e-
XXXvi REPORT—1846.
concentration, as originally suggested by Linnzeus. This has now for the
first time been executed by the Belgian Astronomer, who following out a
plan suggested by himself at our Plymouth Meeting, has brought together
the contributions and suggestions of the naturalists of his own country.
When M. Quetelet remarks, “that the phases of the smallest insect are
bound up with the phases of the plant that nourishes it; that plant itself
being in its gradual development the product, in some sort, of all anterior
modifications of the soil and atmosphere,” he compels the admission, that
the study which should embrace all periodical phenomena, both diurnal and
annual, would of itself form a science as extended as instructive.
Referring you to M. Quetelet’s report for an explanation of the dependence
of the vegetable and animal kingdoms on the meteorology and physics of
the globe, and hoping that the simultaneous observations he inculcates will
be followed up in Britain, I am happy to announce, that the outline of a
memoir on physical geography was some months ago put into my hands
by Mr. Cooley, which in a great degree coinciding with the system of
M. Quetelet, has ultimately a different object. M. Quetelet chiefly aims
at investigating the dependence of organized bodies on inorganized matter,
by observing the periodical phenomena of the former. Mr. Cooley seeks to
obtain an acquaintance with the same phzenomena for the sake of learning
and registering comparative climate as an element of scientific agriculture.
Speaking to you in a county which is so mainly dependent on the produce
of the soil, I cannot have a more favourable opportunity for inculeating the
value of the suggestions of this British geographer. The complete esta-
blishment of all the data of physical geography throughout the British
Islands ; i.e. the registration of the mean and extremes of the temperature of
the air and of the earth; the amount of conduction, radiation, moisture and
magnetism ; the succession of various phases of vegetation, &e. (with their
several local corrections for elevation and aspect), must certainly advance the
cause of science, and promote the material interests of our country.
A minute knowledge of all the circumstances of climate cannot but be of
importance to those whose industry only succeeds through the co-operation of
nature, and it may therefore be inferred, how a report like that with which
I trust Mr. Cooley will favour us, if completed by the addition of tables,
must prove to be a useful public document. Imbibing the ardour of that
author, I might almost hope that such researches in physical geography may
enable us to define, in the language of the poet,
“Et quid quaque ferat regio, et quid queeque recuset.”
At all events, they will tend to raise physical geography in Britain towards
the level it has attained in Prussia under the egis of Humboldt and Ritter,
and through the beautiful maps of Berghaus.
Though our countryman, Mr. Keith Johnston, is reproducing, in attrac-
tive forms, the comparative maps of the last-mentioned Prussian author, much
indeed still remains to be done in Britain, to encourage the study of physical
geography and to place it on a basis worthy of this great exploring and colo-
nizing nation ; and as one of the elementary aids to the training of the youth-
ful mind to acquire some perception of the science, 1 commend the spirited
project of M. Guerin of Paris, to establish in London a georama of vast size,
the objects and details of which he intends to explain during this week to the
geographers present.
Reverting to ceconomical views and the improvement of lands, I would
remind our agricultural members, that as their great practical Society was
founded on the model of the British Association, we hope they will always
ADDRESS. XXXVll
oe
sem
eome to our Sections for the solution of any questions relating to their pur-
_ suits to which can be given a purely scientific answer. If they ask for the-
_ explanation of the dependence of vegetation upon subsoil or soil, our geo-
logists and botanists are ready to reply to them. Is it a query on the com-
parison of the relative value of instruments destined to ceconomize labour,
the mechanicians now present are capable of answering it. And if, above all,
_ they wish us to solve their doubts respecting the qualities of soils and the re-
sults of their mixtures, or the effects of various manures upon them, our che-
mists are at hand. One department of our Institution is, in fact, styled the
Section of Chemistry and Mineralogy, with their applications to Agriculture
and the’ Arts, and is officered‘in part by the very men, Johnston, Daubeny and
Playfair, to whom the agriculturists have, in nearly all cases, appealed. The
first-mentioned of these was one of our earliest friends and founders; the
second had the merit of standing by the British Association at its first meet-
_ ing, and there inviting us to repair to that great University where he is so
much respected, and where he is now steadily determining, by elaborate
experiments, the dependence of many species of plants on soil, air and
stimulus; whilst the third has already been alluded to as one of our best
actual contributors.
If in reviewing our previous labours I have endeavoured to gain your at-
tention by some incidental allusions to our present proceedings, I have yet to
assure you, that the memoirs communicated to our Secretaries are sufficiently
numerous to occupy our Sections during the ensuing week with all the vigour
which has marked our opening day. Among the topics to which our as-
sembling’ at Southampton gives peculiar interest, I may still say that if
geologists should find’ much to interest them in the Isle of Wight, the same
island contains a field for'a very curious joint discussion’ between them and
the mathematicians, with which I became acquainted in a previous visit to
this place. It is a discovery by Colonel Colby, the Director of the Trigo-
nometrical Survey, of the existence of a notable attraction of the plumb-line
to the south, at the trigonometrical station called Dunnose, on Shanklin
Down. The details of this singular phenomenon, which has been verified
by observations with the best’ zenith sectors, will be laid before the Sections.
In the meantime, we may well wonder, that on the summit of a chalk hill of
low altitude which is bounded on the south by the sea (near whose level the
deviation is scarcely perceptible), there should exist an attraction of more
than half the intensity of that’ which was registered’ by Maskelyne, when he
_ suspended a plummet at the side of the lofty Scottish mountain of Schehal-
lion! If those of our geologists, who like Mr. Hopkins of Cambridge have
_ entered bolily into the field of geological’ dynamics; cannot explain this’ re-
_ tnarkable fact, by connecting it with the ridge of dislocated strata that runs
_ through the island as a back-bone from west to east, may we venture to
refer’ it to dense plutonic masses, of rock ranging beneath the surface, parallel
_ to'the line of displacement of the deposits?
_ Another local subject—one indeed of positive practical interest—that
y stands before'us for discussion, is, whether, by persevering in deepening the
_ large shaft’ which they have sunk so deep into the chalk near this tqwn, the’
inhabitants’ of Southampton may expect to be eventually repaid, like those’
of Paris, by a full’ supply of subterranean water, which’ shall rise to the’
surface of the'low plateau on which the work has been undertaken? On’
No occasion, I must observe, could this'town be furnished with a greater’
number of willing counsellors, whose opinions will, it is hoped,. be ade-
quately valued by the local authorities. The question whether this work
Ought to be proceeded with’ or not, will however, I wees be most
a:
+1846.
XXXViil REPORT—1846.
effectively answered by those geologists who are best acquainted with the
sections in the interior of this county, and with the levels at which the upper —
greensand and subcretaceous strata there crop out and receive the waters,
which thence flow southwards beneath the whole body of chalk of the hills
in the south of Hampshire.
Again, as we are now assembled in the neighbourhood of our great
naval arsenal—as some of its functionaries, including the Admiral on the
station, have honoured us with their support, and as, further, I am now
speaking in a town whose magnificent new docks may compete with any
for bold and successful engineering, I must say a few words on our naval
architecture, the more so as we have here a Mechanical Section, presided
over by the eminent mechanician Proféssor Willis, assisted by the great ||
dynamical mathematician Dr. Robinson, and that sound engineer George |
Rennie. Duly impressed with the vast national importance of this subject,
and at the same time of its necessary dependence on mathematical principles, |
the British Association endeavoured in its earliest days to rouse attention to
the state of ship-building in England, and to the history of its progress in:
France and other countries, through a memoir by the late Mr. G. Harvey.
It was then contended, that notwithstanding the extreme perfection to which
the internal mechanism of vessels had been brought, their external forms
or lines, on which their sailing so much depends, were deficient as to ad-
justment by mathematical theory. Our associate Mr. Scott Russell has,
as you know, ably developed this view. Experimenting upon the resistance |
of water, and ascertaining with precision the forms of vessels which would
pass through it with the least resistance, and consequently with the greatest
velocity, he has contributed a most valuable series of memoirs, accompanied
by a great number of diagrams, to illustrate his opinions and to show the
dependence of naval architecture on certain mathematical lines. Employed,
in the meantime, by merchants on their own account, to plan the construction
of sailing ships and steamers, Mr. Scott Russell has been so successful in
combining theory with practice, that we must feel satisfied in having at
different meetings helped him onwards by several money grants; our only
regret being, that our means should not have permitted us to publish the
whole number of diagrams of the lines prepared by this ingenious author.
But however desirous to promote theoretical knowledge on this point, the
men of science are far from wishing not to pay every deference to the skilful
artificers of our wooden bulwarks, on account of their experience and practi-
cal acquaintance with subjects they have so long and so successfully handled.
We are, indeed, fully aware, that the naval architects of the Government, |
who construct vessels carrying a great weight of metal and requiring
much solidity and capacious stowage, have to solve many problems with
which the owners of trading vessels or packets have little concern. All that
we can wish for is, that our naval arsenals should contain schools or public
boards of ship-building, in which there might be collected all the “ constants
of the art,” in reference to capacity, displacement, stowage, velocity, pitching
and rolling, masting, the effect of sails and the resistance of fluids. Having
ourselves expended contributions to an extent which testify, at all events,
our zeal in this matter, we are, I think, entitled to express a hope, that the.
data derived from practice by our eminent navigators may be effectively
combined with the indications of sound theory prepared by approved culti-
vators of mathematical and mechanical science.
I cannot thus touch upon such useful subjects without saying, that our Sta-
tistical Section has been so well conducted by its former presidents, that its
subjects, liable at all times to be diverted into moral considerations and thence
ADDRESS. XXXix
_ into politics, have been invariably restricted to the branch of the science
_ which deals in facts and numbers; and as no one individual has contributed
‘more to the storehouse of such valuable knowledge than Mr. George Porter
‘(asevidenced even by his report in our last volume), so may we believe that
in this town, with which he is intimately connected, he will contribute to
raise still higher the claims of the Section over which he is so well qualified
to preside.
If in this discourse I have referred somewhat more largely to those
branches of science which pertain to the general division of natural history,
in which alone I can venture to judge of the progress made by others, Jet me
however say, that no member of this body can appreciate more highly than
I do, the claims of the mathematical and experimental parts of philosophy,
in which my friend Professor Baden Powell of Oxford, who supports me as
a Vice-President of this meeting, has taken so distinguished a part. No one
__has witnessed with greater satisfaction the attendance at our former meetings
of men, from all parts of Europe, the most eminent in these high pursuits.
No one can more glory in having been an officer of this Association when
it was honoured with the presence of its illustrious correspondent Bessel,
than whom the world has never produced a more profound astronomer.
If among his numerous splendid discoveries he furnished astronomers with
what they had so long and so ardently desired—a fixed and ascertained point
in the immensity of space, beyond the limits of our own sidereal system, it is
to Bessel, as 1 am assured by a contemporary worthy of him, that Englishmen —
owe a debt of gratitude for his elaborate discussion of the observations of their
immortal Bradley, which, in his hands, became the base of modern astronomy.
Passing from this recollection, so proud yet so mournful to us all as
_ friends and admirers of the deceased Prussian astronomer, can any one see with
more delight than myself the brilliant concurrence at our present Meeting of
naturalists, geologists, physiologists, ethnologists and statists, with mathemati-
cians, astronomers, mechanicians, and experimental philosophers in physics and
in chemistry? Surely then I may be allowed to signalize a particular ground of
gratification among so many, in the presence at this Meeting of two individuals
im our Experimental Sections, to one of whom, our eminent foreign associate
Oersted, we owe the first great link between electric and magnetic phenomena,
by showing the magnetic properties of the galvanic current; whilst the other,
our own Faraday, among other new and great truths which have raised the
character of English science throughout the world, obtained the converse
_ proof by evoking electricity out of magnets. And if it be not given to the
geologist whom you have honoured with this chair, to explain how such arcana
have been revealed, still, as a worshiper in the outer portico of the temple of
physical science, he may be permitted to picture to himself the delight which
_ the Danish philosopher must have felt, when on returning to our shores, after
an absence of a quarter of a century, he found that the grand train of dis-
covery of which he is the progenitor, had just received its crowning accession
_ in England from his former disciple, who, after a long and brilliant series
_ of investigations peculiarly his own, has shown that magnetic or dia-magnetic
f forces are distributed throughout all nature.
_ And thus shall we continue to be a true British Association, with cosmo-
‘ _ polite connexions, so long as we have among us eminent men to attract such
foreign contemporaries to our shores. If then at the last assembly we ex-
_perienced the good effects which flowed from a concentration of mathe-
“Maticians and magneticians, drawn together from different European king-
_ doms—if then also the man* of solid learning, who then represented the
sh; * Mr. Everett.
eee: -
d2
xl REPORT—1846.
United States of America, and who is now worthily presiding over the Cam-
bridge University of his native soil, spoke to us with chastened eloquence
of the benefits our Institution was conferring on mankind; let us rejoice
that this Meeting is honoured by the presence of foreign philosophers as
distinguished as those of any former year.
Let us rejoice that we have now among us men of science from Den-
mark, Sweden, Russia, Prussia, Switzerland, Italy and France. The King
of Denmark, himself personally distinguished for his acquaintance with
several branches of natural history, and a warm patron of science, has
honoured us by sending hither, not only the great discoverer Oersted, who
evincing fresh vigour in his mature age brings with him new communications
on physical science, but also my valued friend, the able geologist and chemist
Forchhammer, who has produced the first geological map of Denmark, and
who has presented to us a lucid memoir on the influence exercised by marine
plants on the formation of ancient crystalline rocks, on the present sea and
on agriculture.
As these two eminent men and their associates of the North received me
as the General Secretary of the British Association with their wonted cor-
diality at the last Scandinavian Scientific Assembly, I trust we may convince
them that the sentiment is reciprocal, and that Englishmen are akin to them
in the virtues of friendship and hospitality which so distinguish the dwellers
within the circle of Odin.
Still adverting to Scandinavia, we see here a deputy from the country of Lin-
nzeus in the person of Professor Svanberg, a successful young experimenter in
physics, who represents his great master Berzelius—that profound chemist and
leader of the science of the North of Europe, who established on a firm basis
the laws of atomic weights and definite proportions, and who has personally
assured me, that if our Meeting had not been fixed in the month of September,
when the agriculturists of Sweden assemble at Stockholm, he would as-
suredly have repaired to us. And if the same cause has prevented Nilsson
from coming hither, and has abstracted Retzius from us (who was till within
these few days in England), I cannot mention these distinguished men, who
earnestly desired to be present, without expressing the hope, that the memoirs
they communicate to us may give such additional support to our British ethno-
logists, as will enable this new branch of science, which investigates the origin
of races and languages, to take the prominent place in our assemblies to
which it is justly entitled.
The Royal Academy of Berlin, whose deputies on former occasions have
been an Ehrenberg, a Buch, and an Erman, has honoured us by sending
hither M. Heinrich Rosé, whose work on chemical analysis is a text-book
‘even for the most learned chemists in every country ; and whilst his researches
on the constitution of minerals, like those of his eminent brother Gustave on
their form, have obtained for him so high a reputation, he now brings to us
the description of a new metal which he has discovered in the Tantalite of
Bavaria.
Switzerland has again given to us that great master in paleontology, Agassiz,
who has put arms into the hands of British geologists with which they have
conquered vast regions, and who now on his road to new fields in America,
brings to us his report on the fossil fishes of the basin of London, which will, he
assures me, exceed in size all that he has ever written on ichthyolites.
From the same country we have our warm friend Professor Schénbein, who,
in addition to his report on Ozone, to which I have already referred, has now
brought to us a discovery which promises to be of vast practical importance.
The “ gun-cotton” of Schénbein, the powers of which he will exhibit to his
Fe eeece
ADDRESS. xli
colleagues, is an explosive substance, which is stated to exercise a stronger
projectile force than gunpowder, to possess the great advantages over it of
producing little or no smoke or noise, and of scarcely soiling fire-arms ; whilst
no amount of wet injures this new substance, which is as serviceable after
being dried as in its first condition. The mere mention of these properties,
to which our associate lays claim for his new material, is sufficient to sug-
gest its extraordinary value in warlike affairs, as also in every sort of sub-
terranean blasting, and may well lead me to say, that this discovery, which
may almost rival the inyention of the substance which it is destined to sup-
plant, will signally mark this meeting at Southampton. But, as if British
chemistry were not to be outdone, here also there will be promulgated, for
the first time, the very remarkable discovery of our countryman Mr. Grove,
of the decomposition of water by heat.
Professor Matteucci of Modena, who joined us at the York meeting, and
then explained his various new and delicate investigations in electro-phy-
siology, again favours us with a visit, as the representative of the Italian
Philosophical Society of Modena and of the University of Pisa. This
ingenious philosopher, who has measured the effect of galvanic currents in
exciting through the nerves mechanical force in the muscles, doubtless brings
with him such interesting contribution as will add great additional interest
to the proceedings of the Physiological Section.
Among these sources of gratification, no one has afforded me sincerer
pleasure than to welcome hither the undaunted Siberian explorer, Professor
von Middendorff. Deeply impressed as I am with the estimation in
which science is held by the illustrious ruler of the empire of Russia, I
cannot but hope that the presence of this traveller, so signalized by his
enterprising exploits, may meet with a friend in every Englishman who is
acquainted with the arduous nature of his travels. To traverse Siberia
from south to north and from west to east; to reach by land the extreme
northern headland of Taimyr; to teach us, for the first time, that even
to the latitude of 72° north, trees with stems extend themselves in that
meridian ; that crops of rye, more abundant than in his native Livonia, grow
beyond Yakutsk, on the surface of that frozen subsoil, the intensity and
measure of cold in which he has determined by thermometric experiments ;
_to explain, through their language and physical form, the origin of tribes now
far removed from their parent stock; to explore the far eastern regions of
the Sea of Ohkotsk and of the Shantar Isles; to define the remotest north-
eastern boundary between China and Russia; and finally to enrich St. Peters-
burgh with the natural productions, both fossil and recent, of all these wild
and untrodden lands, are the exploits for which the Royal Geographical So-
ciety of London has, at its last meeting, conferred its Gold Victoria Medal on
this most successful explorer. Professor von Middendorff now visits us to con-
verse with our naturalists most able to assist him, and to inspect our museums,
in which, by comparison, he can best determine the value of specific cha-
racters before he completes the description of his copious accumulations; and
I trust that during his stay in England he will be treated with as much true
hospitality as I have myself received at the hands of his kind countrymen.
It is impossible for me to make this allusion to the Russian empire, without
assuring you that our allies in science on the Neva, who have previously sent
to us a Jacobi and a Kupffer, are warmly desirous of continuing their good
connexion with us. It was indeed a source of great pleasure to me to have
recently had personal intercourse in this very town with that eminent scientific
navigator Admiral Liitke, in whose squadron His Imperial Highness the
_ Grand Duke Constantine was acquiring a knowledge of his maritime duties.
xhi REPORT—-1846.
Besides the narrative of his former voyages, Liitke has since published an
account of the periodical tides in the Great Northern Ocean and in the
Glacial Sea, which I have reason to think is little known in this country.
Having since established a hypsalographe in the White Sea, and being also
occupied from time to time in observations in Behring’s Straits, the Russians
will soon be able to provide us with other important additions to our
knowledge of this subject. Separated so widely as Admiral Liitke and Dr.
Whewell are from each other, it is pleasing to see, that the very reeommenda-
tion which the last-mentioned distinguished philosopher of the tides has re-
cently suggested to me, as a subject to be encouraged by this Association, has
been zealously advocated by the former. Let us hope then that this Meeting
will not pass away without powerfully recommending to our own Government,
as well as to that of His Imperial Majesty, the carrying out of systematic and
simultaneous investigations of the tides in the Great Ocean, particularly in the
Northern Pacific,—a subject (as Admiral Liitke well observes) which is not
less worthy of special expeditions and of the attention of great scientific bodies,
than the present inquiries into terrestrial magnetism; and one which, I may
add, this Association will doubtless warmly espouse, since it has such strong
grounds for being satisfied with the results which it has already contributed to
obtain through its own grants, and by the researches of several of its associates.
Lastly, in alluding to our foreign attendants, let us hope that our nearest
neighbours may respond to our call, and may prove by their affluence to
Southampton, that in the realms of science there is that “‘ entente cordiale”
between their great nation and our own, of which, at a former meeting, we
were assured by the profound Arago himself. No sooner was it made known
that the Chair of Chemistry at this Meeting was to be filled by Michael
Faraday, than a compeer worthy of him in the Academy of Sciences of Paris
Was announced in the person of M. Dumas*, by a letter from that philoso-
pher to myself. To M. Dumas it is well known that we owe, not only the
discovery of the law of substitution of types, which has so powerfully aided
the progress of organic chemistry, but also the successful application of his
science to the arts and useful purposes of life; his great work on that sub-
ject, ‘ La Chimie appliquée aux Arts,’ being as familiar in every manufactory
in England as it is upon the Continent.
Nor, if we turn from chemistry to geology, will such of us as work among
the rocks be backward in welcoming any French geologists who may come
to examine, in our own natural sections of the Isle of Wight, the peculiar
development of their Paris basin, the identity of their chalk and our own,
the fine sections of our greensand and of the Wealden formation of Mantell,
and to determine with us iz situ the strict relations of their Neocomian rocks
with those peculiar strata which at Atherfield, in the Isle of Wight, have
been so admirably illustrated by Dr. Fitton and other native geologists, and
of which such beautiful and accurate diagrams have been prepared by
Captain Ibbetson.
Will it not then be admitted, that the gathering together of such foreign
philosophers, as those above mentioned, with our own men of science, must
be productive of good results? Putting aside even the acknowledged fact,
that numerous memoirs of value are published in one country which are
unknown in another, where is the person, acquainted with the present acce-
lerated march of science, who can doubt that the germs of discovery which
are floating in the minds of distant contemporaries, must often be brought
to maturity by the interchange of such thoughts? ‘The collision of these
* The resolution of M. Dumas to visit the Meeting was arrested by a sudden illness, and
his apology only reached the President towards the close of the Meeting.
mt
i
Mo
i
: =e ‘
ADDRESS. xiii
thoughts may indeed be compared to the agency of the electric telegraph of
our own Wheatstone, which concentrates knowledge from afar, and at once
unites the extremities of kingdoms in a common circie of intelligence.
But although the distinguished foreigners to whom I have adverted, and
others, including our welcome associate M. Wartmann, the Founder of the
Vaudois Society, and M. Prevost of Geneva, on whose merits I would
willingly dilate if time permitted it, are now collected around us; many,
among whom I must name M. de Caumont, the President of the French
Society for the Advancement of Science, have been prevented from ho-
nouring us with their presence, because the national meetings in their
- several countries also occur in the month of September. To remedy this in-
convenience, 1 ventured, when addressing you six years ago at the Glasgow
meeting, to express the hope, that each of the European societies might
be led to abstain during one year from assembling in its own country, for
the purpose of repairing by its own deputies to a general congress, to be
held at Frankfort or other central city under the presidency of the universal
Humboldt. Had the preparation of the ‘Cosmos’ and other avocations of
that renowned individual permitted him to accept this proposition, which
the British Association would doubtless have supported, many benefits to
science must have resulted, and each national body, on re-assembling the
following year in its native land, would, I am convinced, have more vigorously
resumed its researches.
But whether it be considered desirable or not to suspend the national
scientific meetings during one year, I call on my countrymen and their foreign
friends now present, to sustain the proposal for centralizing in a future year
the representatives of the various branches of science of different countries,
when they may at once learn the progress made in each nation, and when, at
all events, they can so appoint the periods of their respective assemblies,
as to prevent those simultaneous meetings in France, Germany, Scandinavia,
Italy, Switzerland and England, which are so much to be deprecated as in-
terfering with a mutual intercourse.
Finally, my fellow-labourers in science, if by our united exertions we have
done and are doing good public service, let me revert once more to the place
in which we are assembled, and express on your part the gratification I know
you experience in being on this occasion as well supported by the noblemen,
clergymen, and landed proprietors around Southampton, as by its inhabitants
themselves—an union which thus testifies that the British Association em-
braces all parties and all classes of men.
Seeing near me Her Majesty’s Secretary of State for Foreign Affairs,
the Speaker of the House of Commons, and several persons of high station
and great influence, who willingly indicate by their presence the sense
they entertain of the value of our conferences and researches, let us wel-
come these distinguished individuals, as living evidences of that good opinion
of our countrymen, the possession of whiche will cheer us onward in our
career. And above all, let us cherish the recollection of this Southampton
Meeting, which will be rendered memorable in our annals by the pre-
sence of the illustrious Consort of our beloved Sovereign, who participating
in our pursuits, in some of which His Royal Highness is so well-versed,
_ thus demonstrates that our Association is truly national, and enjoys the
most general and effectual support throughout British society, from the
-humblest cultivators of science to the highest personages in the realm.
REPORTS
ON
THE STATE OF SCIENCE.
{
Report on Recent Researches in Hydrodynamics.
By G.G. Sroxss, M.A., Fellow of Pembroke College, Cambridge.
At the meeting of the British Association held at Cambridge last year, the
Committee of the Mathematical Section expressed a wish that a Report on
Hydrodynamics should be prepared, in continuation of the reports which
Prof. Challis had already presented to the Association on that subject. Prof.
Challis having declined the task of preparing this report, in consequence of
the pressure of other engagements, the Committee of the Association did
me the honour to entrust it to me. In accordance with the wishes of the
Committee, the object of the present report will be to notice researches in
this subject subsequent to the date of the reports of Prof. Challis. It will
sometimes however be convenient, for the sake of giving a connected view
of certain branches of the subject, to refer briefly to earlier investigations.
The fundamental hypothesis on which the science of hydrostatics is based
may be considered to be, that the mutual action of two adjacent portions of
a fluid at rest is normal to the surface which separates them. The equality
of pressure in all directions is not an independent hypothesis, but a necessary
consequence of the former. This may be easily proved by the method given
in the Exercices of M. Cauchy *, a method which depends on the considera-
tion of the forces acting on a tetrahedron of the fluid, the dimensions of which
are in the end supposed to vanish. This proof applies equally to fluids at
rest and fluids in motion; and thus the hypothesis above-mentioned may be
considered as the fundamental hypothesis of the ordinary theory of hydro-
_ dynamics, as well as hydrostatics. This hypothesis is fully confirmed by ex-
| periment in the case of the equilibrium of fluids ; but the comparison of theory
and experiment is by no means so easy in the case of their motion, on account
_ of the mathematical difficulty of treating the equations of motion. Still
_ enough has been done to show that the ordinary equations will suffice for
_ the explanation of a great variety of phenomena; while there are others the
laws of which depend on a tangential force, which ts neglected in the common
theory, and in consequence of which the pressure is different in different
directions about the same point. The linear motion of fluids in uniform
_ pipes and canals is a simple instance. In the following report I shall first
- consider the common theory of hydrodynamics, and then notice some theo-
ries which take account of the inequality of pressure in different directions.
‘It will be cunvenient to consider the subject under the following heads :—
__ I. General theorems connected with the ordinary equations of fluid motion.
II. Theory of waves, including tides.
* Tom. ii. p. 42.
1846. B
regen
g ' REPORT—1846.
III. The discharge of gases through small orifices.
IV. Theory of sound.
V. Simultaneous oscillations of fluids and solids.
VI. Formation of the equations of motion when the pressure is not sup-
posed equal in all directions.
{. Although the common equations of hydrodynamics have been so long
known, their complexity is so great that little has been done with them
except in the case in which the expression usually denoted by
edepodyptwde ssi. Se ee FAD
is the exact differential of a function of the independent variables 2, y, 2*.
It becomes then of the utmost importance to inquire in what cases this sup-
position may be made. Now Lagrange enunciated two theorems, by virtue
of which, supposing them true, the supposition may be made in a great
number of important cases, in fact, in nearly all those cases which it is most
interesting to investigate. It must be premised that in these theorems the
accelerating forces X, Y, Z are supposed to be such that Xdx+ Ydy+ Zdz is
an exact differential, supposing the time constant, and the density of the fluid is
supposed to be either constant, or afunction of the pressure. Thetheoremsare—
First, that (A.) is approximately an exact differential when the motion is
so small that squares and products of w, v, wand their differential coefficients
may be neglected. By calling (A.) approximately an exact differential, it is
meaut that there exists an expression udx +4+v,dy+wdz, which is accurately
an exact differential, and which is such that uw, v, w, differ from wu, v, w
respectively by quantities of the second order only.
Secondly, that (A.) is accurately an exact differential at all times when it
is so at one instant, and in particular when the motion begins from rest.
It has been pointed out by Poisson that the first of these theorems is not
true+. In fact, the initial motion, being arbitrary, need not be such as to
render (A.) an exact differential. Thus those cases coming under the first
theorem in which the assertion is true are merged in those which come under
the second, at least if we except the case of small motions kept up by dis-
turbing causes, a case in which we have no occasion to consider initial motion
at all. This case it is true is very important. ;
The validity of Lagrange’s proof of the second theorem depends on the
legitimacy of supposing w, v and w capable of expansion according to posi-
tive, integral powers of the time ¢, for a sufficiently small value of that varia-
ble. This proof lies open to objection; for there are functions of ¢ the
expansions of which contain fractional powers, and there are others which
cannot be expanded according to ascending powers of ¢, integral or fractional,
even though they may vanish when ¢=0. It has been shown by Mr. Power
that Lagrange’s proof is still applicable if «, 7 and w admit of expansion
according to ascending powers of ¢ of any kind{. The second objection
however still remains: nor does the proof which Poisson has substituted for
Lagrange’s in his ‘Traité de Mécanique’ appear at all more satisfactory.
Besides, it does not appear from these proofs what becomes of the theorem if
it is only for a certain portion of the fluid that (A.) is at one instant an exact
differential.
M. Cauchy has however given a proof of the theorem§, which is totally —
different from either of the former, and perfectly satisfactory. M. Cauchy
* In nearly all the investigations of Mr. Airy it will be found that (A.) is an exact differen-
tial, although he does not start with assuming it to be so.
+ Mémoires de l’Académie des Sciences, tom. x. p. 554.
+ Transactions of the Cambridge Philosophical Society, vol. vii. p, 455,
§ Mémoires des Savans Etrangers, tom. i. p. 40,
ON RECENT RESEARCHES IN HYDRODYNAMICS. 8
first eliminates the pressure by differentiation from the three partial differential
equations of motion. He then changes the independent variables in the
three resulting equations from 2, y, 2, é to a, b, ec, t, where a, b, ¢ are the
initial co-ordinates of the particle whose co-ordinates at the time ¢ are 2, y, 2.
The three transformed equations admit each of being once integrated with
respect to ¢, and the arbitrary functions of a, 6, ¢ introduced by integration
are determined by the initial motion, which is supposed to be given. The
theorem in question is deduced without difficulty from the integrals thus
obtained. It is easily proved that if the velocity is suddenly altered by
means of impulsive forces applied at the surface of the fluid, the alteration is
such as to leave (A.) an exact differential if it were such before impact.
M. Cauchy’s proof shows moreover that if (A.) be an exact differential for
one portion of the fluid, although not for the whole, it will always remain so
for that portion. It should be observed, that although M. Cauchy has proved
the theorem for an incompressible fluid only, the same method of proof
applies to the more general case in which the density is a function of the
pressure.
In a paper read last year before the Cambridge Philosophical Society, I
have given a new proof of the same theorem*. This proof is rather simpler
than M. Cauchy’s, inasmuch as it does not require any integration.
In a paper published in the Philosophical Magazine+, Prof. Challis has
raised an objection to the application of the theorem to the case in which
the motion of the fluid begins from rest. According to the views contained
in this paper, we are not in general at liberty to suppose (A.) to be an exact
differential when w, » and w vanish: this supposition can only be made when
the limiting value of ‘—2 (wda+vdy+wdz) is an exact differential, where
@ is so taken as that one at least of the terms in this expression does not
vanish when ¢ vanishes.
It is maintained by Prof. Challis that the received equations of hydro-
dynamics are not complete, as regards the analytical principles of the science,
and he has given a new fundamental equation, in addition to those received,
which he calls the equation of continuity of the motion}. On this equation
Prof. Challis rests a result at which he has arrived, and which all must allow
to be most important, supposing it correct, namely that whenever (A.) is an
exact differential the motion of the fluid is necessarily rectilinear, one peculiar
case of circular motion being excepted. As I have the misfortune to differ
from Professor Challis on the points mentioned in this and the preceding
paragraph, for reasons which cannot be stated here, it may be well to apprise
the reader that many of the results which will be mentioned further on as
satisfactory lie open to Prof. Challis’s objections.
___ By virtue of the equation of continuity of a homogeneous incompressible
- fluid, the expression wdy—vd-z will always be the exact differential of a
function of x and y. In the Cambridge Philosophical Transactions§ there
will be found some applications of this function, and of an analogous function
_ for the case of motion which is symmetrical about an axis, and takes place
: in planes passing through the axis. The former of these functions had been
_ previously employed by Mr. Earnshaw.
i II. In the investigations which come under this head, it is to be-understood
that the motion is supposed to be very small, so that first powers only of
i small quantities are retained, unless the contrary is stated.
* Transactions of the Cambridge Philosophical Society, vol. viii. p. 307.
+ Vol. xxiv. New Series, p. 94.
__ } Transactions of the Cambridge Philosophical Society, vol. viii. p. 31; and Philosophical
_ Magazine, vol. xxvi. New Series, Ps 425, § Vol. vii. p. 489,
By B2
4 REPORT—1846.
The researches of MM. Poisson and Cauchy were directed to the inves-
tigation of the waves produced by disturbing causes acting arbitrarily on a
small portion of the fluid, which is then left to itself. The mathematical
treatment of such cases is extremely difficult; and after all, motions of this
kind are not those which it is most interesting to investigate. Consequently
it is the simpler cases of wave motion, and those which are more nearly con-
nected with the phenomena which it is most desirable to explain, that have
formed the principal subject of more recent investigations. It is true that
there is one memoir by M. Ostrogradsky, read before the French Academy
in 1826*, to which this character does not apply. In this memoir the author
has determined the motion of the fluid contained in a cylindrical basin, sup-
posing the fluid at first at rest, but its surface not horizontal. The interest
of the memoir however depends almost exclusively on the mathematical
processes employed; for the result is very complicated, und has not been
discussed by the author. There is one circumstance mentioned by M. Planat
which increases the importance of the memoir in a mathematical point of
view, which is that Poisson met with an apparent impossibility in endea-
vouring to solve the same problem. I do not know whether Poisson’s attempt
was ever published.
Theory of Long Waves.—When the length of the waves whose motion is
considered is very great compared with the depth of the fluid, we may without
sensible error neglect the difference between the horizontal motions of dif-
ferent particles in the same vertical line, or in other words suppose the par-
ticles once in a vertical line to remain in a vertical line: we may also neglect
the vertical, compared with the horizontal effective force. These considera-
tions extremely simplify the problem; and the theory of long waves is very
important from its bearing on the theory of the tides. Lagrange’s solution
of the problem in the case of a fluid of uniform depth is well known. It is
true that Lagrange fell into error in extending his solution to cases to which
it does not apply; but there is no question as to the correctness of his result
when properly restricted, that is when applied to the case of long waves only.
There are however many questions of interest connected with this theory
which have not been considered by Lagrange. For instance, what will be
the velocity of propagation in a uniform canal whose section is not rectan-
gular? How will the form of the wave be altered if the depth of the fluid,
or the dimensions of the canal, gradually alter?
In a paper read before the Cambridge Philosophical Society in May 1837 t,
the late Mr. Green has considered the motion of long waves in a rectangular
canal whose depth and breadth alter very slowly, but in other respects quite
arbitrarily. Mr. Green arrived at the following results :—If 8 be the breadth,
and y the depth of the canal, then the height of the wave OC po y 4, the
horizontal velocity of the particles ina given phase of their motion OC Bt y—*
the length of the wave OC y®, and the velocity of propagation = gy. With
respect to the height of the wave, Mr. Russell was led by his experiments to
the same law of its variation as regards the breadth of the canal, and with
respect. to the effect of the depth he observes that the height of the wave
increases as the depth of the fluid decreases, but that the variation of the
height of the wave is very slow compared with the variation of the depth of
the canal.
In another paper read before the Cambridge Philosophical Society in
* Mémoires des Savans Etrangers, tom. iii. p. 23.
+ Turin Memoirs for 1835, p. 253.
} Transactions of the Cambridge Philosophical Society, vol. vi. p. 457.
ON RECENT RESEARCHES IN HYDRODYNAMICS. 5
_ February 1839*, Mr. Green has given the theory of the motion of long waves
in a triangular canal with one side vertical. Mr. Green found the velocity of
__ propagation to be the same as that in a rectangular canal of half the depth.
_ Ina memoir read before the Royal Society of Edinburgh in April 1839f,
Prof. Kelland has considered the case of a uniform canal whose section is of
any form. He finds that the velocity of propagation is given by the very
%
simple formula a/ Has where A is the area of a section of the canal, and
b the breadth of the fluid at the surface. This formula agrees with the ex-
periments of Mr. Russell, and includes as a particular case the formula of
Mr. Green for a triangular canal.
Mr. Airy, the Astronomer Royal, in his excellent treatise on Tides and
Waves, has considered the case of a variable caual with more generality than
Mr. Green, inasmuch as he has supposed the section to be of any form}. If
A, 6 denote the same things as in the last paragraph, only that now they are
supposed to vary slowly in passing along the canal, the coefficient of horizontal
8.1 ‘ eae, eee
displacement o¢ A~ * 5*, and that of the vertical displacement OC A” * 67%,
while the velocity of propagation at any point of the canal is that given by
the formula of the preceding paragraph. Mr. Airy has proved the latter
formula § in a more simple manner than Prof. Kelland, and has pointed out
the restrictions under which it is true. Other results of Mr. Airy’s will be
more conveniently considered in connection with the tides.
Theory of Oscillatory Waves.—When the surface of water is covered with
an irregular series of waves of different sizes, the longer waves will be con-
tinually overtaking the shorter, and the motion will be very complicated, and
_ will offer no regular laws. In order to obtain such laws we must take a
simpler case: we may for instance propose to ourselves to investigate the
motion of a series of waves which are propagated with a constant velocity,
and without change of form, in a fluid of uniform depth, the motion being in
two dimensions and periodical. A series of waves of this sort may be taken
as the type of oscillatory waves in general, or at least of those for which the
motion is in two dimensions: to whatever extent a series of waves propagated
in fluid of a uniform depth deviates from this standard form, to the sume ex-
tent they fail in the characters of uniform propagation and invariable form.
The theory of these waves has long been known. In fact each element of
the integrals by which MM. Poisson and Cauchy expressed the disturbance
of the fluid denotes what is called by Mr. Airy a standing oscillation, and a
_ progressive oscillation of the kind under consideration will result from the
_ superposition of two of these standing oscillations properly combined. Or,
if we merely replace products of sines and cosines under the integral signs
by sums and differences, each element of the new integrals will denote a
progressive oscillation of the standard kind. The theory of these waves how-
ever well deserves a more detailed investigation. The most important formula
connected with them is that which gives the relation between the velocity of
__ propagation, the length of the waves, and the depth of the fluid. Ife be the
__ velocity of propagation, A the length of the waves, measured from crest to
on
Risa 9
rest, i the depth of the fluid, and m = =, then
1
1s
es g ina p ET a
a es — a Cpe tr ° . . . . . (B.) :
& im ems | sm
i * Transactions of the Cambridge Philosophical Society, vol. vii. p. 87.
T Transactions of the Royal Society of Edinburgh, vol. xiv. pp. 524, 530.
t Encyclopedia Metropolitana, article ‘ Tides and Waves.’ Art. 260 of the treatise.
§ Art. 218, &c.
6 REPORT—1846.
If the surface of the fluid be cut by a vertical plane perpendicular to the
ridges of the waves, the section of the surface will be the curve of sines.
Each particle of the fluid moves round and round in an ellipse, whose major
axis is horizontal. The particle is in its highest position when the crest of
the wave is passing over it, and is then moving in the direction of propaga-
tion of the wave; it is in its lowest position when the hollow of the wave is
passing over it, and is then moving in a direction contrary to the direction
of propagation. At the bottom of the fluid the ellipse is reduced to a right
line, along which the particle oscillates. When the length of waves is very
small compared with the depth of the fluid, the motion at the bottom is in-
sensible, and all the expressions will be sensibly the same as if the depth were
infinite. On this supposition the expression for ¢ reduces itself to ie
T
The ellipses in which the particles move are replaced by circles, and the
motion in each circle is uniform. The motion decreases with extreme rapid-
ity as the point considered is further removed from the surface; in fact,
the coefficients of the horizontal and vertical velocity contain as a factor the
exponential e~”Y, where y is the depth of the particle considered below the
surface. When the depth of the fluid is finite, the Jaw of the horizontal and
vertical displacements of the particles is the same as when the depth is infi-
nite. When the length of the waves is very great compared with the depth
of the fluid, the horizontal motion of different particles in the same vertical
line is sensibly the same. The expression for ¢ reduces itself to ./gh, the
same as would have been obtained directly from the theory of long waves.
The whole theory is given very fully in the treatise of Mr. Airy*. The
nature of the motion of the individual particles, as deduced from a rigorous
theory, was taken notice of, I believe for the first time, by Mr. Green+, who
has considered the case in which the depth is infinite.
The oscillatory waves just considered are those which are propagated uni-
formly in fluid of which the depth is everywhere the same. When this con-
dition is not satisfied, as for instance when the waves are propagated in a
canal whose section is not rectangular, it is desirable to know how the velo-
city of propagation and the form of the waves are modified by this cireum-
stance. There is one such case in which a solution has been obtained. In
a paper read before the Royal Society of Edinburgh in January 1841, Prof.
Kelland has arrived at a solution of the problem in the case of a triangular
canal whose sides are inclined at an angle of 45° to the vertical, or of a canal
with one side vertical and one side inclined at an angle of 45°, in which the
motion will of course be the same as in one half of the complete canalj. The
velocity of propagation is given by the formula(B.), which applies to a rectan-
gular canal, or to waves propagated without lateral limitation, provided we
take for h half the greatest depth in the triangular canal, and for A, or *, a
quantity less than the length of the waves in the triangular canal in the ratio
of 1 to “2. As to the form of the waves, a section of the surface made by
a vertical plane parallel to the edges of the canal is the curve of sines; a
section made by a vertical plane perpendicular to the former is the common
catenary, with its vertex in the plane of the middle of the canal (supposed
complete), and its concavity turned upwards or downwards according as the
section is taken where the fluid is elevated or where it is depressed. Thus
* Tides and Waves, art. 160, &c.
+ Transactions of the Cambridge Philosophical Society, vol. vii. p. 95.
+ Transactions of the Royal Society of Edinburgh, vol. xv. p. 121.
wee?
*
a A
pac
y
ON RECENT RESEARCHES IN HYDRODYNAMICS. 7
the ridges of the waves do not bend forwards, but are situated in a vertical
plane, and they rise higher towards the slanting sides of the canal than in
the middle. I shall write down the value of ¢, the integral of (A.), and then
any one who is familiar with the subject can easily verify the preceding re-
sults. In the following expression x is measured along the bottom line of
the canal, y is measured horizontally, and z vertically upwards :—
g=A(e*¥ +27 *Y) (e%* +2 %*)sin VW 9a(x—ct). . +» +» (CG)
I have mentioned these results under the head of oscillatory waves, be-
cause it is to that class only that the investigation strictly applies. The
length of the waves is however perfectly arbitrary, and when it bears a large
ratio to the depth of the fluid, it seems evident that the circumstances of the
motion of any one wave cannot be materially affected by the waves which
precede and follow it, especially as regards the form of the middle portion, or
ridge, of the wave. Now the solitary waves of Mr. Russell are long com-
pared with the depth of the fluid; thus in the case of a rectangular canal he
states that the length of the wave is about six times the depth. Accordingly
Mr. Russell finds that the form of the ridge agrees well with the results of
Prof. Kelland.
It appears from Mr. Russell’s experiments that there is a certain limit to
the slope of the sides of a triangular canal, beyond which it is impossible to
propagate a wave in the manner just considered. Prof. Kelland has arrived
at the same result from theory, but his mathematical calculation does not
appear to be quite satisfactory. Nevertheless there can be little doubt that
such a limit does exist, and that if it be passed, the wave will be either con-
tinually breaking at the sides of the canal, or its ridge will become bow-
shaped, in consequence of the portion of the wave in the middle of the canal
being propagated more rapidly than the portions which lie towards the sides.
When once a wave has become sufficiently curved it may be propagated
without further change, as Mr. Airy has shown*. Thus the case of motion
above considered is in nowise opposed to the circumstance that the tide
Wave assumes a curved form when it is propagated in a broad channel in
which the water is deepest towards the centre.
It is worthy of remark, that if in equation (C.) we transfer the origin to
either of the upper edges of the canal (supposed complete), and then suppose
hk to become infinite, having previously written A e—“” for A, the result
will express a series of oscillatory waves propagated in deep water along the
edge of a bank having a slope of 45°, the ridges of the waves being perpen-
dicular to the edge of the fluid. It is remarkable that the disturbance of the
fluid decreases with extreme rapidity as the perpendicular distance from the
edge increases, and not merely as the distance from the surface increases.
Thus the disturbance is sensible only in the immediate neighbourhood of the
edge, that is at a distance from it, which is a small multiple of A. The for-
mula may be accommodated to the case of a bank having any inclination by
merely altering the coefficients of y and 2, without altering the sum of the
squares of the coefficients. If i be the inclination of the bank to the verti-
cal, it will be easily found that the velocity of propagation is equal to
eae era ta ‘
F cosi - When 7 vanishes these waves pass into those already men-
tioned as the standard case of oscillatory waves; and when 7 becomes nega-
tive, or the bank overhangs the fluid, a motion of this sort becomes im-
possible.
* Tides and Waves, art. 359.
8 REPORT—1846.
I have had occasion to refer to what Mr. Airy calls a standing oscillation
or standing wave. To prevent the possibility of confusion, it may be well
to observe that Mr. Airy uses the term in a totally different sense from Mr,
Russell. The standing wave of Mr. Airy is the oscillation which would re-
sult from the coexistence of two series of progressive waves, which are equal
in every respect, but are propagated in opposite directions. With respect to
the standing wave of Mr. Russell, it cannot be supposed that the elevations
observed in mountain streams can well be made the subject of mathematical
calculation. Nevertheless in so far as the: motion can be calculated, by
‘taking a simple case, the theory does not differ from that of waves of other
classes. For if we only suppose a velocity equal and opposite to that of the
stream impressed both on the fluid and on the stone at the bottom which
produces the disturbance, we pass to the case of a forced wave produced in
still water by a solid dragged through it. There is indeed one respect in
which the theory of these standing waves offers a peculiarity, which is, that
the velocity of a current is different at different depths. But the theory of
such motions is one of great complexity and very little interest.
Theory of Solitary Waves.—It has been already remarked that the length
of the solitary wave of Mr. Russell is considerable compared with the depth
of the fluid. Consequently we might expect that the theory of long waves
would explain the main phenomena of solitary waves. Accordingly it is
found by experiment that the velocity of propagation of a solitary wave in a
rectangular canal is that given by the formula of Lagrange, the height of the
wave being very small, or that given by Prof. Kelland’s formula when the
canal is not rectangular. Moreover, the laws of the motion of a solitary
wave, deduced by Mr. Green from the theory of long waves, agree with the
observations of Mr. Russell. Thus Mr.Green found, supposing the canal
rectangular, that the particles in a vertical plane perpendicular to the length
of the canal remain in a vertical plane; that the particles begin to move
when the wave reaches them, remain in motion while the wave is passing
over them, and are finally deposited in new positions; that they move in
the direction of propagation of the wave, or in the contrary direction, ac-
cording as the wave consists of an elevation or a depression*. But when we
attempt to introduce into our calculations the finite length of the wave, the
problem becomes one of great difficulty. Attempts have indeed been made
to solve it by the introduction of discontinuous functions. But whenever
such functions are introduced, there are certain conditions of continuity to
be satisfied at the common surface of two portions of fluid to which different
analytical expressions apply; and should these conditions be violated, the
solution will be as much in fault as it would be if the fluid were made to
penetrate the bottom of the canal. No doubt, the theory is contained, to a
first approximation, in the formule of MM. Poisson and Cauchy; but as it
happens the obtaining of these formule is comparatively easy, their discus-
sion forms the principal difficulty. When the height of the wave is not very
small, so that it is necessary to proceed to a second approximation, the theory
of long waves no longer gives a velocity of propagation agreeing with expe-
riment. It follows, in fact, from the investigations of Mr. Airy, that the velo-
city of propagation of a long wave is, to a second approximation, WV g(h+38h),
where # is the depth of the fluid when it is in equilibrium, and 4+£ the
height of the crest of the wave above the bottom of the canalf.
* Transactions of the Cambridge Philosophical Society, vol. vii. p. 87.
+ Tides and Waves, art. 208. In applying this formula to a solitary wave, it is necessary
to take for h the depth of the undisturbed portion of the fluid. In the treatise of Mr. Airy
the formula is obtained for a particular law of disturbance, but the same formula would have
ON RECENT RESEARCHES IN HYDRODYNAMICS. 9
_ The.theory of the two great solitary waves of Mr. Russell forms the sub-
_ ject of a paper read by Mr. Earnshaw before the Cambridge Philosophical
Society in December last*. Mr. Russell found by experiment that the hori-
zontal motion of the fluid particles was sensibly the same throughout the
whole of a vertical plane perpendicular to the length of the canal. He attri-
buted .the observed degradation of the wave, and consequent diminution of
_ the velocity of propagation, entirely to the imperfect fluidity of the fluid, and
its adhesion to the sides and bottom of the canal. Mr. Earnshaw accordingly
investigates the motion of the fluid on the hypotheses,—first, that the particles
once in a vertical plane, perpendicular to the length of the canal, remain in
a vertical plane; secondly, that the wave is propagated with a constant velo-
city and without change of form. It is important to observe that these
hypotheses are used not as a foundation for calculation, but as a means of
ing a particular kind of motion for consideration. The equations of
fluid motion admit of integration in this case in finite terms, without any
approximation, and it turns out that the motion is possible, so far as the wave
_ itself is concerned, and everything is determined in the result except two
constants, which remain arbitrary. However, in order that the motion in
question should actually take place, it is necessary that there should be an
instantaneous generation or destruction of a finite velocity, and likewise an
abrupt change of pressure, at the junction of the portion of fluid which con-
stitutes the wave with the portions before and behind which are at rest, both
which are evidently impossible. It follows of course that one at least of the
two hypotheses must be in fault. Experiment showing that the first hypo-
thesis is very nearly true, while the second (from whatever cause) is sensibly
erroneous, the conclusion is that in all probability the degradation of the
wave is not to be attributed wholly to friction, but that it is an essential cha-
racteristic of the motion. Nevertheless the formula for the velocity of pro-
pagation of the positive wave, at which Mr. Earnshaw has arrived, agrees very
well with the experiments of Mr. Russell; the formula for the negative wave
also agrees, but not closely. These two formule can be derived from each
other only by introducing imaginary quantities.
It is the opinion of Mr. Russell that the solitary wave is a phenomenon
suit generis, in nowise deriving its character from the circumstances of the
generation of the wave. His experiments seem to render this conclusion
probable. Should it be correct, the analytical character of the solitary wave
remains to be discovered. A-complete theory of this wave should give, not
_ only its velocity of propagation, but also the law of its degradation, at least
of that part of the degradation which is independent of friction, which is
_ probably by far the greater part. With respect*to the importance of this
_ peculiar wave however, it must be remarked that the term solitary wave, as
| so defined, must not be extended to the tide wave, which is nothing more (as
| far as regards the laws of its propagation) than a very long wave, of which
the form may be arbitrary. It is hardly necessary to remark that the me-
' chanical theories of the solitary wave and of the aérial sound wave are
| altogether different.
‘Ba Theory of River and Ocean Tides.—The treatise of Mr. Airy already referred
| to is so extensive, and so full of original matter, that it will be impossible ~
ithin the limits of a report like the present to do more than endeavour to
Lk ae
_ pes re , —
Bt pA ORE TAA PISS OS
given as expressing the velocity of propagation of the phase of high water, which it is true is
| not quite the same as the velocity of propagation of the crest of the wave; but the two velo-
| cities are the same to the second order of approximation.
-* Transactions of the Cambridge Philosophical Society, vol. viii. p. 326.
i i arrived at, by the same reasoning, had the law not been restricted. This formula is
10 REPORT—1846,
give an idea of the nature of the calculations and methods of explanation
employed, and to mention some of the principal results.
On account of the great length of the tide wave, the horizontal motion of
the water will be sensibly the same from top to bottom. This circumstance
most materially simplifies the calculation. The partial differential equation
for the motion of long waves, when the motion is very small, is in the simplest
case the same as that which occurs in the theory of the rectilinear propaga-
tion of sound; and in Mr. Airy’s investigations the arbitrary functions which
occur in its integral are determined by the conditions to be satisfied at the
ends of the canal in which the waves are propagated, in a manner similar to
that in which the arbitrary functions are determined in the case of a tube in
which sound is propagated. When the motion is not very small, the partial
differential equation of wave motion may be integrated by successive ap-
proximations, the arbitrary functions being determined at each order of ap-
proximation as before.
To proceed to some of the results. The simplest conceivable case of a
tidal river is that in which the river is regarded as a uniform, indefinite canal,
without any current. The height of the water at the mouth of the canal will
be expressed, as in the open sea, by a periodic function of the time, of the
form asin (mt+a). The result of a first approximation of course is that
the disturbance at the mouth of the canal will be propagated uniformly up
it, with the velocity due to half the depth of the water. But on proceeding to
a second approximation*, Mr. Airy finds that the form of the wave will alter
as it proceeds up the river. Its front will become shorter and steeper, and
its rear longer and more gently sloping. When the wave has advanced suf-
ficiently far up the river, its surface will become horizontal at one point in
the rear, and further on the wave will divide into two. At the mouth of the
river the greatest velocities of the ebb and flow of the tide are equal, and
occur at low and high water respectively ; the time during which the water
is rising is also equal to the time during which it is falling. But at a station
up the river the velocity of the ebb-stream is greater than that of the flow-
stream, and the rise of the water occupies less time than its fall. If the sta-
tion considered is sufficiently distant from the mouth of the river, and the
tide sufficiently large, the water after it has fallen some way will begin to
rise again: there will in fact be a double rise and fall of the water at each
tide. This explains the double tides observed in some tidal rivers. The
velocity with which the phase of high water travels up the river is found to
be V gk (1+3b), k being the depth of the water when in equilibrium, and
bk the greatest elevation of the water at the mouth of the river above its
mean level. The same formula will apply to the case of low water if we
change the sign of 6. ‘This result is very important, since it shows that the
. interval between the time of the moon’s passage over the meridian of the
river station and the time of high water will be affected by the height of the
tide. Mr. Airy also investigates the effect of the current in a tidal river. He
finds that the difference between the times of the water's rising and falling
is increased by the current.
When the canal is stopped by a barrier the circumstances are altered.
When the motion is supposed small, and the disturbing force of the sun and
moon is neglected, it is found in this case that the tide-wave is a stationary
waveT, so that there is high or low water at the same instant at every point
of the canal; but if the length of the canal exceeds a certain quantity, it is
high water in certain parts of the canal at the instant when it is low water
* Art. 198, &c, 7 Art. 307.
ON RECENT RESEARCHES IN HYDRODYNAMICS. ll
in the remainder, and vice versd. The height of high water is different in
different parts of the canal: it increases from the mouth of the canal to its
_ extremity, provided the canal’s length does not exceed a certain quantity. If
four times the length of the canal be any odd multiple of the length of a
free wave whose period is equal to that of the tide, the denominator of the
expression for the tidal elevation vanishes. Of course friction would pre-
_ yent the elevation from increasing beyond acertain amount, but still the tidal
oscillation would in such cases be very large.
When the channel up which the tide is propagated decreases in breadth
or depth, or in both, the height of the tide increases in ascending the channel.
This accounts for the great height of the tides observed at the head of the
Bristol Channel, and in such places. In some of these cases however the
great height may be partly due to the cause mentioned at the end of the last
paragraph.
When the tide-wave is propagated up a broad channel, which becomes
shallow towards the sides, the motion of the water in the centre will be of
the same nature as the motion in a free canal, so that the water will be flow-
ing up the channel with its greatest velocity at the time of high water.
Towards the coasts however there will be a considerable flow of water to
and from the shore; and as far as regards this motion, the shore will have
nearly the same effect as a barrier in a canal, and the oscillation will be of
the nature of a stationary wave, so that the water will be at rest when it is
_ at its greatest height. If, now, we consider a point at some distance from
_ the shore, but still not near the middle of the channel, the velocity of the
water up and down the channel will be connected with its height in the same
way as in the case of a progressive wave, while the velocity to and from the
shore will be connected with the height of the water in the same way as in a
stationary wave. Combining these considerations, Mr. Airy is enabled to
explain the apparent rotation of the water in such localities, which arises
_ from an actual rotation in the direction of its motion*.
When the motion of the water is in two dimensions the mathematical cal-
culation of the tidal oscillations is tolerably simple, at least when the depth
of the water is uniform. But in the case of nature the motion is in three
_ dimensions, for the water is distributed over the surface of the earth in broad
_ sheets, the boundaries of which are altogether irregular. On this account a
_ .eomplete theory of the tides appears hopeless, even in the case in which the
_ depth is supposed uniform. Laplace’s theory, in which the whole earth is
_ supposed to be covered with water, the depth of which follows a very pecu-
liar law, gives us no idea of the effect of the limitation of the ocean by conti-
_ nents. Mr. Airy consequently investigates the motion of the water on the
_ supposition of its being confined to narrow canals of uniform depth, which
in the calculation are supposed circular. The case in which the canal forms
_ a great circle is especially considered. This method enables us in some de-
gree to estimate the effect of the boundaries of the sea; and it has the great
__ advantage of leading to calculations which can be worked out. There can
be no doubt, too, that the conclusions arrived at will apply, as to their general
_ nature, to the actual case of the earth.
_ With a view to this application of the theory, Mr. Airy calculates the
_ Motion of the water in a canal when it is under the action of a disturbing
_ force, which is a periodic function of the time. The disturbing force at a
point whose abscissa, measured along tle canal from a fixed point, is 2, is
_ supposed to be expressed by a function of the form A sin (nt—ma+a).
_ This supposition is sufficiently general for the case of the tides, provided the
* Art. 360, &c.
.
-
T2 REPORT—1846.
canal on the earth be supposed circular. In all cases the disturbing force
will give rise to an oscillation in the water having the same period as the force
itself. This oscillation is called by Mr. Airy’a forced wave. It will be suf-
ficient here to mention some of the results of this theory as applied to the
case of the earth.
In all cases the expression for the tidal elevation contains as a denominator
the difference of the squares of two velocities, one the velocity of propagation
of a free wave along the canal, the other the velocity with which a particular
phase of the disturbing force travels along the canal, or, which is the same,
the velocity of propagation of the forced wave. Hence the height of the
tides will not depend simply on the magnitude of the disturbing force, but
also on its period. Thus the mass of the moon cannot be inferred directly
from the comparison of spring and neap tides, since the heights of the solar
and lunar tides are affected by the different motions of the sun and moon in
right ascension, and consequently in hour-angle. When the canal under
consideration is equatorial the diurnal tide vanishes. The height of high water
is the same at all points of the canal, and there is either high or low water at
the point of the canal nearest to the attracting body, according as the depth
of the water is greater or less than that for which a free wave would be pro-
pagated with the same velocity as the forced wave. In the general case there
is both a diurnal and a semidiurnal tide, and the height of high water, as well
as the interval between the transit of the attracting body over the meridian
of the place considered and the time of high water, is different at different
points of the canal. When the canal is a great circle passing through the
poles, the tide-wave is a stationary wave. When the coefficient of the dis-
turbing force is supposed to vary slowly, in consequence of the change in
declination, &c. of the disturbing body, it is found that the greatest tide oc-
curs on the day on which the disturbing force is the greatest.
The preceding results have been obtained on the supposition of the absence
of all friction; but Mr. Airy also takes friction into consideration. He sup-
poses it to be represented by a horizontal force, acting uniformly from top to
bottom of the water, and varying as the first power of the horizontal velocity.
Of course this supposition is not exact: still there can be no doubt that
it represents generally the effect of friction. When friction is taken into
account, the denominator of the expressions for the tidal elevation is essen-
tially positive, so that the motion can never become infinite. In the case of
a uniform tidal river stopped by a barrier, the high water is no longer simul-
taneous at all points, but the phase of high water always travels up the river.
But of all the results obtained by considering friction, the most important
appears to be, that when the slow variation of the disturbing force is taken
into account, the greatest tide, instead of happening on the day when the
disturbing force is greatest, will happen later by a certain time, p,. More-
over, in calculating the tides, we must use, not the relative positions of the sun
and moon for the instant for which the tide is calculated, but their relative
positions for a time earlier by the same interval p, as in the preceding case.
The expression for p, depends both on the depth of the canal and on the
period of the tide, and therefore its value for the diurnal tide cannot be
inferred from its value for the semidiurnal. It appears also that the phase of
the tide is accelerated by friction.
The mechanical theory of the tides of course belongs to hydrodynamics ;
but I do not conceive that the consideration of the reduction and discussion
of tidal observations falls within the province of this report.
Before leaving the investigations of Mr. Airy, I would call attention to a
method which he sometimes employs very happily in giving a general expla-
*
Al tiny eights ae, gg ROS
—e- 3 P
os
| He . ° . . . . . .
_ tered if we take into account the cooling of the air by its rapid dilatation.
|The experiments above alluded to were made by allowing the air to enter an
exhausted receiver through a small orifice, and observing simultaneously the
ON RECENT RESEARCHES IN HYDRODYNAMICS. 13
_ nation of phenomena depending on motions which are too complicated to
admit of accurate calculation. It is evident that any arbitrary motion may
be assigned to a fluid, (with certain restrictions as to the absence of abrupt-
hess, ) provided we suppose certain forces to act so asto produce them. The
values of these forces are given by the equations of motion. In some cases
the forces thus obtained will closely resemble some known forces ; while in
others it will be possible to form a clear conception of the kind of motion
which must take place in the absence of such forces. For example, sup-
posing that there is propagated a series of oscillatory waves of the standard
kind, except that the height of the waves increases proportionably to their
distance from a fixed line, remaining constant at the same point as the time
varies, Mr. Airy finds for the force requisite to maintain such a motion an
expression which may be assimilated to the force which wind exerts on water.
This affords a general explanation of the increase in the height of the waves
in passing from a windward to a lee shore*. Again, by supposing a series
of waves, as near the standard kind as circumstances will admit, to be pro-
pagated along a canal whose depth decreases slowly, and examining the force
requisite to maintain this motion, he finds that a force must be applied to
hold back the heads of the waves. In the absence, then, of such a force the
heads of the waves will have a tendency to shoot forwards. This explains
the tendency of waves to break over a sunken shoal or along a sloping
beacht. The word tendency is here used, because when a wave comes at all
near breaking, but little reliance can be placed in any investigation which
depends upon the supposition of the motion being small. To take one more
example of the application of this method, by supposing a wave to travel,
unchanged in form, along a canal, with a velocity different from that of a free
wave, and examining the force requisite to maintain such a motion, Mr. Airy
is enabled to give a general explanation of some very curious circumstances
connected with the motion of canal boats{; which have been observed by
Mr. Russell,
IIL. In the 16th volume of the ‘ Journal de l’Ecole Polytechnique §, will be
found a memoir by MM. Barré de Saint-Venant and Wantzel, containing the
results of some experiments on the discharge of air through small orifices,
produced by considerable differences of pressure. The formula for the ve-
locity of efflux derived from the theory of steady motion, and the supposition
_ that the mean pressure at the orifice is equal to the pressure at a distance
from the orifice in the space into which the discharge takes place, leads to
some strange results of such a nature as to make us doubt its correctness. If
we call the space from which the discharge takes place the first space, and
that into which it takes place the second space, and understand by the term
reduced velocity the velocity of efflux diminished in the ratio of the density
in the second space to the density in the first, so that the reduced velocity
- measures the rate of discharge, provided the density in the first space remain
constant, it follows from the common formula that the reduced velocity va-
nishes when the density in the second space vanishes, so that a gas cannot be
_ discharged into a vacuum. Moreover, if the density of the first space is given,
_ the reduced velocity is a maximum when the density in the second space is
‘rather more than half that in the first. The results remain the same if we
take account of the contraction of the vein, and they are not materially al-
* Art. 265, &c, + Art. 238, &c.
t Art. 405, &c. § Cahier xxvii. p. 85.
14 REPORT—1846.
pressure and temperature of the air in the receiver, and the time elapsed since
the opening of the orifice. It was found that when the exhaustion was com-
plete the reduced velocity had a certain value, depending on the orifice em-
ployed, and that the velocity did not sensibly change till the pressure of the
air in the receiver became equal to about 2ths of the atmospheric pressure.
The reduced velocity then began to decrease, and finally vanished when the
pressure of the air in the receiver became equal to the atmospheric pressure.
These experiments show that when the difference of pressure in the first
and second spaces is considerable, we can by uo means suppose that the mean
pressure at the orifice is equal to the pressure at a distance in the second
space, nor even that there exists a contracted vein, at which we may suppose
the pressure to be the same as at a distance. The authors have given an
empirical formula, which represents very nearly the reduced velocity, what-
ever be the pressure of the air in the space into which the discharge takes place.
The orifices used in these experiments were generally about one millimetre
in diameter. It was found that widening the mouth of the orifice, so as to
make it funnel-shaped, produced a much greater proportionate increase of
velocity when the velocity of efflux was small than when it was large. The
authurs have since repeated their experiments with air coming from a vessel in
which the pressure was four atmospheres: they have also tried the effect of
using larger orifices of four or five millimetres diameter. The general results
were found to be the same as before*.
IV. In the 6th volume of the Transactions of the Cambridge -Philoso-
phical Society, p. 403, will be found a memoir by Mr. Green on the re-
flection and refraction of sound, which is well-worthy of attention. This
problem had been previously considered by Poisson in an elaborate memoir.
Poisson treats the subject with extreme generality, and his analysis is con-
sequently very complicated. Mr. Green, on the contrary, restricts himself
to the case of plane waves, a case evidently comprising nearly all the pheeno-
mena connected with this subject which are of interest in a physical point of
view, and thus is enabled to obtain his results by a very simple analysis. In-
deed Mr. Green’s memoirs are very remarkable, both for the elegance and
rigour of the analysis, and for the ease with which he arrives at most im-
portant results. This arises in a great measure from his divesting the pro-
blems he considers of all unnecessary generality: where generality is really
of importance he does not shrink from it. In the present instance there is
one important respect in which Mr. Green’s investigation is more general
than Poisson’s, which is, that Mr. Green has taken the case of any two fluids,
whereas Poisson considered the case of two elastic fluids, in which equal con-
densations produce equal increments of pressure. It is curious, that Poisson,
forgetting this restriction, applied his formulz to the case of air and water.
Of course his numerical result is altogether erroneous. My. Green easily
arrives at the ordinary laws of reflection and refraction. He obtains also a
very simple expression for the intensity of the reflected sound. If A is the
ratio of the density of the second medium to that of the first, and B the ratio
of the cotangent of the angle of refraction to the cotangent of the angle of
incidence, then the intensity of the reflected sound is to the intensity of the
incident as A—Bto A+B. In this statement the intensity is supposed to
be measured by the first power of the maximum displacement. When the
velocity of propagation in the first medium is less than in the second, and the
angle of incidence exceeds what may be called the critical angle, Mr, Green
restricts himself to the case of vibrations following the cycloidal law. He
* Comptes Rendas, tom. xvii. p. 1140.
+ Mémoires de l’Académie des Sciences, tom. x. p. 317,
ON RECENT RESEARCHES IN HYDRODYNAMICS. 15
Ay
_ finds that the sound suffers total internal reflection. The expression for the
_ disturbance in the second medium involves an exponential with a negative
_ index, and consequently the disturbance becomes quite insensible at a di-
_ stance from the surface equal to a small multiple of the length of a wave.
_ The phase of vibration of the reflected sound is also accelerated by a quan-
tity depending on the angle of incidence. It is remarkable, that when the
_ fluids considered are ordinary elastic fluids, or rather when they are such
that equal condensations produce equal increments of pressure, the expres-
sions for the intensity of the reflected sound, and for the acceleration of
_ phase when the angle of incidence exceeds the critical angle, are the same
as those given by Fresnel for light polarized in a plane perpendicular to the
plane of incidence.
VY. Not long after the publication of Poisson’s memoir on the simultaneous
motions of a pendulum and of the surrounding air*, a paper by Mr. Green
was read before the Royal Society of Edinburgh, which is entitled ‘ Re-
searches on the Vibration of Pendulums in Fluid Media+.’ Mr. Green does
not appear to have been at that time acquainted with Poisson’s memoir. The
_ problem which he has considered is one of the same class as that treated by
Poisson. Mr. Green has supposed the fluid to be incompressible, a suppo-
_ sition, however, which will apply without sensible error to air, in considering
_ motions of this sort. Poisson regarded the fluid as elastic, but in the end, in
_ adapting his forthula to use, he has neglected as insensible the terms by
which the effect of an elastic differs from that of an inelastic fluid. The
_ problem considered by Mr. Green is, however, in one respect much more
general than that solved by Poisson, since Mr. Green has supposed the oscil-
lating body to be an ellipsoid, whereas Poisson considered only a sphere.
_ Mr. Green has obtained a complete solution of the problem in the case in
_ which the ellipsoid has a motion of translation only, or in which the small
_ motion of the fluid due to its motion of rotation is neglected. The result is
_ that the resistance of the fluid will be allowed for if we suppose the mass of
the ellipsoid increased by a mass bearing a certain ratio to that of the fluid
displaced. In the general case this ratio depends on three transcendental
quantities, given by definite integrals. If, however, the ellipsoid oscillates in
3 the direction of one of its principal axes, the ratio depends on one only of
_ these transcendents. When the ellipsoid passes into a spheroid, the tran-
_ scendents above-mentioned can be expressed by means of circular or loga-
_ rithmic functions. When the spheroid becomes a sphere, Mr. Green’s result
_ agrees with Poisson’s. It is worthy of remark, that Mr. Green’s formula will
enable us to calculate the motion of an ellipse or oircle oscillating in a fluid,
_ in a direction perpendicular to its plane, since a material ellipse or circle may
_ be considered as a limiting form of an ellipsoid. In this case, however, the
motion would probably have to be extremely small, in order that the formula
should apply with accuracy.
__ Ina paper ‘On the Motion of a small Sphere acted on by the Vibrations of
_ an Elastic Medium,’ read before the Cambridge Philosophical Society in April
_ 1841, Prof. Challis has considered the motion of a ball pendulum, retaining
in his solution small quantities to the second order. The principles adopted
by Prof. Challis in the solution of this problem are at variance with those of
Poisson, and have given rise to a controversy between him and Mr. Airy,
7... will be found in the 17th, 18th and 19th volumes of the Philosophical
w+
Ton
_____-* Mémoires de I’Académie des Sciences, tom. xi. p. 521.
__ * This paper was read in December 1833, and is printed in the 13th volume of the So-
_ ¢iety’s Transactions, p. 54, &c. i i
___ ¢ Transactions of the Cambridge Philosophical Society, vol. vii. p. 333.
‘
’
16 REPORT—1846.
Magazine (New Series). In the paper just referred to, Prof. Challis finds that
when the fluid is incompressible there is no decrement in the arc of oscilla-
tion, except what arises from friction and capillary attraction. In the case
of air there is a slight theoretical decrement; but it is so small that Prof.
Challis considers the observed decrement to be mainly owing to friction.
This result follows also from Poisson’s solution. Prof. Challis also finds that
a small sphere moving with a uniform velocity experiences no resistance, and
that when the velocity is partly uniform and partly variable, the resistance
depends on the variable part only. The problem, however, referred to in
the title of this paper, is that of calculating the motion of a small sphere
situated in an elastic fluid, and acted on by no forces except the pressure of
the fluid, in which an indefinite series of plane condensing and rarefying
waves is supposed to be propagated. This problem is solved by the author on
principles similar to those which he has adopted in the problem of an oscil-
lating sphere. The views of Prof. Challis with respect to this problem, which
he considers a very important one, are briefly stated at the end of a paper
published in the Philosophical Magazine*.
In a paper ‘On some Cases of Fluid Motion,’ published in the Trans-
actions of the Cambridge Philosophical Society+, I have considered some
modifications of the problem of the ball pendulum, adopting in the main the
principles of Poisson, of the correctness of which I feel fully satisfied, but
supposing the fluid incompressible from the first. In this paper the effect of
a distant rigid plane interrupting the fluid in which the sphere is oscillating is
given to the lowest order of approximation with which the effect is sensible.
It is shown also that when the ball oscillates in a concentric spherical enve-
lope, the effect of the resistance of the fluid is to add to the mass of the
= 5° where a is the radius of the ball, 6 that
of the envelope, and m the mass of the fluid displaced. Poisson, having
reasoned on the very complicated case of an elastic fluid, had come to the
conclusion that the envelope would have no effect.
One other instance of fluid motion contained in this paper will here be
mentioned, because it seems to afford an accurate means of comparing theory
and experiment in a class of motions in which they have not hitherto been
compared, so far as I am aware. When a box of the form of a rectangular
parallelepiped, filled with fluid and closed on all sides, is made to perform small
oscillations, it appears that the motion of the box will be the same as if the
fluid were replaced by a solid having the same mass, centre of gravity, and
principal axes as the solidified fluid, but different principal moments of in-
ertia. These moments are given by infinite series, which converge with
extreme rapidity, so that the numerical calculation is very easy. The oscil-
lations most convenient to employ would probably be either oscillations by
torsion, or bifilar oscillations.
VI. M. Navier was, I believe, the first to give equations for the motion of
fluids without supposing the pressure equal in all directions. His theory is
contained in a memoir read before the French Academy in 1822{. He con-
siders the case of a homogeneous incompressible fluid. He supposes such a
fluid to be made up of ultimate molecules, acting on each other by forces
which, when the molecules are at rest, are functions simply of the distance,
but which, when the molecules recede from, or approach to each other, are
modified by this cireumstance, so that two molecules repel each other less
sphere a mass equal to
strongly when they are receding, and more strongly when they are approaching, -
* Vol. xviii. New Series, p. 481. t Vol. viii. p. 105.
t Mémoires de l’Académie des Sciences, tom. vi. p. 389.
ON RECENT RESEARCHES IN HYDRODYNAMICS. 17
_ than they do when they are at rest*. The alteration of attraction or re-
pulsion is supposed to be, for a given distance, proportional to the velocity
with which the molecules recede from, or approach to each other; so that
the mutual repulsion of two molecules will be represented by f(r) — VF (r);
where r is the distance of the molecules, V the velocity with which they recede
from each other, and f(r), F (7) two unknown functions of 7 depending on
the molecular force, and as such becoming insensible when 7 has become
sensible. This expression does not suppose the molecules to be necessarily
receding from each other, nor their mutual action to be necessarily repulsive,
since V and F (7) may be positive or negative. It is not absolutely necessary
that f(7) and F (7) should always have the same sign. In forming the equa-
tions of motion M. Navier adopts the hypothesis of a symmetrical arrangement
of the particles, or at least, which leads to the same result, neglects the irre-
gular part of the mutual action of neighbouring molecules. The equations
at which he arrives are those which would be obtained from the common
@u du du 7 f = h
(Gatgetae) in place of 5 in the
first, and making similar changes in the second and third. AS is nae an
_ unknown constant depending on the nature of the fluid.
The same subject has been treated on by Poisson, who has adopted hy-
potheses which are very different from those of M. Navier. Poisson's theory
is of this nature. He supposes the time ¢ to be divided into 2 equal parts,
each equal to 7. In the first of these he supposes the fluid to be displaced
in the same manner as an elastic solid, so that the pressures in different
_ directions are given by the equations which he had previously obtained for
elastic solids. If the causes producing the displacement were now to cease
to act, the molecules would very rapidly assume a new arrangement, which
would render the pressure equal in all directions, and while this re-arrange-
ment was going on, the pressure would alter in an unknown manner from
that belonging to a displaced elastic solid to the pressure belonging to the
fluid in its new state. The causes of displacement are however going on
_ during the second interval 7; but since these different small motions will
_ take place independently, the new displacement which will take place in the
second interval 7 will be the same as if the molecules were not undergoing a
: " re-arrangement. Supposing now z to become infinite, we pass to the case in
which the fluid is continually beginning to be displaced like an elastic solid,
| continually re-arranging itself so as to make the pressure equal in all
directions. The equations at which Poisson arrived are, in the cases of a
romogencous incompressible fluid, and of an elastic fluid in which the change
of density is small, those which would be derived from the common equations”
d
equations by writing ~ —
d
| py replacing 7’ _ cent to the surface of the pipe is at rest*. This result agrees very well with
an experiment of Coulomb’s. Coulomb found that when a metallic dise was
made to oscillate very slowly in water about an axis passing through its
centre and perpendicular to its plane, the resistance was not altered when
the dise was smeared with grease; and even when the grease was covered
_ with powdered sandstone the resistance,was hardly increased}. This is just
what one would expect on the supposition that the water close to the disc is
_ earried along with it, since in that case the resistance must depend on the
~ internal friction of the fluid; but the result appears very extraordinary on
the supposition that the fluid in contact with the disc flows past it with a
nite velocity. It should be observed, however, that this result is compatible
‘with the supposition that a thin film of fluid remains adhering to the dise, in
onsequence of capillary attraction, and becomes as it were solid, and that
the fluid in contact with this film flows past it with a finite velocity. If we
‘consider Dubuat’s supposition to be correct, the condition to be assumed in
the case of a fluid in contact with a solid is that the fluid does not move re-
latively to the solid. This condition will be included in M. Navier’s, if we
‘suppose the coefficient of the velocity when M. Navier’s condition is ex-
pressed analytically, which he denotes by E, to become infinite. It seems
probable from the experiments of M. Girard, that the condition to be satis-
ed at the surface of fluid in contact with a solid is different according as the
fluid does or does not moisten the surface of the solid.
___M.Navier has applied his theory to the results of some experiments of
-M. Girard’s on the discharge of fluids through capillary tubes. His theory
shows that if we suppose E to be finite, the discharge through extremely
all tubes will depend only on E, and not on A. The law of discharge at
ich he arrives agrees with the experiments of M. Girard, at least when the
es are extremely small. M. Navier explained the difference observed by
: Girard in the discharge of water through tubes of glass and tubes of
opper of the same size by supposing the value of E different in the two
es. This difference was explained by M. Girard himself by supposing that
n film of fluid remains adherent to the pipe, in consequence of molecular
ion, and that the thickness of this film differs withthe substance of which
tube is composed, as well as with the liquid employed{. If we adopt
vier’s explanation, we may reconcile it with the experiments of Coulomb
supposing that E is very large, so that unless the fluid is confined in a
harrow pipe, the results will depend mainly on A, being sensibly the
ne as they would be if E were infinite.
There is one circumstance connected with the motion of a ball-pendulum
scillating in air, which has not yet been accounted for, the explanation of
Which seems to depend on this theory. It is found by experiment that the
orrection for the inertia of the air is greater for small than for large spheres,
t is to say, the mass which we must suppose added to that of the sphere
a greater ratio to the mass of the fluid displaced in the former, than in
atter case. According to the common theory of fluid motion, in which
* See the Table given in tom. i. of his Principes d’Hydraulique, p.93.
+ Mémoires de l'Institut, 1801, tom. iii. p. 286.
} Mémoires de l’Académie des "Sciences, tom. i. pp. 203 and 234,
C2
20 REPORT—1846.
everything is supposed to be perfectly smooth, the ratio ought to be inde-
pendent of the magnitude of the sphere. In the imperfect theory of friction
in which the friction of the fluid on the sphere is taken into account, while
the equal and opposite friction of the sphere on the fluid is neglected, it is
shown that the are of oscillation is diminished, while the time of oscillation
is sensibly the same as before. But when the tangential action of the sphere
on the fluid, and the internal friction of the duid itself are considered, it is
clear that one consequence will be, to speak in a general way, that a portion
of the fluid will be dragged along with the sphere. Thus the correction for
the inertia of the fluid will be increased, since the same moving force has now
to overcome the inertia of the fluid dragged along with the sphere, and not
only, as in the former case, the inertia of the sphere itself, and of the fluid
pushed away from before it, and drawn in behind it. Moreover the addi-
tional correction for inertia must depend, speaking approximately, on the
surface of the sphere, whereas the first correction depended on its volume,
and thus the effect of friction in altering the time of oscillation will be more
conspicuous in the case of small, than in the case of large spheres, other cir-
cumstances being the same. The correction for inertia, when friction is
taken into account, will not, however, depend solely on the magnitude of the
sphere, but also on the time of oscillation. With a given sphere it will be
greater for long, than for short oscillations.
Sixth Report of a Committee, consisting of H. EK. Srrickuanp, Esq.,
Prof. DauBeny, Prof. HeEnstow, and Prof. Linpury, appointed
to continue their Experiments on the Vitality of Seeds.
THESE experiments have again been repeated upon 48 kinds of seeds ga-
thered in 1843, as well as upon 26 kinds of new seeds added to the general
collection in 1845.
Many kinds‘of old seeds, of various dates from 1812 to 1845 inclusive,
consisting of 151 packets, have been contributed by Miss Molesworth. These
were for the most part in small quantities, and were sown only at Oxford, on
a slight hot-bed.
A small quantity of soil from the bed of a freshwater lake of the tertiary
period, at Mundesley, Norfolk, containing scales of fish, elytra of beetles,
seeds of Ceratophyllum and other plants from Sir W. C. Trevelyan, was sub-
jected to three tests; viz. one-third part was placed in a shallow pan, and
kept moist with distilled water; the second portion was kept well-saturated
with the same; and the third portion, also in a shallow pan, under about
one inch of distilled water. The whole was kept under a glass case to pre-
vent the chance of seeds, &c. being deposited in it. No vegetation appeared
in either case.
It may be well to remark, that the seeds have been sown under different
circumstances, and have received different treatment at each of the three
places they have been experimented upon. At Oxford, as in previous years, -
a selection was made from the whole quantity to be sown, of such as usually
require the assistance of heat to enable them to germinate ; these were sown
in pots and placed in slight heat, and the remainder were sown on a small
bed made in a cold frame, and, with the exception of two or three waterings,
left to nature.
At Hitcham they were all sown in a border carefully prepared for them,
and afterwards left to nature.
ON THE VITALITY OF SEEDS, | 21
At Chiswick the whole of the seeds were sown in separate pots and placed
in a pit heated with hot water.
- These several treatments will at once account for the great difference there
has been in many cases between the length of time the seeds required to
vegetate, as well as the greater number of seeds which did vegetate at one
place more than at the other, which will be seen on referring to the following
statement of the results.
No. of Seeds of each : :
Species which vege- | Time of vegetating
e tated at in days at
Name and Date when gathered. A ee ae aE TTY
Ox- |,,. Chis-} Ox- | ,..
ford, | Hitcham.| wick.| ford. Hitcham.
—
.
Asphodelus luteus .........+0
. Arctium Lappa
. Angelica Archangelica
. Ageratum mexicanum
. Aster tenella ,
. Allium fragrans
Bidens diversifolia
. Biscutella erigerifolia
. Borkhausia rubra
. Bartonia aurea
. Callistemma hortensis
. Campanula Medium
Centaurea depressa
. Cladanthus arabicus
. Cleome spinosa
. Cnicus arvensis Bad in 1844,
. Convolvulus major
. Dianthus barbatus....... Seer
. Echium grandiflorum
. Eucharidium concinnum ...
Euphorbia Lathyris
. Gypsophila elegans
Helenium Douglasii
. Hebenstreitia tenuifolia
Heliophila araboides
Hesperis matronalis .........
« Hypericum hirsutum....... ne
. Kaulfussia amelloides
Koniga maritima ..,..........
Leptosiphon androsacea
. Lunaria biennis
Loasa lateritia
ONS Ste Go bo
Cnanthe Crocata
. Phytolacca decandra .....
. Plantago media
Polemonium czeruleum
. Rumex obtusifolium .........
. Silene inflata
« Smyrnium Olusatrum
. Schizanthus pinnatus.........
. Tallinum ciliatum
. Tigridia Pavonia
. Valeriana officinalis
. Viola lutea vars
22 REPORT—1846.
‘gate cnpigh—s ipa of eerste
No tated at days at
Name and Date when gathered. sown. | eae lcuveatenal Remarks
‘ -| Ox- "|
fond, Hitcham. bie ford. Hitcham. mri
1845.
