of the mantles, yet the shells are so alike that they cannot be
distinguished by any external character ; so much so, that one of the species now
referred to the genus by M. Deshayes, who first pointed out this peculiarity in the
animal, was considered as an Anodon by Lamarck.

The animals of Cytherea, Venus, and Venerupis have, like those of most of the allied
genera, a lanceolate foot projecting at the anterior part of the shell ; while the genus
Artemis of Poli, which has generally been confounded with Cytherea, from which it
is not easily to be distinguished except by its usually more rounded form, is provided
with a crescent-shaped foot, exserted at the middle of the lower edges of the valves.

Again, there is but little difference in external characters and habit between Cy-
clas and Pisidium ; but the animals of the latter have elongated siphons which are
not found in the former.

In reference to Univalves it may also be observed, that it is frequently impossible
to distinguish some of the genera of that class without an examination of their oper-
cula. This is the case, for instance, as regards the smaller and more solid Paludince,
inhabitants of fresh water, and some species of Liftorina living on the coast ; several
of the shells described as Paludince by Draparnauld and others appearing rather to
.belong to the latter genus. A similar difficulty exists with respect to other Littorince
as distinguished from Phasianella, and with the Neritince as distinguished from the
Neritce. In the latter case the characters derived from the operculum are so essential

* Institut, 1835, p. 130; and Annales des Sciences Naturelles, N. S., tom.iii. p. 193.

t Lamarck formed this genus on a specimen which had its hinge margin accidentally tubercular and slightly,
crenated; but this character is not found in most of the specimens of the species which he describes. The
English conchologists, misled by this character, have referred to the genus a very different African shell, with a
long series of transverse teeth on the hinge margin, which has lately been separated by Mr. Conrad under the
name of Pleiodon.

MR. GRAY ON TESTACEOUS MOLLUSCA. 305

to the discrimination of the two genera, that M. Rang, looking only to the characters
of the shell, has proposed to reunite them into one. In proof of the little attention
that has hitherto been paid to this very important part, I may mention that three
species referred by Lamarck to the genus Solarium are each furnished with a different
kind of operculum ; and it is deserving of notice that the Monodonta canaliculata,
according to the observations of M. Quoy, has an operculum very different from the
rest of the shells of that genus.

In some shells, again, the differences in character are so slight as almost to throw
an air of ridicule on the attempt to separate them generically from the structure of
the shells alone ; and yet when the animal is examined the necessity of their sepa-
ration becomes so obvious as to be immediately acknowledged. This is especially
the case with my genus Bullia compared with Terehra : the shells of these two ge-
nera are so similar, that Lamarck and all other conchologists have retained them in
one group, no other distinction being observable except that in the former there is a
more or less distinct callous band winding round the volutions just above the suture,
and produced by a slight extension of the inner lip beyond the part of the shell oc-
cupied by the whorl. This extension of the lip is probably deposited by the foot of
the animal, which in the genus Bullia is very large and expanded, while that of Te-
rehra is small and compressed. This, however, is not the only difference between the
two animals, that of the former genus having rather large and eyeless tentacles, while
the Terehrce have very small and short tentacles, bearing the eyes near their tips.

A second example of a similar kind is derived from the genus Rostellaria, in which
Lamarck includes the Stromhus Pes Pelecani of Linnaeus. The animal of this shell
has been figured by Muller, and very much resembles that of Buccinum, having
long slender tentacles with the eyes sessile on the outer side of their base ; while, as
Dr. RuppELL informs me, the Rostellaria curvirostris has an animal allied to Stromhus,
with the eyes on very large peduncles, which give off from the middle of one of their
sides the small tentacles. Notwithstanding this difference in the form of their ani-
mals, I am not, however, aware of any essential character by which the shell of
Aporrhais (as the Stromhus Pes Pelecani has been generically named) can be distin-
guished from the other Rostellarice.

With all this uncertainty with regard to the generic characters of the recent spe-
cies of shells, of which the animals can be subjected to examination, how much must
the difficulty of deciding their genera with certainty be enhanced with reference to
the fossil species, and especially to those which have no strictly analogous form ex-
isting in the recent state. Considerations like these tend greatly to disturb the con-
fidence formerly reposed in the opinion that every difference in the form and structure
of the animal was accompanied by marks permanently traced upon the shell, by
which it might be at once distinguished, and which it was therefore the great object
of the conchologist to point out. But another source of error, particularly interesting
to the geologist, is included under my second head, to the elucidation of which I

shall now proceed.

2 r2

306 MR. GRAY ON TESTACEOUS MOLLUSCA.

2. Of Species belonging to the same natural Genus, inhabiting essentially different

situations.

The general belief that all the species of the same genus inhabit the same kind of
situation, undoubtedly holds good with reference to most of the genera of shells ;
but many exceptions have already been observed, and we may anticipate that many
more will be discovered as the natural habits of the different species become better
known. In bringing together a number of these exceptions, I have been under the
necessity of placing considerable reliance on the observations of others, who have
noted in foreign countries facts similar to those which I have myself witnessed at
home ; but these observations have been chiefly collected from the works of Pro-
fessor NiLssoN of Sweden, of Mr. Say of the United States of North America, and
of MM. Lesson, Quoy, and Rang of Paris, writers who, from their extensive know-
ledge of conchology, are fully capable of accurately recording their observations, and
whose statements may therefore be received as deserving of the most implicit confi-
dence. It is moreover to be observed, that all their observations on this subject were
made simply with the view of extending the knowledge of the history of the species
to which they refer, and without reference to the establishment of any preconceived
theory.

These observations may be classed under the four following subdivisions : 1 st, where
species of the same genus are found in more than one kind of situation, as on land,
in fresh and in salt water ; 2nd, where one or more species of a genus, most of whose
species inhabit fresh water, are found in salt or brackish water ; 3rd, where, on the
contraiy, one or more species of a genus, whose species generally inhabit the sea, are
found in fresh water ; and 4th, where the same species is found both in salt and fresh
water.

Of the first of these classes the genus Auricula, as defined by Lamarck, may be
quoted as a striking example. Of its species, A. Scarahus and A. minima are found
in damp places on the surface of the earth ; A. Judce lives in sandy places overflowed
by the sea ; A. Myosotis, A. coniformis, A. nitens, &c. (separated by De Montfort
under the name of Conovulus,) are found only in the sea in company with Chitons,
Littorince, and other truly marine shells ; and the South American species which I
distinguished some time since under the name of Chilina, including A. Dombeyi of
Lamarck, and A. Jluviatilis of Lesson, inhabit freshwater streams, having most of
the habits of the Lymncece. This disparity of habitation has been in some degree
overcome by dividing the genus into several, as noticed above ; but the characters
employed for their distinction are very slight, and species apparently intermediate
between them are constantly occurring.

The genus Lymnaea has usually been considered as confined to fresh water ; but
M. NiLssoN describes a species under the name of L, Balthica, which is found " in
aqua par^m salsa Maris Balthici ad littora Gothlandise et Scaniae, &c. In maris juxta
Esperod fucis et lapidibus adhserens frequenter obvenit simul cum Paludind Balthicd
et Neritind Jiuviatili ;" and a second under the name of Lymnoea succinea, which is

MR. GRAY ON TESTACEOUS MOLLUSCA. 307

fotind on the shores of the sea near Trelleborg. All the species of Paludina and Bithy-
nia which have fallen under my own observation are essentially fluviatile ; but M.
NiLssoN refers in the paragraph above quoted to a species of the former genus inhabit-
ing the sea. This may, however, like some of the smaller Paludinoe of Draparnauld,
be truly a Littorina, having a horny and spiral, and not an annular, operculum.

According to the observations of my sister, Mrs. Ince, of Mr. Benson, of MM.
Quovand Gaimard, and of M. Lesson, the Indian species of Neritina, like the Euro-
pean, are found only in fresh water ; yet M, Rang, in his Manuel des MoUusques,
p. 193, states that the Neritina viridis is a marine species found on rocks covered by
the sea at Martinique, and that a larger variety of this species is found in similar
situations at Madagascar ; General Hardwicke marks on his drawing of the Neritina
crepidularis, that it was found in "saltwater lakes, April 1816;" and Say has de-
scribed the Neritina Meleagris of Lamarck {Theodoxus reclinatus, Say,) as living both
in fresh and salt water. This is most probably the species to which Mr. Guilding
refers*, when he observes that he has kept Neritina for some time alive in a close
vessel of salt water, which they appear to purify. The animals of some of the tro-
pical species often quit the stream and crawl up the trunks of neighbouring trees, on
which, like the species of Littorina^ Planaxis, and Bulla, which creep up the rocks on
the sea-coast, they attach themselves, and remain exposed to the influence of the
sun. It may be added, that M. Rang has found Neritina Auricula in brackish
marshes near the sea in the Island of Bourbon, in company with Aviculce and Aply-
sice ; and I have little doubt that Neritina Pupa inhabits the sea, it being uniformly
brought to this country in company with marine shells.

Many species of Melania, as, for example, M. amarula, M. fasciolata, and M. lineata,
are found in the freshwater streams of India and its islands. Mr. Say mentions
species found in similar situations in North America ; he also describes one {M. sim-
plex) as found in a stream running through the saltwater valley near the salt-works,
but does not state whether the water of the stream is salt or fresh. On the other
hand, M. Quoy asserts that they are sometimes taken in brackish water ; M. Cail-
LiAUD states that Melania Oweni is found in brackish water ; and M. Rang has
found other species in the Island of Bourbon under the same circumstances with the
Neritina just adverted to. The genus Melanopsis has the same habits ; its species
are often found in large inland lakes. I have myself received M. huccinoidea from
the sea of Galilee ; and Dr. Clark, in his Travels, vol. ii. p. 243, figures M. Dufourii
under the name of Buccinum Galileum. The water of this lake, however, unlike that
of the neighbouring Dead Sea, is, according to the statement of Fuller, perfectly
fresh and sweet. M. Lesson, on the other hand, states that he found the Pyrena
terebrans, regarded by M. de Ferussac as a Melanopsis, in great abundance in
brackish marshes in New Guinea, and at the Island of Bourou.

I am informed by Mr. Sowerby that some species of the fluviatile genus Cyrena
are found in the sea on the coast of South America ; but he thinks it probable that

* See Zoological Journal, vol. /. n. 32

308 MR. GRAY ON TESTACEOUS MOLLUSCA.

the part of the sea in which they are met with may be fresh, like certain parts of the
ocean described by Dr. Abel in his voyage to China. It would be highly interesting
to procure a verification of this observation. Similar phenomena may not be uncom-
mon, for I have myself observed in Torbay a small space in the neighbourhood of
Brixham, the water of which was of a different colour and much fresher than that of
other parts of the bay. With reference to another species of the same genus, Cyrena
VanikorensiSy M. Quoy observes : " Ne I'ayant pas trouvee dans les lieux marecageux,
mais sur les bords de la mer, il est probable qu'elle vit a I'embouchure des rivieres
qui sont saumatres a maree haute*."

The third class of cases, in which species of Mollusca that are generally found in
the sea are taken in fresh water, is much more rare than the preceding. It is ob-
vious that in such instances the animal must be possessed of the capability of adapt-
ing itself to the different characters of the two fluids. This capability exists in much
more highly organized animals, such as fishes, many species of which constantly mi-
grate from the sea and ascend the rivers to deposit their spawn ; but in these cases it
is the result of a regular and determinate habit, while in the Mollusca it appears to
be entirely dependent on accidental circumstances.

In some marshes in the Island of Bourbon, in which the water is almost fresh,
M. Rang has observed specimens of Aplysia dolahrifera in company with Neritmoe
and Melanice.

The greater number of species of the genus Cerithium are truly marine, chiefly
living in sandy bays, like our own Cerithium reticulatum. M. Lesson, however,
found C. sulcatum, and Adanson the African species figured by him, in the pools of
brackish water, sometimes overflowed by the sea, which are situated between the
weeds and the belts of mangrove trees on the shore ; and Mr. Say observes that
the small species, called by him Pyrena scalariformis, but which is a true Cerithium,
is found in great abundance in the fresh water of Florida Keys. He adds : " it is
most certainly a freshwater shell, yet it is destitute of an epidermis."

The genus Bulla is also truly marine ; but the Rev. Mr. Hennah some time since
presented to the British Museum specimens of one of its species, resembling the Bulla
Hydatis, found by him in brackish pools on the coast of Chili ; and Mr. Say has de-
scribed a Bulla Jluviatilis found by Mr. Aaron Stone deeply imbedded in the mud of
the river Delaware-}-.

The Littorinae, again, are all found either on the sea-shore or in the very brackish
water of the mouths of rivers, except two, which although described as Paludince by
Pfeiffer and De Ferussac, and formed into a distinct genus by Ziegler under the
name of Lithoglyphus, agree with Littorina in every character of shell and operculum,
and, as far as I can ascertain from the descriptions, of the animal also. These are
the Paludina fusca of Pfeiffer, and the P. naticoides of De Ferussac ; they are
truly fluviatile.

* Voyage de r Astrolabe, torn. iii. p. 516.

t See for this latter instance the Journal of the Academy of Natural Sciences of Philadelphia, vol. ii. p. 179.

MR. GRAY ON TESTACEOUS MOLLUSCA. 309

•

These anomalies are not restricted to the univalves : bivalves have also their share.
Thus, the genus Solen is generally and properly considered as marine ; but Mr. Ben-
son has lately discovered a species inhabiting the mud on the banks of the Ganges ;
and conceiving, from the nature of its habitation, that it ought to be separated from'
the common species, he has formed a genus for its reception under the name of No-
vamlina. On comparing, however, some specimens of the shell presented to the British
Museum by Mr. Royle, I can scarcely distinguish it as a species from the Solen
Domheyi of Lamarck, which is found on the coast of Peru ; and I have two other
species, very nearly related, one from the rivers of China, and the other from pools of
brackish water on the coast of America. In hke manner M. Nilsson has found his
Tellina Balthica, which appears to be little more than a variety of the Tellina solidula
of our coast, in the brackish water of the shores of the Baltic. Avicula margaritifera,
the mother-of-pearl shell, commonly found in the ocean, has been taken by M. Rang
in marshes in the Isle of Bourbon in the neighbourhood of the sea in which the water
is nearly fresh. Specimens of Mya armaria also are often found so high up the rivers
that the water in which they live is brackish only during high tides. They are found,
moreover, with freshwater shells on the coasts of the Baltic, while all the other spe-
cies of the genus are found only where the water is quite salt.

By far the greater part of the species of Corhulce are truly marine ; but there is a
large species of the genus, called by Dr. Maton* Mya lahiata, brought with fresh-
water shells from the mouth of the Rio de la Plata ; and this agrees in many respects
with the fossil Corbula Gallica, which occurs in what are called the upper freshwater
strata of the Isle of Wight.

The transitions to which the oysters intended for the London market are exposed
may be mentioned as an additional illustration. Many of these are collected in the
sea on the coasts of Guernsey and of France, and are brought to situations in the
mouth of the river where the water is merely brackish during the ebb of the tide,
and where they are consequently subjected to the alternate action of salt and brack-
ish w^ater twice in each day. It is even affirmed that oysters can exist in water abso-
lutely fresh ; for in the Museum of the Bristol Institution there is a large group said
to have been dredged up in a river on the coast of Africa where the stream was so
sweet as to have been used to water the ship. To these shells are attached specimens
of Cerithium armatum ; and the person by whom they were presented to the collection
stated that Cardlum ringens was found abundantly in the same situation.

The genus Cucullcea, again, is universally considered as truly marine ; but Mr. Ben-
son has found in the Ganges a small shell belonging to it, regarded by him as an
Area, but on account of its freshwater origin formed into a new genus under the
name of Scaphula.

On this subject I may observe, that I was some time ago informed that Area senitis
was found in the rivers of Africa in company with Galatea radiata : M. Cailliaud,
* Linnean Transactions, vol. x. p. 326, t. 24, f. 3.

310 MR. GRAY ON TESTACEOUS MOLLUSCA.

however, assures me that this is by no means the case, the shells in question being
found near the mouths of the rivers, but never in the rivers themselves.

One of the most decisive facts regarding the finding of the same species of shell in
both salt and fresh water is noticed by Say*. Speaking of Theodoxus reclinatus, he
observes, " I found this species in great plenty, inhabiting St. John's river in East
Florida, from its mouth to Fort Picolata, a distance of one hundred miles, where the
water is potable. It seemed to exist equally well where the water was as salt as that
of the ocean, and where the intermixture of that condiment could not be detected
by the taste." The shell in question is determined, by specimens which I received
from my late friend himself, (to whom science is so deeply indebted, and especially
for his researches into the zoology of North America,) to be the Neritina Meleagris,
pbtained in such abundance from the West Indian Islands. Nilsson too, as before
mentioned, has noticed the Neritina Jiuviatilis, which in this country is not observed
to inhabit ditches in the neighbourhood even of brackish water, living on the coasts
of the Baltic, in brackish situations, in company with Lymncea Balthica and L. suc-
cinea ; and M. Rang found Neritina auriculata in similar situations.

According to the observations of Olivier, the Ampullaria ovata inhabits Lake Ma-
reotis, where it is taken in company with marine shells found also in the Mediterra-
nean ; and I have lately received (dead) specimens from the locality indicated. The
same species was found by M. Cailliaud in freshwater lakes in the Oasis of Siwah,
where it is called Bozue and eaten as food. It thus appears to be found both in fresh
and brackish water. Two of the species referred to this genus by Lamarck, his Am-
pullaria Avellana and A.fragilis, are truly marine ; but they differ from the others in
animal and operculum, as well as in the sinuated form of the outer lip of their shell.

The common cockle of the shops, Cardium edule, is constantly to be seen in the
ditches of brackish water in the neighbourhood of Tilbury Fort, which gradually be-
come more or less fresh in proportion to the quantity of rain that falls between the
periods of opening the sluices. It is to be observed that the specimens found in this
situation are rather thinner and more produced posteriorly than those usually found in
the sea. The species in question is also, according to Nilsson, found in the brackish
water on the shores of the Baltic, but I am not aware whether or not it is there sub-
ject to a similar variation in form. Nilsson observes, however, that the marine species
found in those localities are generally smaller than those found in other situations.

From this list of exceptions to the general rules which have commonly been re-
garded as decisive of the localities inhabited by recent shells, and of the nature of the
deposits in which the fossil species are found, it is manifest that those rules cannot
safely be made use of for practical purposes without considerable reservation.
* Journal of the Academy of Natural Sciences of Philadelphia, vol. ii. p. 258.

[ 311 ]

XVII. On the supposed existence of Metamorphoses in the Crustacea. By J. O. West
WOOD, F.L.S. 8s Sec. Ent. Soc. Communicated hy J. G. Children, Esq.^ Sec. R.S.

Received May 25, — Read June 18, 1835.

JtERHAPS none of the phenomena of natural history have attracted a greater
share of the attention of mankind in all ages than those exhibited by insects in their
passage to the perfect state, and to which it is not surprising that the name of me-
tamorphoses should have been applied. If this were the case in the darker days of
zoological knowledge, when the true nature of these changes was not understood, it
is not strange that the subject should have lost none of its interest when, owing to
the admirable researches of Redi and Swammerdam, De Geer and Reaumur, all of
the marvellous has been removed, and a series of gradual developments exposed, far
exceeding in peculiarity those exhibited in any of the other tribes of animals.

It will not perhaps be considered out of place if we here shortly glance at those
general principles which regulate these metamorphoses amongst the ^nnulosa. " Si
nous voulons concevoir," observes Latreille, " d'une mani^re claire et positive le
sens qu'il faut attacher au mot de metamorphose, il est necessaire que nous nous for-
mions une idee exacte de celui de mue ; car leurs significations paraissent avoir
beaucoup d'affinite, et il est essentiel de les determiner aussi rigoureusement qu'il est
possible*."

It would, however, lead us to far too great a length were we at the outset to enter
into the question of the gradual formation of the various organs of annulose animals
from the rete mucosum, as insisted upon by Dr. Heroldt in opposition to the ge-
nerally received opinion of Swammerdam, that these various organs are, from the
first exclusion of the insect from the ^^^, in a state of existence, but enveloped in
various coverings which are successively cast off; although the determination of
this question must be considered as having a material influence upon the subject
under consideration, more especially as it seems difficult to account for the repro-
duction of the limbs of the Crustacea when torn off if we do not adopt the theory of
Dr. Heroldt.

Every animated being in its passage to the perfect development of its species un-
dergoes a certain but varied series of changes. In man and most of the vertebrated
animals there is a gradual action of the vital forces in different organs till they are
fitted for reproduction, accompanied, as progress is made to the adult state, by the
acquisition of various appendages, as teeth, horns, pubes, feathers, &c. In addition

* Cours d'Entomologie, p. 271.
mdcccxxxv. 2 8

312 MR. WESTWOOD ON THE SUPPOSED EXISTENCE

to this gradual action, the greater portion of the f^ertehrata are subject to that par-
ticular species of ecdysis which Mr. MacLeay has termed incomplete, consisting
simply in the integuments, hairs, skin, feathers, &c., scaling off piece by piece, or
one by one, as distinguished from that complete change in the identity of the enve-
lope of other less perfect animals which prevails in various degrees amongst the
Annulosa and some few of the Fertehrata, and by means of which the entire envelope
of the animal is shed at once. And here we may be allowed to notice the rationale
of this complete shedding of the envelope which so peculiarly distinguishes the An-
nulosa. In them we find the internal vertebrae of the higher animals converted into
a hard horny or crustaceous external covering, to the inner surface of which the
muscles are attached. This covering would of course, from its very nature, offer an
insurmountable obstacle against the growth of the animal, were it persistent. It is
therefore necessary that, in order to ensure the due increase of size in the animal,
its old covering should be cast off and a new and enlarged one obtained. And this is
what takes place throughout the Annulosa, the shedding of the shell of the Lobster and
the moulting of the Caterpillar being but modified examples of the same principle.

These modifications may be reduced to three principal heads, of which the Spider,
the Grasshopper, and the Butterfly may be cited as well-known examples.

In the first of these, the animal is produced from the e^g in a form which it is
destined to retain throughout its existence, its only change consisting in a series of
moultings of the outer envelope, by which an increase of size, but not an addition of
new 'organs, is acquired.

In the second, the animal at its exclusion exhibits the form which it retains through
life, but it is subject to a series of moultings, during several of the last of which cer-
tain new organs are gradually developed.

In the third, the form of the animal at its exclusion from the egg is totally differ-
ent from that in which it appears in its imago state, this change of form taking
place during two or three of its final moultings, and consisting not only in the varia-
tion of the form of the body, but also in a complete change in the nutritive and di-
gestive systems, and in the acquisition of various new organs. This constitutes what
has generally been termed metamorphosis.

Now, since the Ptilota of Aristotle are preeminently the types of the invertebrated
animals, and as such more distantly removed from the various groups of the Verte-
hrata than the remainder of the Invertehrata, (owing this preeminence not only to the
superiority of their instincts, but also to the development of organs of flight during
the latter moultings,) it will necessarily follow that those Annulosa which are less
typical, or, in other words, more nearly allied to the lowest of the higher groups of
animals, will not exhibit in so remarkable a degree those metamorphoses which, as
we have seen, the Ptilota so peculiarly undergo.

Hence, since the organization of the Crustacea is more clearly analogous to that of
the Vertehrata than that of the Ptilota, we arrive at one of the chief grounds for the

OP METAMORPHOSES IN THE CRUSTACEA. 313

generally received opinion amongst naturalists, that the transformations of the Crus-
tacea consist merely in the periodical shedding of the outer envelope, without any
metamorphosis being undergone or additional organs acquired.

The object of the following pages is therefore to endeavour to ascertain whether
this opinion be correct or not ; and in order to do this satisfactorily we shall be
obliged to test such observations which may negative its correctness, by the applica-
tion of those general principles which, as we have seen, regulate the transformations
or other changes of the Annulosa.

The non-existence of transformations in the Crustacea in general has been asserted
"by every crustaceologist, with the exception of a recent author, John V. Thompson,
Esq., F.L.S., (the accuracy of whose beautiful figures deserves the highest praise,) and
by whom, in the first and succeeding numbers of the Zoological Researches, the dis-
coveiy that the greater number of the Crustacea do actually undergo metamorphoses
of a very peculiar kind, and of a totally different description from those of insects,
has been announced. " So little has this been suspected by naturalists," observes this
author*, "that the contrary has been assigned as one of the distinctive characters
of the class, and been used as an argument for their separation from insects."

Mr. Thompson's views are founded upon some circumstances exhibited by some of
the most singular animals hitherto ascertained to belong to the class, (which consti-
tute the genus Zoea of Bosc,) as recorded by Slabber or Mr. Thompson himself, as
well as upon some other circumstances respecting other portions of the class. These
consist.

In the first place, in a supposed change which the Zoes are reputed to undergo ;
respecting which Mr. Thompson (after alluding to the observations of Slabber, which
he thinks erroneous,) thus expresses himself: "After keeping a full-grown Zoe for
more than a month, it died in the act of changing its skin and of passing into a new
form, but one by no means similar to that expected [from the previous observations
of Slabber], as appears evidently by its disengaged members, which are changed in
number as well as in form, and now correspond with those of the Decapoda (Crabs,
&c.), viz. five pair, the anterior of them furnished with a large claw or pincer : the
metamorphosis not having been completed, prevented any knowledge being acquired
of its general form ; enough, however, has been gained to show that the distinctive
characters of Zoea and of Slabber's changed Zoea were entirely lost ; that the mem-
bers, from being natatory and cleft (as shall shortly be shown), become simple and
adapted to crawling only. On the 1st of May another large Zoea was taken, and
dying towards the end of the month without having the strength to disengage itself
from the exuvium, presented precisely the same results with the former^-." In the
account of the figures of this full-grown Zoe, "behind the corselet the rudiments
of the limbs of the perfect animal, or Crab," are described as " beginning to show
themselves J;" but on comparing this figure with that of the newly hatched "Zoe,

* Zool. lUustr., p. 7. t Ibid., pp. 8, 9. X Ibid., p. 33.

2 s2

314 MR. WESTWOOD ON THE SUPPOSED EXISTENCE

or larva of the common or edible Crab," (PL VIII. fig. 1 .) " the disparity in size
is shown between a Zoe newly hatched and one which has attained its full deve-
lopment, and the changes which the various parts undergo during the growth of the
animal," (No. 2. Addendum,) as in the total absence of subabdominal fins, and in the
natatory division of the two pairs of feet having only four plumose setae in the younger
animal : and in a former passage he observes, that " the larger specimens may be
supposed to differ from such as occur of smaller size in the greater degree of deve-
lopment of all its parts ; thus, the eyes are more distinctly pedunculate, the natatory
division of the feet have an increased number of plumose setae, the rudiments of the
subabdominal fins are quite obvious, and the mandibles show the rudiment of a
palp : in other respects they are essentially the same." (p. 10.)

In the second place, our author states that he had succeeded in hatching the ova
of the common Crab {Cancer Pagurus), which presented exactly the appearance of
Zoea Taurus, with the addition of lateral spines to the corselet. And in the addenda
to his second number he has again stated this circumstance, adding somewhat more
precisely, that he had protected a female Crab with spawn apparently ready to hatch
until the young burst from their envelopes and swam about in myriads under the
exact form of Zoea represented in the Plate.

In the third place, Mr. Thompson has stated that the common Lobster undergoes
metamorphosis, " but less in degree " than any of the other genera in which he states
that he had observed this to take place, and " consisting in a change from a cheliferous
Schizopode to a Decapode, in its first stage being what I call a modified Zoe, with a
frontal spine, a spatulate tail, and wanting subabdominal fins, in short, such an animal
as would never be considered what it really is, were it not obtained by hatching the
spawn of the Lobster*."

The only figure which accompanies this remark is given in tab. xv. fig. 13. of the
same work, of " the cheliferous member of the larva of the Lobster, in which a is the
claw ; b, the outer division of the limb, or future Jlagrum ; and c, the rudimentary
' branchia." In this figure, three organs are represented as arising from a large basal
joint : first, the chelate organ, composed of two joints and a large didactyle chela ;
second, a three-jointed organ, of which the terminal joint is long, slender, and
strongly setose ; and third, a small rudimental branchia.

In the fourth place, " this curious piece of economy," according to Mr. Thompson,
" explains what has ever appeared paradoxical to naturalists, viz. the annual pere-
grinations of the land Crabs to the sea-side, which, although acknowledged to be true
by several competent observers, could never before be satisfactorily accounted for."
(p. 9.) And again, in the Addenda to his second number : " Hitherto the rationale of
this long and dangerous journey did not appear ; naturalists have thought it strange
that an animal entirely terrestrial should not spawn in its native haunts, and rear its
young at home, instead of putting them to the trouble of a tedious and unknown

* Zoological Journal, No. xix. p. 383.

OP METAMORPHOSES IN THE CRUSTACEA. 315

route back again in their very tender age. Scarcely a stronger confirmation than
this very circumstance, of the universality of metamorphosis, could be adduced : for
if there were any exception, it would be in the terrestrial species ; but no, they are,
when first hatched, incapable of living out of water with swimming members ; hence
the parent is impelled by instinct to seek that element for its progeny which Nature
has designed for the whole of the tribe to which they belong. Having lived amongst
West Indian islands, where these facts were constantly before him, neither he, nor any
other person, could invent any plausible reason for this curious piece of economy."

In the fifth and last place are to be noticed Mr. Thompson's general statements.
In the Addenda to his second number he states that he has had a confirmation of
his views in one of the West Indian land Crabs, and in some other of our most widely
separated native genera, authorizing his previous assertion that the greater number
of the Crustacea do actually undergo transformations, of which, in addition to the
facts adduced in his first memoir, further instances will be given in future memoirs.
On the wrapper of his fourth number he has given a list of some of these promised
memoirs, in which we find the Paguri, the Shrimp and Prawn, the genera Porcellana,
Gegarcinus, Hydrodomus, and other genera of land Crabs and Pinnotheres, all stated
to undergo various remarkable metamorphoses ; and in the nineteenth number of
the Zoological Journal he states that the newly hatched young of the following Bra-
chyurous genera. Cancer, Carcinus, Portunus, Eryphia, Gegarcinus, Thelphusa},
Pinnotheres, and Inachus, have been ascertained to be Zoes by himself; and that the
following Macrourous genera are likewise subject to metamorphosis, viz. Pagurus,
Porcellana , Galathea, Crangon, Palemon, Homarus, Astacus. !

Such are the various circumstances upon which Mr. Thompson has built his theory
of metamorphosis. I have given them at rather an inconvenient, but not an unne-
cessary length, and as far as possible in his own words, in order that I might be free
from any charge of misrepresentation in the observations which I may think it ne-
cessary to make upon each of them, with a view to prove that the theory is without
foundation.

For this purpose I propose, in the first place, to enter into a review of Mr. Thomp-
son's observations, whence alone I conceive that no sufficient ground is raised for
the establishment of the theory in question. In the second place, I propose to col-
lect the recent views of the most celebrated crustaceologists, all of whom have ad-
vanced opinions to the like effect. And in the third place, I shall bring forward
some circumstances observed by myself having a precisely similar tendency.

In the first place, therefore, I have to endeavour to prove from Mr. Thompson's
own statements and figures, that there is not sufficient foundation for the theory of
metamorphosis, and for this purpose I shall take in review seriatim the several cir-
cumstances which he has mentioned and above alluded to.

And first with respect to the metamorphosis into Crabs which the Zoes are stated
to undergo, against which six arguments may be adduced.

316 MR. WESTWOOD ON THE SUPPOSED EXISTENCE

1. It is to be observed that the account given of the mode in which this meta-
morphosis is supposed to be effected, is as vague and indefinite as it is possible to be.
It is stated that the Zoe died in the act of casting its skin, but its metamorphosis
not being completed, prevented any knowledge being acquired of its general form ;
and yet it is added that five pairs of legs had become disengaged, and that the cha-
racters oi Zoea were entirely lost. Plate II. fig. 2., however, proves nothing like this.
The limbs of the future Crab are asserted to be beginning to show themselves, and yet
the Zoe retains its original form, without losing a single character which it previously
possessed, — without our being able to trace the least appearance of the animal having
commenced the shedding of the skin, — or without our being able to gain the least idea
how " the members, from being natatory and cleft (as shall shortly be shown), be-
come simple and adapted to crawling only." But Mr. Thompson has omitted to
fulfill this promise, which, if it mean anything, must be understood as an assertion
that the two pairs of natatory and cleft legs are transformed into five pairs of simple
crawling legs.

2. The appearance of these limbs (represented as perfectly disengaged in Mr.
Thompson's Plate II. fig. 11.) previous to the shedding of the cephalothoracic shield
and anterior parts of the body, is totally at variance with the principles of ecdysis
observable throughout the Annulosa, in which the locomotive organs, at least the
legs, are the last which are disengaged, and the thoracic shield of the inclosed animal
the first portion exposed to view. It would, in fact, be impossible for the Zoe to
disengage the thoracic limbs without the thorax itself being previously withdrawn
from its covering.

3. But we will look more precisely at the nature of this supposed disengagement
of the five pairs of legs. This, in the absence of any precise explanation given by
Mr. Thompson, may be presumed to be effected in three different ways.

Firstly, — as indeed Mr. Thompson appears to suppose by his statement that the large
natatory limbs " become" simple ones, — this may be effected by the two pairs of large
natatory limbs entirely throwing away their outer covering, whereby the five pairs of
small simple legs, which had been previously inclosed within them, are disengaged.
This I take to be the true nature of the disengagement of the organs of motion in
the Annulosa ; but if we regard this to take place in Zoea, we shall necessarily have
two conditions totally at variance with the principles of ecdysis, viz. that an exist-
ing organ in a state of incomplete development incloses only a single organ, — thus,
the wings of the Grasshopper are not inclosed within the legs of its larva ; and that
an organ disengaged by the shedding of its envelope is always larger than such en-
velope. This, in fact, is the very end of the metamorphoses of the annulose animals,
the hardness of their outer covering preventing their growth, except by the shedding
of such covering.

Secondly, We may imagine that the five pairs of minute rudimental legs of the
future Crab are not transformed from the two pairs of natatory limbs, but are totally

OF METAMORPHOSES IN THE CRUSTACEA. 317

unconnected with them, being-, as Mr. Thompson himself says, " disengaged from
beneath the clypeus", (and his Plate II. fig. 2. represents the same idea,) and having
no previous existence in the young Zoe. Now if this be the case, setting aside its
disagreement with the recognised conditions of development, we arrive at once at
this startling and important conclusion, namely, that the large natatory organs of
the Zoe are instrumenta cibaria, foot-jaws, in fact, and that the animal in its Zoe
state has no true legs. Without, however, asserting (which might reasonably be
done) that every annulose animal which in its immature state is furnished with loco-
motive organs, is also furnished with instrumenta cibaria, which latter legitimately
represent the instrumenta cibaria of the imago, whilst the former as truly represent
the true legs of the imago, we may assert, that where an immature annulose animal
is furnished with locomotive organs, these, or at least some of them, represent the
true thoracic legs of the imago, and are not, in such immature state, merely rudi-
mental trophi of the perfect animal. Now on applying this principle to the case in
question, we find the Zoe furnished both with trophi and natatory organs ; and if we
regard the trophi, although few in number, as representatives of the trophi, and the
two pairs of natatory organs as representatives of the locomotive organs of the future
Crab, we can only regard the five pairs of disengaged limbs either as representing
the subabdominal appendages of the Crab, or as simple thoracic appendages (distinct
from legs), or as supplemental limbs. But each of these suppositions is so contrary
to nature with reference to the organization of Zoe or the Crab as distinct animals,
that in order to show their futility it will be suflicient to notice the determinate leg-
like form of these disengaged limbs, the first pair of which is cheliferous ; the fact
that the Zoea has distinct subabdominal appendages ; that the Crustacea are not, like
the Myriapoda, furnished with auxiliary limbs ; and that true thoracic locomotive
organs (which in Zoe, according to the principles above stated, must still remain
undeveloped,) are constantly developed at the same time as, or even before, supple-
mental ones.

Thirdly, We may imagine the disengagement of these "future limbs" to take
place in a mixed manner, by considering that the two pairs of natatory limbs of the
Zoe produce the first, or chelate, and second pairs of legs, and that the three posterior
pairs are simply disengaged from beneath the clypeus. Against this idea many of
the preceding observations may be conjointly adduced ; to which it may be added,
that the similar size of these disengaged limbs is sufficient to prove that they must
have undergone an equal degree of development. Moreover, in such case the che-
late members, which are larger than the following limbs, must be produced from the
first pair of natatory limbs of the Zoe, which are much smaller than the second pair.

I have in these observations left unnoticed the small member anterior to the claws,
observed by Mr. Thompson, and considered by him as the rudiment of the outer foot-
jaw, which offers still greater difficulties as to its nature if we adopt Mr. Thompson's
views, but which, as I shall subsequently show, is a necessary organ of the Zoe.

318 MR. WESTWOOD ON THE SUPPOSED EXISTENCE

4. In the next place it is to be observed, that Mr. Thompson's figures and state-
ments relative to the gradual development of the Zoes are totally at variance with one
of the received principles of ecdysis, which may be thus stated. When an animal
undergoes a variety of moultings, attended by alteration in form or development of
organs, there is a gradual tendency towards the organization of the perfect animal.
Now Mr. Thompson expressly states that his large Zoes differed from the smaller
ones in the greater degree of development of all their organs. This therefore is pre-
cisely what would occur in case the large Zoes were perfect animals ; and it is pre-
cisely what would not take place if the subsequent state of the Zoe were a Crab.

5. It is worthy of notice that there are several peculiarities in Zoea so evidently
partaking of the Macrourous type, that it is surprising that Mr. Thompson should
not have noticed that these characters present themselves in so complete a state of
development, when compared with the Macroura, as to negative the opinion that
these animals would ever become Brachyurous. The elongated tail, the rostrated
cephalothorax, but more especially the structure of the mandibles and two pairs of
maxillae, may especially be noticed.

6. If, as we shall subsequently perceive, there be no pretence for doubting the
correctness of Rathke's researches upon the Cray-fish, which is clearly proved to
undergo no metamorphosis, I think we are fully warranted from analogy in consi-
dering that the other Decapods do not undergo metamorphosis. Mr. Thompson, in-
deed, seems inclined to consider that in such case the Cray-fish " can only be regarded
as one solitary exception to the generality of metamorphosis * ;" although he had pre-
viously given his opinion of the weight of analogy in the second number of his Re-
searches, by stating that " metamorphosis having been proved in a single instance
amongst animals so uniform in structure as the Homobranchia, we may safely infer
from analogy, as far as regards the particular tribe alluded to, that it is general."

These six considerations induce me to adopt the opinion that no sufficient ground
has been shown by Mr. Thompson for supposing that a metamorphosis of Zoes into
Crabs takes place.

Secondly, therefore, we will proceed to notice Mr. Thompson's statements relative
to the hatching of the young Zoes from a female of the common Crab, and which he
states took place under his own eye. It is much to be regretted that Mr. Thompson,
having such ample opportunity, did not dissect the ova in various states, so as to
ascertain in the most satisfactory manner the gradual development of the embryo, as
Rathke has done in the Cray-fish. The statement, although short, ha-s, however,
such sufficient precision, that we are compelled to believe either that (notwithstand-
ing whatever may be advanced to the contrary) the young of the common Crab are
Zoes, or that the latter are parasitic animals, which in some unexplained manner are
introduced in the embryo state beneath the abdomen of the Crab ; and if we consider
the large Zoes observed by Mr. Thompson to be perfect animals, there is some ground

* Zoological Journal, No. xix. p. 383.

OF METAMORPHOSES IN THE CRUSTACEA. 319

for the latter opinion in their comparatively less perfect organization, a circumstance
to which a completely analogous case exists amongst the Hyperiidce in the order Am-
phipoda, &c. Zoe, indeed, is not the only animal respecting which this kind of para-
sitic obscurity exists ; the genus Meloe amongst the coleopterous insects is perfectly
analogous, the young of which, according to some authors, are Acari, whilst others
state them to resemble the perfect insect. I am the more anxious to offer this
explanation of Mr. Thompson's argument, in as much as the facts subsequently
stated respecting the ova and young of the Brachyura are totally at variance with
Mr. Thompson's assertions.

Thirdly, As respects Mr. Thompson's statements relative to the young of the com-
mon Lobster, we have again to regret the slightness of the information given to us
upon this branch of the subject. The young is called a modified Zoe, a cheliferous
Scliizopode, with a frontal spine, a spatulate tail, and wanting subabdominal fins,
undergoing a metamorphosis less in degree than the other mentioned genera. We
are left in uncertainty whether there are eight pairs of locomotive organs, as in the
true Schizopods, or whether these organs are all divided into two parts ; the only
evidence of such Schizopod nature being the chelate limb figured ; and yet this is
precisely where information was required. Examine the other characters given of
this " modified Zoe" without reference to its undescribed legs, and we are able to
trace (notwithstanding Mr. Thompson's assertion to the contrary) precisely such
an animal as might be expected for an immature Lobster. But if we examine the
nature of the cheliferous member figured, we shall find the strongest reason for con-
sidering that this " larva" is not a Schizopode. Fig. a. represents the cheliferous
member of the perfect Lobster, as well as of its larva ; but this organ is not provided
in the perfect state with any lateral appendage. And Mr. Thompson himself does
not attempt to prove the connexion of the lateral appendage which he figures with
the cheliferous limb of the perfect Lobster, since he describes this lateral appendage
as thQ future Jiagrum of the Lobster, that is, the lateral division of the exterior pair
of foot-jaws ; consequently, unless Mr. Thompson is prepared to prove that the lateral
appendage of one organ in the immature state becomes the lateral appendage of a
totally distinct organ in the perfect state of the same animal, it must follow that this
gentleman has erred in his dissections of the immature Lobster, and mistaken the
lateral appendage of the outer foot-jaw for a Schizopodous appendage of the Cheli-
ferous limb.

Fourthly, As respects the explanation or " excuse" which this principle of meta-
morphosis enables us to give for the annual migrations of the land Crabs of the
West Indies to the ocean to deposit their spawn, the young produced from which
being natatory animals — Zoes, in fact, — are incapable of living in the same element
as their parents in their early stages, I can very well agree with Mr. Thompson that
if any exception existed amongst the Crustacea, in which the young should not un-
dergo any change from aquatic to terrestrial habits, accompanied of course by a

MDCCCXXXV. 2 T

320 MR. WESTWOOD ON THE SUPPOSED EXISTENCE

corresponding modification of structure, it would be amongst the land Crabs ; but I
cannot agree with this gentleman that scarcely a stronger confirmation than this
very circumstance could be adduced of the universality of metamorphosis, in as much
as it appears to me that Mr. Thompson has arrived somewhat too suddenly at the
conclusion that the young must consequently be Zoes, or even that, although inca-
pable of living out of the water, they are necessarily furnished with natatory mem-
bers. Examine the sea Crab, and no material difference in the structure of its loco-
motive organs is to be observed from that of the land Crab whence a different kind
of motion can be inferred ; hence there can be no actual necessity for the existence
of natatory apparatus in the young land Crab, which must be just as able to support
itself in the water without any such as an ordinary sea Crab. If, moreover, we ex-
amine the structure of the branchial apparatus of the land Crabs, we find still further
evidence in support of this argument. MM. Audouin and M. H. Edwards, in the
Annales des Sciences Naturelles for September 1828, have given an account of this
organization : the exterior of the branchial cavity is furnished with a reservoir for
containing a supply of water ; and in the land Crab there is moreover a second vessel
destined for the like purpose, whence it is evident that in this respect the land Crabs
do not materially differ from the sea Crabs. I will not dwell upon this subject further
than to refer to the conclusive facts subsequently stated in proof that the young of
the land Crabs is neither a Zoe nor furnished with natatory apparatus.

Fifthly, I will only observe with reference to Mr. Thompson's general assertions,
that no great weight ought to be attached to them until the necessary details shall
have been given to the public, more especially if, as I have shown to be the case, we
find cause in those already published to distrust the views of the author.

Having thus gone through the various statements made by Mr. Thompson in sup-
port of his theory, and ascertained from them the apparent want of confirmation of
such theory, I proceed to notice the opinions of crustaceologists whose writings have
established for them some degree of weight as authorities upon the question.

These observations will be confined, firstly, to such as bear directly upon Mr. Thomp-
son's statements, and secondly, to such as relate to facts noticed respecting the trans-
formations in the early stages of various animals in the class ; since it is the more
necessary in endeavouring to ascertain the correctness of the views of an author, to
reject all general assertions made by others to the contrary which have not been
made in reference to such opinion, or which do not rest upon direct observation.
And it is to be regretted that Mr. Thompson's memoirs have been far from generally
known ; this will account for the slight degree of attention which has been bestowed
upon the interesting subject upon which they treat, and for the paucity of notices
respecting them.

We find Latreille *, however, stating that the opinion of Mr. Thompson " a grand
besoin d'etre ^tayee par des experiences positives, si toutefois elle n'est pas erron^e."

* Cours d'Entomologie, p. 385.

OF METAMORPHOSES IN THE CRUSTACEA. 321

M. Edwards, the most celebrated of modern living crustaceologists, observes, that
as the Malacostraca Podophthalma are divisible from the presence or absence of
branchiae to the thorax, inclosed in a peculiar cavity, " on n'aura plus d'incertitude
sur la place que doit occuper un genre tr^s curieux, Zoea ; en efFet, un examen at-
tentif de ces petits animaux m'a convain9u que non seulement leurs yeux sont portes
sur des peduncles, mais aussi de chaque cote de leur thorax il existe sous le carapace
une cavite respiratoire renfermant des branchies semblables par leur structure et
leur position a celles d'autres Macroures. II est done evident pour moi que le Zoe
est r^ellement un Crustace de I'ordre des D^capodes. Mr. Thompson assure que cet
animal n'est autre chose que le jeune de Crabe commun. Cette opinion me ne parait
pas soutenable, mais neanmoins il serait possible que les Zoes observes jusqu'ici ne
soient pas des animaux adultes, et alors il se pourrait bien que par les progr^s de
I'age lis deviennent assez semblables aux Megalops ; question que nous nous pro-
posons de traiter plus au long dans une autre occasion*."