49. Ailanthus glandulosa ........ 50 | 20 7 | 36| 382 51 25
50. Alnus glutinosa .....++++..00+ 1 ST BE ea decen (LM Meaass| Sees swese 40
51. Alons0a iNcisa «...cesses«ssees| 100 |iesere DP AZ Wasceos) cosescces 30
52. Beta vulgaris ....... etd heat 75) 73 10 | 63] 6 14 | 35
53. Browallia elata ............00. BO seg HL he teek, BOC TtAD. | teens 30
54. Chrysanthemum coronarium| 150 | 55 15/104 |...... 12 | 20
55. Cytisus albus ..... ged. fissearet 100 | 20 2 | 63 | 10 25 | 40
56. Eccremocarpus scaber ...... ROO teens f\'vecedoase Pel nee lieiesepebue 30
57. Fagus sylvatica .........c00+. MOD 949] eeccdsace 76 {110 |.......4 40
58. Fumaria spicata ......... Besees 100 | 17 1 | 80 | 36 | ......55 20
59. Gaillardia aristata ............ TOD ccccil deesdcace 87 Wevtccclioecesssst 35
60. Gleditschia triacanthos ...... QO |sis-6| covssread [osboon|ssevee| sesevceee
Gs Aris, SPivssicecasscocedounas sats ID. [owae th evcedecte Wa teccelweleescae 35
62. Knautia orientalis ............ 50 | 6 4 | 29 | 12 18 | 30
63. Lopezia racemosa ..... aseboep 150 | 26 64 (122) 6 14 | 30
64. Lymnanthes Douglasii ...... 50 | 14 35 | 42] 6 13 | 18
65. Petunia odorata .........s0000. LEO TOU secede. ap ESE sccccetlaneses we | 25
66. Schizopetalon Walkeri ......| 50 | 26 24 | 46] 5 ll | 18
67. Secale cereale.........sssessees 200 |160 | 102* 1194] 5 Tap
68. Spartium Scoparium .........) 200 | 5 |......... 117 Joeceee] coeeeeees 40
69. Tagetes lucida ......... vey ROUNpecovsl dtneds can 139 |...000) wecseeees 20
70. Verbena Aubletia ............ 100 | 5 Le 4O sO iscesaces 25
71. Viscaria oculata....0....s00.0. 150 }...00. 2 LSS lasvees 10 | 20
72. Xeranthemum annuum...... OWE coeet| axe dees si MAPaieaks ssl tacespenee 25
Just LOR MAYS lescecestvets.cacetees 100 | 98 Diath has Jae bak 22 | 35
74. Zinnia grandiflora ............ MOO aecicecace SU 5 [3242.3) Seesss 25
From Miss Molesworth :—
z é Ee ! so ‘ a
gE) 2 |B é|3|Ps
Name and Date. a & SA Name and Date. a to | 5.8
a) ben In 6] Fle 2
“12 \é3 “| 3 \83
1812. 1828.
1. Ricinus communis ...... 12; 0 15, Aster lactea .....ssseses 100} 0
16. Galium lucidum......... 8} 0
2. Catananche cerulea ...|100 | 0 17. Helianthemum croceum|100 | 0
5. Cucurbita Citrullus ...) 15 | 0 1829.
1825. 18. Cucurbita, Cucuzza di
4. Swiss Melon ......... «| 5} O Spagna......... ssedeaes Zip
1827. 19. —, Cucuzza Tiascheta 54] 0
5. Brassica, white Cauli- 20. Dory cnium monspeli-
MOWER! Seicicvaccscnscter 100 | 0 ONSE seiacccsscvescoonsbete 100} 0
6. —, Brocoli di Carnivale|100 | 0 21. Hypericum fimbriatum |100 | 0
7. —,— Primotice ...... 100 | 0 92,, Miltum. ©... 6. cssivcoodsd 100} 0
8. —, Cavoli Feguti ...... 100 | 0 28. Rumex alpinus ......... 30} 0
9. Cucurbita Citrullus ...| 10 | 0 P
NOs" Melon ceass tre edsbco cd, ede 30) 0 24, Cytisus leucanthus...... 100 | 0
11. Green Melon .......<..4. 50 | 0 25. Genista candicans ...... 16} 0
12. Water Melon............ 30 | 0 26. Sorghum vulgare ...... 150} 9
Ass.) Hy periGHI .isssencctecss 150 | 0 27. Zea Mays ....cc0cssees.,.,100 | 0
14. Spinacea Oleracea ...... 50 | 0
* At Hitcham, of 3 left, 2 did not flower, and the other produced no seed.
.
1 G5. Cassia, Sp. ...cesceeseeses 40
| 66. Euphorbia arkanocarpa}100
{| 67. — Characias .,.......... 80
| G8. Galega sibirica .....:...}110
69. Heracleum asperum ...|100
| 70. Malva, sp. s.....eesccees 80
71. From Malta ........... 8
MPMOUIIEED aco ceccesccsscansces Ay
PRPDE ENE! a ctaVsvcstasosvctecs 8
WAL Memoja \.i..c806250 58055. 5
} 33. Linaria genistifolia......
eee te
52. Scrophulariagrandiflora|200
1835.
58. Cucurbita ......ceseceee 50
| 54, Echinops, sp. ............ 3
55. Heracleum asperum ...| 35
| 56. Gnothera, sp. ........ 200
57. Orobus lathyroides...... 31
58. Podalyria exaltata ...... 36
| 61. Augusta Beans
| 62. Cassia Canarina.........
64, —, from Lisbon.........
al 76. Papaver sominiferum ...
77. Pyrethrum microphyl-
gE
Name and Date. 3
Zz
1832.
28. Calendula, sp.......s0++| 50
29. Cucurbita Cucuzza...... 40
40
29
100
100
50
18
82. Gypsophila altissima ...
34, Phaseolus compressus
35. Podalyria tinctoria......
1833.
36. Cucurbita, | Candahar
Water Melon ..... «. 50
37. Cucuzza Lunga ........ 5
38. — di Spagna ...... badges 20
39. Mellone di Acqua ...... 90
40. — di Pane Bianca...... 50
41, — della Regina......... 50
42, Orange Gourd ......... 40
43. Cucumber, Kabul ...... 5
1884.
44, Catananche cerulea ...|200
| 45. Coix lachryma ........ 1
AG. Gourd..........sseeseeeees 5
| 47. Valencian Melon ...... 50
48. Iris prismatica ......... 10
49, Pinus Pinea .........04 19
| 50. Plantago bonariensis ...}100
51. Sambucus racemosa .
. Tetragonia expansa ...
Verbascum virgatum ...
1836
75. Enothera, sp.........204.
Rite ate bas. desncssostss
78. Saponaria, sp.............
79. Tragopogon pratensis
No. vegetated.
i]
i)
ocoooocomws
—_
s —— a — i —
oO eceosceoooso ScoowosesSe
oT
ocoe copmpocooesooNroocorscre
Time of vege-
tating in days.
“No
E
Name and Date. a
z
1837.
80. Aubergines......seseesea 150
81. Melon.......0... diusianza «.|150
82. Piments ....,.isessasesees 100
83. Tomates ........s02seeeees 100
1838.
84. Anchusa ochroleuca ...| 14
85. Melon from Cassabah ..| 15
86. Water Melon.........«. 10
87. Melon from Valparaiso} 5
88. Cynoglossum, sp. ...... 20
89. Papaver somniferum ...|150
90.. Pinus nigricans ......... 30
91. Tragopogon, Sp.........- 22
G2. 2 Cassia ......cescenseeees 20
93. ? Dolichos ............ +e.| 50
1839.
94, Augusta Beans ......... 50
95. Calliopsis ........0..+... 150
96. Lapsana communis 100
97. Lepidium Draba ...... 50
58. Pisum, Sp: .-+-.ssccesbess 50:
99. Prunella vulgaris ...... 150
100. Ricinus communis...... 7
101. Salvia verbenaca ...... 200
1840.
102. Calliopsis tinctoria...... 150
103. Chenopodium Quinoa |200
104. Canada Beans ......... 50
105. Balsamina hortensis ...|150
106. Gnothera grandifiora...|100
107. Ornithogalum nutans...) 80
108. Ricinus communis...... 10
109. Salvia patens ............ 12
1841.
110, Algoa Bay %....s.-.se0 1
111. Canada Beans..........+ 16
112. Ferula, sp. ........sseeee. 38
113. Papaver somniferum ...|150
114, Physospermum commu-
TAtUM © s..ccsecscsescdous 100
115. Rumex, sp........seeeeeee 30
116, Salvia, sp. ...........s0-- 150
117.- Vicia grandiflora .....: 150
118. Fullard’s German Mar-
TOW Fat. scssosssveeeees
1842.
119. Brassica, Rapa oleifera |100
120. Ervum, sp...........2s... 100
121. Gossypium ? vitifolium| 8
122. Malva moschata......... 100
123. Melilotus macrorhiza...|100
124. Papaver somniferum .../150
125. Phacelia tanacetifolia...|150
126. Trifolium giganticum...|190
127, —, Alsike Clover ...... 100
128. Vicia sativa............6+ 100
ON THE VITALITY OF SEEDS.
No. vegetated.
_
moocoooors
oo
im")
i]
cs
eccoococ
De
coooorenwncow
to
130)
Time of vege-
tating in days.
11
il
36
10
123
~
_
oo MN OoF
~
24 ‘ REPORT—1846.
3138 | 2/38
|= \F | 2 | 23
Name and Date. | & [ss Name and Date. ste (es
$) 5 |82 213 |\83
“|2 les z |e
1843. 1844,
129. Cheiranthus, sp.......... 80 | 388 | 7 ||141. Augusta Beans ......... 5| 5
130. Dianthus chinensis...... 150 | 62 | 8 |142. Cobbett’s Wheat ......) 27 | 12
131. Diplotaxis tenuifolia ....300 | 4 | 19 1845.
132. Augusta Beans ......... 30 | 30 | 9 ||143. Augusta Beans ......... 30 | 27
133. Linum usitatissimum ...|200 | 56 | 7 |\144. Cobbett’s Wheat ...... 15 | 14
134. Melilotus leucantha ...|100 | 60 | 7 About 23 years old.
135. Onopordon tauricum...|150 | 22 | 10 |145. Cashew Nut ........+ oa: Aa ealD
136. — acanthium............ 100 | 40 | 10 |\146. Brazil Nut ............... 1
137. Trifolium giganticum.../100 | 38 | 4 147. Longan .s......seeseeeees 2| 0
135. —, Alsike Clover ...... 100 | 0 148. Quercus, Sp. secceecesers 4| 0
139. Vicia lutea ..............- 100 | 27 | 31 |/149. — Aigilops..........++... 3| 0
140. Fullard’s German Mar- 150. Ricinus .......-scccesress 5| 0
FOWAEAG toknannspchee === 150 |100 | 7 |151. Rhizobolus Pekza ...... 1| 0
W. H. Baxter, Curator.
On the Colouring Matters of Madder. By Dr. Scuuncx.
Tue organic colouring matters present such a wide tield for inquiry, that it
would require the labour of years to enable one person fully to elucidate their
properties, or even to bring this department of organic chemistry into a state
of development proportionate to the present condition of the science. The
substances included under the name of colouring matters by no means agree
in their chemical characteristics; they merely coincide in being possessed of
certain vivid colours, or in giving rise to coloured compounds. Strictly con-
sidered, some of them ought to be classed among the resins and others among
the extractive matters; and on the other hand, if we attempt a definition of
the class according to their chemical characteristics, we shall find it impossible
to exclude a large number of bodies, which, like tannin and catechin, are
capable of giving rise under peculiar circumstances to brown substances,
which in nowise differ in their general properties from the bright red colour-
ing matters of archil, logwood, &c. Some colouring matters are presented
to us ready formed in the different parts of plants and animals; others are
produced artificially from colourless substances, which undergo very complex
changes during the process ; others arise spontaneously during the first stages
of oxidation or putrefaction following the extinction of organic life. In the
investigation of substances thus widely differing in properties and formation,
it would be vain to expect at present anything approaching to general results
in regard to the class as a whole. I must therefore content myself on this
occasion with giving a short account of the results of some experiments
which I have made on one branch of the subject, at the same time apologising
for their present vague and undefined nature.
I have directed my attention in the first instance to madder, partly because
the colouring matters contained in it are almost unknown, or rather worse
than unknown, viz. known in such a manner as merely to mislead those who
wish to inform themselves by the accounts given of them, and partly because
madder is an article of such an immense importance in the art of dyeing that
every discovery in relation to it acquires immediately a practical bearing.
It will be unnecessary for me to allude to the former numerous investiga-
>
ON THE COLOURING MATTERS OF MADDER. 25
tions of madder, except so far as to mention that Robiquet discovered in it
a erystallized volatile colouring matter, which he called Alizarin, and that
_ Runge described five colouring matters which he obtained from it, viz. madder
_ purple, madder red, madder orange, madder yellow and madder brown. I
may here state as one result of my investigation, that I agree with Runge in
thinking that there is more than one colouring matter in madder, though [
am of opinion that the substances which he enumerates and describes are
not pure. Before however entering on this part of the subject, I shall first
give the results at which I have arrived in regard to alizarin. Alizarin is
doubtless the most interesting and the most definite in its nature of all the
substances contained in madder. It also presents itself the most easily to
the observer even on the most superficial examination. If we heat madder
spread out in a thin layer on a metal plate without carrying the heat far
enough to char the woody parts of the root, we shall in the course of a few
hours find its surface covered with small red or orange-coloured crystals,
which consist of alizarin. In the same way any extract of madder, whether
with water, alcohol or alkalies, evaporated to dryness and gently heated, gives
a crystalline sublimate of alizarin, which is variously coloured from a light
yellow to a dark red or brown. Now one of the first points to be ascertained
__ in regard to this body was whether it exists as such in the root, or whether
_ it is formed by the process of sublimation. Robiquet, the discoverer, states
that it pre-existsin the plant. He considered alizarin as the colouring prin-
ciple of madder, and merely subjected it to sublimation for the purpose of
purifying it. But his investigation presents us with no convincing proof of
_ this opinion, for the extract of madder with water, alcohol, &c., from which
he prepares his alizarin by sublimation, shows no trace of anything crystalline;
and many chemists have asserted in consequence that it is a product of de-
' composition, being formed by the action of heat in the same way as pyrogallic,
_ pyrotartaric acid, and many other bodies. I have however no hesitation
| j in affirming that it exists in the plant as such, having in more than one way
| Obtained it in a crystallized state without the intervention of heat. If we
| make an extract of madder with cold water, we obtain a brown fluid which
By produces no reaction on test paper. After being exposed however to the
j ; action of the atmosphere for some hours, it acquires a distinctly acid reaction ;
_ and if it be now examined carefully, there will be found floating about in it
| a number of long hair-like shining crystals: these crystals are alizarin. If
_ the fluid be still further exposed to the influence of the*atmosphere, a yellow
Tisha substance begins to separate, which I shall mention afterwards.
a
_ This is succeeded by a gelatinous substance, and after some days a complete
_ state of putrefaction ensues. It seems as if the alizarin in madder, or at all
| events that part which dissolves in the water, exists in combination with lime.
_ On exposure to the atmosphere, there is formed, from some constituent
| of the root dissolved in the fluid through the instrumentality of the oxygen,
| some acid, which seizes hold of the lime in the solution and separates the
_ bodies which are combined with the lime. Now the alizarin, being a body
_ of very slightly acid properties, is separated first, and the other substances
- follow in succession. The fresher the madder is, the purer will be the ali-
zarin, which separates on exposure to the atmosphere ; in some instances it
orms on the surtace of the fluid a thick light yellow scum; but in most cases
is mixed with brown or red substances, from which it is separated with
difficulty. It is therefore most advisable to separate the crystals which are
_ deposited after twelve hours’ standing, by filtration. These crystals are then
| washed from the filter and boiled with very dilute nitric acid until they have
| become of a bright yellow colour. They are then dissolved in boiling alcohol,
26 REPORT—1846.
from which they separate on cooling in yellow transparent plates and needles
having a strong lustre. Alizarin prepared in this way .has the following
properties :—It has a pure yellow colour without any admixture of red. It
may be volatilized without leaving any residue. The vapour crystallizes on
cooling in beautiful yellow plates and needles. Itsuffers hardly any change
if exposed to the action of the most powerful reagents. It dissolves without
change in cold concentrated sulphuric acid. Concentrated nitric acid hardly
affeets it even on boiling. It is not changed by chlorine. It is insoluble in
water, but soluble in alcohol with a yellow colour. It dissolves in alkalies
with a beautiful purple colour. Its compounds with the alkaline earths are
red and slightly soluble in water. Its compounds with the earths and metallic
oxides are insoluble in water and exhibit different shades of red. It imparts
no colour to cloth mordanted with acetate of alumina or oxide of iron, on
account of its insolubility in water. Very little alizarin is obtained in this
way; perhaps one 1 gr. from 1]b. of madder, though there is more of it con-
tained in the root.
I shall now shortly describe two other colouring matters which I have
obtained from madder. If an extract of madder be made with hot or cold
water, and a strong acid, such as muriatic or sulphuric acid, be added to the
fluid, a dark reddish-brown flocculent precipitate is produced. This preci-
pitate was separated by filtration and washed until the acid was removed.
On being treated with boiling water, a part of it dissolves with a brown colour.
On adding a few drops of acid to the filtered solution a dark brown pre-
cipitate is produced, which seems to me to be a peculiar colouring matter
similar in its properties to orcein, hematin and other soluble colouring
matters. It dissolves in alkalies with a red colour, and is capable of imparting
very lively colours to mordanted cloth. As far as 1 am aware it has not
been described in the former investigations of this subject, though it seems
to be the principal substance concerned in the production of the colours for
which madder is used in the arts. I have however only examined it very
slightly as yet. The residue left behind by the boiling water was treated
with dilute boiling nitric acid, by which every trace of the preceding substance
is destroyed, and the residue itself acquires a bright yellow colour and
a more powdery consistence. This yellow powder contains alizarin, as is
shown by its giving crystals of that substance on being gently heated; in
fact it contains all the alizarin of the root, but mixed with another substance
of an amorphous nature but very similar properties, from which it is difficult
to separate it. By crystallising from alcohol no separation can be effected,
as they are both about equally soluble in that menstruum. They also behave
in a similar manner towards the alkalies, the earths and most of the metallic
oxides. I have hitherto only succeeded in discovering one method of se-
parating them, which is as follows :—The mixture of the two is dissolved ina
little caustic potash. To the solution is added perchloride of iron, which
produces a dark reddish-brown precipitate consisting of peroxide of iron in
combination with the two substances. Now on boiling this precipitate with ~
an excess of perchloride of iron, the aljzarate of iron dissolves, forming a dark
brown solution, while the iron ‘compound of the other substance remains
behind. On adding muriatic acid to the filtered solution, the alizarin separates
in yellow flocks and may be purified by crystallization from alcohol. The
other substance, to which I have not yet given a name, is obtained by de-
composing its iron compound, which remains behind on treating with per-
chloride of iron, with muriatie acid, and washing till all the oxide of iron is
removed. It seems also to be a colouring matter, as it dissolves with a red
colour in alkalies and gives red compounds with the earths and metallic
ON THE PHYSIOLOGICAL ACTION OF MEDICINES. 27
oxides. It is insoluble in water, but soluble in alcohol with a yellow colour.
- It therefore resembles the resins in its general properties. It cannot be ob-
_ tained in a crystallized state. From a hot concentrated solution in alcohol
__ it separates on cooling as a yellow powder. It imparts no colour to mor-
danted cloth.
On the Physiological Action of Medicines. By J. Buaxn, M.B., F.R.C.S.
- Tue present report is a continuation of those which have already been read
before this section, and which have been published in the reports of the
Association. The only additional experiments I now have to bring forward
have been instituted to investigate the action of the salts of iridium and
osmium, and the acids of selenium and sulphur, when introduced directly
into the blood.
' The experiments that have been made with the salts of iridium and osmium
prove that these substances closely agree in their physiological action with
the salts of palladium and platinum. They are, like these salts, very poison-
ous. A solution containing half a grain of the double chloride of iridium
and ammonia, was injected into the jugular vein of a dog. Before the injec-
q _ tion, the action of the heart was regular and strong*; in eight seconds after
the injection, the action of the heart appeared affected, it being rendered flut-
tering; and after a few seconds there was an apparent obstacle to the passage
of the blood through the systemic capillaries, as the pressure in the arterial
system became greater. In about a minute the pressure again diminished ;
_ the action of the heart was slower, the force it exerted in propelling the blood
being equal to a column of mercury of but three inches and a half, or little
more than the half of that under which the circulation is generally carried
on. The animal appeared to be uncomfortable, owing to the circulation be-
_ coming so feeble. On injecting a solution containing a grain of the salt, the
circulation was arrested in eleven seconds, owing either to the action of the
heart having ceased, or else that its contractions were so weakened that they
did not suffice to force the blood through the pulmonary capillaries. The
‘pressure exerted by the blood in the arterial system became suddenly dimi-
a nished, so as only to support a column of mercury of an inch and a half, at
_ which point the circulation through the capillaries would appear to have
been suspended, for the pressure remained stationary for more than a minute,
' and then sunk to zero, owing to relaxation of the capillaries taking place.
~ Death followed about three minutes and a half after the injection, and the
__eye retained its sensibility to mechanical irritation for three minutes; respi-
_ ration and sensibility continuing nearly two minutes longer than would have
__ been the case had the injection of the salt totally paralyzed the heart. On
Opening the thorax immediately after death, the heart was found contracting
_ tythmically, but very feebly, certainly not with sufficient power to propel its
contents: both cavities were full of blood; in the right it was dark, that in
the left was of a maroon colour, and had evidently been oxygenized, proving
that the circulation had ceased before respiration was suspended. The blood
__ eoagulated imperfectly, and this has been noticed after the introduction of
s the salts of palladium and platinum, which are isomorphous with those of
ui
aia * The state of the circulation is ascertained by the hemadynamometer, an instrument which
enables us readily to detect any change in the action of the heart or in the passage of the
28 , REPORT—1846.
iridium, and which exert, although in such small quantities, a marked effect
in preventing the perfect coagulation of the blood. Another experiment
was performed to observe more particularly the general effects following the
introduction of the salt into the veins ; the hemadynamometer was not used,
and the animal was allowed to run about. On injecting a solution containing
halfa grain of the salt, no immediate effects followed, but in about fort
seconds the animal became unsteady, and there was a tendency to fall back-
wards: in a minute and a half respiration was longer and deeper; sensibility
remained unimpaired; after a few minutes the animal laid down, and the
dyspnoea increased, coming on in paroxysms; in six minutes after the injec-
tion, respiration was suspended for forty seconds, but this was not accompa-
nied by convulsions, or even by loss of sensibility : this occurred four or five
times in the course of ten minutes ; the animal laid perfectly still, and did not
appear to be suffering, although sensibility was unimpaired. A grain of the
salt, on being introduced into the vein, served to increase these symptoms,
although the animal did not die until some minutes after it had been in-
jected. These symptoms are such as would result from the gradual weaken-
ing of the action of the heart, and the consequent diminution of the supply
of blood to the brain; they lead to the conclusion that, when injected into the
veins, this salt does not exert any marked action on the nervous system.
When introduced directly into the arteries, by being injected through the
axillary artery so as to mix with the blood as it passes through the aorta, the
salts of iridium, as those of platinum and palladium, impede the passage of
the blood through the capillaries, to such an extent as to require the heart to
exert more than twice the power that is required in the natural state of the
circulation, to force the blood through them. This sudden increase of the
pressure in the arterial system is attended by general spasm. When a grain
of the salt was injected into the artery, in a few seconds the pressure was equal
to acolumn of mercury of twelve inches; violent spasm immediately came on,
during which respiration was suspended, nor did it again take place regularly.
Six respiratory movements were observed during the next four minutes, after
which there was no further movement. The action of the heart appeared to be
arrested by asphyxia; but even after it had ceased, the pressure in the arteries
was equal to three inches of mercury, showing that the passage of the blood
through the systemic capillaries was still impeded, although the animal had
been dead two or three minutes. When thus brought into direct contact
with the nervous centres, there can be no doubt but that these substances
exert a marked action on them ; it is possible that the violent spasm that im-
mediately followed their injection might be owing to the great pressure the
brain is subject to from the over-distension of the arterial system, but this will
not explain the permanent cessation of its functions.
The salts of osmium are perfectly analogous in their action to those of
iridium, and the other members of this isomorphous group. The salt used
was the double chloride of osmium and potassium, for owing to the chlorides
of both iridium and osmium being decomposed by water, I was forced to use
them combined with another base, although I should have wished to have
avoided this if possible.
The effects produced by selenic and sulphuric acids, when introduced into
the blood, are not very striking, that is, they do not appear to act in a marked
manner On any one organ. They agree in this respect with other bodies,
which either are found entering into the composition of the blood, or have
isomorphous relations with these constituents. The important part which
sulphur takes in the proteine compounds, might lead us to expect that its in-
troduction into the blood, as well as selenium, which is so closely isomorphous
ie
i.
wee
|
i
Le
ON THE PHYSIOLOGICAL ACTION OF MEDICINES. 29
with it, might not produce any very marked effect. In an experiment per-
formed with selenic acid, the following are the symptoms that presented
themselves (the acid used was of specific gravity 1046, containing about five
and a half per cent. of real acid). On injecting three drachms of the acid,
mixed with an equal quantity of water, into the jugular vein, no appreciable
effect was produced ; neither the passage of the blood through the lungs, nor
through the systemic capillaries, appeared at all impeded ; nor was the action
of the heart affected ; in about forty-five seconds after the injection its move-
ments appeared slightly fluttering; after two minutes the respiration was
observed to be rather deeper. Immediately after the introduction of half an
ounce of the acid into the vein, there was a falling off of the quantity of
blood sent into the arterial system; and as this took place five seconds after
the injection, it must have been owing to the passage of the blood through
the pulmonary capillaries having been impeded, for there had not been time
for the substance to reach the coronary arteries and act on the heart. After
thirty seconds the supply of blood to the arteries was restored, and the action
of the heart was as strong as before. There appeared to be no marked effect
produced on any organ, although the quantity of acid introduced was very
considerable (seven drachms) ; after a few minutes the respiratory movements
became longer and deeper, and the action of the heart decidedly weaker, the
force with which the blood was propelled into the arteries being only half
what it is in the natural state of the circulation ; there was no expression of
pain. Half an ounce of the acid was again injected into the veins. The
immediate effect was to arrest the passage of the blood through the lungs, no
blood being sent into the arteries, although the heart could be felt beating
through the parietes of the thorax. Respiration was stopped at a minute
and twenty seconds after the arrest of the circulation, sensibility having dis-
appeared a few seconds earlier, On opening the thorax immediately after the
cessation of respiratory movements, the heart was found beating rythmically :
the right cavities were very much distended with blood, which was dark and
grumous, and apparently physically incapable of passing through the lungs.
The left cavities contained a small quantity of scarlet blood, which was co-
agulated ; the lungs were redder than natural; the heart retained its irrita-
bility some time after death. The above symptoms-do not suffice to indicate
_ any particular organ on which the acid exerts a marked influence; for although
death was produced by the passage of blood through the pulmonary ca-
‘pillaries being arrested, yet this was probably owing to the mechanical
impediment which the coagulated state of the blood must have opposed to
its passage through the pulmonary vessels. In other experiments that I have
made with this substance, I have sometimes seen a serous secretion take place
in the air passages. There is also some action on the nervous system, as the
following experiment will show. The animal was small ; it was not confined,
in order that the effects on the functions of voluntary motion and sensation
might be more accurately observed. A drachm of the acid was introduced
into the veins, without giving rise to any marked symptoms. A second in-
jection, containing a drachm and a half of the acid, did not affect the animal
in any marked degree: after a few minutes it appeared rather dull, but there
was no expression of pain, nor was sensibility impaired. On introducing
two drachms into the veins, the animal fell down in about thirty seconds, and
respiration was much affected ; it got up again in about a minute, and jumped
about ina very curious manner, the movements being evidently involuntary,
as if the animal had chorea: it remained standing quite motionless for a few
“minutes, but gradually became weaker, and death took place ten minutes
after the last injection; there were no convulsions, nor was the sensibility
30 REPORT—1846.
destroyed until immediately before death. On opening the thorax, the heart
was found contracting rythmically. There was a considerable quantity of
frothy secretion in the bronchial tubes, and this renders it difficult to deter-
mine if the asphyxia, by which the action of the heart was finally arrested,
was nervous or pulmonary ; that is, whether the nervous system was affected
by the want of aération of the blood, or whether the respiratory movements
ceased in consequence of the action of the acid directly on the nervous
system. ‘The latter opinion I think the more probable.
Sulphuric acid, when introduced into the veins, gives rise to exactly the
same phenomena, the only organ on which it appears to exert any marked
effect being the lungs, although slight nervous symptoms are produced when
a considerable quantity has been introduced into the blood. The action of
these substances when injected into the arteries, and thus applied directly to
the brain and over the system, without previously passing through the lungs,
is evidently on the nervous system. Two drachms of the diluted acid, mixed
with four drachms of water, were injected into the left axillary artery, so as
to pass into the aorta; in ten seconds all movements ceased ; there was a slight
spasm, which relaxed ina few seconds. During the continuance of the spasm,
the pressure in the arterial system was slightly increased, but it rapidly de-
clined, so that I think the passage of the blood through the systemic capil-
laries is facilitated, rather than impeded by these substances, All effective
contractions of the heart ceased a minute after death, probably owing to the
shock produced by the sudden annihilation of the functions of the nervous
system, for it retained its irritability some minutes after death,
With these experiments I conclude the first part of the series of researches
which I propose to undertake for the elucidation of this branch of physiology.
I have been engaged on it for the last six years, but I trust the results ob-
tained fully repay the labour that has been bestowed on it. The action on
the animal ceconomy of the compounds of twenty-nine of the most important
elements has been experimentally investigated, and the facts which have been
observed have led to the discovery of a new law in vital chemistry which
had escaped the attention of former observers, viz. that the reactions which
take place between the elements of the living body and inorganic compounds
are not governed by the ordinary chemical properties of these substances, but
depend on certain properties they possess connected with their isomorphous
relations. The verification of this law enables us to undertake the investi-
gation of the higher chemical phenomena of living bodies from an entirely
new point of view, whilst its existence accounts for the failure that has con-
stantly attended attempts to explain the chemistry of animal life by analogy
from ordinary chemical phenomena. The fact that we now possess the
means of producing well-marked and definite modifications of some of the
most important physiological properties of various organs, and this too by
means of reagents, the laws governing whose action we are acquainted with,
places in our hands an instrument for discovery which has hitherto been
wanting in physiological investigations. ‘The enumeration of some of the
effects that can be produced at pleasure on the more important functions,
will, I trust, suffice to lead others into this rich field of inquiry. As regards
the functions of the heart, we can annihilate or increase its irritability,
quicken or diminish its pulsations, render them regular or irregular, augment
their force or render thém weaker, destroy the contractility of the auricles,
whilst that of the ventricles remains ; keep up the circulation of the blood
many minutes after every sign of life has disappeared, and this too more
actively than when respiration was being carried on; we can facilitate or
arrest the passage of the blood through the pulmonary and systemic capil-
ON THE ACTINOGRAPH. 31
aries; produce important modifications in the functions of the brain :—in
_ short, the injection of various substances into the arteries and veins enables
us to modify all the most important functions of the body ; and this, as before
stated, by reagents, the laws of whose action we can fairly hope to discover.
My reason for having neglected the closer investigation of these interesting
_ phzenomena, was a determination fully to establish the law of the analogous
action of isomorphous substances. ‘This having been accomplished, I shall
now direct my researches to the elucidation of these secondary questions.
Report on the Actinograph. By Mr, Rosprertr Hunt.
If will be remembered that in 1838 Sir John Herschel proposed an instru-
_ ment for the purpose of registering the variations of the actinic or chemical
rays, and published in the Philosophical Transactions a design for what
he termed an Actinograph, by which it was thought both the chemical action
of the direct solar rays and of the diffused daylight would be registered.
_ Dr. Daubeny, Prof. Nichols and Mr. Thomas Jordan have severally designed,
_ and I believe used, instruments somewhat similar, but it does not appear that
any very satisfactory results have been obtained by either of these inquirers.
At the York meeting I pointed out the importance of some such registration,
and at the request of the committee I had an instrument constructed, which
Texhibited to the Association at the Cambridge meeting. The actinograph
_ Ihave been using differs but little from that proposed by Sir John Herschel,
a modification of Mr. Jordan’s being introduced, by which it was thought
_ the results could be tabulated for every hour of the day. As the form of
_ this instrument is published in the Report for 184.5, it will be unnecessary to
do more than describe such alterations as have suggested themselves during
i the past year. The triangular slit, divided into one hundred parts, has been
abandoned, it being found in practice almost impossible to discriminate be-
_ tween the amount of coloration produced on the paper during an exposure of
three minutes or six; consequently it became quite idle to attempt to register
by this plan to the degree of nicety which it was hoped might be attained.
__ A new external cylinder has therefore been constructed, in which are thirteen
holes, commencing with a mere pin-hole and gradually increasing to a $_
inch diameter. By this means thirteen bands are marked upon the sensi-
tive paper, each one separated from the other by an unaltered line, and it
__ becomes easy to distinguish with considerable accuracy between the tints
_ thus produced.
Bromide of silver was the material which, from the circumstance that all
_ the rays of the prismatic spectrum exert some influence upon it, was em-
_ ployed in procuring most of my registrations. It has however been found
% that under all circumstances this preparation is too sensitive, and that although
- in the winter, when the solar radiations are weak, it answers admirably, yet
in the bright sunshine of summer it assumes too great a degree of darkness,
in even diffused daylight, and during the shortest exposure to which it is ex-
_ posed during the revolution of the’cylinder. Many experiments have been
‘made with other photographic preparations, and the result has been in favour
: of the general use of the ammonio-nitrate of silver. It is true that this paper
_ is not impressed by all the rays of thespectrum, but, as it is acted upon by all
_ the rays beyond the yellow ray, and as the influence of the actinic principle
_ throughout the entire range of the spectrum is, as it appears, always equally
32 . REPORT—1846.
effected by. the increased or diminished intensity of the luminous and calo-
rific rays, and consequently that even the actinism residing in the extreme
violet ray is relatively as much influenced by an increase of luminous power
as that which is detected in the yellow ray itself, we may by the use of the
paper prepared with the ammonio-nitrate of silver arrive at a very close ap-
proximation to the true result.
Although I have not been enabled to realize the hope I held forth last year
of presenting at this meeting a register of actinic influences for the year,(which _
I have been prevented from doing by circumstances which I shall presently
explain, ) yet I have determined, most satisfactorily te my own mind, the prac-
ticability of procuring, in favourable positions, such a registration as shall
afford much valuable information.
The circumstances to which I allude as those which have prevented my
procuring any series of registers, are the impossibility of securing in London
any position free from the constant interferences of smoke and fog, and the
difficulty of placing the instrument so as to be free from the reflected radia-
tions of adjoining buildings. The first alone is a fatal objection ; for instead
of securing, what is desired, a registration of the relative amount of chemical
influence as compared with the quantity of light, heat, and the natural at-
mospheric conditions, we only get a register of the influence of smoke in
absorbing the actinic rays. 1 therefore propose to hand over the instrument
to the Association, requesting that it may be placed in a favourable position
at Kew, under the attention of the excellent observer there, when I do not
doubt some curious and instructive results may be obtained.
It is necessary however to state that my experience has pointed out some
objections to this mode of registration, which indeed militates against the
use of the actinograph as a philosophical instrument.
It is a curious fact that upon almost all kinds of photographic paper the
colour produced by the solar rays at different periods of the day varies
considerably. It is not a mere difference of tint, but an actual change in the
colour; thus frequently the light of both morning and evening will give to
chloride of silver a rose hue, whilst that of noon will change it to a bluish
variety of brown. ‘There is consequently much difficulty in deciding which
is the strongest impression. Thus also the rays upon two days, when the sun
appears equally bright, will in one case produce a red brown, and in the other
a blue brown. It is left to the eye to decide upon the intensity of the effect
produced, and with the utmost care it is frequently impossible to say whether
the actinic influence is greatest on the red brown lines, or those which are
blue brown.
The importance of the inquiry has been peculiarly evident during this
summer; many peculiarities have been observed in the growth of plants, in-
fluenced no doubt by the solar radiations. Many of our garden flowers,
particularly roses, have exhibited an abnormal condition, leaf-buds being
developed in the centre of the flower, arising from the vegetative functions
of the plant overpowering its reproductive functions. Again, during the
intense sunshine and the prevalence of the unclouded skies of the hot wea-
ther of June and July, practical photographists found the greatest difficulty —
in obtaining portraits by the Daguerreotype process. At this time, although
the intensity of effect produced on paper in the actinograph under the usual
circumstances of summer sunlight should have been at a maximum, it was
found that it was far below this point, the maximum point being repre-
sented by 120. During several experiments made at the time mentioned, the
greatest effect indicated was 100; whilst the sky still being unclouded and —
the sun shining brightly, it often fell to 90, and sometimes indeed to 80.
eh are
a i
ON THE INFLUENCE OF LIGHT ON THE GROWTH OF PLANTS. 33
ve
_ These facts show the importance, amongst many others, of some mode of
registration by which these ever-varying solar influences may be carefully
_ observed. There can be little doubt that they exert an influence, sometimes
i baleful, sometimes beneficial, upon the organized creation, and that we have
_yet to discover, in these emanations or influences, the secrets of many of the
_ grand phenomena of the universe.
.
Notices on the Influence of Light on the Growth of Plants.
By Mr. Rosert Hunr.
THE experiments connected with this very interesting inquiry have been
steadily pursued, and a concluding report would have been made at this
_ meeting, but that some experiments, which had been conducted with much
_ eare, with a view of determining the quantity of solid matter in plants grown
under different circumstances, were destroyed by the hail-storm which lately
_ prevailed over an extensive district of the metropolis, the glasses and troughs
of coloured fluids being broken, and the plants themselves washed into the’
soil. As it was impossible to repeat this year these experiments, there was no
alternative but either to present an imperfect report, or to defer the report
for another year. The latter course has been chosen, and the detail of
_ these experiments will be reserved for a future communication ; I have how-
; ever thought it might be attended with some advantages to state a few of the
_ leading facts which have been determined. The order of the arrangements
_ have been the same as those observed in the former experiments, and nearly
tan the results have been confirmatory of those published six years since.
__ The germination of seeds is peculiarly due to the influence of the actinic
or chemical rays; and if these are completely isolated whilst the luminous
ays are permitted to act upon the soil in which the seeds are planted, no
_ germination will take place. This influence is exerted and is most necessary
| up to the point at which the first leaves begin to form, when the luminous
_ Yays are rendered necessary to effect the formation of woody fibre. It must
_be remembered that this was a point upon which I was at issue with some
_ other investigators; and it is due to them that I should state, that the dis-
‘erepancies between us appear to have arisen from our not observing with a
sufficient degree of accuracy the point at which the two influences balance
each other, previously to the more complete exercise of the exciting force
f light, as distinguished from actinism. The vegetative process having been
| Carried on until the plant arrives at its maturity, a new agency, the calorific,
s more decidedly necessary to develope the reproductive functions of the
| plant; and then, again, the chemical rays combined with the calorific be-
ome more active than the luminous rays. In spring we find the chemical
Influences exerting without interference their most decided force: seeds
then germinate, and young buds and shoots are developed. As soon as this
is effected, the luminous rays, with the advance of the sun, become more
ive, and the formation of woody fibre proceeds under their particular
ency ; not that the chemical power becomes dormant, but it is rendered
portionally less active by the agency of light. In the late summer and
autumn the peculiar properties of the calorific rays are required, and
r their agency, with diminished powers of light, the ripening of fruits
| and the production of seed are accomplished.
_ My experiments have also led me to detect some curious influences which
ap a be due to dissimilar rays, and which in their action exhibit great
e D
34 REPORT—1846.,
inconstancy of effect. One class of rays, the same to which Sir J. Herschel
has given the name of Parathermic rays, are so subdued by the influences of
the more refrangible rays, as to be nearly inactive during the spring and early
summer months; and indeed in the spring they scarcely produce any effect
upon dead vegetable colouring matter, unless their action is assisted by the
use of some decomposing agent, such as sulphuric acid. These rays increase
in power towards the autumn, and to them appears to be due the browning
of the leaf.
It is well known that plants will grow in the dark, but that they do not
then form chlorophylle; the formation of this colouring-matter has been an
object of some attention, and I believe I have determined it to result from
the joint influence of the luminous and actinic rays. Boxes of cress have been
grown in the dark, and they have then been brought under the influence of
a large spectrum formed by a water-prism. It has been stated by Dr.Gardner,
that the plants under those circumstances exhibit a lateral movement, bend-
ing towards the yellow ray. This appears to bea mistake; the plants under
the influence of the red rays bend from the light but along the line of the ray ;
and those exposed to the most refrangible rays turn towards it, but still in the
line of the ray. Now the plants which first become green, by careful treatment
in this way, are those which are exposed to the rays situated between‘the mean
green ray and the extreme blue. The action is continued eventually to the edge
of the most refrangible violet below the yellow ray. There is not any change
effected beyond the visible spectrum, notwithstanding the abundance of dark
chemical rays ; and the change is slow where there is really the largest amount
of light. I therefore conclude that the luminous rays are essential in the pro-
cess, producing the decomposition of the carbonic acid and the deposition of
the required carbon, which is afterwards. in all probability, combined with
hydrogen under the influence of purely chemical force as exerted by the ac-
tinic principle.
Such ate the main results I have obtained. I have several experiments
now in progress, and I hope to be enable? in another year to complete this pars
ticular branch of investigation so far as to present to the British Association a
complete report.
Report on the Recent Progress of Analysis (Theory of the Comparison of
Transcendentals). By R. L. Wuxis, M.A.
1. Tue province of analysis, to which the theory of elliptic functions belongs,
has within the last twenty years assunied a new aspect. A great deal has
doubtless been effected in other subjects, but in no other I think has our
knowledge advanced so far beyond the limits to which it was not long since
confined.
This circumstance would give a particular interest to a history of the ree
cent progress of the subject, even did it now appear to have reached its full
development. But on the contrary, there is now more hope of further pros
gress than at the commencement of the period of which I have been speaking.
When, in 1827, Legendre produced the first two volumes of his ‘ Théorie
des Fonctions Elliptiques,’ he had been engaged on the subject for about
forty years; he had reduced it to a systematic form; and had with great
labour constructed tables to facilitate numerical applications of his results.
But little more, as it seemed, was yet to be done; nor does the remark of.
ON THE RECENT PROGRESS OF ANALYSIS. 35
Bacon, that knowledge, after it has been systematized, is less likely to increase
than before, seem less applicable to mathematical than to natural science.
Nevertheless, almost immediately after the publication of Legendre’s work,
the earlier researches of Abel and Jacobi became known, and it was at once
seen that what had been already accomplished formed but a part, and not a
_ large one, of the whole subject.
__ To say this is not to derogate from the merit of Legendre. He created
_ the theory of elliptic functions; and it is impossible not to admire the per-
_ severance with which he devoted himself to it. The attention of mathema-
- ticians was given to other things, and though the practical importance of his
labours was probably acknowledged, yet scarcely any one seems to have
_ entered on similar researches*. This kind of indifference was doubtless dis-
_ couraging, but not long before his death he had the satisfaction of knowing
_ that there were some by whom that which he had done would not willingly
_ be let die.
__ The considerations here suggested have led me to select the theory of the
integrals of algebraical functions as the subject of the report which I have the
honour to lay before the Association.
__ 2. The theory of the comparison of transcendental functions appears to
have originated with Fagnani. In 1714, he proposed, in the ‘Giornale de
Litterati d’ Italia,’ the following problem: To assign an arc of the parabola
_ whose equation is
, y=
such that its difference from a given are shall be rectifiable.
_ Of this problem he gave a solution in the twentieth volume of the same
rnal.
___ The principle of the solution consists in the transformation of a certain
differential expression by means of an algebraical and rational assumption
which introduces a new variable. The transformed expression -is of the same
form as the original one, but is affected with a negative sign. By integrating
both we are enabled to compare two integrals, neither of which can be as-
| Signed in a finite form. It is difficult, however, to perceive how Fagnani was
to make the assumption in question: a remark which applies more or
to his subsequent researches on‘similar subjects.
he theorem which has made his name familiar to all mathematicians, ap»
ed in the twenty-sixth volume of the ‘Giornale.’ In its application to
comparison of hyperbolic ares we find some indications of a more general
lethod. We have here a symmetrical relation between two variables, x and
» such that the differential expression J(#)dx may be written in the form
z. It follows at once that f(z) dz =< dz, and consequently that
WhiOLE +f f(z) dz =f {xdz+zdzx}=x2+ on
3 remarkable manner in which the idea of symmetry here presents itself,
gested to Mr. Fox Talbot his ‘ Researches in the Integral Calculus.’
In applying bis methods to the division of the are of the lemniscate, Fag-
i obtained some very curious results, and has accordingly taken for the
hette of his collected Works a figure of this curve with the singular motto,
eo veritatis gloria.”
3. In MacLaurin’s Fluxions, and in the writings of D’Alembert, instances
3 to be found where the solution of a problem is made to depend on the
ose of M. Gauss, which would doubtless have been exceedingly valuable, have not, I
» been published. They are mentioned in a letter from M. Crelle to Abel. Vide the
eduction to the collected works of the latter, ps Vii.
‘ D2
36 REPORT—1846.
rectification of elliptic arcs, or, as we should now express it, is reduced to
elliptic integrals. But of these instances Legendre has remarked that they
are isolated results, and form no connected theory. MacLaurin is charged, —
in a letter appended to the works of Fagnani, with taking from the latter, —
without acknowledgement, a portion of his discoveries with respeet to the —
lemniscate and the elastic curve.
4. In 1761, Euler, in the ‘ Novi Commentarii Petropolitani’ for 1758 and
1759, published his memorable discovery of the algebraical integral of the —
equation ;
m dx n dy
(A+ Ba4+ Ca? + Das + Eat}? (A+By+Cy+ Dy + Ey)?
m and m being any rational numbers.
He says he had been led to this result by no regular method, “sed id
potius tentando, vel divinando elicui,” and recommends the discovery of a —
direct method to the attention of analysts. In effect his investigations re-
semble those of Fagnani: he begins by assuming a symmetrical algebraical
relation between the variables, and hence finds a differential equation which
it satisfies. In this differential equation the variables are separated, so that
each term may be considered as the differential of some function. With one
form of assumed relation we are led to the differentials of circular, and with
another to those of elliptic integrals, and so on. It is in this manner that
Dr. Gudermann, in the elaborate researches which he has published in Crelle’s
Journal, has commenced the discussion of the theory of elliptic functions.
5. In the fourth volume of the Turin Memoirs, Lagrange accomplished
the solution of the problem suggested by Euler. He integrated the general
differential equation already mentioned by a most ingenious method, which,
with certain modifications, has remained ever since an essential element of
the theory of elliptic functions. He proceeded to consider the more general
equation da dy
where X and Y are any similar functions of a and y respectively, and came
to the conclusion, that if they are rational and integral functions, the equa-
tion cannot, except in particular cases, be integrated, if they contain higher
powers than the fourth. He also integrated this equation in a case in which
X and Y involve circular functions of the variables. It had been already
pointed out in the summary of Euler’s researches, given in the ‘ Nov. Com.
Pet.’ t. vi., that if X and Y are polynomials of the sixth degree, the last-
written equation does not in general admit of an algebraical integral, since,
if so, it would follow that the solution of the equation wisi = 4 , which
[+23 1+
(as the square of 1 + 23 is a polynomial of the sixth degree) is a particular
case of that which we are considering, could be reduced to an algebraical
form. Now this solution involves both circular functions and logarithms, and
therefore the required reduction is impossible. This acute remark* showed
that Euler’s result did not admit of generalisation in the manner in which it
was natural to attempt to generalise it. It was rese#ved for Abel to discover
the direction in which generalisation is possible.
6. The discovery of Euler, of which we have been speaking, is in effect
the foundation of the theory of elliptic functions, as the generalisation of it
by Abel, or more properly speaking, the theory of which Euler’s result is an
* M. Richelot, in one of his memoirs on Abelian or hyper-elliptic integrals, quotes it, in
a slightly modified form, from Euler’s ‘ Opuscula.’
i ON THE RECENT PROGRESS OF ANALYSIS. 37
isolated fragment, is the foundation of our knowledge of the higher trans-
-cendents. We may therefore conveniently divide the subject of this report
_ into two portions, viz. the general theory of the comparison of algebraical
integrals, and the investigations which are founded on it. Mathematicians
have been led, by comparing different transcendents, to introduce new func-
tions into analysis, and the theory of these functions has become an important
subject of research.
The second portion may again be divided into two, viz. the theory of
elliptic functions, and that of the higher transeendents.
This classification, though not perhaps unexceptionable, will, I think, be
found convenient.
_ 7. About sixteen years after the publication of Lagrange’s earlier researches
on the comparison of algebraical integrals, he gave, in the New Turin Me-
_ moirs for 1784 and 1785, a method of approximating to the value of any
a where P is.a rational function of z and R the
- integral of the form
_ square root of a polynomial of the fourth degree. I shall consider this im-
_ portant contribution to the theory of elliptic functions in connexion with the
_ writings of Legendre. At present, in order to give a connected view of the
first division of my subject, it will be necessary to go on at once to the works
of Abel, and to those of subsequent writers. In the history of any branch
of science the chronological order must be subordinate to that which is
_ founded on the natural connexion of different parts of the subject.
__ Ishall merely mention in passing, that in 1775, Landen published in the
Philosophical Transactions a very remarkable theorem with respect to the
_ ares of a hyperbola. He showed that any arc of a hyperbola is equal to the
_ difference of two elliptic ares together with an algebraical quantity. In 1780
he published his researches on this subject in the first volume of his ‘ Mathe-
matical Memoirs,’ p. 23. This theorem, as Legendre has remarked, might
have led him to more important results. It contains the germ of the general
theory of transformation, the eccentricities of the two ellipses being con-
nected by the modular equation of transformations of the second order*. It
is on this account that in a report on M. Jacobi’s ‘ Fundamenta Nova,’ con-
lined in the tenth volume of the Memoirs of the Institute, Poisson speaks
f Landen’s theorem as the first step made in the comparison 6f dissimilar
elliptic integrals. Several writers have accordingly given Landen’s name to
_ the transformation commonly known as Lagrange’s.
_ 8. We have seen that even Lagrange failed in obtaining a result more
eneral than that which had been made known by Euler, and yet, as we now
now, Euler’s theorem is but a particular case of a far more general proposi-
. But in order to further progress, it was necessary to introduce a wholly
ew idea. The resources of the integral calculus were apparently exhausted ;
el, however, was enabled to pass on into new fields of research, by bring-
ing it into intimate connexion with another branch of analysis, namely, the
theory of equations. The manner in which this was done shows that he was
not unworthy to follow in the path of Euler and of Lagrange.
wi pel attempt to state in a few words the fundamental idea of Abel’s
thod.
Let us suppose that the variable z is a root of the algebraical equation
0, and that the coefficients of this equation are rational functions of
in quantities a, b, ...¢, which we shall henceforth consider independent
ables. Let us suppose also that in virtue of this equation we can express
* Vide infra, pp. 50 and 67.
38 REPORT—1846.
certain irrational functions* of a as rational functions of 2, a, b,...¢. For
instance, if the equation were a® + ax + se — 1)=0, it follows that
V7{—x*=a+2. So that any irrational function of the form F (2 “1—z*)
can be expressed rationally (F being rational) in # and a.
From the given equation we deduce by differentiation the following,
dxe=ada+fdb+...+yde,
where a, 6, ... y are rational in a, a, b,...,¢.
Let y be one of the functions which can be expressed rationally in a, &c.,
it follows that ydx=Ada+Bdb+...+Cde,
where A, B, ... C are also rational in a, &c.
The equation fa = 0 will have a number of roots, which we shall call
jy +++, It follows that
Yrdt, +e tyday, =
{A,+..+A,}da+{B,+..+B,}db+...+{Cit..+C,} de,
where the indices affixed to y, A, &c. correspond to those affixed to 2, so
that y,, for instance, is the same function of 2, that y, is of 2.
Now A, +... + A, is rational and symmetrical with respect to #,...#y,
therefore it can be expressed rationally in the coefficients of f («) = 0, and
therefore in a, b..¢c. We will call this sum R,, and thus with a similar
notation for b, &c. we get
Y, a2, + oe. + y, dk, = R,da+R,db+...+R.de.
The second side of this equation is from the nature of the case a complete
differential, and it is rational in a, }, c, &c.; it can therefore be integrated
2.
by known methods; and if we denote Y dz by )(a,), we get
v(a,)+---+ ¥(¢,) =M,
M being a logarithmic and algebraic function of a, b, &c., which we may
suppose to include the constant of integration.
) (x) is in general a transcendental function, while a, 6, &e. are necessarily
algebraical functions of x,,..-, x, and the result at which we have arrived
is therefore an exceedingly general formula for the comparison of transcen-
dental functions.
The simplicity and generality of these considerations entitle them to espe-
cial attention: it cannot be doubted that the application thus made of the
properties of algebraical equations to the comparison of transeendents will
always be a remarkable point in the history of pure analysis, :
A very simple example may perhaps illustrate what has been said, Let us
recur to the equation 1
w+ax + 5(a?—1)=0, . . * . ° e (1,)
and suppose that an wig
y V1 —a®
Differentiating the first of these equations, we find that
(Qa +a)dx+(«#+a)da=0.
* It must be remembered that an algebraical function is either explicit or implicit: ex-
plicit, when it can be expressed by a combination of ordinary algebraical symbols ; implicit,
when we can only define it by saying that it is a root of an algebraical equation whose co-
efficients are integral functions of 2. Thus y is an implicit function of 2 if y°-+-vy+1=0.
The remarks in the text apply to all algebraical functions, explicit or implicit.
ON THE RECENT PROGRESS OF ANALYSIS. 39
‘Comparing this with the general expression of dx, we perceive that
Peay. ol B=&e.=0;
and as 1 = =, (vide ante, p- 38.),*
oy V1 — x?
ee a
yam Qn+a
so that ap Rin UB
Qx+-a
Let 2, and x, be the two roots of our equation, we have thus to find the
value of
; I 1 ue Q(r+%ta) _
=e ala iFoe a Bayt | oid rah a) (a+ a)
since t+ 2,=— 4.
Hence y,da,t+ Yd t= 0,
and v2.4 r= ec
Since 2+ %=—a,
and
teas
ae, g (a1),
we see that af+af=1, orra=V1—2,.
Hence, as W x=sin-'z, our result is merely this, that the sum of two ares
is constant if the sine of one is equal to the cosine of the other.
An infinity of analogous results may be obtained either by varying the
form of y (e.g. by making y = “1—2®), or by changing the equation (1.).
A formula applicable to all forms of y, and which, for each, includes all the
results which can be established with respect to it, is, it will readily be ac-
knowledged, one of the most general in the whole range of analysis. Abel’s
principal result is a formula of this nature; he developed at considerable
length the various consequences which may be deduced from it,
Generally speaking, the number of independent variables a, 6,...¢ will
be less than that of the different roots, 2,,..- 2; hence a certain number,
say m, of the roots may be looked on as independent (viz, as many as there
are quantities a, b,...c), and the rest will be functions of these. It may
be shown that it will always be possible to make the difference py, — m con-
stant, so that the sum of any number of the transcendents p is expressible by
a fixed number of them, together with an algebraical and logarithmic func-
tion of the arguments, i.e. of #,,...@m. In the case of elliptic integrals, it
had long been known that the sum of two may be thus expressed by a third ;
and Legendre pointed out that the sum of any number may similarly be ex-
pressed by means of one. Accordingly it appears from the general theory,
that in this ease 44 — m may be made equal to unity.
9. The history of this important theory is curious. It was developed by
Abel in an essay which he presented to the Institute in the autumn of 1826,
when he had scarcely completed his twenty-fourth year.
Tn a letter to M. Holmboe, appended to the edition of his collected works,
Abel writes, “ Je viens de finir un grand traité sur une certaine classe de
__ fonctions transcendantes pour le présenter a l'Institut, ce qui aura lieu lundi
* The ambiguous sign of the radical is to our purpose immaterial.
40 REPORT—1846.
prochain. J’ose dire sans ostentation que c’est un traité dont on sera satis-
fait. Je suis curieux d’entendre I’opinion de l'Institut la dessus. Je ne
manquerai pas de t’en faire part.” Long before this memoir was published
Abel had become “ chill to praise or blame.” He died at Christiania in the
spring of 1829.
M. Jacobi mentions in a note in Crelle’s Journal, that while at Paris he
represented, and as he believed not ineffectually, to Fourier, who was then
one of the secretaries of the Institute, that the publication of this memoir
would be very acceptable to mathematicians. A long period however was
still to elapse before the publication took place. It was possibly retarded by
the death of Fourier. In 184] the memoir appeared in the seventh volume
of the ‘ Mémoires des Savans Etrangers.’ It was prepared for publication
by M. Libri.
Thus for about fifteen years Abel’s general theory remained unpublished ;
but in the meanwhile Crelle’s Journal was established, and to the third vo-
lume of this he contributed a paper which contains a theorem much less ge-
neral than the researches he had communicated to the Institute, but far more
so than anything previously effected in the theory of the comparison of
transcendents. ‘This is commonly known as Abel’s Theorem. Legendre, in
a letter to Abel, speaks thus of the memoir in which it appeared :—* Mais le
mémoire... ayant pour titre ‘ Remarques sur quelques propriétés géné-
rales,’ &c., me parait surpasser tout ce que vous avez publié jusqu’a-présent
par la profondeur de l’analyse qui y régne ainsi que par la beauté et la géné-
ralité des résultats.” In a previous letter, with reference I believe to the
same subject, he had remarked, “ Quelle téte que celle d'un jeune Norvé-
gien !”
Abel’s theorem gives a formula for the comparison of all transcendental
functions whatever whose differentials are irrational from involving the square
root of a rational function of z.
In a very short paper in the fourth volume of Crelle’s Journal, which
must have been the last written of Abel’s productions, the chief idea of his
general theory is stated; and in the second volume of his collected works we
find a somewhat fuller development of it, in a paper written before his visit
to Paris, but not published during his lifetime.
While Abel's great memoir remained unpublished at Paris, several mathe-
maticians, developing the ideas which he had made known in his contribu-
tions to Crelle’s Journal, succeeded in establishing results of a greater or
less degree of generality. Researches of this kind may be presented in a
variety of forms, because the algebraical function to be integrated, which
we have called y, may be defined or expressed in different ways. For in-
stance, if M and N are general symbols denoting any integral functions of x,
VM a" ae : : 3
N and y as precisely equivalent, since
by an obvious reduction, and by changing the signification of M and N, the
one may be transformed into the other; and so in more general cases. Thus
the same function may assume a variety of aspects, and there will be a cor-
responding variety in the form of our final results.
In Crelle’s Journal we find a good many essays on this part of the sub-
ject: of these I shall now mention several.
M. Broch is the author of a paper in the twentieth volume of Crelle’s
Journal, p. 178. It relates to the integration of certain functions irrational
in consequence of involving a polynomial of any degree raised to a fractional
power. For these functions he establishes formule of summation, which of
the two suppositions 7 =
te gpa
ON THE RECENT PROGRESS OF ANALYSIS. 41
course include Abel’s theorem, since the latter relates to cases in which the
fractional power in question is the (4)th. Subsequently to the publication
of this paper he presented to the Institute a memoir on the same subject, but
gave to the functions to be integrated a different but not essentially more
general form. This memoir, which was ordered to be printed among the
‘Savans Etrangers,’ but which will be found in Crelle’s Journal (xxiii. 145),
may be divided into two portions: the first contains results analogous to
Abel’s theorem; the second relates to the discussion and reduction of the
transcendents which they involve. In this part of his researches M. Broch
has followed the method, and occasionally almost adopted the phraseology
of a memoir of Abel, on the reduction and classification of Elliptic Inte-
grals (Abel's Works, ii. p. 93). MM. Liouville and Cauchy, in reporting on
the memoir, conclude by remarking that the author “ n’a pas trop présumé
de ses forces en se proposant de marcher sur les traces d’ Abel.”
M. Jiirgenson has contributed two papers to Crelle’s Journal on the sub-
ject of which we are speaking. The first, which is very short, contains a
general theorem for the summation of algebraical integrals* when the func-
tion to be integrated is expressed in a particular form. This paper appears
in the nineteenth volume, p. 113. In the second (vol. xxiii. p. 126) the au-
thor reproduces the results he had already obtained, pointing out the equi-
valence of one of them to the theorem established in M. Broch’s first essay.
Besides this, he discusses a question connected with the reduction of alge-
braical integrals.
M. Ramus, in the twenty-fourth volume of Crelle’s Journal, p. 69, has
established two general formule of summation ; from the second he deduces
with great facility Abel’s theorem, and also another result, which Abel men-
tions in a letter to Legendre, published in the sixth volume of Crelle’s
Journal, but which he left undemonstrated.
M. Rosenhain’s researches (Crelle’s Journal, xxviii. p. 249, and xxix.
p- 1) embrace both the summation and reduction of algebraical integrals.
His analysis depends on giving the function to be integrated a peculiar form,
which he conceives leads to a simpler mode of investigation than any other.
A paper by Poisson will be found in the twelfth volume of Crelle’s Jour-
nal, p. 89. It relates to the comparison of algebraical integrals, but is not
I think so valuable as that great mathematician’s writings generally are.
Beside the memoirs thus briefly noticed, I may mention two or three by
_M. Minding: that which appears in the twenty-third volume of Crelle’s
Journal, p. 255, is the one which is most completely developed.
There is also a very brief note by M. Jacobi in the eighth volume of
_ Crelle’s Journal.
_ 10. To the Philosophical Transactions for 1836 and 1837 Mr. Fox Tal-
bot contributed two essays, entitled ‘ Researches in the Integral Calculus.’
These researches may be said to contain a development and generalisation
of the methods of Fagnani. They are however far more systematic than the
writings of the Italian mathematician, and if they had appeared in the last
_ century would have placed Mr. Talbot among those by whom the boundaries
_ of mathematical science have been enlarged. But it cannot be denied that
_ they fall far short of what had been effected at the time they were published,
| nor does it appear that they contain anything of importance not known before.
_Thave assuredly no wish to speak disparagingly of Mr. Talbot; his mathe-
| matical writings bear manifest traces of the ability he has shown in so many
_ * Ihave used the expression “ algebraical integrals,” though perhaps not correctly, to de-
note the integrals of algebraical functions.
42 REPORT——1846.
branches of science*, But as in this country they seem to have been thought,
and by men not apparently unqualified to judge, to contain great additions to
our knowledge, I cannot avoid inquiring whether this be true.
Mr. Talbot points out in the early part of his first paper, that if there are
nm — 1 symmetrical relations among the m variables 2, y...2, then the iden-
tical equation
{y---2}dx+(u...z)dy+t..,+ fy.-.dz=d{ry,..2}
will assume the form
g(x)dxu+ol(y)dy+...+¢(z)dz=d{xy...2},
and thus give us
Sodet+foydy+..+fo(desay...2+C
Precisely the same remark, though expressed in a different notation, is the
foundation of M. Hill’s memoir, published in 1834, on what he calls “ func-
tiones iterate.” It will be-found in Crelle’s Journal, xi. p. 193, A much
more general theorem might be established by similar considerations: they
are of course applicable whether the function ¢ be algebraical or trans-
cendent.
In the course of his researches, Mr. Talbot recognised the important prin-
ciple, that the existence of 2 — 1 symmetrical algebraical relations among
variables may be expressed by treating them as the roots of an equation, one
of whose coefficients at least is variable, the others being either constant or
functions of the variable one. Unfortunately he did not pass from hence to
the more general view, that the existence of » —p symmetrical relations
may be expressed in a similar manner if we consider p of the coefficients of
the equation as arbitrary quantities. Had he done so, it is possible, though
not likely, that he would have rediscovered Abel’s theorem; but as it is, he
has never introduced, except once, and then as it were by accident, more
than one arbitrary quantity. Thus only one of his variables is independent,
and consequently, in more than one instance, his results are unnecessarily
restricted cases of more general theorems,
The character of his analysis will be perceived from what has been said.
If / Xdz be the transcendent to be considered, X being an algebraical func-
tion of «, he makes the following assumption—
X=f(rv),
v being a new variable, and fa rational function. From this assumption he
deduces an algebraical equation in , the coefficients of which are rational
functions of v. This equation then is one of those of which we have spoken,
by means of which the function to be integrated can be expressed in a ra-
tional form, Taking the sum with respect to the roots of this equation, we
get
2(Xd2)=3(f(«v) dz).
It must be remarked that many forms might be assigned to the function f, ©
which would give rise to a difficulty, of the means of surmounting which
Mr. Talbot has given no idea. If # and v are mixed up in f(a w), it is ma-
nifest that we cannot integrate f(2v)d«, since v is a funetion of 2, which
* It must be remembered also that Mr. Talbot admits himself to have been anticipated
to a considerable extent by the publication of Abel’s theorem,
ON THE RECENT PROGRESS OF ANALYSIS. 43
if we eliminate we merely return to our function X. We must therefore
express Xf (xv)d x in the form Vdv, V being a function and, as Abel has
shown, an integrable function of ». Abel has given formule by means of
which this reduction may be effected in all possible cases. But there is no-
thing analogous to this in the writings of Mr. Talbot, and consequently he
could not, setting aside the defect already noticed, obtain results as general
as many previously known. In Mr, Talbot's investigations, f(a v) dz is such
that Bf (xv) dx may be put in the form—
Vi 2{P edz} + V2 {P,xde} + &e., .
$,%, %.x, &c. (of which ¢',x, ¢',2, &c. are the derived functions) being
rational functions of z. Then 2¢ 2 =a rational function of v by a well-
known theorem. Let the form of this function be ascertained, and let us
denote it by %v. Then differentiating,
L@'rdr=xy'vdv,
and hence
ZXde=iUf(«ev)de=[V,x'0+ Vix.vt+..] dv,
and the second side of this equation is of course rational and integrable.
But the form of the function f(«v) is unnecessarily restricted in order that
this kind of reduction may be possible, Nevertheless, Mr. Talbot's papers,
from their fulness of illustration and the clear manner in which particular
cases of the general theory are worked out by independent methods, will be
found yery useful in facilitating our conceptions of the branch of analysis
which forms as it were the link between the theory of equations and the in-
‘ tegral calculus.
4 In Mr, Talbot’s second memoir (Phil. Trans. 1837, part 2. p, 1) he has
5 applied his method to certain geometrical theorems, Three of them relate
__ to the ellipse, and are proved by the three following assumptions :—
4 — e272) 4 1— 3
i — oa =} =1+v2, or= std ve
=, or = :
1 c Aig V4 73) 4 1 el
__ These assumptions are all cases of the following—
{inser iactes :
= ?
1— 2x? a+a'z2
_ where @, a’, ¢, e' are arbitrary quantities. The results of this assumption
_ are completely worked out by Legendre (Théorie des Fonctions Elliptiques,
iii, p. 192) in showing how the known formule of elliptic functions may be
_ derived from Abel’s theorem. Mr. Talbot's first theorem is a case of the
_ fundamental formula for the comparison of elliptic ares. This remark has
_ reference to an inquiry which Mr. Talbot suggests as to the relation in which
his theorems stand to the results obtained by Legendre and others.
Tn conelusion, it may be well to observe that Mr. Talbot has remarked
_ that, apparently, a solution discovered by Fagnani of a certain differential
equation cannot be deduced from Abel’s theorem ; but as this solution may
be easily derived from the ordinary formula for the addition of elliptic in-
Ani, TI.
11. I now come to the history of researches into the properties of par-
_ ticular classes of algebraical transcendents. The earliest, and still perhaps
_ the most important class of these researches relates to the transcendents
44 REPORT—1846.
which are commonly called elliptic functions or elliptic integrals. Fora reason
which will be mentioned hereafter the latter name seems preferable, and it is
sanctioned by the authority of M. Jacobi, though the former was used by Le-
gendre. Elliptic integrals then may be defined as those whose differentials are
irrational in consequence of involving a radical of the form 4/{a@ + Baty x*
+0a3+¢a*}. But it may perhaps be more correct to say that all such in-
tegrals may be reduced to three standard integrals, to which the name of
elliptic integrals has been given.
In the Turin Memoirs for 1784 and 1785, p. 218, Lagrange considered,
as has been already mentioned, the theory of these transcendents. He
showed that the integration of every function irrational in consequence of
containing a square root may be made to depend on that of a function of
the form = P being rational, and R the radical in question ; and that if
under the sign of the square root 2 does not rise above the fourth degree,
dx
Vl + pea) (1 + 9? a?)
where N is rational in x. He thus laid the foundation of that part of the
theory of elliptic transcendents in which a proposed integral is reduced
to certain canonical or standard forms, or to the simplest combination of
such forms of which the case admits. In Legendre’s earliest writings on
elliptic functions there is nothing relating to this part of the subject. Having
thus, in the simple manner which distinguishes his analysis, reduced the ge-
neral case to that which admits of the application of his method, Lagrange
proceeded to prove that if we introduce a new variable whose ratio to x is
the subduplicate of the ratio of 1 + p*2® to 1 + ¢* x*, the last written inte-
gral is made to depend on another of similar form, but in which p and g are
replaced by new quantities p' and q'. If p is greater than q, p! will be greater
than p, and q' less than q, and thus by successive similar transformations we
ultimately come to an integral in which g isso small that the factor 1 + q' 2
may be replaced by unity, and the elliptic integral is therefore reduced to a
circular or logarithmic form. Or by successive transformations in the oppo-
site direction we come to an integral in which p' and g' are sensibly equal,
in which case also the elliptic integral is reduced to a lower transcendent.
This most ingenious method is the foundation of all that has since been
effected in the transformation of elliptic integrals, or at least whatever has
been done has been suggested by it. Thus it is to Lagrange that we owe
the origin of two great divisions of the theory of these functions.
In the Memoirs of the French Academy for 1786, p. 616, we find Legen-
dre’s first essay on the subject to which he afterwards gave so much attention.
We recognise in it what may I think be considered the principal aim of his
researches in elliptic functions, namely to facilitate, by the tabulation of
these functions, the numerical solution of mathematical and physical pro-
blems.
He begins, not with a general form as Lagrange had done, but with the
integral fs W1—e?sin? ¢d¢, which as we know represents an elliptic are,
and shows how other functions, for instance the value of the hyperbolic are,
may be expressed by means of it, and of its differential coefficient with re-
spect to the eccentricity c. The memoir does not contain much that is now
of interest. After writing it he became aware of the existence of Landen’s
researches ; and in a second memoir appended to the first gave a demonstra-
tion of Landen’s principal theorem. This demonstration is founded on
it may ultimately be made to depend on that of
r
i ON THE RECENT PROGRESS OF ANALYSIS. 45
egendre’s own methods, and he deduces from it the remarkable conclusion,
hut if of a series of ellipses, whose eccentricities are connected by a certain
law, we could rectify any two, we could deduce from hence the rectification
of all the rest. The law connecting the eccentricities of the ellipses is that
which would be obtained by making use of Lagrange’s method of transfor-
mation, with which accordingly this result is closely allied.
Legendre’s next work was an essay on transcendents *, presented to the
Academy in 1792 and published separately the year after. It contains the
same general view as that which is developed in the first volume of the
‘ Exercices de Calcul Intégral,’ which appeared in 1811.
12. The theory of elliptic functions, as it is presented to us by Legendre,
may conveniently be considered under the following heads :—
a. The reduction of the general integral,
Lf Pdz
Vat Batya + ox + ext
in which P is rational to three standard forms, since known as elliptic inte-
grals of the first, second and third kinds f.
This classification, though the reduction of the general integral had, as we
have seen, been already considered by Lagrange, is I believe entirely due to
Legendre. If we consider how much it has facilitated all subsequent re-
searches, we can hardly over-rate the importance of the step thus made. | ia
may almost be said that Legendre, in thus showing us the primary forms with
which the theory of elliptic integrals is conversant, created a new province
of analysis: he certainly gave unity and a definite form to the whole sub-
ject.
For the three species of functions thus recognised Legendre suggested the
names of nome, epinome and paranome, the name of the first being derived
from the idea that it involves, so to speak, the law on which the comparison
of elliptic integrals depends. But these names do not seem felicitous, nor
have they I believe been adgpted. To this part of the subject an important
theorem relating to the reduction of elliptic integrals of the third kind,
whose parameters are imaginary, seems naturally to belong.
B. The comparison of elliptic integrals of the same form differing only
in the value of the variable, or as it is often called, the amplitude of each.
This part of the subject divides itself into three heads, corresponding to the
_ three classes of integrals. The fundamental results are to be found in the
memoirs of Euler, of which we have already spoken. By Legendre how-
ever they were more fully developed.
It is interesting to observe that Legendre suggested that the discovery of
I —-
__ * A translation of it appeared in Leybourne’s Mathematical Repository, vols. ii, and iii.
The original I have not seen—it has long been scarce.
+ These three forms are
; eae Fy 1—eat, x dz
af V (1—a®) (=e 2%) SI Set S, Gao
| a Legendre always replaces 2 by sin @, so that the integrals become
® ee @ pa 9 ay
’ SSO nie in2 » SS
4 , vine or ae he a/1—c? sin? 9d 9; St (1+nsin? 9) /1—c? sin?
The radical 4/1—c? sin? @ is often denoted by A.
___ The constant c is called the modulus; the second constant n (in the third kind) is called
the parameter. The modulus may always be supposed less than unity, and if e=sin s, then
€ is the angle of the modulus.
46 REPORT—1846.
dx dy wihy
+ —_7_ = 0 admits of
sg , Vi@)" VF)
an algebraical integral, f (a) being the polynomial a+ 62+ yur +oas pron )
x
Euler (namely that the differential equation
might be generalised, if we consider the differential equation —7—
+4 ot he 0. H ks that this i h fons ety
—=—+ ... + == 0. He remarks that this is perha e on
VF) Vie) Et SWE” >
way in which it can be generalised.
y. Theorems relating to the comparison of different kinds of elliptic fune-
tions. One of the most remarkable of these is the relation between the
complete integrals (those, namely, in which the variable a is unity) of the
first and second kind, the moduli of which are complementary ; that is, the
sum of the squares of whose moduli is equal to unity. Legendre’s demonstra-
tion of it is rather indirect, but many others have been since given. Another
theorem may be mentioned,—that the complete integral of the third kind
can always be expressed by means of the complete integrals of the first and
second. A third and most important result shows that in elliptic integrals
of the third kind we may distinguish two separate species, and that to one
or other of these any such integral may be reduced. A memorable dis-
covery of M. Jacobi has greatly increased the importance of this subdivision,
of which we shall hereafter speak more fully. This part of the subject is,
a entirely due to Legendre.
6. The evaluation of elliptic integrals by means of expansions.
e. The method of successive transformations. The idea of this method
originated, as we have seen, with Lagrange. It is developed at great length
by Legendre, with a special reference to the modifications required in apply-
ing it to the different species of integrals. As Lagrange had shown, the
series of transformed integrals extending indefinitely both ways conducts us,
in whichever direction we follow it, towards a transcendent of a lower kind
than an elliptic integral, or in other words, towards a logarithmic or cireular
integral. There are thus two modes of approximation, one of which depends
on aseries of integrals with increasing moduli, and the other on a series
whose moduli decrease. Thus for the three species of integrals there will
be in all six approximative processes to be considered. In the case of the
elliptic integral of the third kind, we have to determine the law of formation
of the successive parameters 7, 2', &c.
- ¢, Reductions of transcendents not contained in the general formula
(« 9: —) to elliptic integrals.
V1—28
4. Lastly, applications to various mechanical and geometrical problems.
This analysis, however slight, will give an idea of the contents of that part
of the ‘ Exercices de Calcul Intégral’ which relates to elliptic functions, In
the third volume there are tables for facilitating the calculation of integrals
of the first and second kind: they are accompanied with an explanation of
the manner in which they were constructed. The ninth table is one with
double entry, the two arguments being the angle of the modulus and the
amplitude.
13. In 1825 Legendre presented to the Académie des Sciences the first
volume of his ‘ Traité des Fonctions Elliptiques.’ A great part of this work
is precisely the same as the ‘ Exercices de Calcul Intégral.’_ By far the most.
important addition to the theory of elliptic functions consists in the disco-
very of a new system of successive transformations quite distinct from that
of Lagrange.
ON THE RECENT PROGRESS OF ANALYSIS. 47
In the earlier work Legendre had shown that a certain transcendent might
be expressed in two ways by means of elliptic integrals of the first kind.
Comparing the two results, he obtained a very simple relation between the
two elliptic integrals. Their moduli are complementary ; while the ratio of
the A’s in the two integrals can be expressed rationally in terms of the sine
of the amplitude of one. This circumstance seems to have suggested to Le-
=
_ kind) F(ka)=MF (ay), provided that y and a vanish together. The
oe : ; : iad Sues
Pilear that by means of a solution of it we transform the elliptic integral
‘es
iv
gendre the possibility of generalising the result. He accordingly assumed a
relation between the amplitudes of two integrals, of which the equation sub-
sisting in the theorem of which we have been speaking is a particular case ;
and showed from hence that a simple relation perfectly similar to that which
he had obtained in the particular instance existed between the two integrals,
viz. that they bore to each other a ratio independent of their amplitudes.
Their moduli are connected by an algebraical equation, but are not comple-
mentary. This circumstance therefore now appeared to be unessential,
though in the ‘ Exercices’ the investigation is introduced for the sake of ex-
hibiting a case in which an integral may be transformed into another with a
complementary modulus.
Legendre thus obtained a new kind of transformation, which might be re«
peated any number of times or combined in an infinite variety of ways with
that of Lagrange. To illustrate this he constructed a kind of table—a “ da-
mier analytique.” In the central cell is placed the original modulus c. All the
moduli contained in the same horizontal row are derivable from one another
by Lagrange’s scale of moduli; those in each vertical row by the newly-
discovered scale. He seems to have been very much struck by the infinite
variety of transformations of which elliptic integrals admit. The integral of
the first kind is especially remarkable, because of the simplicity of the rela-
tion which connects it with any of its transformations, viz. that their ratio is
independent of the amplitudes.
Legendre’s second work was, as we have remarked, presented to the Aca-
demy in 1825, but it was not published till 1827. In the summer of 1827
_ M. Jacobi announced in Schumacher’s ‘ Astronomischen Nachrichten,’ No.
123, that he was in possession of a general method of transformation for
elliptic integrals of the first kind. He was not acquainted with Legendre’s
discovery of a new scale, and as an illustration of the general theorem gave
two cases of it, the first being equivalent to Legendre’s method of transfor-
mation. Thus much was announced in a letter to M. Schumacher, dated
June 13th; but in one of a later date (August 2nd) he gave a formal
enunciation of his theorem, but without demonstration. The two commu-
nications appear consecutively (Ast. Nach. vi. p. 33).
In No. 127 of the Nachrichten, vi. p. 133, M. Jacobi gave a demonstra-
- tion of his theorein.
If we Gan so determine y in the terms of « as to satisfy the differential
equation
oo ey op Gg
Vv (U—y) i—aty) M V¥(—a*) Ish a)
“it is manifest that we shall have (F denoting the elliptic integral of the first
(M being constant),
question therefore is, how may the differential equation be satisfied, for it is
F(& 2) into another, viz. into F (Ay).
__M. Jacobi shows that if y be equal to a U and V being integral funes
\
48 REPORT—1846.
tions of x, the differential equation will be satisfied, provided U and V fulfil
two general conditions, the second of which is found to be deducible from
the first. He then makes an assumption which is equivalent to assigning
particular forms to U and V, and thence shows, by a most ingenious method,
that these forms of U and V are such as to fulfil the first of the required condi-
tions, which, as has been said, implies the other. He thus verifies, @ poste-
riori, the assumed value of the function y.
In proving that the forms assigned for U and V have the required pro-
perty, it is necessary to pass from an expression of the value of 1—y in terms
of x to one of 1— Ay in terms of the same quantity. This is done by
means of a remarkable property of the functions U and V, namely, that if
1
han
justed) become ne or G Therefore, in any form in which the relation con-
necting y and 2 can be put, we may replace x by i? provided we at the
in both x be replaced by - or y will (the constants being properly ad-
same time replace y by wh This has been called the principle of double
substitution, and by means of it we pass from the expression of 1—y to that
of 1'— ~, and thence obtain that of 1— Ay. It is to be observed that
this principle is used merely to prove a certain property of the functions
U and V. Of course, as the change of 2 into Pm implies that of y into =
in the finite relation between these quantities, the same thing will be true in
the differential equation by which they are connected, a remark which may
very easily be verified. But, on the other hand, it by no means follows that
because it is true in the differential equation therefore any assumed finite
relation between y and x having this property is the integral required. The
property in question therefore does not enable us to verify any assumed
value of y. .
This remark has reference to a communication from Legendre which ap-
pears in No. 130 of Schumacher’s Nachrichten, vi. p. 201. In it he gives
an account of M. Jacobi’s researches, and an outline of the demonstration of
which we have been speaking. I find it impossible to avoid the conclusion
that this great mathematician mistook the character of the demonstration in
question, and that to him it appeared to be in effect a mere verification of
the assumed value of y by means of the principle of double substitution.
He remarks that the direct substitution of the value of y in the differential
equation is impracticable, but that M. Jacobi had avoided this substitution
by means of “ une propriété particuliére de cette équation qui doit étre com-
mune aux intégrales qui la représentent.” This property is the principle of
double substitution ; and after showing that it is true of the differential
equation, the writer proceeds thus: “‘Ce principe une fois posé, rien n'est
plus facile que de vérifier ’équation trouvée y= y? car par la double sub-
stitution on obtient la méme valeur de y 4 un coefficient prés qui doit étre
égal a l'unité;” and, after a remark to our present purpose immaterial, con-
amie : | Oar
cludes, “ Ainsi se trouve démontrée généralement l’équation y = 7 aint
que, etc.”
As we have seen, such a verification would be wholly inconclusive, nor is
.
-
. ON THE RECENT PROGRESS OF ANALYSIS. 49
the essential point of M. Jacobi’s reasoning, namely, that the assumed forms
of U and V satisfy the general condition, laid down at the outset of his de-
_ monstration, here adverted to.
In 1828 Legendre published the first supplement to the ‘ Traité des Fone-
tions Elliptiques,’ &c. It contains an account of the researches of M.
Jacobi, and of a memoir by Abel inserted in the third volume of Crelle’s
Journal. The account here given of M. Jacobi’s demonstration is fuller and
more explicit than that already noticed. It leaves, I think, no doubt of the
error into which Legendre had fallen. No notice whatever is taken of the
_ first part of M. Jacobi’s reasoning: and after remarking that the differential
equation is satisfied when the double substitution is made, he goes on, “ Tout
se reduit donc 4 faire cette double substitution dans lintégrale y = = = et
& examiner si elle est satisfaite.” After showing that it is so, he adds, “ Par
_ ce procédé trés simple il est constaté que l’équation y = _ satisfait.....
_ al équation différentielle dont l’intégrale est F (k 9) =p F(h py), ete.” (Trait.
des Fonct. Ell., iii. p. 10).
Legendre remarks, that although M. Jacobi’s demonstration rests on “ un
principe incontestable et trés ingénieux,” it is still desirable to have another
verification of so important a theorem. He accordingly gives an original
_ demonstration of it, which is however more nearly allied to M. Jacobi’s than
_ to him it seemed to be. This demonstration had already been hinted at in
_ his communication to the Nachrichten. The principal difference is, that
_ while M. Jacobi proved generally that if the first of the two required condi-
tions were satisfied, the second would also be so, and then showed that the
_ forms assigned to U and V satisfied the first condition ; Legendre shows the
assigned forms are such as to satisfy both conditions, on the connection be-
_ tween which it is therefore unnecessary for him to dwell. In the third sup-
; plement to the ‘Traité’des Fonctions Elliptiques,’ Legendre has given an-
, other demonstration of M. Jacobi’s theorem, remarking that it is both more
rigorous and more like M. Jacobi’s than that which he had first given. I
have thought it necessary to make these remarks, because it has been said
that it was in the supplements to Legendre’s work that the demonstration of
_ this theorem received “le dernier degré de rigueur” *.
_ __ 14, In 1829 M. Jacobi’s great work on elliptic functions, the ‘ Fundamenta
Nova Theorie Functionum Ellipticarum,’ was published at Kceenigsberg. It
contains his researches not merely on the theory of transformation, but also
_ with respect to other parts of the subject. But the great problem of trans-
_ formation is the fundamental idea of the whole work; the other parts are
_ subordinate to it, or at least derived from it. The subject is treated with
_ great fulness of illustration and in a manner not unlike that of Euler.