The talented editor of the Zoological Journal has also, in his review of Mr. Thomp-
son's work, expressed his doubts as to the universality of the fact of metamorphosis
taking place in the Crustacea ; and in the eighteenth number of that work he has
stated the confirmation which his doubts had received by the publication of Dr.
Rathke's work, adding, that if there existed no optical delusion or other cause of
error in the isolated observations which Mr. Thompson has given us, the difference
of organization between a Macrourous and a Brachyurous Decapod is much greater
than either analogy or anatomy would have led him to suspect.

And lastly, Mr. Kirby has communicated to me his conviction that the researches
of Mr. Thompson are to be regarded with distrust, the grounds for which opinion
will appear in his forthcoming Bridgewater Treatise.

I now proceed to notice, as concisely as possible, the direct observations made by
various authors upon different Crustaceous animals in the young state.

And in the foremost place are to be mentioned the elaborate researches of Rathke
upon the development of the ova of the common Cray-fish, a work which for minute
and delicate investigation is rivalled only by Lyonnet's celebrated memoir upon the
larva of Cossus. Some idea may be entertained of the extent of these inquiries,
from the fact that five large folio plates are completely filled with details of the
structure, internal and external, of the ova in various states of development, and of
the newly hatched animal. And so beautifully clear are the representations of these
objects, and so completely is the development of the embryo to be traced through
all its stages, that unless we believe the whole to be the work of a fanciful imagina-
tion, it is impossible to arrive at any other conclusion than that the Cray-fish does not
undergo any change which can in the least degree merit the name of metamorphosis.
A full abstract of this valuable memoir is inserted in the eighteenth number of the
ZoologicalJournal, and in the Annales des Sciences Naturelles for August 1831,

* Ann. Sc. Nat., April 1830.
2t2

322 MR. WESTWOOD ON THE SUPPOSED EXISTENCE

the latter of which is accompanied by four plates. I \^dll therefore content myself
with referring the student to these accessible sources, without attempting to give
even an outline of the elaborate investigations in question.

Latreille, speaking of the young of the Cray-fish, says : " Les jeunes ecrevisses,
tr^s moUes au moment de leur naissance, et toute-a-fait semblables a leurs m^res, se
refugient sous leur queue, et y restent pendant plusieurs jours et jusqu'a ce que les
parties de leurs corps soient raffermies *."

Mr. Thompson himself, in the genus Mysis, has clearly shown that these animals,
which he has proved to be most intimately allied to the Decapod Macrowra, undergo a
series of changes, which he states " cannot be considered as metamorphoses, but
simply a gradual development of parts -}-."

The above appear to be all the direct observations hitherto made upon the Podoph-
thalma (with the exception of those subsequently detailed from my own researches) ;
but amongst the sessile-eyed Malacostraca we have more numerous observations.

Of these, as in the former, the researches of Rathke again stand foremost ; since,
in a series of memoirs, very recently published, upon the development of the ova and
embryos of various animals, we find the common Asellus aquaticus to have been in-
vestigated by him, with the result that no material alteration takes place in the form
of the animal %.

In the Annales des Sciences Naturelles for December 1833, is published a valuable
report, by M. Isidore Geoffroy St. Hilaire, upon a memoir of M. H. Milne
Edwards, entitled " Observations sur les changemens de forme que les Crus-
tac^s ^prouvent dans le jeune age." Passing over the more generalized views de-
duced by M. St. Hilaire from the facts noticed by M. Edwards, I shall merely state
the latter. The genus Cymothoa, and some other Isopodous genera, afforded to
M. Edwards an easy opportunity of examining the development of the eggs and the
structure of the young, in consequence of their being inclosed within the large sub-
thoracic pouch. Hence he was enabled to ascertain that some organs which are fully
developed in the adult animal, are either rudimental or absolutely wanting in the early
state : thus, in the latter the animal has only six thoracic segments, and six pairs of
legs, although when adult it has seven segments and seven pairs of legs. On the con-
trary, other organs, which are fully developed in the young, become rudimental in
the adult state : thus, in the former we find a large head, furnished with two large
oval black eyes, and the abdominal segments nearly as large as the thoracic ones ;
whilst in the adult state the head is extremely small, the eyes are not externally
visible, and the abdominal segments are very short and linear. M. Edwards has also
made similar observations upon many other genera, especially upon Anilocra, in
which a pair of legs is also developed after birth (the same likewise takes place in

* Rfegne Animal, torn. iv. p. 90. 2nd edit. f Zoological Researches, p. 16.

X Abhandlungen zur Bildungs ant Entwickelung-geschichte des MenschenundderThiere.4to. 2 parts. 1832,
1833.

OF METAMORPHOSES IN THE CRUSTACEA. 323

Oniscus, as De Geer long* ago remarked) ; upon Cyamus, a genus of Lcemodipoda,
which in the young state is of a slender and cylindric form, but which afterwards be-
comes much enlarged and depressed ; also upon Phronyma, a genus of Amphipoda,
remarkable for its large head, conical thorax, and singular construction of the fifth
pair of thoracic legs, but which in the young state exhibits a head of ordinary size, a
thorax larger in the centre than at the extremities, and the fifth pair of legs not un-
like the others, and not didactyle.

From the modification in form which the existent organs undergo in the passage to
the adult state, M. Edwards deduces this curious theory, — that the changes of form
which the Malacostraca undergo constantly tend to remove the animal to a greater
distance from the type which is common to the greatest number of individuals in the
group, so as to individualize it more and more completely. Thus the form of the im-
mature Cymothoa or Phronyma, for instance, is referrible to the general typical form
of the Isopoda or Amphipoda ; but, by the gradual change of form, these animals are
exhibited in forms the furthest removed from the types of their respective orders.

It is evident, however, from these remarks, that the Edriophthalma undergo no
change worthy of the name of metamorphosis ; and this is most fully supported by the
observations of Latreille upon the Isopoda in general, viz. that the progeny " nais-
sent avec la forme et les parties propres aleur espece, et ne font que changes de peau
en grandissant*="; of Mr. Montague upon Caprella Phasma, who states that he ob-
served ten young ones crawl from the abdominal pouch of the female, " all perfectly
formed" \ ; of Mr. Coldstream in an admirable paper upon Limnoria terebrans, in-
serted in the Edinburgh New Philosophical Journal of Professor Jameson for April
1834 ; and, lastly, of Professor Zencker in his memoir "De Gammari Pulicis Histo-
ria Naturali," 4to, 1832.

Hitherto I have confined these observations to the Malacostraca, because it is in
that division of the class that the non-existence of metamorphoses has been denied.
The Entomostraca are admitted on all hands to undergo very material modifications
of form, as maybe seen from the researches of Jurine, Strauss, Prevost, &c.; whilst
Mr. Thompson's recent memoir upon Artemia. (not Artemis,) is an additional evidence
of the same fact, although the nature of the various alterations is very far from being
detailed in that satisfactory manner which the author seems so capable of doing.

I have therefore now to detail, as the third portion of this essay, such circum-
stances as have fallen under my own observation relative to this interesting inquiry,
the tendency of which is precisely similar to that exhibited by the two preceding por-
tions of my treatise.

We have seen that Mr. Thompson's chief argument is founded upon the supposed
transformations of the Zoe into a Crab. His Zoe, figured as the just-hatched larva
of the common Crab, is not so large as a large pin's head. Slabber's "changed Zoe"
is represented as three lines long ; and Mr. Thompson's Zoe, which died on the sup-

* R^gne Animal, torn. iv. p. 131. t Linnean Transactions, vol. vii. p. 66.

324 MR. WESTWOOD ON THE SUPPOSED EXISTENCE

posed point of transformation into a Crab, is nearly four lines long between the tips
of the spines. Now if Mr. Thompson's views be correct, and these latter Zoes are to
be regarded as the larvae of Crabs, they must be considered as having acquired the
maximum of their Zoe form ; but so far is this from being the case, that I have ob-
tained from the collection of the late Rev. Lansdown Guilding, specimens of a spe-
cies of Zoea ten lines long between the points of the spines ; a size far too large to
allow us to suppose that they would subsequently put off their Zoe form, and appear
as Crabs ; bearing at the same time in mind the minute size of the latter animals in
the very young state, although possessing their ordinary form.

Of this West Indian species I have given, in the accompanying sketch, figures in
detail of the various organs, which I shall not describe at length. The palpigerous
mandibles, the two pairs of antennae, one pair of which is bipartite, the multilobed
inner maxillae, are all characters found in the Macroura and Schizopoda, but not in
the Brachyura. The natatory apparatus of the tail, observed in my species and un-
noticed by Mr. Thompson, is also similarly characteristic, but the locomotive organs
are those to which the highest importance attaches with respect to the real nature of
the animal. At first sight, in addition to and immediately succeeding the two pairs
of maxillae, there appear only two pairs of large locomotive bipartite organs. These
therefore, on the supposition that the Zoe is the young of a Decapod animal, must
either be legs, or outer foot-jaws greatly developed ; and from their bipartite struc-
ture, the latter may be partly assumed ; but upon carefully dissecting the animal, a
series of organs were found, which not only fully proved this to be the case, but also
led at once to the discovery of the real nature of these animals, and gave a clue for
the correction of Mr. Thompson's ideas upon the supposed disengagement of the tho-
racic limbs. Immediately succeeding the outer pair of the natatory organs, and, in
fact, lying between them when at rest, was discovered a pair of slender minute
organs, composed apparently of two joints, one long and one short, and furnished at
the base with a still more minute lateral appendage. Beyond these, in succession,
were found the five pairs of organs precisely similar to Mr. Thompson's " limbs of
the future Crab disengaged from beneath the clypeus." Moreover, a number (unde-
termined) of minute fleshy elongated masses were found near and attached to the
base of these limbs. Are we therefore, with Mr. Thompson, to suppose that in this
Zoe (and all the specimens were alike) metamorphosis had commenced, whilst not
the slightest trace of such a process could be observed beyond this acquisition of
rudimental limbs, which can otherwise be much more satisfactorily accounted for ?
The researches of recent authors, and those particularly of M. H. Milne Edwards,
have clearly proved that in some species of Decapods {Acetes, Sergestes,) one or more
pairs of legs become rudimental, and that their place is supplied by highly developed
foot-jaws.

Now upon applying this theory, to the correctness of which Mr. Thompson bears
witness, to Zoea, we find that the two large pairs of natatory organs represent the

OP METAMORPHOSES IN THE CRUSTACEA. 325

first and second pairs of foot-jaws of the typical Decapods immensely developed ; the
minute pair of organs following these to be the third pair of foot-jaws ; the five pairs
of " limbs of the future Crab" to be the real thoracic legs of the Zoe, and that the
minute fleshy masses are evidently branchiae. Thus we perceive that the possession
of these limbs, instead of being an evidence of the imperfect state of the Zoe, is a
proof of its anomalous perfection ; and thus we arrive at the unexpected conclusion
that Zoea is a genus of Decapod Crustacea, for the reception of which amongst the
Macroura a distinct section must be established.

With reference to Mr. Thompson's statements respecting the hatching of the Zoes
from the eggs of the common Crab, and the arguments adduced from the habits of
the West Indian land Crabs, I am able to offer the following as, I trust, very conclu-
sive observations to the contrary.

In the collection above alluded to were contained, in spirits, the abdomens of seve-
ral female Crabs, having the interior surface covered with hundreds of eggs or newly
hatched young. One of the bottles in which one of these was deposited was labelled
by Mr. Guilding, " Eggs and young of a land Crab not undergoing a metamorpho-
sis." From this specimen I obtained eggs, and young Crabs evidently just hatched,
and others at a rather later stage of their growth.

The eggs are of a dark reddish colour, showing through the outer integument the
rudimental limbs of a future animal of a paler colour. On removing the thin trans-
parent pellicle which surrounded one of these eggs, the eyes of the future animal were
most conspicuous, the tail was seen extended as a narrow plate, nearly reaching to
the eyes, and along its sides lay the large anterior cheliferous and the four following
simple pairs of limbs. The existing organs, although perfectly discernible, occupied
only a small portion of one side of the Q^g, its greater part being filled with hardened
matter composed of minute molecular grains. The animal was in a sufficiently for-
ward state of development not to allow the least doubt to be entertained as to the
nature of these limbs, nor did any organs appear answering to the two large split
pairs of natatory organs of Zoea. The branchiae, in a fleshy and unorganized state,
were also found at the base of the legs. The eggs are \\ line in diameter.

In the accompanying sketches I have represented one of the Crabs evidently just
batched, being about If line long, and having the upper part of the cephalothorax
considerably swollen. From my figures, the very rudimental state of the two pairs of
antennae, and of the feelers or flagrums of the outer foot-jaws, will be perceived ; but
the general form of the animal is thus early exhibited, and the developed state of its
branchiae and the want of subabdominal appendages are especially noticeable. In
the following sketch the animal is seen in a somewhat more advanced stage of its
growth, being rather more than 2 lines long, and in which the upper surface of the
cephalothorax has acquired its ordinary shape, and the antennae have attained a
greater degree of perfection.

326 MR. WESTWOOD ON THE SUPPOSED EXISTENCE

These circumstances are, I trust, amply sufficient to prove that the land Crab
does not undergo any metamorphosis.

It is to be observed that Mr. Guilding has not stated the precise species of land
Crab of which the above-mentioned individuals were the offspring ; but his well-
known acquirements in crustaceology put the question of its being at all events a
species of land Crab to rest. Should this, however, be nevertheless called in ques-
tion, the argument which I would deduce from it will be but little diminished even
were it a sea Crab.

We have seen that Mr. Thompson's supposed full-grown Zoe, which died on the
point of undergoing its supposed metamorphosis, was 3 lines long between the points
of the spines, and the length of which, from the head to the tail, must have been at least
1§ line. But the young of the common Crab is found of a much smaller size than
this, exhibiting at the same time all the form of the full-grown Crab. I have myself
captured the young of Cancer Mcenas not more than § a line long, yet perfectly
formed, and capable of running about with much quickness.

Although disagreeing with Mr. Thompson in respect to his theory, I have already
stated that his figures are very faithful delineations of nature. I have therefore the
more pleasure in stating that his representations of the young of My sis are (as I have
ascertained by extracting them from the subthoracic pouch of the female) correct.

Hence, by taking the preceding observations into consideration, we find that one
or more types of each of the great groups of the typical Malacostracous Crustacea
have been ascertained to undergo no change of form sufficiently marked to warrant
the employment of the term metamorphosis. Thus,

^The Br achy ur a are represented by the Land Crab.

The Macroura Cray-fish.

The Schizopoda Mysis,

The Amphipoda Gammarus and Phronyma.

The Lcemodipoda Caprella and Cyamus.

The Isopoda Asellus, Cymothoa, and Limnoria.

Note. — Since the preceding pages were written, Mr. Thompson has published a
memoir upon the genus Pinnotheres, belonging to the Brachyura, in which the ova
are stated to have been seen to hatch in great numbers under the form of a new kind
of Zoe, without the circumstances attending their development being recorded. And,
on the other hand, some of the late Mr. Guilding's MSS. have been published in the
Magazine of Natural History, in which it is distinctly stated that the land Crabs do
not undergo transformations.

OF METAxMORPHOSES IN THE CRUSTACEA. 327

Explanation of the Plate.

Plate IV. A.

Fig. 1. Zoea Gigas, Westw. natural size.
Fig. 2. Ditto, magnified.
Fig. 3. The outer antenna.
Fig. 4. The inner antenna.
Fig. 5. The labrum.

Fig. 6. One of the mandibles, a representative of the the palpus.
Fig. 7. One of the interior maxillee.
Fig. 8. One of the second pair of maxillae.

Fig. 9. One of the first pair of foot-jaws, developed into a natatory organ.
Fig. 10. One of the second pair of foot-jaws, developed into a natatory organ.
Fig. 11. One of the third pair of foot-jaws, minute and rudimentaL
Fig. 12. View of the underside of the body, as extracted from the cephalothoracic
shield.

a. The first pair of foot-jaws.

b. The second pair.

c. The third pair.

d. The anterior pair of chelate members.

e. The rudimental branchiae.

f. The four posterior pairs of simple members.
Fig. 13. One of the subabdominal appendages.
Fig. 14. The tail, developed.

Plate IV. B.

" Eggs and young of a land Crab not undergoing a metamorphosis." — Guilding, MSS.
a. The egg.

Fig. 1. Natural size.

Fig. 2. Magnified, seen in front.

Fig. 3. The same, seen in front, having the outer pellicle stripped oflf: the legs
on one side extended laterally, the branchiae visible on the other side.

Fig. 4. The same, seen in front, having the outer pellicle stripped off, seen side-
ways.

Fig. 5. The same, seen in front, having the outer pellicle stripped oflf, seen side-
ways, with the limbs and tail extended.

Fig. 6. The tail.

Fig. 7. The legs, with the branchiae at the base, not organized.

MDCCCXXXV. 2 u

32^ MR. WESTWOOD ON METAMORPHOSES IN THE CRUSTACEA.

b. 'J^'he young in its earliest state.
Fig. 8. Natural size.

Fig. 9. Magnified.

Fig. 10. Ditto, seen from beneath.

Fig. 11. Anterior portion of the body, from beneath, showing the outer foot-jaws,

two pairs of antennse, and eyes at the extremity of the peduncles.
Fig. 12 & 13. One of the rudimental internal antennae attached to a large fleshy

tubercle.
Fig. 1 4. One of the rudimental external antennse.
Fig. 15. One of the outer foot -jaws.
Fig. 16. One of the intermediate foot-jaws.
Fig. 17. The branchiae.
Fig. 18. The abdomen, unfurnished with internal appendages.

c. The young at a rather more advanced period.
Fig. 19. Natural size.

Fig. 20. Magnified.

Fig. 21. The anterior part of the body seen from beneath.

Fig. 22. One of the internal antennae separated from its large basal lobe.

Fig. 23. One of the external antennae.

Fig. 24. The abdomen. •

[ 329 ]

XVIII. On the Ice formed, under peculiar circumstances, at the bottom of running
Water. By the Rev. James Farquharson, of Alford, F.R.S.

Received March 17, — Read April 2, 1835.

Ice formed at the bottom of rivers and streams, frequently in great quantities, is
a phenomenon quite common in this climate. I made for several years past a
number of incidental and desultory observations upon it, and became convinced
that the principal explanation of its occurrence is the radiation of heat from the
solid opake materials of the bottom ; but as I conceived this to be also the gene-
rally admitted one, I took no note of the observations, with the view of vindi-
cating the theory of the radiation. It appears, however, from a paper of M. Arago
upon the subject, translated and published in the Edinburgh New Philosophical
Journal, vol. xv. p. 123, from the Annuaire for the year 1833, that he entirely rejects'
the theory of the radiation of heat through a thick layer of water. In the same
paper, although he does not, in conclusion, pretend to give a complete explanation
of the phenomenon, he brings forward, as explanations in part, three circumstances,
which, although accurately stated by him, appear to be not exclusively appropriate
to ice formed at the bottom, and cannot therefore aid us in solving the main question
which we have to discuss here, which I apprehend to be, ff^hy is ice formed sometimes
on the surface of running water, and sometimes at the bottom ?

On reading M. Arago's paper, I became desirous of offering some remarks in an-
swer to it, as without some one doing this, on proper data, a misapprehension con-
cerning the cause of a natural phenomenon, so much at variance with our most fre-
quent experience of the formation of ice only on the surface of all waters, as to have
often greatly excited the attention and even called forth the astonishment of scientific
men, would continue to be propagated under the authority of a distinguished name.
Having, however, no record of my former observations to enable me to refer accu-
rately to the time, place, and other circumstances of them, I delayed till a renewed
occurrence of ice on the bottoms of our streams should enable me to repeat them.

Such an occurrence, on a great scale, took place in the beginning of thife month
of January (1835) ; and I now have the honour of presenting to the notice of the
Royal Society a brief account of the observations I have been enabled to make, and
of the conclusions to which they appear to direct us.

Previously to entering on this detail and discussion, it seems proper to describe the
appearance and quality of the ice formed at the bottoms of streams. A misappre-
hension regarding these may have been one cause of the incredulity of its existence,

2 u2

330 REV. JAMES FARQUHARSON ON THE ICE

entertained by some persons who have never witnessed it, and which M. Arago, in
he paper referred to, has deemed it necessary to remove, by bringing forward the
estimony of many distinguished men to its reality. The ice formed at the bottom
does not resemble the solid glass-like plates which are formed on the surface. It
has nearly the aspect of the aggregated masses of snow as they are seen floating in
rivers during a heavy snow shower ; but, on taking it out of the water, it is found
to be of a much firmer consistence than these, although never approaching to the
firmness and solidity of surface ice. It is a cavernous mass of various-sized, bat all
small, pieces or crystals of ice, adhering together in an apparently irregular manner
by their sides, or angles, or points, promiscuously. Both the firmness of the adhe-
sion and the dimensions of the interstices (the latter filled with water, and their
volume easily estimated by the quantity of it which is discharged when the ice is
lifted out of the stream,) are, however, greatly modified by the intensity and continu-
ance of the previous cold. When the ice begins first to form on the bottoms of the
streams, it presents a rudely symmetrical appearance, which, for illustration, may be
compared to little hearts of cauliflowers, fixed on the bottom, having a similar uni-
form circular outline and protuberance in the centre, with coral-like projections.
These pieces have a shining silvery aspect ; they are dispersed, at first irregularly, in
small numbers, but increase both in size and numbers, till the whole bottom is
covered, and, if the frost continues severe, grow in height, but in a very irregular
manner, so as to obliterate the earlier somewhat symmetrical shapes, till the streams
are raised high above their former levels, and frequently made to overflow their
banks. And here I take the opportunity to notice the incorrectness of an observa-
tion of Desmarest, quoted by M. Arago, and which, M. Arago i bserves, no one has
corroborated, " that it was from the lower parts, which touched the bottom, that the
flakes of ice successively increased." On the contrary, the forms of the surface of the
earlier masses are continually obscured, in succession, by new ice added to the top.

This congealed mass being thus very different in appearance and consistence from
the sheets or plates generally known by the name of ice, it were no doubt well that,
like the Germans, who, M. Arago informs us, name it grundeis, we too designated it
by another name, to prevent confusion or misapprehension when we refer to it. The
inhabitants of this part of the country will furnish us with a better one than even
that of the Germans. In a district where it occurs almost every winter, and often
repeatedly during that season, and where many of the rivers are crossed by means of
fords, its existence influences too much their economical arrangements not to excite
their particular attention, especially as many horses refuse to enter any stream even
slightly impeded by it, being greatly alarmed by the pieces which break and float up
from the bottom by the action of their feet. A body with which all are so well
acquainted is known by an appropriate name. They call it ground-gru ; gru being
the term by which they designate snow saturated with, or swimming in water. I
shall venture to use their term for the ice formed at the bottom.