Mz. Jacobi begins by considering the possibility of transforming the ge-
_ neral transcendent whose differential coefficient is unity divided by the square
root of a polynomial of the fourth degree. Subsequently, having shown that
__ this transcendent may be transformed by introducing a new variable y equal
to the quotient of two integral functions of x, and also that the general
dy
tr nscendent may be reduced to one of the form S- Vaapa—eyy
he proceeds to consider the latter in detail.
¥ The first step of this reasoning, viz. the possibility of the transformation,
en on a comparison of the number of the disposable quantities in the
* Verhulst, Traité Elémentaire des Fonctions Elliptiques.
1846. E
50 REPORT—1846.
assumed value of y with that of the conditions required, in order that the
quantity under the radical in the transformed expression may be equal to
the square of an integral function of x multiplied by four unequal linear
factors. It is shown that the number of disposable quantities exceeds by
three that of the required conditions. But, as Poisson has remarked in the
report already mentioned (Mem. de l'Institut. x. p. 87), and as M. Jacobi
himself intimates, this does nut amount to an absolute @ priori proof of the
possibility of the transformation; xo constat but that some of these condi-
tions may be incompatible.
Granting however the possibility of putting the quantity under the radical
in the required form, it is shown, as in Schumacher’s Journal, that this
condition is not only necessary but also sufficient, or, in other words, that it
involves the second condition already mentioned.
dy
V(1—y*) (1 —a*y*)
suming 7 = a U being composed wholly of odd powers of 2, and V of even
The transcendent may be transformed by as-
powers of it. Ifthe degree of U be greater than that of V, the transforma-
tion is said to be of an odd order, and of an ever order in the contrary
case.
This being premised, M. Jacobi discusses the particular cases of the trans-
formations of the third and of the fifth order. The first is the same as that
of Legendre. It is shown that if we put
_ (w+ 2u)ve + uo x
I~ oy 8 u(v + 2u5) 2”
where w and v are constants connected by the following equation—
ut— ot + Quv{1—wv'} =0,
we shall get
‘ _ dy IL ee se
Va-=y)d—-xy) & “v¥a—#)1—Bey
in which k = x and A=v*. The equation connecting wu and v is called the
modular equation.
The “ principle of double substitution” may be illustrated by writing ai
for x in the expression for y,; which then becomes, according to the principle
in question, ot
If we seek to show that the assigned value of y actually satisfies the dif-
ferential equation just stated, we begin by finding the value of l=y. Re-
ducing this value by means of the equation between and v, we can put it in
the form (1 — z) a R being an integral function of x and V, as heretofore
the denominator of the expression for y. The value of 1 + y is hence got
by changing the sign of z, while that of 1 — vty is obtained by simultane-
ously replacing z and y respectively by Be and a and reducing. Simi-
uta .
larly for 1 + v+y. Hence it will appear that
(—-¥)U-e8y)=0-a) 1 we)... @)
‘ ; ON THE RECENT PROGRESS OF ANALYSIS. 51
be | -
where S, like R, is integral. By differentiating and reducing, we then show
a _v+2u5§
me 2 PI ha x;
i and combining these two results obtain the required verification.
_ The essence ot M. Jacobi’s demonstration consists in showing that if the
_ yalue of y in terms of « is such that an equation of the form («.) subsists,
_ then necessarily d S
P Se saga ag i asth alu a nabldnrd akncenouggs inked
t dx V2
_ where » is a constant; the existence of the two equations (a.) and ({.) being
_ equivalent to the two conditions of which we have already spoken (p. 48).
_ In the particular case we are now considering,
_v+2u
rt & aera tr
15. After considering the transformation of the fifth order (in which the
modular equation is
us — v8 + 5 uv? {u2 — v2} +40 {1 — wv} =0),
, M. Jacobi prepares the way for a more general investigation by introducing
_ anew notation. This step is one of the highest importance.. We have been
d
i in the habit of calling ¢ the amplitude of the fin nM a paaie = = in?
let this integral be called «. The new notation is contained in the equation
6 = vee or if we call sin ¢, x, so that w -f va =e my
_ then z= sin am w.
_ _ A new notation is in itself merely a matter of convenience: what gives it
_ importance is its symbolizing a new mode of considering any subject. We
had hitherto been accustomed to look on the value of the elliptic integral as
_ a function of its amplitude, to make the amplitude (if the expression may so
_ be used) the independent variable. But in reality a contrary course is on
Many accounts to be preferred. We have in the more advanced part of the
theory more frequently occasion to consider the value of the amplitude as
_ determined by the corresponding value of the integral than vice versd ; and
- it therefore becomes expedient to frame a notation by which the amplitude
_ May be expressed as a function of the integral. In a paper in the ninth vo-
lume of Crelle’s Journal by M. Jacobi, which, like many of his writings,
_ contains in a short compass a philosophical view of a wide subject, he has
_ made use of the analogy between circular and elliptic functions to illustrate
_ the importance of the new notation for the latter. When the modulus of an
elliptic integral of the first kind is equal to zero, the integral becomes
fe dz
2 A 2 which, as we know, is equal to the are whose sine is z, or to
°
‘sin-'z. Now this is a function which we have much less often occa-
sion to express than its inverse sin 2, and we accordingly always look on the
latter as a direct, and on the former as an zzverse function. Yet in the case
_ Of elliptic functions, the functional dependence for which we had an explicit
and recognised notation, viz. that of the integral on the amplitude, corre-
ponds to that which in circular functions has always and almost necessarily
een treated merely as an inverse function. ‘The origin of this discrepancy
1s obvious; our knowledge of the nature of circular functions is not derived
: EQ
52 REPORT—1846.
from the algebraical integrals connected with them, and therefore these in-
tegrals are not brought so much into view as in the theory of elliptic func-
tions the corresponding integrals necessarily are; but it is certain that while
the discrepancy continued to exist the subject could never be fully or satis-
factorily developed. The maxim “ verba vestigia mentis” is as true of ma-
thematical symbols as of the elements of ordinary language. 4
We shall see hereafter that Abel took the same step in his first essay on
elliptic functions. At present I shall only remark, that one of the earliest
consequences of the new notation was the recognition of a most important
principle, viz. that the “inverse function” sinam uw, that is, the function
q
f
corresponding to sin x in circular functions, is doubly periodic, or that it re-
tains the same value when w increases by any multiple either of a certain
real or of a certain imaginary quantity. Now M. Jacobi has shown that no
function* can be triply periodic, and therefore these inverse functions pos-
sess the most general kind possible of periodicity, a property which gives
them great analytical importance. ,
Following M. Jacobi, we shall henceforth give the name of elliptic func-
tions to those which are analogous to circular functions. It is on this ac-
count better to call Legendre’s functions elliptic integrals than, as he has
done, elliptic functions (vide ante, p. 44).
By the new notation we are led to consider a great variety of formule
analogous to those of ordinary trigonometry. The sine or cosine of the am-
plitude of the sum of two quantities may be expressed in terms of the sines
and cosines of the amplitudes of each, &c.+; and we have only to make the
modulus equal to zero to pass from what has sometimes, though not with
much propriety, been called elliptic trigonometry to the common properties
of circular functions. ;
M. Jacobi gives a table of formule relating to the new elliptic functions,
and proceeds to apply their properties to the problem of transformation. It
was in this manner that he had treated the problem in the Nachrichten. As
* 7, e, no function of one variable.
+ The fundamental formule are—
sinam ucosamv Aamv- sinam v cosamu A amu
1 — #* sin? am wu sin? am v :
sin am (w+ v) =
cos am ucosamv — sinam usinamvA amu Aamv
] — #* sin? am u sin? am v 3
cos am (wu + v) =
AamuAamv — /* sin am uw sin am v Cos am wu cos am »
Aam (u + v) = 1 — # sin? am u sin? am v 4
k being the modulus, and Aamu= V1—A*sin?amu. If
* =
K= : pee 5 Me and K’ = Sih
» Vi-#sin? 9 » V1—k?* sin?
where #? + #/2 = 1, then it may be shown that
sin am (u-+ 4K) = sinam uw,
and cham
sin am (wu + 2K’ /—1) = sinam u,
so that 4 K is the real and 2K’ /—1 the imaginary period of sinamwu. Hence it is ob-
vious that we shall have generally
sin am (u + 4mK-+ 2nK’ /—1) =sinam u,
m and n being any integers.
be
ON THE RECENT PROGRESS OF ANALYSIS. 53
in his earlier essay, he assumes y equal to a rational function of z, whose
coefficients are elliptic functions, and shows that this assumption satisfies the
_ differential equation already mentioned. It may be asked what is gained by
the introduction of elliptic functions into a problem of which, as we have
seen, particular cases (e.g. the transformations of the third and fifth order)
ean be solved by algebraical considerations. The answer is, that the pro-
_ perties of these functions enable us to transform the assumed relation between
_ yand z in a manner which would otherwise be impracticable. It is con-
ceivable that any particular case might be solved by mere algebra, but it
does not seem possible to discover in this way a general theorem for trans-
formations of all orders, and practically the labour of obtaining the formule
for the transformation of any high order would be intolerable.
Having proved the theorem for transformation in nearly the same manner
as he had already done, M. Jacobi developes the demonstration which, as
‘we have said, Legendre hinted at in No. 130 of Schumacher’s Journal.
He then proceeds to consider the various transformations of any given
order. We have seen that the modular equation for those of the third order
rises to the fourth degree, that is to say, for a given value of the modulus of
the original integral four new moduli exist, corresponding to four new in-
tegrals, into which the given one may be transformed. These four trans-
formations are all included in the general formula for the third order; but
it is to be remarked that in general only two of the roots of the modular
equation are real. Thus there are two real transformations and no more.
The same thing is true, mutatis mutandis, of the transformations of any
prime order (to which M. Jacobi’s attention is chiefly directed), that is to
say, there will be 2 + 1 transformations of the mth order, » —1 of which
_ are imaginary. The two real transformations are called the first and the se-
cond ; the second is sometimes called the impossible transformation, because
it presents itself in an imaginary form*. Of the formule connected with
these two transformations M. Jacobi gives copious tables.
He next shows, in a very remarkable manner, that, corresponding to a
transformation in which we pass from a modulus & to a modulus A, there
exists another, whose formulz are derivable from those of the former, in
__ which we pass from a modulus 1 —k to a modulus 1 — a’, or which
connects moduli complementary to A and k. The latter is accordingly called,
_ with reference to the former, the complementary transformation. The first
real transformation of & corresponds to the second real transformation
Pi V1 —k?, and vice versd.
_ _ The next theorem which M. Jacobi demonstrates is not less remarkable.
_ It is that the combination of the first and second real transformations gives
by a formula for the multiplication of the original integral, or, in other words,
_ that the modulus of the integral which results from this double transforma-
tion is the same as that of the original integral, so that the two integrals
& differ only in their amplitudes. Of this theorem he had in the earlier part
of the work proved some particular casest.
regs,
en!
_ * Mr. Bronwin, in the Cambridge Mathematical Journal and in the Phil. Mag., has
"made some objections to this transformation ; but from a correspondence which I have re-
- cently had with him, I believe I am justified in stating that he does not object either to M.
Jacobi’s result or to the logical correctness of his reasoning, but only to the form in which
the result is exhibited.
+ It may be shown that if we pass from / to a by the first transformation, we can pass
from Vi— 2 to V1 — # also by the first transformation. Also, as has been said, we
_ derive from the transformation {% to a} a transformation { VI —FPto V1— a2}, and
54 REPORT—1846.
After fully developing this part of the subject, he next treats of the nature
of the modular equation, and shows that it possesses several remarkable
properties. One is, that all modular equations, of whatever order, are pare
ticular integrals of a differential equation of the third order, of which the
general integral can be expressed by means of elliptic transcendents.
16. We now enter on the second great division of M. Jacobi’s researches,
the evolution of elliptic functions.
The evolution of elliptic functions into continued products with an infinite
number of factors presents itself as the limit towards which M. Jacobi’s
theorem for the transformatlon of the mth order tends as ” increases sine
limite. It is for this reason that we may look on the problem of transforma-
tion as the leading idea in M. Jacobi’s researches.
We may in some degree illustrate these evolutions by a reference to cir-
cular functions. A sine is, as we know, an elliptic function whose modulus
is zero. Now if & is zero, A is also zero. Thus if we apply a formula of
transformation to a sine, we shall be led to another sine either of the same
or of a multiple are. Accordingly the first real transformation degenerates
in the case in question into the known formula for the sine of a multiple
arc; while the second, leading us merely to the sine of the same are, becomes
illusory. Thus in the case of a sine, transformation is merely multiplication ;
but from the formula for multiplication, viz.
i a : gee sin? 6 mos es sin? 6
sin (2m+1)§=(2m-+1) sin 6 rere gre Fe cai To 2me ae
Q2m+1 ; 2m+1
we at once deduce, by making (2m + 1)4= @and 2m + 1 infinite, the
common formula
ES ¢° 9°
sin 6 = ig Bye (2 geld
Cue ? G 9) ¢ 4s x?
This then is a formula of evolution deduced from the first real transfor-
mation. It is however only when & is zero that the first transformation will
give such a formula. In all other cases it is, for a reason which we cannot
here enter on, impossible to derive from it a formula of this kind. M. Jacobi’s
formule are accordingly derived from the second real transformation, and
therefore are illusory when & is zero, or for the case of the sine. There is
nothing therefore strictly analogous to them in the theory of angular sections.
By means of them we express the function sin am 2 in terms of sin mx, m
being a certain constant.
From the fundamental expressions in continued produets, of which there
are three, many important theorems may be derived, This part of the sub-
ject seems to admit of almost infinite increase, and it is difficult to give any
general view of it. I may, however, mention a remarkable transcendental
similarly from { VI —# to VI — ae a transformation {a to kh. The first and last of
these transformations correspond respectively to the differential equations—
dy Ms 1 dx
Vi-y)G—-x#y) MV/G—2)(1— a?)
da’ 1 dy
Ji — a) (1— a?) M/A —y)(1— ayy
Hence, combining these equations and integrating,
1
Fike’) = ivivtag (ka) ;
and it may also be shown that ats is an integer.
MM’
ON THE RECENT PROGRESS OF ANALYSIS. 55
_ function of the modulus & which is usually denoted by g, and which occurs
perpetually in this part of the theory of elliptic functions. If for the moment
_ we denote this function by FA, so that g = Ff, then if for k we write ,,
which we suppose to represent the modulus of the first real transformation
of the mth order, we find that g" = F &,, so that if g, is the same function of
_k, that qg is of k
In = q"
This singular property, and others of an analogous character, are of great
use in establishing various formule *.
Before discussing the evolution of integrals of the third kind, M. Jacobi
has premised some important theorems. He proves that the elliptic integral
of the third kind, though it involves three elements, viz. the amplitude, the
modulus and the parameter, can yet be expressed in terms of other quantities
severally involving but two. In order to this we introduce either a new trans-
cendent t or a definite elliptic integral of the third kind, whose amplitude isa
certain function of its modulus and parameter. It is almost impossible to
tabulate the values of a function of three elements, on account of the enormous
bulk of a table with triple entry; we therefore see the importance of the step
thus made. M. Jacobi announced this discovery as generally true of elliptic
integrals of the third kind, but his demonstration applies to that subdivision
already mentioned, which was designated by Legendre “ Fonctions du troi-
siéme ordre 4 parametre logarithmique,” and not to functions “4 parametre
eireulaire ¢.” It is probable that this limitation was in M. Jacobi’s mind, but
he does not seem to’ have expressed it. Further on, in the ‘ Fundamenta
Nova,’ we find another mode of expressing integrals of the third kind in
terms of functions of two elements, but this method also applies only to
* fonctions du troisiéme ordre & parametre logarithmique,” the two methods
being in fact closely allied.
Legendre appreciated the importance of this discovery of M. Jacobi. He
speaks of it in a letter to Abel, as a ‘ découverte majeure,” but adds that
his attempts to extend M. Jacobi’s demonstration to the other class of intee
grals of the third kind had been unsuceessful. The same remarks occur in
his second supplement (Traité des Fonet. Ell., iii. p. 141). The distinction
_ thus made between the two classes of integrals of the third kind appeared
_ to Legendre sufficient to make it desirable to recognise in all four classes of
elliptic integrals, so as to make the division between the two species of the
_ third class coordinate with that between either and the first or second.
_ Legendre says explicitly that M. Jacobi had announced, in making known
__ his discovery, that it applied to functions “a parametre circulaire.” This
i * A method of calculating elliptic integrals by means of g was suggested by Legendre,
_ Yide Verhulst, p. 252, and M. Jacobi in Crelle.
7 This transcendent is denoted by ‘, and is defined by the equation
i dg
ty f=
y fi (00) Xe gy’
where E (¢¢)is the elliptic integral of the second kind, If we introduce the inverse nota-
tion, and make 9 = am u,,we can readily establish the following result,
1 .
T= 50 = eff sin? am ud u?,
_ The function Y, which is the logarithm of © (vide infra, p. 66), has many remarkable pro-
perties. ; i
____ = In the former species (1 + 2) ¢ + =) is negative, and in the latter positive (vide
_ ante,p.45). The specific names are derived from the circumstance that for the former the
fundamental formula of addition involves a logarithm, for the latter a circular are.
56 REPORT—1846.
however possibly arose from some misconception of 'M. Jacobi’s meaning.
Dr. Gudermann, in the fourteenth volume of Crelle’s Journal, has given it
as his opinion that the circular species of integrals of the third kind does not
admit of the reduction in question; and remarks, that it occurs much more
frequently than the other species in the applications of mathematics to na-
tural philosophy.
After having discussed at some length, and by new methods, the proper-
ties of elliptic integrals of the third kind, M. Jacobi concludes his work by
investigating the nature of two new transcendents which present themselves
in immediate connexion with the numerator and denominator of the con-
tinued product by which sin amw is expressed. One of them however
M. Jacobi had already recognised by a distinctive symbol, in consequence of
its intimate connexion with the theory of integrals of the third kind.
Such is the outline of this remarkable work: before it appeared M. Jacobi
gave in the third and fourth volumes of Crelle’s Journal (iii. pp. 192, 303,
403, iv. p. 185) notices, mostly without demonstrations, of the progress of
his researches. Almost everything in the first and second of these notices
is found in the ‘Fundamenta.’ In the third we find a remarkable algebraical
formula for the multiplication of the elliptic integral of the first kind. The
fourth and last relates to ulterior investigations, which it was the intention
of the author to develope in a second part of his work. It contains an indi-
cation of a method of transformation depending on a partial differential
equation * ; values of the elliptic functions of multiple arguments ; a method
of transforming integrals of the second and third kinds; a most important
simplification of the method of Abel for the division of any integral of the
first kind, &c. Of this simplification he had already given some idea in a
note in the preceding volume of the same Journal, p. 86.
17. It may not be improper in this place to observe, that in 1818, and
thus in the interval between Legendre’s first and second systematic works on
the theory of elliptic functions, M. Gauss published the tract entitled ‘ De-
terminatio Attractionis,’ &c. The illustrious author begins by remarking
that the secular inequalities due to the action of one planet on another
are the same as if the mass of the disturbing planet were diffused according
to a certain law along its orbit, so that the latter becomes an elliptic ring of
variable but infinitesimal thickness. The problem then presents itself of
determining the attraction exerted by such a ring on any external point.
In the solution of this problem M. Gauss arrives at two definite integrals;
they can readily be reduced to elliptic integrals of the first and second kinds.
For the evaluation of the integrals to which he reduces those of his problem,
M. Gauss gives a method of successive transformation, analogous in some
measure to that of Lagrange. But the transformation of which he makes
use is a rational one, and is in fact the rational transformation of the second
order. The discovery of this transformation appears therefore to be due to
M. Gauss. He has remarked, though merely in passing, that his method is
applicable to the indefinite as well as to the definite integral. The rational
transformation in question leads to a continually increasing series of moduli,
or is, to use an expression of M. Jacobi a transformation “minoris in
majorem.” The law connecting two consecutive moduli is the same as in
Lagrange’s, which is, as we have seen, an irrational transformation ; so that
M. Gauss’s method does not afford us a new scale of moduli. Nevertheless,
as no rational transformation had I believe been noticed when his tract ap-
* Mr. Cayley, to whose kindness I have been, while engaged on the present report, greatly
indebted, has communicated to me a demonstration of the truth of this equation.
a
ON THE RECENT PROGRESS OF ANALYSIS. 57
peared *, his method is, in a historical point of view, of considerable in-
_ terest.
18. In the second volume of Crelle’s Journal, p. 101, we find Abel’s first
memoir on elliptic functions. It was published in the spring of 1827, and
therefore before M. Jacobi’s announcement in No. 123 of Schumacher’s
Journal. But it contains nothing which interferes with M. Jacobi’s disco-
very of the general theory of transformation. Abel’s researches on this part
of the subject appeared in the third volume of Crelle’s Journal, p. 160.
This second communication is dated, as we are informed by an editorial
note, the 12th of February, 1828, and though it is announced as a continu-
ation of the former memoir, it is yet in effect distinct from it, as its contents
are not mentioned in the general summary prefixed to the first communica-
‘tion.
These details may not be without interest, though it is not often that ques-
tions of priority deserve the importance sometimes given to them. There
is no doubt that Abel’s researches were wholly independent of those of
M. Jacobi; and though the coincidence of some of their results is therefore
interesting, yet the general view which they respectively took of the theory of
elliptic functions is essentially different, as different as the style and manner
of their writings.
With M. Jacobi the problem of transformation occupied the first place ;
with Abel that of the division of elliptic integrals. Both introduced a nota-
tion inverse to that which had previously been used, and as an immediate
consequence recognised the double periodicity of elliptic functions. Ex-
pressions of these functions in continued products and series were given by
both, but those of Abel were deduced by considering the limiting case of
the multiplication of elliptic integrals, those of M. Jacobi, as we have seen,
from the limiting case of their transformation. Hence Abel’s fundamental
expressions depend on doubly infinite continued products, corresponding to
the double periodicity of elliptic functions. On the other hand, M. Jacobi’s
continued products are all singly infinite.
_ Other differences might of course be pointed out, but the most remarkable
_ is that which we find in the character and style of their writings. Nothing
_ ean be more distinct. In M. Jacobi’s we meet perpetually with the traces
_ of patient and philosophical induction ; we observe a frequent reference to
4 particular cases and a most just and accurate perception of analogy. Abel’s
"are distinguished by great facility of manner, which seems to result from
_ his power of bringing different classes of mathematical ideas into relation
_ with each other, and by the scientific character of his method. We meet in
_ his works with nothing tentative, with but little even that seems like artifice.
_ He delights in setting out with the most general conception of a problem,
and in introducing successively the various conditions and limitations which
is it may require. The principle which he has laid down in a remarkable pas-
| sage of an unfinished essay on equations seems always to have guided him—
_ that a question should be so stated that it may be possible to answer it.
§ When so stated it contains, he remarks, the germ of its solution +.
:
___ * The fundamental formula of his transformation is incidentally mentioned in Legendre’s
_ second work (Traité des Fonct., i. 61).
___t For instance, Is it possible to trisect an angle by the rule and compass? The ques-
tion thus stated leads us to consider the general character of all problems soluble by the
methods of elementary geometry ; and following the suggestion thus given, we find that it
_ 1s to be answered in the negative. But if the last clause be omitted or neglected, we can
Dowd proceed, as many persons have done, tentatively, 7. e. by attempting actually to solve
oo
: e problem. If we fail, the question remains unanswered; if we succeed, we do answer
it, but as it were only by accident.
58 REPORT—1846.
Ido not presume to compare the merits of these two mathematicians.
The writings of both are admirable, and may serve to show that if ever the
modern method of analysis seems to be an éurepia rather than a réyvn, it
does so, either because it has not been rightly used, or because it is not duly
understood.
To obtain a general view of Abel's writings it may be remarked, that his
earliest researches related to the theory of equations. Of the ideas with
which he was then conversant he has made two principal applications. The
one is to the comparison of transcendents in the manner already described ;
the other to the solution of the equations presented by the problem of the
division of elliptic integrals. The second of these applications is contained
in the memoir published in the second volume of Crelie’s Journal.
He begins by introducing an inverse notation ¢ (w) corresponding to the
function denoted in the ‘ Fundamenta Nova’ by sinamw, while f(w«) and
F (w) correspond respectively to cosam «% and A am w. This notation
has the defect of appropriating three symbols which we cannot well spare.
On the other hand it is certainly more concise than M. Jacobi’s.
He then verifies the fundamental formule for the addition of the new
functions, and goes on to show that they are doubly periodie*. He next
considers the expressions of ¢” a, &c. in ga, &c., and proceeds to prove
the important proposition that the equation of the problem of the division
of elliptic integrals of the first kind is always algebraically soluble.
In order to illustrate this, which is one of the most remarkable theorems
in the whole subject, it may be observed, that as any circular function of a
multiple are ean be algebraically expressed in terms of circular functions
of the simple arc, so may ¢na, fna, Fna@ be algebraically expressed by
means of 6a, fa, Fa.
Conyersely, as the determination (to take a particular function) of sin a in
terms of sin x @& requires the solution of an algebraical equation, so does that
of ¢a in terms of gma. The equation which presents itself in the former
case is, as we know, of the mth or of the (2)th degree as n is odd or even.
But the equation for determining ¢ @ rises to the (®)th degree in the former
case, and in the latter to the (2 x*)th. We may however confine ourselves
to the case in which 2 is a prime number; since if it be composite the ar-
gument of the circular or elliptic function may first be divided by one of
the factors of n, and the result thus got by another, andsoon. Thus setting
aside the particular ease of m = 2, we shall have to consider, in order to
determine sin @ or @, an algebraical equation of the mth or (n®)th degree
respectively.
In consequence of the periodicity of sin a, the roots of the equation in
sin @ admit of being expressed in a transcendental form; they are all in-
cluded in the formula sin { @ + 2p"), in which p is integral, and which
n
therefore admits of only different values.
* The formule in question differ from those already given, only because Abel’s form of
dg 4
iptic i i , which becomes the same as Legendre’s on
the elliptic integral isf- Go ea) peat) 8
making e? = —1, The double periodicity of the functions is expressed by the formula
96=of{(-1)"t" 64 motnoV—)})
with similar formule for f and F. The quantities m and n are integral, and
1 d zt
al dx ras
- ig "V0 = eat) (eat) tag 4 ip VW (1 + c3a%) (1 — a)’
ON THE RECENT PROGRESS OF ANALYSIS. 59
But elliptic functions are doubly periodic, and therefore the roots of the
equation in ¢ a are expressible by a formula analogous to the one just written,
_ but which involves two indeterminate integers corresponding to the two
_ periodicities of the function, just as p does to the single periodicity 2 7.
Giving all possible values to these integers, we get »? different values for
the formula.
The question now is, how are we to pass from the transcendental repre-
sentation of these roots to their algebraical expression? Or, in other words,
how are the relations among the roots deducible from the circumstance of
their being all included in the same formula, to be made available in effect-
_ ing the solution of the algebraical equation ?
The answer to this question is to be found in the following principle: that
if % wu be such a rational function of w that
OT AGS A. Aan aan te A
@, Y, .z being the roots of an algebraical equation, then any of these quan-
tities may be expressed in terms of the coefficients of the equation. This
follows at once from the consideration that we shall have
1
X= TAKetxyY tr letate +x 2}>
& being the number of the roots 2, y,-..2- For the sum within the bracket
_ being a rational and symmetrical function of the roots, is necessarily expres-
sible in the coefficients of the equation, and the same is therefore of course
true of x 2, or of any of the other quantities to which it is equal.
If, therefore, by means of the relations whichwe know to exist among the
_ roots of the equation to be solved we can establish the existence of a system
_ of such functions, x, x’, 9!', &e., each of which retains the same value of
_ whichever root we suppose it to be a function; and if by combining these
functions we can ultimately express z in terms of them, the equation is solved,
since each of these functions may be considered a known quantity.
_ Such is the general idea of Abel’s method of solution. The principle on
_ which it depends, namely, the expressibility of any unchangeable function x,
is one which is frequently met with in investigations similar to that of which
We are speaking. M. Gauss’s solution of the binomial equation is founded
upon it. ;
_ [have already remarked that an important simplification of Abel’s process
_ was given by M. Jacobi. The result which M. Jacobi has stated without
_ demonstration may be proved by means of a theorem established by Abel in
_ the fourth volume of Crelle’s Journal, p. 194.
_ M. Jacobi shows the existence of a system of n° functions y, x/, &e., by
(ppowbining which we can immediately express the values of the roots. In the
_ last of his ‘ Notices’ on elliptic functions we find, as has been said, the ex-
plicit determination of all the roots. The formula given for this purpose is,
_ like the former, undemonstrated, and I do not know whether any demonstra-
_ tion of it has as yet been published; but from a note of M, Liouville, in a
recent volume of the ‘Comptes Rendus,’ we find that both he and M. Her-
_ tite have succeeded in proving it.
_ But in whatever manner the solution is effected it will always involve cer-
ain transcendental quantities, which are introduced in the expressions of the
elation subsisting between the different roots. The solution can therefore
_ be looked on as complete, only if we consider these to be known quantities.
_ They are the roots of a particular case of the equation to be solved. They
_ felate to the division of what are called the complete integrals, We may
_ therefore say that the general case is reduced to this particular one. But
60 REPORT—1846,
the latter is not, except under certain circumstances, soluble, though the
solution of the equation on which it depends can be reduced to the solution
of certain other equations of lower degrees.
But for an infinity of particular values of the modulus, the case in ques-
tion is soluble by a method closely analogous to that used by M. Gauss for
the solution of binomial equations. Thus for all such values the problem of
the division of elliptic integrals is completely solved.
The most remarkable of these cases corresponds to the geometrical pro-
blem of the division of the perimeter of the lemniscate. Abel discovered
that this division can always be effected by means of radicals, and further,
that it can be constructed by the rule and compass in the same cases (that
is for the same values of the divisor) as the division of the circumference of
a circle. Of this discovery we find Abel writing to M. Holmboe, “ Ah qu'il
est magnifique! tu verras*.”
In order to form an idea of the nature of the difficulty which disappears
in the case of which we are speaking, let us suppose that we have to solve
the algebraical equation which is represented by the transcendental one
¢ (3 6) = 0, in the same manner as the equation 4.23 — 32 = 0 is represented
by sin (36) =0.
The roots of 4.23 — 3 7 = 0, are, setting aside zero,
_ on . ar
sin ——, sin —.
3 3
Those of the former algebraical equation, which, as we know, is of the ninth
degree, are, beside zero,
2w 40
niga dg
2ai 4 at
kt Nanas
—— ——
Q(w+2ai) ~4(w+2ai)
‘Sa ee
where i= /— 1.
To satisfy ourselves that these are the roots required, we observe that
@ (mw + nai) =0 for all integral values of mand. Hence the general
eanaae but it will be found that
if we give any values not included in the above table to m and , the resulting
expression can be reduced to one or other of the forms we have specified in
virtue of the formula 9 (9) =o{(—1)™t"0+m wt+nai}. E.g. The non-
5w+2at 4 (w+ at)
3
3
form of the roots of our equaticn is ¢
, Since the
tabulated root is equal to our sixth root ¢
sum of their arguments is 3w + 2a, and the sum of 3 and 2 is an odd
number.
* It is right to mention that M. Libri has disputed Abel's title to the theory of the di-
vision of the lemniscate. I shall, however, not enter on the merits of the controversy which
arose on this point between him and M. Liouville. The reader will find it in the seventeenth
volume of the ‘Comptes Rendus.’ It appears that M. Gauss had himself recognised the
applicability of his method to the equation arising out of the problem of the division of the
perimeter of the lemniscate (vide Recherches Arithmetiques, § vii. p. 429. I quote from
the translation published at Paris in 1809), .
—-
ON THE RECENT PROGRESS OF ANALYSIS. 61
On considering our table, we observe that it consists of 3 + 1 horizontal
‘rows, each containing 3 — 1 terms, and that the arguments of the terms in
each row are connected by a simple relation; that of the second being double
that of the first. If we were to replace 3 by any odd number p, we should
get an equation of the p* degree, whose roots, setting aside zero, might simi-
larly be arranged in p+ 1 rows, each of p— 1 terms, the arguments of the
terms in each row being as 1, 2, 3, &c,
‘ Moreover, sin is rarionally expressible in sin = and generally sin abn
7” and p being any integers we please. So too are all
, eas on
is sO in sin
Qn
the terms in each horizontal row of our table, whether for the particular case
__ we have written down, or for that of any odd number, rationally expressible
in the first term.
Hence it may be shown that when the divisor 2 + 1 is a prime number,
an equation whose roots were the terms in.any horizontal row could be solved
algebraically, by a method essentially the same as that of Gauss, just as we
can solve the equation the type of whose roots is sin se = I" But to con-
t
_ struct this equation, z. e. to determine its coefficients, requires the solution of
an equation of the same degree as the number of horizontal rows, 7. e. of the
_ degree 2+ 2. And this equation is in general insoluble. The difficulty
_ we here encounter may be expressed in general language, by saying that
_ although we can pass from one root to another along each horizontal row, ,
__ yet we cannot pass from row to row.
Our table, however, has the remarkable property, that supposing, as we
may always do, 2% +1 to be a prime number, all the roots are rationally
expressible in terms of any two not lying in the same row. This depends on
a property of the function ¢, which it is very easy to demonstrate, and it is
intimately connected with the relations which exist among the terms of the
same row.
If, then, which is the case for an infinite variety of values of the modulus,
We can express any root rationally in terms of another of a different row,
say in @ cis ae
2n+1 Qn+1
_ it appears that not only are the roots all expressible in one, but they are so
_ in such a manner that the functional dependencies among them fulfil a cer-
_ tain simple condition, which, as Abel shows in a separate memoir (Crelle, iv.
_ p- 131; or Abel’s works, i. p. 114), renders every equation, all whose roots
_ are rationally expressible in terms of one, algebraically soluble. ~
_ To take the simplest case, the are of the lemniscate may be represented by
, all the roots become rational in terms of ¢ - Moreover,
dz death
_ the integral Fag If ¢ be the function inverse to this integral, we have
| the simple relation between roots of different rows, ¢ Poa i= t@ wat ?
_ w being in this case equal to w.
__ To apply what has been said to the solution of the general equation for
determining ¢ a in terms of 9 (2% ain 1) a, it is sufficient to remark that the
anscendents introduced in considering the relations among the roots of this
7 k 2 Qar :
a ee uation, are simply @ ree and @ ry or at least may be algebraically
expressed in terms of these two quantities.
___ The remainder of the first memoir contains developments of the functions
~
62 REPORT—1846.
¢,f and F in doubly and singly infinite continued products and series. They
are derived from the expressions of @ @, &c. in terms of ¢ =, &c., by supposing
m to increase sine limite, and are therefore analogous to the expression of
sin ¢ in terms of ¢ which we have already mentioned.
The second contains the development of what had already been pointed
out with respect to the lemniscate, so far as relates to the division of its peri-
meter by any prime number of the form 4m-+ 1. In an interesting note
which M. Liouville communicated to the Institute in 1844, and which is
published in the eighth volume of his Journal, p. 507, he has proved gene-
rally that the division of the perimeter of this curve can always be effected
whether the divisor be a composite or prime number, real or compleax (that
is, of the form p + “—q, p and q being integers). In order to do this, it
was only requisite to follow m.m., the reasoning by which Abel has shown
that the equation which presents itself in the problem of the division of the
circumference of the circle is always resoluble. Thus, as M. Liouville has
remarked, his analysis is implicitly contained in Abel’s.
This memoir also contains Abel’s theorem for the transformation of elliptic
integrals of the first kind. It is equivalent to that of M. Jacobi; nor is the
demonstration, though presented in quite a different form, altogether unlike
M. Jacobi’s.
Abel begins by considering the sum of a certain series of ¢ functions whose
arguments are in arithmetical progression. He shows that the sum of this
series is a rational function of its first term. If we call this sum (multiplied
by a certain constant) y, and the first term 2, then y is such a function of ¢
as to satisfy the differential equation already mentioned, viz.
va-yyd—vy) M V¥a=2)0—Ray
or rather an equation of equivalent form. In fact y is m.m. the same func-
tion of x that it is in M. Jacobi’s theorem. Thus the sum of the series of
elliptic functions is itself, when multiplied by a constant, a new elliptic fune-
tion, having a new modulus, and whose argument bears a constant ratio to
that of the first term of the series. It appears also that for the sum of the
elliptic functions we may, duly altering the constant factor, substitute their
continued product. Thus, beside the algebraical expression of y, there are
two transcendental expressions of it, both of which are given by M. Jacobi
in the ‘Fundamenta Nova. At the close of the memoir Abel compares his
result with the one in Schumacher’s Journal, No. 123, and mentions that he
had not met with the latter until his own paper was terminated.
19. In the 138th number of this journal Abel resumed the problem of
transformation, and treated it in a more general and direct manner than had
yet been done. This memoir appeared in June 1828. M. Jacobi, in a letter
to Legendre, has spoken in the highest terms of Abel's demonstration of the
formule of transformation: he says, “Elle est au-dessus de mes éloges,
comme elle est au-dessus de mes travaux.” An addition to this memoir,
establishing the real transformations by an independent method, appeared in
Number 148 of the same journal. ‘These two papers are printed consecu-
tively in the first volume of Abel's Works, pp. 253, 275.
In the first of these two remarkable essays Abel makes use of the perio-
dicity of the function ¢ 6, or, as he here denotes it, AG, to determine @ priori
what rational function of 2, y must be in order that the differential equation
dy dz
Vie) (=F) VER8) Gea)
ON THE RECENT PROGRESS OF ANALYSIS. 63
may be satisfied. [I have altered his notation for the sake of uniformity. ]
» Wx be the function sought, then considering y = x as an equation de-
termining x in terms of y, he shows that certain relations necessarily exist
among its roots. Let A be one of them and 6! another, it will readily be
seen that we may put '
. di'!=d6,
_ since each is equal to
- a
Vy) U-#y’)
ih 6! = 6 + a,
Al!
ie @ being the constant of integration, or, which is the same thing, being inde-
pendent of y. Hence a4 being one root, every other root is necessarily of
Rm the form A(§+ a). Again, we see from hence that
] y=) = Yat a)),
iH
a which is to be true for all values of 8, and which therefore implies the exist-
ence of a series of equations, of which the type is
A
i VAG+H—1a)) = (a+ ha)),
§ where # is an integer. Hence A(9 + &«@) is a root, whatever integral value
ba we may give tok. But the equation y= wz has but a finite number of
_ roots, and therefore the values of the general expression A(§ +a) must
Yecur again and again. This consideration throws light on the nature of the
_ quantity a; it must in all cases be an aliquot part of a period (simple or
_ eompound) of the function A 6.
__ All the values of A (@ + ka) got by giving different values to & are roots;
_ but the converse is not necessarily true; all the roots are not necessarily
_ included in this expression. But it is not difficult to perceive that all the
roots are included ina more general expression, viz. A(9+h, a, +h. @.-k, &,),
and conversely, that all the values of this expression are roots. The number
_ mis indeterminate: we may have formule of the form y = Ww 2, in which 2
__ is unity, others in which it is two, &c.; but in all cases a is an aliquot part
f some period of A 6, and & is integral.
It is easy when the roots of y =z aré known, to express y in terms of 6.
wr let Pz = a J and F being integral functions. Then
yFe—fe=(yp—q {(@—Ab) (@— AO +.4)) oe}
is (yp —q being the coefficient of the highest power of « inyFa—fw) an
nti¢ally true equation; whence, to determine y in 9, we have only to assign
a particular value to 2, or to compare the coefficients of similar powers of it*.
This then determines the form which the function y must necessarily be
: the question which Abel goes on to discuss is this: Under what circum-
nees will a function of the form thus determined @ priori be such a func
mn as we require? The character of the reasoning by which this question
treated is similar to that of the method by which Abel had, in his second
Memoir on elliptic functions, verified the form which, without assigning any
reason, he had there assumed for the function y.
The second essay is singularly elegant. If ¢, denote the function inverse
ag
_* T have trot noticed an ambiguity of sign at the outset of this reasoning, as given by
Abel, as for the purposes of illustration it is immaterial.
64 REPORT—1846.
to the imegral | Foy and ¢, the corresponding function for
the modulus ec, then, on introducing the inverse notation, the differential
equation
dy dz
= 24
v7G—y*) iy) V(1—a*) (1—e? 2°)
becomes of course d§' = ad, with c= 6,4 and y= ¢,6'. Hence for a
given increment « of 6, that of 6! isaa.
Let us take the simplest case, and suppose y to be a rational function of
x; then, as 2 or 6,9 remains unchanged when 9 increases by a period of the
function ¢,, ¥ does so too; that is ¢,9' remains unchanged when 6! increases
by a times a period of ¢,, or in other words, a times a period of ¢, is neces-
sarily one of ¢,.
Suppose now & and ¢ to be both real and less than unity; then ¢, and ¢,
have each a real period, here denoted by 2w, and 2w, respectively, and each
an imaginary period w,2 and @w,7 respectively, @, and w, being both real.
Let 6 receive first the increment 2w,, and secondly the increment @, 7, then,
by what has been said,
2aw,=2mw,+ nwt
aa.i=2pu, + qa,t*,
m, n, p, g being certain integers. But can these two equations subsist simul-
taneously? Not generally, since if we eliminate a and equate possible and
impossible parts, we get éwo relations among w, w, w, @;,, Which are con-
tinuous functions of the éwo quantities k and c. Hence both are determinate ;
and if we wish c to remain indeterminate, we must either make m and ¢g
equal to zero, in which case a is impossible, or, making and p equal to zero,
assign a real value to it. When a is real we have
a=m = = q ait
W, ors
and hence the remarkable conclusion, that
wy. Ww,
san ee SY Ns
Dy, @,
m and q being integers.
The commensurability of the transcendental functions “, — is therefore
k G
a necessary condition, in order that an integral with modulus e¢ can be trans-
formed into one with modulus &, the regulator a being real and c indeterminate.
And it may be shown that this condition is not only necessary but sufficient.
Similar considerations apply to the case in which a is impossible.
Simple as this view is, it leads to many consequences of great interest.
The function g, of which we have already spoken (p. 55), is merely e- a
and as we know for the first real transformation of the mth order, it becomes
nw E : wD oT :
e—*-~@. Hence in this case we have Frye ped keg according to the
e
general law. It may be well to remark, that if k = c¢ we have a=m“t=m
Ww,
* here is in M. Jacobi’s notation 2K’, so that 9p¢=9(4+2ma+nwi), mand n
being any integers.
if ON THE RECENT PROGRESS OF ANALYSIS. 65
(an integer). Hence in multiplying an integral, the multiplier must be an
integer, if y is rational in x, except for particular values of c.
_ In the paper of which we are speaking Abel has applied precisely similar
considerations to the case in which z and y are connected by any algebraical
equation.
__ Passing over one or two shorter papers, one of which has been already
referred to at p. 59, we come to a ‘Précis’ of the theory of elliptic func-
tions, published in the fourth volume of Crelle’s Journal, p. 236. The
i work of which it was designed to be an extract was never written, and the
_ §Précis’ itself is left unfinished. A general summary was prefixed to it, from
which we learn that the work was to be divided into two parts. In the first
_ elliptic integrals are considered irrespectively of the limits of integration, and
_ their moduli may have any values, real or imaginary. Abel proposes the
~ general problem of determining all the cases in which a linear relation may
_ exist among elliptic integrals and logarithmic and algebraical functions in
_ yirtue of algebraical relations existing among the variables*.
__ His first step is to apply his general method for the comparison of trans-
cendents to elliptic integrals, which may be done by what is called Abel’s
_ theorem, in at least two different ways: the one, that of which he now makes
use; the other, that which we have seen is applied to the case of four func-
_ tions by Legendre in his third Supplement.
_ He next determines the most general form of which the integral of an al-
_ gebraical differential expression of any number of variables is capable, pro- °
Piet it ean be expressed linearly by elliptic integrals and logarithmic and
algebraical functions. The result at which he arrives admits of many im-
portant applications. It is, that the integral in question may be expressed in
a form in which the sine of the amplitude of each elliptic integral and the
' corresponding A, and also the algebraical and each logarithmic function are
all rational functions of the variables and of the differential coefficients of the
integral with respect to each.
He proceeds by an interesting train of reasoning to establish the remark-
able conclusion, that the general problem which we are considering may
ultimately be reduced to that of the transformation of elliptic integrals of the
first kind. The problem of this transformation is then discussed, and by a
method essentially the same as that of which he had made use in his paper in
‘Schumacher’s Journal. The appearance however of the two investigations is
dissimilar, because no reference is made to elliptic functions (as distinguished
from elliptic integrals) in the first part of the ‘ Précis.’ The relations there-
fore which exist among the roots of y=wW=2 are established by considerations
’ independent of the periodicity of elliptic functions; though it is not difficult
a
x
to perceive that they were suggested by the results previously obtained by
means of that fundamental property. It is shown, that if the equation
y= x, where yz is a rational function, satisfy the differential equation (A.),
hen this equation, considered as determining x in terms of y, is always alge-
raically soluble. As the multiplication of elliptic integrals may be consi-
ered a case of transformation (that, namely, in which the modulus of the
nsformed integral remains unchanged), this theorem may be looked on as
an extension of that which we have spoken of (p. 58) in giving an account of
Abel’s first memoir on elliptic functions. The two theorems are proved by
he same kind of reasoning.
The second part of the memoir was to have related to cases in which the
moduli are real and less than unity ; of this however only the summary exists.
f i In the assumed relation, the amplitude, or rather the sine of the amplitude of each
‘ elliptic integral, is to be one of the variables, and noé¢ a function of one or more of them.
66 REPORT—1846.
Abel proposed to introduce three new functions, the first corresponding to
that which he had previously designated by ¢9*. He now denotes it by Ab. —
The second and third functions are apparently what the second and third
kind of elliptic integrals respectively become, when, instead of x, we intro-
duce the new variable §; 2 and @ being of course connected by the equation
x=A6. The double periodicity of the function A and its other fundamental
properties having been established, it was his intention to proceed to more
profound researches. Some of his principal results are briefly stated. I may
mention one, that all the roots of the modular equation may be expressed
rationally in terms of two of them.
One of the last paragraphs of the summary relates to functions very
nearly identical with those which M. Jacobi discusses at the close of the
‘ Fundamenta Nova,’ and which he has designated by the symbols Hand @.
The second volume of Abel’s collected works consists of papers not pub-
lished during his life. Two or three of these relate to elliptic functions.
The longest contains a new and very general investigation for the reduction
of the general transcendent, whose differential is of the form i P being,
as usual, rational and R a polynomial of the fourth degree; together
with transformations with respect to the parameter of integrals of the third
kind.
20. Having now given some account of the revolution which the disco-
veries of Abel and Jacobi produced in the theory of elliptic functions, I shall
mention some of the principal contributions which have been made towards
the further development of the subject since the publication of the ‘ Funda-
menta Nova.’ In Crelle’s Journal, iv. p. 371, we find a paper by M. Jacobi,
entitled ‘De Functionibus Ellipticis Commentatio.’ It contains, in the first
place, a development of the method of transforming elliptic integrals of the
second and third kind, and introduces a new transcendent Q, which takes the
place of ©, with which it is closely connected. M. Jacobi proves that the
numerator and denominator of the value of y, mentioned above, and which
have been denoted by U and V, satisfy a single differential equation of the
third order. The remainder of the paper relates to the properties of Q (vide
ante, note, p.55). When this function is multiplied by a certain exponen-
tial factor it becomes a singly periodic function, and, which is very remark-
able, its period is equal to one of the single or composite periods of the el-
liptic function inverse to the integral of the first kind. By composite period
I mean the sum of multiples of the fundamental periods. ‘The exponential
factor being properly determined, its product by Q is equal to © multiplied
by a constant. In considering this subject M. Jacobi is led to introduce the
idea of conjugate periods. ‘These are periods by the combination of which
all the composite periods may be produced. It is obvious that the funda-
mental periods are conjugate periods; and there are, as may easily be
shown, an infinity of others.
In the sixth volume of the same journal we find a second part of the
‘Commentatio.’ It contains a remarkable demonstration of the fundamental
* In the ‘Précis’ Abel has adopted the canonical form of the integral of the first
kind made use of by Legendre and M. Jacobi; so that the quantity under the radical is
(1—2) (1—c? 2). It is worth remarking, that in his first paper in Schumacher’s Nachrichten
this quantity is (1—e? x”) (1—c? 2”), while in the second it is the same as in the ‘ Précis.’ To
this form he appears latterly to have adhered.
+ It is not-clear whether by roots of the modular equation we are to understand the trans-
formed moduli themselves, or their fourth roots, i.e. in M. Jacobi’s notation A or v. Vide
supra, p. 50,
a
ON THE RECENT PROGRESS OF ANALYSIS. 67
formule of transformation of the odd orders founded on elementary proper-
4 ties of elliptic functions.
In a historical point of view a notice by M. Jacobi in the eighth volume
_ of Crelle (p. 413) of the third volume of Legendre’s ‘ Traité des Fonctions
_ Elliptiques’ is interesting. It was here, I believe, that M. Jacobi first pro-
_ posed the name of Abelian integrals for the higher transcendents, which we
_ Shall shortly have occasion to consider. After some account of the contents
_ of Legendre’s supplements, the first two of which contain the greater part of
_ M, Jacobi’s earlier researches, he goes on to generalise a remarkable reduc-
tion given by Legendre at the close of his work.
21, I turn to one of the very few contributions which English mathema-
_ ticians have made to the subject of this report, namely, to a paper by Mr.
_ Ivory, which appeared in the Phil. Trans. for 1831. His design is to give
_ in asimple form M. Jacobi’s theorem for transformation. The demonstra-
_ tion is essentially the same as that in the ‘Fundamenta Nova.’ But Mr.
; Ivory does not set out with assuming y= = U and V being integral fune-
_ tions of x, but with assuming it equal to the continued product of a number
_ of elliptic functions (whose arguments are in arithmetical progression), mul-
_ tiplied by a constant factor. This is one of M. Jacobi’s transcendental ex-
pressions for y, and the two assumptions are therefore perfectly equivalent
in the transformations of odd orders; but in those of even orders, or where
_ the continued product consists of an even number of factors, Mr. Ivory’s
_ amounts to making y equal to an irrational function of x. Transformations
__ by irrational substitutions, though long the only kind known (since Lagrange’s
_ belongs to this class), had not of late been considered in detail. Abel
_ indeed remarked in the beginning of the general investigation contained in
a Schumacher’s Journal (No. 138), that the existence of an irrational trans-
_ formation implied that of a rational one leading to an integral with the same
modulus as the other. He was, therefore, in seeking for the most general
modular transformation, exempted from considering irrational substitutions ;
but in a historical point of view it is interesting to see the connection between
Lagrange’s transformation and those which have been more recently disco-
vered*,
ee: a ser
Ify ane, FF where 5?-+-c?=1, then
Mehr tes Ae Sh sna. hub
Gander 0+) Vas acew)
‘This is Lagrange’s direct transformation, The corresponding rational transformation is
_ 1—(1+44) 2?
Y= Ta (1—b) a”
~ which satisfies the same differential equation as before.
Avain 4 dy a ie dr
=" Vi-~)I-#f) 2 Vi-8)(1—-ex)
js a
l+e
_ (le)
~ 1lfex?’
r2
68 REPORT—1846.
ees.
The question presents itself, what is the connection between the irrational
transformation (that of which Lagrange’s is a particular case) and the rational _
transformation of even orders? Perhaps the simplest answer to it (though
every question of the kind is included in the general investigations contained
in Abel’s ‘ Précis’) is found in a paper by M. Sanio in the fourteenth volume
of Crelle’s Journal, p.1. The aim of this paper is to develope more fully
than Mr. Ivory has done the theory of transformations of even orders, and
particularly of the irrational transformations, which M. Sanio considers more
truly analogous to the rational transformations of odd orders than the rational
transformations of even orders; and also to discuss the multiplication of
elliptic integrals by even numbers, a subject intimately connected with the
other. We have already mentioned the existence of what are called com-
plementary transformations, each of which may be derived from the other
by an irrational substitution, by which two new variables are introduced. In
the case of transformations of odd orders, the original transformation and the
complementary one are both rational, and are both included in the general
formula given by M. Jacobi’s theorem; but to the rational transformation of
any even order corresponds as its complement the irrational transformation
of the same order. This remark, which, as far as I am aware, had not before
been made, sets the subject in a clear light *.
22. In the twelfth volume of Crelle’s Journal (p. 173), Dr. Guetzlaff has
investigated the modular equation of transformations of the seventh order: it
is, as we know from the general theory, of the eighth degree, and presents
itself in a very remarkable form, which closely resembles that in which
M. Jacobi, at p.68 of the ‘Fundamenta Nova,’ has put the modular equa-
tion for the third order. Dr. Sohncke has given, at p. 178 of the same vo-
lume, modular equations of the eleventh, thirteenth and seventeenth orders,
none of which apparently can be reduced to so elegant a form as those of
the third and seventh. Possibly the transformation of the thirty-first order
might admit of a corresponding reduction. The whole subject of modular
equations is full of interest. Dr. Sohncke has demonstrated his results in a —
subsequent volume of the Journal (xvi. 97).
In the fourteenth volume of Crelle’s Journal there is a paper by Dr. Gu-
dermann on methods of calculating and reducing integrals of the third kind.
I have already quoted from this paper the expression of the opinion of its
learned author, that it is impossible to express the value of integrals of the
circular species in terms of functions of two arguments. If this be so, it is
which is M. Gauss’s, and is termed in M. Jacobi’s nomenclature the rational transformation
of the second order. It satisfies the equation
dy Ss fe ha il hal
Jaap dara OT aaa iaeaiy
where, as before, _2Vve
1+e
* Lagrange’s transformation being
ay Lagan ae V1 a!
= 1 t = a d = =
” atnen |e ite V1—y? = en
then we find that _ (+2) 2’
while the differential equation becomes
dy’ Ness A
Vay amy ~ OF) aaa) Pa)
where =1—F?*.
ON THE RECENT PROGRESS OF ANALYSIS. 69
a impossible to tabulate such integrals, and therefore our course is to devise
series more or less convenient for determining their values when any pro-
ple, e. g. that of the motion of a rigid body, to which Dr. Gudermann espe-
gially refers, requires us to do so. The formation of such series is accordingly
the aim of this memoir, which contains some remarkably elegant formule ;
one of which connects three integrals of the third kind with three of the
second. :
In the sixteenth and seventeenth volumes of the same Journal, Dr. Guder-
_ mann has given some series for the development of elliptic integrals ; and he
has since published in the same Journal a systematic treatise on the theory
- of modular functions and modular integrals, these designations being used to
denote the transcendents more generally called elliptic. The point of view
from which he considers the subject has been already indicated (vide supra,
p- 36). In asystematic treatise there is of course a great deal that does not
profess to be original, and it is not always easy to discover the portions
which are so. Dr. Gudermann’s earlier researches are embodied and deve-
loped in his larger work ; and in some of the latter chapters (XXIII. 329, &c.)
we find some interesting remarks on the forms assumed by the general trans-
cendent when the biquadratic polynomial in the denominator has four real
roots. Dr. Gudermann points out the existence of a species of correlation
between pairs of values of the variable.
23. The development of the elliptic function ¢ in the form of a continued
product may be applied to establish formule of transformation. ‘This mode
_ of investigating such formule was made use of by Abel in his second paper
in Schumacher’s Journal, No. 148, which we have already noticed; and a
corresponding method is mentioned by M. Jacobi in one of the cursory no-
tices of his researches which he inserted in the early volumes of Crelle’s
Journal. Mr. Cayley, in the Philosophical Magazine for 1843, has pur-
_ sued a similar course. Another and very remarkable application of the same
__ kind of development consists in taking it as the definition of the function ¢,
and deducing from hence its other properties. It has been remarked that
_ the continued products of Abel and M. Jacobi are derived from considera-
tions which, although cognate, are yet distinct; those of the latter being
_ singly infinite, while Abel’s fundamental developments consist of the product
_ of an infinite number of factors, each of which in its turn consists of an in-
| finite number of simple factors. Thus we can have two very dissimilar de-
_ finitions of the function ¢ by means of continued products. M. Cauchy,
who has investigated the theory of what he has termed reciprocal factorials,
that is, of continued products of the form
{i +2)(lféz)......}{(1+¢2-!)(14+ @271)......},
_ which is immediately connected with M. Jacobi’s developments, has accord-
| ingly set out from the singly infinite system of products, and has deduced
| from hence the fundamental properties of elliptic functions (Comptes Rendus,
| kvii. p. 825).
‘4 Mr. Cayley, on the other hand, has made use of Abel’s doubly infinite
| products, and has shown that the functions defined by means of them satisfy
_ the fundamental formule mentioned in the note at page 52, which, as these
| equations furnish a sufficient definition of the elliptic functions, is equivalent
__ to showing that the continued products are in reality elliptic functions. He
| has therefore effected for Abel’s developments that which M. Cauchy had
_ done for M. Jacobi’s. Mr. Cayley’s paper appeared in the fourth volume of
| the Cambridge Mathematical Journal, but he has since published a trans-
| lation of it with modifications in the tenth volume of Liouville’s. On the
70 REPORT—1846.
same subject we may mention a paper by M. Eisenstein (Crelle’s Journal,
Xxvii. 285).
24. M. Liouville has in several memoirs investigated the conditions under
which the integral of an algebraical function can be expressed in an alge-
braical, or, more generally, in a finite form. This investigation is of the
same character as that which occurs in the beginning of Abel’s last published
memoir on elliptic functions (vide supra, p. 65). But while Abel’s re-
searches are more general than M. Liouville’s, the latter has arrived at a
result more fundamental, if such an expression may be used, than any of
which Abel has left a demonstration.
He has shown that if y be an algebraical function of 2, such that J yd
may be expressed as an explicit finite function of x, we must have
Sydaatt Alogu + Blogv +...+ Clog w,
A, B,...C being constant, and ¢, uw, v,...w algebraical functions of a.
The theorem established by Abel in the memoir referred to includes as a
particular case the following proposition, that if
Syde =t+ Alogu+ Blogy+...+ Clogw,
then ¢, u, v, ...w may all be reduced to rational functions of # and y.
Combining these two results, it appears that if #2 yd« be expressible as an
explicit finite function of x, its expression must be of the form
t+ Alogu + Blogv +...+ Clogw,
where ¢, w, v,... w are rational functions of x and y, or rather that its ex- —
pression must be reducible to this form*.
After establishing these results in the memoir (that on elliptic transcen-
dents of the first and second kinds), which will be found in the twenty-third
cahier of the ‘ Journal de l’Ecole Polytechnique,’ p. 37, M. Liouville sup-
poses y to be of the form , where P and R are integral polynomials, and
hence deduces the general form in which the integral cd xz may neces-
sarily be put, provided it admit of expression as an explicit finite function of x.
rE
VR
braical function of xz, it cannot be expressed by any explicit finite function
of it, and finally demonstrates that an elliptic integral, either of the first or
second kind, is not expressible as an explicit finite function of its variable.
In a previous memoir inserted in the preceding cahier, M. Liouville
proved the simpler proposition, that elliptic integrals of the first and second
kinds are not expressible as explicit algebraical functions of their variable
(Journal de l’Ecole Polytechnique, t. xiv. p. 137). His attention appears to
have been directed to this class of researches by a passage of Laplace’s
‘ Theory of Probabilities,’ in which the illustrious author, after indicating the
fundamental, and, so to speak, ineffaceable distinctions between different
classes of functions, states that he had succeeded in showing that the inte-
He shows from hence that if dz cannot be expressed by an alge-
d
geal [ae is not expressible as a finite function, explicit or
implicit, of z. Laplace however did not publish his demonstration.
* An equivalent theorem is stated by Abel in his letter to Legendre for implicit as well
as explicit functions (Crelle’s Journal, vi.).
. = ON THE RECENT PROGRESS OF ANALYSIS. 71
In his own Journal (v. 34 and 441), M. Liouville has since shown that
elliptic integrals of the first and second kinds, considered as functions of the
modulus, cannot be expressed in finite terms.
95. In the eighteenth volume of the ‘Comptes Rendus’ (Liouville’s Journal,
_ ix. 353), we find in a communication from M. Hermite, of which we shall
shortly have occasion to speak more fully, a remarkable demonstration of
Jacobi’s theorem. It is stated for the case of the first real transformation,
but might of course be rendered general. This demonstration depends es-
sentially on the principle already mentioned (p. 59), that any rational func-
~ tion of a root of an algebraical equation which has the same value for every
root of the equation is rationally expressible in the coefficients. The equa-
tion to which this principle is applied is that to which we have so often re-
ferred, viz. y = = considered as an equation to determine 2 in terms of y,
and by means of it, M. Hermite shows at once that a certain rational func-
tion of z is also a rational function of y, the form of which is subsequently
determined.
M. Hermite goes on to prove other theorems relating to elliptic functions.
As elliptic functions are doubly periodic, we may determine certain of
their properties by considering to what conditions doubly periodic functions
must be subject. This view is mentioned by M. Liouville in a verbal com-
munication to the Institute (Comptes Rendus, t. xix.). He states that he
had found that a doubly periodic function which is not an absolute constant
and has but one value for each value of its variable must be, for certain va-
lues of it, infinite; that from hence the known properties of elliptic func-
tions are easily deduced ; and that by means of this principle he had suc-
ceeded in proving the expressions of the roots of the equation for the division
of an elliptic integral of the first kind, which M. Jacobi had given without
demonstration in Crelle’s Journal*. I am not aware that any development
of M. Liouville’s view has as yet appeared.
In the recent numbers of Crelle’s Journal there are many papers by M.
_ Eisenstein on different points in the theory of elliptic functions. Among
these I may mention one which contains a very ingenious proof of the fun-
_ damental formula for the addition of two functions, derived from the differ-
_ ential equation of the second order; which each function must satisfy.
___ Other contributions to the theory of elliptic functions might be mentioned ;
x some of these, not here noticed, are referred to in the index which will be
_ found at the end of this report. But in general it may be remarked that the
_ form which the subject has assumed, in consequence of the discoveries of
_ Abel and M. Jacobi, is that which it will probably always retain, however
_ our knowledge of particular parts of it may increase. What has since been
effected relates for the most part to matters of detail, of which, howevér im-
_ portant they may be, it is difficult or impossible to give an intelligible ac-
- count.
_ 26. It does not fall within the design of this report to consider the various
_ applications which have been made of the theory of elliptic functions ; but
_ Ishall briefly mention some of the geometrical interpretations, if the expres-
_ sion may so be used, which mathematicians have given to the analytical re-
sults of the theory.
The lemniscate has, as is well known, the property that its arcs may be
_ represented by an elliptic integral of the first kind, the modulus of which is
si
___ * M. Liouville has mentioned that M. Hermite had demonstrated the formule in question
_ inadifferent manner. ¢
72 REPORT—1846.
Let Or+oy=u oa'+ oy! =u!
Pitt Pysv Put oy =v.
#E ae dy ff Ces, +3 9 Dla Vix
ba “Ge gt ic which the algebraical integralis 2 V1—y?-+-y V1—2?=C.
ue ach term of this differential equation is a differential of a transcendent function sin wy or
76 : REPORT—1846. .
Then z and y are both given as functions of « and v. We may therefore
put
r=Aa(uvr), y=A (uv);
and similarly,
zl =A(u! v'), ae (u! v'); :
and as gat ¢@b=u+u!
?,a+¢% b=v+I, ;
we shall have a=A(ut+ul,v+v') .
b=A (u+ul, v+v').
Hence the functions A (w+ u', v + v') anda, (u + u!, v + v!) are expres-
sible as algebraical functions of A (uv), A, (wv), A (ul v'), A, (ul v!).
These then are functions to which the integrals are in a certain sense in-
verse, and which have the same fundamental property as circular and elliptic
functions.
In the general case of Abel’s theorem, we introduce (when the degree of
the polynomial is 2m or 2 m—1), m—1 functions analogous to A, each
being a function of m — 1 variables. These functions will, it may easily be
shown, have the fundamental property just pointed out for the case in which
m is equal to three.
Again, the differential equations of which Abel’s theorem gives us alge-
braical integrals, are, if the degree of the polynomial X be five or six, the
following :
dx + dy | dz _ 0.
VX VME YZ
udx ydy zdz
Fo Ws Gu
and generally, if the degree of the polynomial be 2m or 2m — 1, there are
m — 1 such equations, the numerators of the last containing the (m — 2)th
power of the variables. ;
M. Jacobi concludes by suggesting as a problem the direct integration of
these differential equations, so as to obtain a proof of Abel’s theorem cor-
responding to that which Lagrange gave of Euler’s (vide ante, p. 36).
30. Another important paper by M. Jacobi is that which is entitled ‘De
Functionibus duarum Variabilium quadrupliciter periodicis, etc.’ (Crelle, xiii.
p-55). It is here shown that a periodic function of one variable cannot
have two distinct real periods. In the case of a circular function, though we
have for all values of x
sina = sin(x + 2m)
= sin(a +2nzn),
m and m being any integers, yet 2m and 2m do not constitute two
distinct periods, since each is merely a multiple of 27, which is the funda-
mental period of the function. But if we had for all the values of x
S@)=Sf {x + a} =f {x + B},
we should also have
f(z) =f(e@+ma+nfp),
where m and may be any integers, positive or negative. Hencema-+nB
*
i
ON THE RECENT PROGRESS OF ANALYSIS. 77
_ may, provided a and are incommensurable, which is implied in their being
_ distinct periods, be made Jess than any assignable quantity, so that we may
put
; fxe=f(ete)
where ¢ is indefinitely small, and this manifestly is an inadmissible result.
Accordingly we see that one at least of the periods of elliptic functions is
necessarily imaginary.
Again, similar reasoning shows that in a triply periodic function, that is
in one in which we have
f (a) =f {x+m(a+ BV —1)+m! (a! +BY =1)4+-m"(a"+p'V—1)}
for every value of x, m, m', m” being any integers, and in which the three
periods a+ B/—1, &c. are distinct, we can make
: S(2) =f (@ + £)
by assigning suitable values to m, m!, m”; € being as before less than any
assignable quantity. Hence as this result is inadmissible, it follows that
_ there is no such thing as a triply periodic function. Whenever therefore a
function appears to have three periods they are in reality not distinct, and
so @ fortiori when it appears to have more than three. But now we come to
a difficulty. For M. Jacobi proceeds to show that if we consider a function
"(a+ Ph)de
of one variable inverse to the Abelian integral Sharma X being of
the sixth degree in 2, this function has four distinct and irreducible periods.
His conclusion is that we cannot consider the amplitude of this integral as
an analytical function of the integral itself. In the present state of our
knowledge, this conclusion, though seemingly forced on us by‘the impossibi-
lity of recognising the existence of a quadruply periodic function of one va-
riable, is not, I think, at all satisfactory. The functional dependence, the
existence of which we are obliged to deny, may be expressed by a differen-
tial equation of the second order; and therefore it would seem that the
commonly received opinion that every differential equation of two variables
has a primitive, or expresses a functional relation between its variables, must
_ be abandoned, unless some other mode of escaping from the difficulty is dis-
covered. It is probable that some simple consideration, rather of a metaphy-
_ sical than an analytical character, may hereafter enable us to form a con-
E “sistent and satisfactory view of the question, and this I believe I may say is
_ the opinion of M. Jacobi himself. The same difficulty meets us in all the
Abelian integrals: as in the case of those of Legendre’s first class, namely
_ where X is of the fifth or sixth degree, so also generally, the inverse function
has more than its due number of periodicities.
___Abel, in a short paper in the second volume of his works, p. 51, has in
_ effect proved the multiple periodicity of the functions which are inverse to
_ the integrals to which his theorem relates. The difficulty to which this gives
_ rise did not strike him, or was perhaps reserved for another occasion.
_ M. Jacobi next proves that his inverse functions of two variables are
_ quadruply periodic, but that quadruple periodicity for functions of two va-
Tiables is nowise inadmissible.
__ A difficulty however seems to present itself, which is suggested by M.
Eisenstein in Crelle’s Journal, viz. that if for each value of the amplitude
L
ae d
_ the integral ¢ 2 or Wz (vide supra, p.75), has an infinity of magnitudes
4
real and imaginary, and the same is the case for ? y, it is by no means easy to
AY a
in
78 REPORT—1846.
attach a definite sense to the equation « = 9 x + @y, or tosee how the value
of w is determined by it *.
31. Two divisions of the theory of the higher transcendents here suggest
themselves, which are apparently less intimately connected than the corre-
sponding divisions in the theory of elliptic functions, viz. the reduction and
transformation of the integrals themselves, and the theory of the inyerse
functions.
But before considering these I shall give some account of what has been
done in fulfilment of the suggestion made by M. Jacobi at the close of
the ‘ Considerationes Generales.’ Mathematicians have succeeded in effect-
ing the integration of the system of differential equations to the consideration
of which we are led by Abel’s theorem, and which is commonly designated
by German mathematicians as the ‘“‘ Jacobische system ;” its existence and
its integrability having been first pointed out by M. Jacobi.
In Crelle’s Journal (xxiii. 354), M. Richelot, after modifying the form in
which Lagrange’s celebrated integration of the differential equation of
elliptic integrals is generally presented, extended a similar method to the
system of two differential equations which occurs when we consider the
Abelian transcendents of the first class. He thus obtains one algebraical
integral of the system. In the case of Lagrange’s equation one integral is
all we want; but in that which M. Richelot here discusses we require
two. Nowif in the former case we replace each of the variables by its reci-
procal, we obtain a new differential equation of the same form as the original
one, and integrable therefore in the same manner; and if in its integral we
again replace each new variable by its reciprocal, that is by the original va-
riable, we thus, as it is not difficult to see, get the integral of the original
equation in a different form. That the two forms are in effect coincident
may be verified @ posteriori. But the same substitutions being made in M,
Richelot’s equations, which are of course those we haye already mentioned
at p. 76, the first of them becomes similar in form to the second, and vice
versé the second to the first. Thus the system remains similar to itself; and
if in the algebraical integral we obtain of it we again replace the new vari-
ables by their reciprocals, we fall on a new algebraical integral of the original
system ; this integral being, which is remarkable, independent of that pre-
viously got. Thus the system of two equations is completely integrated.
Extending his method to the general system of any number of equations,
M. Richelot obtains for each two integrals, but of course these are not all
that we want. At the conclusion of his memoir M. Richelot derives from
Abel’s theorem the algebraical integrals of the “ Jacobische system.”
Though in this memoir M. Richelot only obtained by direct integration
two of the m—1 algebraical integrals of the “ Jacobische system,” yet he put
the problem of its complete integration into a convenient and symmetrical
form. As there are m variables and m — 1 relations among them, we may
suppose each to be a function of an independent variable ¢ Lagrange, as
we know, in integrating the equation
ae dy _ 0
A Beri AX i000
* The difficulty here mentioned may perhaps be met by saying that the value of ¢ de-
wddx
termined by the integral ergs is necessarily determinate, and so likewise is that of w.
0
That considerations connected with the conception of a function inyerse to ¢# make the
latter quantity appear indeterminate is undoubtedly a difficulty ; but it is, so to speak, a
difficulty collateral to M. Jacobi’s theory, and therefore need not prevent our accepting it.
ee -
he
f
4 ON THE RECENT PROGRESS OF ANALYSIS. 79
introduced such an independent variable by the assumption = = WX, which
_ of course implied that ae = — WY. This assumption is unsymmetrical,
and it is therefore difficult to see how to generalise it. But if we assume
dz xX d Y
aa ws we shall of course have 4 m4 Les and therefore ¢ is symme-
trically related to « andy. Let Fu =0 be an equation whose roots are
2 and y, then, as we know, whenu = a2, Fu =2—y and, when v= y,
¥F'u=y — 2, so that using an abbreviated notation
ae ox vx wnat = vx
d= Brea dt PG)
Nothing is easier than to generalise this result. For instance, the “Ja-
cobische system ” of two equations is
dz dy dz
gde ydy z2dz
hg Bia alle Yar AR
Now if F xz =0 have a, y, z for its roots, the two preceding equations
may, in virtue of a very well-known theorem, be replaced by the three follow-
ing,
de_ V& dy_ VY dz_VZ
dt™ Wa’? di” Fly’ dt” Fz’
which introduce an independent variable ¢, symmetrically related to a, y and
2; and so in all cases,
M. Richelot * then takes a symmetrical function of 2, y,.+. 2, viz. their
_ sum, and by means of the last written equations arrives at an integrable dif-
_ ferential equation of the second order, the principal variable being the said
\
__ * As M. Richelot’s method of demonstrating Euler’s theorem is more symmetrical and
_ far more easily remembered than Lagrange’s, it ought, I think, to be introduced into all
elementary works on elliptic functions, The equation to be integrated being
bi aie vit Ah civ Cy ME Wel i op
Mat Batya pia pia! VatpytyP ty ty |
assume dv_VYatpaty@piepea
a dt y—@
dy_ VetByt oP PPE,
: dt @-y
ne
_ Letp=x+y. Then after a few obvious reductions
; dp 1
- at sp.
a i. deh. :
® Gane tr,
{Vappetye pie pia — Vat pyt PP yryS
oe =B(y— 2) (y°— 27) + #(y? — 2°),
the algebraical integral sought. It may easily be expressed in other forms,
80 REPORT—1846.
sum, and the independent variable being ¢. From the first integral of this
equation it is easy to eliminate the differentials, and we have thus an alge-
braical relation in a, y, ...z, from which, in the manner already mentioned,
M. Richelot deduces another. We now see that if we could find any other
symmetrical function which would lead to an integrable equation we should
get a finite relation among the variables. :
In the next volume of Crelle’s Journal M. Jacobi took the following func-
tion as his principal variable,
V{(e—2) (uy). (e- 2}
p being a root of X =O or fe =0 if we suppose X=fz. Calling this
function v, we get a simple differential equation in v and ¢, and a correspond-
ing integral of the system. Now fx =0 has 2m or 2m — 1 roots, and we
only want m — 1 integrals. The integrals therefore which we get by making
p the first, second, &c. root of fx = 0 are not all independent.
In the twenty-fifth volume of Crelle’s Journal M. Richelot resumed the
subject of his former paper, and discussed it in a very interesting memoir.
This fundamental or principal result may be said to be a generalisation of
M. Jacobi’s. It is that in the function
V {(u — 2) (uy) ++ (n— 2)}
f» may have any value whatever. The resulting differential equation,
though rather more complicated than when, with M. Jacobi, we suppose
a root of fz = 0, is still very readily integrable. We have thus an indefi-
nite number of algebraical integrals, since the quantity ~ is arbitrary, but
of course not more than m — 1 of them are independent.
In the same volume of Crelle’s Journal, p. 178, there is a curious paper by
Dr. Heedenkamp, in which the algebraical integrals of Jacobi’s system are
for the case of a polynomial of the fifth degree under the radical deduced
from geometrical considerations. It is shown that in a system of curvilinear
coordinates (those of which MM. Lamé and Liouville have made so much
use), the equations of the system are the differential equations given by the
Calculus of Variations for the shortest line between two points. Conse-
quently the finite equations of a straight line are the integrals sought. This
very ingenious consideration is afterwards generalised.
32. In the twelfth volume of Crelle’s Journal, p. 181, M. Richelot has
considered the Abelian integral of the first class. The principal result at
which he arrives is, that the only rational transformation by means of which
such an integral may be changed into one of similar form is linear in both
the variables which it involves. By means of this substitution, he transforms,
under certain conditions, the integral in question into a form analogous to
the standard forms of elliptic integrals. The subject of the division of hyper-
elliptic integrals of each class into three genera is also considered, and the
same principle of classification as Legendre’s is made use of. The paper
concludes by pointing out an error which Legendre committed in the appli-
cation of his principle. Legendre had thought that the formula of summa-
tion given by Abel’s theorem for integrals of the form of Vaz could not
involve a logarithmic function. Thus these integrals would belong to the
first or second kind, according to the value of the index e, and of A the degree
of gz. But in reality, though the integrals in question are of the first kind
(that is, they admit of summation without introducing either an algebraical
or logarithmic function) if e be less than a certain limit, yet if it be not so
their formula of summation will in general involve both algebraical and loga- —
j ON THE RECENT PROGRESS OF ANALYSIS. 81
rithmic functions. Either may, under certain conditions as to the form of
@ 2, disappear, but while gz is merely known as the polynomial of the Ath
degree, we cannot decide whether the integral is to be referred to the second
or third kind.
I may mention here a very elegant result due to M. Jacobi. It appears in
the thirtieth volume of Crelle’s Journal, p. 121, and is a generalisation of the
fundamental formula for the addition of elliptic arcs. With a slight modifi-
cation it may be thus stated. If gz involve only even powers of z, the
: 2 pr2m
highest being 2", then the sum of the integrals To is equal to
0
the product of their arguments, that is of the different quantities denoted by
the symbol z. In this case then the logarithmic function disappears, and
the integral belongs to the second kind.
In the twenty-ninth volume of Crelle’s Journal there is a paper by M.
Richelot on a question connected with hyper-elliptic integrals. The reader
will find in it a good many fully-developed results, which may be considered
as particular cases of Abel’s theorem. They illustrate the learned author's
criticism of Legendre’s classification of hyper-elliptic integrals, though they
_ are not adduced for that purpose.
The function M (vide ante, p. 38) is a function of the arbitrary quantities
a, 6, ...c, which, as has been remarked, may themselves be considered func-
tions of the arguments 2,, z,,...2,. To determine M as a function of the
last-written quantities is a necessary ulterior step in almost any special appli-
cation of Abel’s theorem, and this M. Richelot has done in several interesting
cases, establishing at the same time the relations which exist among the
quantities in question. His investigations, however, have an ulterior purpose,
| and are not to be considered merely as corollaries from Abel’s theorem.
Another paper of M. Richelot, on the subject of the Abelian integrals, is
found in the sixteenth volume of Crelle’s Journal, p. 221. The aim of it is
to furnish the means of actually calculating the value of the Abelian integral
_ of the first class by a method of successive transformation, that is, by a method
analogous to that used for elliptic integrals. M. Richelot’s process depends
essentially on an irrational substitution, by means of which we can replace
the proposed integrals by two others which differ only with respect to their
limits. In the development of this idea the author confines himself to the
first kind of the Abelian integrals of the first class, though the same method
“may m.m. be more generally applied*. From the formula which expresses
the proposed integral as the aggregate of two others is deduced another, in
which it is expressed by means of four integrals, the inferior limits of all being
zero. The first and second of these integrals differ only in their amplitude,
| and the same is true of the third and fourth. There are two principal trans-
‘formations, either of which may be repeated as often as we please ; and though
it might seem that the number of integrals would in the successive trans-
formations increase in a geometrical progression, yet by the application of
Abel’s theorem we can always reduce them to the same number. But the
‘development of this part of the subject M. Richelot has reserved for another
“occasion t.
*
{M +Nz}dz
WV {2(1~z) (1—#2z) (1-222) (1—p2z)} Mh at
7 The integral to be transformed is
q
N, &c. being constant. ;
__ t His transformations ultimately reduce ‘the hyper-elliptic integral to elliptic integrals ;
the latter may be considered known quantities, ‘vel per paucas adjectas transformationes
‘directe computentur.”’
82 . REPORT—1846.
At the close of his memoir, M. Richelot has given some numerical exam-
ples of his method for the case of a complete hyper-elliptic integral. The
third example he had previously given in a brief notice of his researches,
published in No. 311 of Schumacher’s Journal.
33. For many years after the death of Legendre the subject of the com-
parison of transcendents was studied principally by German and Scandi-
navian writers*: a young French mathematician, M. Hermite, has recently
made important discoveries in this theory ; but as the principal part of what
he has done is as yet not published, a very imperfect outline is all that can
be given.
In the seventeenth volume of the ‘Comptes Rendus’ we find the report
of a commission, consisting of MM. Lamé and Liouville, on a memoir pre-
sented to the Institute by M. Hermite. This report is reprinted in the eighth
volume of Liouville’s Journal, p. 502. A remark which incidentally occurs
in it, namely, that Abel was the first to give the general theory of the divi-
sion of elliptic integrals, led to a very warm discussion between MM. Liou-
ville and Libri, on the subject of the claims which, as I have already remarked,
the latter had made with reference to this theory.
It appears from the report, that M. Hermite has succeeded in solving the
problem of the division of hyper-elliptic integrals. The division of elliptic
integrals depends on the solution of an algebraical equation; that of the
hyper-elliptic integrals (as the functions inverse to them involve, as we have
seen, more than one variable), on the solution of a system of simultaneous
algebraical equations. This solution can, M. Hermite has shown, be effected
by means of radicals asuming, as in the analogous case of elliptic functions,
the division of the complete integrals) M. Hermite’s method depends for
the most part on the periodicity of the functions considered. A transcen-
dental expression of the roots of the equation of the problem having been
obtained, their algebraical values are deduced from it.
These researches, in themselves of great interest, are yet more interesting,
when we consider how completely they justify the views of M. Jacobi as to
the manner in which Abel’s theorem ought to be interpreted, by showing
that his theory of the higher transcendents is no barren or artificial gene«
ralisation.
At page 505 of the volume of Liouville’s Journal already mentioned, we
find an extract from a letter of M. Jacobi to M. Hermite, in which, after
congratulating him on the important discovery he had made, he points out
that the transcendental functions A (wv), A, (wv) (vide ante, p.'76) are alge-
braical functions of transcendental functions which involve but one variable.
M. Hermite’s subsequent researches have embraced a much more general
theory than that of the Abelian integrals, namely, that of the integrals of
any algebraical function whatever. ‘Thus his views bear the same relation
to Abel’s general theory, developed in the ‘ Savans Etrangers,’ that those of
M. Jacobi in the ‘ Considerationes Generales’ do to Abel’s theorem.
All that has yet been published with respect to them is contained in the
“Comptes Rendus,’ xviii. p. 1133, in the form of an extract of a letter from
M. Hermite to M. Liouville. This extract is reprinted in Liouville’s Journal,
ix. p. 353. It was communicated to the Institute in June 1844.
Following the course of M. Jacobi’s inquiries, M. Hermite proposed to_
determine what are the differential equations of which Abel’s investigations
give the complete algebraical integrals. When this is done it suggests the
* The papers of M. Liouville, already noticed, may be said to be an exception to this
remark,
ON THE RECENT PROGRESS OF ANALYSIS. 83
mature of the inverse functions which are to be introduced. The number
of these functions will of course vary in different cases, just as in M. Jacobi’s
less general theory. Let us suppose this number to be denoted by y, then
each function will involve y variables. And if each of these variables be
replaced by the sum of two new variables, then all the functions are given
as the roots of an equation of the yth degree, whose coefficients are rational
in terms of the corresponding functions of each of the new variables and of
certain known algebraical functions. From hence is derived the theory of
the periodicity of these functions.
After some other remarks on the theory of the higher transcendents, M.
Hermite states that the method of division of which he made use in the
_ problem of the division of Abelian integrals extends also to the new trans-
cendents now considered, but that in the theory of transformation he had
_ not as yet been successful. The greater part of the remainder of this re-
markable communication relates to elliptic functions, and has been already
: noticed. The remark just mentioned as having been made by M. Jacobi for
the functions which are inverse to the Abelian integrals, extends, M. Hermite
: observes, to the functions which he considers.
In conclusion, M. Hermite remarks that the method of differentiation with
respect to the modulus of which Legendre made so much use in the theory
_ of elliptic functions, may be applied to all functions of the form
Sf (ayaa,
where y is given by the equation
y'—-X=0.
_ In concluding this report, it may be remarked that the subject of it is still
_ incomplete, and that there is yet much to be done which we may hope it
_ will not be found impossible to do. It is however difficult to predict the
_ direction in which progress will hereafter be made. Yet I think we may
_ reasonably suppose that the question of multiple periodicity, from the para-
_ doxical aspect in which it has presented itself, and from its connexion with
_ the general principles of the science of symbols, will sooner or later attract the
_ attention of all philosophical analysts. M. Liouville’s idea of considering the
eonditions to which a doubly periodic function must as such be subject, can
_ searcely be developed or extended to the higher transcendents without leading
to results of great generality and interest.
_ The detailed discussion of different classes of algebraical integrals, their
transformations and reductions, form an endless subject of inquiry. But in
this, as in other cases, the increasing extent of our knowledge will of itself
tend to diminish the interest attached to the full development of particular
portions of it; and with reference to analytical problems arising out of
estions of physical science, the theory of the higher transcendents will it
_is probable never become of so much importance as the theory of elliptic
functions. We have occasion to make use of circular much more frequently
than of elliptic functions, and similarly we shall, it may be presumed, have
ss frequently to introduce the higher transcendents than elliptic functions.
merical calculations of the values of the higher transcendents are therefore
important than similar calculations in the case of elliptic functions*.