FORMED AT THE BOTTOM OF RUNNING WATER. 331

It will be better here also to state, generally, the conditions of temperature and
phases of the weather under which the ground-gru is formed. I have seen it occur
only when the temperature of the whole mass of water was reduced to, or nearly to,
32° Fahr., and when the temperature of the air was several degrees below that point.
I have observed it an invariable condition, that it was preceded by a continuance,
for some time, of a clear, or very nearly clear, state of the sky. This is at variance
with another observation of Desmarest, quoted by M. Arago, that " when, in conse-
quence of a cloudy sky, the atmospherical temperature experiences little variation
throughout the day and night, the ice at the bottom of the water uniformly increases
every twenty-four hours ; on the contrary, when the sun shows itself, the ice does
not increase during the day." It is the fact, that while it is forming under the con-
tinuance of a cloudless sky, its increase is impeded during the day. It may be pos-
sible, amidst the infinite variety of measures of cold that may exist at the time, that
the increase of the gru may go on for a little time after the sun has been obscured
by a thin cloud ; but I have always seen, that when a densely clouded state of the
sky supervened, and continued for the space of even only twenty-four hours, the gru
became detached from the bottom, and floated down the stream. Should the tem-
perature of the air continue low, with the clouded sky, or get lower, the ground-gru
is not renewed, but the river is speedily frozen over at the surface. It is, in fact, a
matter of frequent occurrence, in frosty winters, that our rivers, filled, and so im-
peded, by ground-gru, as to be raised above their banks, are found returned into
their natural channels, and there frozen over at the surface, but flowing over a clear
bottom, in a space of time so short as to appear very wonderful to those who have
not investigated the cause. The process is named, by the country people, the Jlittlng
of the ice. In opposition to the observation of Desmarest, and in confirmation of
those which I have made, on this point, I may refer to the Rev. Mr. Eisdale, who,
not satisfied with the explanations of M. Arago, has published one of his own, in the
Edinburgh New Philosophical Journal, vol. xvii. p. 167. His explanation appears
equally unsatisfactory, as will be shown afterwards ; but the part of his statement we
have to do with here is his notice of this observation of Desmarest. The formation
of the ground-gru, under a cloudy sky, is so much at variance with the information
which Mr. Eisdale had received, that he resolves Desmarest's " cloudy sky" into
" an atmosphere loaded with hoar frost, and rendered hazy by its condensation *."
The state of the air, in respect of being windy or calm, deserves also to be noticed.
The ground-gru occurs most frequently during calm, with a deposition of hoar frost
upon the ground at the time ; and this was the condition of matters during the ob-
servations now to be detailed. But it also occurs during a frosty wind, when there
is no hoar frost, which is formed only in a calm state of the atmosphere. The forma-
tion of the gru during wind, and consequently without any deposition of hoar frost
on the ground, is especially to be noticed in reference to Mr. Eisdale's explanation,

* p. 172.

332 REV. JAMES FARQUHARSON ON THE ICE

as will be afterwards seen. It occurred to M. Hugi, as quoted by M. Arago, in the
Aar, on the 16th February 1827, with a west wind, after the river had been com-
pletely open on the 15th ; and one of Mr. Eisdale's correspondents ascribed its oc-
currence in one particular instance, which he related to him, to the prevalence of a
very sharp north-east wind, which had blown during the night of its formation.

The following observations were made in ihe rivers Don and Leochal. The former,
having an easterly course, is about 120 feet broad, and a foot or two deep at the
shallows and fords. The latter, one of the small tributaries of the former, having a
northerly course, is about 20 feet broad, and a foot deep at the shallows. Both rivers
possess a like character of very clear water, and alternating rapids and pools. The
rapids in the Don are reaches, where the water falls two or three, or more, feet, from
a higher to a lower level, within a distance of fifty or a hundred, or sometimes two or
three hundred, yards. They are generally impeded with many large stones, some of
them projecting above the water. The depth varies greatly, but seldom exceeds two
or three feet. The pools between the rapids are on an average much longer reaches,
in which there is little fall, and a greatly diminished velocity of the stream, which
often, in them, flows so equably as to give rise to no ripple on the surface. They too
have in them large stones, but fewer in number. The depth in them too varies
greatly, from two or three to four or five feet. The rapids and pools in the Leochal
are of a similar kind, but both much less deep in this smaller stream. The bed of
this river has however, on the whole, a steeper descent, and owing to this there is
more broken water and spray in the rapids. The character of alternating rapids and
pools, in both streams, is owing to the varying hardness of the granitic and micaceous-
schistose rocks in which their beds are formed. Where the rocks are hard, there is
a rapid ; where more friable, a pool. In the parts of the rivers observed, the original
rocks themselves do not anywhere form the immediate bed of the stream. That, to
the depth of two or three, or more, feet, is composed of the debris of these rocks,
broken up and sometimes much waterworn, and reduced to the size of a very large
gravel, by the action of the stream, but not so small as to deserve to be named sand.
No part of the bottom is muddy.

On the night between the 31st of December 1834 and the 1st of January 1835,
after the mean temperature of the air had continued for three days at 47° Fahr., and
when there had been little frost in the season before, there commenced a hard frost,
with a calm and perfectly cloudless sky, which continued with little abatement till
the 5th of January, at 10 a.m. On the night between the 3rd and 4th, the tempe-
rature of the air was 23° Fahr. ; and on the 4th, the bottoms of the rapids in the
Leochal were seen coated in some places with silvery cauliflower-shaped clusters of
ground-gru. I neglected at this time to examine the temperature of the water.

Between the 4th and 5th, the temperature of the air was down to 19° Fahr. ; and
on the 5th I examined the Don and the Leochal along half a mile of each, beginning
the examination at half-past 8 o'clock a.m. The examination began at the bridge of

FORMED AT THE BOTTOM OF RUNNING WATER. 333

Alford, built of granite over the Don, in the middle of one of the rapids. At this
rapid, the whole bottom, with the exceptions to be immediately stated, was covered
with silvery gvu, appearing from two or three to five or six inches deep. My atten-
tion was particularly directed to the exceptions, as throwing a clear light on the
question of the radiation of heat from the bottom. Round each of the piers, and in
front of the abutments of the bridge, there was a space quite clear of all frozen mat-
ter, excepting at a side of one pier under an arch, where a piece of very still water,
caused by an obstruction at the bottom, was covered by clear sheet ice. On the
south side of the river, two embanking walls, one up and the other down the stream,
each twelve yards long, are built in a line with the water-courses of the abutment.
Close to the bridge these walls are eight feet high from the bottom of the stream,
but as they recede from the bridge the masonry slopes gradually to a lower level, till
the extremities are little above the level of the water. The bottom in front of these
walls was clear of ground-gru, as well as that in front of the abutments ; but the
breadth of the clear space in front of the walls narrowed gradually towards their ex-
tremities, in proportion as the masonry became lower, till at the extremity of the
downward wall especially, which ends at a sloping gravelly bank, the gru came to
the edge of the water. The space of the bottom clear of gru was about five or six
feet broad at the high parts of the walls next the bridge ; and the water runs on the
place at the medium depth and velocity of the rapid. There was another clear space
in the bottom of this rapid. About twenty-five yards above the bridge there is, in the
middle of the stream, a piece of still water, caused by an elevated bed of gravel, just
below it, over which the stream is very shallow. The still water, for an extent of two
or three square poles, was covered with sheet ice, and that again covered by a very
thin, but white, opake deposition of hoar frost. From under this ice the water, flow-
ing rapidly over the gravel bed below, had no ground-gru for a space of eight or ten
yards downwards.

Above this rapid, a pool of moderate stillness, about three or four feet deep, ex-
tends a hundred and fifty yards in length. Over the bottom of this there were
scattered, in an irregular manner, many cauliflower-shaped clusters of silveiy gru,
most of them very small, and none that were observed covering more of the bottom
than a square foot or two at one place. In the deepest and stillest part of the pool
there were several tufts of water starwort, with sooty-coloured decaying leaves, form-
ing the darkest-coloured objects seen at the bottom. These were all densely tangled
with fringes of silvery gru. At the head of the pool, where the velocity acquired by
the water in the rapid immediately above it was not yet greatly diminished, an ap-
pearance of a different kind presented itself. There are here several large stones in
the bed of the stream, but none of them projecting above the water. On the faces of
these opposed to the stream there were seen quantities of gru of a different aspect
from that further down. It was not arranged in the same cauliflower shapes, but in
angular masses, like wreaths of snow blown by the wind. It wanted, too, the silveiy
glance of the other, and had more the appearance of a pale ash-coloured mud. On

334 REV. JAMES FARQUHARSON ON THE ICE

reaching- it with the end of a pole, its consistency was found to be less firm ; in fact,
it was only a heap of detached uncemented spiculse pressed against the stones, and
retained there mechanically by the action of the water, in a certain modified state
of its velocity. The source of these heaps of uncemented spiculse will soon be no-
ticed. This pool, as indeed was the case with all the pools in the river, had at its
edges and in its little bays narrow pieces of surface-ice, extending a foot or two from
the banks.

The rapid immediately above this, not unlike that at the bridge, was covered at
the bottom with silvery gru, with one exception. The river was low at the time from
long-continued deficiency of rarn, and the water had deserted the south side of the
channel, leaving many little pools among the stones, communicating more or less
freely by irregular little currents with the main stream. The pools were covered over
with sheet-ice, and that with a thin opake deposit of hoar frost like snow. In the
little currents returning from under this ice there was no frozen matter.

At the head of this rapid there is a pool much deeper and stiller than that above
the bridge-rapid already described. The depth is five feet, and the stillness such
that, at many points of it, there is no ripple or wave on the surface. None of the sil-
very cauliflower-like ice was seen on the bottom here ; but near the head of it, in a
modified state of the current pouring in from the rapid above it, there were, on the
faces of several large stones opposed to the stream, collections of uncemented icy
spiculse.

The source of these collections was very readily observed in a great rapid imme-
diately above this. In that rapid the water has a much quicker descent than in the
others referred to. It is about a hundred yards long, and cumbered with many large
stones, over which, at many points, through its whole length, the water breaks with
a great deal of spray. Here an immense quantity of gru occupied the bottom, im-
peding much the course of the stream. At the time of observation many pieces of
this gru were seen edging up, and in some instances breaking quite away from the bot-,
tom, apparently by the increasing pressure of the water, as it became dammed back
by the increase of the gru itself. This at least was the appearance, although there
may have been another cause for the disengagement of it from the bottom, and that
is, the impeding, by the imperfectly translucent gru, of that radiation of heat from the
bottom which, I trust in conclusion to demonstrate, is the immediate chief agent in
the whole phenomenon.

It is now to be observed, that a number of pieces of loose gru, the origin of which
was so r;learly ascertained at this last rapid, were floating down in all parts of the
river. In passing through the rapids, they were broken into fragments, and, where the
fall was violent, shivered into minute pieces. The larger pieces that remained after
passing through the rapids floated at the surface, immediately as they got into the
uniformly flowing currents at the heads of the pools ; but the minuter ones, mixed with
the water to all depths by the plunging whirls in the rapids, not being so speedily
„<.„„„]^^ from their cohesion with the water, by the action of ern'^^v floatpH

FORMED AT THE BOTTOM OF RUNNING WATER. 335

for a greater distance immersed in the water, and were intercepted by, and mecha-
nically retained against, the faces of the stones by the action of the stream at the
heads of the pools. Further down, and in stiller water, where no such intercepted
heaps were seen, their buoyancy had, no doubt, by degrees, overcome the cohesion
and raised them to the surface ; and in fact, in the still water, many minute icy frag-
ments were floating in the surface.

Mr. Knight, the celebrated botanist, quoted by M. Arago, has obviously, in part,
but not completely, distinguished between the " frozen matter which reflected a sil-
very kind of whiteness," which covered the stones in the rocky bed of the river, and
" floating spiculae under water," which he found to " accumulate much more abun-
dantly upon such parts of the stones as stood opposed to the current, where that was
not very rapid, below the little falls or very rapid parts of the river."

In the smaller stream of the Leochal, the quantity of ground-gru was compara-
tively much more abundant, occupying the bottoms both of the pools and rapids in
close masses, and in the latter, at many parts, forming such an impediment as to
urge the water over its usual banks. But there were two remarkable exceptions.
One of the pools flows close to the foot of a steep bank about fifteen feet high, and
in the side next the bank there was little ground-gru. In a rapid, which at a turn
of the river has an easterly course, there was a very dense fringe of Phalar-is arundi-
nacea standing, with its dense foliage of withered leaves, in the south edge of the
water. Its height was four feet, and it extended fourteen feet in length along the
stream. At the foot of it the bottom of the rapid was clear of ground-gru to the
breadth of three feet.

The temperature of the air and water, at the time of these observations, was parti-
cularly ascertained. That of the air at sunrise, about an hour before the observations
commenced, had been 23° Fahr. ; but it was rising rapidly during their progress, and
was at 36° Fahr. before their conclusion. The temperature of the water in the Don
varied from 32° to 33° Fahr. ; but the variation could not be distinctly traced as de-
pending on the depth or velocity, as there was a temporary variation in the same
place, both in the pools and rapids. At one of the small streams, returning from
under the sheet-ice on the little pools at the edge of one of the rapids, the tempera-
ture was nearly steady at 33° Fahr. In the Leochal the temperature was nearly
steady everywhere at 32° Fahr.

By 10 o'clock A.M. on the same day, a cloud obscured the whole sky, and at 2 o'clock
P.M. the temperature of the air was 40° Fahr. At this time much gru rose from the
bottom and floated down the streams of both rivers. The relaxation of the frost,
however, was of very brief continuance. Before sunset the temperature of the air
was again down to 31° Fahr., with a perfectly calm air and clear sky ; and the clear
sky continued till the evening of the 7th of January, the thermometer during the two
intermediate nights being at 23°, and during the intermediate day at 26°.

The same parts of the Don and Leochal were again examined at 10 o'clock a.m. on

MDCCCXXXV. 2 X

336 REV. JAMES FARQUHARSON ON THE ICE

the 7th. In the Don the ground-gru now covered all the bottoms of the pools as
well as of the rapids. It was of less depth in the deep still pool below the great
rapid ; but everywhere else it formed a great impediment to the stream, raising it so
much above its former level that it covered deeply the pieces of sheet-ice formed at
the edge on the 5th. New pieces of similar ice were now forming at the same places
on the more elevated surface. The Leochal was still more impeded by the gru than
the Don.

But, what is worthy of particular notice, the clear spaces of the bottom, at the
piers, abutments, and embanking-walls of the bridge on the Don, and at the Phalaris
grass in the Leochal, still continued so, but were now considerably narrowed in their
lateral dimensions, the ground-gru having encroached upon them on the sides next the
streams. The temperature of the air was 24° Fahr. ; of the water, everywhere nearly
steady at 32°.

Several circumstances occurred on some subsequent days which deserve to be no-
ticed, as throwing light, by the contrast which they exhibit, on the phenomenon now
under consideration. On the 8th of January there occurred a thaw, when the ther-
mometer suddenly rose to 47° Fahr. The rivers were speedily cleared of ice and
ground-gru, which last rose from the bottom and floated away with the stream. The
atmosphere at the time was considerably clouded, with a brisk S.W. wind. On the
9th of January the temperature of the air fell to 36° Fahr. ; and on the morning of
10th of January, with a temperature of the air at 29° Fahr., there was a fall of snow,
of about an inch deep, which ceased by 8 o'clock a.m. The snow that fell into the
rivers was observed to be entangled, and stuck fast, in irregular crushed masses, in
many parts of the rapids ; and there were collections formed of loose spiculse of a
muddy aspect, at the sides of the stones opposed to the streams, in the heads of the
pools, where the velocity of the currents was intermediate between that of the rapids
and that of the stiller parts of the pools ; but there was no appearance on any part
of the bottom resembling the symmetrical cauliflower-shaped ground-gru. On the
evening of the 10th the temperature of the air fell to 23°, and continued at from 23° to
21° till the morning of the 12th, with a densely clouded state of the sky. During this
time extensive sheets of surface-ice were formed on the pools of the Don, and many
of the pools of the Leochal were quite frozen over, but the ground-gru was nowhere
renewed; on the contrary, the masses of snow entangled in the rapids on the 10th
disappeared to a great extent, obviously floating away in the stream. In this state
of the river and weather, the collections of uncemented spiculae, on the faces of the
stones opposed to the streams in the heads of the pools, appeared in their places the
same as before, neither increasing nor diminishing in size.

M. Arago, in his paper, refers to three circumstances, as partly, at least, expla-
natory of the formation of ground-gru in running water.

1st. The inversion, by the motion of the current, of the hydrostatic order, by which
the water at the surface, cooled by the colder air, and which at all points of the tern-

FORMED AT THE BOTTOM OF RUNNING WATER. 337

perature of water under 39° Fahr. would, in still water, continue to float on the sur-
face, is mixed with the warmer water below, and thus the whole body of water to the
bottom is cooled alike by a mechanical action of the stream :

2nd. The aptitude to the formation of crystals of ice on the stones and asperities of
the bottom, in the water wholly cooled to 32°, similar to the readiness with which
crystals form on pointed and rough bodies in a saturated saline solution :

3rd. The existence of a less impediment to the formation of crystals in the slower
motion of the water at the bottom, than in the more rapid one near, or at the surface.

There is no denying the justness of these three positions, and yet the slightest re-
flection teaches us that neither singly nor combined do they aid us in answering the
main question before us, " Why is ice formed sometimes at the surface of running
water, and sometimes at the bottom ?" All the circumstances, or conditions, referred
to by M. Arago, are present when ice, as most frequently takes place, is in the course
of being formed only on the surface, as well as when the formation is going on at the
bottom. Were we to admit them as an answer to our question, then running water
ought always to freeze first at the bottom. But a most extensive experience teaches
us that this is not the case. The illustrations of M. Arago, indeed, just and true in
themselves, are not to be overlooked when we would investigate and explain the for-
mation of ice either at the bottom or at the surface. They will serve to enlighten us
greatly in both these events, but they have no exclusive relevancy to either, and we
must therefore look out for another solution of the problem.

M. Arago, in his conclusion, does not present these three circumstances as a com-
plete explanation ; but he says, the reader may ask why he has not done so, and he
answers to this, " that we have no observations which prove that this kind of ice is
seen, until the temperature of the whole of the water is at zero " (centigr.) ; and that
it is not certain that the little icy particles, seen by Mr. Knight, floating on a milldam,
at the time ground-ice was forming in the stream, and which may have acquired in
contact with the air a temperature below zero (centigr.), do not play an important
part in the phenomenon which he has overlooked.

In regard to the former of these points, I cannot say what M. Arago would have
deduced from it, had it been established in one way or the other. The observations
made on the Don on the 5th of January show that the temperature of the whole
water was not quite down to 32° Fahr. when the ground-gru was forming in large
quantity. In regard to the latter, the little icy particles seen by Mr. Knight, the
same condition belongs to them that belongs to the circumstances professedly adduced
by M. Arago as explanations ; that is, they occur as well when the ice is forming on
the surface only as when it is forming on the bottom. They account well, however,
for the collections of frozen matter seen by him at the sides of the stones opposed to
the stream, in parts where its velocity had a certain modification.

And here I may advert to the explanation offered by the Rev. Mr. Eisdale, in his
paper already referred to. From the information he received, he was led to believe

2x2

338 REV. JAMES FARQUHARSON ON THE ICE

the groiind-gru does not occur but when there is a hoar frost on the ground ; and he
explains the ground-gru to be particles, or crystals as he afterwards names them, of
hoar frost precipitated into the water, retaining there the shapes in which they de-
scended, brought into contact with the rocks by the agitation of the water, and
forming nuclei for the accumulation of ground-gru. Could it be proved that such
crystals are precipitated into the water, they would serve no more for explanation
than the icy particles of Mr. Knight. We have learnt, indeed, from travellers in
high northern regions, that, in certain states of cold and moisture of the air, such
crystals, as Mr. Eisdale assumes, are there seen and felt floating in it ; but nothing
of that kind was observed in January last ; and when Mr. Eisdale, from the exist-
ence of spiculae of hoar frost on the ground, would infer the like may be formed in
the air to fall into the water, he neglects to take into the account, that the spiculse
of hoar frost have not fallen from above, but that their symmetrical arrangement,
round on all sides of the bodies on which they are found, and their slow increase,
prove they have been deposited on their places by a gradual deposition of invisible
watery vapour, owing to the substances to which they are attached being cooled
below the temperature of the surrounding air, by the radiation made known to us
by the experiments of Dr. Wells. Besides this we have to remark, that the ground-
gru sometimes takes place, agreeably to the information of one of Mr. Eisdale's own
correspondents, in a windy state of the atmosphere, at which time no hoar frost is
seen.

The interesting experiments of Dr. Wells just referred to enable us to give, after
all, a very satisfactory explanation of the ground-gru ; and Mr. M'Keever, quoted
by M. Arago, had gone far to illustrate it by means of them, although he had over-
looked some conditions necessary to be taken into the account for a complete expla-
nation. M. Arago, however, entirely rejects the explanation of Mr. M'Keever, and
it is fair to set down the terms in which he does so.

After having shown that the ground-gru cannot be explained by the action of the
moon*, according to the sailors, nor by the friction of running water producing more
heat at the surface than at the bottom, nor by referring its source to the smaller
tributaries of the streams, nor to different layers of ice formed at the several surfaces,
when the water in the river, from whatever cause, is in a state of varying fullness,
all of which have been assigned as causes of the ground-gru, M. Arago proceeds :

" We come now to Mr. M'Keever, who, confining himself closely to the most
subtle principles of the theory of heat, has not on this account been more fortunate
than his predecessors. According to this author, *the rocks, stones and gravel,
which generally cover the bottom of rivers, have powers of radiation superior to
those of mud, perhaps on account of their peculiar nature, but chiefly because they

* This explanation of the sailors is a confirmation of what I have stated, that the gru never appears but
under a clear sky. The constant observation of the sailors has associated, in their minds, the shining of the
moon with the ground-gru ; but the moon never shines, to excite great attention, but in a clear sky.

FORMED AT THE BOTTOM OF RUNNING WATER. 339

have rough surfaces. Thus rocks in large or small masses will become much cooler
in consequence of radiation : when the atmospherical temperature is very low, they
of course freeze the water which touches them.' It is unnecessary to examine here
whether heat radiates through a thick layer of water, as Mr. M'Keever supposes, as
the most simple observation is sufficient to overthrow it. Where is the person who
has not observed that the strong radiation, which the Irish philosopher admits, would
be more plainly manifested, or as completely, in still water than in running water ?
but no one has seen a piece of still water frozen at the bottom*."

But there is nothing more easy of experimental proof than that heat radiates through
water, I do not mean, however, to vindicate the reasoning of Mr. M'Keever re-
specting the more powerful radiation of it from stones than from mud. His reason-
ing respecting that matter is, on his own part, conjectural, to explain the readier
formation of gru on a stony or gravelly bottom ; but the gru also forms on a muddy
bottom, a fact which M. Arago notices, when he brings the attachment of mud to
the under side of the floating flakes as a proof that they have been formed at the
bottom. Mr. M'Keever was driven to his conjecture from having overlooked the
more complete and sudden inversion of the hydrostatic order that takes place over
stones than over mud ; which last is deposited only in places where the water has a
stiller and more equable motion. In such places the ground-gru is later in forming,
and therefore is more rarely seen ; and it is doubtful whether Mr. M'Keever had a
proper opportunity for noticing it in them.