* The Academy of Sciences has proposed as the subject of the great mathematical prize
+ 1846 the following question :—“ Perfectionner dans quelque point’ essentiel la théorie
des fonctions abéliennes ou plus généralement des transcendantes qui résultent de la con-
‘sidération des intégrales de quantités algébriques.” The memoirs are to be sent in before
the Ist of October. ‘
G2
84 REPORT—1846.
The following index is intended to contain references to all the papers in
the first thirty-one volumes of Crelle’s Journal, and in the first ten volumes
of Liouville’s Journal, more or less connected with the subject of this report,
together with a considerable number of others.
In the following Index Crelle’s Journal is denoted by C., Liouville's by L.,
and the present Report by R.
pdx
VR
ganze Functionen sind. —C.i. 185. This paper contains formulz of re-
duction. It is mentioned by M. Liouville, ‘Journal de I’Ecole Polytech-
nique, 23d cah. p.38. It appears in French in Abel’s collected works,
tom. i. 33.
——. Recherches sur les Fonctions Elliptiques.—C. ii. 101, and iii. 160
[1827]. . Abel’s works, i. 141; also R. p. 57.
——. Remarques sur quelques Propriétés Générales d’une certaine sorte
de Fonctions Transcendantes.—C. iii. 313. This paper contains the
theorem commonly known as ‘ Abel’s Theorem.’ V. Abel’s works,
i. 288; also R. p. 40.
——. Sur le Nombre de Transformations Différentes qu’on peut faire subir
4 une Fonction Elliptique par la Substitution d’une Fonction donnée
du premier dessé.—C. iii. 394. V. Abel’s works, i. 309.
——. Théoréme Général sur la Transformation des Fonctions Elliptiques
de la seconde et de la troisiéme espéce.—C. iii. 402. The theorem is
stated without demonstration. V. Abel’s works, i. 317.
Note sur quelques Formules Elliptiques.—C. iv. 85. This paper con-
tains developments of elliptic functions, &e. V. Abel’s works, i. 299.
——. Théorémes sur les Fonetions Elliptiques.—C. iv. 194. They relate
to the demonstration of the theorem stated by M. Jacobi in the third
volume of Crelle’s Journal, p. 86, by means of which Abel’s method
for the division of elliptic integrals is greatly simplified. V. Abel's
works, i. 318; also R. p. 59.
——. Démonstration d’une Propriété Générale d’une certaine Classe de
Fonctions Transcendantes.—C. iv. 200. This short paper contains the
fundamental idea of the memoir presented to the Institute in 1826.
V. Abel’s works, i. 324; also R. p. 40.
——. Précis d’une Théorie des Fonctions Elliptiques.—C. iv. 236 and 309.
This précis was left unfinished. V. Abel’s works, i. 326; also R. p. 65.
——. Extracts from Letters to M. Crelle, one of which relates to the com-
parison of Transcendents.-—C. v. 336. V. Abel’s works, ii. 253.
——. A Letter to M. Legendre.—C. vi. 73. Works, ii. 256. It contains a
theorem proved by M. Ramus in the twenty-fourth volume of Crelle’s
Journal, p. 78 ; and another, proved by M. Liouville in the twenty-third
cahier of the ‘Journal de l’Ecole Polytechnique. V. R.p.41 and p.’70.
——. Mémoire sur une certaine classe de Fonctions Transcendantes. Pre-
sented to the Institute, Oct. 30, 1826, published in 1841 in the ‘ Mémoires
des Savans Etrangers,’ vii. 176. It is the only memoir of Abel’s not
contained in the collected edition of his works published in 1839; the
editor, M. Holmboe, not having been able to procure a copy of it.
V.pR..ps39-
——. Solution d’un Probléme Général concernant la Transformation des
Fonctions Elliptiques.—Schumacher’s Astronomische Nachrichten, No.
138, vi. 365. V. Abel’s works, i. 253; also R. p. 62.
AsrL. Ueber die Integration der differential Formel wenn R and p
_ ON THE RECENT PROGRESS OF ANALYSIS. 85
Apex. Addition au Mémoire Précédent—Schumacher’s Astronomische
Nach. No. 147, vii. 33. V. Abel’s works, i. 275; also R. whi supra.
_. . The following papers were published for the first time in Abel's col-
- lected works. ‘The references are to the second volume :—
——. Propriétés remarquables de la Fonction y=¢ 2, etc., p. 51. The
- multiple periodicity of a function inverse to a hyper-elliptic integral is
here mentioned. V. R. p.77.
—. Sur une Propriété remarquable d'une Classe trés étendue de Fone-
tions Transcendantes, p. 54. This paper contains a generalisation of a
theorem relating to elliptic functions.
—. Extension de la Théorie Précédente, p. 58.
_——. Sur la Comparaison des Fonctions Transcendantes, p. 66. This paper
contains a somewhat fuller development of his general theory than that
which is inserted in the fourth volume of Crelle’s Journal, p. 200.
V. R. p. 40.
——. Théorie des Transcendantes Elliptiques, p. 93. V. R. p. 66.
_ — +. Démonstration de quelques Formules Elliptiques, p. 210.
_ Brocu. Sur quelques Propriétés d’une certaine classe des Fonctions Trans-
cendantes.—C. xx. 178. An extension of Abel’s theorem. V. R. p.40.
Mémoire sur les Fonctions de la forme
§
SSS
SJ—7?-" F(a?) (Ra?) "? da, ete.—C. xxiii. 145 and 201.
This memoir, of which the first part may be considered a generalisation
of the preceding, is accompanied by a report of MM. Liouville and
Cauchy. V.R.p.41.
Bronwin. On Elliptic Functions—Camb. Mathematical Journal, iii. 123.
Mr. Bronwin puts the transcendental formula of transformation in a
very neat form.
——. On M. Jacobi’s Theory of Elliptic Functions.—Lond., Ed. and Dub.
Phil. Mag. xxii. 258. V. R. p. 53.
-——. Reply to Mr. Cayley’s Remarks.—L., E. & D. Phil. Mag. xxiil. 89.
e:: V. R. ubi supra.
Caratan. Surla Réduction d’une Classe d’Intégrales Multiples.—L. iv. 323.
_—. Sur les Transformations des Variables dans les Intégrales Multiples.
Mémoires Couronnés par Académie Royale de Bruxelles, xiv. ade
partie, p.1. The third part contains a transformation of a multiple
integral leading to properties of hyper-elliptic integrals analogous to
é known properties of elliptic integrals.
Caucuy. Comptes Rendus, xvii. 825.—V. R. p. 69.
Cavtry. Mémoire sur les Fonctions doublement Périodiques.—L., x. 385.
An enlargement of his paper on the inverse elliptic functions, published
in the fourth volume of the Cambridge Mathematical Journal. V. R.
iy p-:'69.
_——. Remarks on the Rev. B. Bronwin’s paper.—L., E. and D. Phil. Mag.
xxii. 358.
—. Investigation of the Transformation of certain Elliptic Functions.—
L., E. and D. Phil. Mag. xxv. 352. V. R. p. 69. ;
5, a the Inverse Elliptic Functions—Camb. Math. Journal, iv. 257.
- KR. p. 69.
‘Cuastxes. Comptes Rendus de l'Institut, xvii. 838, and xix. 1239. M.
-_ Chasles in these two communications presents to the Institute notices
of his geometrical researches illustrative of the theory of elliptic func-
tions. V. R. p. 74.
86 REPORT—1846.
Ciausen. Schumacher’s Nachrichten, xix. 178. On a particular Integral
mentioned by Legendre.
——. Schumacher’s Nachrichten, xix. 181. It is shown that the ares of
one of the curves, known as the Spirica of Perseus, may be rectified
by means of an elliptic integral.
EIsENsTEIN. Théorémes sur les Formes Cubiques.—C. xxvii. 75. At the
end of this paper we find some developments of elliptic functions in con-
tinued fractions. This subject is continued in the following paper of
M. Eisenstein’s.
Transformations remarquables de quelque Séries——C. xxvii. 193.
and xxviii. 36. See also Theorema, C. xxix. 96.
Bemerkungen zu den elliptischen und Abelschen Transcendenten.—
C. xxvii. 185. M. Jacobi has criticised this paper (of which a trans-
lation appears in Liouville’s Journal, x. 445) in the thirtieth volume of
Crelle’s Journal.
Elementare Ableitung einer merkwurdiger Relation zwischen zwei
unendlichen Producten.—C. xxvii. 285. V. R. p.’70.
- Beitrage zur Theorie der Elliptischen Functionen.—C. xxx. 185,
211. This paper contains a demonstration of the fundamental formula
of elliptic functions. V. R. p. 71.
GupErmann. Integralia Elliptica Tertiz Speciei Reducendi Methodus
Simplicior, &e.—C. xiv. 159, 185. V. R. p. 68.
—. Einige Bemerkungen iiber Elliptische Functionen.—C. xvi. 78.
——. Series nove quarum ope Integralia Elliptica Prime et Secunde
Speciei computantur, &c.—C. xvi. 366. and xvii. 382.
——. Theorie der Modular Functionen und der Modular Integrale-—
C. xviii. 1, 142, 220, 303; xix. 46, 119, 244; xx. 62, 103; xxi. 240;
aes, 301; xxv. 281. A systematic treatise on elliptic functions. V.
- p- 69.
Girziarr. Equatio Modularis pro Transformatione Functionum Ellipti-
carum Septimi Ordinis——C. xii. 173. V. R. p. 68.
dod
HAEDENKAMP. i li 5 :
Pp. De Transformatione Integralis Sf (sin?v—sin® 008")
—C. xx. 97. It is shown to be the product of two elliptic integrals.
——. Uber Transformation vielfacher Integrale—C. xxii. 184. Analo-
gous to the researches of M. Catalan in the ‘ Mémoires de Bruxelles,’
which appears to have been previously published.
——. Uber Abelsche Integrale—C. xxv. 178. V. R. p. 80.
Hermite. Sur la Théorie des Transcendantes a Différentielles Algébriques.
—L. ix. 353. Extracted from the ‘Comptes Rendus’ [June 1844].
This note, which contains scarcely more than an indication of M. Her-
mite’s results, may be said to mark the furthest advance yet made in
the theory of the comparison of transcendents. V. R. p. 82.
Hitt. Exemplum usus Functionum Iteratarum, &c.—C. xi. 193. This
paper contains some interesting applications of the calculus of functions
to the comparison of transcendents. V. R. p. 42.
Jacosi. Addition au Mémoire de M. Abel sur les Fonctions Elliptiques.
—C. iii. 86. A short note, containing an important simplification of
Abel’s method of solving the equation of the problem of division.
VR. p.59.
——. Note sur la Décomposition d’un Nombre donné en quatre quarrés.—
C. iii. 191. The demonstration referred to is founded on elliptic
functions. :
——. Note sur les Fonctions Elliptiques.—C. iii. 192.
ON THE RECENT PROGRESS OF ANALYSIS. 87
_ Jacosi. Suite des Notices sur Jes Fonctions Elliptiques.—C. iii. 303.
_ —. Suite des Notices, &c.—C. iii. 403.
——. Suite des Notices, ete—C. iv. 185. These notes contain theorems
stated for the most part without demonstration. V.R. p. 56.
-——. Ueber die Anwendung der elliptischen Transcendenten auf ein
bekanntes Problem der Elementar-geometric, u.s. w.—C. iii. 3°76.
This paper contains a geometrical construction for the addition and
multiplication of elliptic integrals of the first kind, A translation of
the most important part appears in Liouville’s Journal, x. 435. V. R.
» 73.
aay De Functionibus Ellipticis Commentatio.—C. iv,371. Transforma-
tions of integrals of the second and third kinds, &c. V. R. p. 66,
——-. De Functionibus Ellipticis Commentatio altera.—C. vi. 397. We
find here an elementary demonstration of M. Jacobi’s theorem. V. R.
. 66.
eg Note sur une nouvelle application de l’Analyse des Fonctions Ellip-
tiques a l’Algébre.—C. vii. 41. It relates to the development in con-
tinued fractions of a function of the fourth degree.
--—. Notiz zu Théorie des Fonctions Elliptiques de Legendre, Troisiéme
Supplément.—C. viii. 413. V. R. p. 67.
——. De Theoremate Abeliano—C, ix.99. V.R.p.41.
——. Considerationes Generales de Transcendentibus Abelianis——C. ix.
394 [1832]. This memoir lays the foundation of the theory of the
higher transcendents. V. R. p. 75.
—. De Functionibus Duarum Variabilium quadrupliciter Periodicis, &c.
—C. xiii. 55. M. Jacobi here proves the impossibility of a function of
one yariable being triply periodic. V. R. p. 76.
——. De usu Theorie Integralium Ellipticorum et Integralium Abeliano-
rum in Analysi Diophantea.—C. xiii. 353. It is here pointed out that
a problem of indeterminate analysis, discussed by Euler in the posthu-
mous memoirs recently published by the Academy of St. Petersburg,
is in effect that of the multiplication and addition of elliptic integrals.
Suggestions are made as to the corresponding application that might be
made of the Abelian integrals.
——. Formule nove in Theorid Transcendentium Fundamentales.—C. xv.
199. Elegant elementary formule.
_ =. Note von der Geoditischen Linie auf einem Ellipsoid, u. s. w.—
C. xix. 309. M. Jacobi has here announced the important discovery
that the equation to the shortest line on an ellipsoid is expressible by
means of Abelian integrals of the first class. As this is perhaps the first
application made of Abelian integrals since their recognition as elements
of analysis, I have thought it well to mention it in this place. A trans-
} lation of the note is found in Liouville’s Journal, vi. 267.
_-——. Demonstratio nova Theorematis Abelianii—C. xxiv. 28. V. R.
p- 80.
_—- Zur Theorie der elliptischen Functionen.—C. xxvi. 93. This paper
contains series for the calculation of elliptic functions, and a table of
the function q.
_ -—-. Ueber die Additions-theoreme der Abelschen Integrale zweiter und
x, ie Gattung.—C. xxx. 121. We find here some remarkable formule.
q » R. p. 81.
_ ——. Note sur les Fonctions Abéliennes.—C. xxx. 183. This note relates
f principally to the fact announced in M. Jacobi’s letter to M. Hermite.
V. L. viii. 505.
| 88 REPORT—1846.
Jacosi. Ueber einige die Elliptischen Functionen betreffenden Formeln.—
C. xxx. 269.
—. Extrait d’une Lettre a M. Hermite.—L. viii. 505. V. R. p. 82.
—. Extraits de deux Lettres de M. Jacobi, &e.—Schumacher’s Nach-
richten, vi. 33 [Sept. 1827]. They contain the first announcement of
his theorem.
—. Demonstratio Theorematis ad Theoriam Functionum Ellipticarum
Spectantis.— Schumacher, vi. 133. The first published demonstration
of his theorem. See also Legendre at p. 201 of the same volume.
V. R. pp. 47 and 48.
Jircensen. Sur la Sommation des Transcendantes a Différentielles Algé-
briques.—C. xix. 113.
——. Remarques Générales sur les Transcendantes a Différentielles Algé-
briques.—C. xxiii. 126. V.R.p. 41.
Ivory. On the Theory of the Elliptic Transcendents—Phil. Trans., 1831,
p- 349. V.R. p.67.
Lisrr. Sur la Théorie des Nombres.—Mémoires des Savans Etrangers, v. 1.
——. Sur la Résolution des Equations Algébriques, &¢e.—C. x. 167. These
memoirs are referred to in the controversy between MM. Liouville and
Libri.
Liouvitte. Sur les Intégrales de Valeur Algébrique.—Journal de l’Ecole
Polytechnique, cah. xxii. 124.and149. These two memoirs are printed
also in the fifth volume of the ‘Mémoires des Savans Etrangers,’ pp.
76, 105. Poisson’s report on them is inserted in the tenth volume of
Crelle’s Journal, v. infra.
——. Sur les Transcendantes Elliptiques de Premiére et de Seconde
Espéce.—Journ. de l’Ecole Polytech., cah. xxiii. 37. V. R. p. 70.
—. Note sur la Détermination des Intégrales dont la Valeur est Algé-
brique.—C. x. 347. This note is appended to Poisson's report.
——. Sur I'Intégration d’une Classe de Fonctions Transcendantes.—C. xiii.
93. On the same general subject as the preceding memoirs.
——. Sur la Classification des Transcendantes.—L. ii. 56, and iii. 523.
These papers contain an exposition of the principles on which this clas-
sification is to be effected.
——. Surles Transcendantes Elliptiques de Premiére et de Seconde Espéce
considérées comme Fonctions de leurs Modules.—L. v. 34 and 441. It
is proved that these transcendents so considered cannot be reduced to
algebraical functions.
Rapport fait 4 ?Académie des Sciences, &c.—L. viii. 502. =a
on M. Hermite’s memoir. V.R. p. 82.
—. Sur la Division du Périmétre de la Lemniscate—L. viii. 507.
V. R. p. 62.
—. Rapport sur le Mémoire de M. Serret sur la Représentation Géo-
metrique des Fonctions Elliptiques et Ultra-elliptiques—L. x. 290. A
note is appended to this report generalising M. Serret’s theory. V.R.
p- 72.
- Sur un Mémoire de M. Serret, &c.—L. x. 456. V.R. p.73.
Losarro. Surl'Intégration de la Différentielle reer
—C. x. 280. at CE ane
LucuTEeRHANDT. De Transformatione Expressionis
dy
Cc.
Oy Hit(y—-a)(y B)(y—4)]’
—C. xvii. 248.
i ‘ae ,
ON THE RECENT PROGRESS OF ANALYSIS. 89
Ogee
| MacCutracu. Transactions of the Royal Irish Academy, xvi.'76. An ele-
_ gant geometrical proof of Landen’s theorem.
Minpinc. Théoréme relatif 4 une certaine Fonction Transcendante.—
C. ix. 295. The function in question was shown by M. Richelot to be
reducible to elliptic integrals. a6.
. Sur les Intégrales de la forme /“22P¥P, &e.—C. x. 195. An ad-
dition to this memoir is found at p. 292 of the same volume.
——. Recherches sur la Sommation d’un certain nombre de Fonctions
Transcendantes, &c.—C. xi. 373. These researches relate to an exten-
sion of Abel’s theorem.
—. Propositiones quedam de Integralibus Functionum Algebraicarum
unius variabilis e principiis Abelianis derivatee.—C. xxiii. 255. This.
_ memoir is mentioned by M. Hermite.
Poisson. Rapport sur deux Mémoires de M. J. Liouville, &c.—C. x. 342.
V. supra, Liouville.
——. Théorémes relatifs aux Intégrales des Fonctions Algébriques.—
C. xii. 89. V. R. p. 41.
Bete Bemerkungen zum Principe der doppelten Substitution, u.s. w.—
- xv. 191.
dagen De Integralibus Differentialium Algebraicarum.—C. xxiv. 69.
- R. p. 41.
Ricnetor. Note sur le Théoréme, &c.—C. ix. 407. V. supra, Minding.
——. De Integralibus Abelianis Primi Ordinis Commentatio Prima.—
C. xii. 181. V.R. p. 80.
—. De Transformatione Integralium Abelianorum Primi Ordinis Com-
mentatio.—C. xvi. 221 and 285. V. R. p. 81.
——. Ueber die Integration eines merkwiirdigen. Systems Differential-
gleichungen.—C. xxiii. 354. These equations are those known as the
“ Jacobische System.” V. R. p. 78.
——. Einige neue Integral-gleichungen des Jacobischen Systems Differen-
tial-gleichungen.—C. xxv. 97. The results contained in this paper are
much more general than those of the preceding one. V. R. p. 80.
—. Nova Theoremata de Functionum Abelianorum cujusque ordinis
* Valoribus, &e.—C. xxix. 281. V.R. p. 81.
_ —. Ueber die auf wiederholten Transformationen beruhende Berech-
nung der ultra-elliptischen Transcendenten.—_Schumacher Astr. Nach.
xiii. 361 [July, 1836]. V.R. p. 82.
_Roserts. Sur une Représentation Géométrique des Fonctions Elliptiques
de Premiére Espéce.—L. viii. 263.
-—. Sur une Représentation Géométrique des Trois Fonctions Ellip-
tiques.—L. ix. 155. Mr. Roberts’s papers relate to curves formed by
the intersection of a cone of the second order with a sphere. The fol-
i lowing paper contains a more general exposition of his views.
_ —. Mémoire sur quelques Propriétés Géométriques relatives aux Fonc-
tions Elliptiques.—L. x. 297. V. R. p. 73.
Rosenuain. Exercitationes Analytic in Theorema Abelianum de Inte-
- gralibus Functionum Algebraicarum.—C. xxviii. 249, and xxix. 1.
oe VR. p. 41.
‘Santo. De Functionum Ellipticarum Multiplicatione et Transformatione
que ad numerum parem pertinet Commentatio.—C. xiv. 1. V. R.p. 68.
Serrer. Note sur les Fonctions Elliptiques de Premiére Espéce.—L. viii.
145. V.R. p.72.
90 REPORT—1846.
Serret. Propriétés Géométriques relatives 4 la Théorie des Fonctions
Elliptiques.—L. viii. 495.
—. Note al’occasion du Mémoire de M. William Roberts, &c.—L. ix.
160.
——. Mémoire sur la Représentation Géométrique des Fonctions Ellip-
tiques et Ultra-elliptiques. Addition au mémoire précédent.—L. x.
257 and 286. It was on this memoir that M. Liouville made so favour-
able a report to the Institute. V. R. p. 72.
——. Développemens sur une Classe d’Equations relatives a la Représen-
tation des Fonctions Elliptiques—L. x. 351.
——. Note sur les Courbes Elliptiques de la Premiére Classe.—L. x. 421.
——. Sur la Représentation des Fonctions Elliptiques de Premiére Espéce.
—Camb. and Dublin Math. Journ. i. p. 187.
Souncke. /quationes Modulares pro Transformatione Functionum Ellip-
ticarum et undecimi et decimi tertii et decimi septimi ordinis.—C. xii.
178. M. Sohncke here gives the results which he investigates by a ge-
neral method in the following paper.
/Equationes Modulares, &c.—C. xvi. 97. V. R. p. 68.
Taxzot. Researches in the Integral Calculus.—Phil. Trans. 1836, p. 177;
1837, p.1. V.R.p. 41.
On Comparative Analytical Researches on Sea Water.
By Prof. ForcHHAMMER.
In a paper read today in the Chemical Section, I have tried to show that
in the ocean between Europe and America, the greatest quantity of saline
matter is found in the tropical region far from any land; in such places 1000
parts of sea water contain 36°6 parts of salt. This quantity diminishes in
approaching the coast, on account of the masses of fresh water which the
rivers throw into the sea; it diminishes likewise in the westernmost part of
the Gulf-stream, where I only found it to be 35-9 in 1000 parts of the water.
By the evaporation of the water of this warm current, its quantity of saline
matter increases towards the east, and reaches in N. lat. 39° 39' and W. long.
55° 16’, its former height of 36°5. From thence it decreases slowly towards
the north-east, and sea water, at a distance of sixty to eighty miles from the
western shores of England, contains only 35°7 parts of solid substances ; and
the same quantity of salt is found all over the north-eastern part of the At-
lantie as far to the north as Iceland, always at such a distance from the land
that the influence of fresh water from the land is avoided. From numerous
observations made on the shores of Iceland and the Faroe islands, it is evi-
dent that the water of the Gulf-stream spreads over this part of the Atlantic
Ocean, and thus we see that water of tropical currents will keep its character
even in high northern latitudes.
Besides the southerly direction which any current flowing from the north-
ern polar regions must take, it will, according to well-known physical laws
depending upon the rotation of the earth, always take a direction towards the
west, and thus be driven towards the eastern shores of the continents, while
any tropical current flowing towards the north will, according to the same law
of rotation, take a direction towards the western shores of the continents. —
This is at present the case in the Atlantic Ocean, and its effects upon the
shores of Europe, which by a branch of a tropical current are surrounded by
warm water, produce a mild and moist climate.
ANALYSIS OF SEA-WATER. 91
_ The water of the different seas is much more uniform in its composition
_ than is generally believed. In that respect my analyses agree with the newer
_ analyses of atmospheric air, in showing that the differences are very slight
_ indeed. Sea water may contain more or less salt, from a very small quantity,
as in the interior part of the Baltic, to an amount of 37°] parts in 1000 parts,
_ which I found in water from Malta, and which is the greatest quantity I ever
_ observed ; but the relative proportion of its constituent saline parts changes
_ very little.
In order to get rid of those differences which might arise from the dif-
ferent quantity of saline matter in sea water, I have compared sulphuric acid
oo lime with chlorine, and the following results are the mean of many ana-
lyses :—
In the Atlantic, the proportion between chlorine and sulphuric acid is
10,000 : 1188; this is the mean of twenty analyses, which differ very little
from each other.
In the sea between the Faroe islands, Iceland and Greenland, the same
proportion, according to the mean of seventeen analyses, is 10,000 : 1193.
In the German Ocean, according to ten analyses, it is 10,000 : 1191.
i In Davis's Straits, according to the mean of five analyses, it is 10,000: 1220.
In the Kattegat, according to the mean of four analyses, it is 10,000: 1240.
_ Thus it appears that the proportion of sulphuric acid increases near the
shores, a fact which evidently depends upon the rivers carrying sulphate of
_ lime into the sea.
The proportion between chlorine and lime in the Atlantic Ocean, according
_ to the mean result of seventeen analyses, is 10,000 : 297; and in the sea
_ between Farde and Greenland, according to the mean of eighteen analyses,
it is 10,000 : 300.
In the longitude of Greenland, and more than 100 miles to the south of
the southernmost point of that large tract of land, sea water contains only
35°0 in 1000 parts. In going from this point towards the north-west it de-
" creases constantly, and in Dayis’s Straits, at a distance of about forty miles
1 from the land, it only contains 32°5 parts of salt in 1000 parts of sea water.
_ This character seems to remain in the current which runs parallel to the
shores of North America; and at N. lat. 433° and W. long. 464 the sea water
_ contained only 33°8 parts of salt. Thus tropical and polar currents seem not
_ only to be different in respect to their temperature, but also in the quantity
_ of salt which they contain ; from which it appears, that while the quantity
_ of water carried away from the éropical sea by evaporation is greater than
_ that which rain and the rivers give back to that sea, the reverse takes place
in the polar seas, where evaporation is very small and the condensation of
_ vapour very great. The circulation must on that account be such, that a
"part of the vapour which rises in tropical zones will be condensed in polar
regions, and in the form of polar currents flow back again to warmer climates.
_ Although my analyses are only made on water from the ocean between Eu-
Tope and America, yet little doubt can be entertained that that part of the
Ocean which separates America from Asia is constituted in a similar manner,
and that currents flowing from the poles are the rule, and currents flowing
wards the poles the exception.
_ Lime is rather rare in the sea around the West Indian islands, where mil-
lions of coralline animals constantly absorb it, the proportion according to
five analyses being 10,000 : 247; and it is rather copious in the Kattegat,
here the numerous rivers of the Baltic carry a great quantity of it into the
oe
ey
ocean. The proportion is there, according to four analyses, 10,000 : 371.
‘
a
"
92 REPORT—1846.
On the Calculation of the Gaussian Constants for 1829. By A. ERMAN.
As purely theoretical speculations on natural phenomena remain highly
unsatisfactory until they can be founded on a sufficient number of observa-
tions, in the same manner collections of the most careful observations must
be almost useless before they are thoroughly elaborated according to a given
theory. Nay, the accumulation of observed numbers, notwithstanding the
value they possess when viewed by themselves, may even become injurious
to science, by retarding its progress. Indeed the aspect of progressively in-
creasing, but not duly elaborated, materials, must at last give rise to the ap-
prehension, both on the part of those engaged in furnishing them, and of
every one interested in the results to be gathered from them, that the means
may be wanting to bring such a stock of matter to bear for their proper
purpose. The loss of the whole, that is to say, of data which have not been
acquired without the exertion of considerable scientific labour, and which
seemed pregnant with beautiful germs, would then be a most discouraging
consequence.
The British Association for the Advancement of Science has many times
proved itself convinced of the truth of this principle. A resolution adopted by
the Association in 1833, during its first meeting at Cambridge, warded off the
peril just mentioned, even from a department of science whose long-established
rate of progress had not been able to protect it sufficiently against such a
risk. The reduction of the Greenwich observations of planets, undertaken in
consequence of this resolution, and now published by order of the Lords
Commissioners of the Admiralty, has been fully appreciated by all astrono-
mers, and particularly by the late M. Bessél, who in the last moments of his
life welcomed it as the beginning of a new period in astronomy. Moreover,
the condition that a uniform progress of observation and calculation is equally
indispensable in less-developed or only nascent branches of physical science,
has been expressed by the British Association at its second meeting at
Cambridge in 1845; first, by several of the members being inclined to
raise the question, whether the continuation of magnetic and meteorological
observations were desirable, as long as a great part of the materials collected
by them are still waiting their first employment ; and, secondly, by including
the calculation of the Gaussian constants of terrestrial magnetism for 1829
within the sphere of their own operations, being pleased at the same time to
entrust me with the superintendence of the same, and to place at my disposal
the sum of £50, granted for this purpose for the year 1845 to 1846. I shall
endeavour to point out in a few words the fruits this arrangement seems to
promise, and the results it has already obtained.
I think we are authorised to suppose that all those phenomena which we
have learned to express by numbers, with the help of remarkably accurate
instruments, will at length lead us to a theory of the forces which produce
them ; and that, in consequence, the intriusic value of observations on such
phenomena—a value which hitherto could not be demonstrated—will then
at once become most evident. It was this expectation alone which often
encouraged observers to persevere in labours apparently rather tedious, and
the zeal with which the meteorological and part of the magnetic variations
are pursued by your members in British and colonial observatories, is, I think,
attributable to the same cause. In the branches of physics which they cul-
tivate, these observers, it is true, have still to look to futurity for both kinds
of progress, viz. the discovery of an abstract theory, and the true establishment
of the same by means of observed numbers. As to the first and most import-
A
ON THE GAUSSIAN CONSTANTS FOR 1829. 93
ant of these steps, they have a consolation in the fate of their predecessors
in most similar labours: I allude to the long series of philosophers who de-
voted themselves during the first thirty years of this century to ascertaining
the mean values of magnetic elements for as many points on the surface of
the globe as possible, and whose undertakings are so carefully recorded by
one of them—I mean Col. Sabine, in his admirable report on magnetic in-
tensity. They too were long enough under the necessity of restricting the
immediate application of their operations to refuting some evidently super-
ficial or erroneous theoretical views, and then, after detaching from their re-
sults every accidental influence, to register them in the annals of science, as
contributions to a theory which they only hoped might be attained. But M.
Gauss’s admirable theorem, that any terrestro-magnetical element, that is
_ to say, any observable part of the intensity of magnetic force at a given point
of the earth, or any angle formed by this force with a given plane or line, can
be represented by combining with given functions of the latitude and longi-
tude of this point a limited number (probably twenty-four) of constant quan-
tities, and the way pointed out by him for deriving these constants from a
sufficient number of observed mean values of magnetic elements, have ina
short time so completely realized these hopes, that a great encouragement
was held out, both to former observers of mean magnetic elements, and
to those who were then, and are still employed in less-advanced branches of
physics: nevertheless this encouragement was but an imperfect one. To
complete it, the possibility of applying those former observations had to be
changed to a reality. On this account I am inclined to think that the com-
mittee appointed to conduct the cooperation of the British Association in the
system of combined magnetic and meteorological observations, have parti-
cularly contributed to the satisfaction of their own observers, by encouraging
the calculation of the Gaussian constants for 1829; for, by so doing, they in the
first place have confirmed their adhesion to the general principle, that no set of
observations whatever must remain longer than is indispensably necessary
_ without reduction to theory; and secondly, they have made the immediate ap-
_ plication of the mean magnetic values for 1845, that may be furnished by the
combined British and Russian observatories, the more probable, as it will then
_ be already preceded by a similar application of the analogous values for 1829.
_ Besides this, to prove the influence of your resolution on the department of sci-
ence most directly connected with it, I may remark that a more and more exact
_ determination of magnetic constants (the Gaussian) is equally indispensable
at the present moment (and for the same reason), as the obtaining of the con-
_ stants for planetary orbits was formerly, from the moment in which Kepler’s
_ and Newton’s discoveries opened a possibility of arriving at them. Whatever
~ may be the analogies once to be found in magnetism for the secular varia-
tions and other perturbations of planetary orbits, the entrance into these
“untouched fields of science cannot fail to be effected by fixing the actual
values of Gaussian constants. ©
It was under these circumstances that I long ago felt it to be a debt I had
contracted towards science, that the magnetic elements which I observed
_ from 1828 to 1830, at about 650 equidistant stations, on a line encircling
| the globe, between latitudes 67° north and 60° south, conjointly, perhaps,
with the magnetic elements that had been observed in Europe during the
Same years, should be fully applied to the development of the now existing
‘theory. For the undertaking of such a work, however, it was evidently ne-
_ essary to have more time at my disposal than I have ever enjoyed. M.
_ Henry Petersen, too, a most industrious and talented young mathematician,
_ who in 1842 had undertaken and performed at my request a small part of
|
——*
94 REPORT—1846.
this comprehensive task, found his leisure hours unequal to its completion.
Now, on the contrary, the support of the British Association has enabled and
induced this gentleman to suspend his other official duties for the year just
expired, and to devote himself entirely to the prosecution of the work in
question, in which his success will, I think, be appreciated by the Association,
from the results which I have the pleasure of laying before you, accompanied
by some remarks on the means employed to obtain them. What proportions
these one year’s results bear to the final term of the whole labour, and how
far they deserve to be continued, is a subject which I shall take the liberty
of touching upon at the conclusion of this paper.
The object of the calculations committed to my superintendence may be
stated to consist in finding, by a sufficiently large series of observations,
twenty-four corrections,—
BY, AGP Ry ERO wets tyhshi ves nen cve va Ag'!, Ahi},
to be singly applied to the twenty-four preliminary values,
g*, g*, hts, ht? AOC ew eee eee sereeeeesoes g, 1,1,
which M. Gauss assigned to the constants of terrestrial magnetism, and in
calculating at the same time the probable errors of the so-corrected constants.
To this effect (preserving the literal denominations used in M. Gauss’s theory
of terrestrial magnetism, and marking by AX, AY, AZ, Aw, wAd, pAi, the
differences (theoretical value—actual (or observed) value)), the following
expressions have been derived :—
0=AX + Ag!°sinw—cosu(Ag')!.cosA + Ah!.sin A) +2 cosu.sinu.Ag®°
—cos 2u.(Ag*®!.cos A+ Ah®!.sin A)—sin 2 w(Ag??.cos2A
+ Ah®2. sin 2a)+3 -Ag°.( cos? u—=)sinu—( 3 cos? u—2 cost).
(Ag3:!. cos A+ AA3:!. sin A)—sin %.(3 cos? w—1)(Ag>?. cos 2A
+ Ah3*.sin 2A)—3 cos wu. sin? u(Ag>3 . cos 3 A+ Ah3.5 .sin 3 A)
27
3 , 3 (1.)
+4(costu—5 cos w)sin u.Agt?— (4 cos u* 7 cos? % ++ =)
(Ag*!.cos A+ Ah*! sin A) —2(2 cos’ —F00s usin u.(Ag**.cos20
+ Ah**.sin2A)—(4:cos*u—1)sin?u(Ag*.cos 3 A+ Ah*3. sin 3A)
—4 cos u.sin’ u(Ag*:+.cos 4A+ Att. sin 4A).
O=AY + Ag!!.sinA—Ah!s! . cos A+ cos u (Ag®:! . sin A—Ah®! . cos A)
+2 sinu(Ag®?.sin2 A—Ah**.cos2A) + (Ags:!.sin A — AAS! cosa).
(cose u-=) +sin 2 u.(Ag’:?. sin 2 A—Ah3:2 . cos 2 A)
+8 sin? w (Ag%-’ . sin 3 A—Ah33 . cos 3A) + (cos? u—= cos u). (2.)
(Ag*!.sin A—Ah*!.cos A)+ (2 cos? u—; sin u(Ag+?.sin2 a
—Ah*? cos 2A)+3 cos uw. sin? u (Ag*> .sin 3 A—Ah*3 cos.3 A)
+4 sin’.u (Ag**. sin 4 /—Ah*+* .cos 4A).
!
y
ON THE GAUSSIAN CONSTANTS FOR 1829. ' 95
a
O=AZ+2 cos uw. Ag'°+2 sinu. (Ag'! . cos A+ Ah!) . sin A)
+.B eos? w—1) . Ag? +3 cos u . sin w (Ag! .cos A+ Ah! . sin A)
}
. + 3sin2u(Ag*?.cos 2A + Ah®*.sin 2 A)+ (4 cos$ u -2 cos u) Ags?
+ (4 costa —= )sin & (Ag>:!cos A+ Ah! sin A) +4 cos u sin? wv.
(Ag32.cos2.A + Ah32.sin 2A) +4sinw.(Ags.cos3 A+ Ah®.sin3a) ¢(3-)
+ (5 cos wa cos? + =).ag'" + (5 cos? u-2 cos u).
sin u (Ag*! cos A+ Ah*! sin A)+ (5 cos? u—2) sin? u(Ag*®.cos2A
+ Ah*!2 sin 2 A)+5 cos 4. sin’ w (Ag? .cos 3 A+ Ah*3 .sin 3 A)
+5 sint uw. (Ag**.cos 44+ Ah**. sin 4A);
and denoting by AX, AY, AZ their just-mentioned developments according
to the corrections of constants,
O=Aw —cosd. AX Se) Se er C2)
O=w.Ad.+sin 3. AX 008 GA Yo,s (ope. oe ijouihen Ga)
O=w. Ai +sin i(cos .AX+sin d.AY)—cosi.AZ . . (6.)
and then 283 numerical primary equations, relating to magnetic elements,
observed on a line from Berlin to the east coast of North Asia, at the port
of St. Peter and St. Paul, have been formed, by alternately recurring to one
or the other of these six formule. For the sake of uniformity, their first term,
which always meant the value of the magnetic element calculated with M.
Gauss’s numbers—the observed value of the same element,—has always been
marked by the letter x, independently of its having been derived by the Ist,
the 2nd, ...... the 6th of these formulz ; and also the whole numerical primary
equation has been represented by
O=n + coeff.Ag*°.(Ag*°) + coeff.Ag*!.(Ag*!) + coeff-Ah*}.
4q 4 0 meter + coeff.Ah's!.(Ah"),
_ independently of their origin from formule (1) (2) ............ or (6).
In five of the accompanying tables you will find, according to these de-
- nominations,—1. the numerical values for
log. n, log. coeff. Ag+°, log. coeff. Ag*', log. coeff. Ah*...... log. coeff.Ah!>! 4,
furnished by each single element; 2. the name, the latitude and the lon-
gitude of a station to mark the place of observation; and 3. one of the letters
_X, Y, Z, w, ¢ or i, which respectively indicate that the observed element has
been the northern or the western component of horizontal force, the vertical
force, the whole horizontal force, a declination or an inclination*. In the
three last cases in which therefore ~ denotes the value of Aw, of wAd, or of
WAitt, it must still be noticed that the values of the declination (¢) in the
first, and respectively of the horizontal force (w), or of the total force (f) in
‘
:
;
|
n* of is understood that, according to M. Gauss’s memoir, the meaning of the letters em-
Dloy is—
X Northern horizontal force. 3 Declination.
Y Western horizontal force. i Inclination.
w Total horizontal force. wu North polar distance of the station.
Z Vertical force. a Longitude east from Greenwich of the
_ 4p Total force. station.
Instead of log. coeff. the further abbreviation |.c. being usually employed.
The arcs Ad and Ai being previously changed to the ratio of their sines to unity.
96 REPORT—1846.
the two other, being only approximately required for this purpose, have been
merely calculated by theory, viz. by those values of constants which we are
about to correct.
The correctness of the numbers in those 283 primary equations for the
twenty-four unknown, has then been controlled by determining the theoretic
values of the X, the Y, the Z, or of the two or three of them that were required
for the composition of w, of tang @ or tang 2, a second time in a somewhat
different way. It consisted in calculating according to
X=F(u)+F' (u) cos A+F" (wu) sin A+ F™ (w) cos2 A
2 eee +F™(u) cos 4A+F"™"(u) sin 4A,
or to a quite analogous expression for Y and Z, for which the nwmerical values
contained in F(w), F\(u)..... E(w) are given as resulting from the pre-
liminary values of the twenty-four constants in M. Gauss’s theory of terres-
trial magnetism, § 27.
This part of the task being completed, the second, and by far the most
laborious one, consisted in forming out of the coefficients in each primary
» 25 x 26.5 ws
equation 9 = $325, and therefore altogether 325 x 283=91975 products
of two factors, each according to this form,—
ae A CAGE Ye Ieee Ne sisnis tna tae ole vosce'ocedsncnnbes ans n.(c.Ag'), n(c.Ah!"),
(c.Ag*°).(c.Ag*°), (c.Ag*°).(c.Ag*!),...(c.Ag?).(e.Ag''), (e.Agt?).(c.Ah!1),
(c.Ag*!).(c.Ag*!), ... (e.Ag*!).(e.Ag'!), (e.Agt!).(c.Ah!"),
SOR e eee reese see sesessseseee
See mem eee eee eeeeeeeeeeeeeseses
(c.Ag?').(e.Ag'"), (c.Ag'!).(e.Ah''),
(c.Ah!)!).(¢.Ah!").
The 283 products, assembled under each of these 325 titles, were then
separately summed up, and by this means (marking by [ ] a sum of analogous
terms) the twenty-four final equations of the following form were obtained: —
— [n.(e.Ag*?) ]=[(c.Ag*?).(e.Ag*?) ].Agt?+ [(eAgt)(c.Agh!) ].Agt!+..
+ [(c.Ag*?)(e.Ag'!) Ag+ [(c.Agt)(c.Ahe!)]. Ahh,
_ inane ee [(c.Ag*!).(c.Agt) ].Agt° + [(e.Ag*!)(ce.Ag*!) ].Agt!+..
eee et + L(¢.Ag*"')(e.Ag'!) ].Ag!! + [(e.Ag*!)(e.Ahb!)]. AA,
— [n.(c.Ah*!)] = [(e.Ah*!).(c.Agt?) ].Agt? + [(e.dht!)(c.Agt!)].Agt! +.
Boch EA + [(e.Ah*!)(e.Ag'!)].Ag'! + [(e.Aht!)(c.Ahb!)] Ak'!,
—[n.(e.Ah'})] = [(e.Ah!) (e.dg4) ].Ag49+ [(cAh!!)(c.Agt!)].Agtt +.
Srseestsane + [(¢.Ah).(e.Ag'!)].Ag!! + [(c.Ah!)(c.Ak}!) ].ARL
The numerical expressions of these equations will be found in the table
marked VI. Hitherto they have been controlled by the calculation leading
to them from the primary equations, being repeated a second time in the
same manner as the first, but with the suppression of one decimal figure in
the products and in their sums. To obviate the danger, arising from the ad-
dition of such extensive rows of numbers, lest the compensation of opposite —
errors might produce an illusory agreement, M. Petersen, besides the forma-
tion of new primary equations, has proceeded to subject these final equations
to another kind of control,—I mean the process usually employed in similar —
re eee
ii
1,
qu
" ON THE GAUSSIAN CONSTANTS FOR 1829. 97
cases, and which consists in the formation for each primary equation of a
supplementary term s, equal to the sum of the other, viz. in one case, in the
calculation of
s=coeff. Ag*:° + coeff. Ag*:! + coeff. Ah*:!+.....+ coeff. Ag!:! + coeff. Ah!)!,
whereby we obtain as controlling equations, .
[sz] =[n.c.Ag*° ] + [n.c.Ag*!] + [n.c.Ah*!] +... + [2.c.Ag'!] + [.c.Ah'1],
[s.c.Ag*]=[ (e.g) (c.Ag#")] +[(eAg*®)(e.Ags!)] tut [(cadg'?)(ALY)],
MIAE (C0. AblA)(oiAg4\] 44 calen scscccsccneeceoE Gecdhl)(@AROI) I>
independently of the extension which is given to the sums marked by [ ].
If we now consider, in the first place, the linear primary equations con-
tained in the Tables annexed, we shall find that the values of the Gaus-
sian constants hitherto accepted sufficiently approximate to the truth to
authorise the supposition from which we start, that the powers of their cor-
rections superior to the first can be neglected ; but, on the other hand, that
these values are still so erroneous, that the elements calculated by them differ
from the empirical ones by far more than can be ascribed to errors of obser-
vation, and in quite another manner than would arise from local irregularities
of terrestrio-magnetic power. Indeed we see that when the places of obser-
vation are in similar parts of the globe, the values of 2 belonging to them
remain nearly enough equal to each other; whereas on the longitudes of the
places increasing, these values of m are gradually lessened, and at length
replaced by a series of values with opposite signs. Of course, to observe this
regularity of progress, we must only compare such values of 7 as relate to
magnetic elements of a similar character; as for instance, all to 2, or all to
_ w, and so on.
_ The value [nn ]=233423, marked in the Table of Final Equations as re-
' sulting from 283 equations, shows that for the part of the earth on which
the observations hitherto considered have taken place, the inean difference
between an observed magnetic element and the corresponding calculated one
amounts to 29, the intensity of the whole force at Loaten being =1372 ; and
_ in agreement with this result, we find, for example, by immediate inspection
of the Table of Primary Equations,—
Lat. 56. | 56. | 67. | 54. | 59. 56.
The mean difference —E——E—————EEE— EE
Long. 43. | 60. | 67. | 100.) 145.| 222.
Tn northern horizontal force} +46, |+39)+23/— 6/—28 4.35
In western horizontal force +18 |+19/+40) O|—25
| In perpendicular force ...... +11 {+13)+35)—15|/+30) +38
in whole hori-
zontal force
The concluding table contains besides, as already mentioned, twenty-four
final equations for the twenty-four unknown quantities, by which, mathema-
tically speaking, the whole problem in question would appear to be ready for
a definitive and now most easy solution. In practice, however, this is evi-
dently far from being the case. Thus indeed it is plain, even at a first
glance, that each observation, hitherto registered, has already contributed
to the solubility of the problem all that it will ever be able to do; there
is not in this circumstance alone a sufficient reason for that solubility being
re and then that, on the contrary, the probability of the value to
— -:1846. H
98 REPORT—1846. ‘
t
be obtained for any one of the twenty-four unknown quantities, for ex- —
ample, Ag!' depends entirely on its weight, that is to say, on the magni-
tude of the coefficient with which this quantity remains in the equation —
containing at the origin the terms ...... + [(c.Ag!!).(c.Ag'!)].Ag'!, after
the elimination of the twenty-three others ; and that these weights, as is easily —
shown, will only become sufficiently extensive when there are neither two
nor more of the unknown quantities whose coefficients remain in a constant,
or in a nearly constant relation in the whole series of primary equations, tri-
butary to the final ones. Hence the examination in this same respect of the
above expressiuns for Aw, Ay, .........++. Ai, will easily show that by reason
of the similarity of the latitudes in which by far the greatest part of the ob-
servations till now calculated have been effected, the solution of the final
equations as hitherto obtained would give but a very trifling weight to almost
all the corrections we are seeking for, and therefore be still without interest.
Even the seventy elements that, according to date of observation, follow
next to the 283 finished ones, and for which M. Petersen has also nearly
accomplished the primary equations, will, by their contributing to the final
ones, most sensibly improve them in respect of solubility. Indeed in full
opposition to the now finished ones, these latter elements relate to points of
a line rather northern than eastern in its direction, and extending from 57°
latitude north to about the equator. It is therefore precisely those unknown ~
quantities whose coefficients have hitherto exhibited the least variations, or
followed in their varying a course parallel with that of the coefficients of
other unknown ones, that will vary the most, both relatively and absolutely
speaking, in the set of primary equations next to be formed, and thus will
add to the final equations just what is requisite for increasing the weight of
each of the quantities sought for and thereby preparing their due separation.
M. Petersen will at all events subjoin, in the course of the ensuing months,
this next continuation of his present labour, which I shall then forward to the
Association.
It is plain, notwithstanding, that even then we shall not have reached the
most favourable state which our fund of observations for the year 1829 would
allow of attaining in the knowledge of the Gaussian constants for the same
year. Indeed even then, by substituting, as could be effected through your
further patronage, a full execution of the task to a but partial one, the places
of observation contributing to the final equations may be trebled, and what
is still more important, a considerable improvement be attained in their re-
petition over the globe.
I thought it my duty to submit to the Association my opinion of the
benefits to be derived from the continuation of M. Petersen’s labours, leaving
it to their decision whether they will consider it advisable to grant him their —
further support in devoting himself entirely to the prosecution of his task.
835m |3°31498n |9°48677n
62337 |8°32996n |9°48 5297
7790650 |9°45285n
8°87940 |9°17657n
8°87372 |8°47099n
8°84974 |8°33986n
$°89717 |8°14350
$°96857 |8°81254.
8'96640 |8°92877
8"90906 |9'00657
8°59045 |9'29898
8°46569 |9°37007
$°64810 |9°38158
9°67581n 19°38 7814,
9°67603n |9°87835
9°65364n |9°89819
9°58289n |9°954.16
9°55004M 19°96 567
9°54.970N |9°96487
9°53368n |9°96639
9°508 107 |9°96613
9° 500697 |9°96388
9°499877 |9°95945
9°4.7524N |9°93149 |
9°4605 5 \9°91924.
9°44.99 52 |9°92003 |
9°74430 |9°62987
9°74.504 |9°62756
9°75721 |9°61558 |
9°75777 |9°63108
9°78061 |9°58067
9°79616 |9°53372
9°80841 |9°49290
9°82241 |9°42509
9°83297 |9°35665 |
9°84630 |9°24762
9°87632 |8*70909 |
9°87978 |8°57363 |
9°89227 |8°38284n
9°90866 |9°06160
9°91535 |g°17617”
9°92172 |9°243067
9°92757 |9°29531"
9°93353 |9°34119"
9°94380 |9°43176n
9°95197 |9°49765”
9°96138 |9°56069n
9°96279 |9°58373%
8°89625 19°504837
8°87698 |9°281227
8°33713” |9°262437,
8°63757M |9°221607
8°44862n 19°1734.37
8°12926n 9'1 10944
{e«
|
1
ey ————— -
: TABLE OF PRIMARY EQUATIONS FOR THE GAUSSIAN CONSTANTS IN 1899. ¥
[To face puge 98.
Log. nef. Log. coef, Log. coef,
ap i B ah
Stations and observed elements.
0, By"). Alt, Ag’ AltA, Agi. AlAs,
| =r | = —-
H50215 19°74494 |9'27112 |9°03775 |9'17975n |9'42879n|7'89258 [9°69 968n\9'35279 I9'57074n|g'91651 |8°54835n 8°31498n |9°48677n 9'73581n S'00672 |9°81382n|9r93804 |9'63364n |9'40027n 19°69 r0n |9'S7814N |9'69974 |9'87349n |9'6gor2N
154580 19°74535 |p'26864 |9'03629 |9'179150 |9"43027n|7'96985 \9'6g922n |9'35453 9*5685on |9'91649 /8'56233n /8:32096n|9'48529n 9'73641n 8'08369 |9'81306n |9'93775 |9'63428n 9'40193n Biren '9'87835n \9"69929 [9'87338n |9'6g 1030
163175 1972600 |9°34813 19113233 |910590n|9'39191|(8°55486. |9'71552n |9'44798 19°59843n|\9°91702 |8'12229 |7°90650 |9-45285n 9°73886n 8'68201 |9'84267n '9°58919” 19'37339n 9'61218n |9'Sq8t9n|\9°71786 |9°86246n |9'64666n
180693 9'67578 9'42938 19°31653 |8'72354n |9'30395n 19132986 |9°70380n|9'71024 |p'46194n|9:91167 |8'99225 |8°87940 197176570 \9°75698n 9'48542 |\9'85936n 49°45287n |9°35002n 19°37375n \9'95416n |9°75032 |9'81597n [9703120
174008 |9'68424 19797795 19735536 [803651 |\9°3 30940 |9'55154 |9:61651n \9°75673 |8:75541n|9-91296 |8:89533 887372 |8"47099n |9°77442N 19'70270 |9°76767n 9439347 |9°41774n |8'66224n J9'96567n |9'74582 19'77938" 19'75778N
166652 19168767 19'36818 |9°35228 |7'91274n|9'34893n [9'56008 |9:60798n\9'75286 |8°61831n |p'91345 8'86564. /8'84974 |8'33986n |9'77605n 970444 |9'75724n \9'96516 |9r42276n |9'42686n|8+52868n or96487n 9°74392 |9'77750n |9'70160n
—__ :
Log. epef.|Log. coef Log. coef: Log. coet|Log. coef Log. coef.|Log. coctLog. coef |Log. coefLog. coef|Log. evef|Log. coef |Log. coef Log. cott Log, eoeflLog. eoet| Log. eoet Lon. f !
Log. HN Ah Bhi, | AgA3, 3, ae, | ays. | alan ap2. | ale, | a. | Ai Age, | syate| Vesti eel
Petersburgh, 1-.-..
Petersburgh, 2.
Nowgorod -
Moskwa, 2-
Doskino-......
Nijnei Nowgorod........
Tcbugunul.-... 56 6 1166717, [9°68328 19'36291 I9'47307 |7'70689 |9°33783n|9°60r47 |g:57097m\9'75978 [843011 |orgx282 |8'88701 [889717 [814350 9°77444N |9°75316 |9°72266n|9°96651 |9°42190n|9743206n|8°33545 |9'96639n |9'74636 |9'76346n |9'7736an
Angikowo . F 173340 |9°67529 19195563 19740359 |8'35849 |9'31459n|9'65013 |9°50386n|9'76025 |9'11053 g'91158 |8'92061 896857 [8'81254 |9°76864n \9'80593 |9°65966n \9'96877 |9°38761n|9°43557n \g'01003 |9'96614n |9'75054 |9'74138M |9'78034n
Kasan... 1172107 19'67668 |9'34506 |9'40783 |8°47778 |9'31634n|9'66464 |9'47088n\9'75082 |g'22252 9'91180 |8'90364 [896640 [8192877 |9'76733n |9'81974 |o'62s08n 996839, |9°38173M |9°44450m|9'12532 [9°96388n|9°74983 |9°73738M|9'79014n
Mitjechka 1167624 (968556. |9°32364 |9°39831 {857487 |9°33741n|9'67277 |9'43938nl9'73117 |9'28282 |9'91314 |8'33439 8190906 j9'00657 |9°76911n \9'82326 |9'58988n|9°96583 |9'39058n|\9.46525m (919691 |9"95949n \9'74512 |9'7a864n \9'80331N
Dubrowa - 161972 19'71308 921933 [9136617 |8'92528 |9'38798n|9°70646 |9'17751n|9'608qx |g's0a14 |g:91031 [844361 S*59045 |9'29898 |9'76168n 984155 |9:31260n|9°95585 |9'39627n|9'54311m\9°46879 |9'93149n |9°72783, \9'6g087N|9'83771N
Perm «+ 158591 19°71837 \9'18572 19'36053 |9'00726 |9'3908om|9'71313 |g'01g03n|9°55248 |9:55141 |9°91669 |8'29088 8'46569 |9°37007 |9'75361n|9'84505 |9r14585n|9'95351 |9°38743n |9's6224n|9°53570 |g'91924n |9'72396 |9'67346n |9'S48a7n
Krullasowo ..+..
Potersburgh, tess
sree .)57 33 45] 56 37 38 l1"s2009 [9171067 J9'20192 19°38323 |9'00307 |9'36988n |9'71912 |8'97066n |orss45q 9'57742 |g'gx61x 846679 |8'64810 |9:38158 |9°74839n [985558 [g'107127[9'95683 |9°36841n|9°s4972n|9°55322 |992003n 9172947 |9°66676n \9'84807n
se M159 56 17 $2)r1g988 | —oo I9'14599 |9°37936m 19'72352 |9'47448n|9°81382 |8:co672 |grb3347 [9'41552 | —zo |9'44250 |9:67581n|9'8781q |p-62910n 19'87655 [806945 | —s |9'64012 |9'87349n|9'94087 [9°69183n| —c2 [9'70285 |9'9362an
Petersburgh, aa rtadon | See j9'24760 |9:37995"|9'72395 |9'47283n |9'81306 |8'0836 |9'63108 lorgr7ax | —oo [9'44368 9:67603n|9'87835 |9'62723n|9'87564 [814627 | —oe 9164103 |p'8738ml9-94094 l9'68q81n| —eo |9°70361. lo°93506n
Nowgorod . 2/1"19003 = 19'12190 19°33769n |9'73406 |9'4480sn |9'84267 |8°68201 |9°66758 |9'51713 = |9'43785 |9'65364n|9'89819 [p61218n|9'91182 [875116 | —co |9°64666 |9'86246n|9796734 |9'68133n| —o2 |o°71582 |9'93162n
Moskwa, 2. 18 |1'23704 | —ce |p*x0921 |9'22206n |9'76961 |'18920n |9'85936 |9'48s42 |9°s4463 |9'79293 | —oo |o'47004 19°58289n |9°95416 |9°37475n 206 |9°56812 | —oo [9770312 |9'S1597n|0'03685 |o'45644n| —co |9'78s8r |o'8q866n
Doskino... 36 |1'23603 | oo |9:17478 |9'19638n|9'78425 |8'48082n|9'76767 |9'70270 |8'83605 |9'83737 | —oo |o:s2Rqq Ip*sso0qn \9'96567 |8'G6224n \9'34831 |9°78335 | —s> |9°75778 |9°77938n\o'04631 |8'74288n| —co |9'83842 |9'86c02n
Nijnei Nowgorod ... ssseeee 156 19 20] 43 57 4|1'29270 | —o2 |'18308 19°19898n |9'78474 |8°34855n|9°75724 |9'70944 |8'69810 |9°83265 —2 19°53380 |9°5497cn |9'96487 |8*52868n |9'83703 |9°78923 = |9'76160 |o°77750n|0'04466 |8'60847n| —co |9'84139 |9'85729n
2
Tebugunui sss... ++. crores ys{56 6 241 45 go 1211'23905 = |9°18936 |9°17920n |9'78460 |8:15366 |9°72266 |9°75316 |8'51099n|9'84066 | —co |9°54384 19°53368n |9°96639 |8°33545 [9'8035q |9'S340g | —eo |9'77362 |9'76346n |0'04727 |8'41633 —™~ 985450 |9'S44q4n
Angikowo . Jorg1sg0 | ee j9'19483 |9'14687M|9'78141 [882531 [9165966 980593 |9'19333n|9'84305 | —e |9°55606 |gr50810m|9r96613 |gro1c03 |9'74346 |9'88873 | —oo |9°78934 |9'74138n\0'04893 |9'09283 | —co |o'87214 lo:8aqisn
Kasan. 33 |1103060 | —2 19/0374 |9'14063n19'77965 |8'94109 |9'62598 |9'81974 |9'30499n|9'83329 | —e |9756346 |g*sco69n|9r96388 lo12532 970845 |o'90221 | —2o 19°79614 |9°73538M |0'04634 |9'20778 | —ce |o'8786x |g'81s84n
Mitjechka . 4|roo860 | ea g-az201 Ipr14734n19'77851 I9'01597 |o's8988 |9'B2326 [9°36314n|9'B1149 | —e> |9'57454 |9r49987n |9'95045 |g'19691 |9:67020 |9°90358 | —cxo |9'8033x |9'72864n 0103977 |9'27723 | —oo 9'88363 |9'8o896n
Dubrowa ... 129688 | —a5 I9'29391 |9'14707m |9°76160 |g'ag8g0 [9'31260 |9'84155 |9"57515n|9'68192 | —oo |9'62208 |9'47524n|9'93149 |9'46879 [938561 |o-91456 | —e [9:84771 |o'69087m|o'co450 |9's4180 | —oo |orguo7a |9r76388n
Perm... ++ . 114) 56 13 56 )12167 | —oo |:g1210 |9°13129n|9'75164 |9'36810 |9'14585 |9°84505 |9'6228qn|9'62396 | —co 9"46055n [9'91924 |9'53570 [9121743 |9'91653 | —c2 |9'84827 |9'67346n|9'99072 |9'60718 | —e |9'91975 |9'74494n
Kruilasowo uC Y+157 33 45) 56 57 38)r'18554 | —co 30088 puutos7n 9°749 14 S823 l9'10712 1985558 |9'65109n|9'62821 | —co 944995" 19°55322 9718079 |9'92925 | —ce [9'84807 |9'66676n|9'°99370 |9'62688 | —e2 {o'9a174 [9:74043n,
Petersburgh, 1 ss e+ ss0es ++ 2/59 56 29] 30.17 §2/1'62408 |8'37912 1977807 |9°54470 |9'57216 |9'82120 |7°92831n|9'73541 |9'21217n|9'43012 |9'71286 9°74430 987891 |7°89q13n|9'70123 lo'ogs99 [or05035 |g'81698 |9'56766 [9°81670 |o'24830 |9'93699 |9'7036a
Potersburgh, 2 » q 168789 |8'40815 [9°77822 |9°54587 |9°57007 |g'Ba119 |Br00q84n|9'73421 |9'21332n|9'42729 |9'71450 9'74504 987868 |7797051n|9'69988 |orog652 \o'04979 |g'81745 |9's65320 |9°81632 |o-24845 |9'93629 |9°70394
Pomorania...
Nowgorod .-.
1989997 |8*548scn |9'72392 lovo86ar jo'osrr1 |9°83457 [955606 [9'84045 |o'23560 [994045 |9°74390
142955 |7'72428n |9'76612 |9°54958 |9'55388 |9'33827 |8'57988n |9'75540 |9'288q9n|9'44226 |9'68242 lo-7572%
17 5 913873. 9°30386 |y'84y87 H i 7 9791709 |8°59396n|9°75462 loro7257 \o'5744 |9°84165 |9°57529 |9'86130 Jo'2z189 |o:95051 [9°73471
155157 [8'64038n 19'75453 19°53873 [9°56386 |o'B4987 |8'62169n |9'78238 |9°33191m/9'48236 19'63763 |9'97357 |9°75777
Waldai 138328 |8'84850n|9'73616 |o°552 "50 87132 |9'03179n19°79578 |9'43304n|9'46298 |g'60256 [9'96384 |9°7806x |9°58067 |9:94264 |9'00678n\9'77077 [0106246 |o'05256 |p:86933 [9752762 |9'88959 |o'22913 |9'94837 9'76514
Woichnei Rearen S-o38>3n pe7a368 Beate Brae 3 88387 19°19632N 19'79890 [9'49002n|9°43388 |9°5823x |9'95622 |9°79616 |9°53372 |9'95745 |9°77284n (977539 |o'05670 |o'0q762 |'88757 |948219 p'90sg2 joraa76 |9°94404 97889
Twer 1558331 [9'07282n 1970337 |9°56377 [9°41378 |'8q922 |9'32 1197 |9'81362 [9°55660n|9'42129 |9°53091 |9'9480r |9'8084x |9'49290 |9'97834 |930137n 19179380 |o'o4277 |o'04600 |o-g0640 |9'44505 "93049 9194700 9" 748
Moskwa, 140072 9'218387 1967135 19°55850 |9'33746 |9:91787 |9'45759n|9'83153 |9'64o16n|9°31186 |o'44006 [9'93526 |9r8az4x [9742509 |o'00550 |9'44537n|9'81731 |orozrrs |o'04341 [9'93056 |9'38985 9796326 9195000) p'8373
Platowa 154444 |9'24513n |9'66554 |9's6961 |9'26923 |9°92157 |9'51086n |9°81942 |9'65s82n|9'32660 |9'44272 |9'92890 |9'83297 |9°35665 loco899 |9°49649n \9'80505 0702176 |0'03676 |gr94084 [g'31424 "96658 994321 piaa7e9
Dmitrew 135812M |9'19058n |y'66164 |9°58683 [916190 |9°92363 |9°56272n|9°79657 |9'66319n|9'21570 |9'46167 |9'92110 |9'84630 |9'24762 |o'c0935 |9's4724N |\9'78109 |oro2609 |o'ox6g4 |9'93214 |9'20410 |9'96583 9'93227 |9'85747
MIDS hbloacaccesceccs "17205 |9'64117 9°61 8°62458 |9'92801 |9'67027n 19'73524 |9'68010n|8°67878 |9747467 |9'89792 |9'87632 [870909 |o'01252 |9'65410n|9°71907 |o'02914 |0'00232 |9"98072 p'968a2 9'90687 /9'88527
Nijnei Nowgorod ....... eaeaben pr6a387 rece Btageax 593660 Perea 1972301 |9:67348n|8:53893 948845 |9'89568 |9°87978 |8+57363 jo°co982 |9'6s8o9n\9'70589 0'03242 |or998sq [9198264 19'96467 990224 988634
Tehugunui 9177820 |g°62. "63469 |8'29796n|p'92890 9:72 137n |9'69087 |9'68393n /8'35426n |9'47072 |g'88210 |o'Bo227 [8738284n loro1378 |o-7a534n |9'67484 [ov02820 |o'9B694 [oroq7t0 |8'33878n|9'96972 o'22015 |9°89173 |o'g0189
Saacene Beets Raven 3973790 92989 9°77832m|9'63205 |9:6g05en|9'04078n 19743824 |9'86070 |9'90866 [gr06160n lo'o1770 |o'76421m\9'61794 |o'oa074. |9'9b6904 [oro1760 |pro1946n 9197536 betes or87575 fo'gaa7x
g'2r360n fois8o44. |9:65220 fo'o8886n|9:92742 [9'79142n|9°59763, |o"6Sooanlo-15i7an 44397 985259 fo'91535 |o'x76x7n|o%01473 |g'77699n|9°58329 lo'ozz05 |o'96033 |oroago9 |or13370n 9197236 or23836 |o-8007x, b'gaga7
9'16423m19°59143 |9°66610 |9'rs903n \9'92157 [9°79024M /9°55685 |9°65352n|9'20517M|9'47985 |9'84705 |9'92172 |9'24306N |o'o0sb0 |9°77364n|9'5q026 |0:03037 |9"950B8 |o'oass5 |9'x9846n\9'96098 Jor2zz071 9'B551x |9'9297'
3 79%
0'94988
i " y , - ‘ : , : r76758n 9% i y "94859 |o'22297 |9'84322 |p'92928
Milet = 1112385 |9'10288n/9"59362 |9°67968 |o'21471M |9'91487 |9°78643n |9'51357 |9'62428n|9'24279n |9'51540 |9°84151 |9'92757 |9'29531n |9'99547 |9'76758n|9'49472 \0'03906 9'94125 joroa73x |9'24823n|9'94! ¥ } i
Kojil .. 185336 prorg67n pegoz0, 60440 9'26457n|\9'90654 |9'77950n|9'46247 |9's8883n [9'27110NI9°5s419 |9°83533 |9'93353 |9'34119" /9'98316 [9°75802n |9'44099 |o'o4g08 19193034 oroasse piagieen 9193365 Ra 982968 9:92.78
Bins coe 3122220, |8'94379n |9'58618 |9'71023 [9°35773M |9'89604 /9°78489n|9°36406 |9°54447n 19'34520N 19'57793 |9°81975 |9'94380 |9°43176n|9'97007 |9'76173m |9'34088 fo'ossso |9'91173 or03578 jo\a8assn 9192880 lorsa740 |p'Scoa7 "93342
Dubrowa .. 1126458 [B'90910M 19'57387 |9'72071 |9°42467n |9'88737 |9'79123n |9'26228 |9"s065n |9'39988n |9'58774 |9'80513 |9°95197 |9°49765n [9196035 |9°76732n|9'23837 |oros820 |g'Bgs82 oro4266_j9'44572n 99084: es 9279274 |9'9395
Perms sissiene as 56 |1"42813 [8'82328n |9'56022 19°73503 |p'49000n 1987354 |9'79086n|9:09176 |9'44483n|9'44376n |9'60798 |9°78657 |9'96138 |9°s6069n|9°94423 |9'76544n |9'00633 jo706392 p'87454 eio4a 3s 9'50723n Be uy) or22955 97 993 994474
Kruilasowo. ... 38 |1°14082n |8*94099n |9'54801 |9'72932 |9°50974 |9'87657 |9'80690n|9'05844 |9°45459n |9'47749n |9°57868 |9°78148 |9°96279 |9°58373n 995053 |9°78366n|9'03520 |or05572 |9'87335 o'05466 |9°53245n |9'899 736 |9'77093 |9'95224
H . . 9 . , i Seecpy EEG lee . y y y y "48059n|9'80793n |9'87961n |g'76101 |9°B18547|\9'63438n
Berlin«« +++ 13.24 28166304 |9"56685 [9° 861906 |803326n 20n ;con |9°74667n |9'234350 |9'8sagon |9'87160 |o'41370 [889625 |9'50483n|9"70354n|\9'61299n |9'90778n |9'96170 |p'2 58cm 9'48050M [0 5 ) H 684385
Tosna.. ‘ a ran = Reiare Ban Raa 892859 B-Bas8cn Be Rpae Bade '9'69784n |9'47926 |9'52637n |g'91289 822997 pepe pice e777aen paisa patecte 93787 Pouce ease aabrsre peer oes Paseo Boers
Pomoranii 1 16'4 —|1"59988 19°73369 |9°33796 [8196133 |8'81133n |9'47219n [908227 |9'69763n \9'50072 |9'51934n|9'91330 |8'34663 |8'84713n |9'26243n \9'77812N (916347 |9'Bx i K b i i B i
Snizowo ” aa ay Renan Bee Patoeg aya S008 sn Boers 9'15616 |gr70426n (9'55524 |9'52937M|9:91357 [872560 [8163757 |9'2a100n |9'77704n |9'25031 |9'83404N|9'94767 |9-50745n 9751353 |9'42980N |9'93178n |9'71657 [9°12 79m |9'74331N
Waldai 2.222220)
Waich sine 33.154 [163256 |o'71412 19139207 |g*10879 |8'61280n |9r4284sn |g'22810 |9:70156n |9'59495 |9°50798N|9°91377 |8'80337 |8'4486an |9'17343n 9'77754N |9°33311 |9'83593M |9795134 |9'49103N |9'50254M|9°39066n I9'93849n \9'72221 |9'BO744n |9'74552n
uiichnei Wolotschok .
34 40% [160969 [9'70947 |9'39662 |9'15547 |[8'512417 [9'41556n |9'29870 |9'69483n [963207 |9'46900M/9'91398 [885229 |8:12926n|g'12094M|9°77830n 9°41338 |9'83284n |9'95424 19°47793" |9'49287M 19° 33591" 19'94454N |9'72 061 |9'80197M|9°74867n
)
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Ta24111
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» | Lij72702
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| T¢g 1101
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$176890
Sii'92 132
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T¢569542 |9°96437
Pf22138
0F35744
Br32.868
KP 84524
Tr85125
ee
TABLE OF PRIMARY EQUATIONS FOR THE GAUSSIAN CONSTANTS IN 1829 (Continued).
coef. |Log. coef |Log. coef. Log. coef.
ay
v62221
9*32001M g'94974n
19'27809n 9'95291n
19'16191n 9'96379"
g'10694n 9°96479"
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19'79738"
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9°78 14.10 |9°
19'77935”
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9'76947"
976791 9769050
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19:75753M |9°77988n
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1974401” 19°79596n
3'79740n 9'96896n
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9'73832n |g'Bo8o8n
9°71265n |9'821290
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19633340 |9'8 56350
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(2)
KPI 5% |8°99933
GPT 52 |8°92808
rh 142 |8°76821
4 O'O1147
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0°01289
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0700440
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9°98914
9°98557
9°97767
9°96918
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9°02258
9'04.691
9°05866
9°07560
9°09897
9°49574
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TABLE OF PRIMARY EQUATIONS FOR THE GAUSSIAN CONSTANTS IN 1899 (Continued).
Long. East, Log. coef.|Log. coe,
jj
¢ ii ‘Log: coef.|Log. coef-|Log- coef,| Log. coef.| Log. coef. Log. coef.|Log. coef.|Log. coef.|Log. coef.|Log. coef.|Log. coef.| Log. coef.|Log. coef.|Log. coef. |Log. coef.|Log. coef| Log. coef-|Log. cocf,|Log. coef.|Log. coef. Log. coef.
Stations and observed cements. [Latte | HOM, | tog, [Hse bg. se ie es et get eg ae aga ng ct geet lg ca Lg ot tg, tg coat Lag et Log set og eet. at og sat ag ot Log. et Log. cog
pe al) fa) eee,
Latinsk w.)59 20 | 60 9'¢ — |1"26007 |9°73531 897337 |o'33522 |8'98782 I9'45318n [970570 |8-78716n|9'4280r |9°56885 |org1493 [973219 |8:06625 |9r37773 |9:7616rnl9'82521 |8'84865n \g'94113 |9°49176n I9'57101M |9'55016 |9'90526n\9'70553 |9'70B0In |9'84138n
Bjelaika...... w.|56 49 | Gr 53.4 |1"57611 19°09436 |g'08623 [9°45430 |8'85356 |9:37054n \9°73407 |8°53550n 19°44524 |9'67637 |gr91173 |S*10817n [8:99939 |9'38749 \9'74585r 19'87726 |8'48403n |9'95898 |9°43723n |'48q58n|9'60184 |g'91764n 19173526 |9'6q415n \9'83137n
| Kamuischlow w./56 50 | 62 37°4 — |1°57078 |9'69452 |9'06930 |9'4s64x |8:88015 |9'36969n |9°73478 |8'20299n |9'40789 19168736 |prg1160 |8-20a15n|8'99933 |9:40777 9:74244 (9'87741 |8:65482n |9°95870 19'43523" |9'48814n|9'62073 |9'91293n |9'73490 |9'68go0n |9'83433n
Sosnowsk to. |§7 13 G6 14 149262 |9'70174 [Br9B1bx [9'45140 |ot04540 [9°36093m|9'72639 |8'91878 |p'10829 |9:71580 |o'91256 |8:43276n|8'92808 |o'51134 |9'71488M|0'80334 lgrr1445 |o'95627 19°52565n |9'70900 |9°87861n \9°73059 [9°64934n |9'85q57n
Chutarbitka w.|57 58 | 67 584 — |1"28533 Jor7t405 |8°87358 [9'432612 |9°13262 |9°37585n [9°71148 |9°11517 |8'76363 |o°70263 991320 |8r66514n|8'76821 |g"s5511 |9*70229n |9'83993 |9'28180 |9'95049 19°55925|9°73957 |9'85477n \9'72119 |9'63487N |9'36497n
Uwazk ...- #159 3 | 68 45% [119368 |8:27531 |9°38960 [9'79994 |9'76191m|9'72376 |9°71855n |9'4x190n 848641 [9*sq214N|9'66727 |g:60113, lororsg7 |or82g50n |9°78735 |9°68835n \9- 381700 lo'o8153
lorogro6 |gr76a71n\9'72912 |o'23432 |9°57134 |9'98168
| Tugalowsk 69 55'4 [1708707 |816584n 19°37520 |9'81234 |9°76729n |9'69346 |9'68065n|9'43805n /8-73420 |9*50169n |9'70346 |9°57729 loor443 |9'82625n\9°75242 |9'64731n 97404710 [0'09293 lo-08857 |9:76488n|9'69104 |o'23746 |9'53891 |9'97605
| Sawodinsk 69 344 — |x'1g376 |8:57173n 19738784 [981681 |or755s4n |9'6g245 |9:'66876n 9'40749n /8:64250 |9™4788snlor72594 \9:g8392 lororz89 |g'B1x50n |9'7484x (9°63338n \9-372110 [0'10029 Jo-08350 |9'74809n |9'685c0 |o'23950 |9'53997 [996804
Sarnarawo .. -- 68 42°4 [0°75511 |8'80346n|9'41079 |9°82000 |9r73519n |9'69856 |9:65986n |9°35034M 837986 |9°45330n|9'75029 |g6c025 |o00946 |9'78779n \9°75116 |9:62219n |9°31267n [010846 1007614 |9'7a209n |9'685q6 o'2g179 |9°55c08 |9'95929
Kewaschinsk =.\61 37 | 67 45°¢ [095856 |gc02g18n|9:43689 [9°82519 |pr706san |9'69874 |9°63759n |9'27111n |7°66036 |9'40702n|9'78707 |9'61614 |o'00440 |9°7538qn |9'74606 |9:59632n |9'22982n |o'12126 lo'06495 |9'68452n|9°67674 Jo'agsqr |o'55618 |o'94448
| Kondinsk 2. |62 24 66 284 o"41330 |9°16628n\9°46591 [9'82706 |g'67190n|9'70305 |9761864n\9'16586n \8'217410 |9:36130n 1981756 |9'63649 |9'99764 |9'71466n |o'74581 |9°57420n [9121420 [o'r 3227 Jo"05282 |9'64219n |9'°67334 |o'24856 [956805 |9'92920
|/Kunduwansk .. +63 17 | 65 64 [107737 |9'28364n|9:49434 |9°82778 |g'63085n |9'70373 |9'59265n |9'03032m |8'53113n |9'30412n|y'84944 |9'65570 lorg8q14 |p:6686qn lo'74154 |o's4477n|S'98244n [o'14q16 1003855 |9'59273n|9'66563 |o25200 |9°57805 |9'91149
| Beresow. . - ©|1"13609 |9°35382n19°49798 |9°83063 |9'61619n |9'69032 |9'56553n|8'99963n |8"49864n |g'26419n \9'87123 |9'6s292 |9'98557 |o'6soson|9'72463 |9's1523n|8'94931n [0'15250 |p'69827 oroz092 |grs7215m\9'64628 |o'25444 |9°56877 |9'90142
| Katschegatsk 154245 |9°45378n|9°50527 |9'83311 9'58609n \9°66772 |9751784n /8:92953n |8'46849n 19:19186n lo'90594 |9°64983 [9'97767 |9'61463n|9'69626 |9-46345n|8'87517M [0116619 |9'6885x loro16y5 |9'53224n|9'61387 |or2s848 [9755497 g788281
Wandjask 105154 |9°55721M |9°49254 |9°83699 |9°56397M \g'62001 |9°44413n |8'92866n [8210110 |9'09716n |9'94659 |9°62473 |9:96918 |9'5855an|9'64156 |9°38482n|8'86935n 0'18270 |9°65532 |g'99978 |9'49818n \9'55422 |0'26343 [9751684 |9'86129
| Obdorsk....... 55|1°54777 \9°s5829n 1947463 |9'84045 [o"580B1n |g'6osra |9°435297 |8'99861n |7°84804n |g'0og981M \9-94696 |960668 |9'97251 |g’60227n 9162658 \9'37592n|8'93924n o'18291 9°63718 loroogor |9'sx487m\9°53918 \0'26349 |9'49863 |9'86447
Kototschikowo o'55871 |9'10534 \9°30907 \9°76614 [o'81716n [971756 |9°76847n |9'56881n \gro1261 |9°64833n |9°51423 |9°55722 |o'01429 |9°89788n |9'79822 |9°74970N |9's5004n 0103876 |9'65711 Jo-1z418 |9'8s108n\9'75142 |o'22289 [9755916 |ov01623
Tara ... 156 54 0) 74 4°4 — |0°97313 |9'06781 |9'23424 19'77885 |9'84997m|9°64328 |9°70345n |9'66124n \9'29442 |9:60062n |9°53286 1947823 \o'02284 |o'92881n |g'72212 |9'68344n |\9'64123n 0104350 [9757588 [o'12049 |9'88077N|9'67408 |o22413 |9'47669 |o102130
Pokrowsk 1°30363n |9'22427 |9'10774 |9'76103 |9°B8994n 19755966 |9°65397n19'76773n [9750971 |9'58754n (9743514. |9°37266 Jo"02595. I9'97800n 19'64772 |9*64003n |9'75379n \0'02007 |9'48131 |0'13460 |9'93603n |9'60575 lor21806 |9°38819 crogrgs
Tschuluim 141996 |9'28375 |8'9404g |9°75266 |grox749n |9"41674 |9°531710 |9'83816n |9°64240 |gr48827M |9°37650 |g'21676 lo'oz8g8 loroxog3n |9'50968.|9's2094m|9'82739n [0'00759 124 |or14346 |9'97163m |9'47088 jo'21489 |g'24129 |o'os35r
|Uwazk ...... 1°10346) |9'72987 7478 19°37736 |9°19866 |o'4oargn |9"69542 |9'16400 |8'47553 1966939 [9791374 |8°B2633n 830406 |9°57523 [969924 [9°81343 |9'31360 |9'94187 |9°43675n |9'59635n 1974384. [9'S3859n 1970749 |9°63301n \9'87233n
|Tugalowsk .. . 145561 19°73864 jB'61013. |9°34154 |9°24885_ [9'41035n |9'67890 \9'23188 |7°73878M l9°64053, |9r91270 |8-90714n|\7°7528an|9°59833, |9'68gcano'79014 |9'36944 |9'93569 |o'442920 |g'62133n|\9°7568x |o'81973n |9'69823 [o°63423n p'8793sn
Sawodinsk .. 146060 |9°74406 [855413 |9°31341 |9'2580a |9"42400n |9°67527 |9'20404 |7'70415 |9'63014 |9'91211 |8-9q596n |8°34124N \9'59367 |9°69380n|9°78280 |9'33790 |9:93158 |9°45573n \g'63264n |9'74657 |9:82006n|9'69207 |9°63076n\9'879910
Samarowo
143917 |9°74980 |8'50147 |9'27713 |9°25744 |9'44254”|9°67345 |9°13757 |8'45939 |9'60986 |9:91123 |898605n |8'60086n |9'57944 |9°70353n19°77708 |9'26903 [9192677 9°47379" |9'64307N |9'72653 |g'82529n\9°68497 [9643150 |9'87879n
Kewaschinsk w.J6x 37 | 67 454 [x'3410% |9'75789 834908 |p'arx23 |p'26245 |9146678n |9'66546 [o'04817 [870834 \9r57469 |o'909x1 |pro4Bgan |8'8406%n |9rs6277 |o:7x322n|9:76264 |o'17522 |o'91847_ |nr49849n |9166074n|9°70042 |g'82739M 19767306 |9'65756n |9'87
Kondinsk -- aries 66 24 fesse Beg 36017 I9'r4000 for25421 [9'48936n |9'65779 [890445 [888947 19°53738 |9:90655 |g'09948n|8'97649n |9:53745 |9'7250an|9°74956 |o'03189 |9'91058 |p752292n |9r6738on 06733 pt8azean yee. 9673990 97876470
Kundowansk.... 5 w.|63 17 | 65 6:4 — |arx1x60 |g'76y55 [7-6053x |pro4z10 |oragzir |orsrrssn |9764556 [868476 [899978 |9r49086 |o:q0388 |9'15306n |o'o899xn |9:50744 |o'73370n|9°73138 |8'82060 |p'90113, |gr5485em |9:68767n |9'62871 9°B3464n |o'649%4 p*60047n |9:8744n
Katschegatsk ... caver eet (65 3 5% 49°¢ —|1'29270 |9°77571 [8419130 |8'74210 [926493 |o'55283m \9'60938 [858850 [895036 lorgrrr4 |g'Roara |9'24632m |9'25890n |9'49574 |9°72971n |9'68319 [871113 |9'87978 |g's8o120 |9:72157m 959958 981631" p'S2229 97601 m9 879098
Schuruschkarsk ae w./66 13 | 64 524 |x'17173 |9°77665 |867413n |8'26340 |gr27991 |9°540930|\9°58159 |8°57031 |8'89337 [9°35685 |o'883x3 |g'29697n|9'341750 |\9'49088 |9'722G2n |9'64800 |8'67997 |9'86409 9159750n 9-74253n 9°58410 |o-Boo7on 1 Gs re UE
Wandjask - Ww. |66 30 | 65 39°4 [075967 |9°77629 |8*72884n|7'95952 9730036 [9'5370%M |9'57260 |8°70346 [880963 |935005 |9'B8045 |9'30544M |9'36275n |9'50613 |9°71500M |9'63717 |8'79962 |9'85990 |9's96c2n |9'75037n |p's9651 |9'79039n |9'59647 |96g978n|\9'S865
Kototschikowo vross-.156 39 | 70 45"4 — |1"53920 |9'69059 |8°87938 |9'48373 |g'r1863 [g'31049n |9°70402 |9°31048 |8°61246n |9'74480 |g'g1071 |8'49443n\9'0T908 |9'59468 |9'66679n |9'84340 |9'48087 [995944 |9°51925" I9'52.505n 1979596 |9'83082n 19:73656 |9"59578N \g'S6g11n
lo'87332 \9'67069 |8'66247 |o'52 717969 |9'20463n|9°61820 |9's6519 |o'4809sn|9°72156 |or90758 |8'55206n|9'13354 [0767881 |o5s644n|y'76068 |y'73292 |9'96509 |9'26939n |9-51738m|9'88780 |o°72x70n|9'74702 |o'48816n |p'88678n
agit 977621 Bisaqe8 835733 937986 d4ss6on 961815 piosaat Soran 47779 Bees 8*g2207n \9'25472n \9'60465 |9'67878n I9-70082 9'13491 |9'89732 |9'40290n 19'73555n pr7ebs9 i9'7807an pieaa8s 9;578270 yioseg2n
55|132940 |9'78050 }7°75889n |8'12472m \9'43295 |9'45726n 19°54730 Jg'x1062 |8°11321 |9°36498 |9'88452 |9'06985n /9°43568n |9'62027 |9°64458n |9°61306 |9°17038 |9°89387 "431300 9797138 9708 srzast7n pr6c03; 9,559) 0955
141847 |9'69894 [8°92783 |9'47244 |9'30665 |9'09996n |g6or10 |9°55889 |9°38334n|9'68954 |9'91489 [8°33766 |8°88227 |9'70990 |9'50321"19°74433 |9'70212 s'98140 p.oaaan to's B78 9/89057 (9:68 383n |9°73797. |9/387490 9: 90810"
1742275 |9'66084 |8°73447 |9°54669 |9'25765 |8'75090n|9°38924 |9'69569 |9'70178n|9"54765 |9'90913 |8'35752 |9°26974 |9'74453 |9'24378N\9'55229 [985874 |9°97246 |8'72067H \9"53289M 19'95184 [945 109M 19°75757 |9°09655n|9'908771
°
‘i . . . . . = 0. . ; . - "91092 |9°57827n|9'82731 |9'75318 | —2 |or95751 |y'62486n
B BoD +5 = 48878 |9'15613n 1964950 1957537 |9°13491N|9'70082 |9'52440n |8'75875 c= |9°74063 |g'40798n|9'78072 |p'70659 Io:x8149n |9°74741 s [991092 I9°57! i H i tots
Obdorsk. . y = Baer Bear Bea Bees Bera 3.62306 9402 52n |8'15075 —ce |9'77007 |9'40424n19'72517 |9°70086 |9'21392n |9'65060 —o 9192551 9"55968n 976272 9°73840 3 9198305 prsozaan
Tara... ap —20 |9°34261 |8'79800n|9'50807 |9'71476 |y:70213n \9'74433 |9'76644n |9'460zgn| —o2 |9'68351 [9°13890n |9'68382 |9:89081 |o'77902n |9'82123 | —s |p'90610 9-361490 9:76072 |or9@74x | —e jor98300 jov4a839n
‘Tschuluim -.--- ny =e |g'ag6ra |8'48390n |9'26123 [9'76198 |o'B5874n\9'55229 |o'63379N|9°78792n| —co |9'66935 [8'857 x30 lo'4stog [y'95484 |p'9448Bn|0:63843 | —o lgrg0877_ Ipiogbssnjaisa7e2 foroa797 | ee \p'aaggr |ors8zGgn
Tomsk ......... Aa 969123 |8%43168 |orso30a |p:3sx75 |8'58457m [9713467 |o°72045 |or72363n/0'27037 loroxa92 |7'90571 [897705 |o77148 |p'co4son|o:28218 |9'86796 |o'96407 '53877m sg0rim |9°47767 [8-72049 [9174196 |8°84818n 91979520
Krasnojarsk ... ©.\56 0) 92 57 19 |0"15836n|9'68140 |8'23400n |9'52114 |9°33075 |8°34580 |8'92571n19'73263 |9°75352M |9'07428n |g'91252 |7'76858n|9'05572 |9'77146 |8'78651 |9'07838n |9'88530 \9'96706 [828648 |9°57362m|9'49242 18'50747 1974737 |8'63094 |9°9 |
, . 5 y , y i Hl i ¥ y "81278 [9'98584 |8'79354 |9'38617m|\9'52658 [9'25429 |9'78668 |9'29177 |9'S84gon
Irkuzk .. . 6 2 "91428n |9'68 yors84n |\9'60847 |8'96 B:70110 }9°58382n|9°61425 |9°59250n|9°78542n |9'Bg274 |8'So148n|9°39411 [967271 [9'41042 |9'78235n |9'81273 9" " y i i H i e
oo sek sh See oe amine ene ate etn aoe tr ei ey ae et, ee a el ares eee lett ey etl te Oe
| Monachonowo . #.\50 58 6106 28 59 |1-21643n/9'53423 |9'09864n |9°62750 [872018 [853213 |9762937n|9'56164 |9°50035n \9'85038n|q'BB204 [893403 |9'46289 9163154. 9" ream 777278) isogese zeta) 2 97x eer p1a340> 12 Z9e27, aeaes WazeO En
| Arsentschewa 51 16 6 rORBI4N |9'sg6rr |grroggin |9'62147 |8'78115 [860786 |9°63851n |o'ssort |9-46178n \g'B4q317 |9'88477 |8°92916n|9°44572 |y'63256 |9'45927 |p'B5r04n|9'76264 |9'98948 |8'80147 |9:31803n|9" "33849 (9° i nage
Botowsk x Re zs % ra An os 87 39¢n 60258 so7aoan sae aarp 8'99169 |960056n |9:58357 |9'46544n|9'73055M|9'90946 |8'58991n|\9"15066 I9'70013, |9'47455 |9'76276n p:74578 9197307 8°96433 prs2 go8n p4d779. jor2zeax 979679 Beery egetsen
Tomsk ¥-\56 29 39] 85 9 olr00173 | —2 19734555 |8'27421n|9:01183 |9'77901 |9'86796n |9'28218 |9'34929N |g'Bo25sn| —o0 |9'69329 |8'62195n|9'19064 |9'95782 |9°94688n|9'30110 | —% lg'91952 |8'84818n |9'2695 3674 9
Krasnoj . , 5 i : : = : D 5 y +96664n|9'15972n| — |g'91808 |8°63094 [g'06113n \o'04608 | —co |9'99942 [871228
Krasnojarsk oe ye |56 8 - "331 B'04425 |8' on |9°7822 88530 |9'07838n|9'15562 |9'83486n ee |9'68745 |8'40031 |9'97979n 9°96474 9°9! F Me i I ‘ 3 “
poe a ee Rue ca ees | LE Se ATS) ria) eae ieee (ae pel mea eal all eelee yt a |
Troizkosawsk Y.|§0 21 5106 28 © 24|1"39533n| —o2 |9'08391 [8755478 |9'49461n [968299 |9°78661n \9'85389n\9°97707 \9'62783n| —co 9°: 888, 956180 ee 9187208 |9°34322 |9'8: 02396 | —e 9°98. 45291
: i y y i 5 = 9'83591n Joro239) 19'98177 |9'4529
Monachonowo 8 6/106 . - Bet 8°58591 |9°49918n \9'68723 |9°77876n \9'84649n |9'96007 |g'6r004n| —o2 |o's8752 [9105866 |o'72622n|9'91427 |9'BB845n I9'95 Sats 9 y : = i f
Rsaentaphanee iltceenalcetee Salirgaon| cee [irakse |eereo0 [perasin|y'68480 [g-7éaGan loBerogn l-gszar lors6ge8n| =o lgregai6 |g'o7s60. lotzase7m seaseze |i Sega ast Am | ee) ese 7a0) isseg eae once 4 Bee Preepe
Botowsk...... ¥:|55 9 58\105 22° — |r02078n] —e2 |g'28790 |8'72715 |9'49145n|9°71703 |9°74577"|9'76276n|9'81630 |o'55x19n| —e [9'65972 |9'09897 |9'68o70n |9'90628 |9°83152M \9'B4851m 19°89842 (9°33767 |9°76645n 199
(3)
- a et ll
A >
__ JANTS IN 1829 (Continued
Dg. coef.|Log. coef.|/Log. coef.| Log, coe:
—
‘ 03184 o'01421” |9°40731 |9°41789
* 103731 |o*0008 1m |9°23363 |9°'22800
_ 103830 |o*co8oon |8°84385 8842210
© [P3688 joror314m |9"028 197 |9°03203 |
_ |P3430 |0'00927M |9°34462m |9°34884 |
_ 122475 |o°01307M |9°57680n |9°594.59
61637 |0°016122 |9°66700n |9°69570
0395 |0°01677M |9°75448n |9°79584 |
99305 |9°99050n |9°84332M |9°87880
_ 98298 |0°02216n |9°83378n |9°89723
_ 198875 |0'0144.77 |9°82642n |9°88029
99047 |0°00604n |9°83275n |9°88003
199688 |9°996317 |9°82169n |9°85710
p0046 jotors rim |9°77620n |9°8 1982
po8or |0*°00048n |9°76157% |9°78871
P1443 |9°97925n |9°75194” |9°75857
B1857 |9°96410m |9°73849n |9°73024
P2116 |9°93992m |9°73425% |9°70589
—
1984. |9°902 597 |9°75232n |9°69875
16302 |9°72820 |9°40843n |9°60002
80343 |9°76698 |9°18166n |\9°27549
P6595 |9°77337 |8°62980 \g°'21546n
B1237 |9°74834 |9°13395 |9°54753%
29957 |9°72513 |9°25186 |9°65725”
_ [#0822 9°64720 |9°45661 |9°847557 |
~ 189580 |9°65793 |9°43431 |9°82632
40289 |9°67973 |9°36636 |9°77950n
B3243 |9°69547 |9°38146 |9°76391%
23067 |9°70799 |9°40826 |9°753597
97287 |9°72264. |9°44746 |9°734307 (9
WOOO DO Wao wiam—
79973 |9°71365 |9°50672 |9°75134n \9|
©1937 |9°8g016m |9°75376n |9°69154 19
D1608 |9°85830n |9°7694.6n |9°68834 |9
01065 |9°82009n |9°7904.6n |9°68873 |9
Y 00193 |9°76370n |9°8 1201” |9°68177 |9
199342 [9°71 150M |\9°82673n |\9°67203 8
_ }98819 |9°69409n |9°86042n |9°70667
- [98032 9°63967n |9°86285n |9°68403
+ 195980 |9°50091” |9°88328n |9°65516
| 93574 |9°29653” \9°88533n |9°59404
| #92253 |9°25124m \9°88326n 19°5 5657
90894. |8°93365n |9°88807N |9°52678
8
8
8
9
9
9
8°54281n |9°88612n |9°48588 |g
7°15099N |9°892.54n |9°46986 |g
8°48978 |9°89615n|/9°44847 |9
18°58613 |9°90230n|9°45286 |9°
8°74775 |9°90239n|9°43712 |9°
$°95506 |9°90886n |9'41633 |9
9
9
9
9
9
9
9°20483 |9°90895n |9°33763
9°33917 |9°92092m |9°28653
9°40173 |9°93331m |9°26666
9°40297 |9°933017 |9°26463
9°54107 |9°93052n |9'05462
9°71700 |9°89399” |8°74271”
TABLE OF PRIMARY EQUATIONS FOR THE GAUSSIAN CONSTANTS IN 1529 (Continued).