But to return to the main point which we have here to maintain in opposition to
the reasoning of M. Arago, the radiation of heat through a body of water. When
we construct an achromatic object-glass for a telescope, it does not the less remain a
burning-lens when we have included in it a transparent fluid, and no experiment has
proved that were the fluid water the case would be altered. We are aware of the
danger that has been incurred of setting fire to an apartment by an ornamental glass
globe filled with water, and placed in the sun at a window. But as I cannot parti-
cularly refer to circumstances of time and place of the cases now mentioned, I made
an experiment on the subject with such apparatus as I could find readily at hand,
having no access to better in a remote country place-f . In a room, of which the
temperature was 50° Fahr., a semiglobular tumbler filled with water, containing
about a pint and a half, was placed inside a window, in the rays of the low but clear
winter sun. The bulb of a thermometer, which had been previously placed in a
similar situation till it rose and remained steady at 61°, was shifted into the brightest
part of the fan-shaped focus of rays, into which the light was refracted through the
tumbler. In this position it was raised in four minutes to 72°. It was again shifted
into the unconcentrated rays passing through the window, when it fell, but more

* Edinburgh New Philosophical Journal, vol. xv. pp. 132, 133.

t It may seem absurd to have had recourse to experiment in a case so plain ; but the procedure seemed, at the
same time, indispensable, to meet reasonings promulgated with the authority of such a distinguished name.

340 REV. JAMES FARQUHARSON ON THE ICE

slowly than it had risen ; and the experiment was repeatedly renewed with similar
results, leaving no doubt that the heat, like the light, radiated through, and was re-
fracted by the water. If the fact is so in regard to the radiation of heat through a
mass of water four or five inches thick, where ought we to set the limits of thickness
of the mass through which it cannot pass ? Obviously only where the thickness is so
great, that the aggregation of the fluid, and of its minute impurities, prevents the
transmission of light, as in the deeps of the sea, but not within the ordinary depths
of our clear streams.

Of the effect of radiation in cooling down the surface of the ground, and substances
placed upon it, during a clear sky, we cannot give a more lucid account than that of
M. Arago, in his paper " On the supposed Influence of the Moon on Vegetation."
" No one had supposed," says he, " before Dr. Wells, that terrestrial substances, ex-
cepting in the case of a very rapid evaporation, may acquire during the night a dif-
ferent temperature from that of the surrounding air. This important fact is now well
ascertained. On placing little masses of cotton down, &c. in the open air, it is fre-
quently observed that they acquire a temperature 6°, 7°, or even 8° centigr. below

that of the surrounding atmosphere These differences of temperature between

solid bodies and the atmosphere only rise to 6°, 7°, or 8° of the centesimal scale, when
the sky is perfectly clear. If the sky is clouded they become insensible." This lucid
statement, however, requires one modification ; for the greater cooling of the solid
substances, under a clear sky, takes place not only during the -night, but also during
the day, in places not directly exposed to the sun's rays.

This radiation, as it passes freely through the transparent atmosphere, may, as we
learn from the above experiment, pass also through the transparent water, to cool
down the solid substances at the bottom below the temperature of the surrounding
fluid. That fluid is permeable to radiating heat as well as the atmosphere. The
application of the thermometer, in the hands of Dr. Wells, instructed us regarding
the cooling of the surface of the ground ; but the water of a river, placed under the
veiy same condition of a clear sky, fluid above and freezing below, is a great natural
thermometer, teaching us that a corresponding cooling is going on on the surface of
the solid opake substances of the bottom. In fact, if we may so speak, the pheno-
menon of the ground-gru is the result of an experiment in the water, entirely similar
to that of Dr. Wells on the land, performed by nature on a large scale, and pre-
sented to us for our interpretation and instruction. And when we look back to the
observations made in the month of January, we find the results of the modifications
of this great natural experiment corresponding with those of similar modifications of
the experiment on the dry land.

The cooling of the surface of the ground by radiation, discovered by Dr. Wells,
takes place only under a clear sky. It is therefore greatly modified on parts of the
ground screened from a part of the sky by opake objects, as walls, trees, hedges.
In illustration of the extent to which a screening or shading body, near at hand.

FORMED AT THE BOTTOM OF RUNNING WATER. 341

modifies the radiation, 1 shall detail some observations I made on the 7th of January
last, incidentally in the first instance, but then extended, in reference to the obser-
vations on the ground-gru, which I was making at the time. Having occasion that
day to dig into recently hoed ground, in the middle of a garden, remote from shade,
the soil was observed to be frozen to the depth of four inches, by the clear frost,
which had continued from the 1st of January, with the trifling intermission above
mentioned. On digging into similar ground at the north base of a wall six feet
high, the soil was found, close at the foot of the wall, frozen to the depth of only
half an inch ; at a foot distance from it, about an inch ; at two feet, little more ; and
it was only at the distance of ten or twelve feet that it was frozen hard to the depth
of three inches. A similar modification of the effect of radiation was observed in
the shade of trees. Under the Scotch fir the soil, slightly covered with decaying
herbage, was not at all frozen ; although in similar ground similarly covered, but re
mote from shade, it was hard frozen to the depth of two or three inches.

Now the ground-gru in the rivers was modified in a way strictly similar by the
effect of shade. The bridge of Alford, over the Don, is happily situated for illus-
trating this, being on one of the rapids, where the ground-gru is earliest and most
abundantly formed. While the other rapids, and the unshaded parts of this one,
were quite occupied by gru on both the 5th and 7th of January, spaces in the shade
of the masonry at this bridge were quite clear of it. It cannot be admitted as an
explanation of this fact, that heat may have been there laterally transmitted to the
water by contact with the piers and walls ; for if this took place, why then did the
clear spaces on the bottom narrow gradually towards the low extremities of the em-
banking walls ? Besides, the transmission of heat laterally had not hindered the for-
mation of surface-ice, in contact with a pier, on a piece of still water under one of
the arches. The modification of the radiation by shade was also exhibited in the
absence of all gru on the bottom, along the foot of the dense tuft of Phalaris grass
in the Leochal, where there could be no more transmission of heat laterally, than at
the general line of the grassy banks of this stream.

The water, too, returning warmer from under the surface-ice, on the little pools at
the edge of one of the rapids, is another instance of the modification of the radiation
by shade. The thin white opake covering of hoar frost on the ice prevented radia-
tion, at least in a great measure, and the heat of the bed of the river, in the course
of continual transmission upwards, from strata not yet cooled to much depth by the
frost, finding no outlet by the radiation, was expended in heating the water by con-
tact.

There was another phenomenon observed on the 5th of January, (although no
longer seen on the 7th, being then concealed by the immense formation of gru,)
which can be readily explained by the admission of the radiation of heat through
the water, and therefore goes to support the justness of the theory. The tufts of
water starwort, in the deepest and stillest parts of one of the pools, were the darkest-

342 REV. JAMES FARQUHARSON ON THE ICE

coloured objects seen at the bottom, and they were fringed in every part with spi-
culse of gru, at a time while it yet occupied little of the bottom of this pool. The
experiments of Boyle, Franklin, Rumford, Leslie (although he denies the conclu-
sion himself), Davy, and Stark appear too uniform in their results to leave any
doubt remaining, that dark -coloured bodies both absorb and radiate heat more freely
than those which are light-coloured. It is in consistency, then, with an ascertained
law of the radiation of heat, that the very dark-coloured tufts of the water starwort
should have been the first bodies in the pool cooled to a very low temperature, and
of course first covered with gru.

In arguing the whole question, let us not forget to assign a proper value to the
illustrations of M. Arago. The first of them suggests a ready and satisfactory answer
to one of the objections which he brings against the theory of radiation, which is,
that the effect of it should be as readily manifested in still as in running water, and
yet no one has seen a piece of still water frozen at the bottom*.

In still water, that hydrostatic order, which M. Arago has so well illustrated as
belonging to water when reduced to a temperature under 39° Fahr., has free play to
establish itself, and is not inverted by the mechanical action of a stream. When the
temperature of a body of water is under 39°, then the coldest portions of it are the
lightest, and naturally rise and float on the surface. When in a still pond the water
nearest the bottom has been cooled below the general temperature by contact with
the solid materials cooled by radiation, it is displaced by the heavier warmer water
above. Hence ice forms first on the surface by the meeting there of both the cold
of radiation and that acquired by contact with the incumbent cold atmosphere.

M. Arago's illustrations also furnish us with a satisfactory explanation of the
curious facts, that the ground-gru makes its first appearance in the more rapid and
agitated parts of the stream, and begins to show itself on the bottoms of the stiller
parts, and to accumulate there in quantity, only after a longer continuance of the
clear frosty weather. In the rapids the hydrostatic order is overturned, and the
colder, which is also the lighter, water not only mixed with the warmer below, but,
at the whirls of the greatest rapids, brought suddenly, without much mixing, into
direct contact with the bottom, cooled still lower than itself by radiation. If the
water is at the temperature of 32° Fahr. it can give out no heat to the colder bottom

* There is an exception to the universality of this position, which, although rare, I have sometimes witnessed;
and as the phenomenon is in accordance with the theory of the radiation of heat from the bottom, it deserves
notice. In little ponds of a foot or two deep, dug to obtain the materials for building or agricultural purposes,
of which there are many examples in this neighbourhood, after they have been covered, owing to hard and long-
continued frost, by a thick sheet of ice, that is sometimes nearly melted off, and the remaining fragments
driven to the lee side by a strong westerly gale of high temperature. Such a gale, in this climate, frequently,
towards its conclusion, shifts to N.W., when the temperature of the air falls again below the freezing-point of
water, with a generally clear sky. In such peculiar circumstances the little ponds are suddenly filled with gru,
commencing at, and shooting up from the bottom. The whole water is here at 32° Fahr. when the gru be-
gins forming, and the hydrostatic order is deranged by the wind.

FORMED AT THE BOTTOM OF RUNNING WATER. 343

without part of it being converted into ice, the spiculae and crystals of which find a
solid body for their attachment at the very point where the heat is given out*.

But while in this manner we can explain some of the incidents, may it not be held,
as above demonstrated, that the chief cause of the ground-gru is the radiation of heat
from the bottoms of the rivers ? Every branch of the phenomenon is of easy expla-
nation when we admit the radiation ; and among the rest a circumstance to which I
have yet made no reference, and that is, the disappearance at the bottom of the water
of the immense quantity of heat, 140° of Fahr., which constitutes the caloric of
fluidity disengaged, when water at 32° Fahr. is converted into ice at the same tem-
perature.

The answer to our original question then is. That ice is formed sometimes on the
surface of running water, and sometimes at the bottom, because frost sometimes
takes place with a clouded sky, which is incompatible with radiation of heat from
the bottom of the stream, and sometimes with a clear sky, when that radiation takes
place through the water, in the same manner as the experiments of Dr. Wells prove
it goes on, under a like sky, through the atmosphere. The bottom is by this cooled
down below the freezing point of water, before the water itself; ice is formed on it,
and its detachment by transmitted heat from below prevented, as long as the radia-
tion continues.

* We may observe also, that there is a local source of greater cold of the water in the rapids, in its being
brought into more active and extensive contact with the air by the sharp ripple and spray.

MDCCCXXXV.

2 Y

[ 345 ]

XIX. Observations on the Theory of Respiration. By William Stevens, M.D. D.C.L.
Fellow of the Royal College of Physicians in Copenhagen, Fellow of the Royal
College of Surgeons in London, ^c. S^c. Communicated hy W. T. Brande, Esq.
V.P.R.S.

Received April 30,— Read May 14, 1835.

A HE cause of the dark colour of the blood in the venous circulation has long been
a subject of discussion ; but even at the present moment the question has not been
satisfactorily decided.

It is universally admitted that the expired air contains carbonic acid, but it is still
doubtful in what part of the system this acid is formed. Lavoisier maintained that
carbon was the cause of the dark colour of the venous blood, and that the acid was
formed in the pulmonary organs, by the combination of that carbon with the oxygen
of the air. At one period this theory was generally adopted, though the evidence in
its favour is almost entirely hypothetical ; for hitherto there has not been even one
well-conducted experiment which proves the existence of any form of free carbon in
the venous blood.

Another class of physiologists maintain that the carbonic acid is formed, not in
the lungs, but in the general round of the great circulation ; in proof of which
some experimentalists have asserted that they had obtained carbonic acid from
venous blood ; but others, of equal respectability, who have repeated the same expe-
riments, deny the existence of this acid in the venous current. The air-pump has
hitherto been almost exclusively used for the purpose of deciding this question ; but
the positive proofs which have been brought forward by the one class of physiolo-
gists have been so completely contradicted by the negative proofs of the other, that
a great majority remains still in favour of the old theory. In fact, Tiedemann and
Gmelin, the latest writers on this subject, are decidedly of opinion that venous
blood does not contain carbonic acid. As this is a very important question, the fol-
lowing experiments were made in reference to it.

1. A glass vessel containing a small quantity of warm and fluid venous blood was
put under the receiver of an air-pump. In proportion as the air was exhausted, a
number of globules appeared to escape from the blood, which were at first small, but
in proportion as the air was removed they became larger in size.

2. A small quantity of venous blood, contained in a glass vessel, was covered with
a layer of barytic water. This was put under the receiver of an air-pump. When the

2 y2

346 DR. STEVENS ON THE THEORY OF RESPIRATION.

pump was used, globules were observed to escape from the blood, which passed
through the barytic water, but the transparency of the latter was not affected.

The annexed sketch is a representation of an apparatus which was invented by
Mr. Squire, of Duke Street, Grosvenor Square, and used in the fol-
lowing experiments. To a double-necked pint bottle, a, two glass
tubes were fitted, one, b, ascending, the other, c, descending. The
ascending tube is terminated by an air-tight box, having an aper-
ture, over which a slide is moved by means of a strong wire. The
descending tube is terminated by a brass orifice, which is closed at
pleasure by a brass cap, having a cone in the centre surrounded with
leather, and moved with a sliding wire, d represents a four-ounce
phial with a loop of wire round the neck, by which it is connected
with the descending tube. The phial was filled to the double line
with distilled water.

3. The pint bottle and both tubes being filled with pure hydrogen gas, the ori-
fice of the upper tube was placed on the skin, near the bend of the arm ; a vein was
then opened, and the orifice slid carefully along until it included the incision which
had been made by the lancet. The valve was opened, and as the blood passed into
the bottle, hydrogen was expelled through the descending tube, the orifice of which
was immersed in distilled water. As soon as five or six ounces of blood had entered
the bottle, both the orifices were carefully closed. The orifice of the descending tube
was then immersed in barytic water, and the valve being opened, the whole was
placed under the receiver of an air-pump. In proportion as the air was removed,
the hydrogen, as well as any gas that might escape from the blood, passed through
the barytic water, without, however, producing the slightest change in its trans-
parency.

From the first of these experiments it might be inferred that a gas is capable of
being removed from venous blood by the air-pump : but this supposition may pos-
sibly be erroneous ; for similar globules appear to arise when we use water, even
after it has been boiled and then cooled in a close vessel to 98°. The second expe-
riment shows that this appearance is not due to the escape of carbonic acid ; and
from the third experiment it is very obvious that carbonic acid cannot be so obtained
from venous blood which has not been exposed to air.

4. About four ounces of serum were put into a Hope's eudiometer, the upper divi-
sion of which contained four tenths of a cubic inch of carbonic acid : they were
agitated together, and after a few minutes the serum had absorbed the whole of the
acid. This impregnated serum, without being exposed to the air, was transferred into
the double-necked pint bottle, which had previously been filled with hydrogen, and
which was immediately put under the receiver of the air-pump. When the pump
was used, the hydrogen, as well as the gas which appeared to escape from the serum,
passed through the baiytic water ; but its transparency was not affected.

DR. STEVENS ON THE THEORY OF RESPIRATION. 347

From this experiment it is obvious that serum (consequently blood or other albu-
minous fluid,) may absorb carbonic acid, and so retain it as not to be separable by
the mere removal of the pressure of the air.

The air-pump has hitherto been used almost exclusively by the experimenters on
venous blood ; and those who deny the existence of carbonic acid in it, do so almost
entirely on such evidence. The fact of their not having thus obtained this gas is cor-
rect ; but there is an error in the conclusion drawn from it, which is the chief cause of
the difference of opinion on this subject ; for such experiments only afford a positive
proof that carbonic acid cannot always be obtained from blood placed under the ex-
hausted receiver of the air-pump : but, with respect to the existence or non-existence
of such acid in the blood, the proof is merely negative ; for in experiment 4. the pump
did not separate carbonic acid from serum previously impregnated with it : conse-
quently such experiments are inconclusive.

5. Carbonic acid was introduced into an empty bladder that had been previously
well moistened with warm water. When the bladder was distended about one third,
its neck was firmly tied with a waxed thread, by which it was suspended in the centre
of a receiver of an air-pump. When the pump was worked, the bladder increased in
volume, and in a few seconds was much distended. Nearly the whole of the atmo-
spheric air was exhausted from the receiver, but the bladder, though apparently very
tense, did not burst, neither did it decrease in size. A shallow glass vessel contain-
ing barytic water had been placed under the same receiver, but the transparency of
this was not affected. Hydrogen was then transmitted into the receiver, and the
bladder was reduced to the same size as when first suspended under it ; but, after an
interval of four hours, it had become perfectly flaccid. In fact, there was scarcely a
particle of carbonic acid left in it, and the barytic water within the receiver contained
a quantity of carbonate of baryta.

6. The double-necked bottle was carefully filled with pure hydrogen, and about
five ounces of blood were drawn into it from a vein in the arm, in the same manner
as in experiment 3. Both the orifices of the bottle were then closed, and the blood
and the hydrogen well agitated together. After this the lower orifice was immersed
in distilled water, and the bottle left undisturbed for nearly an hour, to allow the
hydrogen to act on the blood. The orifice of the descending tube was then immersed
in barytic water, the lower valve was opened, and the whole apparatus put under the
receiver of the air-pump. When the pump was used, the gas which was over the
blood passed through the barytic water, and immediately rendered it turbid. This
experiment seems to prove that venous blood does contain carbonic acid ; and as the
only difference between experiments 3 and 6 was, that in the former the pump was
used immediately, and before the hydrogen had time to act on the blood, whilst in
the latter the hydrogen was allowed to act nearly an hour, it would appear that the
hydrogen has some power of removing the carbonic acid, and that this removal may
even take place through a membrane. In the last experiment^ the blood which was

348 DR. STEVENS ON THE THEORY OF RESPIRATION.

used had been carefully excluded from atmospheric air, and the hydrogen was pure ;
consequently the carbonic acid could have been derived from no other source than
the venous blood itself.

7. A few ounces of venous blood were drawn into a double-necked bottle pre-
viously filled with hydrogen. After having been gently heated, the hydrogen was
found to contain carbonic acid. This experiment was made at Copenhagen in the
beginning of 1833^ by Professor Forchammer and myself; but the conclusion which
we drew from it respecting the existence of carbonic acid in the blood was by some
objected to, in consequence of the interference of heat : the air-pump experiments,
however, remove all such objections.

Dr, Edwards confined some animals in an atmosphere of hydrogen, and they con-
tinued to live for a considerable period, during which it was found that the hydrogen
had acquired a portion of carbonic acid, which in some cases was equal in bulk to
the size of the animals. By some these experiments were considered as conclusive of
the evolution of carbonic acid from venous blood ; but others maintained that there
might have been a sufficient quantity of oxygen in the pulmonary cells to account
for the formation of the carbonic acid. This objection is also removed by the above
experiment.

Dr. Mitchell of Philadelphia made an experiment in 1830 with hydrogen and
venous blood, but without obtaining any carbonic acid. Mr. G. H. Hoffman of Mar-
gate made a similar experiment in 1832, and obtained a sufficient quantity of car-
nic acid, not merely to render lime water turbid, but even to render the hydrogen
uninflammable. These contrary results seem to me to have arisen from Dr. Mitchell
having used the air-pump immediately, and before the hydrogen had time to act on the
blood so as to displace its carbonip acid ; whereas Mr. Hoffman agitated the hydrogen
with the blood, and probably allowed a sufficient time for their mutual action.

8. A small quantity of venous blood was drawn into the double-necked bottle,
containing atmospheric air, the valve at the orifice of the ascending tube was closed,
and the orifice of the descending tube was immersed in barytic water. The bottle
was put under the receiver and the pump immediately used. But in this experiment
the barytic water was not more affected than it would have been by a similar quan-
tity of common air. This proves that when the blood is exposed even to common
air, carbonic acid cannot be obtained, when the pump is used immediately, and before
any change of colour in the blood has taken place ; that is, before the air has had
time to act upon it.

9. A small quantity of blood was drawn into the double-necked bottle containing
atmospheric air, as in the last experiment. Both of the valves were closed, and after
agitation, the bottle was allowed to stand about an hour, during which the colour of
the blood changed from venous to arterial. The lower orifice was then immersed in
barytic water, the apparatus was put under the receiver of the air-pump, and when
the pump was used, the gas which escaped gave a milky appearance to the barytic

DR. STEVENS ON THE THEORY OF RESPIRATION. 349

water. In the eighth experiment the pump was used immediately, and before the air
had time to act on the blood, or the blood on the air. In the last, one hour was al-
lowed for the action of these agents upon each other ; during which the blood on
the surface changed from venous to arterial, and the air over the blood received the
addition of carbonic acid.

Those who maintain that carbonic acid informed in the lungs will say, that in the
last experiment the carbon of the blood attracted the oxygen of the air, and that the
carbonic acid so formed was then evolved. But there is one circumstance which is
I think fatal to such an explanation, for all the acids blacken the blood, and carbonic
acid possesses this blackening property in a remarkable degree. When we agitate
a small quantity of carbonic acid gas with arterial blood, the colour immediately
changes to venous, and when we add carbonic acid to venous blood it becomes
almost black. Now, if the carbon of the blood attracted the oxygen of the air, and
if the carbonic acid were thus formed in the blood itself, it is evident that the Jirst
effect of the air on the blood would be to make this fluid blacker than it had been
before ; but the opposite of this is the fact, for the Jirst effect of the air is, not to
blacken, but to brighten the blood ; consequently, from this alone, we may infer, that
the acid is not formed during the experiment, but that it exists ready formed in the
blood, and that it is only removed, and not produced or formed, by the atmospheric
air.

I have already observed that one class of experimenters have obtained results by
means of the air-pump which are in direct opposition to those obtained by others.
May we not now, from the above experiments, explain this difference by supposing
that those who could not obtain carbonic acid made their experiments before the air
had had time to act on the blood, whilst the others had allowed some time to elapse ?

From the preceding statement we may, I think, conclude,

1st, That venous blood contains carbonic acid;

2nd, That the mere effect of diminished pressure upon the surface of the blood is
not necessarily followed by the escape of its carbonic acid*.

We have seen in some of the above experiments that atmospheric air possesses a
property of removing carbonic acid from venous blood ; it becomes therefore a
question how this effect is produced. I have ascertained that nitrogen is ineffective;
we may therefore infer that the oxygen is the principal agent ; and that such is the
fact is proved by the following experiments.

1 0. A piece of moist bladder was tied firmly over the mouth of a tumbler contain-
ing pure oxygen gas. This was introduced into a large bell glass filled with carbonic
acid. In a short period the membrane which had been tied over the glass became
convex, and so tense that it appeared to be on the point of bursting. On examining
the air contained in the tumbler, it was found that the oxygen had drawn in a large

* In performing the above experiments I was assisted by Mr. Squire, to whom I feel under great obligation
for the zealous and able manner in which he aided me in the whole of the present investigation.

350 DR. STEVENS ON THE THEORY OF RESPIRATION.

quantity of the carbonic acid ; but no oxygen appeared to have passed out of the
tumbler.

11. A piece of moist bladder was tied over the mouth of a tumbler containing car-
bonic acid ; this was introduced into a bell glass filled with pure oxygen. In a short
period the membrane became concave, and the oxygen in the larger vessel was found
to be mixed with carbonic acid.