Long. East,
——— —
Log. coef.| Log. coef. Log. coef. Log. coef.|Log. coef.|Log. coef,| Log. coef, Log. coef. Log. coef,| Log. coef, . coef.|Log. coef. Log. coef.|Log, coef.|Log. coef.|Log. coef.|Log. coef.|Log. coef.|Log. coef,| Lo: cea) . coef, ey Log. coef.
Greenwich. | 1° ™ | "ayt0, | Ayst, | ak an, | aes, | ayt | a eal ahh, | gS ai | aya. | Aue | pe | age | dpe. | aaa Hae | awe. | agi. | agll | hh.
—
1216170 |9'26150n /8'84566 |9'76008 |9'92423n\9'31632 |9'42992n |9'84961n |9°66565 |9°38728n |9'40057 lorn1742 |o'o3284 lo'orgzam|o°40731 |9'41789M|y'83758n lorora58 |p'22958 forrg4o0 |yrq741sn|9'36725 Jo'21615 |9°13837 \0'05279
9°94939 |9'12743n /8°7151q |9°78648 [9°918g1n |9°15173 |9'24599" \9°83177n |9'64142 |9'1B816n|\9'50215 |8'96597 |0°0373% |ovooO81n |9'23363 |9'22800n |g'81378n 10°03576 |9'06726 jo'13860 |9:95479n |9'78761 jovz2211 |8:97009 jo'04143
0°84572M |9'14270n |8°31986 |9'78554 [9'92525n|876110 |8'85964n |9'84686n 960777 8'80669n 19°49321 |8'57262 [003830 |oco8oon|8:84385 |$'84221n \9'82943n [0103361 (867492 |o'14060 |9:9625qn|8°79839 [o°22155 |8+57831 (0'04399
1703543M |9°18865n |8"49059n|9'77773 |9'92756n |3'94261n 904760 |9'8545an|9°67914 |8'99990 |9°46312 |8'74976n [003688 |o‘01314n |9'02819N |9'03203 |9'338g5n o'02642 |8'85sazn|0'14257 |9"96954n (8'98459n [0'21969 |8-76068n o'04782
¥°32573n |9'21338M |8-B005Qn |9:77126 |9'92200n |9'25735n 19'36330 |9'84333” |9°65743 [9°31468 [9'44404 [9'06363n [0°03430 |or00927 |9'34462n |9°34884. |9'82887n lo'oa211 |9°17133n|0'14200 |9796678n |9'30219n [0"21858 |g707769n c'c4836
11096 56n |9°33224M |8°98577M \9°73694 |9'91538n \g'47911n jpreeaae 9°83788n \9'63692 |9°56420 |g'31269 |9°27358n 0'02475 [aroxg07M|9'57680n|9'59459 |9'83019n |9799538 |9'39378" lo'14495 |9'9735n |9'54x08n |o'2118x |g°;06pIn orOS¥C8
102 3% —_|1'28035n|p'40218n |9'03660n|9'70701 |9"90985n\9°56073n |9°69788 |9'83392n |9°61945 |9'66847 |9°17447 |9'34596n (0101637 |o'1612n |9°66700n |9°69570 |9'83174n |9'97284 |9'47651n |0'r4692 |9'99591n |9'63679n 021630 |grz95t5n
104 19 54 /0'82737n|9'47100n |9'07183n |9°66446 [9'8qq21n |9'63692n |9°79088 |9'821310 |9°57796 |9'77088 |8'90763 |9'4113an |0°00395 |o'01677n|9'75448n \9'79584 |9°82627n |9'94281 [9'55557n 0"14820 |9°99370n \9°73141M [O'19916 |9-48135n
107 44 10 /0°67210n |9"49220n |9'14648n |9°64155 |9'86868n |9°72150n |9°87117 |9°74500n 937711 |9'83878 |8:75035 |9'49798n |9"99305 9°99050M |9°34332n |9°87880 |9°75263n 19'93131 sere (0°14250 /9°97010n |9'822g2n 0'19649 |9°57588n
lor06556
007398
9107095
Troizkosawsk 3|50 21 5/106 28 24.|109587n|9°55004n |9'05863n |9'58776 |9'88581n \9°69743n [9'38062 |9'S1334n |9°87886 |8°33041m|9°45385n|9'98298 |ovo2a16n |9°33378n |9'89723, \9'82995n 9°89132 1gn|o'15027 |9r01074n |9'82236n |o"18751 |9°55857n 008070
Monachonowo 2,|§0 §8 6/106 28 59 |1°33325n|9'52750m |g'o8405n |9'61291 |9'88434n |9°69629n \9'86751 |9'79978n 9°85615 |8:02694 |9'45989n |9'98875 |o'01447n|\9°82642n |9'88029 |9'81256n g'g0861 Baca 0°14837 |9°9992an [9'B81xa7M |o%19134 |9°553h1n o'o8197
Arsentschewsk F|51 16 42/106 55 49 )/1°17898n|9'51534n |r1072an|9°62478 |9'87899n\9°70570n \9'86914 |9°78074n|9'46274 |9'85027 |8°43393 |9'47391N |9'99047 |orcobo4n 191832750 |9'88003 |9'79163n 9191704 \9°62977n \0'14633. [998890 \9'81561n [o'19323 _|9°56148n lo'o7 804
Tarakanowo - 3 |106 53°4 — |1°56855n|9°48159M |9°15395M 1965160 |9'87668n|9'70206n |9'85084 |9'76432n|9'43615 |9'82021 |8'83759 |9°47923n [9199688 |9°99633n |9'82169n |9'85710 |9'77058n |9'93724 \9'62601n|0'14366 1997454" |9'79992n [019786 |9°55309n [0'07074
Kadilnoja - 59 |104 59° —|0"O9285n|9'48473n [91081143 |9°65339 |9'89485n |9°65594n \9°81316 [981361 |9°55647 |9°79432 |8°81398 |9'42821n \o'00046 jo‘orsrin|9°77620n |9'81982 |9'82027n |\9°93552 |9'57576n|o"14801 |9°99374n|\9'75483n [019746 |9'50324n [0°07549
Olsonsk « 2 r4 [451970 |9°43096n |g-a4sx8n|9°68743,|g'8892n [9:65 101" 19°78816 \9-78861n |9°51499 |9°75284 |9'08877 |9743576n \orc080r |orcoa48n|9)76157n|9'7887x |9'78gx6n |g'96150 |y's7150n\0'r4375 |9'97300n \9'73409n(0'20357 |9'49387n|o'cbs22
Tjumenows! " 1°36922M |9°35247M |9°15882n |9°72106 |9'87931n |9'65200n \9'76481 |9'75010n |9'44690 |9°70841 |9'27966 |9'45219n |o'01443 |9'97925n |9°75194n |9'75857 |9'74386n 998944 |9°57509n |0"13733, |9°94498n (9°71767n 0'21036 |9°48967n joroszgx
Botowsk. 187448n |9'27704n |9°18291n|9'74366 |9'87176n 9'64618n 19:74140 |9'724410 |9'40489 |9'67000 |9'38410 |9:4578an|o'01857 \9'96410n |9°73849n \9'73024 |\9°71325n (C'Og14 |9'57158n [013233 |9'92491N [9169933 (0'21528 |9'48124N |o'04199
Bojarsk - 1144855 |9'15806n|9'22268n|9'76642 |9'85627n |9°65060n \9'72273 |9'67915n|9°32169 |9'63079 |9'48396 |9'47752 lo'oa116 |9'93992n|9°73425n \9'70589 |9°662q1n 0703135 |9's8079n |o'12453 |g 8qs04n|9'68938n[0'22096 |o°48477n lo'oz8sr
Potapowsk
1451177 |8'97955n |9'28603n |9'78362 |9'67704n |9°82731n 972112 |9°59950n 9°14758 |9'59986 |9°56674 |ots2225n lo"o1984 |g’90259n|9'75232n |9'69875 |9°57713n '05244 |9°61567\0'11426 |9'8s219n\9'70x92M\0'22649 |or51q120 |oror171
Kolaiwan -
115045 |9'66277 |8'20361 |o's4154 [9123170 |9'08823n\9°46319 |9'67676 |9°68708n\9°56049 \g'90650 [8G4315n 9'16302 \9°72820 |g'go843n \9'60003 \9'84234 9'96751 |9'16808n |9'52461n|9'93736 |9°56x97M |9°75136 |9'35449n 9'89990n
Podjelnik . . 106930 |9'68569 |819705n|g 50605 |o°33812 |S94988n |g'16875 |g°72214 |9°73641n|9°19845 |9'91032 |8'7506an |9'00343 |9°76658 |9°18266n 9'27549 |9°87199 9'96157 |9'0564an |9's7991n|9°95617 |9'29387n|9'74002 |9°17387n |9'91488N
Kanskji Ostrog -|55 48 | 96 6: |rr08849 \9r67504 [8+73865n \9'52230 |p°33343 |7'97808n|g:0r951m|9°73307 |9°74758n 9'26393n |9°91005 |8'7510—n\9'06595 [9°77337 |B'62980 [9'21540n 9188530 9:96660 /8'54630M |9's7110n |9r96684 898580 |9°74802 |7°31419M |9°91836n
Kursan ... -\54 31 100 3° | 1rogz0an |9°64574 |8'883877N\9°55807 |9'24685 |8°31335 |9°36242n /9'70632 [9°71593N |9'56764n |9'90552 |8°78639n \g'21237 |9'74834 |9°13395 |9°54753" 19°87202 9797456 |7'27144 [9'51865n|9°96046 |9°39726 |9'76276 |8:87102 [9'g0g48n
Salaria -
-/53 31 |x02 34 Jorgroogn|g:61910 |8'96229M |9'58x98 |o:x0003 [844232 |9'46467n |g'68x49 \9'68579” 19°67376n |9'90043 |B'83462n l9'29957 |o:7a513 |g'asx86 |9:057350 9°85893 9°97983 |8'22351 |9'47054n|9°95303 |9'51088 |o°77353 |pr05x18 [g-g0%36n]|
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Werchnei Udinsk
Tarakanowo
Kadilnoja -
0°34830 |9'56565 |9'126g0n |9'60847 [891448 |8°60557 |p*64000n \g'ssorx |9'42304n |9'841z0n 19'8B912 |8"96820n p'40821 [9°64720 |9'4566r |9'84755n 9'75019 |9'98743, |8'72377 |9'36286n|9'90808 |9'73106 |9'79093 |9'33317 [987861
jo"82086n pre7a6e prrogogn 960584 [895868 [859951 |g'6z121n \9'57621 |9'48s95n 9'82427M |9'89090 |8'94759n|9'39580 |9°65793 |9'43431 |9'83632n|9'77295 \9'98652 |8168423 [9'37987n19'91704 [9°70643 9'78867 |9r30228 Deb rets
v22246n \9'57119 |g:06218n|g'61092 |8°97374 |8'446r4 [9°57119M |9°62549 |p'60169n|9°79146n \9'8g023 |892732n \9'40289 |9'67973 |y'36636 |9'77950n |9'82281 [9:93664 [851648 |o'38178n19°93643 |9'O4655, 78947 si23048 98 76n
1'27985n|\9'60519 |9'04514N /9°58864 |p'0g195 [8163451 |9°57007n |9'62554 |9'57804n|9°76589n \9'89773 |8'88172n |9°33243 |9°69547 |9°38146 9:763910 9'8o8o7 {9198233 |8*6o105 9'44024n |9°93262 |9'64059 s:7787 pe sr89se6n
1936173 963948 |groags4n|9'55735 |9°19075 |8'72527 |9°57574M \9'61556 [9'53169m)9°74128n |9'90482 |8'82374n 19/3067 |9°70799 |9'40826 9°75359" 9'78400 |9'97657 |8'70587 |9'4980an |g'92440 "64405 9176621 9.239) 7 |9" 936m
0°83885n \9°68615 |8°99507n 19'49170 |9'30672 |8°97369 |g"s8041n|\9'59168 |9'44483n |g'6966an |g'g1282 |B8-69640n|8'97287 |9°72264 |9'44746 |9°73430" 9'73740 |9'96508 |8°B4214 |9°57784n|g'90822 |9'64902 |9'74412 |9'26821 |g'90906n| |
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Potapowsk. o*89s42n |9'70728 |8'99248n|\9°44354. 19°33973 |9'09545 |g*61048n|9'53814 |9'29934n|9'68909n \9'9 1548 /8°57753n |8'70973 [9°71365 |9'50672 |9'75134n |9'67233 |9'95775 |8'97569 |9'61166n |o'S8405 |9'68897 |9'73125 J9°33586 9"
Kirensk . 18/108 474 rag8ten -8874an keeee Sytoae o:81780n 9°68 40m |9'71586 |9°57360n \9'08013 |9°58497 |9°59333 [9153304 |0°O1937 |9'B9016n|9'75376n|9'09154 |9'54938n |o%05977 |9'62299n |o"10932 rsa78in pizerain pears grs1949n preosta
Itschora 109 3514 |r'6r416n |8-64885n|o°34814n|9'79680 |pr79107M |9'702231 |9°71602. |o'49874n 8'87019 |9'5623x |9'03673 |9°56739% lororG08,|9°858 on |p°76946n|9°68834 |p'47106n|o‘o7a28 |9'65x39M lor1oce8 |p'8o269n 9-71385n)o'25180 [9'544530 |9'99322
Paschinsk 1sjirx 31-4 |1'81224n|818752n|\9°39604m|9'8cor> |p'75699n |9°72730n \9171936 |9'39639n [837356 |9°53920 |9'67128 |9'60657n\o'o1a65 |9'82c09n|9-7q046n |9'68873, |9°36586n ‘08274 |9'68558n|or08966 |yr761530 9:73tgen|or23465_|9°57587n 9°97995
Kantins 54 tg 54 °72156n |8°34044 |9°45224M\9'80180 |9'705720 |9°75403" \9°71577 |9'22053n |8°544537 1949741 |9°71083 |9°65234N I0'00193 \9°76370N |9'S1201n \9°68177 \9°18653M \o'09532 |9°72533M |o'O7492 srzere7n 9°7499 in ease: ; pee G.) 99) Hs
Terbinsk z.|60 28 1/116 15-4 —_|1'28307n|8*6gs04 |9749357n|9'80047 |965713n |9'77236n |g'70849 |g'00636n |888388n [945502 |9°73751 |9'68652n\9°99342 |9'71150n \9'82674n\9'67203 |8'96gg0M lo'10415 |9'75527n 0106217 |9'64701N|9°70224n|0'24058 |9°63963n |9'94653
Beresowskji Ostrow
0268 |9'71124n|9'98819 |9'69409n |9'36042n|9'70667 |8-758s9no-09269 |o'78549n |o'06244 |9'63279n |9'79912n|0'23739 |9'67304n 19194999
Olekma .......
i 8 ) 78589 |9°6 "801371 |9° 8+79186n \g'07 1447 |9°47767 i ; H
Hes reseed Pape 1 DR) (ee a ce ee 73328 |9°73397n|9'98033 |9'63967n |9'86285n |9'68403, |B:o4984n lo'10273 |9'80340n|o%04975 |9°57558n|9'79876n |o'24or8 |9°688r6n \9'9 3451
1°44917M |8°65273. |9°53986n |9'78621 |9's8472n \9'80790n |9772009 |8'085gon |9"14991n |g'42011
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Sanajachtatsk 1'49748n |8°846 59670M 19°77197 |9°449147 |9°83149M |9'69340 |8'99089 |9'29679n \9'29749 [9°75621 |9°78453m |9'95980 |9'50091N |9'88328n |9'65516 [895263 jorr1049 |9'Bso2qnjo'oz 551 19°43464N/9) % i i
Tojon Aruin odofain prowess Benet a Regancn 19'83830n |9°63553 \9'27009 |9°34650n 19'O8858 [9'78905 |9'82scon|9':93574 (9°29653m \9°88534n\9'59404 |9'22860 |o-12197 |9'88516n 9°99599 si227088 parse era4sex p76445n 987523
Takuzk ...- 1'45040n |9*10534 |9°66781N\9°74785 |9'10632m |9°83834%19'59951 |9°34771 \9'35412M |8'93832 |9°80324 |9'84249" |9'92253 |9'15124N \9°88326n 1955657 |9'30477 Jo'12705 [g'g0020M |9'98024 piceeaas Dees jo'2470% 9778 oes ;
Porotowsk - 1593187 |9*10449 |9:68606n |9'73420 |8:88870n |9°84312" 1956970 |9'42285 |9'37357|8'72559 |9'80}02 |g'B6oBon|p*q0894 |8'93365n |9'8S807n |9'52678 |9'37993 |or12698 |9'91854n |9'96668 27.0 |9°817 4704 |9°79644n 98445)
‘| 9 a f i i , ; % , 2 , 95184 |8-47118n|9'81449n|0'24772 |9"80936n|9°82906
Lebegine v122505n|9°13290 |9'70268n|9'72238 |8:4o884n \9'84215n |9's2948 |g'47024 |9'37282n|8'33143 |g'80956 |9'87555n|9'89sas_ |8'54281n |9'8861an |9'48588 [9'42666 |or12936 |g'93214N |9°95184 {8 } y } !
Nochinsk . Faeaen Barres Bc Rea ieeect 9°84716n |g"s125x |grsx013 |9°38849n|6'94799 \9'So020 \9'8Rb07n \9'RR686 |7°15099M |9'8p254n|9°46986 |9'46750 jor12596 |y'o4431n progsze yokes a8 Bere o'24675 pie z2508 982329
Three wersts from Bjelshi Perewse 043450 |9'06183 |9°71799n|9°70095 844345, |9'84982" |or49044 [9°54165 |9'39635n|8'291697 19°79379 |9'89s33n \9'87829 848978 |9'Bo6r5m/0°44847 |o'49968 Jo'12305 [9'95470m 19°93766 |41978. 9/8 Sr5m aera Begsesan orBs8s6
Mschernoljesk 1754258n |9'00924 |9'71770n |9'69674 [853824 [9°85441" |9°49376 |9°55685 |9'41046n|8:39633n 9°78322 |g'89804n|9'87708 8'58613 |gr902;0n|9'45286 |9°51595 Jorx1990 [9'95920M |993824 BeS2 7B Iain SBN eee eal tgae aang
Jamastach. 1°55255n |g'00292 |9'72188n|9'69148 |8*69969 |9°85433"\9'47790 |9°56968 |9'40975n|8'55828n |9'78202 |g'90253n 987213, |8°74775 |9'90239n|9'43712 |9°52890 Jorx1948 |9°96390N 19193350 Hee Peo ea a8 eae ra laren
Allachjuna lo'25285 |8'92169 |9°72687n |9'67866 |q0492 |9'85872"|9'45569 \g'60275 |9'42226n|8'77491N |9'76769 \g'91154n|9'86335 [8'95506 |9'90886n|9'41633 1956339 "11446 |9'97533”|9'92712 767 |9'84147n/0'24348 |9'85679n |g'8o85
: ‘ ; ° : % ‘ ; : ¥ , * y "90811 |9'13848 |9'84260n|o'sg244 |9°87590n|9°79061
Tudomsk "38 "85126 |9'74022n |9165. "15318 |9°85730n |9°37595 |9°64608 |9'41262n|9'02684n \9°75703 |9'92784n 1984255 |9'20483 |9'90895n |9'33763 |9"60776 Jo'r1078 |9'9934cn|9'90 pet R “ , 9"
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a 143 11 "36 1764345" \9'73806m \9'61212 |9°34020 |9'87178n |9'29825 |9°72733 |9'45284n|9'26155M 19'08355 I9'94537" |9'81943 |9'40173 |9'93331M |9'2 PELL 10% x i is i % 4
Rea te Haak Ob eta (OStg=s)) 59 22 Bre 3 A He Cats Bes 67796 Beyer Bieagic 9'29626 |9'72728 |9'45186n|9'26242n |9'68402 \9'94551n \'B1915 [940297 |9'933010 19° 26463 9'69565 "08673 oroaabany pieabag 9734333 Beer eae Beer Paes
Seaiof Ochork 5845 of1g6 5 41 /1"47144n|8'51720n [9174536 |9°57281 |9'47543 |9'86490n \9'08345 |9°76669 |9'41303m|9'40302n y'65085 |9'96108n|9°78853 |9'54107 |979305an|9'05462 9'73786 |o'o7650 Jo'o4307" sie7e5 Berea 9°83935n (o'23073 |9'96714n lg'6g612
Item 58 16 x7\151 49 — § 1134753 |8°74076n\9°76438M (9749337 |9'64807 |9'82506n |8-76932n|9'78940 |9'16956n|9°54747M \9'62317 |9'9870An|9°7160r |9'71700 |9'89399n|3'74271M |9'76279 |o'ob830 |o'o7294n|9'So1g }9'6625! 3935)
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Stations and observed elements. {Log B: Fare 1g. coef. Log, B CORE log ae (eg. soct eer ee Sod jag coef. g. coef. ]
Sea of Ochozk «
Magascinskji Pad).
8°7435 1M |9°78376n |9'40738
19'0672.6n |9°77 126n |9°31039
9° 124.50n |9°76347M |9°30721
19°357557 19°75996
9°42092n |9°75749
7'90432n |9'58279n |9°62280
9°59410n \9'60814
9°63 569 (9°53270
9°33097R 19°73338
g°7 62870 0329. 56
9°742 74" C'22412
9°54095n 19°7 3881
9°55337™ |9°7 5472
oro1765n
oro2186n
o°02877n
19'20575n \9°7469
9°28 556n \9"7271
I9°75513" O'22223
9°79092M [0°21893
Ig’ S1gssm o'21478
19'42651 |9'67270n |9'27340
0°04736n
loroggban
jo’ob219n
g'9961an
9°93294"
g'Sg8ain
oneee I9°87151n |o"20400
St. Peter and St. I9'866g0n jo"20342
19'43241n |9'67083n |9'26244 |9
19°52459 |9"59691M |9°23313n
9°63992M |9'45944n
"64.78 5n |9'58307
1965 582m |9'63438n
196 5114n |9°64446n
9°97088n |9'91078
99 §85n \9'97425
197693147 0°43 54
19°668 son |o"04602
Item (harbour of Siteha) .
988955"
941910
8°94316n |9'42949
8°94884n |9°35292
962498 |9°95521
946423 |9°94496
9°09172 |9°93337
gr4ghs
95853
963225
9°75183
19"77009
9'78610
9°79481
1980370
ig’ 80802
983813
1989645
19°89853
989614
988969
988368
19°87093
S*17002 |9°93421
9°4.5461n \g'9 183%
19°52967m |9°91837
9°57948n |9°9 1664
19°61590n |9°9 1913
19° 5662n |9'92340
19'66907M 1992366
19°79819" 1994300
9°81171M 19°95349
9°79967M \'96141
I9'Bog29n |9°9639%
9°83613n |9°96797
19°35726n |9°97259
19°89 488n |9°98237
8°48 160n 19°79777 Hrd Beer
19°39341M |9°92500
19°81398n 19°79138
19°8 5690n |9°75245
19°857130 19°75856
19'84667n |9°78369
19°84261n 19°79940
19'84.308n |9'82001
Magascinskji Padj
St. Peter and St. Paul....... .
9'89191n |9'98281
19°8 7157
9°85352
9°97802
19°96861
9°95271
9°93945
19°93830 |9"99025 9°85296n 1979843
988584
i9'8 7222
19°91705n |9"94011n
9°91142n |9'94694n
19°84933" |9°98952
I9'85296 |9'82565n Jo'og7 51m 19°60384
19°76468n 19°58709 19°94
St. Peter and St. Paul -
19°48974n 19°85352
9709289 19°64 100n |9°8 5341
I9'26847 [9663982 19°77436
197938307 19°49463
19°63 589n |9°46383
9'62670 J9's994iM
9°35866" I9'19971
i y 9°72755 |9°71782
o"79449n \9'72552 preo7%4 |9's6263 g'80068 \9'70018
19'674.09n |9°91677
19°52259
9°63397 965585
7 . 9
sra7scee ioazoee I9'55219 (9'70928 ig'S15220 |8
96 384.3m |9'91646
19'69930n |8'78616
I9"19920 |9°61606n \9°91673
9°33487 |9°34261
Beresowskji Oftrow .
964 125m \9°69583
"89826 19°93983
1'02938n |9'74246 9724252 |9°39564
9°85448 \9'70244 |9'59908 |9'88475n
(5)
7°379
7°767
"575790 |8°377
"7508 5n |9'411
‘71926 |9°38x
05340 |9°342
"08657 19°335
11'5592
18°6579 |
0'2149
19325 ||
73°9182
55°4073
+ 275941 ||
= 17°3423
— 13°2269 |;
— I0°I757
+ 46°2468
+ 32973]
= 21125
+106°0129
— 61°8273 |;
+ 3°5400
— 22458
+ 74°7282
+ 874.568 ||
— 18413]!
+127°3487)
+ 12°4076
+ 79°1037
+ 11°2201
TABLE OF PRIMARY EQUATIONS FOR THE GAUSSIAN CONSTANTS IN 1829 (Continued).
| Long. East,
|
Greenwich Log. n. Log. coef, |Log. coef.| Log. coef,| Log. coef. Log. coef.|Log. coef. Log. coef,| Log. coef.|Log. coef,|Log, coef. Log. coef.
|Log. coef:|Log. coef.|Log. coef.|Log. coef, Log. coef.|Log. coef.|Log. coef.|Log. coef,| Log. coef,| Log. | Log. coef.
apt | apt | atte | apts, | “ait. | “apts. | aise. | “ays. | canis, | ays. | agen. | alol, | aga | aise. | ayes. | ante | pe, | dgtt | ists | “Agee cal Hog. eet xn,
Stations and observed elements. Latitude.)
ou
jSerusecialay 123 344 [138364n)9°75516 [p'or008n |g'18858 |9'09235 [9°47967 |9°67807m|8'98183n [9'45513 [9'45358n |9'91496 [864875 |8-Booqan|g'37775 |9°76373 |9'78418n|9'08728n |9'92952 19746834 |o'64o22n\9's1010 |o'89552 |9'68716 |9'68758 |g'B60s1n
Tojon Aruin .--- ie 46° — |1'27944n 976226 |8'98505n|9'10062 |8'91997 1951774 |9'63700n |9'27576n|9'51860 |9'25741n |9'91293 |8'83417 |8°93176n |pr18921 ° iB iets |neeeen patria Breteler \brcera isc
2. "78474. 697" Ton \9"921 "52961 |9°63633n I "908 "676 7 "841380
Three wersts from Bjelskji Perewse tw. |61 47 136 74 1°327977 |9'76324 |9'04870n \9'02933 Brogg81m 9°53333 "4959579" 54567n|9°56987 |8'45658 |g'91255 |8'91189 |8*g008on |8-37133n Eee resacenlet Reese Beas Beat pr63633n 931377 ear 567468 RgorsG Bata
Allachjuna. - - 5 . 238 10" 1385787 19°7577% |g'a1917N |9'06927 [855511 \9°51715 19°44734n|9°59308n|9°58442 893444 [991435 [881852 |8°77666n|8°84549n|9°79538 \g°55112N \9°69698n |y'92699 |9°59936 |955278n|8'96544n |9°92438 |9'68351 |9'81419 \9'7671an
Tudomsk - 11)140 35° — |1°54357M|9°75533 |9°45737" \'06414 [8°77788n|9'50645 |9°36707N |9'62974n 997136 917755 |9°91492 |8'77173 [8:72176n\g'o68x1IN |9°79001 |9°47238n 9°73582n 19°92933 |9°60046 |9°52944M 19'20246n |9"92157 |9°68689 |9'82706 |9'74749n
Arki ... 6 [a 20°4 1°43949M |9'74680 [9°22557N |9'10552 |8'87612n |9°48013 |9'29744n \9'66020n|9°57504 |9°31776 |9°91631 |8°54797 |8°50038n|g'18527n\9'78270 \9'40928n \9°77412N |9'93603 19°59648 |9'49366n |9°32824n |9'92305 |9°69763 |9°83403 |9'72804n
Bank of Knshtin near Ochozk.
SO022 | 243028 14 /1:33465n) 9°73780 |9'27589n \9°14385 |8'g0660n 9°45495 |9°25630n\9°67781n \9°58427 |9°38875 |9'91696 [810508 |8'12092n|9'24425n 19°77676 |9°37460n 9'79721N |9'94292 |9°58230 |9'46478n |9'38530n|9'92561 |9'70717 |9°83625 |ov71563n
Sea of Ochork .--. . 158 0}146 § 41 |1'78504n|9°72936 |9132748n |'14202 |8:99662n \9742321 |9'05760n|9'70324n|9°53965 |9°5x658 |9'91705 |7"96477n |7°37927n \9'34754n |9'76142 |9°17830n |9°82840n 9°94789 |9°57612 |9'42665n 950794" \9'91725 19°71494 |9°84631 [9'68Sqan
Item ..- 8 16 r7/r51 49 5 1°47305N19°72195 |9'38191M |9'07234. \g'11706n 9°37894 [8°35547 |9'71898n|9'52577 |9'5071 |9'91656 |8+50222M |7°76762n |gr4qq0gn |gr72521 |8°54648 |9'84821n|9'95131 19757765 |9'37981n |9'66409n |9'B8465 |9'72058 |9'80390 |9'63885n
Item .. 815 54/157 11 $9 |1'67888n|9°72101 |9°40446n /8'94283 |g'20190N |9°34945 |9'16568 |9°70245n|3"70794 |9'69275 |9'91580 |8°57579n |8°37777M \9°58527N \9°08340 |9°31242 io B3orin |9°95055 |9°5885x |9°35695n |9°75732n |9'83830 J9'71991 |9°87796 |o"s9464n
Pacific Ocean 334 37/213 25 23 |1'09237n|9°58130 |9'41210n |9'41034N |9°44 504N |8°39631N |9°40354 19°75214 |9'24373 |9°83370N |9'S6726 |8'75085n |g'41101n \9°74960n|9'49760N |9'46183 |9'89841 |9'94002 |9'60927 |9*10730n \9'8984an |9°784.51n |9'73338 |9'92360 |8'78407
Ttian'}; so cvieecscoee 5
15220 45 21 /1°51957 |9°62186 [9723501 |9'43402n |9°47429n |9'14100n [860198 |9°78248 [961699 |9°67033n |9'86143 |8'71926 |9°38194n |9'6g378n
965994 8702664n |9r91831 9°92033 |9'68705 |8'85884n |9°79797n |9'°87383M |9'70303 [993050 9'14102
3.35 11)1°58320 |9°64398 |9°08661n |9°42435n |9'47532N |9'29158n |8°61800N |9°77164 |9°65131 |9°548q1N\9°85991 \9'05340 |9°34253n|\9'66130n |9'70744n
433 34 /0°99476n |9°64553 |gto5525n |9'42536n |\9'46853n 19°318 557 |8°84320n |9°76866 |9'66216 |9°50719N |9°85930 |9'08657 |9"33590n |9°64651n
Item 91043670 |9'89007 19'90639 |9'72492 |8°62157n |\9'74484n \9'Sg189N |9'68225 9193487 |9'22083
19°720270 9°16 561 \9°88429 19'90461 |9°72909 |8*52125n |9'72488n |9'90023n \9'67982 |9°93443 |9°25076 |
FINAL EQUATIONS FOR THE CORRECTIONS OF GAUSSIAN CONSTANTS, DERIVED FROM 283 OBSERVED ELEMENTS.
ag, | Agi. AW, | agi. alt. Ag! alts, Ag, |* Ants, Ag, Agi. Ania, Ag}. A182, 4933. Ani, Ag?. Ag? Area. Ag? 4122, gh. Ag",
| | | —_——| | :
. to | AcE “288< 5 % ys 7 5 AY Je ety 1 Le. arts 7g37) ||| =) Aten! Cs | Seen arr 4 = 152839 |-+ 1570106|— 5'2827
— =) +3376423 | + 03856 | + 74550 |+ 5'9292 | — 62885 | + 7'7261 | — 40981 | + 8'8918 4675371 0°9548 7°6516| +11'2025 11°5592|+ 9°7937 42273 \+ 440515 | 3°4183 29'4357 ae 14°8789 | ns28ag ig !
03856 | 4+-20°9350 + 371436 — 2°6433 $19:1153 — 62171 | — o'o2z10 | + 0'5697 1°3258|+30°7629 |+ 4'0848|— 2°3692 |4+ 18'6579|— gorgs | — 06867 |+ 10568 |-+ 342°3000|-+ 3°4058|— 1'2624|+ 123184 — 2841 + 214271
74550 | + 3°1436 | +34°7352 | —19°5229 | 4+ 10130 | — 2°6505 | — 374168 | — 019765 39°1814| + 374737 | 58'6617| —20:0157 |— 0'2149| — 1°7290 | — 476575 |-+ 76°6369|\+ 1'8450|-+ 53°6054/— 16%4226/— 1'9981)+ 93°7050|— 11314
5'9292 | — 276433 | —19°5229 | +43°0555 | — 21662 | + 16852 | +31'4607 | — 8:7596
62885 | +1971153 |+ 10130 | — 2°1662 | +55:0245 | —37°1425 | + 0°6655 | —10°1216
7°7261 | — 6'2171 = 2'6505 | + 176852 | —37°1425 | +56'2684 | — 6°6373 | — 274670
3'8640| — 9°1377 |— 38°8651| +58'9842 |— 1'9325| + Vo710 | +34'0877 |—
2"g002 | -+38°8037 |-+ 3:4874| — 2°3235 |+ 73'9182 | —g0"1238 | + r109x j++ 4°2763
72553 | —16'8569 |— 8'1499| + o'7102 |— 55'4073| +65'2033 | — 7°3404 [+
— 564565
458088 |4+ 58814)
28'0272|— 14/0941 |
57150 625017 |— 1°1283|— 37'0991/— 4°4352
2°1878|+ 76'5958|+ 14'0163|-+ 539110
114313 |— 63°3826|— 5°7536|— 28'9792
(Mr fi
| i ; c Y . : — 810472 | -+65'7055 |— + 13°8777
= grog8r | — o'oz10 | — 3°4168 | +31"4607 | + 0°6655 | — 6°6373 | +56'7423 | —30°4774 — 4¥8575|+ 41391 |— 770914) +46'7312 |+ 25941) — 810472 | +65°7055 : ; f : ip ae pee ae tek
- 3'8918 | 0°5697 | — 0'9765 | — 87596 | —10°1216 | + 7°5330 | —30°4774 4.39'0950 + 4'1892 |+ 8:9773|— 3°3307 |— 573843 | —13°8286 |— 17°3423| + 9°4512 | —36°8534 |+ 46798 818833 — 770176) nora araths = 50384 xx9289
-— 0'4936 | + 0°7236 | — 271582 | + 277294 | — 876742 |+34°6182 — 48492 |+ 371894 |+-43:5196 |— 0°7064|-+ 31605 |— 4°3685| + 3°8279 |— 13'2269) +41'4770 | — 57606 |— 22930 075845 |— 9°5804 4/8506 |— 15°1690 33|+ 0°9703
+
fg
4°7174 | 1173801|— 10'1565|+ 53'2076|-+ 4:1294|— 1'9238
= FE
fren =| eerste | 173258 | +
; =-
: | . . “8575 . =F Es 5h 7 , = 10° i — 59819 |+134°4645|— 5°2934/+ 7'7983) 8'1633|— 16°2021|+4120'0916|— 8'2970|— 30°1954
+39'1814 | — 3°8640 | — 29002 | + 7°2551 | — 3°8575 | + 89773 07064 |+ 979864] — 11215 |+ 34°7185|-+ 2'5301 |— 10°1757| + 919702 5:9819 ; 17633 Pee ae selina, eerie “rca
2 et |r : Pee eon a4 oe Be #36 : 66 6'1789| — 511738 |+ 46'2468 | —15°5200 | ++ 4°5929 |— 3°6935|+ 68'9793|+ 8'5044) 37906 |+ 42°2261 49 Sree "5239
Sel - eee neo i ate Ba eee areens | eatiaees A alae pean leseeets ih a6racaz Sere + aera — 7719060 | — 79634 |+ 97°0813|4+ 615771 |+107'6467 | 44°6190|+ 2'4725|+139'9645\+ 375282|+ 87'0724
+
Sojb6x7 |= 8:BO5x) | thai 874 |p BItA | ie fT 5°3843 |— 473685 |+ 34°7185| + 6'1789
+
+
! i i : f — 47° F = 2 : 2 = 1910963|— 7'0457|— 77°2129|-+ 95'4952|— 1'3396|— 39'9794|— _5°7323|— 79'8057
—1650°'280=| +11°2025 | — 2°3692 | —20'01 8'9842 2 0°7102 67312 | —13°8286 | + 3'8279 2°5301| — 5'1738 4777003 | +85'5186 211125] wossx | +52°8321 7910903 Hh Ee i : ao
+ nr eee eal Race - Guia, ae ae 73: qoiee re 1 Bei —13°2269 10°1757| +46'2468 |+ 3°2973] — 21125 |+-106'0129 | —61'8273 | + 2°5400 |— gras? Le Tas oe wast is aeatd pee lee zr agi he RH + ess
— 642'674=|+ 9°7937 | — 470145 | — 17290 | + 10710 | —40°1238 | 4652013 | — 8'0472 | + 974512 | +41°4770 9°9702| —15"5200 |— 7'g060| + x'0551 |— 61°8273| +77'5280 | — 8°7326 + 65774 |— 28'9625|— 15°243 539 A
Bi ts | 1 5 = 5 ti l= ph 5 yaa 846)
= 584°743=|— 3°9394 | — 0°6867 | — 36575 | +3487 | + x109x | — 773464 | +65'7055 | —36°8534 | — 5:7606 |— 5'9819|-+ 4°5929 | 7°6677 ei2esa4 he eee i Bigg26 at AiSee Fees: as if ae 9338) a Bee + a Heyes it ae ip Bere
20617483 | 4431971 + 03662 | +76'8295 | —214204 |+ 4°3797 | + 2°7456 | — 3°8914 | + 4:1312 |— 18620 |+135°3653| — 3°3773 |+ 96°8795| —18'1711 2245 9! 58354 Hee vtellsemter ee peivget
+ 347'481=| — 374183 | +3373000 | + 1°8450 | — 5:7150 | +45'8088 | —28'0272 | +-10°3801 | — 8°8833 | — 05845 |— 52934 +68'9793 |+ 65771] — 7'0457
+
ie 747282 | —28'9625 | +12'4700 |— 8°7663 | 1016462 |-+ 10° 9619, — 670079
: ; " ; = 79° ; "3606 |+ 9° “858
| +1206'502=| —29°4357 |-+ 3'4058 | +53°6054 | = 56'4565 | + 58814 | —1470942 | —10"1565 | — 70176 | —29°580q |+ 777983] + 7'5044 |+107°6467 | —77'2129 |+ 8-4568 | —15'2438 | —11°9338 |+ 80°6660 if 10°9619 r59ra 184 79°3469 9°5822\+150°3606|+ 9'9241|-+142°S589
+
69 +1118 iS 6 5°5329|— 89'8458
. . . =; — 447 , i H 625119 |— 7°6839 6'0079 |— 7973469 +111'8913|— 4°3096|— 30°5177 |— i |
—1796 8789 | — 6: — 1674226 62° — 2°1878 | + 174313 | +5372076 | —16"1483 | + 48506 |+ 1073870 3°7966 44°3672 | +95'4952 178413 | + 119292 Sr 5 g B i panes % aU sey 2
Fes Selene eta len 3184 areca ee erase | Frérsoc8 eens eae Saag —15'1690 |— 172021 |-+4272261 | 274725] — 13396 [41173487] —74°4018 | + 5'9868 |— 9'8457 + 77 3465|+ 975822 473096 |+136'2878/+ 5*1461|-+ 8974715 \-+ 14°1133
: p vara eeadae : eee P CoA oath as
|= 1659'851— +15'0106 fe 12841 | -+93'7050 | —37'0991 | + 1410163 |— 5'7536 | — 179238 | — 570384 | — 18033 |4+120'0916| — 49200 |+139'9645 | —39'9794 |+ 324076] — 216227 | — 43623 pee Roses Be Geral *s309 Be er meer eesti 783s
pragwa17=|— 52827 | 4214277 |— a1314 | — 474352 | +53'9110 | —28'9792 | +13°8777 | — 119249 | + 0'9703 |— 8'2970| 4582491 |+ 315282) — $17323 | 7912037 | 3217250 | F171799 | Ne aSk MST agg |— BB84s8 (+ x4ez133|+ 94°4043 [+ 12'7835|-+153'8617
|+1761884=| —45'5888 | + 08749 |-+33°1458 | —54'5557 | + 6'5484 | — 162783 | — 1077560 | — 9°4498 | — 8/1958 |— 30°1954 + 515239 |+ 87°0724| —79'8057 |-+ 112201 | —17°6483 | — 13/2836 |+ 24/0745 7 }
=
n
~~
ON THE IRON MANUFACTURE IN GREAT BRITAIN. 99
On the Progress, present Amount, and probable future Condition of
the Iron Manufacture in Great Britain. By G.R. Porter, .R.S.
In obedience to the request of the Council of the British Association, made
at its meeting in June 1845 at Cambridge,—a request from that body being
- equivalent to a command,—I avail myself of the first moment of leisure that
has since presented itself, to investigate the condition of the iron manufac-
ture in Great Britain.
The incessant claims upon my time, of public duties, which have called in
their performance for the most anxious and unremitting labour, throughout
all of the present year that has hitherto elapsed, may perhaps be allowed to
plead in excuse for the imperfect manner in which I am able to perform my
task. I wish, most sincerely, that it had been otherwise, and that it had
been possible to devote to its accomplishment an amount of time and a de-
gree of research that might have enabled me to present a work more worthy
of the acceptance of this body, and better proportioned to the importance of
the subject.
* It was, doubtless, a conviction of the great and growing influence which
the progress of the iron manufacture must exercise upon other important
branches of our national industry, that led the Council of our body to desire
information concerning it, and all that has since arisen in the course of our
legislation has given additional interest to the subject, so that it has become
more than ever of consequence to know the actual condition of this great
branch of our industry, and of the capabilities which present themselves for
its increase. The enormous demand for iron caused by the general and
simultaneous construction of railways all over this kingdom, and not here
only, but in various parts of Europe and in the United States of America,
and also by their promised extension to India, is calculated to produce much
of anxious inquiry into the subject, in order to ascertain, in the first place,
whether, and in what way, that enormous demand can be met, and then to
satisfy ourselves that through the cessation of that demand, which from its
nature must be in a chief degree temporary, we may not be exposing to
ruinous depreciation establishments for the formation of which vast capitals
have been and will be sunk, in which many skilled workmen are trained, who:
during the continuance of the existing great demand will be receiving high
wages, but who.when it ceases may, many of them, be thrown out of em-
ployment, and who must be so, unless some new and permanent uses can be
found for the produce of their industry.
_ The object of the present inquiry does not call for any research into the
“remote history of the iron manufacture. It will not assist us in the solution
of the questions now pressing upon our attention, to ascertain whether, in
“eenturies preceding the Christian zra, when the Pheenicians traded with our
‘ancestors for tin, the Britons did, as some writers have assumed, know and
| oiteig the manufacture of iron. Certain it is, that the rise of that manu-
facture upon any scale deserving of notice as a national object, dates from a
‘time within the memory of persons now living. In 1788 the whole quantity
of pig-iron made in England and Wales is said to have amounted to no more
than 61,300 tons, of which quantity 48,200 tons were made with coke of
and the remaining 13,100 tons were still made with charcoal (see
Appendix No.1). In the same year the production in Scotland did not
exceed 7000 tons. In Ireland charcoal-iron was made on a moderate scale
during the seventeenth century. Sir William Petty tells us in his ‘ Political
Anatomy of Ireland,’ that in 1672 the quantity of iron made there was about
1000 tons, giving employment to about 2000 persons of both sexes. Works
eh H 2
100 REPORT—1846.
established by Sir William Petty in the county of Kerry in 1660, continued
to be carried on until the exhaustion of the timber in the neighbourhood
brought them to a stand, and in 1788 there does not appear to have been
any iron-work in existence in Ireland.
About this time the iron-masters in Great Britain began to avail them-
selves of Mr. Watt's improvements of the steam-engine, and were thus en-
abled greatly and rapidly to increase the productive power of their works,
so that in eight years from 17788 the quantity of British-made iron was nearly
doubled. An inquiry made in 1796, consequent upon the proposal of Mr.
Pitt, which was afterwards abandoned, to place a tax upon coal at the pit’s
mouth, showed the make of British iron to be then—
In England and Wales... 108,993 tons.
In Scotland ......... een 16,086 tons.
Together ...... 125,079 tons. (See App. No. 2.)
Ten years later, in 1806, it was proposed to tax the production of iron,
and again on that occasion an account was taken of the number of furnaces
and the quantity of iron produced, which was found to have been more than
doubled in ten years; the production being
In England and Wales... 234,966 tons.
TneScotldnd alto. desieds 23,240 tons.
Together ...... 258,206 tons. (See App. No.3.)
Of this quantity it was stated that about 95,000 tons were converted into
bars and plates, and that the capital engaged in the manufacture amounted
to £5,000,000. The proposed tax was so powerfully opposed in the House
of Commons, that the bill was carried through the Committee by a majority
of only ten, and the measure was abandoned.
The next account of this manufacture which has been given, was prepared
by Mr. Francis Finch, formerly member for Walsall, and had reference to
the year 1823. From that account (see App. No. 4) it appeared that in
seventeen years the make of iron in Great Britain had been increased from
258,206 tons to 452,066 tons. Between 1823 and 1830 there were erected
ninety-six new furnaces; and in the latter year it was found, on a further ex-
amination by Mr. Finch, that the quantity of pig-iron made in Great Britain
amounted to 678,417 tons (see App. No.5). Our confidence in the cor-
rectness of the quantities here stated should be confirmed by their having
been adopted in his evidence before the Committee on Import Duties in 1840
by Sir John Guest, whose authority upon this subject is conclusive.
From this time (1830) a series of improvements has been introduced
into the processes of making iron, which has had the effect of improving
the quality of the metal and of materially ceconomising the cost of its pro-
duction. One of the most important of these improvements was made the
subject of a patent in 1829 by Mr. Neilson of Glasgow, and consisted in the
artificial heating of the air previously to its being passed into the furnaces.
The effect of this plan in saving fuel has been most remarkable. In 1829,
at the Clyde Iron Works, where Mr. Neilson’s experiments were made, and
in which his patent was first adopted, it required more than § tons of coal,
when converted into coke, to produce | ton of cast iron. This was when
the air was forced into the furnace at its natural temperature. By heating
the air to 300° Fahrenheit preparatory to its introduction, it became neces-
sary to consume for each ton of iron produced only 5 tons 34 cwt. of coal
converted into coke; but in heating the air to the required degree, nearly
Se tae
ON THE IRON MANUFACTURE IN GREAT BRITAIN. 101
8 ewt. of coal was consumed. The saving was thus found to be 22 tons of
coal for each ton of iron. Thus encouraged, further experiments were made.
The previous heating of the air was raised to 600° Fahrenheit, and it was
then found, not only that a further great ceconomy was produced in the fuel,
but that coal could be used for smelting in its raw or uncoked condition. It
was further discovered that the same blast-machinery, when the air was thus
heated, sufficed for a greater number of furnaces, so that the power neces-
sary for three furnaces, when cold air was employed, became ample for four
furnaces of equal size when the air was previously heated. The result may
be thus stated :—
In 1829, using coke and cold air, each ton of iron required for its produc-
tion 8 tons 1 cwt. 1 qr. of coal.
In 1830, using coke and heated air, each ton of iron was made with 5 tons
3 ewt. 1 qr. of coal.
In 1833, using raw coal and heated air, each ton of iron was made with
2 tons 5 ewt. 1 qr. of coal. .
The saving in fuel is thus seen to amount to 72 per cent.
The effect of the hot-blast upon the quality of the iron produced has
been the object of many experiments to determine. As those experiments
were in great part undertaken at the instance of the British Association, and
as their results have been published from time to time in its Transactions, it
cannot be necessary to notice them further here. Mr. Neilson’s invention
was for a long time greatly decried, and to this day it is the practice with
some few of our leading engineers, when drawing specifications for works, to
forbid the use of hot-blast iron. Under these circumstances, the introduc-
tion of this plan has been by no means universal in thé iron-works of England
and Wales, although it is otherwise in Scotland, where the increased make
of iron, from 37,500 tons in 1830, to nearly 500,000 tons in the past twelve
months, may be in great part, if not altogether, ascribed to the ceconomy
which Mr. Neilson’s plan has occasioned. But for the introduction of that
plan, we should in all likelihood not have witnessed the unequalled develop-
ment exhibited during the past fifteen years in this, which has now become
one of the greatest branches of our national industry. Without this discovery
our railroad system could not have marched forward with such giant strides,
and in all probability the application of iron to the building of ships,—an
application from the extension of which, in future years, so many advantages
may be made to arise,—might have continued unthought of.
In a letter which has reached me while writing, from a most intelligent
iron-master in the North of England *, the subject is thus noticed :—
“ Previously to this invention, metal was made with such coal only as was
easily destructible before the blast, thereby admitting a greater quantity of
air into the furnace. Air is the food of fire. Coals of a stronger or more
bituminous character were not serviceable; the current of cold air at the
Tuyeres had the effect of caking the coal and choking the admission of air,
by which the process of reduction was stopped. But when Mr. Neilson intro-
duced his method the difficulty was conquered. By heating the air up to 600°
Fahrenheit, the caking at the Tuyeres no longer took place; the air entered
freely into the furnace, and coal hitherto unserviceable was enlisted into the
service of mankind, and applied to the great improvement of their condition.
“It was pretended that the metal made with hot-blast was not so good;
that it was weaker; and for a long time it was tabooed in all contracts; but
this delusion is gradually giving way to truth. There was no foundation for
such prejudice. It is known that air does not burn until it reaches 3000°
* Charles Perkins, Esq.
102 ; REPORT—1846.
Fahrenheit ; the raising of it to 600° before admission to the furnace was
nothing, nor did it destroy any of its elementary qualities ; it only secured
its admission and ensured its regularity of action in the process of reduction.
This was an increase of man’s power over elementary matter: it is by the
additions to and the increase of this power that men will in time accomplish
a greater and more powerful condition.”
The disinclination to adopt an innovation, which as we have seen in this
case of the hot-blast, has not been entirely overcome by more than fifteen
years’ experience of its advantages, has not been confined to that instance,
but has been allowed for a much longer period to influence, in another case,
the proceedings of our iron-masters. It was as long ago as 1801, that Mr.
David Mushet, to whom the world is greatly indebted for his scientific re-
searches and his practical exertions in this important branch of metallurgy,
discovered when crossing the river Calder, in the parish of Old Monkland, a
description of ironstone, to which the name of black-band, or Mushet-stone,
has been given. For many years following this discovery the black-band was
used only in the Calder Iron Works, which were established in 1800 by Mr.
Mushet, and it was not even there employed alone, but was used in combi-
nation with other iron ores of the argillaceous class. It was not until 1825
that it was first used alone by the Monkland Company, whose success in the
experiment led gradually to its adoption by other establishments, and to the
erection of additional works.
Mr. Mushet, in his ‘ Papers on Iron and Steel,’ p. 128, thus describes the
advantages of this kind of ironstone :—
“Instead of 20, 25 or 30 ewt. of limestone formerly used to make a ton of
iron, the black-band now requires only 6, 7 or 8 cwt. to the production of a
ton. This arises from the extreme richness of the ore when roasted, and
from the small quantity of earthy matter it contains, which renders the ope-
ration of smelting the black-band with hot-blast more like the melting of
iron than the smelting of an ore. When properly roasted, its richness ranges
from 60 to 70 per cent., so that little more than a ton and a half is required
to make a ton of pig-iron; and as one ton of coal will smelt one ton of
roasted ore, it is evident that when the black-band is used alone, 35 ewt. of
raw coal will suffice to the production of one ton of good gray pig-iron.”
This calculation is strongly corroborated by a statement which was pro-
duced by Dr. Watt to the Statistical Section of the Association at Cambridge,
from which it appeared, that to make 400,400 tons of iron in the counties of
Lanark, Ayr, Stirling and Clackmannan, the quantity of coal consumed was
934,266 tons, or 2 tons 6 ewt. 2 qrs. 18 lbs. for each ton of iron, part of which
is the produce of argillaceous ores.
The statement of these discoveries appears necessary in order to account
for the great and rapid extension given since 1830 to the production of iron
in this kingdom, and especially in Scotland.
In 1836 every iron-work in Great Britain was visited, and an account taken
of its produce, by a highly-gifted gentleman, M. F. Le Play, “ Ingénieur en
chef,” employed in the Ministry of* Public Works at Paris, under whose di-
rection are made the yearly reports describing the progress of mining indus-
try in France, of which I have on former occasions availed myself in pre--
paring papers read before this Section of the Association. The result of his
inquiries showed that in that year the quantity of iron made reached to
1,000,000 tons, an amount then deemed almost incredible, but which in the
years immediately following was greatly exceeded. In his ‘ Papers on Iron
and Steel,’ to which reference has already been had, Mr. Mushet states
(p- 421) that the quantity of British iron made in 1839, was 1,248,781 tons
(See App. No. 6).
4
ON THE IRON MANUFACTURE IN GREAT BRITAIN. 103
In the following year a very elaborate inquiry into this subject was made
by Mr. William Jessop of the Butterley Works in Derbyshire, and the result
of his inquiries was printed by him for private distribution. His statement
embraces every iron-work in Great Britain, and gives the number of furnaces
in blast and out of blast, with the weekly produce of each establishment.
From Mr. Jessop’s tables it was shown that the number of furnaces in blast
in that year (1840) was 402, and the number out of blast 88; the weekly
produce of the 402 furnaces being 27,928 tons, and consequently the yearly
produce, taken at 50 weeks’ working, 1,396,400 tons. In the production of
this quantity Mr. Jessop states that there were consumed 4,877,000 tons of
coal, being at the rate of 3 tons in Scotland, and 3 tons 12 ewt. in England
and Wales, for each ton of iron. This was exclusive of the coal used in
converting pig-iron into wrought iron, and which he sets down at 2,000,000
tons additional (see App. No.7). At the time Mr. Jessop’s account was
taken, it appeared that out of 420 furnaces erected in England and Wales,
there were 82, or | in 5, out of blast, and that of 70 furnaces in Scotland,
6, or 1 in 11, were in that condition. The rapid increase of this manufac-
ture during the preceding ten years forbids the belief that this large number
of furnaces could have been idle through dilapidation. In fact, the country
was then suffering under an amount of commercial depression of no ordinary
character, and which continued to press heavily upon almost every branch of
its industry, until the abundant harvest of 1844, joined to the effect of the
fiscal reforms introduced in 1842, caused the return of healthiness to our
trading interests. The continuance of the depression, which had no doubt
extinguished so many of the furnace fires in 1840, caused still more of them
to be put out of blast in the years immediately following, and it was shown
by a statement drawn out under the direction of an association of the iron-
masters of Yorkshire and Derbyshire, that the quantity of iron made in the
first six months of 1842 in Yorkshire, Derbyshire, Staffordshire, Shropshire,
South Wales and Scotland did not exceed 523,214 tons, or at the rate of
1,046,428 tons per annum. The quantity of iron made in those divisions of
the kingdom in 1840 was, according to Mr, Jessop’s statement, 1,343,400
tons, so that the diminution of production was at the rate of more than 22
per cent., which rate was probably experienced throughout the kingdom;
and in this case the whole quantity of iron made in 1842 did not much ex-
ceed one million of tons, the quantity ascertained by M. Le Play to have
been made in 1836.
A great impulse had been given at that time to this branch of industry by
the demand arising from the construction of railways. This impulse, and
the subsequent depression, may be easily inferred from the following state-
ment of the number of railway acts passed in each year from 1831 to 1843,
distinguishing such as were for new lines from those which authorized ex-
tensions or amendments in former acts, and giving the amount of capital
authorized by Parliament to be raised under those acts.
Acts passed for
Years. = aac Capital authorized.
New Lines. |Extensions,&c. P
£
1831. 5 r| 1,799,873
1832. 5 4 567,685
1833. 5 6 5,525,333
1834. 5 9 2,312,053
104 REPORT—1846.
TABLE (continued).
Acts passed for
Years. ———_————}_ Capital authorized.
New Lines. |Extensions,&c.
£
1835. 8 11 4,812,833
1836. 29 6 22,874,998
1837. 15 27 13,521,799
1838. 2 1g 2,096,198
1839. 3 24 6,455,797
1840. wie 24 2,495,032
1841. 1 18 3,410,686
1842. 4 18 5,311,642
1843. 5 19 3,861,350
We see from these figures, that in the two years 1836 and 1837, Parliament
passed 77 railway bills, of which 44: were for new lines, and that the capital thus
authorized to be raised, amounted to more than 36 millions of money. The
length of the lines then sanctioned amounted in the aggregate to nearly
1200 miles, and would call for the production of more than 500,000 tons of
iron. The price of bar-iron, which in 1834 had been 6/. 10s. per ton, and
in 1835 was 7/. 10s., advanced in 1836 to 11/., and this gave a powerful
stimulus to the extension of the manufacture. So great a rise in the market
value of the metal checked its use however for a great variety of purposes,
and when, in the years following 1837, the railway speculation so far sub-
sided, that only 15 acts were passed for the construction of new lines in the
six years from 1838 to 1843, the price of iron fell as rapidly as it had previ-
ously risen, and it could with difficulty be sold at less than half the price
which it commanded in 1836. In this state of things, the iron-masters
sought to lighten their loss by limiting the production, rather than by forcing
their goods into use by lowering the price. This appears to have been done
to a greater extent in England and Wales than in Scotland, where for reasons
already explained, the cost of production had been so lessened as to enable
the iron-masters to work to a profit at prices by which their English compe-
titors were losing on every ton they brought to market.
Since Mr. Jessop made his statement in October 1840, not any attempt
has been made to ascertain the progress of the iron manufacture throughout
England and Wales, from which any result can be confidently given. In
Scotland, where the principal extension has occurred, several statements of
the kind have been put forward. One of these, the correctness of which has
been generally admitted by those whose knowledge upon the subject should
give weight to their opinion, states the number of furnaces in blast in March
1845, and the weekly and yearly produce from the same to have been 76
furnaces, yielding 8250 tons of iron weekly, or in the year of 50 weeks, 412,500
tons. At that time there were, according to this statement, 22 more fur-
naces built and building, and the whole of these it was expected would be
in blast in the course of 12 months from that time. It is stated by a respect-
able firm in Glasgow, that in December 1845, there were 87 furnaces in
blast in Scotland, the number at the end of 1844 having been 69; the in-
creased make of pig-iron in 1845 as compared with 1844 is stated at 60,000
tons. The lowest price at Glasgow in January 1844 was 40s. per ton, and
the highest price for the year, caused in great part by the purchases of spe-
ON THE IRON MANUFACTURE IN GREAT BRITAIN. 105
culators tempted by that extremely low price, occurred in April, when the
quotation stands at 65s. per ton: in September the price was again reduced
to 50s., and the average price of the year was 55s. 6d. per ton. In 1845, the
lowest price, which also occurred in January, was 60s., and in March the
price had advanced to 100s.; in May purchases were freely made at 110s.;
and we cannot wonder that with a rise in price equal to 175 per cent., so great a
stimulus should be given to the extension of iron-works. On the authority
of the same firm, it is stated, that the number of furnaces in blast, which at
the end of 1845 was 87, was on the 30th of June 1846 increased to 97, and
that the computed make of pig-iron in Scotland, in the first six months of
the present year, is 260,000 tons, equal to 520,000 tons in the year, showing
that the production has been more than doubled in the six years since 1840.
I have before me a detailed account of the iron-works of Scotland in
August 1846, which gives 105 as the number of furnaces in blast, 21 as those
out of blast, in addition to 11 more building. The weekly make of pig-iron
at the 105 furnaces is said to be 11,010 tons, equal to 550,050 tons per
annum ; estimating that each furnace is in action during 50 weeks. This ac-
count is in part corroborated by a table kindly sent tome by Dr. Watt, of the
works in Lanarkshire, and which places the yearly produce of that county at
390,000 tons. It is further stated, that notwithstanding the great increase in
the quantity made, according to the concurrent testimony of all parties, the
stock of iron in the hands of the makers and dealers has materially decreased.
The stock in Glasgow at the end of 1845 was 210,000 tons
and on the 30th of June 1846, only .... 140,000
TO Yeteh ats oye” mPa (2 LAY gee Nae eee ae eR 70,000 tons.
It may be assumed that this increase of production, although it may have
been at first called forth by speculation, has not been sustained by those
means, since the stock has thus diminished in the face of that increase, while
the price has been declining. In January it was 80s. and in June 68s. per ton.
A statement which appeared in the ‘Glamorgan Gazette’ computed the
make of iron in 1843 at 1,210,550 tons, of which quantity 238,750 tons were
assigned to Scotland. The entire quantity was stated to have been the pro-
duce of 339 furnaces in blast, while there were said to be 190 furnaces out
of blast in different parts of the kingdom. Another statement, communicated
to me by Mr. Buckley (Member of Parliament for Newcastle), differs but
slightly from that which was inserted in the ‘Glamorgan Gazette,’ the total
quantity made being given as 1,215,350 tons (see App. No. 10).
In the absence of any authentic statement of the make of iron in England
and Wales at this present, time, an attempt bas been made by correspondence
to ascertain the facts as they exist in different localities. The result of in-
quiries thus conducted cannot have the same value as the investigations made
by Mr. Jessop in 1840, but is offered here as the best which it has been in
my power to produce.
It is given as the opinion of several most intelligent iron-masters whom I
have consulted, that nearly all the increased production of iron in this king-
dem since 1840, has been drawn from Scotland. It is true that insome of the
Scotch works there is already experienced a short supply of materials, but on
the other hand, new fields are discovered and brought into working. Mr.
_ Jessop states, that “a new field of coal and iron has been opened out in
_ Ayrshire, but not so favourable as the Airdrie and Coalbridge district.” The
_ great demand at present experienced, and that which is sure to follow from
_ the extent of the railway projects which have received legislative sanction in
- 1845 and 1846, have naturally stimulated every establishment to its utmost
. 106 REPORT—1846.
point of production. But in order to add materially to the make of iron, a
great variety of circumstances must be brought to concur. One of the
greatest difficulties with which the manufacturers have to contend in such
circumstances is offered by the workmen, who naturally enough, perhaps,
strive to obtain for themselves the largest possible share of the increased value
of that which they produce. To be of much use in any branch of this ma-
nufacture a man must have undergone a season of instruction, and as the
number of skilled workmen is limited, these, whenever any great or unwonted
demand arises, hardly know how to set limits to their demands. On this
subject, a recent number of the ‘ Merthyr Guardian’ contains the following
paragraph.
* Prosperity in the Iron Trade.— We believe the iron trade in this district
was rarely ever known to be in a more thriving state than at the present
time. Forgemen and puddlers realize from 10/. to 182. per month. But
this state of prosperity brings its attendant snare, inasmuch as the surplus
which should be accumulating in the Savings’ Banks, is in too many cases
squandered in debauchery or lavished in vice. The state of things calls
loudly for a remedy.”
This complaint will not surprise us when we call to mind the fearful de-
scription of the state of the population of Merthyr, read before this section
of the Association at Cambridge, by Mr. Kenrick. But the same complaint
is made in other quarters, and there is but too much reason to fear that it
might be universally preferred. In a letter now before me, an extensive
iron-master in the north of England writes on the 15th of August last,—“ The
cost of making iron from the recent spirt of prosperity has increased so
enormously that the ‘ prosperity’ has well-nigh ruined many makers! wages
are so ruinously raised.”
A gentleman writes from Scotland in June 1845,—* This is the present
position of the trade. The speculators were first bitten by the mania of an-
ticipated consumption; then the masters took the fever, and, as was to be
expected, the workmen follow, and say they must have a rise of wages equi-
valent to the 110s. price. It is nothing to them that iron has again fallen;
they say, first put us up equivalent to the high price before you can ask us
to conform to the present. The iron-master will therefore find that he must
give the wages corresponding to 110s., although he may sell at ‘70s. or less.”
It is understood that chiefly from this cause the cost price of iron in Scotland
has been increased about 15s. per ton.
May we not reasonably allow ourselves to indulge the hope, that at some
future, and perhaps not very distant day, the two classes of employers and
workmen may come to the better understanding of their mutual interest, so
that the sun of prosperity, whenever it arises, may shine equally for both ?
Statements were inserted in the course of last year in the ‘ Mining Journal,’
and were made the subject of remark by different persons without impugn-
ing their accuracy, to the effect that the make of iron in Great Britain during
1845 would amount to about 1,330,000 tons. If the statement concerning
the production in Scotland already mentioned should be correct, this would
leave for the make in England and Wales 917,500 tons, being 134,000 tons
less than the quantity stated by Mr. Mushet as made in 1839, and 238,000
less than the produce of 1840, as given by Mr. Jessop. The increase in
Scotland during the five years was, on the other hand, 171,500 tons, thus
leaving the whole produce of 1845 less than that of 1840 by 66,500 tons.
It will doubtless appear extraordinary, that with so much cause for increa-
sing the quantity as had arisen last year out of the actual and anticipated
demand for railway purposes, the produce in England and Wales should not
+A
*
i
q
q
if
i
DY "4
ON THE IRON MANUFACTURE IN GREAT BRITAIN. 107
at least have overtaken that obtained in 1840, and that it had not done so
ealls for explanation. In the endeavour to obtain this I have been met by
statements which might appear to be in some respects somewhat contradic-
tory of each other, the different writers representing matters as presented to
their own views and experience, and without possessing that general acquaint-
ance with the facts existing in other districts which it is so desirable to attain,
One most highly intelligent iron-master whom I have consulted writes, “I
consider now,” that is, since the discovery of the hot-blast system, “that all
the ironstone and coal of this country is applicable to the production of iron.
I fear however that the deposits of ironstone exceed very much those of coal,
and that the increasing demand upon this latter article will before many years
show its effects. I think in Staffordshire they already feel a want in the high
price of coal, and the iron trade seems migrating northward, where coal is
more abundant and different deposits of ironstone are continually discovered.”
The gentleman who thus writes is interested in iron-works in the county of
Northumberland, where the make of iron has increased and is increasing
greatly and rapidly, but still not sufficiently to compensate for the falling off
of production elsewhere.
Another gentleman, from whom I have received great assistance in my
inquiries, writes, “ In some of the localities in Scotland there is beginning to
be a great scarcity of ironstone, several furnaces being recently put out in
consequence ; and in Staffordshire still more so. People’s ideas about increase
of make of iron travel much faster than the reality. In fact, during 1845
great numbers of the furnaces in Staffordshire were going on ha/f-quantity,
simply from want of materials; this J know.” It is corroborative of this re-
presentation, that a powerful iron company, having works in Staffordshire, has
for some time had two new furnaces completed without putting them in action.
From a third correspondent, whose interest is in the great iron district of
South Wales, I hear of so great a number of new works building in Durham,
Cumberland, Northumberland and Scotland, that any account taken of the
produce in those districts, even so recently as last April, must necessarily be
very imperfect. He adds, “They are progressing so rapidly, and can pro-
duce iron at such a cheap rate in these new iron districts, as to lead to the
conclusion that ultimately the principal seat of the iron manufacture will be
removed from South Wales to the North of England and Scotland.”
On the other hand, Mr. Mushet, whose acquaintance with the subject is
probably of a more general nature than that of my correspondents previously
quoted, writes so recently as the 16th of August in the present year,—“ The
principal object in the iron trade which now attracts attention is the recent
discovery of an extensive district of black-band ironstone, ranging from
beyond Cwm Avon, through Maesteg, towards the valley of the Taffe. The
two principal beds or veins of black-band lie high in the coal series, and in
this respect differ from the Beaufort black-band, which wa’ found over the
lowest coal, and from the Scotch, which was found descending in the coal-
series at various depths. These beds measure fifteen inches each in thick-
ness, and will each yield fully 3000 tons per acre. The lower bed contains
40 per cent. of iron, and is put raw into the furnace ; the other is previously
roasted, as it contains more shale, and when so roasted yields the same quan-
tity of iron as the other when raw. As this range of minerals occupies both
sides of the line from Cwm Avon to Cwm Taffe, large tracts of black-band
ironstone must unavoidably be found, and it may not be hazardous to pro-
nounce that this in time may rival Merthyr, and become an extensive iron-
making district, probably the Lanarkshire of South Wales.” Mr. Mushet
furnishes a list of fourteen furnaces in which this black-band ironstone is
108 REPORT—1846.
partly used, and mentions three other furnaces now building in which it will
be employed.
Referring to the counties of Durham and Northumberland, Mr. Mushet
gives a list of thirty-five furnaces where twenty years ago only one blast-
furnace, at Chester-le-street, was known to exist; and he mentions, but not
as of his own knowledge, another source of supply as about being brought
forward into notice from the spoil and waste of the lead-mines in Weardale,
“which are now worked and have been so for ages.” He says, “‘ The rider
of the lead-ore is a true carbonate of iron, some of it yielding from 25
to 40 per cent. A small blast-furnace has been erected at Stanhope, where
a very important and interesting experiment has been made, aud a suc-
cessful result obtained, in which this rider ironstone has been smelted, and
pig-iron of a strong and excellent quality produced. This ore, even after
being ground and washed, still contains some particles of galena, and which
in smelting gives out at the furnace-top a heavy cloud of sulphurous smoke,
of a forbidding aspect. The pig-iron, however, when remelted, yields no
smoke from its surface, which would be the case if a small quantity of me-
tallic lead were thrown in, from which it may be inferred that the lead is in
the process of smelting entirely dissipated and driven off. What effect may
be produced upon the conversion of this iron into bar-iron remains to be de-
termined. The result of this experiment has been deemed so satisfactory as
to induce the company to erect large smelting-works about three miles from
Wolsingham. These works consist of two powerful blast-engines and six
large blast-furnaces. In this enterprise we shall by and by behold the spoil
of ancient mines, which has reposed for ages, brought to light, no longer as a
useless, but as a useful material for the production of the common and ordi-
nary sorts of pig-iron. Great and beneficial results are calculated upon, and
should they be realized, will no doubt contribute greatly to the produce of
our iron manufacture.”
Other authorities do not speak so hopefully of this discovery, and certain
it is, that of the six blast-furnaces of which Mr. Mushet speaks, only three
have hitherto been erected, and only one of these is lighted. A great part
of the furnaces now existing in Durham are chiefly employed in reducing
ores procured from Whitby and from Scotland, and occasionally small quan-
tities of hematite ore are procured from Devonshire and from Cumberland.
There is a considerable quantity of ironstone of the argillaceous kind in the
eastern division of Durham, but it is for the most part found at inaccessible
depths, or in such positions of dislocation as to render the cost of working it
too great. At a place called Shottley-bridge, about fifteen miles west of
Newcastle, where the ore is plentiful and very accessible, there have been
eight furnaces at work for some time, and six others are now about to be
lighted. The argillaceous ironstone found at that place resembles in quality
the ironstone of Staffordshire. This is the only portion of the county of
Durham in which it has hitherto been found practicable to make iron in any
large quantity with materials wholly found on the spot. I have a list of
twenty-two furnaces now in blast in the two counties of Durham and North-
umberland yielding weekly 1895 tons of pig-iron, equal to a yearly produc- —
tion of 94,750 tons, the quantity made in 1843 having been estimated at
25,750 tons, and in 1844 to only 21,250 tons. In various localities in North-
umberland there is abundance of clay-ironstone in the immediate vicinity of
plenty of excellent coal and limestone, and in the course of years large quan- —
tities of iron may be made in that district. The great obstacle to any sudden
increase there and elsewhere is offered, as already mentioned, by the difficulty
of procuring skilled labour. Any addition to the number of coal-miners can
ON THE IRON MANUFACTURE IN GREAT BRITAIN. 109
be made only by slow degrees, and the same condition applies to all other
classes of persons whose labour is required for the manufacture of iron. It
is hopeless to stimulate the exertions of the persons already employed. They
are naturally ready enough to exact higher rates of wages when the demand
for their labour becomes more urgent, but sueceeding i in this they prefer to
obtain the same amount of earnings, with higher rates a wages, to the secu-
ring of greater gains by the exertion of even “the same amount of toil, so that
a greater urgency in the demand may be, and frequently is, accompanied by
a lessened production.
Under these circumstances, how the enormous demand existing and to arise
from carrying out the railway schemes already sanctioned is to be met, it
would be most difficult to say. The laying down of these lines and providing
them with the needful working stock of carriages, &c. would absorb all the
iron which it is reasonable to expect will be made in Great Britain during
the next three years, and it affords no satisfactory solution of this difficulty to
say that the quantity required will only be called for progressively, and that
the demand will be spread over the same three years. To render this circum-
stance effective, we should be assured that no further projeets will be sanc-
tioned during the time spent in their construction, an assurance for which
we can hardly look, and even then we should be left without a ton of iron
applicable to the thousand other purposes for which this metal is so indis-
pensable. If the difficulty presented by the want of labour could be sur-
mounted, there appears no rational ground for supposing that we should, for
a very long time to come, experience any deficiency in the means for making
iron. In-the anthracite coal district of South Wales, where clay-ironstone is
thickly interstratified with the coal seams, there appears to be no reason to
doubt that if the means employed in the anthracite district of America for
: smelting the clay-ironstone were adopted, it would prove equally successful.