These two experiments prove that oxygen possesses the power of attracting carbo-
nic acid, even through the medium of a membrane which is much denser than that
interposed in the lungs betwixt the air and the blood ; consequently, the extreme de-
licacy of the pulmonary membrane can be little impediment to the transmission of
carbonic acid in the process of respiration.

I have ascertained that such transmission, or, in other words, the peculiar power by
which oxygen abstracts carbonic acid from the blood, is more energetic in a high
than in a low temperature. Hence venous blood drawn in a warm room changes
colour more rapidly than blood drawn in a cold atmosphere.

12. A few ounces of venous blood were drawn into the double-necked bottle which
had been previously filled with pure oxygen ; the valves were closed, the blood was
well agitated with the gas, and the colour immediately changed from venous to arte-
rial. The bottle was allowed to stand about half an hour, and was then placed under
the receiver of an air-pump. When the pump was used the oxygen was found to be
strongly impregnated with carbonic acid ; in fact, the first bubbles of air which passed
through the barytic water rendered it milky.

From the rapidity of the change of colour from venous to arterial, or from dark to
florid, in this experiment, it seems very improbable that any carbonic acid shoidd
have been ybrmec? in the blood, but that, on the contrary, it had previously existed in
the blood, and that the whole of this blackening gas had been instantly removed by
the oxygen.

13. A piece of the intestine of a rabbit that had been recently killed was filled
\dth carbonic acid, and suspended in a bell glass containing owygen. In a short pe-
riod the acid escaped, and the intestine became quite flaccid.

14. A piece of intestine, similar to that used in the last experiment, was filled with
oxygen, and suspended in a bell glass of carbonic acid ; the intestine began to swell
almost immediately, and in three minutes it burst.

15. The lung of a rabbit was filled with oxygen, and suspended in a bell glass of
carbonic acid ; it began to swell almost instantly, and in one minute it burst.

16. The lung of a rabbit was carefully inflated with carbonic acid, and was then
suspended in a bell glass of oxygen. In a very short period it became flaccid, and the
external oxygen was impregnated with carbonic acid.

These experiments show how admirably the structure of the lungs is adapted for
the action of oxygen on carbonic acid. Vitality may have some share in accelerating
this process in the pulmonary organs, but we know that by the agency of oxygen

DR. STEVENS ON THE THEORY OF RESPIRATION. 351

dead blood may be changed from venous to arterial, even through a dead mem-
brane.

This power which gases possess of acting on each other is in some respects similar
to that which takes place in fluids, and which has been described by Dutrochet
under the name of endosmosis and exosmosis. In the experiments detailed by this
philosopher the intervening septum is supposed to contribute materially to the phe-
nomena. In the experiments with gases the intervening membrane does not prevent,
but it does not contribute to, the change. But independent of this, the existence of
this power in gases was not known to Dutrochet until after the fact had been fully
ascertained by others. Mr. Dalton many years ago proved that hydrogen possessed
the power of penetrating or mixing with carbonic acid in opposition to gravity ; that
oxygen possesses the same property, but in a higher degree, I ascertained in the
island of St. Thomas in 1 827. I afterwards made experiments on a larger scale, in
1830, at the high rock of Saratoga, where there is an atmosphere of natural carbonic
acid ; and the result was communicated to many physicians in America previously
to any of the American publications on the subject.

It is now more than probable that the changes which Lavoisier believed to occur
in the lungs take place in reality in the extreme circulation. Some later writers
have assumed that the elements of carbonic acid exist in the blood, and that its for-
mation commenced in the large vessels as they leave the left side of the heart, and
was not finally completed until the blood arrives in the right auricle. But that this
opinion is erroneous, is evident from the fact, that the blood even in the smallest
arteries is as completely arterial as that in the left side of the heart, whilst the blood
in the smallest veins is equally venous.

There is in the capillary system, over the whole body, an intermediate structure
which connects the arterial with the venous circulation, and it is in this structure
that the blood 4s changed from arterial to venous. When the arterial blood leaves
the minute arteries, it is no longer confined in actual vessels, but in cells that are
formed by the surrounding tissue. When this cellular structure is examined in
living animals, with the assistance of a good microscope, minute globules are seen to
leave the cells and penetrate the surrounding solids, whilst other globules are seen
to return and mix with the blood in the cells. Now as we know that it is in these
cells that the blood becomes dark and venous, from the addition of carbonic acid,
may we not suppose that the globules which leave the blood are minute particles of
oxygen, attracted perhaps from the arterial blood by the fixed carbon of the solids,
and that the globules which return are minute particles of carbonic acid ? This can-
not be easily proved ; but as carbon is a principal ingredient in the solids when these
are converted into fluids, previous to their removal by the lymphatics, it appears to
me not improbable that a part of their carbon may be liberated, perhaps for the pur-
pose of evolving heat. We have seen that the blood which receives oxygen in the
lungs passes unchanged through the arteries into the capillary system ; and it is ap-

MDCCCXXXV. 2 z

352 DR. STEVENS ON THE THEORY OF RESPIRATION.

parently there that animal heat is evolved. When carbonic acid, which is the result
of the above process, is added to the venous blood, it not only blackens the colour,
but renders it incapable of supporting life. For this reason warm-blooded animals
have a double circulation, one for circulating the arterial, and another for purifying
the venous blood*.

When we obtain hcematosine, or the colouring matter of the blood, in a pure state,
it is black ; but a solution of any neutral salt possesses the peculiar property of
striking a beautiful scarlet or arterial colour with it. When we make an incision
into a clot of blood which has just coagulated, we find that the clot is then all equally
red : when we cut out a thin slice of this red clot, and immerse it in distilled water,
the salt serum oozes into the water. In proportion as this takes place the clot be-
comes darker ; and when the whole of the serum is removed, perfectly black. When
in this state neither atmospheric air, nor even pure oxygen, is capable of changing
its colour ; but when we immerse this black clot in a clear saline solution, it in-
stantly changes from jet black to a scarlet, or arterial colour. From these facts we
may conclude, that oxygen is a secondary agent in the change of colour from venous
to arterial ; and that if the scarlet colour of the blood be essential to life, it is pro-
duced, not by oxygen, but by another cause. The mere removal of the carbonic acid
from venous blood would not produce any change of colour, were it not that there
is in the blood itself another agent which produces the arterial tint, the moment
that the blackening effect of the carbonic acid is removed : this is effected by the
action of the natural saline ingredients of the blood on the colouring matter. When
oxygen is added to blood it may have a slight share in brightening the colour,
but it can only perfectly effect this when the colouring matter is in contact with a
saline fluid. Oxygen is so far from being the sole cause of the arterial colour, that
even pure oxygen is of itself inert as a colouring agent ; whilst a saline fluid changes
the colour of the blood from venous to arterial even in an atmosphere of carbonic
acid.

Many authors describe the changes which occur in respiration, by asserting " that
oxygen disappears, and carbonic acid is emitted." But from some of the experiments
which I have detailed, it is evident that the removal of the acid is the first part of
the process, and the addition of oxygen the last. Others have maintained that when

* It is well known that cold-blooded animals use very little food. If a rattlesnake gets one good meal
in three months, it is all that he requires : but even this is not actually necessary ; for I have seen one of these
animals that had not tasted food or water for twelve months, as plump, active, and venomous as those in the
wild state. On the other hand, all those animals that have warm blood require an immense quantity of food,
and if they do not receive this they soon perish ; but nineteen twentieths of this appears to be taken into the
system for the evolution of animal heat. The carbon is ultimately derived from the nourishment that we use,
and the oxygen is directly derived from the arterial blood : a constant supply of nourishment is therefore
necessary in warm-blooded animals, but a very small part of the blood which is formed from this is required
for nuttition, and if the whole of it were expended in this way, it is very clear that there would be none left to
return by the veins.

DR. STEVENS ON THE THEORY OF RESPIRATION. 353

two gases act upon each other, the one penetrates the membrane at the same mo-
ment that the other is removed. But if this were the case, why did the membrane
become convex in experiment 10, and concave in experiment 11 ? If the action were
equal, the membrane would remain unchanged ; but this is so far from being the
case, that in some experiments the membranes became distended to such an extent
that they actually burst.

It was supposed by Spallanzani, and afterwards by Dr. Edwards, that in the pro-
cess of respiration the carbonic acid was merely exhaled from the lungs. We have
seen, however, that venous blood so retains that acid that it cannot be removed,
even with the aid of an air-pump ; consequently, were there not an active agent for
the purpose of removing the carbonic acid from the venous blood as it circulates
through the lungs, it would remain unchanged, and almost instantly cause death.
It is the power which oxygen possesses of attracting carbonic acid, which renders
oxygen essential to life. As hydrogen also possesses this power, it supports life for a
longer period than most of the other gases ; but hydrogen has a deleterious effect
on the blood ; and when animals are forced to breathe it, though the carbonic acid
is removed, a part of the hydrogen is at the same time absorbed, which blackens
the blood, and the animals soon die.

The property which oxygen possesses of attracting carbonic acid, furnishes the
following explanation of the process of respiration. When the venous blood arrives
in the lungs, the oxygen of the atmosphere is, in the first instance, the active or at-
tracting agent. It removes the carbonic acid, which had been the cause of the dark
colour of the blood. When this is removed, or perhaps in proportion as it is re-
moved, the blood becomes the attracting agent, and a portion of oxygen is attracted
into the blood, and takes the place of the carbonic acid. From the peculiar struc-
ture of the lungs, these changes are rapidly effected, particularly at the high tempe-
rature of 98° ; and when the process is fully completed, we know from the great
discovery of Harvey, that the blood which has received the pure air passes rapidly
on to the arterial, and from this again to the capillary system.

If the above theory be correct, it follows that the blood is converted from arterial
to venous in the extreme circulation, by the loss of oxygen and the addition of car-
bonic acid ; whilst the venous blood is converted into arterial, by the loss of carbonic
acid, and the addition of oxygen ; consequently, the essential difference betwixt venous
and arterial blood is, that the former contains carbonic acid, and the latter oxygen.

I have said that black is the natural colour of the colouring matter ; but when this
agent is diffused in a saline fluid, such as the serum, it is of a bright scarlet tint,
which is, in fact, the natural colour of arterial blood. When carbonic acid is added
to this blood in the extreme circulation, it becomes dark red ; but when this acid is
removed in the pulmonary organs, the blood then resumes its natural scarlet or
arterial colour ; and this, as I have said, is produced not directly by oxygen, but
chiefly, if not entirely, by the action of the salts of the blood on the colouring matter.

2z2

354 DR. STEVENS ON THE THEORY OF RESPIRATION.

Oxygen, it is true, changes the colour from venous to arterial ; this, however, is ef-
fected not by any specific action, but by the removal of the carbonic acid, which
had been the cause of the dark colour in the venous circulation.

Many objections have been made to the above theory, some of which are frivolous;
but there are two which are worthy of notice. The first was made by Mr. Prater
of Edinburgh, who stated, that according to this theory the blood ought to become
arterial under the exhausted receiver of the air-pump. This objection is removed by
the foregoing experiments, which prove that the mere removal of the air's pressure
is insuflicient to overcome the attraction that subsists between the carbonic acid and
the blood. The second objection was made by Dr. Gregory and Mr. Irvine of Edin-
burgh. These gentlemen admit that if the blood were a stronger saline fluid than
it is, the salts would be capable of producing all the effects described ; but they con-
ceive that the blood is not sufficiently impregnated with saline matter to account for
the whole of the phenomena. This objection, even if proved, would only require a
modification of the theory ; but that there was a fallacy in their experiments which
neutralized their conclusion, has been proved by a paper in the Medical Gazette of
the 12th of April, 1834.

[ 355 ]

XX. Discovery of the Metamorphosis in the second type of the Cirripedes, viz. the

Lepades, completing the Natural History of these singular Animals, and con-

Jlrming their affinity with the Crustacea. By J. V. Thompson, F.L.S, Deputy

Inspector-General of Hospitals. Communicated hy Sir James Macgrigor, Bart.

M.D. F.R.S.

Received January 3, — Read March 5, 1835.

The Fourth Memoir, published in my Zoological Researches and Illustrations,
No. III. page 69, &c., having first made known the real nature of the Cirripedes, the
key of which remained concealed in their metamorphosis, it might have been expected
that some naturalist favourably situated to investigate the oceanic tribe of these
animals, would have been the first to make the same discovery in regard to these, and
thereby complete their natural history. It was scarcely to be expected that the
honour of this discovery also should be reserved for the author, fixed to one spot,
where none of them naturally exist, and are but casually thrown upon our shores by
the waves of the Atlantic, attached to pieces of wreck, or brought into port fixed to
the bottoms of ships returning from distant voyages. Fortunately, however, two
ships of this description came into this harbour (Cork), one from the Mediterranean,
the other from North America, which, not being sheathed with copper, had their bot-
toms literally covered with Barnacles of the three genera of Lepas, Cineras, and Otion ;
and having persons employed expressly for the purpose, numbers of these were brought
alive in sea water, amongst which were many with the ova in various stages of their
progress, and some ready to hatch, which they eventually did in prodigious numbers,
so as to enable him to add the proof of their being, like the Balani, natatory Crusta-
cea in their first stage, but of a totally different facies and structure ; a circumstance
which determines the propriety of the separation of the Cirripedes into two tribes,
and evinces the sagacity of Mr. MacLeay in being the first to indicate that these two
tribes, the Balani and Lepades, were not so closely related as generally supposed *.

The larvae of the Balani, described in Memoir IV. under the external appearance
of the bivalve MonocuU {Astracoda), have a pair of pedunculated eyes, more numerous
and more completely developed members, approximating to those of Cyclops, and of
the perfect Triton ; while, in the present type, or Lepades, the larva resembles some-
what that of the Cyclops, which Muller, mistaking for a perfect animal, named Amy-
mone, and which can be shown to be common to a great many of the Entomostraca ;

* See Horae Entomologicae.

"356 MR. THOMPSON ON THE METAMORPHOSIS

or the resemblance is still more striking to that of the Argulus Armiger of Latreille,
which, in fact, is but an Amymone furnished with a tricuspidate shield at the
back.

The genus Cineras was the first in which the larvae were observed to hatch, July 27,
three days after the arrival of the ship ; then in Lepas anserifera, August 19 ; and a
few days later in Lepas dentata ; in all of which there is a perfect accordance, with
very slight differences, which probably resulted from the more or less perfect develop-
ment of the larva. The very remarkable and beautiful one of Lepas anserifera may
be regarded as the perfect type to which all the others are to be referred (fig. 5.).

In the whole of this tribe of the Cirrlpedes, the ova, after expulsion from the ova-
rium, appear to be conveyed by the ovipositor into the cellular texture of the pedicle,
just beneath the body of the animal, which they fill to the distance of about an
inch. When first placed in this situation they seem to be amorphous, and inseparable
from the pulpy substance in which they are imbedded ; but as they approach to ma-
turity, they become of an oval shape, pointed at both ends, and are easily detached.
Sir EvERARD Home has given a very good representation of them, at this stage of
their progress, in his Lectures on Comparative Anatomy, from the elegant pencil of
Mr. Bauer.

During the stay of the ova in the pedicle, they render this part more opake, and of
a blueish tint ; the ova themselves, and the cellular texture with which they are sur-
rounded, being of a pale or azure blue colour. It is difficult to conceive in what
manner the ova are extricated from the situation above indicated ; but it is certainly
not by the means suggested by Sir Everard Home in the above-mentioned Lecture,
viz. by piercing outwards through the membranes of the pedicle, for the ova are sub-
sequently found forming a pair of leaf-like expansions, placed between either side of
the body of the animal and the lining membrane of the shells in Lepas (fig. 1 .), or of the
leathery internal tunic in Cineras. These leaves have each a separate attachment at
the sides of the animal to the septum, which divides the cavity occupied by the
animal from that of the pedicle : they are at first comparatively small, have a rounded
outline, and possess the same blueish colour which the ova had in the pedicle ; but
as the ova advance in progress these leaves extend in every dimension, and lap over
each other on the back, passing through various lighter shades of colour into pale
pink, and finally, when ready to hatch, become nearly white (fig. 2.). These leaves
appear to be composed of a layer of ova irregularly placed, and imbedded in a kind
of parenchymatous texture, out of which they readily fall when about to hatch, on
its substance being torn asunder ; indeed, it appears at length to become so tender as
to fall entirely away, so that after the period of gestation is past, no vestige of these
leafy conceptacles is to be found.

When the larvae, barely visible to the naked eye, burst forth from the ova, their
development goes on with such rapidity that they seem to grow sensibly while under
observation. These changes have been depicted in Cineras at figg. 6. 7. & 8., which

IN THE SECOND TYPE OF THE CIRRIPEDES. 357

last probably did not possess sufficient vitality to pass into the next stage, such as
we see that of Lepas anserifera (fig-. 5.).

The larva of the Lepades, then, is a tailed Monoculus, with three pairs of members,
the most anterior of which are simple, the others bifid, having its back covered by an
ample shield, terminating anteriorly in two extended horns, and posteriorly in a
single elongated spinous process*.

It must ever remain uncertain how long the larvae of the Lepades remain in their
first or free state, but it is probably for a longer or shorter period of time, according
as they sooner or later meet with a substance adapted to their respective habits :
thus, those of the Lepas fascicularis attach themselves in preference to Gulf-weed
or floating Fuci ; Lepas minima to slender species of Antipathes ; Lepas anserifera^
and dentata, Cineras vittatus, and Otion, to the bottoms of ships ; Lepas anatifera% to
floating timber, and to one another; w\\\\q Lepas sulcata seems to prefer the backs of
Turtles and the shell of the lanthina : the species, however, have not been sufficiently
discriminated, nor observations of this kind made with the requisite care, to enable
us to prosecute further this part of their natural history. It is evident that they
possess locomotive powers which enable them at every instant to change their situa-
tion, and a conspicuous eye to guide them in their choice.

These remarkable and important discoveries, connected as they are with those re-
lating to the Crustacea §, complete the natural history of this tribe, and lead us to
the following important results, viz.

I. That the Cirripedes do not constitute a distinct class of animals, as they have
been considered by all late naturalists. Dr. Leach, Latreille, Lamarck, Cuvier, &c.,
being connected with the Crustacea decapoda through the Balani, and with the En-
tomostraca by means of the Lepades.

II. That they have no relation or affinity whatever with the Testacea, as supposed
by LiNNiEus and all the older systematists.

III. That the Crustacea now therefore furnish examples of a class in which we have
animals free and fixed, with eyes and eyeless, and with the sexes separated in some
and united in others, all of which are characters to which naturalists have attached
the greatest importance as regards classification.

IV. That the proof of metamorphosis being fully and satisfactorily established, tends
still to maintain the affinity so long recognised between the Crustacea and Insecta.

Note. — The same economy in regard to the disposal of the ova has been observed
in Otion, but hitherto no individual has been found with the ova on the point of
hatching.

* Compare with the larva of Artemis (Brine Shrimp). Zoological Researches, No. v, Plate II. f. 7, 8. (here-
with sent).

t Philosophical Transactions, vol. i. Plate xxxiv. fig. 5.
X Philosophical Transactions, vol. i. Plate xxxiv. fig. 6,
§ Zoological Researches, Memoir I. and Addenda, p. 63.

358 MR. THOMPSON ON THE METAMORPHOSIS OF THE CIRRIPEDES.

PLATE V.

Fig. 1 . Lepas amerifera, opened from behind to show the first stage of the leaf-like
conceptacles of the ova (m).

a. Animal.

o. Ovipositor.

V. Valves,

p. Pedicle.
Fig. 2. Another individual, showing the conceptacles in an advanced stage, the

right conceptacle being turned back (m).
Fig. 3. A portion of the conceptacle magnified.
Fig. 4. An ovum ready to hatch.

Fig. 5. Fully developed larva of Lepas anserifera, viewed in front, highly magnified.
Fig. 6. Larva of Cineras vittatus, just excluded from the ovum.
Fig. 7. The same more developed.

Fig. 8. The fully developed larva of the same, viewed in front and highly mag-
nified.

[ 359 ]

XXI. On the Double Metamorphosis in the Decapodous Crustacea, exemplified in
Cancer Msenas, Linn. By J. V. Thompson, F.L.S. Deputy Inspector-General of
Hospitals. Communicated by Sir James Macgrigor, Bart. M.D. F.R.S.

Received May 21, — Read June 4, 1835.

XN the Memoir published in my Zoological Researches, p. 1, with its sequel, p. 63,
having first made known the fact of the Brachyura of the Decapoda (Crabs) passing
through the intermediate form of Zoea ; I have now to announce that they undergo
another metamorphose, no less singular and unlooked for, in which they assume the
form of the genus designated by the name of Megalopa by Dr. Leach, from the dis-
proportionate size of the eyes. This second stage we may therefore consider analo-
gous to that of pupa in the class Insecta.

By the former memoir it appears that the young of Cancer Pagurus, the common
market Crab, first presents itself as a Zoe *, and that a full-grown Zoe was observed
passing into some other more perfect form -f-, which at that time was considered to
be that of some species of Crab : the discovery now first detailed, however, shows
that it must have been only passing into that of a Megalope.

The first proof I had of this new and extraordinary fact, which cancels another
anomalous genus of the Crustacea, was obtained by keeping in regularly renewed sea-
water a number of individuals of a Megalope % which makes its appearance in the
river Lee, just below the city of Cork, in considerable abundance every summer :
these, to my very great surprise, began, after a short time, to change into a mi-
nute Crab §, until the whole of them, to the amount of about two dozen, were so
metamorphosed. I have frequently since observed the same circumstance, and came
to the conclusion that these must be the progeny of the only Crab that is ever found
in the higher parts of the river, where these Megalopce were taken, viz. Carcinus Mcenas,
our common Shore Crab. The young Crab, it will be noticed, has not the distinctive
characters of its parent, which it probably acquires only after several casts of its
shelly covering.

To complete the series of metamorphoses in this species of Crab now became a
matter of research ; and I have been so fortunate as to succeed in hatching its mature
spaw^n, so as to be enabled to give a representation of its Zoe ||, or first stage^ and
thereby render complete its natural history. In this stage it does not appear to differ
materially from that of Cancer Pagurus, formerly figured in Zoological Researches

* Pages 9 and 64. f Page 8. % Fig. 2. § Fig. 6. || Fig. 1.

MDCCCXXXV. 3 A

360 MR. THOMPSON ON THE DOUBLE METAMORPHOSIS

PI. VIII. fig. 1 . It is, however, certainly much smaller, and of a greenish tinge, with
a few darker spots.

If the above facts do not warrant the conclusion I have drawn, what other proof
can be required ? Is it necessary that the young Crab should be traced through its
subsequent changes until the character of the species becomes more apparent ? or
that the grown Zoe should be actually seen to change into a Megalope ? Neither of
these is impracticable, but may yet for a long time elude the most zealous and scru-
tinizing observers.

It appears, then, that the animals of this division of the Crustacea not only undergo
metamorphosis, as formerly stated, but that they even undergo a double metamor-
phosis, being hatched from the ova under the singular and grotesque form of Zoea,
then assume that of Megalopce, and finally that of their parent Crab. How long they
remain in each of these two intermediate states it may be difficult to determine with
exactitude ; but judging from the very considerable size of the Zoe I observed about
changing its condition *, compared with their very minute size when first hatched,
and also from Megalopce not appearing before May or June, while Zoea are seen so
early as March and April, I think a month may be assigned as the probable duration
of the Zoe stage. The other, or Megalope stage, is less within the scope of observa-
tion ; but as there is not that very great disparity of size between young and full-
grown Megalopce, it is likely that it does not exceed half that of the former.