The difficulty consists in the sluggish nature of anthracite, which requires a
: more rapid draught than can be provided by the ordinary means of bellows
and tall chimneys; and this is overcome in America by obtaining a great
volume of air by means of fanners. The iron made with raw anthracite coals
has been found by Mr. Mushet to be much stronger than iron made with
coke, and after a variety of experiments, the earlier of which afforded but
small encouragement, this fuel has been adopted by the proprietors of twenty-
three furnaces, who avail themselves of only the ordinary means for providing
a blast. The manner in which the railway demand has already limited other
__ uses of iron, may be gathered from the following extract from a letter of
_ recent date written to me by Mr. Mushet :—
_ At the above period (1840) merchant bar-iron, boiler-plate, sheet-iron
_ and rod-iron, principally occupied our mills; but these of late, particularly in
_ South Wales, have given way in a great measure to the manufacture of
railway bars, so as to eclipse in a striking manner the varied and extensive
assortments required by the merchants’ demands.” The long period of dul-
ness that intervened between 1839 and the beginning of 1845, accompanied
as it was by a continued fall in the market price of iron, caused this metal to
_ be applied, most advantageously, to a variety of new purposes, from which it
will be prejudicial henceforth to withdraw it. In a well-known mercantile
circular letter issued in February 1845 by Messrs. Jevons of Liverpool, it is
‘stated that there had arisen “a new and increasing demand for iron roofs,
iron houses, and fire- proof buildings in Liverpool,” and that during the year
_ then just passed upwards of 20,000 tons of cast and wrought iron had been
- sousedinthattown. These gentlemen further stated that preparations were
_ going forward for the erection of still more extensive ranges of buildings of
110 REPORT—1846.
similar construction during 1845, and that the sailing-ships and steam-vessels
then under construction in that port would require 25,000 tons of plate-iron
and angle-iron.
The employment of iron for the purpose last mentioned, that of ship-
building, has already been an object of very great national importance. The
extent to which this use for the metal may be carried in future years it is
not possible to foresee, but we may base upon even our present limited ex-
perience the hope that by this means our furnaces and forges may be pro-
vided with some employment when our system of railways shall be completed.
The tonnage of mercantile shipping belonging to the British empire in 1845
was 3,714,061 tons, and exceeded the amount in existence in 1814 by
1,097,096 tons, but during that interval there were built and registered ships
amounting in their measurement to. 5,476,957 tons, so that there were required
to be built ships of the aggregate burthen of 4,379,861 tons, in order to re-
pair the waste occasioned by wear and tear and by losses: altogether the
building of ships has gone forward at the average rate of 176,676 tons
yearly. Assuming for the moment that this same rate of building will be
called for in future years, and that the whole of the mercantile shipping con-
structed would be built of iron, this would prove a very insufficient substitute
for the demand now existing for railway purposes. I have before me a
statement of the weight of iron used in building eight large sea-going steam-
vessels, the aggregate measurement of which was 5922 tons, by which it is
shown that the metal used was 2877 tons weight, or 9 cwt. 2 qrs. 24 lbs. for
each ton of measurement, and at this rate the construction of 176,676 tons of
shipping in each year would provide a market for no more than 85,814 tons
of wrought iron, equal to 115,849 tons of pig-iron. We cannot suppose,
however great may be the advantages attendant upon the substitution of iron
for timber in ship-building, that this use of the latter material will be all at
once, or indeed for many years, abandoned. There are many existing inter-
ests opposed to the change, and there is much of prejudice still to be over-
come before all our merchant-ships will be built of iron. We must likewise
bear in mind the now well-established fact, that iron ships are far more durable
than those built of timber, that they require much less repair, and that they
are less subject to accident and to loss. It cannot be necessary, however, to
enlarge upon this subject, since the Association has already been favoured
by Mr. Fairbairn at one of its former meetings—that held at Glasgow in
1840—with a valuable paper upon the subject.
Placing this subject in another point of view, may we not however feel
justified in believing, that when opposing interests shall have been silenced,
and existing prejudices shall be overcome, and the fast increasing commerce
of this country shall have experienced some degree of that development
which is expected to spring from late changes in our commercial legislation,
the rate of increase hitherto sufficient to supply the waste of our mercantile
marine, and to provide what has been necessary for its increase, will no longer
suffice to that end, and that although our iron ships may outlast by three or
four times the less durable vessels now constructed, and through all their
existence may call for little or no materials to be used for their repair, that
the necessity for additional shipping may in great part prove an equivalent
for the lessened demand otherwise arising ?
The building of iron ships is at this time proceeding at a greater rate than
at any previous moment since their first introduction, although the price of
iron has so materially advanced, and this should give us the assurance that
when, as we may expect it will happen, the falling off of railway demand, or
the exertions of our iron-masters, shall have restored the equilibrium between
ON THE IRON MANUFACTURE IN GREAT BRITAIN. i Ria
supply and demand, and the price shall again have become more moderate,
an impetus will be given to the production of shipping, not alone for the
uses of our own merchants, but for carrying on the trade and navigation of
other countries. The cost of our shipping will then be so materially reduced,
both their first cost and the expense of their maintenance, that the objection
so often and unfortunately so successfully offered by our shipowners to any
relaxations in our commercial code affecting their business, that the greater
cheapness with which shipping can be produced in foreign countries prevents
their successfully competing with ships of those countries, can no longer be
urged with any plausibility; but on the contrary, that ships of English con-
struction will then be the cheapest in the world. It has been said that fluc-
tuations in the price of iron do not cause any considerable difference in the
cost of iron vessels, so large a proportion of their whole cost consisting in
labour. A reduction of 20s. per ton in the price of the material will, how-
_ ever, cause an ceconomy of 10s. per measurement ton in the cost of the ship,
and it will hardly be said that the very possible rise or fall of 3/. or 4d: per
ton in the price of iron plates is an immaterial circumstance to the ship-
builder. But the cheapness here spoken of will no doubt be principally
found in the greater durability and the insignificant cost of repairs of metal
ships.
A statement was inserted a few months ago in a Scotch newspaper, giving
the particulars of the iron ships then under construction in the Clyde; they
amounted to twenty-four in number, and were of the aggregate burthen of
14,032 tons (see Appendix No.8). These were all steam-vessels, to which
class of shipping iron has hitherto been principally applied, although there is
no reason for supposing that it is not equally applicable to every description
of naval architecture. The reason for this circumstance may probably be
found in the fact, that the construction and employment of steam-vessels has,
for the most part, been undertaken by persons not previously interested in
shipping, and who consequently had no prejudice or habit to overcome in
their choice of material. i
This statement, imperfect as it necessarily is, would be more glaringly so
if it did not present some particulars of our external iron trade.
So recently as the beginning of the present century more than two-fifths
of all the iron used in this kingdom was imported from the north of Europe.
Foreign metal was then used for very many of the purposes to which iron
was at that time generally applied in England, and it was so used indiscrimi-
nately with British iron. In 1806 the use of foreign iron had been lessened
by nearly one-third, while the home production was so increased as to form
seven-eighths of the quantity used. In a few years after our make was be-
yond our own wants, and foreign iron ceased to be imported for any pur-
poses to which the produce of our own forges could be applied. Thence-
forward our demands have been confined to metal of the qualities from which
alone steel can be made. Our exports of British iron have, on the contrary,
increased progressively, and have now become an object of great national
importance. The statement given in the Appendix, No. 9 shows the yearly
progress of the trade since 1827 up to the year 1845 inclusive. . It will be
seen on consulting this statement, that the quantity had increased from 92,313
tons in 1827 to 351,978 tons in 1845, and that’ the declared value of the
shipments advanced in that interval from £1,215,561 to £3,501,895. A
column has been added to the table, exhibiting the average value per ton of
all forms of iron exported in each year, from which it will be seen how great
an influence price has, in its advance and its diminution, upon the lessening
or increase of our exports. In 1840, when the average value appears to have
112 REPORT—1846.
been 9/. 8s. 2d., the quantity of British iron exported was 268,328 tons. The
price in the following years fell rapidly, and the demands from other countries
increased as rapidly. In 1843, when the average price is represented by
5l. 15s. 5d. per ton, the exports were 448,925 tons. In 1844 the quantity was
slightly increased, viz. to 458,745 tons, although the price had advanced to
6l. 19s. 2d. per ton; but in 1845, the further advance in the average declared
value to 9/. 18s. 11d. per ton, reduced our foreign shipments to 351,978 tons,
or by more than 23 per cent.
It is worthy of remark, that we now export largely, more largely than in
former periods we ever imported from the same quarter, iron in its crude
state, and articles manufactured with the same, to the countries whence we
once drew the largest proportion of what was used by us. In 1844 our ship-
ments of iron, in its various forms, to the north of Europe amounted to
178,635 tons, equal probably to 200,000 tons of pig-iron; and in 1845, not-
withstanding the great speculative demand and rise in price at home, our
shipments amounted to 140,006 tons, equal probably to 160,000 of pig-iron.
In those two years the whole of our colonies and dependencies took from us,
in 1844, '78,594 tons; and in 1845, 60,683 tons.
Our largest customers are found in the United States of America, and it
is probable that they will long continue to be so, unless the citizens of those
states in which materials for producing iron are found should be unduly
stimulated to increase their home production through the existence of high
prices in this country. An increased demand from that quarter is expected
when the more liberal tariff recently passed at Washington shall come into
operation, but it is clear that the realising of that expectation must depend
greatly upon the state of markets in this country (see Appendix, No. 11).
A writer of the protectionist school, in an article inserted in the ‘ National
Magazine,’ published in New York in July 1845, states that the make of iron
in the United States in that year from 540 blast-furnaces would amount to
486,000 tons, and that the domestic supply would ere long be brought to
meet the entire wants of the country. New furnaces and rolling-mills are,
according to this writer, being erected in every direction, and those works
that had been inoperative and unproductive, from the low prices of iron in
1843 and 1844, were again at work, so that it might soon be unnecessary to
import a ton of the metal from Europe. With a moderate price in England
we need not put much faith in this assertion, which was put forth as an in-
ducement to Congress to add to the high protection then afforded by the
tariff, but which is now reduced.
France, notwithstanding the exorbitant duties charged on importation,
takes from us a considerable and constantly increasing quantity of this metal
(see Appendix, No. 12), and although the production of pig-iron in that
country has increased from about 220,000 tons in 1831 to about 420,000
tons in 1843, and is still increasing, the want of a sufficient supply of this
all-important metal is severely felt in that country, and the high price is
found to weigh grievously upon various branches of industry. In particular
a cry has been raised, which it is expected may be successful, in favour of
the admission, free of duty, of plate-iron suitable for ship-building, but the
eagerness now shown to obtain this concession will be much abated should
the price of the material advance in any great degree in England. At this
time we are certainly not in any condition to meet the demand that might
come upon us should that concession be made by the French Chambers.
With the exception of England, Sweden appears to be the only country
which has or can be expected to have any disposable quantity of iron for export-
ation, and it does not seem likely that we shall be a customer for any, except
ON THE IRON MANUFACTURE IN GREAT BRITAIN. 113
that which we need for converting into steel, to which use Swedish iron is
peculiarly applicable, and for which its high price causes'it to be reserved. To
gg our shipments of this metal are fully equal to the quantity imported
thence.
After much consideration given to the circumstances in which our iron
manufacture is now placed, and to its prospects for the future, I venture,
with some hesitation, to offer the following opinion.
Legislative sanction has been given in this and the two preceding years
to the construction of many thousand miles of new railways, in the comple-
tion of which so many interests are engaged, that we must not expect any
considerable portion of them to be abandoned by their projectors. We must
for this reason expect that for some few years to come, during which these
works will be going forward, the price of iron will be high. The tendency
of this high price will be, to give an impetus to the manufacture, and to cause
much new capital to be invested for its extension, for which ample opportu-
nity presents itself in different localities, although in other places, as in
_ Staffordshire, where the manufacture has hitherto flourished, there is more
reason to expect diminution than increase, owing to a failure in the supply
of materials. The great obstacle to the forming of new establishments, and
to the extension of those already in operation, consists in the difficulty of
procuring the necessary amount of labour, miners, furnace-men and others.
This obstacle will, however, be gradually and progressively lessened, and
when the present exaggerated railway demand shall have ceased, as it must
necessarily do through the completion of the lines which alone can be pro-
fitably opened, and the demand thence arising for iron shall be limited to
the quantity—still, however, considerable—which will be needed for keep-
ing the lines in repair (see App. No. 13), we shall find ourselves in posses-
sion of means for making iron much beyond what have at any previous time
existed, and very greatly beyond any probable demand to arise from other
and existing channels of employment at home, or from foreign countries.
The price will consequently fall, as it has done at former times and under
analogous circumstances. We shall then find that this metal will again be
employed in uses from which it may have been excluded by the previous
high price. From the improvements already made, and from others which
we may expect will be introduced into the processes of manufacture, we may
even find that the market price will fall to a lower point than has hitherto
been witnessed, and new uses may in consequence be discovered whereto to
apply this metal. All this, however, must be the work of time, and it seems
but too probable that in the meanwhile our iron-masters will have to undergo
a somewhat lengthened season of adversity, for the enduring of which they
are in a measure prepared by former experience.
114
REPORT—1846.
AppEnDIx No. 1.
Manufacture of Pig-iron in England and Wales, 1788.
Made with coke of pit-coal.
——— 48,200
Counties, No. of Furnaces. Tons of Iron,
SEP BIILES eds fey sdapaneseonten ens » SU UNEE ve rade egstt spueed 23,100 |
MIGAHOTASITE 5 seneseas¥eeesasbsens CD iE RE ee 6,900
WeEpysOITe sepecesresnaccdcaacane NY (TEAR: 4,200
NVOPKSHITG cceaseceeactsasees cep odnen Rank ea 4,500
Gimberlandets. peer tee 1 i hae ahaa A 700
Chigshire ite erie recent eeesets | Wane eR ee 600
Glamorganshire ......c.sssesees GS Gi cccavediotdeeis 6,600
Brecknockshire ......... Teer By aig Aone: veo e008
Made with wood-charcoal.
Gloucestershire ........ss000e ps ava oh eee eee te 2,600
Monmouthshire ........seessseres iS era ssacddeiecieds 2,100
Glamorganshire ..........0009 eas hl MLD Wicwede keene a ap ae 1,800
Carmarthenshire ,,.....0ccersceees | ees eee 400
Merionethshire ........eseeeeeeee 1 Lp SP Bari ve Ire 400 .
RUNIPOPSIINGs caaanenass ipaesccnevoens piasaei sates andar 1,800
Derby shite Wecssaps-spsseyscsese sins’ NUprc eS acccscosenes te 300
RYOrKSNne te cont othe eater eaeete 1 eRe ACHEP EEE 600
Westmoreland .........ccccscessees GRR ie 400
Crimberland yee ieescce ct Tt Rea 300
Lancashire 2304. see tess Beatesa eae ees 2,100
PUIGBORK iain davies cdathavte caeeedeuad D sice Mv cpentactexkep 300
DN GtAl i dca tuccavakavarastiaceussicsscaeheotade 61,300
AppENDIx No. 2.
Manufacture of Iron in Great Britain in 1796.
Counties. No. of Furnaces. Tons of Iron.
Chester ..2.:..60055 MEOW Lue CL Bs aetna eae 1,958
Cumberland 4.....6..c0000. 00004 Boi. Save sia Saeie 2,034
Derbyshire’ \);...0.0caveeeacawes Bel ask dad sivas ene: ead
Gloucestershire ......... ey CA ree 380
Herefordshire .........+ececeees Dir casetbeeseedsdeece 2,529
Lincolnshire............ Wiavoceas DR co auction conte 705
BHPOPSNINE oo. c5ezerdancxemandee BS) \aisersavent press 32,969
MSSEK. aairsheccecestaresore PS ok.) Meee 4 et Sr. 173
Mouph Wales sccccschecesecshos OR ah scieccs ase 34,251
INOrEaiWales Vecvacsccclacsossves By aibiccsuiecdseeee 1,434
Staffordshire...c....scsecccessess At Halse eere ets 13,211
Yorkshire...... .. tile See is QO asi eeiee eed 17,242
104. ccacassecmcadierns 108,993
SICOLLANG Nevsadercsaeascoecevssans 17... didepacdaassesdaos 16,086
Total—Great Britain ... 121 ..occcscosscessoe 125,079
=
:
;
:
|
F
7
4
é
ON THE IRON MANUFACTURE IN GREAT BRITAIN. 115
9 ApPrENDIX No. 3.
k Production of Iron in 1806 in Great Britain.
: Counties, No, of Furnaces, Tons of Pig-iron.
% Cumberland ...........ceseeeeee. 2 ie dase ae ap a 1,491
i Derbyshire .....4...00 Badberces Wyo TePereeeweanranseeces 10,329
4 Gloucestershire ...... cori cce i eer pe et ae astues 1 1.629
fi Lancashire .............+8 sake impr -e ree veese 2,000
Monmouthshire ............... i atdieeteserdeaes: 2,444
} Shtopshire’ ............esesesees NRE Pe heir RE es 54,966
i sDRAMORCEMIE ;.2...,.....5-.-00058 lea Pb fob aae'rs 49,460
i 28 ee ei bmn Hl des een lh 26,671
‘ South Wales........csccccseesues S| al REESE ehh ae 75,601
% aa Wales: aR ieccesuccrccsuaeee 2,075
i Old charcoal furnaces in dif-
N ferent counties .......00..0..- } T] ssseseeseeeerense 7,800
; Total—England and Wales 155 ssesssesssssseases 234,966
; erin oe a lt Bea Miter cgaee eno 23,240
Total—Great Britain ...... Bs apecdane vse Pl 258,206
j
: Appenpix No. 4.
4 Production of Iron in Great Britain in 1823.
' Counties, No. of Furnaces. Tons of Pig-iron.
b) Staffordshire ..,...... AP ESE Ome Bana eehapeeans 133,590
Shropshire ......... Rav auce cakes Stele Ee sahacaees 57,923
Workshire . c.2d.décccscec.cso0es DOT) wines ra. bathaceens 27,311
Derbyshire ...... iebatyackos. Wich cokes en NG 14,038
Northumberland and Durham = 2... sca eceeee ere oy Ky
South Wales ..........0..0ee08 PF OCS AO OR « 182,325
North Wales (estimated)...... MeCN eansiancs vavacive 10,000
NG. ccesax Risceceanacs 427,566
RCOCLADE ooo .c cscs hevasiilh Ne i ea 24,500
Total—Great Britain ...... 259 ..ccccsceessssere 452,066
APPENDIX No. 5.
Production of Iron in Great Britain in 1830.
Counties. No. of Furnaces. Tons of Pig-iron.
Staffordshire ......... doattugce DS as epee 212,604
ESMTOPAUIEG ssspeiysn esas anshines rasa Bees pera w. 73,418
Yorkshire .......ceccecceeeeeee DN caen Pe Oba tt 28,926
PIPED VENI, 5 ansceseuacdesesetae PB wakes geatacceets 17,999
Northumberland and Durham = 4._—Ck.. esc ec cen ceee 6,827
South Wales .......eecesceeees PTS ea ay 277,643
North Wales (estimated)...c. 1... scccesensssssceses 25,000
BBS vecene wachebaaeete 640,917
Seotland 56) b tit ae C7 GR een See 37,500
Total—Great Britain ...... SHON ace sossesees 678,417
12
116 REPORT—1846.
AppENDIXx No. 6.
Quantity of Iron made in Great Britain in 1839, as stated by David
Mushet, Esq.
Districts. No. of Furnaces, Tons of Pig-iron.
South Wales ......cc.cccsssecsees De ere sanvaccccocucee 453,880
POGrEGt AGH AE ea nas Ream sewsee 18,200
PHO PHENRS Eisschthen ties ncswdane at teatns: SaaNer cases 80,940
Staffordshire (SOME) ("5 ec saese NOG arate totes ssc vs 346,213
Staffordshire (North)............ Me arbepnccneutae eee 18,200
Neat WV alee ce 1 Seder SE ie aca 33,800
Derbyshire ............ ARR Le eas a: Mamudiont« 34,372
NWeorighie oe eacsndeb We. Mistees sate anenters 52,416
Northumberland and Durham BG SR) ccereteenes 13,000
PUD laid srg see. asks cues ve caes OE i inci sc esracceeuene 196,960
OUh. caiscesatoenneee 1,247,981
Lancashire (charcoal-iron) ......sc.sssssessenseseessaseeces 800
Total of pig-iron in Great Britain ............ 1,248,781
APPENDIX No. 7.
Production of Iron in Great Britain in the year 1840, as ascertained by
Mr. William Jessop, of the Butterley Iron Works, Derbyshire.
Number of Furnaces
Districts. Iron made. Coal used.
In blast. |Out of blast.
tons. tons ;
Forest of Dean .........06. + . 15,500 60,000
South Wales ..........s000 132 31 505,000 1,436,000
North Wales ...........00- 12 3 26,500 110,000
Northumberland............ 5 1 11,000 38,500
Workshines G4 i.deies cor: 25 7 56,000 306,500
Derbyshire .........csseeeee- 13 5 31,000 129,000
North Staffordshire ...... 7 9 20,500 83,000
South Staffordshire ...... 116 19 407,150 1,582,000
SHEOPERIRG: gressceceerases: 24 7 82,750 409,000
Scola a, Govncesesecserise 64 6 241,000 723,000
402 | 88 -| 1,396,400 | 4,877,000
Coal used in converting to wrought-ir0n..........sseeseeeeeeseoene 2,000,000
6,877,000
Of the above 402 furnaces, there were using hot air, 162; cold air, 240.
j ON THE IRON MANUFACTURE IN GREAT BRITAIN. _117
AppENDIXx No. 8.
Iron Steam-Vessels being built in the Clyde during the Spring of 1846.
1 of 2,000 tons burthen and 750 horse-power.
520
: PESO cas sescrvissniyotss
GMOS 5... LLRs 450
Be WOO: 5. eseaNeeee 400
Eig oa cap AN 400
BRE PRU Siac tacl verse cs 400
Ba ZOD sana aawrseveheae 280
Te Tar Te inline cated 300
ATG TTT he ent a 220
Bs SOO. cman ee 300
Ee ROU: Scacetecmmseoretcees 200
He AHO) | cat Oupeptscp-ee 250
Be Wane a AM I 250
PER ABO pias ies 150
a PeMee aia cer Mee ecu 50
Tec AN ee ba, os Oh va 50
9 ag ie a Sea 160
BRT re cceaceac\oe 35
SC» NO cae A 35
Pee ates tee gous 35
Ga MEU oe ores tocpaioen 120
[Att | DR EO 100
Tee ee bdstle 65
WS UP sy veceatsesnnateaats' 60
24 14,032 | 5,580
AppEnpDIx No. 9.
Quantities of British Iron exported, with the declared value of the same, and
the average value of each ton exported in each year from 1827 to 1845
inclusive, stated in tons.
nee EE EEEET [SEER SSNEASEN GREE
Declared Average de-
Years, | Bar-iron. | Pig-iron. | Castings. | All kinds*. value. clared value
per ton.
£ £8 d
1827.| 45,284 | 7,095 | 6,292 | 92,313 | 1,215,561 | 13 3 5
1828.| 51,108 | 7,826 | 6,205 | 100,403 | 1,226,617 | 12 4 4
1829.| 56,178 | 8,931 | 8,219 | 108,275 | 1,162,931 | 10 14 9
1830.| 59,885 | 12,036 | 8,854 | 117,420 | 1,078,523 | 9 2 8
1831.| 64,012 | 12,444 | 10,361 | 124,312 | 1,123,372 | 9 0 8
1832.| 74,024 | 17,566 | 12,495 | 147,636 | 1,190,749 | 8 1 3
1833.| 75,333 | 22,988 | 14,763 | 162,815 | 1,405,035 | 812 7
1834.|. 70,809 | 21,788 | 13,870 | 158,166 | 1,406,872 | 8 17 10
1835.| 107,715 | 33,073 | 12,604 | 199,007 | 1,643,741 | 8 5 2
1836.| 97,762 | 33,880 | 19,891 | 192,352 | 2,342,674 | 12 3 7
1837.| 95,663 | 44,387 | 12,373 | 194,292 | 2,009,259 | 10 6 10
1838. | 141,923 | 48,554 | 14,942 | 256,017 | 2,535,692 | 918 1
1839. | 136,452 | 43,460 | 10,836 | 247,912 | 2,719,824 | 10 19 6
1840.| 144,719 | 49,801 | 9,886 | 268,328 | 2,524,859 | 9 8 2
1841. | 189,249 | 85,866 |14,077 | 360,875 | 2,877,278 | 719 5
1842. | 191,301 | 93,851 | 15,934 | 369,398 | 2,457,717 | 613 0
1843. | 198,774 | 154,770 | 16,500 | 448,925 | 2,590,833 | 515 5
1844. | 249,915 | 99,960 | 18,969 | 458,745 | 3,193,368 | 619 2
1845.| 153,813 | 77,362 | 22,036 | 351,978 | 3,501,895 | 9 18 11
po
* * Including the kinds stated in the previous columns, together with bolt- and rod-iron, iron-
__ wire, anchors, grapnels, &c., hoops, nails, and all other sorts not included in the foregoing.
118 _ REPORT—1846.
Appenvix No. 10.
Make of Iron in 1843 compared with 1840.
1840, 1843. Decrease, | Increase.
tons. tons. tons, tons.
Forest of Dean .........0.000+ 15,500 8,000:'} 7,500
South Wales .......scsseseree 505,000 457,355 | 47,650
North Wales ..............00.- 26,500 19,750 6,750
Northumberland ............. 11,000 ay (3) Ul RABE ce 14,750
IVOLKSIING: oc 0c acctcncaacoms seer 56,000 42,000 | 14,000
Derbyshire... ...2ccss-sasasso a0. 31,000 25,750 | 5,250
North Staffordshire ......... 20,500 P17 DU lecdacusoseae 1,250
South Staffordshire ......... 407,150 300,250 | 106,900
Shropshire......... Renae ecasess 82,750 76,200 6,550
Scotland
ot
:
i
u
i
ON ATMOSPHERIC WAVES. 119
Apprenpix No. 13.
Estimated quantity of Iron required for the construction and putting into
* operation each mile of Railway.
Tons per mile. Tons of Pig-iron.
Rails, 75 Ibs. per yard .....seeseeeees sees 235 equal to 3172
Chairs, 40 lbs. each ......... sivddane diztses DOG Aisiekscasenss 125
Locomotive engines, 1 per mile ciscsseee 2D seveeevenees 332
Wagons and carriages, iron-work ..00.. 20 ssssesseeeee 333
TA gE OCG) Irautdeata nemnde sd cons. aie cebtbate UE as Pie we ncteie
Turntables, points and sidings............ OU iiaraehs ahs 110
Workshops ..,..+sceseserssseeeses eee AE iE) Lah Een 402
Coke, ovens and sundries........sesesss0e. Loe ALPE 5
Bridges, roofs, stations, &c. ..sesseeceee 380 eeseeeeeeee 404
711
Required to maintain the above, each year—
Rails, chairs, locomotives, turntables, &c., 50 tons of wrought- and cast-iron,
equal, each year, to 61 tons of pig-iron.
N.B. ‘The above estimate has been furnished by an experienced railway engineer
to the chairman of a railway company. The quantities are greater than are com-
monly assigned, but an abatement of 25 per cent. would not disturb the calculation
made by me (page 109); and when provision is made for maintaining in repair the
railways now open, it would absorb all the iron which will probably be made in the
next four years, to construct, at that abatement of 25 per cent., the lines now sanc-
tioned by Parliament.
Third Report on Atmospheric Waves.
By Wiuu1aAM RapcuirF Birt.
Tue two former Reports which I have had the honour to present to the Asso-
ciation necessarily possessed a fragmentary character. Sir John Herschel,
in his Report on Meteorological Reductions (1843), distinctly traced two
well-defined atmospheric waves which passed over the British Isles and the
west of Europe, one in September 1836, the other in December 1837. These
may be regarded as the earliest instances of our detecting and clearly appre-
hending the character of the atmospheric undulations constantly traversing
our oceans and continents, and mark the commencement of that era in atmo-
spheric research to which Mr. Forbes alluded in his Report on the Recent
Progress and Present State of Meteorology, presented to the Association in
1832, when he said, “ The great extent of country over which the accidental
variations of the barometer take place, is one of their most striking features ;
and in a future and more advanced state of meteorology we may be able to
draw the most interesting and important conclusions from the great atmo-
spheric tidal waves which are thus perpetually traversing oceans and conti-
nents.’
Sir John Herschel, in the conclusion of the report to which allusion has
been made, noticed the larger fluctuations which I had observed in the
autumn of 1842, especially the symmetrical wave which occupied thirteen
_ days in November for its complete rise and fall. The curves representing
these larger undulations were appended to Sir John Herschel’s report; and
the Association, under the direction of the Magnetical Committee and the
immediate superintendence of Sir John, entrusted me with the further in-
120 REPORT—1846. ;
vestigation of these waves, especially that of November. The mode of in-
vestigation and the partial results arrived at during the period between the
sittings of the Association in 1843 and 1844 form the subject of my first re-
port, which, as before stated, must be regarded only as a fragment.
During the further investigation of the wave of November various obser-
vations came to hand, which appeared to throw considerable light on the
general character of atmospheric undulations. The publication of the Green-
wich and Toronto observations afforded an interesting comparison of the
passages of certain maxima at these distant stations, and by extending this
comparison to Prague and Munich, several interesting features of certain
secondary waves during the transit of a supposed normal wave appeared so
clearly to be made out, that it was deemed desirable to include the whole of
this comparison in the succeeding report, rather than run the risk of its being
lost by deferring it until after the examination of the great wave should be
completed. Another most interesting result arrived at about this time, was
the recurrence of the great wave of November. The return of this interest-
ing phzenomenon appeared so strikingly distinct in 1843 and 1844, that to
have omitted noticing it in the Report would have greatly contributed to re-
tard the inquiry. It accordingly forms the second section of the Report of
1845. These circumstances, with the further investigation of the great wave
of November 1842, give to the second report a more fragmentary character.
Previous to entering on the immediate subject of the present report, it will
be desirable to review the steps that have been taken for observing the great
symmetrical wave on its return in 1845; and also to notice any other cir-
cumstance that may have transpired during the past year at all calculated to
throw any light on the subject of our investigations. With regard to the first
point, certain instructions were drawn up, which were forwarded to gentle-
men interested in meteorological research, and otherwise circulated, in con-.
sequence of which a number of interesting and valuable observations were
obtained. The results of the examination of these observations, as far as it
has yet proceeded, will form the first part of the present report. In the Phi-
losophical Magazine for April in the present year Mr. Brown published a
voluminous paper on the oscillations of the barometer, with particular refer-
ence to the meteorological phenomena of November 1842, the month in
which I first observed the great symmetrical wave. This paper is accom-
panied by diagrams representing the direction of the wind in England, Scot-
land and Ireland every day, from the Ist to the 26th inclusive. Upon a very
careful perusal of it, I found that the observations, as given in the diagrams,
very beautifully illustrated Prof. Dove's theory of parallel currents or alter-
nately disposed beds of oppositely directed winds, and appeared to throw so
clear a light on the real character of the atmospheric undulations, that I was
induced to enter upon a very careful examination of the barometric obser-
vations in connexion with the diagrams of the wind. The result of this ex-
amination has been to give the inquiry a completeness which it was before
destitute of. It was previously difficult to define the real notion we formed
of an atmospheric wave ; not so much from the distribution of pressure over
a tract of country gradually decreasing on each side a line of maxima, as
from the relation of the aérial currents or winds to this distribution of
pressure of which we were to a certain extent ignorant. The examination
of these observations has exhibited very clearly the distribution of the aérial
currents in relation to the distribution of pressure, and enabled us to define
the nature of an atmospheric wave both as regards its undulatory and mole-
cular motion. This definition, with the examination of the observations,
forms the second part of this report.
poe
ON ATMOSPHERIC WAVES. 121
Part I.—ReECURRENCE OF SYMMETRICAL WAVE.
The following were the instructions drawn up for observing the Great
Symmetrical Wave on its return in 1845.
“The recurrence of the great November Wave observed in 1842 (an en-
graving of which is inserted in the Report of the Thirteenth Meeting of the
British Association for the Advancement of Science), during the autumns of
1843 and 1844, renders the barometric movements of the months of October
and November highly interesting. It is accordingly proposed that meteoro-
logical observations, on a similar plan, should be made as extensively as pos-
sible, with a view to observe this particular wave; and meteorologists are
invited to direct their particular attention to the oscillations of the barometer
during the months above-named.
“ Times of Observation.
“The following hours are the most suitable for the object now in view:
3 A.M., 9 A.M., 3 P.M. and 9 p.M.; these hours divide the day into four equal
parts; they have been recommended by the Royal Society as meteorological
hours, and are the hours at which observations are made daily, by direction
and under the superintendence of the Honourable the Corporation of the
Trinity House, which have been most advantageously used in the examina-
tion of atmospheric waves.
In cases, however, in which the observation at 3 a.m. may be inconve-
nient or impracticable, it will be important to substitute for it two observa-
tions, one at midnight and the other at 6 in the morning, so that the hours of
observation will in such cases be 6 A.M., 9 A.M., 3 P.M., 9 P.M. and midnight.
“To individuals who cannot command these hours, it is recommended
that observations should be made as near them as possible; these will still be
valuable, although not to so‘great an extent as those made at the regular
hours. In these cases, however, it will be absolutely necessary to substitute
two readings for every one of the regular hours omitted—one previous to,
the other succeeding the hour so omitted; and these should, if possible, in-
clude an equal interval both before and after such hour. In all cases the
exact hour and minute of mean time at the place of observation should be
inserted in its appropriate column in the form sent herewith.
“ At the regular hours of observation, or any others that the observer may
fix upon, in accordance with the foregoing instructions, it will be necessary
to observe,
“Ist. The barometer, with its attached thermometer, and enter in the
form the actual height observed with the temperature of the mercury.
“2nd. The external and dry thermometer.
“3rd. The wet bulb thermometer.
“[ These observations are particularly essential in order to separate the
pressure of the vapour from the aggregate pressure, as measured by the mer- .
curial column. |
“Ath. The direction and force of the wind.
“These are important to determine the connexion between the undula-
_ tory and molecular motion of the wave. ]
"
®
+
Vs
‘
A
*
a
** 5th. The character of the weather at the times of observation; which
may be recorded by Capt. Beaufort’s symbols.
“Tt is proposed to commence the observations on the 1st of October next,
_ and continue them daily until the end of November, unless it should be found
that at that time the Wave is not completed, in which case it will be requisite
to continue them a few days longer.
“ft will be necessary, on returning the form when filled, to accompany it
122 REPORT—1846.
with the following data for reduction. A blank is left for this purpose on
the back of the form.
“The geographical co-ordinates of the place of observation, viz. latitude
and longitude.
** The altitude of the cistern of the barometer above the level of the sea,
exactly ; if not, as near as it can be obtained.
“ The internal diameter of the tube of the barometer.
** The capacity, neutral point, and temperature.
“‘ [These are usually engraved on the instrument. ]
“If the co-efficients of the diurnal and annual oscillations have been de-
termined for the place of observation, include them.
“ Those sets of observations which may be reduced by the observers, should
be accompanied with the original observations, and a reference to the tables
used in their reduction, also the data above-mentioned.
“ All observations that may be made in accordance with these instructions
and forwarded to me, will be carefully examined and reported on at the next
meeting of the British Association. ‘Ww. R. Brrr.”
“2 Sidney Place, Cambridge Road, Bethnal Green.”
In accordance with these instructions observations were received from the
following stations and observers.
Taste I.
Station. Vessel or Establishment. Observer or Authority,
Sandwick Manse, Orkneys .....| ......sssssssessscsssesscessees Rey. Charles Clouston.
West coast of Scotland ......... H.M.S.V. “ Shearwater”| Commander C. G. Robinson.
East coast of Great Britain ...) H.M. Ketch “ Sparrow”) William Turton, R.N.
Firth of Forth ........sesseseeeces H.M.S.V. “ Mastiff” ...| The Officers.
Longstone, Northumberland ..| Lighthouse ............... William Darling.
Newcastle-upon-Tyne ......... Philosophical Society ...| George Muras, Esq.
EltUst,y LICIAMIL ccc agetssarctctkedl(vcenvess-s¥eees Wabstecrcesetas Dr. Stevelly.
MtOKESEY;' YOTKBHILE sive. c tel cocvdsdsocessctacisissvobasccct John Cail, Esq.
Markree) Ireland ..iisicdscaveca|Wecdaskebsoncttis sdb tdesssse sce Edward J. Cooper, Esq., M.P.
MOUK: -ciaiess oaschtsveseecahogs sddea]/tesbunccechtactavedstysulocieut John Phillips, Esq., F.R.S.
Heligoland .......... Bo dhacceuinben Lighthouse.
Galway, Ireland ..............+6 ndlpexatietiesesaaca teas « aieeud sate Lieut. Sidney, R.N.
Lough Corrib and Galway ...| ........sccsescsessccssercesees Lieut. Beechey, R.N.
Porttarlington, T'eland) sitiwesel lic iecevessddsesessbs.cccese M. Hanlon, M.B.
Dublin, Ireland ...........2...00- Ordnance Survey Office .| Capt. Larcom, R.E.
Hamerick:. Ireland n...destesaescaliugendevndeexsthandseke vante cae R. T. Maunsell, Esq.
Bardsey Island off Wales ...... Lighthouse.
BUCMINPHAM | y.,.csseseansancedes Philosophical Institution} William Onion, Esq.
Haisboro’, Norfolk.......+2..0+ Lighthouse.
Coast of Suffolk...... near tuteeee H.M.S.V. “ Blazer”...... Capt. Owen Stanly, R.N.
South of Ireland ..........es0e. H.M.S.V. “ Lucifer” ...| Commander G. A. Frazer.
South of Ireland ..........0..4. H.M.S.V. “ Tartarus”...| Commander James Wolfe.
South Bishop off Wales......... Lighthouse.
Pembroke HeM.S.V. “Hirefly”’.«.... Capt. Beechey, R.N.
GIOMCESHOR PF. Nose ds co casccveseesnelisvas.¥allvcduesttercancavcs ibe Johu Jones, Esq.
Harwich ........0008 H.M.S.Y. “ Porcupine ’’.| The Officers.
ViGHOONceasepeaneeecesesn cares oves|\scseacccse=s dp cfaestos aveaen st W. R. Birt.
Ramsgate H.M.S.V. “ Porcupine ”’.| The Officers.
MICHIVTLBIES uromtspcccencccccosart ns Lighthouse .—> xe Fig. 1.
w
7
1
1
1
i
H
!
1
1
4
‘
ke
W, The crest. wa, The amplitude. a, The origin *,
W a, The front. W h, The height. w, The end.
W w, The back.
* Mr. Scott Russell designates the point a the origin; a better term I apprehend would be
commencement.
ON ATMOSPHERIC WAVES. 135
the crest, the posterior trough, w (the end of Mr. Scott Russell's water wave) ;
the line w...h, as measured by the mercurial column, the altitude of the wave;
the slope W a, the anterior slope or front of the wave; the slope W w, the
posterior slope or back of the wave; w a constitutes the amplitude of the wave,
and x x in the same direction, the axis of translation.
The existence of atmospheric currents, especially the equatorial and polar,
has been well-established ; and there is a class of philosophers who attribute
the barometric oscillations entirely to the effects of these currents as con-
tra-distinguished to the effects of waves such as we have just mentioned. In
contemplating the transference of the barometric maxima and minima, we
regard only the wave-motion—but very different must be the atr-motion.
Prof. Dove, in his letter to Col. Sabine relative to the magnetical and mete-
orological observations, has announced his opinion that the equipoise of the
atmosphere is maintained in the temperate zone by currents on the same level
flowing in opposite directions (Report, 1845, page 61) ; thus we have a bed or
stratum of air moving from the S.W., and on each side of this are strata of
N.E. winds. We may here inquire, how are these alternate aérial currents
related to the waves before alluded to? Itis one of the objects of the following
y Fig. 2.
a i ain
m— > > US SCO SS > = SS
SW s—S> Sa Si SS 3—S> Sas evans sw
PS DS Sei => >> .
Vox =e le K << eK mE v
NO =<—_—« 29°92
Paris... <3: - 29°86
Slopes.—Lines of greatest diminution of pressure.
Anterior slope, Crest No. 2, Orkneys to Paris...... 37
Posterior slope, Crest No. 1, ” Corks 20. “31
Currents.—Wind on S8.W. side of Crest No. 1, mostly S.E.
” S.E. ” ” ae afew N.E.
The progression of the crest, which was so distinctly developed on the Ist
towards the N.E. and the succeeding S.E. current, is most decided. The
altitudes at Belfast and Christiania are nearly equal, indicating that the crest
is between them. The wind, with but few exceptions, is S.E. over nearly
the whole of Great Britain and Ireland, while at Christiania on the anterior
slope itis N.N.W. The posterior slope from the Orkneys to Cork is well-
exhibited. Altitude from Cork to Orkneys = °31.
The line of greatest diminution of pressure this day, Orkneys to Paris,
crosses that of yesterday nearly at right angles; this arises from the advance
of the anterior slope of the wave (Crest No. 2); at a few stations the wind
is N.E. that of the advancing slope, and these in the neighbourhood of a
line where the wind appears to have been variable. Altitude from Paris to
Orkneys = °37.
ON ATMOSPHERIC WAVES. 143
November 3, 1842.
Crest No. 1.
N.W.——_——_———_S..E.
Crest No. 2.
S.W. N.E.
Posterior slope, Crest No. 1.
Max. Christiania... 30°31 Bristol .... 29°96
Orkneys.... 30°24 Plymouth .. 29°91
Belfast .... 30°18 »Cork....... 29°83
Shields .... 30°10 Paris......% 29°73
London .... 29°96
Slope.—Line of greatest diminution of pressure.
Posterior slope, Crest No. 1, Christiania to Paris...... 58
Currents——Wind on S.W. side of Crest No. 1, S.E.
ie S.E 5 ce 2, N.E. towards trough.
” N.E. 5; » 1, N.W. Christiania.
The crest No. 1 is now approaching Christiania. The observations of
this day offera decided contrast to those of the 1st; the posterior slope of
crest No. | is well-developed, the point of greatest pressure being to the
west of Christiania: the point of least pressure is still Paris, where the
barometer has been falling since the 1st: this station appears to be near the
intersection of the troughs of both waves. The progress of the maximum
point is extremely interesting. On the 1st we find it at Belfast, on the 2nd
at the Orkneys, and on the 3rd at Christiania; the direction of the progres-
sion is consequently undoubted. The general direction of the wind over
England, Scotland and Ireland, is ‘S.E.; that due to the posterior slope, at
Paris and in the South-east of England, the wind is E. and N.E., the anterior
slope of crest No. 2.
November 4, 1842. .
Crest No. 1.
N.W.———_————__ SE.
Crest No. 2.
S.W.———————_NE.
Anterior slope, Crest No. 2.
Max. Orkneys.... 30°49 Plymouth .. 30°15
Belfast .... 30°45 Bristol .... 30°14
Christiania... 30°37 London .... 30°13
Shields .... 30°34 Parigy 21.0. chee 29:80
Cork ..... . 30°16 :
Slope.—Line of greatest diminution of pressure.
Anterior slope, Crest No. 2, Orkneys to Paris...... °69
Currents.—Wind on S.W. side of Crest No. 1, S.E. at a few stations.
ee S.E. 4s » 2, N.E.
The anterior slope of crest No. 2 is well-developed, and the evidence of
__ its extending over the whole of the British islands extremely strong ; also the
_ establishment of its proper wind N.E.; a few stations exhibit the S.E. wind
as the posterior slope of crest No. 1 is passing off. The line of the greatest
diminution of pressure is identical with that of the 2nd, namely, Orkneys to
Paris, but it is nearly doubled in value, being now equal to ‘69, showing
that the greatest curvature is approaching.
The crest No. 1 appears now to be over Christiania, or a little to the east of it.
144 REPORT—1846.
November 5, 1842.
Crest No. 1.
NW. SE.
Crest No. 2.
S.Wette ero NE.
Max. Belfast ...... 30°55
Orkneys. ..... 30°52 > Probable direction of Crest No. 2.
Gork ,...00-8 18032
Shields ...... 30°33)
Christiania.... 30°27
Plymouth ..., 30°22
Bristol en fu 30°20
Hondon =... .COULZ
Paris). eo TO
Slope.—Line of greatest diminution of pressure.
Anterior slope, Crest No. 2, Belfast to Paris...- *80.
Currents.—Wind on S.E. side of Crest No. 2, N.E.
The anterior slope of crest No. 2, extending from Cork, Belfast and the
Orkneys to Paris, is well-developed. Belfast is the highest point, Paris the
lowest. Altitude from Paris ‘80. The posterior slope of crest No. 1 is now
scarcely perceptible. The wind is that due to the anterior slope of crest
No. 2. The following table will show the gradual approach of the anterior
slope of this wave. Paris the lowest point :—
Belfast to Paris,
November 1........ *29
ee, Gee 32
“ CW hee 45
3 AU Wire al avergra ‘65
sy Big o ciagieeds “80
November 6, 1842.
Crest No.2.
SW JE.
Anterior slope, Crest No. 2.
Max. Belfast .... 30°51 Plymouth .. 30°24
Orkneys,,.. 30°46 Christiania,, 30°21
Shields .,.. 30°35 London,... 30°16
COrk ig. «5 30°30 Paris ...... 29°83
Slope—Line of greatest diminution of pressure.
Anterior slope, Crest No. 2, Belfast to Paris.... *68.
Currents.—Wind, with but few exceptions, N.E., anterior slope of Crest
No. 2.
Nearly the same state of the barometer is maintained over the area as on
the 5th, with nearly similar winds. The anterior slope of crest No. 2 is still
strikingly developed. The greatest curvature has passed with a very slight _
fall at Belfast and a very slight rise at Paris.
ON ATMOSPHERIC WAVES. 145
November 7, 1842.
Crest No. 2.
We NE
Crest No. 3.
We
Crest No. 2. Posterior slope, Crest No. 2.
Max. Belfast.... 30°43 Max. Belfast.... 30°43
Cork .... 30°33 Orkneys... 30°15
Shields .. 30°27
Plymouth 30°24
- Bristol... .. 30°18
London .. 30°13 }Anterior slope, Crest No. 2.
Christiania 30°02 |
Paris .... 29°89 J
Slope.—Line of greatest diminution of pressure.
Anterior slope, Crest No. 2, Belfast to Paris...... "54.
Currents.—Wind on S.E. side of Crest No. 2, N.E.
stn Nes 4 3, 5 W-
advancing anterior
3, N.W. he
slope of new wave.
» N.E. ”
The crest No. 2 has now passed the Orkneys, which exhibits a falling
barometer and the §.W. wind. The trough between crests 1 and 3 is now
to the N.E. of Belfast and Paris; the higher readings in the south-west part
of the area, with the lower in the north-east, clearly indicate the advancing
anterior slope of the new wave. Diminution of pressure from Belfast to
Christiania, *41.
November 8, 1842.
Crest No. 2. ;
SW ee ON
Crest No. 3.
NIG saa eB
Anterior slope, Crest No. 2. Posterior slope, Crest No. 2.
Max. Plymouth.. 30°13 Max. Plymouth.. 30°13
London .. 30:08 Corkins. cOOL
Bristol .... 30°07
Paris” ...3) 29°90
Anterior slope of Crest No. 3.
London...... 30°08 Christiania...... 29°67
BeWese cy. ss 30°04: CHICBEYS 4.7 = = t= 29°63
Shields ...... 29°97
Line of greatest diminution of pressure. Plymouth to Orkneys .. *50
Currents—Wind on S.E. side of Crest No. 2, N.E.
a N.W. a 2, S.W.
46 N.E. c 3, N.W.
The crest No. 2 appears on this day to pass from Plymouth towards Bris-
_ tol and London. The direction of the line of greatest diminution of pres-
f sure varies considerably from that of the three preceding days; this partly
_ arises from the great fall which commenced on this day at the northern ‘sta-
_ tions, Orkneys, Belfast and Christiania; and from the anterior slope of the
+ wave (crest No.3). The direction of the wind is closely in accordance with
crest No. 2, passing in the direction from Plymouth towards London, being
_S.W. on the north-west side of the crest.
: 1846. L
146 REPORT—1846,
Anterior slope, Crest No. 2.
The wave (crest No. 2), with its front towards the south-east, has been
very distinctly developed during the preceding days. The altitude of the
crest appears to have subsided as the wave progressed ; the highest reading
at Belfast was 30°55 on the 5th, at London 30°16 on the 6th, and at Paris
99:90 on the 8th. The following tables exhibit the features of the anterior
slope. Table VI. shows the barometric rise and fall at stations arranged
more or less with regard to a line cutting the crest of the wave transversely.
The depressing influence of the wave, crest No. 1, is clearly seen at London
and Paris on the 5th. Tables VII., VIII. and IX. exhibit the depression of
the south-easterly stations below those to the north-west of them while the
anterior slope passed.
Taste VI.—Barometric differences arising from Anterior and Posterior
Slopes of Crest No. 2.
Epoch. Belfast. Bristol. London, Paris
Nov. 2 —15 —13 —07 —18
hy 00 —09 —'14 —'13
Pa | +:27 +:18 +17 +:07
a +:10 4-06 aes | a
» 6 a Oe Baa 4-04 4-08
Bary é —'08 —'O1? —'03 +:06
ae —'39 —ll —05 +01
Belfast. London. Tondap:
30°33 30°17 — 16
18 10 —'08
18 29:96 —'22
“AD 30°13 —'32
5D 12 —43
“51 16 —'35
“43 13 —'30
30-04 30-08 +04
Taste VIII.
Epoch. London. Paris. =_
Nov. ] 30:17 30°04 —'13
ar: 10 29-86 —24
» 3 29°96 73 —'23
ie | 30°13 80 —-33
pant) 12 ‘75 —37
68 16 ‘83 —'33
orenid 1 “89 —"24
= 8 3008 29-90 —18
Se ee ee
TaseE IX.
Epoch. Belfast. Paris. bie
Noy. 1 30°33 30°04 —-29
Bi 18 29°86 —32
We 18 73 —-45
oe 45 80 —65
Uirneg 55 75 —'80
» 6 51 +83 —'68
na | 43 “89 —54
8 30°04 29°90 —'14
4
ON ATMOSPHERIC WAVES. 147
November 9, 1842.
Crest No. 2.
S.W. N.E.
Posterior slope, Crest No. 2.
Max. Paris...... 29°76 Belfast .... 29°41
Plymouth .. 29°72 Christiania... 29°37
London..,. 29°70 Shields .... 29°28
Bristol .... 29°60 Orkneys.... 28°80
orks: S18 a 29°42
Slope.—Line of the greatest diminution of pressure. Paris to Orkneys, ‘96
Current.—Wind on N.W. side of crest, S.W., fully established.
The posterior slope of crest No. 2 now comes into full view, stretching
from Paris to the north-west coasts of Ireland and Scotland, with its proper
wind S.W. The altitude of this slope from the Orkneys to Paris is *96.
The greatest altitude of the anterior slope, from Paris to Belfast, was °80.
It will be seen that the greatest oscillation has been in the north-west, Paris
exhibiting but a very slight oscillation, 17, while that at the Orkneys has
amounted to 1°72.
The following table exhibits the fall of the barometer on the 8th and 9th:
TasLE X.—Fall of Barometer, November 8 and 9, 1842.
Station. November 8. | November 9.
| Orkneys........00. “52 83
Christiania........ 35 30
39 63
30 69
32 59
‘ll AZ
‘ll Al
05 38
+01 14
From these numbers we learn that the greatest barometric fall, as well as
_ the greatest oscillation, occurred in the N.W. The fall gradually decreases
as we approach the S.E.
It appears to me that the difference of oscillation at two stations, as the
Orkneys and Paris, may be thus explained. The curves in the north-west
_ of Ireland, as determined by the discussion of Sir John Herschel’s hourly-
_ Observations, are remarkable for boldness and freedom of contour and great
range of fluctuation. The late Professor Daniell found, from an examina-
_ tion of the Manheim observations, that the range increased towards the north-
_ west, and that the greatest oscillation occurred in the neighbourhood of water.
_ Now a wave generated in any way and approaching the continent of Europe
_ from the north-west, would most probably impinge on it with a high and in
i some cases acuminated crest 5 Veale but as it passed onward
the crest would gradually subside Cee et ea tis) gy BO Ga eae eae
ae considerably to the south-east the fluctuations would be very much
less than at or near its point of genesis. Again, a negative wave, with a
deep trough also approaching from the north-west , would
present large fluctuations as it impinged on the land; but after passing on-
L2
148 REPORT—1846.
wards, the opposite to subsidence would take place; the depth of trough
would decrease™ ~~ -~____—_ , and the oscillations to the south-east
would also decrease. Such phenomena appear to be presented by the ob-
servations from the 5th to the 10th of November 1842.
November 10, 1842.
Crest No. 2.
S.W. N.E.
Crest No. 3.
N.W. SE,
Max. London...... 29°64
Shields... 9958 (Near crest No.8
Belfast ...... 29°57
Plymouth.... 29°48
Bristol soi as 29°46 pe posterior slope, No. 3.
ark co42 3024" 29°20
Orkneys .... 29°39
Christiania .. 29°24
Slope-—Line of greatest diminution of pressure on posterior slope of
Crest Now2. Londen to Cork (5. psi eeccd seats ne. oS "44.
Altitude of anterior slope, Crest No. 3. Christiania to London.. *40.
Altitude of posterior slope, Crest No. 3. Cork to Belfast........ "37.
Currents.—Wind on N.E. side of Crest No. 3, N.W.
se. DW 9% 5 3, S.E.
* posterior slope of Crest No. 2, S.W.
oS anterior slope of Crest No. 4, N.E.
Trough succeeding Crest No. 2 now transits Christiania.
The direction of the crest No. 3 is nearly identical with that of No. 1,
which passed Great Britain and Ireland on the Ist. This appears to suggest
that they were either successive crests of the same system of waves, or were
succeeding waves produced by the same disturbing causes. The altitude of
crest No.3 is about half an inch less than that of crest No.1; but between
the transits of the two crests a wave from the N.W. with a deep posterior
trough has passed the area, which has probably depressed crest No.3. The
interval between the crests Nos. 1 and 3 is equal to nine days.
It was noticed in the remarks on the 9th, that the great difference in the
oscillation at the Orkneys and Paris most probably resulted from the sub-
sidence of the crest as it progressed. The crest No.3 came from the S.W.,
so that a line from Plymouth to Christiania would cut it more or less trans-
versely ; the ranges however are nearly the same at both stations. The crest
which traversed England on the Ist arrived at Christiania on the 4th; at this
time the barometer had commenced rising at Plymouth from the anterior
slope of crest No. 2, and it continued rising until the 7th, when the crest
passed. At Christiania the barometer had fallen from the posterior slope of
crest No.2. It appears from a careful comparison and consideration of the
barometric movements at Plymouth and Christiania, that crest No. 2 passed
Christiania about a day earlier than it did Plymouth, that is, the longitudinal
direction of the crest was such as to cause it to pass over Christiania while
Plymouth was still under the anterior slope of the wave, the sections passing
over Christiania and Plymouth being separate and distinct. The character
of the passing wave is well-determined at both stations, the posterior slope
\ Under anterior slope, No. 3.
exhibiting a rapid and deep fall, which took place alike at Christiania and 7
Plymouth.
_—
ON ATMOSPHERIC WAVES. 149
The crest No. 2 passed Cork, Belfast and the Orkneys on the 5th, Ply-
mouth on the 7th, and Paris on the 8th, with a diminution of oscillation.
We find however no diminution of oscillation at Christiania as compared with
Plymouth. It is highly probable, the subsidence of the crest, as it proceeded
towards Paris, resulted from the influence of the land in England, while both
at Plymouth and Christiania the crest was but slightly interfered with by
the influence of land, the difference of level resulting from the anterior slope
of crest No. 3.
These considerations exhibit a large wave of considerable breadth and slow
motion, extending in a longitudinal direction from the extreme south-west of
England towards the Swedish capital.
Nov. 10.—Mr. Brown’s diagram for this day very distinctly and beautifully
exhibits the change of currents resulting from the transit of crest No. 3, as
well as from the progress of the posterior trough of crest No.2. The trough
of the latter wave is now between the Orkneys and Paris (the deep trough
before mentioned), the wind in the south-eastern portion of the diagram is
S.W., the strength increasing-towards the trough. At Thurso and North
Shields the wind is N.W., the anterior slope of crest No. 3; in the south-
west of Ireland, the wind is S.E. (posterior slope). The N.E. wind on the
anterior slope of the wave succeeding crest No. 2 is seen on the north-west
side of the trough.
November 11, 1842.
Crest No. 2.
s.W.——_____—_————_N.E.
Crest No. 3.
N.W.—__—_—————-S.E.
Max. Christiania ...... 29°48 Crest No. 3.
3 sea 7 het, site \ Under posterior slope of Crest No.2.
ee ‘dibt pins In the neighbourhood of posterior
Shields... .l..u0. gaooe} ) troughs Crest No.2,
Cork .......... 28°91} Posterior trough, Crest No. 3.
( Under anterior slope of wave succeed-
Meliast tes 29°02 . :
2 ing Crest No.2 and posterior slope
Orkneys ........ 29°24. i i aa No. 3. P P
Max. Christiania ...... 29°48
Orkneys ‘o/s 29°24:
Belfast.......... 29°02 >Under posterior slope, No.3.
Shields........ -. 28:99 |
Cork stent auatt.« 28°91 J
London ........ 29°00
Paris: ii6 oes wie) ast 202)
ie aa ahr page Under posterior slope, No. 2.
emis ih oda 28°91
Slopes.—Lines of greatest diminution of pressure.
On posterior slope of Crest No.3. Christiania to Cork.. *57 «
On posterior slope of Crest No 2. Paris to Cork ..... » “34
Currents —Wind on N.W. side of Crest No.2, S.W.
i S.W. 7 ef 3, S.E.
* Depressed by posterior trough of Crest No. 2.
+ Depressed by posterior trough of Crest No. 3.
150. . REPORT—1846.
The progressive motion of the two posterior slopes is very discernible.
Crest No. 3 has passed the Orkneys and arrived at Christiania seven days
after crest No. 1 passed that station. We found an interval between the
crests as they passed the central parts of England of nine days. Most pro-
bably a discussion of observations at shorter intervals and more numerous
stations, especially to the north-east of Christiania, would explain the dis-
crepancy. The difference in level is very much greater than that which cha-
racterized the transits of the crests over the centre of England, but in the
interval between the crests passing England and Sweden, the deep trough of
crest No. 2 has advanced, which must very considerably have depressed the
crest at Christiania, as compared with the English stations ; indeed so great
was the depressing influence of the wave, crest No. 2, that no rise is recorded
as crest No. 3 passed Plymouth.
Crest No. 2 is situated considerably to the south-east of Paris, so that its
progress is not perceptible on the area; but that of its posterior slope is very
clear. On the 9th, the deep posterior trough of this wave passed the Orkneys
with a depression of 28°80 ; (bearing in mind thet its direction was S.W.—N.E.)
another section passed Christiania on the 10th, 29°24; and a third passed
Plymouth on the 11th, 29°12.
Symmetrical Wave.—On this day the great symmetrical wave commenced
at London; the position of this station was nearly similar under both slopes,
November 12, 1842.
Crest No. 3.
N.W.———_———-S..E..
Crest No. 5.
N.W.—— S.E.
Christiania ...... 29:20
Orkneys .......- 29:10 >Under posterior slope, No. 3.
Mint. a Shields.)-ee sere 29:07
Trough.
Belfast: ee rehet 29:21
Cork, .: 29°31
Sa 5 age es Under anterior slope, No. 5.
Panis: awisen sae 29°43
Max. Plymouth ...... 29°46
Slopes.—Lines of greatest diminution of pressure. —
On posterior slope of Crest No. 3. Christiania to Shields.. 13
On anterior slope of Crest No. 5. Plymouth to Shields.... +39
Currents.—Wind on S.W. side of trough, N.W.
A few stations exhibit a S.W. wind on the posterior slope of Crest No. 2.
The receding posterior slope of crest No 3, the intervening trough, and
the approaching anterior slope of crest No. 5, are brought fully into view
this day ; the wind also is in close accordance with the transit of these waves.
The wave (crest No.3) appears to be much smaller than that of No. 1; the
interval between the crests, as passing the centre of England, was found to
be nine days; the epoch of the passage of the intervening trough occurred
on November 7 ; interval between the troughs five days, taking the last in-
terval as the amplitude in time of the wave; it is clearly much smaller than
the preceding.
Symmetrical Wave-——London is situated under and rising from the ante- —
rior slope of wave No. 5.
ON ATMOSPHERIC WAVES. 151
November 13, 1842.
Crest No. 2.
S.W. N.E.
Crest No. 5.
N.W. S.E.
Anterior slope, Crest No. 5.
Max. Paris ...... 29°53 London...... 29:26
Plymouth .. 29°46 Shields ...... 29°24
Cork fk 29°40 Orkneys .... 29°35
Belfast .... 29°27 Christiania .. 28°94
Slope—Line of greatest diminution of pressure.
Anterior slope, Crest No.5. Paris to Christiania.. *59.
Trough succeeding Crest No. 2. Between Paris and Orkneys.
Trough between Crests Nos. 3 and 5 now transits Christiania.
Currents.—Wind on S.E. side of trough No. 2, S.W.
2? rm 9? 39 ”» ”?
The anterior slope of crest No. 5, the third wave of the S.W. system, is
well-developed; but the prevailing winds are those due to the S.E. and N.W.
sides of the trough succeeding crest No. 2.
It appears from a consideration of the continuation of the tables appended
to Nov. 8, that one or two small waves rode in the trough succeeding crest
No. 2, which entered on the area on the 9th, and most probably traversed it
during the next four days, presenting the same slowness of motion as the
crest itself. :
Symmetrical Wave.—London is situated under the anterior slope of crest
No.5 and the posterior slope of crest No. 2, and falling either from the latter
slope or the posterior slope of one of the small waves riding in the deep
trough.
November 14, 1842.
Crest No. 5.
N.W. S.E.
Crest No. 4.
. S.W. N.E.
Max. Belfast ......-- 29°91
Shields ......-- 29°82 Near the Crest No. 5.
London......-. 29°80
Orkneys ....-- 29°76 d
Glsiute BN mini" Sy Under anterior slope, No. 5.
Plymouth ...... 29°68 ;
ee aT oe Under posterior slope, No. 5.
Cork. .antiaties: 29°60
Slope—Line of greatest diminution of pressure.
Anterior slope, Crest No. 5. Belfast to Christiania... *56.
Currents.—Wind on advancing slope of Crest No.4, N.E.
ij N.E. side 3 5 5, N.W.
” S.W. ” ” ” 5; S.E.
The crest No. 5 now passes over Great Britain and Ireland much in the
same direction as the crests Nos. 1 and 3 (compare Nov. 1 and 10). Its
altitude is about -25 higher than that of the last S.W. crest; the advancing
slope of the second N.W. wave has approached, raising the present crest.
152 REPORT—1846.
Symmetrical Wave.—The crest No. 5 forms the second subordinate maxi-
mum on the anterior slope of the great symmetrical wave (see plate 2 ap-
pended to Sir J. Herschel’s Report, 1843, and plate 3, illustrating the volume
of Reports, 1845). The first strongly developed rise and fall on the anterior
slope of the symmetrical wave appears to be a small wave riding in the
trough (A%).
It appears highly probable that the large wave from the N.W. possessed
both a broad crest and broad trough, with a very slow progressive motion.
The anterior slope of crest No. 4 appears to have commenced riding over
Christiania on the 10th.
November 15, 1842.
Crest No. 5.
NN ee
Crest No. 4.
4 Ogata are apre mmr sO
Anterior slope, Crest No. 5. Posterior slope, Crest No. 5.
Max. Orkneys.... 30°01 Max. Orkneys.... 30°01
Christiania, 29°70 Shields .... 29°83
Belfast .... 29°82
Plymouth .. 29°64
London.... 29°62
Bristol .... 29°61
Pats ee 29°55
Cark 17,22 29°37
Slope.—Line of the greatest diminution of pressure.
Posterior slope, Crest No.5. Orkneys to Cork.. *64
Currents.—W ind on anterior slope of Crest No. 4, N.E.
P posterior As As 5, S.E,
The southern coasts of England exhibit a S.W. wind.
The progression of the crest No. 5 in the same direction as crest No. 1
(see Nov. 2), is very discernible; there can be no doubt of its being a wave
of the same system.
Symmetrical Wave.—The barometer at London has fallen from the pos-
terior slope of No. 5, but the anterior slope of No, 4 is gently raising it.
November 16, 1842.
Crest No. 5.
N.W. S.E.
Crest No. 4.
S.W.—____N.E..
Anterior slope, Crest No. 5? Anterior slope, Crest No. 4.
Max. Orkneys.... 30°22 Max. Orkneys.... 30°22
Christiania.. 29°86 Belfast .... 20°06
Shields .... 30°03
London.... 29°79
Bristol .... 29°78
Plymouth .. 29°70
Corks: ..2eea2ore8
Paris: ch.':im 29°50
Slope.—Line of greatest diminution of pressure. f
Anterior slope, Crest No. 4, Orkneys to Paris.. *72 f
Currents.—The winds this day appear to be those due to the anterior slope
of crest No. 4, or resultants of that and the posterior slope of erest No. 5. ‘
«2suntnige nia tls pel
ON ATMOSPHERIC WAVES. ° 153
The posterior slope of crest No. 5:is well and strikingly developed, and the
advancing slope of crest No. 4, the succeeding wave to that of No. 2, is in-
dicated by the line of greatest pressure, Orkneys to Paris, *72 (see Nov. 2,
when the first wave from the N.W. was coming up).
Symmetrical Wave.—London is situated under the posterior slope of crest
~ No. 5 and anterior slope of crest No. 4, and slightly rising from the latter.
:
J
November 17, 1842.
Crest No. 7.
ON eer
Crest No. 4.
Anterior slope, Crest No. 4. Anterior slope, Crest No. 7.
Max. Belfast .... 30°51 Max. Belfast .... 30°51
Shields .... 30°45 Orkneys... .~ 30°35
Bristol .... 30°36 Christiania.. 29°94
Plymouth .. 30°36 Posterior slope, Crest No. 7.
London .... 30°36 Max,,. Belfast. ... 30°51
Prarie iat 6 ae. 29:99 rl) sion 6 30°31
Slopes.—Lines of greatest diminution of pressure.
Belfast to Paris........ "52
Belfast to Christiania .. *57
Currents.—Wind on anterior slope of Crest No. 4, N.E.
» posterior ,, > Sil des
In the south-west of Ireland and England the wind is easterly, being the re-
sultant of these forces.
The anterior slope of crest No. 4, extending from Belfast to Paris, is well-
developed with its proper wind N.E. This anterior slope may be advantage-
ously compared with the anterior slope of crest No. 2, which occupied the
same area on the 5th (interval twelve days). The altitude on that occasion
from Paris to Belfast was equal to °80, on the present it is only equal to ‘52.
This may to a certain extent be explained by the presence of crest No. 7,
which this day passes over Belfast, so that this crést elevates the anterior
slope of No. 4. The anterior slope of crest No. 7 is well-developed towards
the Orkneys and Christiania, and the diminution of pressure resulting from
_ the posterior slope is conspicuous at Cork; we have consequently two crests
_ traversing the area and crossing each other at Belfast.
Crest No. 4 passes the Orkneys, Belfast, Shields and Cork this day.
Symmetrical Wave.—London is situated nearly under the crest of No. 7
_ and under the anterior slope of crest No. 4, and rising from the latter.
November 18, 1842.
Crest No. 7.
N.W.——______———-S..E..
Crest No. 4.
S.W.——_——__——_—_——_N.E.
Transit of the Crest of the Great Symmetrical Wave.
a Anterior slope, Crest No. 4. Crest No. 4:
— Max. London .... 30°53 Max. London.... 30°53
WAPIG/ lower level
Cork ...... 29°92) ;
Belfast .... 29°86
aiths /Bhidkisitiy< at Near the trough between 9 and 7.
Orkneys.... 29°91 ‘
Ghirinteg net Saat Under posterior slope, Crest No. 7.
Slopes.—Line of greatest diminution of pressure.
Paris to Shields.... °40
Currents.—Wind on posterior slope, No. 4, S.W.
” ” ” ” Te S.E.
Symmetrical Wave.—London is situated under the posterior slope of crest
No. 4 and anterior slope of crest No. 9, not far removed from the preceding
trough.
The crest No. 4 has now passed considerably to the S.E. of Paris, which 9
exhibits the greatest pressure ; the posterior slope extends in the direction to- _
wards Belfast, although Shields is the minimum point. The trough between —
crests 7 and 9 passes somewhat near Belfast and Shields.
ON ATMOSPHERIC WAVES. 155
November 20, 1842.
Crest No. 9.
MO ee a ee
Crest No. 6.
SU te ee.
Anterior slope, Crest No. 6. Anterior slope, Crest No. 9.
Max. Orkneys.... 29°96 Max. Orkneys.... 29°96
Belfast’ °) 2. 29°91 Christiania.. 29°60
CORRS S FG 29°80
Shields .... 29°85
London .... 29°77
Plymouth .. 29°73
Paris <2) .'5's - 29°55
Slope.—Line of greatest diminution of pressure.
Anterior slope, Crest No. 6. Orkneys to Paris .. *41
Currents.—Wind on anterior slope of Crest No. 6, N.E.
5 posterior ,, J » 9, S.E. and E.
The observations of this day, both barometric and anemonal, indicate the
presence of an anterior slope of a wave succeeding crest No. 4 of the N.W.
system. Crest No. 9 now passes over the Orkneys and between Christiania
and Paris..
Symmetrical Wave, two days after transit.—London is situated under the
anterior slope of crest No. 6 and posterior slope of crest No. 9.
On the 16th, two days before transit, London was similarly situated with
respect to waves Nos. 4 and 5, with nearly the same barometric pressure.
On the 13th a permanent rise took place at London, which continued until
crest No. 4 passed the station. It appears that this should be carefully distin-
guished from the rise and fall of the 16th to 19th, the latter being due to
a separate and distinct wave.
The curve from noon of the 16th to midnight of the 19th appears to re-
present the form of the N.W. wave riding on the top or superposed on the
normal or great symmetrical wave.
November 21, 1842.
Crest No. 11.
N.W.2-—— SE.
Crest No. 6.
S.W.—@____—___-N.E..
Crest No. 11.
Max. Belfast .... 29°95
Shields .... 29°89
Max. Belfast .... 29°95
Orkneys.... 29°86 } Under anterior slope.
\ Near the crest.
Min. Christiania... 29°54
the Pastis ue, ae \ Under posterior slope.
Crest No. 6.
Max. Belfast .... 29:95)
Corks wins ins 29°83
SS Ni na aah De Meo the anterior slope at
Plymouth .. 29°79 different levels.
London .... 29°82
Min. Paria 6 s Under posterior slope, No. 13.
Shields .... 28°78 |
Cork ...... 28°54)
London .... 28°92
* The barometric fall between the 21st and 23rd, that occurred at all the stations except
one, appears to have given rise to an apparent regression of the trough observed in the neigh-
bourhood of Belfast and Shields on the 22nd. It was shown that on the 22nd the anterior
slope of crest No. 6 was coming up from the N.W., so that the fall of the 21st resulted from
the posterior slope of crest No.9. On the 23rd the crest No. 6 passes London, and we have
at some stations a much more sudden fall than resulted from the passage of the posterior slope
of crest No.9. We may therefore regard the trough in the direction of Cork and Bristol as
an indication of the approaching trough of crest No. 6, rather than a new trough between 13
and 15. Should this view be correct, the line of greatest diminution of pressure, Christiania
All except Christiania under posterior
slope of Crest No. 6.
_ to Cork, will be on the posterior slope of crest No. 9,
158 REPORT—1846.
Paris 5 ou 2 29°02 }
hee aa + Under posterior slope, No. 6.
Cork ...... 28°54 J
Slopes.—Lines of greatest diminution of pressure.
Christiania to Cork.... 1°12. Slope, No. 13.
Paris 59) fas} avela ts Me AS a 34
Currents.—Wind on posterior slope of Crest No. 6, S.W.
” ” ” » » 13, S.E.
East in the north of Scotland and the Orkneys.
The progressive motions of the two slopes are well-seen from the obserya-
tions of this day, which may be very advantageously compared with those of
the 11th, when the movements were similar; crest No. 13 has advanced. to
Christiania with the succeeding trough ; crest No. 6 has advanced to or be-
yond Paris.
Symmetrical Wave.— London is situated under the posterior slope of crest
No. 6, not far removed from and to the S.W. of the posterior trough of
crest No. 13.
November 25, 1842.
Crest No. 13.
hfe nae ee ee EH
Crest No. 6.
SVS ee Ns
Max. Christiania.. 29°62)
Paris pate cie ss) ZO
London.... 28°88
A fae i % pi \ Most probably all under the posterior
Shields .... 28°82 slope of Crest No. 6.
Cork. jom:< 28°80
Belfast .... 28°82
Orkneys.... 29:07
Max. Christiania.. 29°62 }
Orkneys.... 29°07
Belfast .... 28°82 Under posterior slope, No. 13.
Shields .... 28°82 |
Ea ay lat 28°80 J
London .... 28°88
Paris’... 2. 29°01
Plymouth .. 28°93
Bristol .... 28°84
OF tains 28°80
Slope.—Lines of greatest diminution of pressure.
Posterior slope, No. 13. Christiania to Cork., *82
Under posterior slope, No. 6.
Posterior slope, No.6. Paris to Cork ...... 21
Currenis.——Wind on posterior slope of Crest No. 6, 5.W.
2? te 9 ” ” 13, S.E.S.
59 anterior ,, 3 gg? LE NW
The barometric state of the atmosphere much the same as yesterday ; the
greatest difference occurs at Cork, most probably from the advancing slope
of the wave, crest No. 15. The wind is closely in accordance with the wave
slopes.
ON ATMOSPHERIC WAVES. 159
November 26, 1842.
Crest No. 13.
S.E.
Crest No. 6.
PN ns eid EE oe EN
Crest No. 15.
NENA eee eee ee
Max. Christiania,. 29°57
Orkneys.... 29°10
Min. Shields .... 28°99 Trough.
Belfast «... 29:04)
\ Under posterior slope, No. 13.
Corks css 29°04:
rea? Bee ai + Under anterior slope, No. 15.
Pariatisé.. 803 29°17
Plymouth .. 29°20
Paristie gee 29°17 )
London .... 29°17 |
Bristol .... 29°14 pe posterior slope, No. 6.
Belfast .... 29°04
Cork:.4 4% . 29°04 j
Slopes.—Lines of greatest diminution of pressure.
Posterior slope, No.13. Christiania to Shields .. °58
eS 3 gy Oe.” Paris tot @ork: men en: 13
Anterior ,, ,, 15. Plymouth to Belfast .... °16
Currents.—W ind on posterior slope of Crest No. 6, S.W.
” ” ” » » 15, N.W. -
The advance of the anterior slope of crest No. 15 is well-seen from the
observations of this day. The wind proper to it, N.W., has increased in the
S.W. portion of the area. It appears that the motion of the waves—crests
Nos. 13 and 15 with the included trough—is slower than that of the waves,
erests Nos. 3 and 5 (see Nov. 11 and12). The same arrangement of stations
as to the distribution of pressure which required only ene day to establish
in the case of waves 3 and 5, has occupied éwo days in the case of waves 13
and 15. The distribution of pressure was similar on the 11th and 24th; it
was also similar on the 12th and 26th.
Section III.
Results of the foregoing Discussion,
In collecting the results of this discussion, I have arranged in Tables XI. and
XII. the principal lines of diminution of pressure; the succession of waves
as well as the distinct systems become very apparent from these tables. The
succeeding Tables XIII.and XIV. exhibitthe principal features of the respective
waves of each system. The most prominent result appears to be the con-
firmation of Prof. Dove's suggestion of parallel and oppositely directed cur-
rents. The diagrams of the wind in connection with the barometric obser-
vations clearly exhibit such currents, and we see by a glance at Tables XIII.
and XIV. that the beds of these currents varied considerably in breadth. At
the opening of the observations they were very much broader than at the
close, and the N.W. system (waves No. 2, 4, 6) were altogether larger than
the S.W. We have in fact two systems of waves or currents crossing each
160 REPORT—1 846.
other at right angles, the individuals in both gradually decreasing in size. In
the speculation which has been ventured relative to the S.W. system, the
mass of terrestrial surface forming the N.W. boundary of the great eastern
continent has been assumed as the rarefying surface, producing the set of
parallel and oppositely directed S.E. and N.W. winds, the currents gradually
shifting towards the N.E. The gradual contraction of the beds of each
system as the observations proceed is a highly interesting feature, which re-
quires a more extensive discussion for its elucidation.
Tasie XI.—Exhibiting the principal lines of the greatest diminution of
pressure of the N.W. system of waves, Nos. 2, 4, and 6.
Epochs. Directions. Values. Slopes,
Nov. 1 [Belfast to Paris ......... ‘29 Anterior, No. 2
2 {Orkneys to Paris......... 37 2
4 Orkneys to Paris......... 69 2
5 {Belfast to Paris ......... 80 2
6 |Belfast to Paris ......... 68 2
7 |Belfast to Paris ......... “54 2
9 |Paris to Orkneys......... 96 Posterior, No. 2
10 |London to Cork ......... “44 2
IL, AN Paris'to0\Cork ‘scceceessaes 34 2
16 |Orkneys to Paris......... 72 Anterior, No. 4
17 _—‘|Belfast to Paris ......... 52 4
18 |London to Cork ......... 35 Posterior, No. 4
18 {London to Orkneys...... 35 4
20 |Orkneys to Paris......... “Al Anterior, No. 6
21 ‘|Belfast to Paris ......... 38 6
22 [Cork to Paris «........... “45 6
24 _|Paris to Cork: s.....0s0s.< “48 Posterior, No. 6
25 .|Paris to,Cork -ssvs-seneess “21 6
26) "Paris to Cork s.,..cck-- es 13 6
TasLe XIJ.—Exhibiting the principal lines of the greatest diminution of
pressure of the S.W. system of waves, Nos. 1, 3, 5, 7, 9, 11, 13, 15.
Epochs, Directions. Values. Slopes.
Noy. 1 [Belfast to Christiania... "55 Anterior, No. 1
3 |Christiania to Paris...... 58 Posterior, No. 1
1l_‘|Christiania to Cork...... 57 3
12 |Christiania to Shields... 13 3
12 |Plymouth to Shields ... “39 Anterior, No. 5
13 ‘|Paris to Christiania...... 59 5
14‘ |Belfast to Christiania ... “56 5
15 |Orkneys to Cork......... “64 Posterior, No. 5
17 _—_‘|Belfast to Christiania ... 57 Anterior, No. 7
18 |London to Christiania... 42 7
21 ‘| Belfast to Christiania ... “41 Anterior, No. 11
23 |Christiania to Cork...... 52 Posterior, No. 13
24 Christiania to Cork...... 1:12 13
———
ON ATMOSPHERIC WAVES. 161
TABLE XIII.—Exhibiting the principal features of the waves of the N.W.
system Nos. 2, 4, and 6.
Wave No. 2.
Winds.
Epochs. Phases. Directions and Localities. VACANCES eae
Anterior | Posterior
— _Slope._|_Slope._
Nov. 1 Crest. N.W. of the United Kingdom ......
2 Crest. N.W. of the United Kingdom ...... N.E.
3 Crest. N.W. of the United Kingdom ...... ae N.E.
4 Crest. N.W. of the United Kingdom ..,....; 3049+] N.E.
5 Crest. From Cork to the Orkneys ......... 30°55 N.E.
6 Crest. SiH; Of, Belfastil nosee's detsaoscaasecaces 30°51+| N.E.
7 Crest. S.E. of the Orkneys .......sssesessseee 3043+] N.E. | S.W.
8 Crest. Passes Plymouth..........s..cseeeseeees 30°13
2 Crest. NH Of Barigg 22-64 s50scsfGncsanntsessés 29-904 S.W.
9 | Post. Trough. [Passes the Orkneys.......06 sessecesees 28°80 S.W.
10 | Post. Trough. |Near the eastern coast of Ireland
: extending to Christiania............ 29°24 S.W.
11 Crest. Considerably S.E. of Paris............
11} Post. Trough. /Passes Plymouth....... matehecs EEE 29-12 S.W.
Wave No. 4.
Noy. 17 Crest. Passes Belfast ........ssssssesceceesecees 30:51 | N.E. E.
18 Crest. Passes London .......ssceeceseeeeeenes 30:53 | N.E. S.W.
19 Crest. Considerably S.E. of Paris....... aah
Wave No. 6.
Noy. 21 Crest. N.W. of Belfast and Cork ........ Fr ha cercce N.E.
22 Crest. Near Cork, Belfast and Orkneys...... 29°58
23 Crest. Passes London ......sssenseseseescaees 29°59 S.W.
24 Crest. Near to or S.E. of Paris...... cae Perse S.W.
Tazsrie XI1V.—Exhibiting the principal features of the waves of the S.W.
system Nos. 1, 3, 5, 7, 9, 11, and 13.
Wave No. 1.
Winds.
Epochs. Phases. Directions and Localities. Algtudes.| |=
Anterior | Posterior
Slope. Slope.
Nov. 1 Crest. Belfast to Paris <.......cececessseeceeee 30°33 | N.W. S.E.
2 Crest. Between Belfast and Christiania ...| 30°23+-|N.N.W.| S.E.
3 Crest. W. or S8.W. of Christiania ............ 30:31+]| N.W. S.E.
7 | Post. Trough. |N.E. of Belfast and Paris ............
Wave No. 3
Nov. i Ant. Trough, |N.E. of Belfast and Paris ............
Crest. S.W. of Belfast and London ......... Peecen SNA
o Crest. Belfast to! Paris” cccccccessecncsec-oce0se 29°64 | N.W. S.E.
11 Crest. |Near Christiania ............ce0...sceeee 29:48 S.E.
12 | Post. Trough. |Between Belfast and Shields......-.. |
1846. M
162 REPORT—1846.
Tasie XIV. (continued).
Wave No. 5.
Winds,
Anterior. | Posterio:
Directions and Localities,
Slope.
Noy. 12 | Ant. Trough. |Between Belfast and Shields.........
13 Crest. S.W. of Cork, Plymouth and Paris...
14 Crest. Belfast to London ......sessssseeseeees S.E.
15 Crest. Passes the OrkneyS......+ecseceecseceee S.E.
16 Crest. Between Orkneys and Christiania... Eg
Wave No. 7.
Noy. 17 Crest. Pasnes CMAs 203s 2ccercesscenspess cones 30°51 S.E. E>
18 Crest. Between Cork and the Orkneys......
19 | Post. Trough. |Near Belfast and Shields ............. S.E.
Wave No. 9.
Nov. 19 | Ant. Trough. |Near Belfast and Shields ............
2 Crest. Passes the OrkneyS.......s0ee+.seee0++- 29°96 S.E.
Wave No. 11.
Noy. 21 Crest. Near Belfast and Shields ............ 29°95 | N.W. |S.E.E.>
22 | Post. Trough. |Near Belfast and Shields ............
Wave No. 13.
Noy. 23 Crest. S.W. of Christiania.....,...0-2...-0+0s- 29°62
Post. Trough. |Cork to Bristol ............+6 “Prepeh f
b Resultants of N.E. and S.E. currents.
Part II].— Desiderata.
In addition to briefly reviewing the progress made in this inquiry, it may —
be well to glance at the desiderata that now present themselves to our notice.
The object of this report, in connection with the preceding ones, has been to
show that we have observed on some occasions the successive returns of ex-
tensive barometric undulations, that these undulations have exhibited a certain
physiognomy, and that we have been able to recognize and characterize them ;
that when these undulations have been observed at various and distant
stations, and the observations carefully reduced and compared, they have been
resolved into separate and distinct waves of pressure, each having an advan-
cing front, a crest extending in a certain direction, a receding posterior slope,
and bounded by an anterior and a posterior trough. It is the object of the
second part of this report particularly to show that these characteristic
features of a wave are intimately connected with a certain arrangement of
the aérial currents first suggested by Prof. Dove, consisting of horizontal
and parallel beds of oppositely directed winds. In his letter to Col. Sabine,
the Professor speaks of these currents as northerly and southerly, the mean
direction being converted into south-westerly in the northern hemisphere by
the rotation of the earth. The examination of Mr. Brown’s data has clearly
developed a set of parallel and opposite currents at right angles to these,
Hiatthiicrrintonscs
——
vt ON ATMOSPHERIC WAVES. 163
namely, from N.W. and S.E.; and it has been suggested that these two sets
of oppositely directed currents, N.E.—S.W. and N.W.—-S.E., continually cross-
ing each other, occasion the complexity of the barometric and anemometric
phenomena, and that in future discussions these should be particularly taken
into account. Should the views thus advanced be substantiated, we are
beginning to unravel some of the complicated problems of meteorological
research : still much remains to be done; we are as yet only on the thresh-
hold of the vast meteorological arena now opening upon us. The subject, over-
whelming with interest, naturally divides itself into two branches. First, the
determination of the phases of the larger undulations,—-the barometric curves
which include complete elevations and depressions of the barometer, and
which represent, and are exponents of, the effects resulting from contemporane-
ous transits of waves or systems of waves such as have been previously
noticed. These, with the smaller secondary waves superposed on their slopes,
form the types of the various seasons of the year. Second, the absolute extent
of each normal wave of each system in space, as it exists with the smaller
superposed waves riding on its slopes. ‘The direction of its crest, its am-
plitude in miles, the altitude of its crest above, and the depression of its
troughs below the surface of general repose of the atmosphere, the place of
its formation, the manner in which it is propagated, the precise direction and
extent of its motion, the force with which it is translated from place to place,
and the locality of its final extinction, are questions which the present state
of our knowledge is inadequate to resolve.
These desiderata regarding the waves as resulting from parallel and op-
positely directed currents, may be thus expressed. The absolute extent, both
as regards length and breadth of each current with that of its counter and
oppositely directed current, together forming the two slopes of the wave
with its included trough ; the points or lines of intersection of the two systems
of parallel and oppositely directed currents; the precise direction of the
conterminous edges of the currents, the lines in which the velocity of the
wind is greatest answering to the included trough; the amount of the dimi-
nution of pressure resulting from this velocity below the mean pressure of
the atmosphere ; the locality of the formation of these currents; the direction
in which they advance with a lateral motion; the force with which they are
translated by means of such lateral motion from place to place, and the
locality of their final extinction or disappearance.
With respect to the first branch of inquiry, the phases of the larger un-
dulations, the seasonal barometric types, but little has yet been done towards
its accomplishment. ‘There is some hope, as mentioned in the foregoing re-
marks, that we have obtained the type of fourteen days in November for one
locality only ; and we have also a glimpse of the character of the movements
during a portion of October. This is however very small compared with
the extent of the problem. At the utmost it will only amount to the twelfth
partof the annual type; even the 24th cannot yet be said to be fully established.
Again, the station of observation is to be taken into account; were the
entire year's observations for one station projected, and year after year such
observations compared, we should only have the annual type at thaé station.
The examination of the symmetrical wave of 1842 has already shown that
there is a line of greatest symmetry as far as that wave is concerned, namely
Dublin, Birmingham, Brussels and Munich; and the discussion of the equi-
noctial and solstitial observations, 1835 to 1838, has clearly established
Brussels as a nodal point, and we find it situated on this line of greatest
symmetry. At very short distances N.E. and S.W. of the line of greatest
symmetry of 1842, the symmetry is departed from. On the return of the
great wave in the autumn of 1845, the line of greatest symmetry appears to
M 2
164 REPORT—1846.
have been confined to the southern shores of England: Brussels is not far
removed from this line; so that while the symmetry on the last return is
considerably departed from at Dublin, it is highly probable that at Brussels
the movements are more in accordance with its nodal character. It is there-
fore important for the complete determination of the problem, not only to
obtain the annual type at one station; we also require it at numerous stations ;
and we ought to be furnished with local types similar to those, but more ex-
tensive, which Sir John Herschel has established for different stations from
the observations of 1835 to 1838.
It has already been observed that the barometric curves at any one station
do not give sections of waves passing the station, that is, the curve as pro-
jected is not a section of the wave then transiting, but exhibits the effects
of two or more systems of waves passing at the same time. Now as like
causes produce like effects, it is highly probable that there may be a general
flowing of the larger normal waves in the same direction, about the same
season of the year ; and as we have seen in the case of the symmetrical wave
that the secondary waves are erratic, sometimes falling on one point and
sometimes on another of the normal waves, these normal waves may be
crossed at these seasons by similar systems of secondary waves slightly re-
moved froma normal epoch year after year, giving rise to a similarity, within
certain limits, between the eombined barometric curves as observed at the
stations. These combined curves furnish us with the local and annual types.
While this labour is accomplishing, and we are in progress of obtaining
annual and local types, we may be accumulating information that will bear
considerably on the second branch of our inquiry. At present we are un-
able to answer these questions fully. We have obtained some glimpses of
the vast extent of these waves, and in our contemplation of them we must,
as Sir John Herschel beautifully observes, enlarge our conception till in the
extent of their sweep and the majestic regularity of their progress they
approach in some degree to the tide waves of the ocean; still our knowledge
of them is very small. The volume of any one atmospheric wave, the extent
of surface it covers, indeed any particular feature we may name and which
we may wish to be exhibited to us in all its details, we must still reckon among
our desiderata.
In closing this report, I beg to acknowledge the valuable assistance I have
received from the following public bodies and gentlemen.
To tHe British GovERNMENT I am indebted, through the hands of the
Astronomer Royal and Lieut-Col. Sabine, R.A., for the volumes of Greenwich
Magnetical and Meteorological Observations for the years 1840 to 1843, and
the volume of similar observations made at the Colonial Observatory, Toronto,
in the years 1840, 1841 and 1842. Iam also indebted to both the above-
named gentlemen for the readiness with which they have furnished me with
extracts from the records of their respective observatories, and for many
valuable suggestions which I have received, especially from Col. Sabine.
To tHE Lorps ComMISsIONERS OF THE ADMIRALTY I am indebted for
several valuable sets of observations made on board our surveying vessels,
and received through Rear-Admiral Beaufort, our excellent hydrographer.
To this gentleman I am peculiarly indebted for the lively interest he has
taken in forwarding the inquiry, and also to the officers under whose directions
the observations have been made, for the care and fidelity with which they
have been executed. The names of the respective officers of Her Majesty's
surveying vessels will be found in Table I.
To tHE HonouRABLE THE CORPORATION OF THE TRINITY HousgE, I am
indebted for the ready access which has been afforded me to the records of
meteorological observations kept at certain lighthouses; and I take this op-
ON ATMOSPHERIC WAVES. 165
portunity of testifying to the care and fidelity with which the observations
are made daily by the lighthouse keepers. The situation of the lighthouses
at which observations have been made especially to assist in this inquiry, will
be found in Table I. ; and I am greatly indebted to the Corporation for certain
- modifications in the observations at these lighthouses, which have been made at
my suggestion in order that the subject should receive the fullest investigation.
To tHe Roya Socrery I am indebted for several sets of observations
extracted from records preserved in its archives. In connection with the
Society, I may mention the kind assistance I received from the late Pro-
FEssoR DaAnrELL; and IJ take this opportunity of recording the kindness
and urbanity which he ever manifested, when applied to in reference to this
or any other scientific inquiry.
To Sir Joun F. W. Herscuet, Bart., I am under peculiar and
especial obligation: the kindness I experienced from that gentleman while
engaged in discussing the quarterly observations, called for and collected by
himself, demands the most lively gratitude ; and I take this opportunity of ac-
knowledging this kindness, and particularly the publication, in the report
drawn up by Sir John, of the remarks which had been suggested in the course
of my labours, and which I had communicated at intervals. I need scarcely
mention that this report forms the foundation of all my subsequent labours,
and that we must ever regard Sir John as the first individual who has given
an impetus to this inquiry, and who has first trodden the field to which Prof.
Forbes some years since directed the attention of meteorologists. It has been
well-said by Col. Sabine, “that Sir John Herschel is the father of all our
modern researches in meteorology ; to him we owe all our hourly observations,
and to him we are indebted for those systematic arrangements by which
meteorology will take its due place among the sciences.” The observation
of the great symmetrical wave in November 1842, was an immediate con-
sequence of the discussion of Sir John’s hourly observations. It resulted in
fact from a continuance (at such intervals as I could command) of the
observations until a complete rise and fall of the barometer had been observed,
and projected in a curve on a similar but reduced scale to that used in the
projections of the quarterly observations. My former reports carry on the
history ; in them I have mentioned the further assistance I have received from
Sir John, which I have now great pleasure in acknowledging.
To Cart. I.arcom, R.E., I am indebted for a valuable series of observa-
tions, accompanied with curves during October, November, and December
1845. I have already alluded to these in the body of the report.
To Proressor Puitiies and Dr. Stevetty I am indebted for some
valuable series from the north of England and Ireland. I am also indebted
to Dr. Luoyp for several extracts from the records of the Dublin observatory :
also to Str THomAs BrisBaAneg, Proressor Nicuor and Sirvanus THoMp-
son, for observations made at their respective observatories.
To Proressor QueETELET I am indebted for a valuable series from the
observatory at Brussels, and for several series of the quarterly observations
collected by himself, which may be most advantageously used in such inquiries
__as the present.
To E. W. Bray ey, Jun., Es@., of the Lonpon Instirurion, I am greatly
indebted for the valuable assistance which he has on several occasions in con-
nection with this inquiry most readily afforded me; especially the great in-
terest which he manifested at the commencement of the discussion of Sir
John Herschel’s quarterly observations which materially contributed to the
_ reductions being entrusted to my hands; and I take this opportunity of acknow-
_ ledging, not only such assistance, but also the direction which that gentleman
_has given to my earlier studies, and the advice he has offered me in prosecuting
166 . REPORT—1846.
my inquiries. The interesting conversations on this and kindred subjects that
Ihave had with him during the last ten years, have greatly assisted me in my
labours. I am also indebted to GEorcr GwittT, Esa. and to E. Jonnston,
Esgq., for the assistance afforded by those gentlemen, in my earliest endeavours
to observe and trace a complete wave.
To the gentlemen named in the third column of Table I., I am indebted
for observations at the stations recorded in the first column of that table,
which have been made with great care, and mostly at the hours named in the
instructions.
I cannot close this report without remarking, that many of the observations
which have thus been collected and partially discussed, owe their existence en-
tirely to the auspices of this Association ; and should the further discussion
of them be entrusted to my hands, the same care shall be manifested which
I have endeavoured to exhibit in my previous labours; and by examining
them in every point of view and under every possible aspect, I trust the re-
sult will be such as fully to accord with the great object of the Association ;
and should no new facts be elicited, yet it is to be hoped that these observa-
tions, called for as they have been by the Association, will confirm the sug-
gestions, and throw considerable light on the labours of several eminent
meteorologists, so that in these respects subjects at which we have only ob-
tained a glance, may be brought fully into view, and thus by means of these
observations the science in some degree advanced.
Of the grant of £7 placed at my disposal I have expended £3 3s. 3d. As
nearly the whole of the observations on the return of the great wave in the
autumn of 1845, as well as those during the previous October are at present
unreduced, I respectfully request a continuance of the grant.
W. R. Birt.
Postscript, April 10, 1847.
During the period between the sitting of the Association and this report
passing through the press, I have been furnished, by the liberality of the
Royal Society, with the magnetical and meteorological observations made
during the year 1842 at various stations in the Russian empire. These
stations embrace’an area extending over 195 degrees of longitude. The ob-
servations at St. Petersburgh, the nearest station to those given by Mr. Brown,
in a great majority of cases fully confirm the results arrived at in the pre-
ceding discussion, and in others the views obtained by means of Mr. Brown’s
observations are corrected, and considerable light thrown on the real character
of the smaller waves traversing Great Britain and Ireland. In addition to
these advantages, the Russian observations, in connexion with others, exhibit
to us the vast area over which the slopes of these waves extend, so vast that
they actually approach in the extent of their sweep and the regularity of their
progress to the tide-waves of the ocean. But this is not all ; the records of the
Russian observatories contain ample materials for carrying out the suggestion
of Sir John Herschel, expressed in the close of his Report on Meteorological
Reductions (Report, 1843, page 98), “ that when dealing with undulations of
such extent, it is by no means a visionary speculation to consider the possi-
bility of tracing them over the whole of our globe.” The area embraced by
Mr. Brown’s and the Russian observations extends over 235 degrees of lon-
gitude ; and it is apparent from the observations themselves, that the greater
fluctuations are readily traceable. Our Colonial Observatory at Toronto will
carry on the observations from Sitka, and the stations on the eastern shores
of America will enable us to trace the waves from the eastern to the western
shores of the Atlantic, over the vast continents of Europe and Asia.
The following table contains the altitude of the barometer at St. Peters-
burgh during the twenty-six days included by Mr. Brown's observations.
————
,
ON ATMOSPHERIC WAVES. 167
Whenever the results obtained by means of Mr. Brown’s observations are
either confirmed or illustrated by them, a reference is made to the day on
which the particular wave, as indicated by the observations given in page 141,
is either identified with one as developed by my previous investigations, or
more clearly exhibited and its true character more distinctly brought to light.
TaBLe XV.—Barometric readings at St. Petersburgh, 1842. Nov. | to 26,
at noon, illustrating Table V.
Date, Eng. In. Date. Eng. In, Date. Eng. In,
Noy. 1 | 29°449 | Nov. 10 | 29:890 | Nov.19 | 30-155
1] “659 20
2 | 29-795 29°866
3 | 30213 12 870 21 “776
4 222 13 617 22 “419
5 251 14 530 23 | 29-585
6 | 30-164 15 139 24 | 30:032
7 | 29:961 16 ‘450 25 080
8 963 7 682 26 110
9 | 29-916 18 848
November 5. Crest No. 1.—The observations of Nov.1 indicated a crest
which passed across England and Ireland with a general direction N.W.—S.E.
This crest is now vertically over St. Petersburgh. We have traced it from
Belfast, past the Orkneys to Christiania, and we now find it at St. Petersburgh.
The observations of this day, as given by Mr. Brown, clearly indicate the
direction of crest No. 2, so that the point of intersection of the two crests,
Nos. 1 and 2, must have been situated towards the north-west of Norway.
This at once explains the greater amount of pressure in the north-west of
Europe in the early part of November.
November 8. Posterior slope, crest No. 2.—This slope was characterized
by a deep barometric fall, which was very considerable, especially at the north-
western stations. A very careful comparison of Mr. Brown’s observations
with those made at St. Petersburgh and those given in my last report, Sec-
tion III. (Report, 1845, pp. 124 to 128), identifies crest No. 2 with wave A°
of the last report. The direction of the crest, from a comparison of the num-
bers over the larger area, including St. Petersburgh, appeared to extend from
the south-west of England past Norfolk to the east of Christiania, and be-
tween this station and St. Petersburgh.
It has been observed in the remarks under the head anterior slope, crést
No. 2 (page 146), that the altitude of this crest (No. 2) appears to have sub-
sided as the wave progressed. This subsidence was aiso observed at Chris-
tiania and St. Petersburgh. At Christiania the crest passed with about the
same altitude as it passed Plymouth, 30°27, and at St. Petersburgh it was
slightly under 30 inches.
November 9. Posterior slope, crest No. 2.—On this day this posterior
slope comes into full view. We have already identified crest No. 2 with wave
A® of my former investigations. The observations of this day give us the
direction of the posterior slope, which more or less accords with the sections
of atmospheric pressure at 3 P.M. of this day, as exhibited in plates 45 and 46,
Report 1844.
November 10. Crest No. 3.—The direction of this crest is nearly identi-
eal with that of No.1, which passed over Great Britain and Ireland on the
lst. A comparison of Mr. Brown’s observations with those at St. Peters-
burgh and those given in my last report, identifies this wave, crest No. 3,
with B° (see Report, 1845, page 125).
Crest No. 2.—This crest is situated to the east of St. Petersburgh on this
day, at the same time that its posterior trough is situated to the east of the
168 REPORT—1846.
Orkneys. This will give some idea of the extent of country covered by this
wave and the vast amount of its amplitude. The direction of the trough is
indicated on plate 42, Report, 1844. i
November 11. Posterior troughs, crests Nos. 2 and 3.—On Nov. 5 we
distinctly traced the directions of the crests Nos. 1 and 2, and the observa-
tions at St. Petersburgh assisted us in indicating the locality of their inter-
section. The observations of this day, Nov. 11, indicate the contemporane-
ous existence of the posterior troughs of crests Nos. 2 and 3.
It appears probable, from a consideration of the observations of November
12, that the depression which occurred at Plymouth (sce page 150) was oc-
casioned by the crossing of the posterior troughs of crests Nos.2 and 3. If
so, we are enabled to form a correct estimate of the direction of these contem-
poraneous troughs. The posterior trough of crest No. 2 now passes St.
Petersburgh. Table IX. (Report, 1845, page 125) clearly indicates that the
depression of this day, in the south of England, was due to the posterior
trough of crest No.3. We find Paris under the posterior slope of crest No. 2,
so that the intersections of the troughs must have been situated in the neigh-
bourhood of Plymouth, or between Cork and Plymouth: the direction of the
trough of crest No. 3 appears to have extended from Paris towards Cork
while the crest was passing Christiania. It appears the velocity of crest No.
3 was greater than that of crest No. 1, which may, to a certain extent, explain
the discrepancy noticed in page 150.
November 12. Crest No. 3.—This crest now passes St. Petersburgh, while
its posterior trough passes Belfast and Shields.
November 15. Anterior trough, crest No. 5.—This trough now transits
St. Petersburgh. The fact of the succeeding crest (No. 5) passing the Ork-
neys at the same time, clearly indicates the wave to be much smaller than the
preceding two.
November 17. Crest No.’7.—It appears from a comparison of the Chris-
tiania and St. Petersburgh observations that the wave, crest No.7, was very
small.
November 18. Crest No. 4.—This wave, which forms the crown of the
great symmetrical wave, has been very distinctly developed by the discussion
of Mr. Brown’s observations. The altitude it attained, especially in the
south-east of England, has contributed to bring it prominently into view.
The observations at St. Petersburgh make us acquainted with the great ex-
tent of its longitudinal direction. Its crest passed Dublin on the 17th, Lon-
don on the 18th, and Munich on the 19th (see plate 2, appended to Sir John
Herschel’s Report on Meteorological Reductions, Report, 1843). In the fol-
lowing table the transit of its crest at the three northern stations, the Orkneys,
Christiania and St. Petersburgh, is readily seen. The direction in which the
wave progressed being N.W. to S.E., the section which passed over St. Peters-
burgh was more northerly than the others. The maximum occurred at St.
Petersburgh at least twelve hours later than at Munich, and about two days
later than at Dublin.
Taste XVI.
Epoch. Orkneys. Christiania. | St. Petersburgh.|
Nov.17 | 30:35° 29:94 | 29-68
18 30:18 30-11° 29-85
19 29:91 29°91 30:16¢
© Crest.
[For Addenda to this Report see end of the Reports. |-
OP i EO
Pres]
Repori on the Archetype and Homologies of the Vertebrate Skeleton.
By Prof. Owen, F.R.S.
Part I.—Speciat Homotoey.
Introduction.
Wuen the structure of organized beings began to be investigated, the parts,
as they were observed, were described under names or phrases suggested
by their forms, proportions, relative position, or likeness to some familiar ob-
ject. Much of the nomenclature of human anatomy has thus arisen, espe-
cially that of the osseous system, which, with the rest of man’s frame, was
studied originally from an insulated point of view, and irrespective of any
other animal structure or any common type.
So when the exigences of the veterinary surgeon, or the desire of the
naturalist to penetrate beneath the superficial characters of his favourite
class, led them to anatomise the lower animals, they, in like manner, seldom
glanced beyond their immediate subject, and often gave arbitrary names
to the parts which they detected. Thus the dissector of the horse, whose
attention was more especially called to the leg as the most common seat
of disease in that animal, specified its ‘cannon-bone,’ its ‘great’ and ‘small’
pastern-bones, its ‘coffin-bone,’ and its ‘nut-bone’ or ‘coronet’: some
cranial bones were also named agreeably with their shape, as the ‘os qua-
dratum,’ for example. The ornithotomist described, in the same irrelative
manner, the ‘ossa homoidea,’ ‘ossa communicantia’ or ‘ interarticularia,’
the ‘columella’ and ‘os furcatorium.’ Petit* had his ‘os grele’ and ‘os
en massue ;’ Herissant+ his ‘os carré’; which, however, is by no means the
same bone with the ‘os carré’ or ‘os quadratum’ of the hippotomist. The
investigator of reptilian osteology described ‘ hatchet-bones’ and chevron-
bones, an ‘os annulare’ or ‘os en ceinture,’ and an ‘os transversum’: he
likewise defined a ‘columella’; but this was a bone quite distinct from that
so called in the bird. The ichthyotomist had also an ‘os transversum,’ which
again was distinct from that in reptiles, and he demonstrated his ‘os discoi-
deum,’ ‘ os ccenosteon,’ ‘os mystaceum,’ ‘ossa symplectica prima,’ ‘secunda,’
‘tertia,’ ‘suprema,’ ‘postrema, &c. Similar examples of arbitrary names might
easily be multiplied ; many distinct ones signifying the same part in different
animals, whilst essentially distinct parts often received the same name from
different anatomical authors, occupied exclusively by particular species.
Each, at the beginning, viewed his subject independently ; and finding, there-
fore, new organs, created a new nomenclature for them; just as the anthro-
potomist had done, of necessity, when, with a view to the cure or relief of
disease and injury, he entered upon the vast domain of anatomical science by
the structure of Man, or of the mammals most resembling man.
* Observations Anatomiques sur les mouvemens du bec des Oiseaux, Mémoires de l’Acad.
des Sciences, 1748, p. 345.
+ Mém. de l’Acad. des Sciences,-1774, p. 497.
1846. N
170 REPORT— 1846.
It may well be conceived with what a formidable load of names the me-
mory must have been burthened, if any could have been found equal to it,
had the anatomy of animals continued and made progress under its primitive
condition of an assemblage of arbitrarily described and uncompared facts.
Happily the natural tendency of the human mind to sort and generalize its
ideas could not long permit such a state of the science, if science it could be
called, to remain. A large and valuable portion of the labours of the com-
parative anatomists who have honoured the present century, has been devoted
to the determination of those bones in the lower animals which correspond
with bones in the human skeleton; the results being usually expressed by
applying to the parts so determined the same names, as far as the nomen-
clature of anthropotomy allowed. Few, however, of the parts of the human
body have received single substantive names; they are for the most part in-
dicated by shorter or longer descriptive phrases, like the species and parts of
plants before Linnzeus reformed botanical nomenclature.
The temptation to devise a systematic Nomenclature of Anatomy, generally
applicable to all animals, increases with the advance of the science, and from
the analogy of what has taken place in other sciences it may one day be
yielded to and exercise the ingenuity of some ardent reformer. But the same
analogy, especially that afforded by chemical science since the time of Lavoi-
sier, would rather lead the true friend of anatomy to deprecate the attempt
to impose an entirely new nomenclature of parts, however closely expressive
of the nature and results of the science at the period when it might be devised.
For there is no stability in such descriptive or enunciative nomenclature ; it
changes, and must change with the progress of the science, and thus becomes
a heavy tax upon such progress.
If the arbitrary term ‘ calomel,’ which, like ‘ house’ and ‘dog,’ signifies the
thing in its totality, without forcing any particular quality of its subject
prominently upon the mind, be preferable, on that account as well as its
brevity, to the descriptive phrases ‘submuriate of mercury,’ ‘ chloride of
mercury,’ or ‘ proto-chloride of mercury,’ in enunciating propositions respect-
ing the substance to which it is applied ; and if it possesses the additional ad-
vantage of fixity, of a steady meaning not liable to be affected, like a descrip-
tive name or phrase, by every additional knowledge of the properties of the
substance; the anatomist, zealous for the best interests of his science, will feel
strongly the desirableness of retaining and securing for the subjects of his
propositions similar single, arbitrary terms, especially if they are also capable
of being inflected and used as noun adjectives.
The practice of anatomists of the soundest judgement has usually been,
to transfer the anthropotomical term or phrase to the answerable part when
detected in other animals. The objection that the original descriptive or
otherwise allusive meaning of the term seldom applies to the part with equal
force in other animals, and sometimes not at all, is one of really little moment ;
for the term borrowed from anthropotomy is soon understood in an arbitrary
sense, and without regard to its applicability to the modified form which
the namesake of the human bone commonly assumes to suit the ends required
in the lower species. No anatomist, for example, troubles himself with the
question of the amount of resemblance to a crow’s or other bird’s beak in the
‘coracoid’ bone of a reptile, or with the want of likeness of the kangaroo’s
‘coccyx’ to the beak of a cuckoo; or of the whale’s ‘vomer’ to a plough-
share; or ever associates the idea of the original mystic allusion in the ana-
tomical term ‘sacrum’ with his description of that bone in the megatherium
or other monster. Common sense gratefully accepts such names when they
become as arbitrary as cat or calomel, and when such concretes or adjectives
as ‘coccygeal, ‘yomerine’ and ‘sacral’ can be employed to teach the pro-
perties or accidents of their subjects.
Gt
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~
ON THE VERTEBRATE SKELETON. 211
dismemberments of the human temporal bone ; and we cannot climb to the
higher generalizations of anatomical science, except by the firm steps of true
and assured special homologies. There are more important subjects than
homologies, no doubt ; but nothing is more important than truth, in whatever
path we may be in pursuit of her.
Orbitosphenoid.—As evidence will be given in the section on ‘General
Homology’ that both squamosal and tympanic belong to a quite distinct
category of bones from the parts of the ‘temporal’ which have just been
discussed. I shall proceed next to the neurapophyses that precede the
alisphenoid.
As the determination of this bone (c in all the figures) involves that of
the orbitosphenoid (10), which has rarely been mistaken* for any other bone
‘than 6, there remains little to be added in proof of its homology after
what has been advanced respecting the alisphenoid. The most constant
character of the orbitosphenoid is its relation to the optic nerve, which either
perforates or notches it, whenever the ossification of the primitive cartilage
or membrane holding the place of the bone is sufficiently advanced, which
is not always the case in fishes, especially those with broad and depressed
heads, and still more rarely in lacertine saurians. The recognition of the
orbitosphenoid is also often obscured by another cause, viz. the tendency in
the class Reptilia, and especially in ophidians and chelonians, to an extension
of ossification downwards into the primitive membranous or cartilaginous
neurapophysial walls of the brain-case, directly from the parietal and frontal
bones.
_ In the fishes with ordinary-shaped, or with high and compressed heads,
the orbitosphenoids are usually well-developed: they are, however, repre-
sented by descending plates of the frontal in the garpike ; and they are, like the
alisphenoids, mere processes of the basisphenoid in the polypterus, which thus
offers so unexpected a repetition of the human character of the correspond-
ing partst. In the cod (fig. 5, 10) they are semielliptic, raised above the pre-
sphenoid (9), suspended, as it were, between the alisphenoid (6) and the
frontal (11), and bounding the sides of the interorbital outlet of the cranium:
the optic nerves pierce the unossified cartilage closing that aperture, imme-
diately beneath the bone itself. In the malacopterous fishes with higher
and more compressed heads, the orbitosphenoids are more developed ; they are
directly pierced or deeply grooved by the optic nerves, and are pierced also
by the ‘nervi pathetici’ in the carp. The crura of the olfactory ganglions
(rhinencephala) pass out of the interorbital aperture of the cranium by the
upper interspace of the orbitosphenoid, into the continuation of the cranial
cavity which grooves the under surface of the frontal, in their course between
the orbits to the prefrontals. The orbitosphenoids protect, more or less, the
sides of the prosencephalon ; and this function, their transmission of the optic
nerves, their anterior position to the alisphenoids, and their articulation
above with the frontals, establish their special homology from the-fish up to
man.
In certain fishes a distinct centre of ossification is set up in the median
line of the fibrous membrane or cartilage, closing the interorbital aperture
of the cranium, below the orbitosphenoids, and extending forwards as the in-
terorbital septum. ‘The bone (represented in outline in fig. 5, at 9') extends
downwards to rest upon the presphenoid (2b. 9), and bifurcates, as it ascends,
' * Geoffroy in his memoir on the skull of birds (Ann. du Mus. x.), indicates the orbitosphe-
noid at P, fig. 2, pl. 27, as the ‘rocher’: and Cuvier describes it as part of his ‘os en cein-
ture’ in anourous batrachia.
_ + Agassiz, Recherches sur les Poissons Fossiles, ii. p. 38.
212 REPORT—1846.
to join and prop up the elevated orbitosphenoids in the perch and carp (not
in the cod). The relations of this ossicle are precisely those of the part
forming the conjoined bases of the orbitosphenoids in mammals, and usually
called the ‘ body of the anterior sphenoid, in them; though this is deve-
loped from two distinct centres. In the young whale I found it supported
by a direct extension of the basisphenoid forwards, which joins the back-
wardly prolonged vomer, as in fishes. The common base of the orbitosphe-
noids is peculiar, as a distinct bone, so far as I know, to fishes. It has been
ealled by Bojanus* the ‘ basis alaruam minorum sphenoidei seu rostrum sphe-
noidei’ ; by Geoffroy ‘entosphénal’ ; and by Cuvier ‘le sphénoide antérieure.’
M. Agassiz opposes these determinations by the following remarks, founded
on the embryological researches of the ingenious Dr. Vogt :—“In fishes
with a short and thick muzzle, the cartilaginous embryonal plate (‘ plaque
faciale’ of Vogt), which serves as the base of support to the prosencepha-
lon and the nasal fossz, is transformed into an independent bone, “se trans-
forme intégralement en os.” It is then, he says, “ represented by the cranial
ethmoid (le sphénoide antérieure of Cuvier), an azygous bone, ‘os impair,’
short, of an almost square form, in which are pierced the canals for the
transmission of the olfactory nerves. But in the fishes with elongated
muzzles, and of which the eyes in place of preserving their primitive lateral
position at the sides of the mesencephalon are carried forwards. in advance
of the cranium between that and the nasal fossz, the relations of the
‘plaque faciale’ are necessarily altered: part of the plate remaining in its
primitive situation is transformed into the ‘cranial ethmoid,’ the other part
is carried forwards, but is never transformed into a distinct bone: it re-
mains cartilaginous as the nucleus of the muzzle; or if, indeed, the ossifi-
cation of the muzzle is completed, it disappears by virtue of the progressive
encroachment of the exterior ossification. This is the reason why fishes
have never a true ‘ nasal ethmoid’ (the bones called ethmoid by Cuvier are
the nasals), but only a cranial ethmoid+.” Influenced by the deservedly
high authority of M. Agassiz, I adopted his homology of the bone 9! in the
‘ Hunterian Lectures on Vertebrata,’ delivered in 1844. But since the notes of
those lectures were printed, having been charged with the formation of a new
Osteological Catalogue of the Hunterian Museum, I have carefully reconsi-
dered this question. Passing over, for the present, the assertion that the homo-
logue of the ‘ nasal ethmoide’ does not exist in fishes, I would first observe,
that if the orbital aperture (or what appears to those who deem the rhinen-
cephalic crura to be olfactory nerves, the anterior aperture) of the cranium
were homologous with the aperture closed by the cribriform plate in man, then
any bony bar or plate tending to close that aperture might be held to be homo-
logous with the cribriform plate or crista galli of the ethmoid: but the inter-
orbital aperture of the cranium is always bounded laterally, in fishes, by the
orbitosphenoid ; and the rhinencephala and their crura extend forwards, toa
considerable distance in most fishes, before the olfactory nerves sent off from
the rhinencephala escape by those perforations in the prefrontals, which are the
true homologues of the single foramina of the olfactory nerves in the so-called
ethmoid of birds, and of the cribriform foramina in mammals. The inter-
orbital groove or canal in the skull of fishes, which is continued from the
presphenoidal or interorbital aperture to the prefrontal foramina, is as essen-
tially a part of the cranial cavity as is that contracted anterior olfactory
chamber of the cranium of mammals, which, in the thylacine, for example,
extends forwards, from where the orbitosphenoids sustain the frontals, ex-
* Oken’s Isis, 1818, p. 508.
+ Recherches sur les Poissons Fossiles, t. i. p. 120.
Rw ee ee
eo 1.
ON THE VERTEBRATE SKELETON. 213
panding, to where the frontals and the modified prefrontals (ethmoid) form
the actual anterior boundary wall of the cranial cavity; the chief distine-
tion between the condition of this boundary in the mammal and the fish,
being, that whereas it is perforated by numerous apertures in the mammal,
the olfactory nerves in the fish escape each by a single foramen or groove
in the homologous bones. As beautiful as true was that clear perception
by Bojanus of the homology of the simply perforated prefrontal of the fish,
with its sieve-like homologue in the class in which the olfactory sense reaches
its maximum of development and activity, and modifies all around it. The
coalesced bases of the orbitosphenoids, forming the anterior boundary of the
bed of the optic chiasma, answer to the separate ossification called ‘ eth-
moide cranien’ by Agassiz, in fishes: it has the same relation with that con-
tracted area of the cranium answering to the interorbital aperture of the cra-
nium in fishes, which the so-called eranial ethmoid (entosphenoid) presents
in fishes ; aud this same entosphenoid (fig. 5, 9’) has as little relation to the
formation of the canals pierced by the olfactory nerves in fishes, as the
orbitosphenoid has in mammals. The olfactory, rhinencephalic or anterior
division of the cranial cavity in most fishes has its lateral bony walls incom-
plete, and it opens freely, in the dry skull, into the large orbital chambers
below, which are then said to have no septum: we see a similar want of de-
finition of the cranial cavity in relation to the great acoustic chambers in most
fishes. But in manimals the orbits are always excluded from the rhinence-
phalic, or olfactory compartment of the cranium* ; and a like exclusion
obtains in some of the highly organized ganoid fishes and in the plagiostomes.
As the prosencephalic parts of the brain progressively predominate, and the
rhinencephalic parts diminish, in the higher mammals, the compartment of
the cranium appropriated to the latter loses its individuality, and becomes
more and more blended with the general cavity. In the elaborate ‘Icono-
graphy of Human Anatomy’ by Jules Cloquet, for example+, the small pe-
culiarities of the ‘trou borgne’ and the ‘apophyse crista galli’ are both in-
dicated, and very properly; but the rhinencephalic or olfactory division of
the cranial cavity, though defined by the suture between the orbitosphe-
noids and prefrontals and lodging the olfactory ganglia or rhinencephala,—
so important an evidence of the unity of organization manifested in man’s
frame and traceable in characters, strengthening as we descend to the lowest
osseous fishes—is wholly unnoticed. Thus, very minute scrutiny, con-
ducted with great acuteness of perception of individual features, qualities
highly characteristic of the anthropotomists of the school of Cloquet, being
directed from an insulated point of view, prove inadequate to the apprecia-
tion of sometimes the most constant and important features of their exclusive
subject. .
But to return to the homology Fig. 13.
of the orbitosphenoids. In the me-
nopome these neurapophyses are
elongated parallelograms, perfo-
rated by the optic nerves, and are
distinct bones. In the great bull-
frog (Rana boans) they present a
similar form (fig. 13, 10), but are ee
confluent with the prefrontals (14): Side view of cranium (Rana oans), nat. size.
in both batrachians an unossified sPace intervenes between them and the ali-
_ * This is not to be confounded with the olfactory chamber itself, lodging the organ of
smell.
T Manuel d’Anatomie Déscriptive, 4to, Atlas, pl. 8, fig. 2.
214 REPORT—18446.
sphenoid (6). In most lizards the wider roof of the cranium, supported by the
long mastoids, squamosals, postfrontals and malars, like a bony scaffolding
on each side, is independent of its proper (neurapophysial) walls for support,
and these retain, through the ceconomy of nature, their primitive semi-mem-
branous, semi-cartilaginous state. A dismemberment of the alisphenoid
(which may be discerned as a process of that bone in the piscine genera
Xiphias, Sphyrena) props up the parietal upon the pterygoid, so like a post
or pillar, that the name ‘columella’ may well be retained for it. At the
sides of the membrane forming the orbital aperture, rudiments of the orbi-
tosphenoids may be seen in most lacertia: I find them, e. g. in the form of
a slender osseous filament on each side, slightly bent inwards and bifurcate
above, in a large Australian lizard (Cyclodus gigas). In the crocodile (figs.
9, 20, and 22, 10) the orbitosphenoids attain their maximum of development,
but retain all their typical characters: they bound the orbital aperture of the
cranium ; are notched below, as in many fishes, by the optic nerves (op);
are perforated by the pathetic and other orbital nerves at the ‘ foramen spheno-
orbitale’ (s); they protect the sides of the prosencephalon ; support above the
frontals (and by their backward development also the parietals); and they
rest below upon a peculiar development of the presphenoid (9), which seems
to answer to the entosphenoid in fishes.
Some salient points of resemblance between the cranial organization of fishes
and birds have elicited remarks from more than one comparative anatomist.
Not to dwell upon the more obvious correspondence arising out of the mo-
bility of the upper jaw, chiefly through its connection with the pedicle of the
lower jaw, I may indicate the overhanging position of the orbitosphenoid
(figs. 8, 23, 10), raised high above the presphenoid (9), at the back part of the
interorbital septum: we see exactly the same position of the orbitosphenoid
in many fishes. Cuvier accurately represents it in the skull of the perch*.
This beautiful trait of unity of organization is completely put out of sight by
the false homology of the orbitosphenoid in fishes with the alisphenoid in
birds and mammals. The progressive recession of the orbitosphenoid and .
alisphenoid, as we descend from mammals to fishes, transfers indeed their
characteristic nerve-notches or foramina from their posterior to their ante-
rior margins. But the notch (op, fig. 8) at the posterior margin of the orbito-
sphenoid in the bird for the escape of the optic nerve by a foramen common
to it and the nerves of the orbit, is not less significant of its true homology
than is the anterior notch in the crocodile or fish; the osseous connections
with the sphenoid below, with the frental above, and with the alisphenoid
behind, being the same.
Prefrontals.—If the cranium of a cod-fish be bisected horizontally and
longitudinally, its most contracted part will be found at the upper part of
the interorbital aperture, bounded by the orbitosphenoids, which mark the
division between the prosencephalic and rhinencephalic compartments of the
cavity: the latter extends as a triangular channel or groove on the under
part of the frontal, opening below into the orbits, gradually expanding as it
advances forwards, and dividing into two canals, which diverge to the inter-
spaces left on each side of the nasal, between it and the bones (fig. 4, 14), that,
meeting behind the anterior expanded end of the nasal, bound the anterior
extremity of the true and entire cranium. The diverging canals of the rhi-
nencephalic compartment are formed by the two bones in question: the rhinen-
cephala or olfactory ganglions are sometimes lodged at the extremities of these
canals, and they send out the olfactory nerves by the apertures formed be-
tween the bones 14 and 15, which then ramify upon the vascular olfactory sacs,
* Histoire des Poissons, pl. ii. figg. i. vii. 14.
Kee He ee
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Z ON THE VERTEBRATE SKELETON. 215
supported by the bones 19, fig. 5. For the arguments by which the olfactory
ganglions in the cod are shown to be homologous with the olfactory ganglions
that rest upon the cribriform plate in man, and by which the medullary cords
or crura connecting them to the rest of the brain are shown to be homologous
with the so-called ‘ olfactory nerves’ in the human cranium, and for the ge-
neral homology of both as primary divisions and peduncles of the encephalon,
the reader is referred to Dr. Desmoulins, ‘ Anatomie des Systémes nerveux
des Animaux a Vertébres,’ 1825, 8vo. t. i. p. 169; to Mr. Solly’s excellent
treatise ‘On the Human Brain,’ 1836, p.’78; and to my ‘Lectures on the
Vertebrata,’ 1836, p. 184. I there adopt the expressive name applied by
MM. Vogt and Agassiz to this most anterior of the four primary divisions
of the brain of fishes, and apply to the peduncles of the ‘rhinencephala,’
which are frequently of great length in fishes, the name of ‘rhinencephalic
crura, since they are serially homologous with the prosencephalic or cerebral
erura; and I eall that division of the cranial cavity which specially lodges
these crura and their lobes the ‘rhinencephalic’ chamber or compartment.
The right appreciation of the above essential characters of the most anterior
division of the brain and the brain-case is indispensable to the accurate pur-
suit of the homologies of the bones 13, 14 and 15, whose development, espe-
cially of the pair no. 14, is governed by that of the rhinencephalon. In man
the all-predominating cerebrum, overarching the mesencephalon and epen-
cephalon behind, and the rhinencephalon in front, so modities the surround-
ing cranial bones as to obliterate every part of the rhinencephalic division,
save the terminal fossa that immediately supports the so-called ‘olfactory
ganglia,’ which fossa seems, as it were, to be unnaturally drawn in and
blended with the great prosencephalic chamber, by reason of the enormous
outswelling development of the proper spines or roof-bones of that chamber,
the frontals. Still, even here, through the absence of any commissural band
connecting tegether the rhinencephala, a fibro-membranous process of the
endoskeleton extends between them, and into this septum ossification extends
' from below, called the ‘crista galli. In the cod-fish the homologous parti-
tion between the rhinencephala is cartilaginous, and it extends some way back
between their crura, not being opposed by a coextended overhanging cere-
brum with great transverse commissures. In many fishes (e. g. Xiphias) the
outlet of the olfactory nerves, which notches the inner side of no. 14 in
the cod, is converted into a foramen by the extension of ossification around
the mesial surface of the nerves. Where the olfactory nerves are sent off
from the ganglions in great numbers (e. g. Raia), they perforate a mem-,
brane before reaching and ramifying upon the vascular pituitary sac. In
man, the homologous membrane, or basis of the olfactory capsules, is ossi-
fied, and called from its numerous apertures the cribriform plate. The holes
which these cribriform plates fill up are homologous with the foramina, or
grooves forming the outlets of the olfactory nerves in the bones no. 14 in fishes
(figs. 4 and 5).
The grounds for this homology are so plain that we cannot be surprised
that they should have been early appreciated, as e. g. by the painstaking and
philosophic Bojanus in 1818*. I never could comprehend the precise mean-
ing of the statement with which Cuvier opposed his view :—“ M. Bojanus, par-
tant sans doute du trou qu'il a dans plusieurs poissons pour le nerf olfactif, en
fait une lame cribleuse de l’ethmoide ; mais cette opinion, qui n’a pas ce soutien
dans toutes les especes, est réfutée d’ailleurs par les autres rapports de cet os
avec les os voisins}+.” Cuvier seems to have thought the ground of Bojanus’s
opinion to be cut away by the fact that in the cod and some other fishes the
* Isis, heft iii. p. 503. t Ilistoire des Poissons, i. p. 235.
216 REPORT—1846.
olfactory nerves groove instead of perforate the bones no.14._ But the trige-
minal still determines the alisphenoid, whether it perforates or notches that
neurapophysis in its escape: the relation of the alisphenoid to the division
of the 5th, including the gustatory nerve, and that of the orbitosphenoid to
the nerve of sight, are not more constant than is the relation of no. 14 to the
nerve of smell. The differences of connection of no. 1a—‘les autres rap-
ports’—are not specified by Cuvier, and I know none that affect its essential
character.
No. 14 is however the, most anterior of the neurapophysial or lateral
bones of the true cranium, and is in relation with the anterior terminal divi-
sion of the encephalon and with the first or anterior terminal pair of nerves.
Like all extreme or peripheral parts, it is subject, as we should be prepared
to find it, to a greater extent and variety of modifications than the more
central neurapophyses. The difference between its connections in the fish
and that of the cribriform plates and their sustaining basis in man may
therefore be expected to reach the extremes of possible homology. It will
be interesting to inquire whether there are intermediate modifications by
which the nature of that difference may be appreciated, and how many of
such links are permanently retained in the intervening species.
We might anticipate the smallest amount of departure from the fun-
damental vertebrate type, as respects form, size and connections of the bones
in question, in that class where the principle of vegetative repetition most
prevails and the archetypal plan is least obscured by teleological adaptatious.
Adopting the name modified from the phrase applied to these bones by Cu-
vier in those vertebrata in which they present their most typical characters,
we find the ‘prefrontals’ in all bony fishes resting below upon the vomer (figs.
4 and 5,13) and on part of the presphenoid (9), sustaining by their mesial and
upper surfaces the nasal (15) and fore-part of the frontal (11), affording the
whole or part of the surface of articulation for the palatine (20) or the palato-
maxillary arch, and giving attachment exteriorly to the large suborbital or
lacrymal bone (figs. 22 and 25, 73), when this exists. Besides their protec-
tive functions, in relation to the olfactory ganglions and nerves, they close the
cranial cavity and bound the orbits anteriorly. The most constant and cha-
racteristic connections appear to be with the vomer, nasal, palatine and frontal.
In the murenoid fishes, where confluence begins to prevail in the cranial bones,
we find that the prefrontals coalesce with the vomer and nasal, not with the
true frontal. This fact, though not of a class materially affecting relations
of homology, is not devoid of significancy in regard to the real character of
the bone usually described as one of the ‘ deux démembremens du frontal*.’
A elew not to be neglected in tracing the homologies of the prefrontals is
their histological progress, although the value of such embryonic characters
has been overrated and their application sometimes abused. The substramen
of their ossification, like that of the exoccipitals, mastoids and post-frontals,
is a cartilaginous mass, a part of that which M. Dugés has called ‘ cartilage
cranio-faciale,’ and M. Vogt ‘ plaques protectrices latérales.’ The frontals
and parietals, being ossified in supra-cranial fibrous membrane with so rapid
and transitory a cartilaginous change as to have escaped general recognition,
have been, on that account, rejected from the vertebral or endo-skeletal system
of bones by Dr. Reichert, and with as little real ground as the rejection of the
vomer and sphenoid from the same system, because they are ossified in mem-
brane extended from the under and fore-part of the sheath of an evanescent
subcranial ‘ chorda dorsalis,’ like the homologous basal ossification beneath
the coalesced anterior abdominal vertebra of the siluroids.
* Agassiz, op. cit. i. p. 123.
y
ON THE VERTEBRATE SKELETON. 217
M. Dugés, who has accurately figured the ‘cranio-facial’ cartilage of a
gadoid fish in pl. ii. of his valuable Monograph*, gives as accurate a figure
of the same cartilage in the Rana viridis (pl. i. figs. 6,7, of the same work),
out of which has been ossified a bone which transmits the olfactory nerve to
its sense-capsule: this bone (15 in the figures cited) rests below upon the di-
vided vomer and on the end of the presphenoid, sustains above the nasal and
fore-part of the frontal, affords an articular surface on its outer part for the
palatine, and only fails to repeat every characteristic connection of the pre-
frontals in fishes, because (as likewise happens in certain of that class) there
is no lachrymal bone developed in the Batrachia. The sole modification
. of any consequence tending to mask the homology is this; that whereas we
find in many fishes ossification extending into the persistent part of the cra-
niofacial cartilage connecting, whilst it separates, the prefrontals, so as to
cireumscribe the canals for the transmission of the olfactory nerves, such ossi-
fication proceeds in the anourous batrachia to anchylose the prefrontals with
each other, and convert them into a single bone. This difference however
sufficed with Cuvier to make of it a new and peculiar bone—an ‘os en cein-
ture+.’ It would have been as reasonable to have given a new name to the
supraoccipital in the Lepidosteus, because it is divided in the middle line in-
stead of being single, or to the frontal in the species where it is single instead
of being divided, or to the vomer in the frog because it is double instead of
single, or to the exoccipitals in the same reptile, which manifest the same
mesial and annular confluence as the prefrontals. But, adds Cuvier, in refer-
ence to the single bone (fig. 13, 14) resulting from this modification, “ Je ne
Yai pas trouvé divisé, méme dans des individus trés-jeunes qui avoient encore
un grand espace membraneux entre les os du dessus du crane.” Nor did the
great anatomist ever find the rudiments of the radius and ulna distinct at any
’ period of development of the single bone of the Batrachia, which he never-
theless rightly describes as representing both. bones of the fore-arm: nor
did he ever find a division of the single parietal in the embryo crocodile,
which he equally well recognized, nevertheless, as the homologue of the two
parietals, which in most fishes have been subject to greater modifications in
their connections and relative position than the single prefrontal presents in
the anourous batrachia. These are not the only instances where relations of
homology are by no means obscured, nor ought to be, by reason of the con-
fluence or even connation{ of essentially distinct elements. The capsule of
‘the olfactory organ, partly protected by the anterior infundibular expansions
of the connate prefrontals, undergoes no partial ossification homologous with
the ‘turbinal’ (19, fig. 5) of fishes, but remains cartilaginous, like the scle-
rotal and petrosal.
_ The prefrontals, however, are not only connate with each other in the
frog, but coalesce with the contiguous neurapophyses—the orbitosphenoids
(io, fig. 13). And this modification has led Cuvier, notwithstanding the
connection of the bone 10 with the presphenoid below, with the frontal
above, and with the prosencephalon, optic nerve (op) and orbit, to charac-
terise the batrachian skull as having “un seul sphénoide sans ailes tempo-
rales ni orbitaires ;’ the true and distinct ‘alisphenoid’ (6, fig. 13), with its
typical connections and nerve-perforations (¢r), being described as the pe-
* Recherches sur l’Ostéologie, &c. des Batraciens, 4to, 1835. :
+ Ossemens Fossiles, 4to, t. v. pt. ii. p. 387. He had before applied the name of ‘ ceinture
osseuse’ to the scapular arch in fishes.—Lecons d’ Anat. Comp. i. (1800) p. 332.
_ £ L use these terms in the same definite sense as the botanists ; those essentially distinct
parts are connate which are not physically distinct at any stage of development, those united
parts are confluent which were originally distinct.
1846. Q
218 REPORT—1846.
trosal, ‘rocher*.’ But the real difficulties which beset the quest of general
truths in comparative osteology are such that we may well dispense with any
over-statements of the amount of deviation from the cranial archetype which
much-modified skulls like those of the anourous batrachia may present.
Fortunately the light which the development of such skulls throws upon
their mature characters, is aided by the persistent larval stages manifested
by the perennibranchiate species.
In the menopome, for example, the prefrontals remain distinct, both from
each other and from the orbitosphenoids+, their characteristic connections
and functions being the same as those of their coalesced homologues in the.
frog, except that they are notched, instead of being perforated by the olfac-
tory nerve, which grooves their inner border, as in ‘the cod and some other
fishes. Cuvier just hints at the possibility of his ‘os en ceinture’ in the frog
representing “a la fois le frontal principal et l’ethmoide},” or as having an
equal pretence to one or the other name.
The suture, however, which marks the limits between the frontal 11 and:
parietal 7 is persistent in the menopome, and indeed. in all batrachians but
the anourans; and even in the very young larve of these, Cuvier admits
(and the observations of M. Dugés warrant the admission ) * que l’on sépare
une partie postérieure de forme ronde de l’antérieure qui est allongée” (Jbid.
p- 387). The permanently distinct frontals present a similarly elongated form
in the urodeles, and are therefore recognized by. Cuvier in the salamander,
e.g. at ¢, pl. xxv. fig. 1, op. cit.; in the newt, pl. xxvi. fig. 6 ; in the menopome,
fig. 4; in the axolotl, pl. XXVii. fig. 24; in the siren, 7b. fig. 2; and in the am-
phiuma, ib. fig. 6. In all these crania the true frontals are indicated by the
same letter ¢; in none of them do they close the cranial cavity or bound the
orbits anteriorly, or are perforated by the olfactory nerves, or articulate with
the vomer below, or perform any of the essential functions, or combine the cha-
racteristic connections of the prefrontals of fishes, all of which concur in the
‘os en ceinture.’ But the frontals do present the chief connections and occupy
the relative position of the anterior half of the bone (11—, fig. 13) which
Cuvier calls the parietal in the frog. The evident tendency to coalescence of
essentially distinct bones which pervades the skeleton in the adult anourans
greatly diminishes the difficulty, through the loss of the suture between the
parietal and frontal, of recognizing the homology of the latter bone, which,
with that exception, not only repeats the characters of the frontals in fishes,
but of those in most tailed batrachians.
Next, then, with regard to the ethmoid, the second of the two bones to
which Cuvier restricts the choice of the homologues of the ‘os en ceinture,’
no. 14. No name has been applied more vaguely or with a less definite
meaning than this same ‘ethmoide.’ In the sense in which Cuvier would
permit its application in the present instance, it is a bone which forms the
* Op. cit. p. 386.
+ The menopome, which represents a gigantic tadpole of the tailless batrachia, manifests
a. beautiful conformity to the general type, and well illustrates the real nature of the apparent
deviations which take place in the course of the remarkable metamorphoses of the anourans.
At first sight the orbitosphenoids seem to be barred out from their normal connection with
the frontal by the junction of the parietal with the prefrontal in the menopome, as appears,
for example, i in the figure given by Cuvier in the ‘ Ossemens Fossiles,’ v, pt. ii. pl. Xxvi. fig. 4,
where c’ h divides ec from u. Remove, however, the prefrontal h from the parietal e ’ (which
may be readily done, the suture, which i is not indicated in the figure cited, being persistent),
and the anterior and mesial half of the orbitosphenoid (z) is then seen extending inwards
(mesiad), beneath the parietal and prefrontal, to join a triangular surface formed by a de-
scending process from the middle of the outer edge of the frontal.
t Op. cit. p. 388.
—
, ey ee ae ee
i
pet er eS
ON THE VERTEBRATE SKELETON. 219
anterior and antero-lateral walls of the cranium, defends the rhinencephala
and transmits the olfactory nerves, but is altogether distinct from and pos-
terior to the capsules of the organs on which those nerves are ramified.
In the crocodile Cuvier restricts the term ethmoid to the cartilaginous
lamine, capsules, or supports of the olfactory ramifications after the nerves
have left the cranium. In mammals the ethmoid is made to include both the
bones that close the cranium anteriorly, support the rhinencephala, give exit
to the olfactory nerves, and those which defend and sustain the enormously
developed. and complex superior parts of the organ of smell*. Whilst this
confusion is permitted to vitiate osteology, it is plain that no intelligible
homological or other proposition can be predicated of the ‘ ethmoid.’
When Cuvier, with.reference to the hypothetical possibility of the homo-
logue of the frontal forming part of the bone 7—11 in the frog, adverts to
the second chance of bringing the ‘cs en ceinture’ into the ordinary cate-
gory of cranial bones, by viewing it as the ‘ethmoide,’ he adds, that it would
then be “un ethmoide ossifié, ce que sera une grande singularité” (2.
p- 388). Here it is obvious that the predominating idea of the ethmoid was
that presented to his mind by the capsules of the olfactory organ in the
crocodile“and other reptiles,;which he had so called, and which are wholly or
in great part cartilaginous. But the parts of Cuvier’s ethmoid in birds and
mammals, which are in functional and physical relation with the cranial cavity,
thinencephala and olfactory nerves, are ossified : the bone, also, to which he
gives the name ‘ ethmoid’ in fishes (fig. 5, 15) is ossified ; and, what is more
to the purpose, the bones (11) in fishes, ophidians, chelonians and saurians,
which repeat the essential characters of the batrachian ‘ os en ceinture, are
likewise ossified.
General homology teaches that the bone or bones in relation to the defence
of the rhinencephala and the transmission of their nerves belong to one class,
and that the parts of the skeleton, whether membranous, gristly or bony,
which form the capsule or sustain the olfactory organ itself, belong to another
and very different class of parts of the skeleton. But, not to anticipate what
belongs more properly to a subsequent section of this report, observation
shows the two parts to be physically distinct in all vertebrates except mam-
mals, and to be distinct in the foetus of these. Whether we restrict the term
*ethinoid’ to the neurapophysis or to the sense-capsule (which in mammals
constitutes the ‘ conchz superiores’ and cells of the ethmoid), the term must
be applied arbitrarily in its extended or homological signification, since the
neurapophysis dismisses the nerve by a single foramen or groove in all the
vertebrates below mammals. The multiplied foramina in the neurapophysial
or cranial part of the anthropotomical ‘ ethmoid,’ whence that name, as well
as the special designation of the part called ‘lamina cribrosa,’ are modifica-
tions peculiar to the mammalian class, but not constant here, and they form
no essential homological character of the bone in question. It appears to
me preferable, since we have two essentially distinct parts of the skeleton
combined in the mammalian and human ethmoid, to restrict the term to the
* Objecting to Oken’s idea, that the prefrontal in the crocodile was homologous with the
part of the ethmoid called ‘os planum’ in anthropotomy, Cuvier says, “ Or l’os planum ne
parott jamais sur la joue; il ne se montre plus dans J’orbite 4 compter des makis si ce n’est
un petit point dans les galeopitheques et dans quelques chats. Dans tous les autres mam-
miféres l’ethmoide est entiérement enveloppé et caché par le palatin’”’ (note that significant
connection) “et par le frontal et spécialement par cette partie du frontal dont il est main-
tenant question et qui se détache dans les ovipares. Le véritable ethmoide est enveloppé
de la méme maniére dans le crocodile, quoique presque toutes ces parties restent cartilagi-
neuses.”—Ossem. Foss., v. pt. i. p. 73. i
Q
220 REPORT— 1846.
part which appertains to the sense-capsule, i.e. which is directly concerned
in the support of the membrane and cells of the olfactory organ.
But leaving for the present the question of names, and returning to things,
let us pursue our search and comparisons of the bones which continue in the
higher classes to repeat the essential characters of those called ‘ prefrontals’
in fishes. Were it necessary to add to the reasons above assigned for regarding
no. 14, fig. 13, as the homologues of 14 in the fish, notwithstanding they are
connate in the batrachian, I would cite the structure and relations of those
bones in the sword-fish. The whole of the anterior part of the, extensive
interorbital space is occupied by the prefrontals, which join each other at the
median line by an extensive vertical cellular surface: they form the anterior
border of the orbit, and the posterior wall of the nasal fossa; they close the
cranial cavity anteriorly, and transmit the olfactory nerve to the capsule by
a central foramen. They are almost entirely covered by the frontals above,
which they support by a broad flat surface; a very small portion only ap-
pearing on the upper surface of the skull at the anterior angle of the orbital
ridge. Were the frontals separated, the prefrontals would then appear, as in
the frog, at the median line: were the suture between the two prefrontals
to be obliterated in Xiphias, an ‘os en ceinture’ would be produced like that
of the frog. The nasal bone of the sword-fish, which Cuvier calls ‘ ethmoide,’
presents a cellular structure of its base, designed to break the force of the
concussion arising from the blow which is delivered by the ‘sword.’ But the
prefrontals manifest more extensively this peculiar cellular structure, which
Cuvier well says, “l’on prendrait presque pour les cellules de lethmoide d’un
quadrupéde*.”
Cuvier, not perceiving or not appreciating the grounds of the homology of
the ‘os en ceinture’ with the prefrontals, describes the divided nasal (1s, fig.
13), in the batrachia as the ‘ frontaux antérieures’ ; and reciprocally, having
called the bones in fishes, homologous with the bone 14, (which he thought
might represent the ethmoid in the frog) ‘frontaux antérieures,’ he gives the
name ‘ ethmoide ’ to the bone 15, fig. 5, whether single or divided, in ‘fishes.
It is not necessary to add anything to the arguments by which M. Agassiz
has sustained the conclusion of Spix, that Cuvier’s ‘ethmoid’ in fishes is the
‘nasal.’ And it needs, I think, only to compare the connections of the
bones 15, fig. 13, with either the single or the divided nasals in fishes, and to
glance at the obvious homology of the bones / in Cuvier’s pl. xxiv. fig. 1—6,
with the bones gg in figs. 4 & 6 of pl. xxvi. (‘ Ossemens Fossiles,’ t. v. pt. 2),
to ensure the acceptance of the conclusion, that his ‘ frontaux antérieures’
in the frog and the other anourans are the true nasal bones.
In the python Cuvier transfers the name ‘frontaux antérieures’ to the
lacrymal bones. The bones in this serpent, which are in neurapophysial
relation with the olfactory nerves, and which present other essential charac-
ters of the prefrontals (14) in fishes, are also two in number, in the form of
thin osseous plates, intervening on each side, anterior to the frontal, between
the vomerine and nasal bones, bent outwards, in the form of a semicylinder
about the olfactory nerves, which they support and guide to the cartilaginous
capsule of the organ of smell, and having the palatine bones articulated to
their under and outer sides. The bones, which thus present every essential
character of the prefrontals, are those (ss in pl. ix. figs. 1, 2, 3, ‘ Régne
Animal,’ t. iii. 1830) which Cuvier there calls ‘cornets inférieures.’ But
the true ‘cornets’ (turbinals) are cartilaginous in serpents as in every other
reptile, and give attachment to the palatines in no animal. The bones 06 in
* Hist. des Poissons, t. viii. p. 194.
~
ON THE VERTEBRATE SKELETON. 221
the same figures, to which the name of ‘anterior frontal’ is given, have no
relation whatever to the protection of the rhinencephala or the exit of the
olfactory nerves, but they have a large perforation for the passage of the
muco-lacrymal duct from the eye. They repeat indeed the single and
least essential character of the prefrontals, in standing anterior to the fron-
tals and the orbits; but these are characters common to the great anterior
mucous scale-bone in fishes, whose essential function—the transmission of a
mucous duct—they superadd to the repetition of its connections, viz. with
the prefrontal, nasal and superior maxillary bones*.
The bones, which more resemble the anchylosed prefrontals in the frog, are
the frontals of the python; but the resemblance is confined to one character
only, and that an exaggeration of a character common to the frontal bones of
many birds, and of the ornithorhynchus among mammals, viz. a develop-
ment of a median bony partition from the line of the frontal suture into the
median interspace of the encephalon. In the python each frontal sends
down at the fcre-part of this suture such a partition, which is therefore double,
as the falx essentially is in man and the mammalia, in which it retains its
primitive histological condition of a fibrous membrane. The ossified lamin
of the falx in the python bend outwards and coalesce helow with the external
or orbitosphenoidal plates of the frontal, and thus surround the lateral divi-
sions of the fore-part of the brain; in fact, the olfactory nerves, drawn back
in the progress of the concentrative movement of the cerebral centres, so as
also to occupy the prosencephalic segment of the cranium, the prosencepha-
lon being, in like manner, protected chiefly by the mesencephalic bony arch.
The change is precisely analogous to that which takes place at the opposite
extremity of the neural axis in ‘higher animals. In the python every segment
of the spinal chord retains its primitive relation to the segment of the endo-
skeleton, through which it transmits its pair of nerves. In the mammal the
concentrative movements of the spinal chord draw its segments in advance
of their proper vertebre, and the primary relation is indicated by the nerves
which these vertebrz continue to transmit, and by which alone we are guided
from the segment of the endoskeleton to that of the neural axis which origi-
nally governed its development.
~ So, likewise, at the opposite end of the skeleton, we trace the relation of
the anterior osseous segment, which transmits the olfactory nerves to their cap-
sule, to its proper segment of the neural axis, by following those nerves back
to the retracted ganglions (rhinencephala) from which they take their origin.
The connections of the annular frontals of the python with the parietals
and post-frontals behind, with the connate orbitosphenoids, and through
them with the presphenoid below, prevent their homology being mistaken ;
for they are far from completely representing or repeating the essential cha-
racters of the coalesced annular prefrontals of the frog.
Not to lengthen unnecessarily this exposition of the homologues of the pre-
frontals (14, figs.4 and 5) in fishes, I pass at once to the highest of existing rep-
tiles, the crocodile. Here we find, in the dry skull, the condition of the cranial
* No one could better. appreciate the value of the functional character of the lacrymal
perforation in a homological discussion than Cuvier, when the more obvious features of the
prefrontals of fishes were so repeated in any higher animal as to have led him to distinguish
the prefrontals in that animal from the lacrymal bone. Thus with regard to the pre-
frontals of the crocodile, Cuvier says, ‘‘ Quant a M. Spix, entrainé par un autre systéme et
négligent le trou lacrymal, qui cependant est bien visible, et qui, spécialement dans le cro-
codile, est percé tout entier dans l’os auquel je donne ou plutét auquel je maintiens le méme
nom, c’est mon frontal antérieur qu’il appelle lacrymal.’” (Ossemens Fossiles.) Change
python for crocodile and Cuvier for Spix, and the criticism equally applies in the present
instance to its original author.
299 REPORT—1846.
cavity in the fish beautifully and closely repeated: the prosencephalice part
opens freely by the aperture bounded by the orbitosphenoids (fig. 9, 10) into
the common orbital cavity (07), and the rhinencephalic division of the cranium
is prolonged, as a groove upon the under surface of the coalesced frontals
(ib. 11) above the orbits, expanding as it advances, until it is arrested by a
boundary formed by two bones (7d. 14), which rest below upon the vomer
and give attachment there to an ascending process of the palatines (20), which
sustain by their mesial and upper expanded surfaces the nasal (15) and fore-
part of the frontal (11); and articulate exteriorly with the large lacrymal
bone (fig. 22,73) perforated as in the fish and serpent by a mucous duct from
the orbit. They are each grooved on their inner or mesial surface (indicated
by the numerals 14, in fig. 9) by the olfactory nerve, where it escapes from
the cranium to spread upon the membranes sustained by the cartilaginous
capsules anterior to the bones in question; below these grooves the bones
(14) extend inwards and meet at the mesial linc; but do not coalesce there
as in the frog, nor extend their mesial union upwards, so as to convert the
olfactory grooves into two complete canals. They, therefore, retain or resume
much more of their primitive piscine character than do their homologues in
the frog or serpent, and manifest it conspicuously by developing a subtrian-
gular external plate which appears on the upper surface of the cranium at
the anterior angle of the orbit between the frontal, the lacrymal and the
nasal bones. In short, the homology of the bones 14 in the crocodile (figs. 9,
21, 22) with those so numbered in the fish (figs. 4 and 5), was quite unmis-
takeable ; and, with the exception of Spix, all anatomists have concurred in
this respect with Cuvier: only some of them have extended further and
expressed differently the homologies of the bones in question.
Now, bearing in mind the small brain of the cold-blooded crocodile, and
the concomitantly restricted development of the spine or roof-bone in special
relation with the cerebrum, viz. the frontal (11), which is aided in its se-
condary function in relation to the orbit by distinct supraorbital bones in all
crocodiles, and contrasting the condition of the part of the brain which,
chiefly governs the development of the frontal bone with that of the same
division of the brain of mammalia,—-let us proceed to make the comparison
which Cuvier recommends*, in order to trace the homologues of the croco-
dile’s prefrontals in the mammalian class.
We place the skull of a ruminant (the red deer, e. g.) by the side of that
of a crocodile, and delineate a suture which would detach a portion from the
frontal, having the same superficial connections as the upper peripheral plate
of the prefrontal has in the crocodile. It appears to be far from presenting
the same figure; but most assuredly such artificially detached portion of
the ruminant’s frontal has not the same functions (‘emploi’) as the pre-
frontal has in the crocodile. For if we even include with the part so
detached the anterior portion of the descending orbital plate of the frontal,
we find it joining below the orbitosphenoid without any connection with the
vomer, or any attachment to the palatine: it forms no immediate part of the
supporting plate of the rhinencephalon, nor of the foramina for the exit of
the olfactory nerves. Such artificially detached portions of the mammalian
frontal are entirely separated from each other; whilst one of the important
* “T] suffit en effet de placer une téte de mammifére, de ruminant par example, a cdté
d’une téte de crocodile, pour s’assurer qu’il s’est fait ici (‘ du frontal antérieur’) un démem-
brement du frontal. On pourroit, sans rien déranger, dessiner sur le frontal du mammifére
la suture qui existe dans le crocodile, et on détacheroit ainsi dans le premier un frontal
antérieur qui auroit la méme position, presque la méme figure, et absolument le méme emploi
que dans le crocodile.”—Ossem. Fossiles, y. pt. ii. p. 73.
dS
ON THE VERTEBRATE SKELETON. 923
points of resemblance between the prefrontals of the crocodile and those of
the fish are the mesial approximation and junction of their descending (neu-
ropophysial or rhinencephalic) plates—the most constant and important parts
of the bones in question.
If the frontal of the ruminant or other mammal were expanded only at
the parts corresponding with the detached bones called “frontaux anté-
rieures” in the crocodile, there might then be a primd facie probability that
such expansions were connate parts, dismembered in the crocodile’s skull.
But the vastly increased lateral as well as anteroposterior development, and
the more or less vertical convex expansion of the frontal in the highest
vertebrate class, naturally indicate, in the first place, an inquiry into the
concomitant modification of the nervous centres by which the development
of that bone is mainly governed; and if such modification should then be
found to exist, in the cerebrum, for example, which, from the ascertained
correlative progress of the frontal in other classes, ought to cause or be
associated with such a general development of that bone as characterises the
skull in the mammalian class, it must surely be superfluous and gratuitous
to explain that development by the hypothesis of a coalescence of another
essentially distinct element of the cranial parietes: especially if that element
be proved by a similar tracing of its relations to the progressive development
of the cerebral centres, to have as essential and exclusive a dependence
upon the rhinencephalon as the frontal bone has upon the prosencephalon.
_ The position of the upper peripheral part of the prefrontal in the situation
in which it is seen in the crocodile, is, in fact, the least constant and import-
ant of the characters of that bone. in the bull-frog, for example, the ex-
posed part of the prefrontal is mesiad of the conjoined parts of the nasals
and frontals instead of being lateral: in the sword-fish the prefrontals barely
appear, and in the python they do not appear at all upon the upper surface
of the skull; but they retain in each their more typical neurapophysial po-
sition, with all their more constant and essential characters. The enormously
developed frontal of the mammal masks these characters, and usurps the
less constant and least important one, viz. superficial position, on which alone
Cuvier insists as proving the prefrontal of the crocodile, with its complex
functions and connections, to be such a dismemberment of the true frontals
if the ruminant, as may be marked off with the pen on the upper surface of
the skull.
The descending [rhinencephalic] plates of the prefrontal in the crocodile
(fig. 9, 14) are subcompressed in the axis of the skull, and expanded laterally,
especially at their upper part ; where, in the alligator, I find them forming a
shallow cup, concave forwards for the lodgment of the cartilaginous olfactory
capsule,—of that part, namely, which is ossified in mammalia, and there de-
veloped into the great labyrinth of the superior turbinals and ethmoidal cells.
The vertical plates, continued forwards from the prefrontals, which extend
above to the nasal suture and descend into the vomerine groove below, to aid
in forming the ‘septum narium,’ are cartilaginous in the crocodile: they are
more or less ossified, and form the ‘lamina perpendicularis ethmoidei’ in
mammals. The median plate, dividing the olfactory nerves at their exit, and
developed backwards as a partial septum of the rhinencephalic chamber of
the cranium, and continued into the simple interorbital septum of the croco-
dile, also remains cartilaginous: when ossified in mammals, it forms the
‘crista galli.’ Now not one of these cartilaginous representatives of the parts
of the compound bone called ‘ ethmoid’ in anthropotomy, is united or con-
nected with the portions of the frontal in mammals which Cuvier has assumed
to be the homologues of the prefrontals in the crocodile ; those bones being
224 REPORT—1846.
in that reptile, as the prefrontals are in fishes, chiefly concerned in closing
the anterior end of the cranial cavity, in giving exit to the olfactory nerves,
in suspending the palatine arch, in connecting the vomer with the nasal ver-
tically, and the nasal with the frontal and lacrymal horizontally, repeating in
the crocodile for the latter purpose the development of the upper or horizontal
plate which had almost or entirely disappeared in some of the intervening
forms of reptiles. In most chelonians this portion of the prefrontal coalesces
or is connate with the short nasal: but I have found the instructive exception
presented by the existing freshwater tortoise (Hydromedusa) of the persistent
suture between the nasals and prefrontals, repeated in two fossil chelonians
(Chelone planiceps and Chelone pulchriceps)*.
Proceeding in the ascensive track of the homologies of the prefrontals,
I have selected from the class of birds the skull of the ostrich (figs. 8 and 23),
the representative of an aberrant order, in which every deviation from the
type of the class that has been supposed to tend towards the Mammalia, tends
equally or more towards the Reptilia+, and in which, conformably with the
lower development of the respiratory system, the original sutures of the
cranium, or in other words, the signs of the vertebrate archetype on which it
is constructed, are longest retained. Were we to cut off the corresponding an-
terior angles of the frontals, no. 11, to those supposed to represent in mammals
the bones we are in quest of, we should have even fewer of their characters
than in the higher class alluded to, because the descending orbital plate is
less developed, and the frontal, though its general size is much augmented,
retains more of its oviparous horizontality as an expanded spine or roof-bone
of the cranium.
There is a large bone (fig. 23,73) bounding the anterior border of the orbit,
and from which, as we have seen in the parrots, ossification sometimes extends
backwards along the inferior contour of the orbit to the postfrontal. But this
bone, besides its repetition of the connections of the lacrymal in the fish and
crocodile, resting as in the latter animal upon the true malar bone, is either
perforated or grooved by the lachrymal duct, which it defends in its course
from the eye to the nose, and has none of the essential characteristics of the
prefrontal. But we see on the exterior of the skull of the ostrich and other
struthious birds, a distinct rhomboidal plate of bone interposed between the
frontals and nasals, precisely in the situation in which the upper surface of
the coalesced prefrontals appears in the skull of the frog and other anourous
batrachians. In a nearly full-grown ostrich’s skull, I removed the left fron-
tal, nasal, lacrymal and tympanic bones, and the zygomatic arch, as in fig. 8,
and found the facet in question to be the upper and posterior expanded
surface of a large irregularly subquadrated compressed bone (7d. 14), consist-
ing of two vertical compact plates coalesced at their periphery, and including
a loose cancellous texture. The upper and posterior expanded surface of the
bone extends a short way back beneath the frontals, descends and closes the
anterior aperture of the cranium, and sends out from each side a plate of
bone which arches over the o!factory nerves and forms the canals by which
they are conducted along the upper part of the orbits. The anterior and upper
surface of the bone again expands (at 14!, figs. 8 and 23), and there sustains,
and is covered by, the nasal bones, and again overarches, and is sometimes
* Report on British Fossil Reptiles, Trans. Brit. Assoc. 1841, pp. 169, 172. :
+ The urinary bladder and intromittent organ, e. g.: the modification of the feathers in
the Struthionide is a degeneration of a peculiarly ornithic character ; but not, therefore, an
approximation to the hairy covering of mammals.
+ In the emeu (Dromaius ater) at 14, fig. 1. pl. 39. Zool. Trans. t. iii.: and in the casso-
wary at f, fig. 3, taf. i. in Hallmann’s ‘ Vergleichende Osteologie des Schlifenbeins.’
F
ee
ON THE VERTEBRATE SKELETON. 925
perforated by the olfactory nerves (the course of which along the rhinen-
cephalic continuation of the ‘cranial cavity, is shown by the arrows, ol. 14,
figs. 8 and 23) prior to their final expansion on the olfactory organ; the
main body of the bone forms the fore-part of the interorbital septum and
the back part of the nasal septum, a slight outstanding ridge or angle
dividing the two surfaces: it rests below upon the rostral prolongation of
the presphenoid, which, however, barely divides it from the semicylindrical
grooved vomer (13) which sheathes the under part of that process. The
posterior extremities of the palatines develope broad horizontal plates mesiad
and upwards (fig. 23, 20), which join the lower border of no. 14, where it rests
upon the presphenoid. The outer margins of the anterosuperior expansion
of no. 14 come into contact with the lacrymals: the posterior border of the
vertical or rhinencephalic plate joins and soon coalesces with the orbitosphe-
noids (10). Thus we have all the essential characters of the prefrontals in
the fish, the frog and the crocodile, with a repetition of their first important
modification in the tail-less batrachians, viz. that of median confluence ; and
it is not unimportant to observe that this is associated with the obliteration of
other cranial sutures, by which also those batrachians resemble birds. The
first step in the progress of this median approximation of the prefrontals, is
the development of the plates which, in certain fishes, convert the olfactory
grooves into foramina; these mesial plates next come into contact at the middle
line, e. g. in Xiphias and Ephippus ; they proceed to coalesce in the frog, and
the pretrontals are so much further compressed in the bird that the olfactory
grooves open upon the outer or lateral instead of the inner or mesial surfaces of
the rhinencephalic plates: they are, however, very deep grooves in the ostrich.
and in the apteryx are canals protected by a distinct external-plate. The
interruption of the direct vomerine connection by the prolonged presphenoid
is the chief secondary modification of the prefrontals in the bird. No other
bone in the bird’s skull repeats the more essential characters of the prefrontals
in fishes and reptiles, save the bone no. 14, figs.8 and 23. Cuvier calls this bone
the ‘ethmoide’; but blames the clear-sighted and consistent German anato-
mists who applied that name to the prefrontals in fishes and reptiles ; yet the
part of Cuvier’s ethmoid in the bird answering to the ‘ lamina cribrosa’ of the
mammal, sometimes gives passage to the olfactory nerve by a single foramen,
sometimes by merely a groove, a difference which does not prevent him
adopting the homology here, though he opposes it to the adoption, by
Bojanus, of the homology of the same part in the fish (ande, p. 215). The
smooth plate forming, with the orbitosphenoid, the interorbital septum, is
the ‘os planum,’ or papyraceous plate of the bird’s ethmoid, with Cuvier :
the masking of this part in most mammals by the downward development
of the orbital plates of the frontal, offered no difficulty to the ethmoidal de-
termination of no. 14 in the bird; and it forms as little valid objection to
Oken’s mode of expressing the ethmoidal homology of the prefrontals in the
cold-blooded ovipara.
For the reasons before assigned, viz. that the terms ‘ frontal antérieur’
had been given to the bone in question, no. 14, in those animals in which it
deviates least from its general type, as the nasal neurapophysis, I retain the
name prefrontal for it under all its metamorphoses. Cuvier, after balancing
the characters of the bones nos. 15, 22 and 7a (fig. 23) in birds, inclines to the
opinion that 15 is the true nasal, and 22' an essential part (nasal process) of
the premaxillary : with regard to 73, he says, “les os externes et plus voisins
de l’orbite seraient presque comme on le voudrait, ou des frontaux anté-
rieurs ou des lacrymaux.” In which case, no. 14 having been described as
the ‘ethmoid,’ one or other of the above-named bones would be wholly absent
226 REPORT—1846.
in birds. ‘Ce que pourrait faire croire que c’est le frontal antérieur qui
manque, c’est que dans les oiseaux iln’y a point de frontal postérieur, et que
la paroi antérieur de J’orbite, a l’endroit ou le frontal antérieure se trouve
ordinairement, est manifestement formée en grande partie par une lame
transverse de l’ethmoide*.” But the postfrontal is not always absent in
birds: it is present as a distinct bone, though small, in the emeu’s skull,
figured in the ‘ Memoir on the Dinornis’ above-cited ; and it is still more
developed in the remarkable extinct (?) genus, the immediate subject of that
memoir. Besides, to anticipate the subject of a subsequent part of this report,
a parapophysis always disappears from a typical segment of the skeleton
sooner than a neurapophysis. ‘The rest of Cuvier’s difficulty in the recog-
nition of the prefrontal in birds was more nominal than real.
The ethmoid, in the restricted sense in which Cuvier applies the term in the
crocodile and other animals with divided prefrontals, and in which I would
apply it in those animals also in which the prefrontals have coalesced, is
present but remains cartilaginous in the bird. In the mammal it becomes
bony and contracts anchyloses not only with the still more reduced debris of
the coalesced prefrontals, but also, in consequence of the change of position
of the prefrontals through the further progress of concentration, whereby
they are drawn backwards closer to the prosencephalic part of the cranium,
and in consequence of the concomitant expansion of the true frontals,—with
the orbital plates of the frontals ; whereby these plates usurp in most mammals
the office and the position of the external parts of the prefrontals in the cold-
blooded vertebrata+.
The posterior part of the coalesced prefrontals (figs. 24 & 25, 14) divides
the anterior aperture of the cranium into two outlets, upon the inner cireum-
ference of which the rhinencephala rest ; each outlet being commonly closed
by part of the olfactory capsules, which are ossified and perforated to receive
the divisions of the olfactory nerves. When the prefrontals extend backwards
and beyond the cribriform plates, they form what is termed the ‘ crista galli’:
this exists in comparatively few mammalia ; but is as large in the seal tribe
as in man. In the tapirs the prefrontals expand above and overarch the ol-
factory capsules, but their upper horizontal plates are overlapped by the
nasals and true frontals. In the Delphinide, where the olfactory capsules
are absent, the prefrontals expand posteriorly, and diverge from their median
coalesced portions constituting the septum of the nasal passage, in order to
form the posterior boundaries of those passages and the anterior wall of the
cranial cavity. They again expand and form a thick irregular mass anterior
to the nasal passages in some Delphinide, and in Ziphius ossification extends
along the fibrous continuation of the prefrontals forwards to near the end of
the premaxillaries{. They are connate with the orbitosphenoids behind, and
soon coalesce with the vomer below; they rise anterior to the frontals and
support the stunted nasals which are wedged between the prefrontals and
frontals. The cetacea are the only mammalia in which the prefrontals appear
upon the exterior of the skull, and which in this respect resemble the reptilia.
* Lecons d’Anat. Comp. 1837, t. ii. p. 580.
+ Cuvier takes this ground in objecting to Oken’s ethmoidal homology of the prefrontal
in the crocodile, and says, “the ethmoid coexists in a cartilaginous state with, and is enve-
loped by, the prefrontal, ‘comme la partie antérieure du frontal enveloppe l’ethmoide des
ruminans.’”’—Hist. des Poissons, vy. p. 235. The correspondence is exaggerated, but it
matters not. There are other characters of the mammalian ethmoid, as the closing of the
cranium anteriorly, the transmitting the olfactory nerves, &c., which are nowise manifested
by Cuvier’s cartilaginous ‘ethmoide’ in the crocodile, and are very satisfactorily so by the
prefrontals in that animal.
t Ossem. Foss. y. pt. i. p. 351.
ON THE VERTEBRATE SKELETON. po7
Cuvier describes the posterior and superior expanded and diverging plates
of the prefrontals as “a lame cribreuse de l’ethmoide:” the coalesced part
forming the septum, he ascribes to the vomer*. Dr. Kostlint, also, who
rightly recognises the ethmoid to be no proper bone of the skull, but only
an ossified organ of sense, yet describes, after the anthropotomists, the coa-
lesced prefrontals as the cribriform and azygos processes of the ethmoid
(‘Siebplatte’ and ‘ Scheidewand des Siebbeins,’ pp. 85. 89) in cetacea which
have no organ of smell. In a young balenoptera, in which the frontals, the
vomer and the nasals were ossified, I find the prefrontals as two cartilaginous
plates, extending from the nasals above to the groove of the vomer below. In
the manatee the essential parts of the prefrontals which close the cranial
cavity anteriorly, and give exit to the olfactory nerves, are thick and unu-
sually expanded. But in no mammal do these parts, with their continuation,
the ‘lamina perpendicularis,’ which, as the coalesced neurapophysial plates
of prefrontals, bring the vomer below in connection with the nasals above,
ever undergo such modifications as to obliterate their true and essential ho-
mological characters.
In proceeding next to consider the special homologies of the bones of the
arch closed by the premaxillaries (22) and constituting the ‘upper jaw,’ I
commence with the palatines (20), because they form, throughout the verte-
brate series, the most constant medium of suspension of that arch to the
anterior cranial segment formed by the vomer, prefrontals and nasal. This
‘secret affinity,’ as Goethe would have termed it, before the knowledge of
the general type had revealed its nature, is manifested by the process of the
palatine in man, which creeps up, as it were, into the orbit to effect its wonted
union with the prefrontal, to that part of the bone, viz. of which Cuvier had
recognised the homologue in his ‘ ethmoide’ of the bird}. It is the very
constancy, indeed, of these and other connections which has exempted the
palatine from the different determinations and denominations attached to
other bones, and which renders further discussion of its special homology
unnecessary here.
Passing over, for the same reason, the maxillary (21) and premaxillary (22),
and referring to the excellent treatise by Dr. Kostlin§ for the grounds of
the determination of the ‘pterygoid’ (21), I proceed to notice other bones
which, diverging from the maxillary arch, serve to give it additional fixation
and strength in the air-breathing vertebrates. The first of these is the malar
bone (fig. 11, 26), the homology of which has been traced without difference
of opinion throughout the mammalian class ; where, however, the inconstancy
of its proportions, number of connections, and very existence, is sufficient to
indicate its comparative unimportance as an element of the maxillary arch.
_ It is absent in many insectivores (Centetes, Echinops, Sorex): it has not
___ been detected as a distinct bone in the zygomatic arch in the monotremes, on
__ aecount perhaps of its early coalescence, as in birds, with the maxillary
(fig. 12, 21, 26): in Myrmecophaga gigantea and Manis, it projects back-
_ wards, as a styliform appendage, from the maxillary, but does not attain the
squamosal; whilst in the sloths and their extinct congeners the gigantic
megatherioids, the malar presents its maximum of development and complex-
ity||. In the Delphinide, again, the malar is much reduced: its slightly ex-
panded maxillary end forms part of the orbit and joins the frontal ; the rest
extending backwards, as a very slender style, beneath the orbit to the squa-
el
Te
* Ossem. Foss. v. pt. i. pl. xxvii. fig. 3, A.
+ Der Bau des Knéchernen Kopfes, p. 11.
t See the passage above quoted from the ‘ Lecons d’Anat. Comp.’ ii. p. 580.
§ Op. cit. p. 328. || Description of the Mylodon robustus, 4to, p. 19.
228 REPORT—1846.
mosal. The malar joins the post-orbital process of the frontal in the Mana-
tus senegalensis, the hippopotamus, the solipeds, and ruminants, some carni-
vores and the lemurs; in the true quadrumanes and man it joins the alisphe-
noid, and sometimes also the parietal.