If further proof of this double metamorphosis be desired, I have been so fortunate
as to trace it, but not in quite so satisfactory a manner, in one of the Swimming Crabs,
or Portuni, and also in Inachus, belonging to the section of Triangular Crabs. These
examples, derived from some of the principal groups of the Brachyura, may be sup-
posed quite sufficient to satisfy the most scrupulous, as to their metamorphosis ; I
propose, however, in future memoirs, to bring under the notice of the yet sceptical,
proofs of the same thing in the following genera, viz. Eriphia, Thelphusa, Gegarcinus,
and Pinnotheres -f . The three former genera, it may be observed, are foreign, which
friends in the East and West Indies have enabled me to add to the first proofs of
metamorphosis, by having females with ova on the point of hatching, sent home in
spirits : the larvae of these, consequently, have not been seen in the living state ; but
by examining such as have burst from their envelopes, without being completely de-
veloped, it is quite evident that they are Zoea.

With regard to the other great division of the Decapoda, viz. the Macroura, or
those with extended tails, I shall only now say, that as far as my observations have
gone they also undergo metamorphosis, being Ipizopoda when first hatched, and
during the whole of their progress to the perfect animal ; such is the case in Astacus
marinus, Palinurus, Palcemon Squilla, Crangor, Galathea, Pagurus, and Porcellana.

To return to the immediate subject of the present memoir, the Carcinus Mcenas.
In its first or Zoe stage it is wholly natatory from structure, while in its second it

* Zoological Researches, p. 8. t This has since been published in the Entomological Magazine.

IN THE DECAPODOUS CRUSTACEA. 361

occasionally walks by means of its thoracic members, now become simple, but more
commonly swims by the motion of its subabdominal fins, which are greatly developed
for this purpose =»<=. In both stages it is therefore a Macroura, but only in the latter
evidently related to the Decapoda.

It will be quite superfluous to enter into a minute detail of the structure of this
Megalope, further than may be collected by a reference to the figure and its accom-
panying explanation.

It must certainly be considered surprising that so many curious facts should have
remained until the present time undiscovered ; but still more, that from the first
announcement of metamorphosis no person has attempted to follow it up ; so that I
have not only the honour of the discovery, but also the entire merit of having ren-
dered this interesting part of the natural history of the Crustacea nearly complete,
as the announcements in the previous part of this memoir testify, and my subsequent
memoirs will prove.

The facts connected with the metamorphosis in the Crustacea and the Cirripedes
are indeed so much at variance with our previous knowledge, with the dicta of some
of our leading naturalists, and of so very extraordinary a nature, that the scepticism
which still exists with regard to them may admit of some excuse. The approaching
summer I hope will put it in my power to remove all doubts upon the subject, by
submitting such of them as offer themselves to the scrutiny of other observers, a cir-
cumstance which never occurred to me as necessary beyond the circle of my own
family ; had there been any zoologists in my neighbourhood the case would have
been different, but in respect of this branch of science I here unfortunately stand
alone.

Whatever indifference may be charged to our own zoologists in regard to these
important discoveries, we must do our scientific neighbours the French the justice of
noting, that they immediately took up the subject, and two naturalists were selected
and deputed to spend a summer at Isle Re, to make their observations. However,
by a subsequent report of one of these gentlemen, M. Milne-Edwards, to the French
Institute, it appears that so far from verifying the metamorphosis in Crustacea, he
pronounced that they were hatched with the form and structure of their adult
parent ! The observations upon which this decision was based I have not seen
stated ; but whatever they may have been, they are completely invalidated by the
positive proofs I have given and enumerated in the present memoir.

The animals of this class are so recondite in their habits, so difficult to preserve
alive for any time, so little known to naturalists beyond the more common species,
that the investigation is necessarily attended with great difficulty and frequent dis-
appointment. It must be allowed that I have been peculiarly fortunate ; and I am
so sensible of the obligation I owe to that Source from whence springs all our

* Fig. 3.
3 a2

362 MR. THOMPSON ON THE DECAPODOUS CRUSTACEA.

knowledge and intelligence, that I hasten to acquit myself of so sacred and valuable
a trust with all the ability I am yet permitted to retain.

PLATE VI.

Fig. 1. Zoe of Carcinus Mcenas, magnified, and also of its natural size.

Fig. 2. Megalope of the same, magnified, and also of its natural size. The termi-
nations of three pair of the subabdominal fins are only seen in the figure.

Fig. 3. One of its subabdominal fins more highly magnified.

Fig. 4. The posterior pair of fins magnified.

Fig. 5. One of its inner antennae, highly magnified.

Fig. 6. The Young Crab, resulting from the above Megalope, magnified, and also
of its natural size.

INDEX

TO THE

PHILOSOPHICAL TRANSACTIONS

FOR THE YEAR 1835.

A.

Atmospheric tides j and meteorology of Dukhun (Deccan), East Indies, on the, 161.

B.

Bakerian Lecture. On the proofs of a gradual rising of the land, &c., 1.

Bell (Sir Charles). Continuation of the paper on the relations between the nerves of motion

and of sensation, and the brain ; more particularly on the structure of the medulla oblongata

and the spinal marrow, 255.
Brewster (Sir David), K.H. On certain peculiarities in the double refraction and absorption of

light exhibited in the oxalate of chromium and potash, 91.

C.

Cirripedes, discovery of the metamorphosis in the second type of the Lepades, Sec, 355.
Crustacea, on the supposed existence of metamorphosis in, 311.

————— (decapodous), on the double metamorphosis of, exemplified in Cancer Mcenas, Linn.,
359.

D.

Daubeny (Charles, M.D.). Some account of the eruption of Vesuvius which occurred in the
month of August 1834, extracted from the manuscript notes of the Cavaliere Monticelli,
Foreign Member of the Geological Society, and from other sources ; together with a statement
of the products of the eruption, and of the condition of the volcano subsequently to it, 153.

Davies (Thomas Stephens, Esq.). Geometrical investigations concerning the phenomena of
terrestrial magnetism, 221.

Differential equations of motion of an attracting or repelling system, transformations of the, 96.

Disturbing function of the fourth order, on the determination of the terms in the, &c., 57.

Double refraction and absorption of light, exhibited in the oxalate of chromium and potash, on
certain peculiarities in, 91.

Dynamics, on a general method in (second essay), 95.

E.

Electric current, on its influence by induction on itself, and on the inductive action of electric
currents generally, 41.

364 INDEX.

Electricity, experimental researches in. Ninth series. 41.

. , Tenth series. 263.

Equations of motion, integration of, by means of one principal function, 98.

Expression for the principal function in any problem of dynamics, general method of improving

an approximate, 101.
Expressions, differential, simplification of, &c., 135.

F.

Faraday (Michael, D.C.L.). Experimental researches in electricity. Ninth series. 41.

Tenth series. 263.

Farquharson (Rev. James). On the ice formed, under peculiar circumstances, at the bottom of

running water, 329.
Fossil shells found in Sweden, list of, ZS.
Fox (R. W.). Note on the electrical relations of certain metals and metalliferous minerals, 39.

G.

Gray (John Edward, Esq.). Remarks on the difficulty of distinguishing certain genera of tes-
taceous Mollusca by their shells alone, and on the anomalies in regard to habitation observed
in certain species, 301.

H.

Hamilton (Prof. W. R.). Second essay on a general method in dynamics, d5.

I.

Ice formed, under peculiar circumstances, at the bottom of running water, on the, 329.
sometimes formed at the bottom of still water, note 342.

L.

Light, researches towards establishing a theory of the dispersion of, 249.

Lubbock (J. W. Esq.). On the determination of the terms in the disturbing function of the fourtii

order, as regards the eccentricities and inclinations which give rise to secular inequalities, 57.

Discussion of tide observations made at Liverpool, 275.

Lyell, Charles, Jun., Esq.). The BaTterian Lecture. — On the proofs of a gradual rising of the

land in certain parts of Sweden, 1 .

M.

Magnetism, terrestrial, geometrical investigations concerning the phenomena of, 221.
Metals and metalliferous minerals, note on the electrical relations of, &c., 39.

N.

Needle {magnetic), on the points of the earth's surface at which it takes a position vertical to the

horizon, 245.
Nerves of motion and of sensation, and the brain, on the relations between, &c. — Continuation of

the paper on, 255.

P.

Partial differential equations of the first order, &c., investigation of a pair of, 100.

INDEX. 365

Perturbations, rigorous theory of, &c., 10^, 104, 107, 110.

Pond (John, Esq., A.R.). Continuation of a former paper on the twenty-five-feet zenith telescope

lately erected at the Royal Observatory, 145.
Powell (Rev. Baden). Researches towards establishing a theory of the dispersion of light, 249.

R.

Rattlesnake, its extraordinary power of living without food, note 352.

Respiration, on the theory of, 345.

Rising of the land in certain parts of Sweden, on the proofs of, &c., 1. ^

S.

Single point, formulae for the motion of a, 1 14.

Stevens (William, M.D.). Observations on the theory of respiration, 345.

Sykes (Lieut.-Col. W. H.). On the atmospheric tides and meteorology of Dukhun (Deccan),

East Indies, 161.
System, ternary or multiple y with one predominant mass, case of a, &c., 133.
Systems, attracting, resumed, 130.

T.

Testaceous Mollusca, remarks on the difficulty of distinguishing certain genera of, by their shells

alone, &c., 301.
Thompson (J. V., Esq.). Discovery of the metamorphosis in the second type of the Cirripedes,

viz. the Lepades, completing the natural history of these singular animals, and confirming

their affinity with the Crustacea, 355.
^ On the double metamorphosis in the Decapodous Crustacea, exemplified

in Cancer Mcenas, Linn., 359.
Tide observations, made in June 1834, at the Coast Guard Stations in Great Britain and Ireland,

on the results of, 83.

■ discussion of some made at Liverpool, 275. *

Twenty-five-feet zenith telescope, erected at the Royal Observatory, continuation of a former

paper on, 145.

V.

Vesuvius, some account of the eruption of, in 1835, &c., 153.

Voltaic battery, on an improved form of, 2Q3.

some practical results respecting the construction and use of, 2QS.

W.

Westwood (J. O., Esq.). On the supposed existence of metamorphosis in the Crustacea, 311.
Whewell (Rev. W.). On the results of tide observations made in June 1834 at the Coast Guard

Stations in Great Britain and Ireland, 83.
Wooden house, a small one found at the depth of sixty-four feet under a stratified mass of sand,

gravel, and clay, in digging the Sodertelje Canal, 8.

LONDON:
PRINTED BY RICHARD TAYLOR,

RED LION COURT, FLEET STREET.

METEOROLOGICAL JOURNAL,

KEPT BY THE ASSISTANT SECRETARY,

AT THE APARTMENTS OF THE

ROYAL SOCIETY,

BY ORDER OF

THE PRESIDENT AND COUNCIL.

OBSERVANDA.

Height of the Cistern of the Barometer above a Fixed Mark on Waterloo Bridge =83 feet 2 J in.

above the mean level of the Sea (presumed about) .... =95 feet.

The External Thermometer is 2 feet higher than the Barometer Cistern.

Height of the Receiver of the Rain Gauge above the Court of Somerset House =79 feet.

The hours of observation are of Mean Time, the day beginning at Midnight.
The Thermometers are graduated by Fahrenheit's Scale.
The Barometer is divided into inches and decimals.

METEOROLOGICAL JOURNAL FOR JANUARY AND FEBRUARY, 1835.

9 o'clock, A.M.

3 o'clock, P.M.

Dew

External Thermometer.

1835.

Point at
9A.M.
in de-
grees of

Rain, in

■ inches.

Read off

at9A.M

Direction

of the

Wind at

9 A.M.

REMARKS.

Barom.

Attach
Therm

Barom.

Attach
Therm

Fahrenheit.

Self-registering.

"■

Fahr.

9A.M

3 P.M.

Lowest.

Highest

T 1

30.107

51.8

30.398

51.9

48

47.9

46.0

46.3

48.6

S

A.M. Liffhl fogf and rain. P.M. Lightly cloudy— light brisk wind.

F 2

30.794

46.4

30.819

47.3

35

40.2

42.4

38.9

41.8

N

f Light fog and wind.— A.M. Overcast— light haze. P.M. Fine

l and clear.

Fine light haze and wind. P.M. Fine light cioudt and wind.

S 3

30.782

44.7

30.725

45.4

32

38.9

40.6

36.8

40.5

NE

0 4

30.622

40.9

30.570

41.3

29

32.9

35.2

30.2

34.5

NE

Fine and cloudless— light wind. Evening, light fog.

M 5

30.564

38.2

30.556

40.4

32

34.3

40.3

30.6

39.4

E

< Hoar frost— light fog.— P.M. Light clouds and wind. Evcn-
(. ing, Ane and clear.
Thick fog.-P.M. Light haze.

T 6

30.552

37.3

30.475

37.9

32

31.6

34.7

29.0

33.3

E

W 7

30.307

35.0

30.212

34.3

27

27.9

29.9

25.8

28.5

E

Thick fog.-P.M. Light rain. Evening, frosty.

T 8

30.128

33.2

30.063

34.6

29

30.0

33.7

25.0

35.8

ENE

Sharp frost— light fog and wind.

>, F 9

29.875

36.7

29.703

38.6

32

37.2

44.0

28.4

47.5

S

Lightly cloudy— Ihaw.—A.M. Overcast. P.M. Light rain.

« S 10
g 011
< M12
'^ T 13

29.825
29.800

40.6
44.6

29.841
29.853

42.2
46.2

36
42

38.9
46.8

43.8
50.3

35.8
37.2

46.9
49.6

.113

ssw

Svar.

f A.M. Fine— light clouds with light brisk wind. P.M. Overcast

t. —drizzling rain.

A.M. Lightly overcast— light unsteady wind. P.M. Light rain.

29.930
29.707

46.4
46.3

29.918
29.594

47.8
46.7

44
40

47.8
40.2

49.0
45.4

45.7
39.8

49.7
45.3

SW
ESE

( Overcast- deposition — A.M. Fine light clouds. P.M. Lightly

I cloiKiy— light wind.

A.M. Fine— light clouds and wind. P.M. Lightly overcast.

#W14

29.479

47.2

29.473

48.8

42

45.7

49.4

39.9

48.8

SE

Overcast— deposition.-P.M. Overcast— very light rain.

T 15

29.656

48.7

29.693

49.8

43

46.6

48.3

44.2

47.8

SW

fA.M. Lightly cloudy. P.M. Fine light clouds and wind.—
1. High wind througlinul the nixht.

F 16

29.091

48.8

29.197

49.6

44

47.2

44.2

44.2

49.6

SW var.

f Overcast— very light rain.— A.M. Fine light clouds. P.M. Fine

\ and cloudless — light haze.

Fine— light clouds and wind. Evening, sharp frost.

S17

29.598

43.2

29.685

44.6

38

35.2

40.3

31.9

39.3

SW

018

29.808

39.2

29.604

40.3

27

31.5

36.6

27.8

42.2

ESE

f Hoar frost-alight haze.— P.M. Lightly overcast. Evening,
1. light snow and rain.

M19

29.101

49.7

29.172

41.6

35

39.9

38.8

29.5

42.3

SW var.

( Lijfhily cloudy.- A.M. Overcast— light unsteady wind. P.M.

l Cloudy— deposition.

Fine & frosty— light brisk wind. Even. fine& clear— sharp frost.

T 20

30.083

37.3

30.091

38.0

26

32.0

33.5

30.5

32.4

NE var.

W21

30.328

34.7

30.253

35.7

17

27.4

31.9

24.9

35.7

SW

fA.M. Fine and frosty— light fog. P.M. Liglit fog. Evening,
I snow — sharp frost.
Overcast— light wind.

T22

30.134

36.6

30.220

38.4

33

37.2

39.2

25.3

38.6

NE

F 23

30.344

38.6

30.301

39.9

32

38.8

41.4

33.8

44.2

SW

Light fog.— Evening, overcast— light rain.

S24

30.115

41.7

30.154

43.8

40

45.4

47.6

37.2

47.6

.069

SW

fOvercasI— deposition.— A.M. Fine light clouds and wind.
I P.M. Overcast— very light rain.

025

30.200

43.6

30.214

45.4

39

45.3

49.9

37.2

49.7

s

Overcast— deposition— light wind.

M26

30.332

45.6

30.332

47.4

41

47.7

48.7

42.8

49.7

SW

Fine— light clouds.

T 27

30.425

46.2

30.406

47.3

37

44.5

46.6

40.6

45.9

SW

Overcast— light fog. P.M. Light clouds and wind.

OW28
T29

30.362

45.3

30.279

46.2

37

40.9

47.0

38.6

41.7

SW

Overcast — deposition.

30.188

45.0

30.128

46.9

38

42.0

48.2

39.8

47.7

Svar.

(■ Fine- lighlly cloudy— light haze.— A.M. Fine and clondless—
X light haze. P.M. Fine light clouds.

P30

30.087

46.3

30.035

48.3

41

44.2

46.4

40.8

47.6

S var.

fA.M. Light fog and wind. P.M. Fine and cloudless— light
(. haze. Evening, cloudy.

S 31

30.000

44.0

30.047

45.5

36

38.6

42.0

35.0

43.6

S

Overcast— light fog and wind.

Means . .

30.075 42.4

30.065

43.6

35.6

39.5

42.4

35.3

43.1

Sum. Mean of Barometer, corrected for Capil- ) 9 A.M. 3 P.M.
,182 larity and reduced to 32° Fahr j" 30.048 30.034

0 1

30.275

46.0

30.289

48.2

41

44.7

50.0

36.9

49.6

S var.

("Overcast— light rain and wind.— P.M. Fine— lightly cloudy.

l Evening, overcast.

A.M. Overcast— light rain and wind. P.M. Lightly overcast.

M 2

30.142

48.4

30.178

50.3

45

50.2

53.2

43.3

53.2

SW

T 3

30.352

47.7

30.376

50.0

43

45.0

51.2

42.2

50.6

SW Fine— light clouds and wind. |

W 4

30.459

48.0

30.441

50.2

40

43.2

50.3

41.0

50.2

SW

fA.M. Fine— light clouds and fog. P.M. Fine and clear— light
t clouds and wind.

T 5

30.200

48.0

30.033

50.3

42

45.6

50.9

40.7

50.8

SW var.

/Fine— light clouds with light brisk wind.— A.M. Cloudy.
\ P.M. Fine and clear— light wind.

F 6

30.172

44.6

30.259

46.2

30

38.0

43.7

35.2

45.4

Svar,

A.M. Fine i<i clear— light haze & wind. P.M. Fine It. elds. & wind.

So 8

30.067

46.2

29.918

48.3

39

46.6

50.9

36.8

50.5

SW

Lightly overcast— light wind. Evening, cloudy.

29.697

47.0

29.661

48.3

32

42.6

44.7

40.8

46.2

WSW

Fine and clear-light haze & wind. Evening, cloudy— light rain.

^ M 9

29.849

43.0

29.922

44.3

27

36.7

41.0

33.8

39.8

.061

SW

f A.M. Fine and cloudless— lij<ht haze and wind. P.M. Fine and
X clouiiless- light brisk wind. Evening, fine and frosty.

g T 10
« W 11

30.091
30.435

38.6
37.8

30.255
30.372

40.6
41.3

22

24

32.4
33.3

39.5
41.9

29.8
27.9

38.2
44.7

NE var.
S

f Fine— sharp frost— light brisk wind — snow during the nighl.
X Evening, line and clear— sharp frost.
Cloudy— light frost and wind.

T 12

30.132

43.2

30.168

44.5

35

46.0

45.2

31.8

46.3

SW

Overcast— light rain and wind. Evening, fine and clear.

OF 13

30.336

41.9

30.247

45.2

32

39.3

46.3

35.0

46.8

.125

SW

A.M. Fine and cloudless— light haze and wind. P.M. Overcast.

S 14

30.014

44.9

29.917

46.6

• 40

43.4

49.4

37.5

49.8

SW

Overcast— light rain.

015

29.701

48.2

29.956

50.2

42

47.6

51.0

42.3

51.4

SW

Overcast — deposition.- A.M. Fine— light elds. Rven. overcast.

M16

29.530

46.3

29.592

48.0

40

43.2

46.2

40.0

47.3

NWvar.

A.M. Lightly cloudy. P.M. Overcast— light brisk wind.

T 17

29.711

45.9

29.728

48.0

40

42.4

45.8

38.6

46.7

S var.

Overcast— drizzling rain. — A.M. Fine and clear. P.M. Cloudy.

W 18

29.469

46.3

29.461

48.4

40

44.6

49.2

38.8

49.3

S var.

Overcast— light rain— brisk wind. Evening, cloudy.

T 19

29.465

45.0

29.396

48.0

38

41.3

47.5

35.7

48.3

SW

fFine-nearly cloudless.— A.M. Overcast. P.M. Fine— light
1 elds.— brisk wind. Eve. overcast— heavy rain — liieh wind.

F 20

29.273

45.0

29.271

47.6

34

39.9

47.6

37.0

48.2

.061

WSW

f Fine & cloudless.— A.M. Lightly overcast. P.M. Fine— light
1 clouds & wind. Eve. overcast— light rain— high wind.

S 21

29.295

43.3

29.346

46.4

34

38.4

43.7

33.2

45.8

.133

WSW

Fine and cloudless— light wind. Eveninj, cloudy.

0 22

29.758

42.7

29.614

45.9

35

38.8

43.8

34.2

49.5

WSW

i Fine&cloudless— It. haze&wind.— A.M.CIdv. P.M. Overcast
X —light rain. Eve. rain — hii;h wind tlirouglmiit the night.

M23

29.26'7

45.6

29.483

48.2

39

46.3

48.6

37.0

49.6

.033

SW var.

/A.M. Fine — lightelouds— liieh wind. P.M. tine— nearly cloud-
X less. Evening, cloudy— high wind.

T 24

29.780

43.2

29.827

45.8

32

38.4

45.4

33.9

45.3

WSW

Fine— light cloudsand haze. P.M. Lightly cloudy— high wind.

W25

29.604

44.8

29.412

46.9

40

46.2

49.4

36.0

49.3

SE var.

fA.M. Cloudy— high wind. P.M. Overcast— light drizzling rain

X and wind.

Fine— light clouds and wind. Eve. very light rain — high wind.

T 2G

29.287

46.5

29.459

49.0

40

44.6

48.5

42.8

49.7

W

• F 27

29.227

45.9

29.279

48.5

40

44.4

49.8

38.4

49.3

SW var.

A.M. Overcast— strong wind. P.M. Fine— light clouds & wind.

S 28

29.685

44.8

29.817

46.6

31

41.2

45.2

37.2

44.7

S var.

f Fine and clear— light clouds and wind.— Evening, cloudy, light
X brisk wind.

Means ..

29.831

45.0

29.845

47.2

36.3

42.3

47.1

37.1

47.7

Sum.
.413

Mean of Barometer, corrected for Capil- ) 9 A.M. 3 P.M.
larityand reduced to 32° Fahr j" 29.796 29.803

METEOROLOGICAL JOURNAL FOR MARCH AND APRIL, 1835.

9 o'clock

, A.M.

3 o'clock, P.M.

Dew

External Thermometer.

1835.

Point at
9 A.M.

in de-
grees of

Fahr.

Rain, in
inches.
Read off

Direction
of the
Wind at

REMARKS.

B&rom.

Attach.

Attach.

Fahrenheit.

Self-registering.

Therm.

Therm.

9 A.M. la P.M.

Lowest.

Higliest

atSA.M

9 A.M.

0 1

29.257

42.9

29.364

43.6

32

36.8 38.7

34.8

38.3

SW

Overcast— light rain and «now.

M 2
T 3

30.150

40.6

30.079

42.7

33

35.5

41.6

32.7

47.9

wsw

Overcast-deposilion-liyht wind. ETenin;, cloudy.

29.677

45.2

29.780

46.4

34

47.3

45.9

34.6

47.2

.027

SW var

A.M. Fine— lighl elds.-liighwind. P.M. Fine-nearly cloudle»».

W 4

29.887

42.5

29.639

45.3

36

40.3

47.8

35.7

46.8

SW

T 5
F 6

29.974

40.6

29.978

43.9

29

38.6

45.2

33.8

45.8

.101

SW var.

A.M. Fine— liglii clouds and wind. P.M. Orerca*!- beary rain,
f Fine and (loudlesB-liglii iiaze and wind. Evening, Overcaat
I —very llgiil rain. *'

29.378

44.7

29.588

47.2

38

43.5

49.2

37.2

49.6

W

^ 7
0 8
M 9

29.011

45.5

28.855

47.3

38

46.2

45.5

40.0

47.8

Svar.

Fine-liKiii clds-brl.lt wind. Et. overcast-light rain and wind,
f A.M. LlKl.lly oyercast-brisit wind. P.M. Overcasi-rain and
I liaii— brisk wind.

( Fine and cloudless— light haze and wind. ETenlOK. overcaw
(. — lilith wind.

29.798
29.261

42.0
44.6

29.827
28.912

44.9
46.0

32
38

38.4
45.2

44.2
48.2

34.2
37.2

44.2
48.4

SW var.

SE

WSW

Svar.

NWvar.

SW
SE var.

S
WSW
S var.
N var.

T 10
Wii
T 12

29.495
29.550
29.756

41.8
44.8
45.6

29.602
29.598
29.701

45.0
47.2
48.8

31

42
42

38.2
48.5
46.3

45.8
49.9
50.7

32.7
36.9
40.5

47.6
52.7
53.4

Cloudy-very liglil rain and wind. Evening, fine and clear.
Fine and cloudless— light wind. Evening, rery high wind.
Overcasl- very light rain and onsteady wind.

F13

30.160

45.6

30.218

48.8

36

41.4

48.8

37.2

49.2

•Oil

Overcast- light rain and wind. Erening, fine and clear.

OS 14
a015
S M 16
^ Ti7
S W18

29.994
29.837
30.067
29.893
29.930

46.5
47.8
46.6
47.5
45.9

29.998
29.908
30.051
29.742
30.004

49.7
50.0
49.5

48.8
48.7

41
41
39

40
38

45.2
46.2
45.0
45.7
43.3

54.6
49.3
49.9
50.2
47.7

40.0
43.9
38.9
43.0
39.9

54.2
49.5
50.6
49.7
48.6

A.M. Fine— light fog. P.M. Fine— light clouds and wind.
A.M. Overcast— deposition— light wind. P.M. Fine and clear.
A.M. Overcast-light rain. P.M. Fine-light clouds and wind.
A.M. Fine and clear— light clouds. P.M. Lightly overcast.
Overcasl— very light rain- unsteady wind.
fA.M. Lightly ovcrcast-lisht brisk wind. P.M. Clondv- brisk
1 wind. Evening, line and clear.

Foggy-

A.M. Lightly overcast. P.M. Thick haze.

Overcast- very light rain.

T 19

30.259

43.2

30.247

44.2

30

36.6

42.5

34.7

44.7

N

F 20
S 21

30.334
30.243

45.0
47.3

30.307
30.208

48.4
49.1

38
42

45.8
48.2

52.2
51.0

35.0
45.2

52.3
51.3

S
SW

022

30.261

47.8

30.257

48.7

41

45.9

46.4

43.9

47.6

ENE

A.M. Thick fog. P.M. Overcast— lighl rain-brisk wind.

M 23
T 24

30.259
30.219

45.5
44.8

30.229
30.360

48.2
47.3

40
38

43.7
42.7

47.4
45.0

37.4
39.0

47.7
46.0

NNE
E

/A.M. Lightly ..vercasi- light wind. P.M. Fine— light clouds.

X Evening, cloudy.

fOvercdsl-very light rain— brisk wind. P.M. Fine— light

I cl. uds and wind.

Fine— light clouds and haze. Evening, cloudy.

W25

30.540

42.3

30.532

45.5

33

39.8

47.9

32.9

47.3

N

T 26
F27

S 28

30.474

41.8

30.372

44.9

34

36.5

47.6

32.9

46.8

S

A.M. Lightly overcast. P.M. Fine and cloudless— light baze.

30.344

44.2

30.301

47.0

38

42.5

49.2

35.7

49.3

ENE

A.M. Thick fog. P.M. Cloudy- light wind.

30.216

44.0

30.130

45.8

35

42.2

43.7

38.7

43.6

E

Clondv—liirlit brisk wind.

• 029

30.090

43.3

30.018

46.2

34

41.4

44.7

34.2

45.2

E

fA.M. Fine— light clouds— haze and wind. P.M. Cloudy— light

1 wind.

A.M. Fine— thick haze. P.M. Fine— nearly cloudless.

M30

29.871

41.4

29.806

45.2

31

39.6

50.5

33.0

50.6

E

T31

29.816

45.3

29.720

47.7

37

47.8

51.6

36.9

54.2

ssw

A.M. Fine— lightly cloudy. P.M. Overcast— light rain.

Means ..

29.936

44.4

29.914

46.8

36.5

42.7

47.5

37.2

48.3

Sum.
.139

Mean of Barometer, corrected for CapU- \ 9 A.M. 3 P.M.
larity and reduced to 32° Fahr. ..: .. j 29.903 29.874

W 1

29.966

50.0

29.952

53.2

48

54.0

61.3

47.2

62.8

SSW

Fine — light clouds and wind.

T 2

29.881

53.8

29.804

56.4

49

55.7

65.3

48.6

66.2

S

A.M. Fine— light fog. P.M. Overcasl. Evening, Light rain.

F 3

29.804

56.8

29.823

59.0

50

56.2

59.4

52.7

61.4

SW

Overcasl. Evening, Light rain.

S 4

30.130

54.6

30.148

55.4

48

49.0

52.8

48.0

52.6

ENE

Overcast— light rain and wind.

0 5

30.214

52.3

30.249

53.7

47

48.0

49.3

45.3

49.2

.094

E

Overcasl— light rain and wind. '

M 6

30.328

51.3

30.366

54.5

42

48.4

57.0

40.4

57.2

.033

E

( A.M. Fine and cloudless— light haze. P.M. Lightly overcasl.
1 Eveninif , Fine and clear.

T 7

30.410

50.6

30.352

54.5

42

49.3

59.9

41.8

60.4

E

Fine and cloudless— liglit haze. Evening, Fine and clear.

W 8

30.344

54.9

30.263

57.0

44

54.3

64.7

43.4

64.7

SW

Fine and cloudless— light haze. Evening, Fine and clear.

T 9

30.210

56.1

30.148

58.9

47

54.7

61.2

45.8

62.6

SSW

Fine— light clouds and wind. Evening, Cloudy.

F 10

30.182

56.7

30.212

59.3

51

55.0

58.2

52.8

58.8

WSW

CA.M. Overcast— lli;lit wind. P.M. Fine— light clouds and
I wind. Evening, Fine and clear.

S 11

30.348

54.0

30.380

54.8

39

47.3

50.0

41.2

60.8

NE var.

Fine— lighl clouds and wind. Evening, Fine and clear.

012
Om13

30.317
30.196

52.2
52.7

30.237
30.152

54.5
55.4

39
44

46.0
49.3

56.2
58.7

36.8
40.8

55.8
61.0

SW

SW

Fine an<l cloudless— light haze.

fA.M. Fine and cloudless— light haze. P.M. Cloudy. Even-

1 ing, Fine and clear.

^ T14

30.188

55.6

30.091

57.0

38

53.3

61.5

45.0

61.8

S

Fine and cloudless— light haze.

fA.M. Thick haze. P.M. Overcast— lighl brisk wind. Evening,

1 LislU rain.

S W15

29.944

54.7

29.911

56.8

43

49.4

51.0

42.0

59.6

WSW

^ T 16

30.206

48.6

30.130

49.8

26

39.7

46.5

32.8

46.7

.033

NE

A.M. Fine & cidless— It.haze. P.M. Overcast— snow— hail & rain.
fA.M. Fine— light clouds and wind. P.M. Snow— light wind.
\ Evi-ning, Fine and clear.

Fl7

30.186

46.5

30.176

47.3

29

38.0

40.2

30.0

43.8

.144

NE

Sl8

30.082

46.3

29.964

48.2

36

44.3

48.0

34.8

49 7

SW

piiie— liglitly cloudy. Evening, Overcast— lighl rain.

fA.M. Fine-light clouds and wind. P.M. Cloudy. Evening,

t Fine and clear.

019

30.295

49.6

30.358

50.7

34

45.3

51.4

37.0

51.3

.027

NE var.

M20

30.473

48.7

30.467

52.4

42

49.8

56.3

44.3

57.3

SW

A.M. Tliick haze. P.M. Cloudy-Ughl wind.

T 21

29.462

51.3

30.425

53.9

43

51.2

56.7

45.5

569

SW

Cloudy— light rain and wind.

W22

30.445

52.5

30.420

55.5

47

52.7

58.6

46.0

59.6

.061

NNE

A.M. Fine-light clouds and wind. P.M. Cloudy.

T 23

30.465

55.6

30.402

55.3

42

53.3

53.4

45.2

55.7

WNW

Overcast-lighl wind.

F24

30.388

54.0

30.309

56.8

47

52.8

57.4

48.3

59.4

SW

A.M. Thick haze. P.M. Cloudy— light brisk wind.

S 25

30.148

58.0

30.029

56.6

38

52.0

51.5

46.2

55.4

NWvar.

Fine— lighl clouds and wind. Evening, Overcast-lighl wind.

©26

29.718

51.0

29.675

52.3

34

44.4

47.6

40.2

47.8

NW

A.M. Cloudy-brisk wind. P.M. Overcast-hail and lighl rain.

• M27

29.631

50.3

29.621

50.6

32

43.4

47.5

34.2

48.2

NE

A.M. Fine and cloudless— light haze & wind. Evening, Cloudy.

T28

29.835

50.3

29.808

51.4

33

45.4

50.7

34.4

51.2

NE

Fine-light clouds & lighl brisk wind. Evening, Fine and clear.
fA.M. Overcast-light rain and wind. P.M. Lightly overcast.
{ Evening, Overcasl— light steady rain. r_.„.-.

W29

29.679

46.4

29.627

48.8

41

44.4

46.8

39.6

46.6

NTNEyar

T30

29.528

48.6

29.556

50.6

45

47.2

49.6

41.9

50.2

.677

ENE

fA.M. Overcast-liglit steady rain. P.M. Overcasl. Eyening,
\ Overcasl— lighl steady rain.

Means , .

30.133

52.1

30.102

54.0

41,3

49.1

54.3

42.4

55.8

Sura.
1.069

Mean of Barometer, corrected for Capil- ) 9 A.M. 3 P.M. 1
larity and reduced to 32° Fahr f 30.077 30.040 1

METEOROLOGICAL JOURNAL FOR MAY AND JUNE, 1835.

0 o'clock, A.M.

3 o'clock, P.M.

Dew

External Thermometer.

Point at

Rain in

Direction

1835.

Attach.
Therm.

Attach,
rherm.

9A.M.
in de-

Fahrenheit,

Self-registering. |

inches.
Read off

of the
Wind at

REMARKS.

Barom.

Barom.

grees of
Falir.

at9A.M.

9 A.M.

9 A.M.

3 P.M.

Lowest, j Highest.

F 1

29.635

50.0

29.649

53.0

46

47.4

52.3

44.6

52.6

.158

SW

Orercast— very light rain and wind.

S 2

29.647

51.7

29.626

54.6

45

51.5

54.5

44.0

57.8

S

A.M. Fine— light clouds. P.M. Orercasl— light rain and vind.

0 3

29.770

54.2

29.804

55.5

43

51.9

53.6

45.0

53.6

.036

WNW

Overcast— lixht wind.

M 4

29.883

56.2

29.922

56.3

43

52.5

54.3

44.7

59.2

SW

A.M. Fine— liglit clouds. P.M. Overcast— light brisk wind.

T 5

30.109

54.6

30.083

57.4

44

49.5

58.5

45.0

59.7

NE

Overcast— light rain and wind.

W 6

29.865

54.7

29.835

58.6

49

53.6

61.4

48.9

62.3

.133

S

JA.M. Lightly oven asi— very light rain. P.M. Fine— light
1 clouds, liveuiiig. Fine aud clear.

T 7

29.968

60.5

30.008

60.3

48

56.6

60.9

45.6

61.2

SW

/A.M. Fine— liglit clouds and wind. P.M. Cloudy. Evening,

1 Fine anil cle;ir.

Overcast— Evening, Fine and clear.

F 8

30.109

60.3

30.079

61.6

51

55.4

63.5

46.0

63.9

ssw

S 9

30.004

64.3

29.913

64.7

55

62.6

67.2

54.5

68.4

s

Fine— light clouds.

010

29.816

63.6

29.794

65.0

49

59.8

64.8

50.0

65.6

SW

fA.M. Fine— light clouds. P.M. Cloudy. Evening, Fine and
1 clear.

Mil

29.984

64.5

29.972

64.2

50

57.0

60.6

45.7

63.7

SW

A.M. Fine— lighlly cloudy. P.M. Overcast— light rain.

OT 12

29.833

59.6

29.766

63.6

50

57.2

608

52.4

63.6

.033

SW

Fine — light clouds & wind. Even. Overcast— light steady rain.
(A.M. Lightly ovi-rcast— liglit b.isk wind. P.M. Fine— light
1 clouds and wind. Evening, Overcust— heavy rain.

W13

29.604

65.3

29.631

64.0

48

59 3

61.8

50.9

63.2

.097

SW

T 14

29.495

55.2

29.558

56.2'.

47

48.9

48.4

45.4

55.0

1.033

E

fA.M. Overcast- liglit steady rain. P.M.Overcasl— heavy rain,
I. with distant lliuinler and li;;htning.

t« F 15
S S 16

29.720
29.774

56.6
59.8

29.730
29.829

58.8.
60.7

47
48

54.5
58.5

56.5
63.2

45.2
47.4

58.6
63.2

.369
.183

S

s

fA.M. Fine— light clouds and wind. P.M. Thunder, accom-
(. panied Willi heavy rain. Evening, Cloudy.
Fine— light clouds, bveuing. Fine and clear.

017

30.004

65.5

29.976

62.2

50

59.8

64.0

46.8

64.5

SE var.

Fine— nearly cloudless.

M18

29.930

63.9

29.885

64.0

50

65.0

70.0

48.4

72.8

E

fA.M. Fine and cloudless— light Iiaze. P.M. Fine-lightly
(. cloudy— light brisk wind.

T 19

29.873

63.2

29.851

65.2

52

63.9

66.6

54.2

68.7

E

Fine — light clouds and wind.

W20

29.942

59.9

29.976

62.4

53

55.6

60.9

52.8

61.8

E

Overcast— light rain and wind.

T 21

30.208

62.8

30.200

64.2

49

56.7

61.3

50.3

62.3

.047

E

fA.M. Fine— light clouds and wind. P.M. Cloudy— light brisk
t wind.

F 22

30.174

62.8

30.103

63.5

46

55.4

65.5

47.6

66.7

N

fA.M. Thick haze. P.M. Fine— light clouds and wind. Even-
l ing. Overcast— liglit (ain.

S 23

30.186

64.3

30.128

66.0

53

60.7

68.2

52.6

69.6

.052

NNE

Fine— light clouds. Evening, Cloudy.

024
M25

30.156

66.5

30.075

66.8

56

66.6

70.4

55.7

71.4

S

Fine— light clouds. Evening, Cloudy.

29.881

64.6

29.770

66.2

50

60.6

65.2

56.0

66.4

SW

/A.M. Cloudy. P.M. Fine— light clouds and wind. Evening,
I Cloudy— very light rain.

T 26

29.542

62.4

29.456

62.8

50

55.9

58.0

48.6

58.6

SW

Overcast— jiglit rain and wind.

9W27

29.695

60.6

29.748

62.7

50

55.7

59.5

46.2

61.6

.097

SW

/A.M. Cloudy— liaht wind. P.M. Overcast— thunder and light-
X ning— heavy rain.

T 28

29.656

58.3

29.968

61.2

49

54.8

56.0

46.2

58.7

.241

E

Cloudy— light brisk wind. Evening, Fine and clear.

F 29

30.069

59.4

30.077

61.2

43

54.1

58.8

43.0

59.8

NE

Fine— light clouds and wind. Evening, Cloudy.

S 30

30.103

59.5

30.061

60.0

40

52.2

57.7

41.7

58.0

N

/A.M. Cloudy— light brisk wind. P.M. Fine— light clouds and
X wind. Evening, Fine and clear.

03]

30.045

58.3

29.966

60.8

42

54.7

60.4

43.8

64.2

S

/A.M. Fine— light clouds and wind. P.M. Cloudy. Evening,
X <»V(ri asl — lieht rain.

Means , ,

29.893

60.1

29.885

61.4

48.3

56.4

60.8

48.0

62.5

Sum.

Mean of Barometer, corrected for Capil- \ 9 A.M. 3 P.M.
larity and reduced to 32° Fahr j 29.813 29.801

2.479

M 1

29.911

56.2

29.954

58.9

48

52.7

56.6

48.6

62.8

.116

S

Overcast— light rain and wind.

T 2

30.047

61.6

30.027

62.0

50

63.0

66.3

46.0

66.7

.063

ESE

A.M. Fine— light clouds. P.M. Overcast— light rain.

W 3

29.901

58.6

29.897

62.4

52

58.8

67.6

52.7

68.4

.200

E

/A.M. Overcast— light rain. P.M. Fine— light clouds & wind.
X Evening, Cloudy.

T 4

30.006

62.7

30.023

64.5

58

61.8

63.8

55.9

65.3

N

Lightly overcast— light rain and wind.

F 5

30.083

59.6

30.081

63.4

53

55.7

61.7

50.5

65.2

.036

S var.

Overcast— light brisk wind. Evening, Fine and clear.

S 6

30.079

65.2

30.071

67.2

59

65.3

75.2

52.8

75.5

NE

Fine and cloudless- light haze and wind.

0 7

30.160

67.6

30.130

69.6

60

65.3

75.9

57.7

77.3

N

f Fine light clouds and haze, with distant thunder. Evening,
X Fine and clear.

M 8

30.141

74.3

30.113

72.8

75

74.0

78.6

60.6

80.2

N

Fine and cloudless — light wind.

T 9

30.239

75.8

30.208

74.5

64

75.0

79.3

62.8

80.6

S

Fine— light haze and wind. Evening, Fine and clear.

Owio

30.331

76.6

30.321

75.4

63

75.2

81.7

62.0

81.8

E

Fine and cloudless— light brisk wind.

T 11

30.394

77.2

30.378

77.2

66

77.2

82.3

65.4

83.6

N

Fine and cloudless— liglit haze and wind.

F 12

30.416

77.0

30.370

77.6

65

75.3

81.7

63.4

82.2

N

/ A.M. Fine and cloudless— light haze and wind. P.M. Fine—
X light clouds. Evening, Clo"dv.

a S 13

30.352

68.2

30.299

72.0

58

58.9

69.2

57.0

69.9

N

/ A.M. Overcast— light wind. P.M. Fine— light clouds. Even-

t lug. Cloudy.

Fine— liglit clouds and wind. Evening, Cloudy.

5 014

30.285

67.3

30.214

69.7

■ 50

59.6

70.6

52.6

71.5

N

•^ M15

30.237

72.4

30.221

72.9

61

68.8

74.7

59.4

75.4

NE

/A.M. ClondN— light brisk wind. P.M. Fine— light clouds.
X Evening, Cloudy.

T 16

30.295

76.6

30.244

74.2

58

70.2

74.0

60.0

75.8

NW

/Fine light clouds and wind. Evening, Overcast— heavy rain
X during the night.

W17

30.154

73.0

30.111

74.5

63

71.6

73.7

65.2

75.9

.133

N

/ Fine— light clouds— brisk wind. Evening, Overcast— light
1 sliower, with distant thunder.

T 18

30.115

68.4

30.103

72.6

58

62.6

70.0

57.5

70.8

.027

NE

Cloudy— light wind. Evening, Fine and clear.

F 19

30.202

74.7

30.172.

71.6

50

63.2

67.8

54.9

69.2

NE

Fine— light clouds. Evening, Cloudy.

/A.M. Lightly overcast. P.M. Fine light clouds and wind.

I Evenina, Cloudy.

S 20

30.010

67.0

29.980.

.70.3

53-

62.6

70.0

58.2

70.8

SW

0 21

30.095

74.2

30.019.

.70,6

52

64.2

71.9

51.8

72.5

SW

/A.M. Cloudy — light wind— P.M. Fine— nearly cloudless.
X Evening, Cloudy.

M22

29.853

67.7

29.768

70.5

58

65.2

72.4

58.2

73.7

SW

/ A.M. Cloudy— ligiit brisk wind. P.M. Fine— light clouds and
X wind. Evening, Overcast— heavy rain and wind.

T23

29.681

69.2

29.724

69.4

52

62.8

65.3

55.3

67.8

.391

SWvar

Fine — light clouds, and light brisk wind.

/A.M. Overcast— light rain— lirisk wind. P.M. Heavy rain—

X very high wind. Evening, Overcast— light continued rain.

W24

29.542

63.7

29.215

,64.3

53

58.6

60.4

49.3

60.8

ESE

T 25

29.447

67.2

29.548

60.5

45

54.7

53.6

46.7

59.6

.352

W

Overcast— light rain throughout the day.

• F 26

29.901

67.5

29.742

62.2

' 45

59.3

52.3

44.6

62.6

.250

SW

A.M. Fine— light elds. P.M.Overcast— heavy rain & high wind.

S 27

30.012

65.9

30.111

62.2

46

55.2

55.5

45.4

59.8

.630

SW

A.M. Fine— light clouds k wind. P.M. Cloudy— light showers.

028

30.269

65.2

30.247

62.7

45

58.3

61.8

47.4

62.8

wsw

A.M. Fine-light clouds and wind. P.M. Cloudy.

M 29

30.253

64.3

30.190

63.3

48'

58.2

62.7

46.3

63.7

E

A.M. Fine— light clouds and wind. P.M. Cloudy.

T 30

30.162

64.0

30.119

64.9

46

62.3

66.0

50.4

68.3

E

Fine— light clouds and wind.

Means..

30.086

68.3

30.053

68.5

55,1

63.9

68.8

54.6

70.7

Sum.

2.198

Mean of Barometer, corrected for Capil- \ 9 A.M. 3 P.M.
larity and reduced to 32° Fahr | 29.981 29.948

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