The presence, form and connections of the malar are much more constant
in the class of birds ; where, however, it must be sought for as an indepen-
dent bone at an early period. In the young ostrich (fig. 23, 26) it is reduced
to the form of a simple, straight, slender style, and coalesces first with the
similarly-shaped squamosal (27), and next with the malar process of the
maxillary (21’). In the crocodile the malar bone (fig. 22, 26) becomes more
developed, and adds the connections with the postfrontal (12) and the ecto-
pterygoid (24') to the more constant ones with the maxillary (21) and squa-
mosal (27), which alone sustain it in birds. In most of the chelonians the
malar presents the same connections as in the crocodile, but is transmuted
from a ‘long’ to a ‘flat’ bone. It retains the expanded shape in the agama ;
but in most other lizards it resumes the styloid form ; being broadest, how-
ever, in those genera, e. g. Iguana, Thorictes, Tejus, in which it extends from
the maxillary to the postfrontal and squamosal; in the Varani it projects
freely backwards, like a styliform appendage of the maxillary, as in the
toothless mammalian Bruta, above-cited.
There is no malar bone in ophidians and batrachians. The lower portion
of the tympanic pedicle in the Anowra sends forward a process which joins a
backward prolongation of the maxillary: in all other batrachia the lower
portion of the tympanic pedicle is restricted to its normal connections and to
its function of affording articulation to the lower jaw. With regard, there-
fore, to the zygomatic modification of this portion of the pedicle in anourous
Batrachia, some may deem it the homologue of the malar; and, in marsu-
pial quadrupeds, the malar actually forms part of the glenoid cavity for the
lower jaw: or it may be regarded as the squamosal, which constantly sup-
ports the lower jaw in mammals: or it may be viewed as the coalesced homo-
logue of both bones: or finally, as a simple modified dismemberment of the
tympanic pedicle of the higher reptiles and birds; effecting a union with
the maxillary bone which makes it analogous to, but not, therefore, homolo-
gous with, the distinct malar and squamosal in those higher vertebrates. This
is a question of special homology on which I am unwilling at present to
express a decided opinion: but viewing the inconstancy of the squamosal in
reptilia, and its deprivation of the function of exclusively supporting the
mandible in all ovipara, I am disinclined to adopt the idea of its sudden resti-
tution to that mammalian function in frogs and fishes ; yet, if either of the
bones 26 and 27 are to be selected as the homologue of the hypotympanic (28d)
of batrachians and fishes, I should regard the claims of the squamosal to be
stronger than those of the malar, which Cuvier has chosen. The further sub-
division, however, of the tympanic pedicle in fishes, prepares us, in the as-
censive comparison, for the simple division of the pedicle in batrachia, and
for recognising in the lower articular portion a vegetative dismemberment of
as in the crocodile.
The characters and chief changes, in respect of connections and functions,
of the squamosal (27) in the mammalia have already been noticed in the dis-
cussion of the homologies of other elements of the complex ‘ temporal bone’
in that class. In birds the bone (fig. 23, 27) undergoes the same change of
form which has been noticed in the jugal, viz. from the squamous to the
styloid. It continues, however, to connect the malar with the tympanic as
it does in figs. 11 and 12, but it bas no connections with other bones. Cu-
vier having been led to recognise the squamosal in the mastoid (fig. 23, 8) of
ON THE VERTEBRATE SKELETON. 229
birds, does not distinguish 27 from 26, the true ‘jugal:’ and Geoffroy v iewing
the ‘portion écailleuse’ of the temporal in that cranial bone of the bird, which
he figures under the letter R, fig. 17, pl. 27 (Annales du Muséum, x.), calls
the true squamosal, the original separation of which from the malar he had
noticed in the chick, ‘jugal postérieure.’ He did not admit that this division
of the zygomatic style was constant or common in the osteogeny of the skull
of birds: but I have always found such division in the embryo, and it con-
tinues longer than usual in those very species, e. g. the duck and ostrich
(fig. 23, 26, 27), in which Geoffroy denies its existence (J. ¢., p. 361). Oken
accurately describes the two constituents of the zygoma in the skull of the
goose, in his characteristic and original Essay *, where he calls the posterior
piece (27) the humerus, and the anterior one (26) the radius of the head.
Bojanus+, who also recognised the fact of the essential individuality of the
bone (27) in birds, but who saw the homologue of the squamosal rather in the
tympanic (23), calls it ‘os zygomaticum posterius.’ I could cite other testi-
monies to the primitive existence of the distinct bone in birds connecting the
malar with the tympanic; but the fact which chiefly concerns us here is, that
if the special homology of no. s with the mastoid, and that of no. 2s with
the tympanic be proved, we then have a bone presenting ‘the most constant
connections of the squamosal in no. 27: if, however, that name be transferred,
as has been done by Cuvier, Bojanus{ and Geoffroy, to other bones, then a
new boue and a new name must be introduced into vertebrate craniology,
for which, as I trust I have shown, there is no sufficient ground.
Both Oken and Bojanus rightly discern in the permanently distinct bone
which, in the crocodiles (fig. 22, 27) and chelonians, connects the malar (26)
with the tympanic (28), the homologue of the bone they call ‘cranial hume-
rus, or ‘zygomaticum posterius’ in the bird. Cuvier is more accurate in his
determination of this bone (fig. 23, 27) as the ‘squamosal’ in reptiles; but
again at the expense of his consistency in regard to the characters of his
squamosal in the bird: for the homology of no. s (Cuvier’s ‘squamosal’) in
fig. 22 with no. s (Cuvier’s ‘ mastoid’) in fig. 23, is as obvious and unmistake-
able as is that of no. ev (Cuvier’s ‘ squamosal’) in fig. 22 with no. 27 (his dis-
memberment of the jugal) in fig.23. The squamosal is relatively stronger in
crocodiles than in birds, and in many chelonians resumes its flat, scale-like
form ; although, as Cuvier well observes, it answers, in function, only to the
zygomatic part of the mammalian squamosal :—“ c’est un temporal dont la
partie craniale a disparu§.” In lizards the squamosal again resumes the zy-
gomatic or styloid shape, connecting the mastoid and tympanic with the
postfrontal, and usually also with the malar ; the posterior connections being
here, as in mammals, the more constant ones.
As the squamosal varies in form with the malar, so it likewise disappears
with it in ophidians ; unless the anatoinist, tracing it descensively, prefers to
see it again in the peculiarly developed hypotympanic of the anourans. Ac-
cording to this view of the sudden resumption of its mammalian function in
regard to the lower jaw in batrachia, the name ‘squamosal’ may be trans-
ferred to the hypotympanic in fishes; and, if we must view the pedicle
(23 a—d, fig. 5) as ‘homologically compound,’ and not, like the mandibular
_ ramus, ‘ teleologically compound,’ 2sd seems to me a less arbitrary selection
from the pieces of that long and subdivided pedicle, for the representative
* Ueber die Bedeutung der Schadelknochen, 4to, 1807, p. 12.
+ Anatome Testudinis Europe, fol. Parergon, 1821, p. 178, fig. 196, 7.
' = The tympanic bone 23 is described in the same work as ‘squamosum sive quadratum,”
(fig. 196, g.): the mastoid is rightly named.
§ Ossemens Fossiles, 4to. t.v. pt. ii. p. 85.
230 REPORT— 1846.
of the squamosal, than the proximal or uppermost piece (23a) to which Cu-
vier has applied that name. If, indeed, Bojanus could have determined to
his own satisfaction or that of other anatomists, that the pedicle (2s, fig. 23),
articulated by one end to the mastoid, and by the other to the mandible, in
birds, was the ‘squamosum, then there would have been some ground for
regarding the bone (2sa, fig. 5) connected in fishes, with the mastoid as the
‘ squamosum.’
But when Cuvier had persuaded himself that the bone no. s, fig. 23, in
birds, to which the tympanic pedicle is articulated, was the ‘ écaille du tem-
poral,’ we feel at a loss to know on what principles special homologies can
be traced, when we find the name transferred to the upper part of the tym-
panic pedicle in fishes (fig. 5. 28 a), which is articulated to the bone (s) un-
equivocally answering to Cuvier's ‘ écaille du temporal’ in birds. M. Agassiz
is more consistent, and abandons with reason the Cuvierian determination of
the squamosal in fishes: if, however, the grounds assigned are conclusive as
to the homology of no. s, figs. 8 & 23 in birds with the mastoid of mammals
and reptiles, M. Agassiz cannot be correct in regarding the bone no. s, fig.
5 in the fish, as the ‘ écaille du temporal.’
With reference to the idea entertained by Spix, Geoffroy and Agassiz, of
the homology of the suborbital muciferous scale- bones in fishes with the malar
bones of higher vertebrates, I may refer to what has already been said in
regard to the actual repetition of the osseous arch connecting the prefrontal
with the postfrontal in certain birds, where that arch coexists with, and in-
dependently of, the bone recognised as the ‘malar’ by both Spix and Geof-
froy. The connection of the malar with the lacrymal and post-frontal is
less constant and characteristic of the bone than that with the maxillary and
squamosal. And it may further be remarked, that the functional character
of circumscribing a mucous duct, manifested by the lacrymal or anterior
end of the upper zygomatic or suborbital arch in the parrot, is superadded to
the character of connections in proof that such arch, and not the true zygo-
matic arch below, is homologous with the suborbital chain of bones in fishes.
All these discrepancies as to the jugal and squamosal in fishes arise, in my
- opinion, out of the circumstance that those bones are normally absent in
that class; both 26 and 27, figs. 11, 22, 23, 24, 25, being accessory parts, de-
veloped only in saurians, chelonians, birds and mammals, for additional fixa-
tion of the upper jaw, or for additional expansion of the cranium, or for both
purposes*.
According to this view, I regard the tympanic (2s) as essentially charac-
terized in the oviparous vertebrates (fishes, reptiles, birds) by its free articu-
lation by a convex condyle with the mastoid above, and by a convex condyle
with the mandible below; and I regard its subdivisions in the lowest of
these vertebrates, in the same light as the subdivisions of the mandible itself.
The formation of the tympanic cavity and support of the tympanic membrane
are secondary functions. The tympanic pedicle is essentially a single cranial
element, and actually so in all air-breathing vertebrates above batrachians.
We see plainly, even in the frog, that the portion which supports the ‘mem-
brana tympani’ is a mere exogenous process of the pedicle : it has still less the
appearance of a distinct part or process in the saurians, chelonians and birds :
and when the tympanic is excluded by the squamosal in mammals from its
normal office of supporting the mandible, it still manifests its character of
* The inconstant ossicle suspended to the back part of the free extremity of the maxillary
in the percoid fishes would have the best claim to homology with the malar, if the further
subdivision of the maxillary in the herring and lepidosteus did not indicate it to be a vege-
tative dismemberment of that bone.
ON THE VERTEBRATE SKELETON. 931
unity, whether it be expanded into a ‘bulla ossea, extended into a long tube
or meatus, or both, as in fig. 24, 28, or whether, as in fig. 25, it be reduced to
a mere ring or hoop supporting the tympanic membrane, until it coalesces
with other parts of the temporal, to form the tympanic or ‘ external auditory
process’ of that bone. In no air-breathing vertebrate have I ever found, or
seen described, the separation of the part of the tympanic forming the wall
of the tympanic chamber from the part supporting the tympanic membrane,
or this distinct, save in batrachia, from the part supporting the lower jaw*.
The tympanic pedicle is still further subdivided in fishes; but M. Agassiz’s
original idea of the ‘epitympanic’ as a dismemberment of the pedicle, which
he proposed to call ‘os carré supérieur,’ is, in my opinion, much more consist-
ent with nature than his later determination of that bone as the ‘ mastoid,’
or than Cuvier’s attempts to find the homologues of both the mammalian
‘squamosal’ and ‘jugal’ in the piscine subdivisions of the same pedicle.
There is as little ground for making the zygomatic process a distinct element
from the squamous portion, as for severing the annular process from the rest
of the tympanic. This idea of the zygomatic as an independent piece, which
Dr. Kostlin has also adopted, seems to rest only on the mal-determination
by Bojanus and Oken of the true squamosal in birds and reptiles as the
‘zygomaticum’ or ‘jugale posterius’: and the idea was perhaps further
strengthened in the mind of M. Agassiz, by what he deems to be the essen-
tial and characteristic function of the squamosal. But its protective cere-
bral or cranial scale is a peculiarly mammalian development ; much reduced
in the ruminants and cetacea, and totally disappearing in the oviparous ver-
tebrates. The zygomatic functions and connections are, notwithstanding a
few exceptions, as in the scaly manis and a few lizards, the essential] homo-
logical characters of the ‘squamosal.’ The necessity for forming an opinion
of the essential nature and general homologies of the parts blended together
in the human ‘os temporis’ by the ascensive or synthetic method, is strikingly
exemplified by the results of the application of M. Agassiz’s idea of its nature
to his determination of the bones in the head of fishes.
As the palato-maxillary arch in most air-breathing vertebrates supports, ac-
cording to my views, certain appendages, e. g. the malar and squamusal, which
are not present in fishes; so, I believe, with Cuvier, that the tympano-man-
dibular arch supports in fishes, certain appendages, which are not developed
in any other class. It is this fact, chiefly, that has led to so much discrepancy
in the attempts to determine by reference to bones in higher vertebrates the
opercular bones of fishes,—the chief battle-field of homological controversy.
All the four opercular bones forming the diverging appendage of the tym-
pano-mandibular arch (fig. 5, 34 to 37) were deemed by Cuvier to be peculiar
ichthyic super-additions to the ordinary vertebrate skeleton ; whilst by Spix,
Geoffroy, and De Blainville they are held to be modifications of parts which
* M. Agassiz applies the subjoined analysis of the ‘temporal bone’ to elucidate the homo-
logies of the skull of fishes :—‘‘ Nous distinguons encore dans le temporal complet les parties
_ suiyantes: l’écaille, servant de complément a la paroi latérale du crane dans sa partie posté-
rieure; le mastoidien, servant de rempart postérieur a la cavité tympanal ; Ja caisse, logeant
les parties principales de la cavité tympanale; l’anneau tympanique, servant d’appui a la
membrane du tympan; l’apophyse jugal, formant l’appui postérieur de l’arcade zygomatique 5
_ Vapophyse styloide, offrant une insertion a l’os hyoide, par laquelle ce dernier se fixe au crane;
et enfin l’os carré, formant la surface articulaire sur laquelle la machoire inférieure exerce
ses mouvemens. . La maniére variée dont ces différentes piéces se soudent ensemble, se séparent
et se combinent, occasionnent ces innombrables variations auxquelles le temporal est sujet
dans son ensemble. L’écaille du temporal est destinée, comme nous venons de le voir, 4 pro-
__ téger les parties cérébrales postérieures de la téte, sur la face latérale du crane.” —Recherches
sur les Poissons Fossiles, t. ii. pt. 2, 1843, p. 62.
232 REPORT—1846.
exist in the ordinary or endo-skeleton of other vertebrata. The learned
Professor of Comparative Anatomy in King’s College, London, who regards
this as “the more philosophical mode of considering them*,” has briefly
stated the homologies proposed by the supporters of this view, viz. that the
opercular bones are gigantic representatives of the ossicles of the ear (Spix,
Geoffroy, Dr. Grant+): or that they are dismemberments of the lower jaw
(De Blainville, Bojanus),—a view refuted by the discovery of the compli-
cated structure of the lower jaw in certain fishes, which likewise possess the
opercular bones: he then cites a third view, viz. that they are parts of the
dermal skeleton; “in short, scales modified in subserviency to the breathing
function ;” an opinion which Professor Jones correctly states that he derived
from my Lectures on Comparative Anatomy, delivered at St. Bartholomew’s
Hospital in 1835, and which he adopts, although its accordance with his first
proposition is not very clear. I have subsequently seen reason to modify that
view, though it has received the sanction of the greatest ichthyologist of the
present day, M. Agassiz; and, as I have since found, had presented itself so
early as 1826, under a peculiar aspect to the philosophical mind of Professor
Von Baer. In his admirable paper on the endo- and exo-skeleton, M. Von Baer
expresses his opinion, that the opercular bones are (dermal) ribs or lateral
portions of the external cincture of the head{. The idea of the relationship
of the opercular flaps to locomotive organs is presented by Carus, under the
fanciful view of their homology with the wing-covers of beetles and the valves
of a bivalve shell§. In 1836, M. Agassiz propounded his idea of the relation
of the opercular bones to scales in a very precise and definite manner ;
though, as I have elsewhere shown ||, the chief ground of his opinion is erro-
neous. He says, “Les piéces operculaires des poissons ne croissent pas,
comme les os des vertébres en général, par irradiation d'un ou de plusieurs
points d’ossification; ce sont, au contraire, des véritables écailles, formées,
comme celles qui recouvrent le tronc, de lames déposées successivement
les unes sous les autres, et dont les bords sont souvent méme dentelés
comme ceux des écailles du corps. Tels sont l’opercule, le sub-opercule, et
* Professor Rymer Jones, General Outline of the Animal Kingdom, 8vo, 1841, p. 509.
+ Lectures, Lancet, Jan. 11, 1834, p. 573; Outlines of Comp. Anat. p. 64.
t “In mancher Beziehung gehoren die Kiemendeckel zu ihr, und ich halte sie um so
mehr fiir (Haut) Rippen, d. h. fiir Seitentheile der aussern Ringe des Kopfes, da ich sie auch
in den gewohnlichen Knockenfischen fiir nichts anderes ansehen kann. Hat bei diesen auch
der oberste Knochen des Kiemendeckels wenig Aehnlichkeit mit Rippen, so geht dagegen
der unterste so unverkennbar in die strahlender Kiemenhaut iiber, das der Uebergang gar
nicht zu verkennen ist.”—Meckel’s Archiv, 1826, 3 heft, p. 369.
An analogous idea of the relation of the opercular bones to the inferior or costal arches was
proposed by Geoffroy St. Hilaire (Annales des Sciences, t. iii. pl. 9), and Cuvier (Hist. des
Poissons, i. p. 232), and has been adopted by the learned Professor of Comparative Ana-
tomy in University College, who, speaking of the occipital vertebrz, says, “‘ The two external
and the two lateral occipitals form the upper arch, and the two opercular and two sub-
opercular bones constitute the lower arch.” (Lectures, Lancet, 1834, p. 543.) He subse-
quently, however, adopts and illustrates (p. 573) the homology of the opercular bones with
the ‘ossicula auditis’ of mammalia; and in the ‘ Outlines of Comp. Anat.’ cites only the
Spixian and Blainvillian hypotheses (pp. 64, 65). In my Hunterian Lectures (vol. ii. 1836,
pp- 113, 130), I have adduced the grounds which have led me to the conclusion that the
opercular bones are neither ribs of the exo-skeleton, nor inferior arches of the endo-skeleton,
but persistent radiating appendages of an inferior (hemal) arch ; not, however, of the occipital
vertebra, but of the frontal ; just as the branchiostegal rays are the appendages of the hamal
arch of the parietal, and the pectoral fins of that of the occipital vertebra. That parts of
both endo- and exo-skeleton may combine to constitute the opercular fin is the more pro-
bable, inasmuch as we see the same combination of cartilaginous and dermal rays in the
pectoral fins of the plagiostomes, and in the median fins of most fishes.
§ Urtheilen des Knochen und Schalengeriistes, fol. p. 122.
|| Lectures on Vertebrata, p. 139.
ae ee
ON THE VERTEBRATE SKELETON. 233
Yinter-opercule. Le supra-scapulaire méme peut étre envisagé comme la
premiére écaille de la ligne latérale, dont le bord est également dentelé. On
pourrait dire aussi que le scapulaire n’est qu'une trés grande écaille de la
partie antérieure des flancs*.” And he adds, “‘L’opinion que j’ai émise 4
leur égard prouve que je suis loin d’admettre les rapports que l’on a cru
trouver entre les piéces operculaires et les osselets de l’oreille interne.”
I apprehend that the idea of the development of the opercular bones by
the successive excretion or deposition of layers, one beneath the other, ac-
cording to the mode in which M. Agassiz supposes scales to be formed, was
derived merely from the appearance of the concentric lines on the opercular,
subopercular, and interopercular bones in many fishes. I have examined
the development of the opercular bone in young gold-fish and carp, and I
find that it is effected in precisely the same manner as that of the frontal and
parietal bones. The cells which regulate the intussusception and deposition
of the earthy particles make their appearance in the primitive blastema in
successive concentric layers, according to the same law which presides over
the concentric arrangements of the radiated cells around the medullary canals
in the bones of the higher vertebrata: and the term ‘successive deposition,’
in the sense of excretion, is inapplicable to the formation of the opercular
bones. The argument in favour of their dermal character drawn from the
phzenomena of the development of the opercular flap, would equally apply to
prove the bones (ulna, radius, carpus, &c.) supporting the pectoral fin, to be
‘dermal’ bones tf.
The interopercular as well as the preopercular bones exist in the Lepi-
dosiren annectens with all the characters, even to the green colour, of the rest
of the ossified parts of the endo-skeleton ; the preopercular, as an appendage
to the tympanic arch, retaining its primitive embryonal subcylindrical form,
the interopercular being partly attached to the hyoid arch. Of the supra-
scapular there is no trace in the lepidosiren; but in the sturgeon it plainly
exists as part of the cartilaginous endo-skeleton, under the same bifurcate
form, and double connection with the cartilaginous skull, which it presents
in most osseous fishes. The large triangular bony dermal scale firmly adheres
to its broad, triangular, flat, outer surface. The epi- and meso-tympanic
cartilages in like manner expand posteriorly, and give a similar support to
the large opercular ganoid scale. Were the supporting cartilages of the
opercular and suprascapular scales to become ossified in the sturgeon, they
might become anchylosed to the dermal bony plates, and bones, truly homo-
logous with the opercular and suprascapular in ordinary osseous fishes,
_ would thus be composed of parts of the endo- and exo-skeleton blended
_ together. I cannot, therefore, concur with Von Baer in the opinion that the
opercular bones are ribs of the exo-skeleton, nor with Agassiz that both the
opercular and suprascapular bones are merely modified scales. In explaining
my views of the opercular bones, I am compelled, believing them to have no
special homologues in higher animals, to express those views in the terms of
a higher generalization. The suprascapular bone (fig. 5, 40) is the upper or
first part of the hemal arch of the occipital segment of the skull, and corre-
sponds in serial homology with the epi-tympanic portion (2s a) of the mandi-
_ bular arch, and with the palatine portion (20) of the maxillary arch. The
opercular bones are the diverging appendages of the tympano-mandibular
* Recherches sur les Poissons Fossiles, livraison 6me, 1836, tom. iv. p. 69.
+ Ib. p. 73.
{ “L’embryologie nous prouve, en effet, que la formation de l’appareil operculaire n’est
bo qu’un simple produit de la peau, qui peu-a-peu s’étend par dessus les branchies, d’abord
_ entiérement dégagées dans l’embryon.”—ZJb. p. 64.
1846. R
324 REPORT—1846.
arch, and correspond, in serial homology, with the branchiostegal appendages
of the hyoid and the pectoral appendages of the scapular arches, and have
the same title to be regarded as cephalic fins, and as parts of the normal
system of the vertebrate endo-skeleton; but neither opercular bones nor
branchiostegal rays are retained in the skeletons of higher vertebrata. All
diverging appendages of vertebral segments make their first appearance in
the vertebrate series as ‘rays’; and the opercular bones are actually repre-
sented by cartilaginous rays, retaining their primitive form in the plagio-
stomes. Inthe conger the subopercular still presents the form of a long and
slender fin-ray.
The opercular and subopercular, in ordinary osseous fishes, may frequently
coalesce, like the suprascapular, with their representative scales of the dermal
system ; but they are essentially something more than peculiarly developed
representatives of those scales. M. Agassiz, indeed, excepts the preoper-
cular bone from the category of “piéces cutanées,” believing it to be the
homologue of the styloid process of the temporal bone in anthropotomy, or
the ‘stylo-hyal’ of vertebrate anatomy, as the piece, viz. which completes the
hyoid arch above. “C'est en effet,” he says, “cet os ala face interne duquel
los hyoide des poissons est suspendu, qui s‘articule en haut avec le mastoi-
dien et trés souvent méme sur l’écaille du temporal.” So far as my obser-
vation has gone, it is a rare exception to find the hyoid arch suspended to
the preoperculum ; the rule in osseous fishes is to find the upper styliform
piece of the hyoid arch (fig. 5, 3s) attached to the epi-tympanic (28 a) close
to its junction with the meso-tympanic bone (28). It is equally the rule to
find the preopercular (34) articulated with the epi-, meso-, and hypo-tym-
panics ; and it is an exception, when it rises so high as to be connected with
the mastoid (‘écaille du temporal’ of Agassiz). If the stylo-hyal be not the
upper piece of the hyoid arch displaced, and if the upper piece connecting
that arch with the mastoid is to be sought for in osseous fishes, I should
rather view it in the posterior half of the epi-tympanic (2s a), which is usually
bifurcate below and very commonly also above, when the posterior upper
division articulates with the mastoid, and one of the lower divisions with the
hyoid arch.
The normal position, form, and connections of the preoperculum clearly
bespeak it to be the first or proximal segment of the radiated appendage of
the tympano-mandibular arch: the opercular, subopercular, and interoper-
cular bones form the distal segment of the same appendage.
M. Vogt, in supporting M. Agassiz’s views of the Ganoid order, reiterates
his original idea that the preopercular bone is the proximal piece (styloid)
of an arch distinct from the tympano-mandibular one ; but as the chief ground
of this opinion rests on a simple question of fact easily determinable, viz.
whether, as a rule, the hyoid arch is suspended from the preoperculum, and
this from the mastoid in fishes, neither of which accord with my observation
of their connections of those parts, the verdict may be left to the experience
of other observers. From a remark of M, Vogt’s*, viz. that “ M. Miller
attache, 4 ce qu'il parait, trop peu d'importance a ce fait, que toujours le
préopercule, et cela aussi chez les Siluroides, sert de point d’attache a l’are
hyoidien,” it would seem that, perhaps, the accomplished physiologist and
ichthyologist of Berlin had not found the fact ; and, therefore, gave not more
than its due importance to the rare exceptional circumstance of such an at-
tachment. The preopercular can be removed in most fishes, except where,
as in the siluroids, it coalesces with the tympanic arch, without dislocating
* Annales des Sciences, 1845, p. 56.
ON THE VERTEBRATE SKELETON. 935
or disturbing the connections of the true stylo-hyal (fig. 5, 28) with the epi-
tympanic (2s@) from whjch it is normally suspended.
M. Vogt correctly observes that the ‘temporal’ Sa 28a), ‘sym-
plectique’ (mesotympanic, 2s 6), and ‘jugulaire’ (hypotympanic, 23d), “a
eux seuls forment déja un arc suspensoir complet, 4 la face postérieure
duquel le préopercule est seulement accolé*.” But this only proves that the
preoperculum is an appendage to such arch, not that it is a suspensory pier
of a second arch.
The only essential modification which the siluroids present is the confluence
of the preoperculum with the true tympanic pedicle, here reduced to a single
piece. But this does not disprove its character as an appendage of the
‘tympano-mandibular arch, any more than does the confluence of the ulna and
radius with the scapular arch in the sturgeon disprove the character of those
elements as appendages of that arch. I have not been able to trace in the
siluroids the primitive boundaries of the coalesced preoperculum to such an
extent as to justify the statement, that it is intercalated between the epitym-
panic and hypotympanic, replacing the mesotympanic : but, if the preopercular
should extend in any siluroid fish so far as M. Vogt describes, this excep-
tional development would rather prove it to belong essentially to the tym-
panic and not to the hyoidean arch: at least it is only through this abnor-
_ mal encroachment that the preopercular can detach the stylohyal from the
epitympanic.
As the otosteals, or ‘ ossicula auditts,’ have borne a prominent share in the
discussions of the special homologies of the tympanic pedicle and its append-
ages, I may here remark that the extension in the embryo ‘mammal of the
long and slender process of the malleus in the direction of the mandible, and
its continuation or connection with the cylindrical cartilage (hemal portion
of the tympano-mandibular arch) from which the lower jaw is subsequently
developed, is a circumstance which renders the idea of the malleus, at least,
being a modified element of the tympano-mandibular arch ia batrachians
and fishes, worthy of consideration. The prolongation from the mesotym-
panic of the cylindrical cartilage, described by Meckel, and around which
the mandible is ossified in fishes, and the characteristic cylindrical or styloid
form of the mesotympanic, have induced M. Vogt+ to view that bone, the
*symplectique’ of Cuvier, as the homologue of at least part of the malleus;
and at the same time of the bone called ‘tympano-malléal’ by Dugés (my
‘hypotympanic’) in, the batrachians, M. Vogt offers no other reasons for
‘the determination. | find that the cartilage which in the batrachians forms
the medium of communication between the semi-ellipsoid ossicle (stapes)
closing the fenestra ovalis and the tympanic membrane, is repeated or repro-
duced in the more malleiform cartilage connecting the columelliform stapes
of the saurian reptiles to the membrana tympani. In birds a portion of the
cartilage attached to the tympanum becomes ossified and coalesces with the
columelliform stapes; and at the angle of union one or two cartilaginous”
processes exist, which some anatomists have compared with the incus. But
all anatomists have concurred in recognising the homology of the peripheral
bent-down portion of the long columella, which adheres to the membrana
tympani, with the part of the malleus called ‘manubrium,’ or handle, in
mammalia. The superadded modifications characteristic of the otosteals in
this class, have their seat between the manubrium mallei and the stapes, and
chiefly result in the development of the new bone called ‘incus’ and its epi-
physis, which has been termed the ‘os orbiculare.’ Notwithstanding, there-
_ fore, the connection of the ‘processus gracilis mallei’ with the embryonic
* Annales des Sciences, 1845, p. 55. + Loc. cit. p. 58.
R@
236 REPORT— 1846.
heemal or visceral cartilage of the mandibular arch in mammals, the homo-
logy of the malleus is so clearly traceable down to.its first independent ma-
nifestation in coexistence with the tympanic membrane of the batrachia, to
which it connects the unequivocally acoustic ossicle representing the ‘stapes,’
that the reference of all the additional ossicular mechanism of the ear-drum
to the same system of the skeleton as the petrosal itself, appears to me to be
most consonant with the recognised facts in their development and compara-
tive anatomy.
M. Agassiz has never countenanced the idea of the reproduction of the
mammalian tympanic ossicles in a magnified form in either the tympanic
arch or its opercular appendages. Returning to the consideration of these
bones in the last volume (p.68) of his admirable ‘ Recherches,’ he reaffirms
his opinion, that the opercular, subopercular, and interopercular are ‘ osse-
lets particuliers de la peau;’ but calls them ‘ branchiostegal rays.’ If he
had meant that they were parts essentially distinct, but comparable to the
true branchiostegals, he would have accurately enunciated their ‘serial ho-
mology.’ M. Agassiz, however, expressly repudiates this idea of represen-
tative relation, and affirms them to be part of one and the same series of
rays. “Mais en disant que les piéces operculaires sont des rayons branchio-
stégues, je n’entends point faire une simple comparaison, mais bien affirmer,
que je considére ces plaques osseuses simplement comme les rayons bran-
chiostégues supérieurs *,” This idea is, in fact, a necessary consequence of
M. Vogt’s conclusion, that the preoperculum is the upper or styloid element
of the hyoidean arch. The combination of the opercular rays or bones with
the branchiostegals in the support and movements of the continuous gill-
cover and gill-membrare, does not prove them to be diverging appendages
of the same arch, any more than the similar combination of the rays of the
pectoral and ventral fins in the sucker of the Cyclopterus proves those rays
to be parts of the same arch. And I may repeat that, admitting the humerus
to be, as Bakker surmised, confluent in all fishes with the bone sg, fig. 5;
and since in the plagiostomes, sturgeons and lophioids, the second segment of
the rudimental fore-limb is not liberated from the supporting arch ; so, like-
wise, the proximal member of the opercular limb may remain, or become in
some instances confluent with its sustaining arch, without that exceptional
state invalidating the determination deduced from its more constant and re-
gular character as the proximal element of the free appendage to that arch.
The third inverted arch of the skull is suspended in fishes by a slender
styliform bone, the ‘stylohyal’ (fig. 5, 3s), from the lower end of the epi-
tympanic (2s a) close to the joint of the styliform ‘mesotympanic’ (2s b) ;
and it is connected, through the medium of the posterior division and
joint of the epitympanic, with the mastoid (s). Now, either that division
of the epitympanic may be viewed, by virtue of its proper articular condyle
_ above, and its connection with a distinct inverted arch below, as the proximal
piece of that arch, coalesced with the proximal piece of the next arch in
advance, which articulates with the post-frontal; or, it may be viewed as an
excessive development of the proximal piece of the tympano-mandibular arch,
which, extending backwards, has displaced the hyoid from the mastoid, just _ f
as the squamosal, by a similar backward development, in mammals, displaces
the mandibular arch from the tympanic. J
According to the first view, the bone no. 3s would be a dismemberment
of the proximal element of the hyoid arch ; according to the second view, it
would be the entire element reduced and displaced: in both cases it would
be homologous with the proximal slender piece of the hyoid arch in all
* Recherches sur les Poissons Fossiles, v. pt. ii. p. 68.
ON THE VERTEBRATE SKELETON. 237
yertebrata, and to which piece the term ‘styloid’ or ‘stiliform’ has been
given from the fish up to man (see TasreI.). The homology, indeed, is so
obvious, that M. Agassiz, in accepting the conclusion of M. Vogt, that the
bone (fig. 5, 34), peculiar to osseous fishes, which so rarely articulates di-
rectly with the mastoid or with the hyoid arch, and so constantly sustains
the distal segment of the operculum, was the homologue of the ‘processus
stiliformis ossis temporis,’ nevertheless retains the name ‘styloide’ for the
part no. 3s in question.
The true homology of no. 34, already explained, removes the anomaly of
viewing that peculiarly piscine bone as the homologue of a constant element
of the hyoid arch in all the vertebrate classes, and the greater anomaly of
the introduction of a new element—a styloid piece of the os hyoides—in
addition to the ‘styloid process of the temporal’ in fishes. The ‘stylohyal’
articulates below to the apex of a triangular piece (39), which is pretty con-
stant in fishes, and to which I give the name of ‘ epihyal,’ as being the upper
of the two principal parts of the cornu or arch: the third longer and stronger
piece is the ‘ceratohyal’ (¢. 40).
The keystone or body of the inverted hyoid arch is formed by two small
subcubical bones on each side, the ‘basihyals’ (76. 41). These complete the
bony arch in some fishes: in most others there is a median styliform ossicle,
extended forwards from the basi-hyal symphysis into the substance of the
tongue, called the ‘ glossohyal’ (#b. 42), or ‘os linguale’; and another symme-
trical, but usually triangular, flattened bone, which expands vertically as it
extends backwards, in the middle line, from the basihyals; this is the ‘ urohyal’
(ib. 43). It is connected with the symphysis of the coracoids, which closes below
the fourth of the cranial inverted arches, and it thus forms the isthmus which
separates below the two branchial apertures. In the conger the hyoidean
arch is simplified by the persistent ligamentous state of the stylohyal, and
by the confluence of the basi-hyals with the ceratohyals: a long glossohyal
is articulated to the upper part of the ligamentous symphysis, and a long
compressed urohyal to the under part of the same junction of the hyoid arch.
The glossohyal is wanting in the Murenophis.
The appendages of the hyoidean arch in fishes retain the form of simple,
elongated, slender, slightly curved rays, articulated to depressions in the outer
and posterior margins of the epi- and cerato-hyals: they are called “ bran-
chiostegals,” or gill-cover rays, because they support the membrane which
‘closes externally the branchial chamber. The number of these rays varies,
and their presence is not constant even in the bony fishes: there are but
three broad and flat rays in the carp; whilst the clupeoid Hlops has more
than thirty rays in each gill-cover: the most common number is seven, as
in the cod (fig. 30, 41). They are of enormous length in the angler, and
Serve to support the membrane which is developed to form a great receptacle
on each side of the head of that singular fish.
Branchial Arches.—In the class of fishes, certain bony arches, which ap-
pertain to the system of the visceral skeleton, succeed the hyoidean arch,
with the keystone of which they are more or less closely connected. Six of
these arches are primarily developed, and five usually retained ; the first four
of these support the gills, the fifth is beset with teeth and guards the opening
of the gullet: this latter is termed the ‘ pharyngeal arch,’ the rest the ‘ bran-
chial arches.’
The lower extremities of these arches adhere to the sides of a median chain
of ossicles, which is continued from the posterior angle of the basi-hyal, or
from above the uro-hyal, when this is ossified: the bones which form those
extremities are the ‘hypobranchials’; and they support longer bent pieces,
238 REPORT— 1846.
called ‘cerato-branchials.’ It is with these elements of the branchial arches
in fishes and perennibranchiate batrachians that we are chiefly concerned
in tracing the homology of the hyoid apparatus in the air-breathing verte-
brates. With regard to the branchial and pharyngeal arches, which attain
their full development only in the class of fishes, I regard them as appertain-
ing to the system of the splanchno-skeleton, or to that category of bones to
which the heart-bone of the ruminants and the hard jaw-like pieces support-
ing the teeth of the stomach of the lobster belong. The branchial arches
are sometimes cartilaginous when the true endo-skeleton is ossified: they are
never ossified in the perennibranchiate batrachians, and are the first to dis-
appear in the larve of the caducibranchiate species; and both their place
and mode of attachment to the skull demonstrate that they have no essential
homological relation to its endo skeletal segments.
The hyoid arch or apparatus retains most resemblance to that of fishes in
the Siren lacertina ; the basihyal is simplified into a single osseous spatu-
late piece, with the bowl of the spoon anterior, and supporting a broad and
flat semicircular glossohyal. A strong and thick ceratohyal is articulated
by means of a small cartilage to the side of the expanded part of the basi-
hyal, and a cartilaginous epihyal arches backwards from its upper end. A
cartilaginous urohyal extends from the hind end of the basihyal, and ex-
pands into a radiated disc, which supports the membranous trachea and the
simple glottis. One pair of bony ‘hypobranchials’ is articulated to the
basi-uro-hyal joint and a second pair to the sides of the urohyal: and to the
upper and outer ends of these are attached four pairs of cartilaginous ‘ cerato-
branchials. The fimbriated branchiz are attached to the three anterior
ceratobranchials.
In the proteus the urohyal is absent, and it is not again developed in any
batrachian. The long subcylindrical basihyal supports a subcircular carti-
laginous discoid glossohyal, and at the angle of union the bony ceratohyals
are sent off. A pair of hypobranchials diverge from the end of the basihyal ;
to which a second small pair of basibranchials are loosely connected by an
aponeurosis. These support three ceratobranchials on each side, which are
bony.
Ru the newts there is neither a glossohyal nor urohyal, or but a rudiment
of the latter, to each side of which are articulated two hypobranchials, whose
distal ends converge on each side to support a single cartilaginous gill-less
rudiment of a ceratobranchial. The special homologies of all those parts of
the complex hyoid, rendered more complex by the retention of part of the
branchial skeleton, are clearly demonstrated by pursuing the metamorphoses
of the hyo-branchial skeleton in the larve of the anourous batrachians. In
the full-gilled tadpole a short and simple basihyal supports laterally two
thick and strong ceratehyals, and posteriorly two short and broad hypo-
branchials, to which four ceratobranchials are attached: all the parts are
cartilaginous. The type of this stage is retained in the siren, with the histo-
logical progress to bone in the hyoid and hypo-branchial pieces. The second
well-marked stage in the tadpole shows an extension of the external and
posterior angles of the hypobranchials, with progressive absorption of the
cartilaginous ceratobranchials. The growth and divergence of the posterior
angles of the hypobranchials refer to the development of the larynx, now
commencing, which part they are destined to support. That period may be
described as the third stage at which the ceratobranchials have disappeared,
and the posterior angles of the hypobranchials increase in length and assume
the character of posterior cornua of the os hyoides. The last and adult
stage shows the ossification of the elongated angles of the hypobranchials,
ON THE VERTEBRATE SKELETON. 239
the coalescence of their cartilaginous bases with the basihyal, the expansion
of the basihyal and extension of its anterior and external angles ; in front of
which the now long and slender ceratohyals usually coalesce with the basi-
hyal; their opposite ends having shifted their attachments and retrograded,
like other hemal arches of the skull, in the course of the metamorphosis.
In the case of the hyoid arch of the frog, the change of place is from the
tympanic pedicle backwards to the persistent cartilaginous petrosal: and
this is a very suggestive and significant change. All the parts of the hyoid
‘remain cartilaginous except the appended and persistent detachments from
the visceral system of the branchial arches: these long ‘hypobranchials’
(‘cornes thyroidiennes’ of Cuvier and Dugés) diverge and include the larynx
in their fork. The relative position, connexions and office in subserviency
to the larynx, to which the retained parts of the splanchno-branchial arches
are introduced in the lowest of the air-breathing vertebrates, are preserved in
‘all the higher classes. The ‘hypobranchials’ are as constant in their ex-
istence, therefore, as the upper larynx itself, and attach themselves more
especially to the thyroid element of that larynx. We recognise them by this
relation in birds and man (as, figs. 23 and 25), where they always much ex-
ceed the parts of the true hyoid arch (cerato- and epi-hyals) in length; and
in birds, where these elements (ao, fig. 23) are sometimes obsolete and always
rudimental, the hypobranchials have been mistaken by both Cuvier and
Geoffroy * for the ceratohyals or anterior cornua.
For the modifications and special homologies of the complex hyoid appa-
ratus in lizards, I refer to my ‘ Lectures on the Vertebrata.’ The crocodiles
offer a well-marked ordinal difference from those inferior sauria in this as
in most other parts of their structure. The basihyal and thyrohyals have
coalesced to form a broad cartilaginous plate, the anterior border rising like a
valve to close the fauces, and the posterior angles extending beyond and sus-
taining the thyroid and other parts of the larynx. A long bony ‘ ceratohyal’
(fig. 22, 40), and a commonly cartilaginous ‘epihyal’ (7b. 39), are suspended
by a ligamentous ‘stylohyal’ to the paroccipital process ; the whole arch
having, like the mandibular one, retrograded from the connection it presents
in fishes.
In birds as in chelonians, the ceratohyals are much reduced, and the chief
‘cornua’ of the hyoid are represented by the hypo- and epi-branchials (thy-
rohyals), which here attain their maximum of length and tenuity. The basi-
hyal (fig. 23, 41), as in Chelys, is long and slender, but is always a simple
piece ; and, as in lizards, is usually most expanded posteriorly, from which
expansion the thyrohyals (48) are sent off. Conforming with the long and
slender tongue in most birds, the basihyal extends forwards, and is articu-
lated with the rudimental ceratohyals (40), when these exist, at some distance
from the thyrohyals. A commonly long and slender, sometimes spatulate
glossohyal (42), is articulated to the fore-part of the basihyal; and a con-
stantly long, slender and pointed urohyal (43) is articulated with the posterior
end of the basihyal, and extends backwards beneath the trachea. The thyro-
hyals (46) diverge and include the larynx in their fork ; and support at their
extremities a bony or gristly (cerato-branchial) style (a7). This is never
attached by ligament to the base of the skull, but is suspended freely, as in
the chelonia, by the glossohyoid and omohyoid muscles ; it, however, curves
over the back and upper part of the cranium in the woodpeckers, and the
extremities of both cerato-branchials are inserted, by way of rare exception
_ in that bird, into the right nostril.
- * Dugés appears to have first pointed out this error, but without, however, perceiving the
true homology of his ‘ cornes thyroidiens’ with the hypobranchials of fishes.
240 REPORT—1846.
In mammals the normal completion of the hyoidean arch, as it first ap-
pears in fishes, is again resumed, and that not by a slender cartilage, as in
the frog, but by a chain of bones, in which we again recognise the cerato-
(fig. 24, 40), epi- (39) and stylo- (3s) hyals suspending the basihyal (41) and
the tongue to the base of the skull, often to the petrosal, sometimes to the
tympanic, or to the mastoid, or to the exoccipital. The ungulates and the
true carnivora best display this type.
In man (fig. 25) the ceratohyals are reduced, as in birds, to mere tuber-
cles of bone (40), and the extent of the arch between them and the stylo-
hyals, which become anchylosed to the temporal bones, retains its primitive
ligamentous condition. Occasionally, however, ossification extends along
the stylohyoid ligament, and marks out, as in the specimen figured by
Geoffroy St. Hilaire (Philosophie Anatomique, pl. 4, fig. 87), the more nor-
mal proportions of the ceratohyal, and also the epihyal. Other examples of
this ‘ monstrosity’ are recorded in works on anthropotomy. The thyro-
hyal (4s)—the last remnant of the branchial arches—maintains more con-
stancy in its existence and proportions ; but manifests its true character of
free suspension below the skull, and an articulation by short ligaments to the
angles or horns of the thyroid cartilage.
The remarks already made on the special homologies of the parts of the
scapular arch and its appendages, preclude the necessity of further extending
the present part of this Report.
Part II].—GeneraL Homotoey.
On taking a retrospect of the results of the researches of anatomists into
the special homologies of the cranial bones, the student of the science, how
little soever practised in such inquiries, cannot but be struck with the amount
of concordance in those results. It must surely appear a most remarkable
circumstance to one acquainted only with the osteology of the human frame,
that so many bones should be, by the common consent of comparative ana-
tomists, determinable in the skull of every animal down to the lowest osseous
fish. This fact alone, so significant of the unity of plan pervading the ver-
tebrate structure, has afforded me, at least, a large ground of hope and
much encouragement to perseverance in the reconsideration of those points
on which a difference of opinion has prevailed ; and in the re-investigation of
what is truly constant and essential in characters determinative of special
homologies.
In this, as in every other inquiry into nature, the first labours are neces-
sarily more or less tentative and approximative: but if errors have to be
eliminated in the course of successive applications of fresh minds to the
task, truths become confirmed and established. And I regard the body of
such truths (see Table I.) to be now so great, in respect of the determination
of the homologous bones in the heads of all vertebrate animals, as to impe-
ratively press upon the thinking mind the consideration of the more general
condition upon which the existence of relations of special homology depends.
Upon this point the anatomical world is at present divided, lacking the
required demonstration. The majority of existing authors on comparative
anatomy have tacitly abandoned*, or with Cuvier and M. Agassiz, have
* Waaner, ‘ Lehrbuch der Zootomie,’ 8vo, 1843, 1844. Srezonp and Srannivs, ‘ Lehr-
buch der Vergleichende Anatomie,’ 8vo, 1845, 1846. Mrtne-Epwarps, ‘ Elemens de
Zoologie,’ 8vo; 1834. Prof. Rymer Jones, ‘ Outline of the Animal Kingdom and Manual
of Comparative Anatomy,’ 8vo. 1841. The sentiments which this pleasing and instructive
writer expresses, are probably akin to those which haye influenced the above-cited authors
ON THE VERTEBRATE SKELETON. 241
directly opposed the idea of ‘ special homology’ being included in a higher
law of uniformity of type.
Yet the attempt to explain, by the Cuvierian principles, the facts of special
homology on the hypothesis of the subserviency of the parts so determined
to similar ends in different animals,—to say that the same or answerable bones
occur in them because they have to perform similar functions—involve many
difficulties, and are opposed by numerous phenomena. We may admit that
the multiplied points of ossification in the skull of the human feetus facilitate,
and were designed to facilitate, childbirth; yet something more than such a
final purpose lies beneath the fact, that most of those osseous centres repre-
sent permanently distinct bones in the cold-blooded vertebrates. The cra-
nium of the bird, which is composed in the adult of a single bone, is ossified
from the same number of points as in the human embryo, without the pos-
sibility of a similar purpose being subserved thereby, in the extrication of
the chick from the fractured egg-shell. The composite structure is repeated
in the minute and prematurely-born embryo of the marsupial quadrupeds.
Moreover, in the bird and marsupial, as in the human subject, the different
points of ossification have the same relative position and plan of arrange-
ment as in the skull of the young crocodile, in which, as in most other rep-
tiles and in most fishes, the bones so commencing maintain throughout life
their primitive distinctness. These and a hundred such facts force upon the
equal and knowing anatomist the inadequacy of the teleological hypothesis
to account for the acknowledged concordances expressed in this report by
the term ‘special homology.’ If, therefore, the attempt to explain them as
the results of a similarity of the functions to be performed by such homo-
logous parts entirely fails to satisfy the conditions of the problem; and if,
nevertheless, we are, with Cuvier, to reject the idea of their being manifes-
tations of some higher law of organic conformity on which it has pleased
the divine Architect to build up certain of his diversified living works,
there then remains only the alternative that special homologies are matters
of chance.
This conclusion, I apprehend, will be entertained by no reasonable mind;
and reverting, therefore, to the more probable hypothesis of the dependence
of the special resemblances upon a more general law of conformity, we
have next to inquire, what is the vertebrate archetype? The gifted and
deep-thinking anatomist, OKEN, obtained the first clew to this discovery by
?
4
Q
ts
on this subject. ‘It is not by any means our intention to engage our readers in discussing
all the conflicting and, sometimes, visionary opinions entertained by different authors re-
lative to the exact homology of the individual bones forming this part of the skeleton; and
we shall, therefore, content ourselves by placing before them, divested as far as possible of
: superfluous argumentation, Cuvier’s masterly analysis of the labours of the principal inquiries
__ concerning this intricate part of anatomy.”—p. 494. A later English author, who has em-
_ bodied a most valuable amount of careful and exact osteological observation in the article
z “ Zoology” of the ‘ Encyclopzdia Metropolitana’ (4to, 1845), seems scarcely to regard even
7 & the determination of special homologies as a necessary object of anatomical research. Thus,
in discussing the differences of opinion respecting the coracoid (fig. 5, 48). he says, “ Bakker’s
| view, however, if it be absolutely necessary to hunt up analogies, seems more correct.”—
, . 302.
a This reserve is, however, perhaps less obstructive to the philosophical progress of anatomy
___ and to the requisite resumption of original inquiry to that end, than the mere reproduction
ie of the transcendental views of others without criticism or attempt to explain or refute the
; objections to such views which have been promulgated by so great authorities as Cuvier and
Agassiz. Thus Bojanus’s 4-vertebral theory of the cranial part of the skull is adopted by
M. De Blainville (Ostéographie, 4to); whilst Dr. Grant (Outlines of Comparative Anatumy,
8yo, 1835, p. 63) deems the composition of the skull, in fishes, to correspond nearly with
Geoffroy’s theory of this part of the skeleton being composed of seven vertebrz, each con-
sisting of a body with four elements above and four elements below. Rent,
242 ; REPORT—1846.
‘the idea of the arrangement of the cranial bones of the skull into segments,
like the vertebree of the trunk. He informs us that walking one day in the
Hartz forest, he stumbled upon the blanched skull of a deer, picked up the
partially dislocated bones, and contemplating them for a while, the truth
flashed across his mind, and he exclaimed “ It is a vertebral column !*” Oken
afterwards tested and matured this happy inspiration by examining the skulls
of a cetacean, a chelonian, and a cod-fish in Dr. Albers’s museum at Bremen ;
and on his return to Jena in 1807, he published his beautiful generalization in
a now very scarce Introductory Lecture, or ‘ Programm beim Antritt der Pro-
fessur,” entitled ‘ On the signification of the bones of the skull’. He illus-
trates his views by reference to the skull of a ruminant. “Take,” he says,
“a young sheep’s skull, separate from it the bones of the orbit, also those
cranial bones which take no share in the formation of the ‘basis cranii,’ e.g.
the frontal, parietal, ethmoid and temporal, and there will remain an osseous
column which any anatomist, at first glance, would recognise as three bodies
of a kind of vertebra with transverse processes and foramina. Replace the
cranial bones with the exception of the temporals, for, without these, the
cavity is still closed, and you have a cranial vertebral column, which differs
from the true one (‘von der wahren’) only by its more expanded neural
canal (Ruckenmarkshohle). As the brain is a more voluminously developed
spinal chord, so is the brain-case a more voluminous spinal column. As
the cranium includes, then, three vertebral bodies, so must it have as many
vertebral arches. These are next to be sought out and determined. One
sees the sphenoid divided into two vertebre ; through the foremost pass the
optic nerves, through the hindmost the maxillary nerves ( par trigeminum).
I call one the ‘ eye-vertebra’ (Augwirbel), the other the ‘ jaw-vertebra’
(Kieferwirbel). Upon this latter abuts the basilar process of the occipital
bone and the petrous bones: both belong to one whole. As the optic nerve
perforates the ‘ eye-vertebra,’ and the trigeminus the ‘jaw-vertebra,’ so the
acoustic nerve takes possession of the hindmost vertebra. I call it, there-
fore, ‘ear-vertebra’ (Ohrwirbel): and I regard this as the first cranial ver-
tebra; the jaw-vertebra as the second, and the eye-vertebra.as the third.”—
ib. p. 6.
After entering upon the difficulties which beset him in determining whether
the petrosal belonged to the first (Ohrwirbel) or the second (Kieferwirbel),
and enunciating his views on the essential relations of each cranial vertebra
with a single special sense (excluding, however, smell and taste, as being
inferior in dignity to the others), Oken proceeds, in his characteristic bold
metaphorical language :—“ Bones are the earthy hardened nervous system :
Nerves are the spiritual soft osseous system—Continens et contentum.”
«« Between the sphenoid and occipital, between the sphenoid and petrosal,
between the parietal (the temporal being removed) and the occipital, there
runs a line which defines the anterior boundary of the first vertebra. In the
line between the two sphenoids, or that which in man extends anterior to
- * “Tm August 1806 machte ich eine Reise iiber den Hartz,’’—“ ich rutschte an der Siid-
seite durch den Wald herunter—und siehe da; es lag der schénste gebleichte Schadel einer
Hirschkuh vor meinen Fiissen. Aufgehoben, umgekehrt, angesehen, und es war geschehen.
Es ist eine Wirbelséule! fuhr es mir wie ein Blitz durch Mark und Bein—und seit dieser
Zeit ist der Schadel eine Wirbelsaule.”—TIsis, 1818, p. 511.
+ Uber die Bedeutung der Schadelknochen, 4to, 1807. I am indebted to my friend
Mr. Tulk, the able translator of ‘Wagner’s Comparative Anatomy,’ for the opportunity of
perusing this most suggestive and original essay, which does not exist in either the Library
of the British Museum, that of the College of Surgeons, or that of the Medico-Chirurgical
Society. Mr. Tulk is at present engaged in the arduous task of translating the “ Lehrbuch
der Natur-philosophie ” of Oken for the ‘ Ray Society.’ ;
ON THE VERTEBRATE SKELETON. 243
the pterygoid processes laterally and upwards through the fissura orbitalis
superior, anterior to the great ala, and finally between the frontal and the
parietal bones, we trace another line, which divides the second from the
third vertebra ” (7b. p. 7).
* Now,” says Oken, “take the ear-vertebra from a foetus of any mammal
or of man, place near it an immature dorsal vertebra, or the third cervical
of a crocodile, and compare the pieces of which they consist, their form, their
contents, and the outlets for the nerves.
“ According to Albinus and all anthropotomists, each vertebra of the
foetus consists of three distinct parts—the body and the two neurapophyses
(bogentheile). You have the same in the occipital bone, but more clearly
and more distinctly: the ‘pars basilaris’ is separated as the body of the ver-
tebra from the ‘partes condyloidez,’ which form the lateral parts: these
are still more distinct from the ‘pars occipitalis’ which forms the spinous
process: even this part is often bifid, like the spinous processes in spina
bifida” +
ey Since then the foramen magnum is the hinder or lower opening of a
vertebral canal, the condyles true oblique vertebral processes, the foramen
lacerum an intervertebral foramen, and the crista occipitalis a spinous pro-
cess, proved to be such by both its position and the muscles inserted into it,—
since lastly the whole occipital bone in relation to its form as well as its
function—inclosing the cerebellum as a production of the spinal chord,—is
a true and in every sense characteristic vertebra, it is unnecessary to dwell
more diffusely on parts, the bare mention of which suffices to make their
nature recognizable.”—2b. p. 7.
This will serve as an example of the close observation of facts, the philo-
sophical appreciation of their relations and analogies, and, in a word, of the
spirit in which Oken determines the vertebral relations of the cranial bones
of the skull: and I refer to Taste II. for his conclusions as to the parts of
the second and third cranial vertebre.
Reverting to the petrosal, Oken thus beautifully and clearly enunciates
its essential nature and homology :—* You will say I have forgotten the
‘pars petrosa.’ No! It seems not to belong to a vertebra, as such; but to
be a ‘sense-organ’ (Sinnorgan), in which the vertebral- or ear-nerve loses
‘itself; and, therefore, is as distinct an organ from a vertebral element as is
any other viscus (Eingeweide), or as is the eyeball itself. The (cause of)
delusion (as to the homology of the petrosal) lies in this, viz. that it must be
_ossified agreeably with its nature (wesen),just as the eye must be crystallized.”
Although Oken does not in this essay formally admit a fourth vertebra
anterior to the ‘ eye-vertebra,’ he recognises the vertebral structure as being
earried out rudimentally or evanescently, by the vomer, as the prolongation
of the cranio-vertebral bodies, by the lacrymal bones, as their neurapo-
physes, and by the nasal bones, as the spinous process. His ideas of a
vertebra have evidently at this period not extended beyond the ordinary
anthropotomical one of centrum and neural arch with its transverse, oblique,
and spinous processes. When he indicates (beautifully and truly) the general
homology of the palatine bones, as pleurapophyses, under the name of an-
ehylosed or immoveable ribs of the head, it has reference to the transcen-
dental idea of the repetition in the head of all the parts of the body. Thus
the squamosal in mammals and the tympanic in birds represent the ‘scapula’
of the head, and at the same time, also, the ilium. The homologue of the
squamosal (fig. 21, 27) in the bird is the ‘humerus capitis’: the malar (26)
and the maxillary (21) are the ‘ oberarm’ (radius and ulna capitis) : the pre-
maxillary (22) is the ‘manus capitis.’ The segments of the hind limb are
244 REPORT—1846€,
represented by divisions of the compound lower jaw in the crocodile and
embryo bird (see Tasie, No. III.). The pterygoids (24), the essential di-
stinction of which from the sphenoid Oken clearly recognises, are his ‘ clavi-
culz capitis.’ Oken hints at, without accepting, the (serial) homology of
the hyoid arch with the pelvis; but he regards the stylohyal (ss) as. the
‘sacrum capitis’ (7b. p. 16).
The year after the publication of Oken’s famous ‘ Introductory Lecture,’
Prof. Duméril, apparently unacquainted with its existence, communicated
to the French Institute a memoir entitled ‘ Considérations générales sur
Yanalogie qui existe entre tous les os et les muscles du trone dans les ani-
maux, the second paragraph of which is headed “ De la téte considérée
comme une vertébre, de ses muscles et de ses mouvements.” In this para-
graph, repeating the homological correspondences, demonstrated by Oken,
between the basioccipital as a vertebral centrum, the condyles as ‘ oblique
processes,’ and the occipital protuberance as a spinous process, he adds, that
the mastoid processes are entirely conformable to transverse processes. And
M. Duméril has, I believe, here the merit of having first enunciated the
general homology of the mastoids, although he does not aim at showing to
which vertebral segment of the skull they properly belong. Nor, indeed,
-with the exception of an observation that ‘ very often the body of the sphe-
noid, like the ‘apophyse basilaire’ of the occiput, resembles the body of a
vertebra,” does he push the transcendental comparisons further. Geoffroy
St. Hilaire tells us*, that even the moderate and very obvious illustrations
of the general homologies of the cranial bones, which M. Duméril deduced
from the anatomy of the occiput, excited an unfavourable sensation in the
bosom of the ‘ Académie; and that the phrase ‘ vertébre pensante,’ which a
facetious member proposed as an equivalent for the word ‘ skull,’ and which
circulated, not without some risibility, along the benches of the learned
during the reading of the memoir, reaching the ears of the ingenious author,
the dread of ridicule checked his further progress in the path to the higher
generalizations of his science, and even induced him to modify considerably
many of the (doubtless happy) original expressions and statements in the
printed report, so as to adapt it more to the conventional anatomical ideas
of his colleagues.
As the truth of Oken’s generalization began to be appreciated, it was remem-
bered, as is usually the case, that something like it had occurred before to
others. Autenrieth and Jean-Pierre Frank had alluded, in a general way, to
the analogy between the skull and the vertebral column : Ulrich, reproducing,
formally, Oken’s more matured opinions on the cranial vertebre, says,
“ Kielmeyerum preeceptorem pie venerandum quamvis vertebram tanquam
caput integrum considerari posse in scholis anatomicis docentem audivi.’
And the essential idea was doubtless present to Kielmeyer’s mind, though
he reversed M. Duméril’s proposition, and, instead of calling the skull a ver-
tebra, he said each vertebra might be called a skull. But these anticipations
detract nothing from the merit of the first definite proposition of the theory.
It would rather be an argument against its truth, if some approximative idea
had not suggested itself to other observers of nature, who only lost the merit
of developing it, from not appreciating its full importance. He, however,
becomes the true discoverer who establishes the truth: and the sign of the
proof is the general acceptance. Whoever, therefore, resumes the investiga-
tion of a neglected or repudiated doctrine, elicits its true demonstrations,
and discovers and explains the nature of the errors that have led to its tacit
* Annales des Sciences Naturelles, t. iii. 1824, p. 177.
ON THE VERTEBRATE SKELETON. 245
or declared rejection, may calmly and confidently await the acknowledgments
of his rights in the discovery.
It has been unfortunate for Oken, that, with one exception—the gifted
Bojanus—his successors in the development of the vertebral theory of the
skull have hitherto exaggerated rather than retrenched the errors of their
guide. Spix* lends an almost servile aid to Oken in endowing the artist’s
symbol of the cherub with all that it seems most to want, a thorax, abdomen
and pelvis, arms, legs, hands and feet. He adopts Oken’s original number
and composition of the cranial vertebrae, and gives them new names, which
being dissociated from Oken’s peculiar idea of the essential subserviency of
the cranial segments to certain organs of sense, are likely to be retained.
: Bojanust+ seems first to have determined the true elements of the neural
arch of the nasal vertebra; and was as happy in perceiving the pleurapo-
_ physial relations of the tympanic pedicle, as Oken had been in reference to
__. the palatine bone. He was less accurate in his idea of the vertebra to which
it belonged. The analysis of Bojanus’ craniovertebral system given in Table
ILI. precludes the necessity of dwelling upon it in the brief historical sketch
here attempted.
3 The modifications of his original idea which Oken has introduced into his
___ edition of the ‘ Natur-philosophie’ of 1843, bring it into close accordance with
that of Bojanus, excepting that Oken conceives the cranial neurapophyses to
answer also to ribs :—“ An den Seiten eines jeden Korpers liegen Filiigel-
fortsitze, welche den Querfortsaétzen der Halswirbel oder den Rippen ent-
_ sprechen: ‘die Gelenkképfe des Hinterhauptsbeins’ (exoccipitals), ‘die
grossen’ (ali-) ‘und kleinen Fliigel’ (orbito-sphenoids’), ‘und die beiden
Seiten des Siebbeins ’ (prefrontals),” p. 304. With regard to the facial bones
of the skull, Oken still includes the explanation of their general homology in
his original idea, that “ the head is (a repetition of ) the whole trunk with all
its systems. .... The encephalon is the myelon (riickenmark); the cranium,
the vertebral column ; the mouth is intestine and abdomen ; the nose, lungs
and thorax; and the jaws, limbs (glieder).”— Op. cit. p. 300. An idea which
__ vitiated his original essay, and which has had the effect of obscuring a great
& truth in nature in the smoke of a sacrifice to a false system.
F This seems the place to notice a virtual testimony to the general accuracy
of the Okenian cranial system, published in 1816 by the present eminent
3 -osteologist who holds the chair of Comparative Anatomy in the ‘ Jardin des
Plantes.’ In a note to his ‘ Prodrome d’une Nouvelle Distribution Systéma-
5 tique du Régne Animal,’ published in the ‘ Bulletin des Sciences par la So-
eiété Philomathique,’ 1816, p. 105, M. de Blainville says, “ J’essayerai de
montrer (1!) que la téte dans les animaux vertébrés est composée, 1° d’une suite
d articulations ou de vertébres soudées, chacune développée proportionnelle-
‘ment au systéme nerveux particulier qu’elle renferme, comme dans le reste
_ de la colonne vertébrale ; 2°, d’autant d’appendices paires qu'il y a de ces
fausses vertébres, et pouvant avoir des usages différens” (p. 108). M. de
Blainville does not (like Bojanus) expressly mention the general homology
of any of these appendages to the ribs, or parial appendages of the true ver-
tebree ; but he leaves it to be so understood by his subsequent enumeration
and classification of the ‘ appendices paires ou symmétriques,’ which he de-
scribes as being always in relation with a vertebra or median piece. He
says, e.g. “Ils peuvent étre divisés en simples ou en composés, ou peut-étre
daprés leurs usages. Les appendices simples sont les cétes. Les appendices
' eomposés sont les membres, les machoires, les appareils des organes des
* Cephalogenesis, fol. 1815.
T Isis, 1818, and ‘ Parergon’ in the ‘ Anatome Testudinis Europe,’ fol. 1821.
246 REPORT—1846.
sens, le styloide, les branches de l’hyoide, qui sont ordinairement formés d’un
plus ou moins grand nombre de piéces placées bout 4 bout. Quelquefois
ces appendices sont libres 4 leur extrémité, d’autres fois ils se réunissent
dans la ligne médiane inférieure en entr’elles, ou au moyen d’une piéce mé-
diane, qu’on peut comparée, jusqu’d un certain point, au corps des ver-
tébres; d’ou il résulte ce quon nomme ‘sternum’ dans les mammiféres,
appareil branchial des poissons, hyoide, sternum des oiseaux,” ete. (7b. 1817,
p- 110). Reserving the consideration of some of these propositions for a
subsequent part of the present Report, I shall only notice, en passant, the
complete concordance between these views of the general homology of the
locomotive members with those which Oken expresses with his usual apho-
ristic brevity :—“Freye Bewegungsorgane konnen nichts anderes als frey
gewordene Rippen seyn.”
Cuvier includes amongst the general characters of the class Mammalia the
arrangement of their cranial bones into three annular segments, corresponding
essentially with those of which Oken had demonstrated the vertebral relations.
‘“ Leur crane se subdivise comme en trois ceintures formées; l’antérieure,
par les deux frontaux et l’ethmoide ; l'intermédiaire, par les pariétaux et le
sphénoide ; la postérieure, par l’occipital: entre l’occipital les pariétaux et
le sphénoide, sont intercalés les temporaux, dont une partie appartient propre-
ment a la face*.”
What M. de Blainville (1816) pledges his efforts to demonstrate, Oken
(Isis, 1817) was exulting in the reception of, ‘not only in Germany but all
Europe. “ Seit Erscheinung dieser Schrift und nun 10 Jahre verflossen.—
Man spricht nun von Kopfwirbeln, Kopfarmen und Fissen, von Bedeutung
der einzelnen Skeletknochen wie von einer uralten Sache; die schon in der
Bibel und den Propheten gestanden,” p. 1204. The chief differences, as
compared with Oken’s definition, are, that Cuvier, finding the frontal arch
to rest upon both ethmoid and presphenoid, assigns to the former bone the
completion of the anterior cranial cincture below; and completes, in like
manner, the parietal cincture by the sphenoid in its anthropotomical sense,
making no distinction between the anterior and the posterior divisions of the
bone. Cuvier does not apply this principle of arrangement of the cranial
bones to the skull of the lower classes of vertebrata (in which, nevertheless,
it is more clearly manifested than in mammals): in generalising on the con-
stitution of the vertebrate skull, he classifies the bones, after the anthropoto-
mists, into ‘those of the cranium which encompass the brain, and those of
the face, which consist of the two jaws and the receptacles of the organs of
sense. + With regard to the skull of fishes, in which Bojanus had found so
clear an illustration and confirmation of the Okenian views, Cuvier merely
says, it is almost always divisible into the same number of bones as that
of other ovipara. The frontal is composed of six pieces; the parietal of
three ; the occipital of five ; five of the pieces of the sphenoid and two of each
of the temporals remain in the composition of the cranium {.
In his great works the ‘ Histoire des Poissons’ and the ‘ Lecons d’Ana-
tomie Comparée,’ posthumous edition, he expresses more decidedly his ob-
jections to the views of the segmental or vertebral structure of the skull.
Gothe, in a small fasciculus of ‘ Essays of Comparative Anatomy,’ which
he published in the year 1820, entitles the 8th, “ Can the bones of the skull
* Régne Animal, 8vo, 1817, t. i. p. 62.
+ “La téte est formée du crane, qui renferme le cerveau, et de la face, qui se compose
des deux machoires et des receptacles des organes des sens.”—Reégne Animal, i. ed. 1817,
p. 62; ed. 1829, p. 52.
t 1c. ii. (1817), p. 107; (1829), p. 125.
ON THE VERTEBRATE SKELETON. 247
be deduced from those of the vertebral column, and thence receive an ex-
planation of their forms and functions?” He states that the idea of the
three facial vertebre occurred to him in the year 1790, prior to which time
he says “die drei hintersten erkennt ich bald.” The idea is developed in his
essay as follows :—‘ The skull of mammalia is composed ef six vertebra;
three for the hinder division inclosing the cerebral treasure ; three composing
the fore part which opens in presence of the exterior world, which it seizes
and introduces.
“ The first three vertebrae are admitted (he alludes to Oken and Spix) :
they are,—
“ The occipital.
“ The posterior sphenoid.
“ The anterior sphenoid.
“ The three others are not vet admitted; they are,—
“ The palatine bone.
“The upper maxillary.
« The intermaxillary.
_ Tf some of the eminent men who ardently cultivate this subject should
feel interested by this simple enunciation of the problem, and would illus-
trate it by some figures indicating by signs and ciphers the mutual relations
and secret affinities of the bones, its publication would strongly draw the
thinking mind in that direction, and we may, perhaps, one day, ourselves
give some notes on the mode of considering and treating these questions.”
Professor Carus of Dresden has best responded to this appeal of his ims
mortal countryman: but it must be admitted that the detailed and complex
exposition of the theory of the six vertebra and intervertebre, of which the
general results are given in Table IIL. have yielded to anatomical science a
result which is hardly equivalent to the zeal and pains manifested in the at-
tempt, or to the artistic merit of the illustrations, published by the accom-
plished author of the ‘Urtheilen des Knochen und Schalengeriistes’ (fol.
1828).
Coe St. Hilaire deems the skeleton of the head to be composed of
seven vertebre ; and he has the merit of having more steadily sought the
homologies of the inferior arches of the cranial vertebre than his predeces-
sors, who seem not to have sufficiently appreciated the essential character of
these portions of the primary segments of the vertebrate endo-skeleton.
Nevertheless it must be admitted that Cuvier has made good the grounds of
his rejection of Geoffroy’s theory, as one based less on observation than on
purely @ priori views, according to which the bones of the skull, real or
imaginary, are arranged into seven vertebrze, composed of nine pieces each *,
The cranio-vertebral system of Geoffroy is liable to the further objection,
a that he has combined, as in the ease of his typical vertebra from the tail of
the flounder, parts of the exo-skeleton (e.g. the suborbitals) with parts of
the endo-skeleton to which alone the vertebral theory is applicable.
In the fasciculi of the magnificent ‘ Ostéographie’ with which Professor de
Blainville has enriched his science, the descriptions follow the plan of the
classification of the bones of the skeleton propounded in the above-cited Me-
moirs in the ‘ Bulletin des Sciences’ for 1816 and 1817. In the Prospectus of
the ‘ Ostéographie’, M. de Blainville briefly refers to the great questions of
comparative anatomy, which the German organologists have comprehended
under the name of ‘ Signification of the Skeleton, in allusion only to the
‘gross errors and opinions almost extravagant, of some of the persons who
have occupied themselves with these questions:” whilst he reprobates, on the
* Cuvier, Histoire des Poissons, 4to, t. i. p. 230.
248 REPORT—1846.
other hand, in equally general terms, “ those who have been unable to elevate
themselves to these kind of questions, partly on account of the nature of their
minds, partly from the want of proper and sufficient subjects of contempla-
tion*.”
Neither the first step, the most difficult of all, nor any of the succeeding
steps in the acquisition of such views of the ‘ Signification of the Skeleton’
as M. de Blainville adopts are noticed : no objection to the vertebral system
of the skull is answered: no error that may have opposed itself to a reception
of the doctrine is explained or refuted: of the particular labours and dis-
coveries of individual homologists the author of the ‘ Ostéographie’ is silent.
He defines a vertebra, in the language of anthropotomy, as a single bone :—
« Une vertébre, considérée d’une maniére générale, et par conséquent dans ~
son état complet, est un os court, médian, symmétrique, formant un corps,
partie principale de la yertébre, aux deux faces opposées de laquelle, externe
ou dorsale, interne ou ventrale, s’'applique un are plus ou moins développé,
d’ou résultent deux canaux, l'un au dos, l’autre au ventre.” (7b. fase. i. p. 6.)
We discern the influence of the ideas of his ingenious contemporary, Geoffroy
St. Hilaire, in the admission of the ventral or inferior, as well as the dorsal or
superior arch; and, like Geoffroy, he recognises the physiological relation
of the upper arch to the protection of the nervous system, and that of the
lower arch to the protection of the vascular system : but, overlooking or re-
jecting the idea of the relation of the ribs as the inferior protecting arches of
the expanded central organ of the vascular system, he considers the ventral
(hzemal) arches as arriving at their maximum of development in the tail. The
dorsal and thoracic vertebrz are, accordingly, characterized as those which are
provided with costiform appendages diversely articulated to them; over-
looking, I may remark, the costal appendages of the cervical vertebre in the
saurians and those which become anchylosed to the cervical vertebrae in
birds, as do, frequently, their serial homologues to the dorsal vertebre in the
same class. M. de Blainville seems, also, wholly ignorant of the fact that the
bent-forward ends of the long transverse processes of the lumbar vertebree of
the hares, cavies, and many other rodents, are primarily developed as distinct
costal rudiments : the same rudiments of lumbar ribs are found in the feetus
of the hog, and in the first lumbar vertebra of many mammalst. “ Les lom-
baires,” says M. de Blainville, “n’ont plus de cétes, méme incomplétes.”
The ribs not being regarded as essentially parts of the inferior or hemal
arches of vertebra, the sternal bones which complete these greatly expanded
arches are accordingly regarded as a distinct series of bones, and called
« sternebers.’ M. de Blainville, as we have seen, had before ( 1817) compared
them to vertebral bodies. In the ‘ Ostéographie,’ however, he rightly regards
the body of the hyoid as their serial homologue, but does not extend his com-
parison to the bones that in like manner complete the mandibular and max-
illary arches. These, with the cornua of the hyoid, and the sternal and verte-
bral ribs, he classes with the bones of the extremities, under the name of
appendages (appendices), adopting, in his larger work, as in his original essay,
essentially the idea of Oken, that the locomotive members are liberated ribs.
After much additional research and comparison since the first publication
of my ideas of the constitution of the typical vertebra or primary segment
of the endo-skeleton}, I have found no reason for modifying them, but have -
derived additional evidence of their accuracy ; and I therefore reproduce the
diagrammatic figure with which they were originally illustrated (fig. 14).
* Ostéographie, Prospectus, April, 1839, p. 9.
+ Thirle, in Miiller’s Archiv fur Physiologie, 1839, p. 106.
+ Geological Transactions, 4to, 1838, p. 518.
ON THE VERTEBRATE SKELETON. 249
Although my investigations of the fundamental type of the vertebrate
skeleton were first made upon the class of fishes, where vegetative uniformity
or irrelative repetition most prevails, and where, therefore, the type is least
obscured by the modification of one part in mutual subserviency with an-
other, I soon found that I should be led astray by confining my observations
to fishes, and by borrowing my illustrations from that class. Comparison
of the piscine skeleton with those of the higher animals demonstrates that
the natural arrangement of the parts of the endoskeleton is in a series of
segments succeeding each other in the axis of the body. These segments are
not, indeed, composed of the same number of bones in any class or throughout
any individual animal. But certain parts of each segment do maintain such
constancy in their existence, relation, position, and offices, as to enforce the
conviction that they are homologous parts, both in the constituent series of the
same individual skeleton, and throughout the series of vertebrate animals.
For each of these primary segments of the skeleton J retain the term ‘ verte-
bra’; but with as little reference to its primary signification, as a part
specially adapted for rotatory motion, as when the comparative anatomist
speaks of a sacral vertebra. The word may, however, seem to the anthro-
potomist to be used in a different or more extended sense than that in which
it is usually understood ; yet he is himself, unconsciously perhaps, in the
habit of including in certain vertebra of the human body, elements which he
excludes from the idea in other natural segments of the same kind, influenced
by differences of proportion and coalescence, which are the most variable.
characters of a bone. Thus the rib of a cervical vertebra is the ‘ processus
transversus perforatus,’ or the ‘radix anticus processus transversi vertebrae
colli’*: whilst in the chest, it is ‘ costa,’ or ‘ pars ossea costz.’ But the ulna
is still an ulna in the horse, although it be small and anchylosed to the radius.
The osteology of man, therefore, cannot be fully or rightly understood
until the type of which it is a modification is known, and the first step to
this knowledge is the determination of the’ vertebral segments, or natural
groups of bones, of which the myelencephalous skeleton consists.
I define a vertebra, as one of those segments of the endo-skeleton which con-
stitute the axis of the body, and the protecting canals of the nervous and
vascular trunks: such a segment may also support diverging appendages.
Exclusive of these, it consists, in its typical completeness, of the following
elements and parts :—
Te Kile ee ie cca ROSMAN esis Spine is
Fig. 14.
| Bm neural spine.
zygapophysis. ~~. i
lll.
neurapophysis.
© >....pleurapophysis.
parapophysis. pe @
h rr
~~~ heemapophysis.
fps A
zygapophysis. |
je hemal spine.
Ideal typical vertebra.
* Soemmerring, De Corporis Humani Fabrica, 1794, i. p. 239.
1846. 8
250 " REPORT—1846.
The names printed in roman type signify those parts which, being usually
developed from distinct and independent centres, I have termed ‘ autoge-
nous’ elements. The italics denote the parts, more properly called pro-
cesses, which shoot out as continuations from some of the preceding elements,
and are termed ‘exogenous’: e.g. the diapophyses or upper ‘transverse
processes,’ and the zygapophyses, or the ‘ oblique’ or ‘articular processes’ of
human anatomy.
The autogenous processes generally circumscribe holes about the centrum,
which, in the chain of vertebrae, form canals. The most constant and exten-
sive canal is that (fig. 14, 2) formed above the centrum, for the lodgment of
the trunk of the nervous system (neural axis) by the parts thence termed
‘neurapophyses. The second canal (fig. 14, 2), below the centrum, is in
its entire extent more irregular and interrupted ; it lodges the central organ
and large trunks of the vascular system (hemal axis), and is usually formed
by the laminz, thence termed ‘hzmapophyses.’ At the sides of the cen-
trum, most commonly in the cervical region, a canal is circumscribed by the
pleurapophysis or costal process, by the parapophysis, or lower transverse
process, and by the diapophysis, or upper transverse process, which canal
includes a vessel, and often also a nerve.
Thus a typical or perfect vertebra, with all its elements, presents four
canals or perforations about a common centre; such a vertebra we find in
the thorax of man and most of the higher classes of vertebrates, also in
the neck of many birds. In the tails of most reptiles and mammals, the
hemapophyses (as in fig. 14) are articulated or anchylosed to the under
part of the centrum; space being needed there only for the caudal
artery and vein. But where the central organ of circulation is to be
lodged, an expansion of the hzmal arch takes place, analogous to that which
the neural arches of the cranial verte- Fig. 15
bre present for the lodgment of the
brain. Accordingly in the thorax, the
pleurapophyses (fig. 15, pl) are much
elongated, and the heemapophyses (fig.
15, h) are removed from the centrum,
and are articulated to the distal ends
of the pleurapophyses ; the bony hoop
being completed by the intercalation
of the hemal spine (fig. 15, As) be-
tween the ends of the hemapophyses.
And this spine is here sometimes as
widely expanded (in the thorax of birds
and chelonians, for example) as is the
neural spine (parietal bone or bones)
of the middle cranial vertebra in mam-
mals. In both cases, also, it may be
developed from two lateral halves, and
a bony intermuscular crest may be ex-
tended from the mid-line, as in the
skull of the hyzna, and the breast-bone
of the bird (fig. 15, hs). To facilitate
the comparison of the merits of the
preceding view and nomenclature of
the typical vertebra with those of other
comparative anatomists, I have thrown
the results into the form given in
Table II.
Natural typical vertebra: thorax of a bird.
ON THE VERTEBRATE SKELETON. 251
To the question why I should have invented new names when Geoffroy St.
‘Hilaire had already proposed others for the vertebral elements, I can only re-
peat the regret with which I found myself compelled to that invidious step,
after having arrived at the conviction, that the learned Parisian Professor had
sometimes applied the same term to two distinct elements, and sometimes
two distinct names to one and the same element: and I am glad to be able to
cite the authority of Cuvier for the propriety and advantage of such a step.
His words are in reference to an analogous case, ‘‘ Donner a un mot connu un
sens nouveau est toujours un procédé dangereux, et, si l’on avoit besoin
d’exprimer une idée nouvelle, il vaudroit encore mieux inventer un nouveau
terme, que d’en détourner ainsi un ancien *.” Now there is scarcely one term
in the first column in Table II. which is synonymous with its opposite in the
second column, or which expresses exactly the same idea; and the discrepancy
becomes greater in regard to the terms applied to the vertebral elements of the
head, in columns 1 and 5 of TableIII. The respective concordance of the views
of the vertebral archetype entertained by Geoffroy and myself with Nature will
be determined and judged of by succeeding impartial and original observers.
With regard to the term cycléal, ‘de xvxdos, cercle, pour rappeler sa
forme annulaire, permanentes chez les premiers,” (Articulata, Dermoverte-
brés, Geoff.) “et, au contraire, non persévérante chez les derniers” (Verte-
brata, Hauts-vertébrés, Geoff.), it is understood by its author to apply to the
annular segment of the crust of the insect, as well as to the ‘centrum’ of the
endoskeletal vertebra. Geoffroy’s primary division of the parts of a vertebra
is into the centre or nucleus (noyau) and the lateral branches. The upper
‘ branches laterales’ or ‘ périaux’ are equivalent to my neurapophyses and
also to my neural spine, in fishes : the lower lateral branches or ‘ paraaux’ are
sometimes free and floating+, when they answer to my ‘pleurapophyses’;
but they are sometimes so united as to form a canal, when they answer
to my ‘ parapophyses’ in the tail of fishes t, and to my ‘hamapophyses’ in
the tail of cetaceans. Geoffroy supposed, for example, that the hemal canal
in the tail in all fishes was formed by the ribs, bent down and anchylosed
at both ends§, and that the hemal canal in the tail of the crocodile and
whale was constituted by a like metamorphosis of the same vertebral elements.
He, also, argued that, as the small spinal chord of fishes did not demand
so great a development in breadth of the neurapophyses, they were permitted
to attain to unusual length; and that, coalescing together, they thus consti-
tuted not only the neural arch but the neural spine, to which latter, therefore,
he extended the name ‘ périal’; whilst to the corresponding: part in mammals
he gives the name of ‘épial’. But, again, in fishes, he calls the dermal
spines developed in the embryonic median fold of integument which is meta-
morphosed into the dorsal fins, ‘épiaux’ ; and the corresponding dermal spines
of the ventral fin ‘ cataaux.’ The lepidosiren, however, manifests the neural
spine distinct from both the neurapophyses below and the dermo-neural spine
above: and such neural spine is unequivocally homologous with the anchy-
losed neural spine in osseous fishes ||. It is quite in harmony with the position
of the class of fishes at the bottom of the vertebrate scale that they should
present a greater degree of calcification of the parts belonging to the same
category of the skeletal system as the shells and crusts of the invertebrates :
hence it is that whilst the median dermal fins of the marine mammalia have
* Mémoires du Muséum, t. xx. p. 123.
+ As they are illustrated in the abdominal vertebra of the fish figured by Geoffroy in the
‘Mémoires du Muséun,’ t. ix. (1822), pl. 5, fig. 4, o. t Jb. fig. 2,0 0.
§ This occurs as an exceptional condition, in the lepidosteus, and perhaps in lepidosiren.
|| Linn. Trans, vol. xviii. p. 23, fig. 4, ¢, d.
s2
252 REPORT—1846.
their supporting skeleton in the primitive histological Fig 16,
fibrous state, the corresponding parts are ossified in fishes:
rarely, however, are such parts in answerable number to fg
the vertebre; and the true spines of these vertebrae, a z
when the median fins and their bony spines are removed, Sf) 8
in fishes, show as little indication of the place or existence & E
of such fins, as do the vertebre in the porpoise of the a
existence of its dermal fin. In proportion as ossification
has extended into the dermal system of fishes it has been
arrested in the vertebre, which in the trunk and tail of
fishes present their least complex condition. Two of the * 4
autogenous elements, the ‘ hzmapophyses,’ are absent, and g 5
are commonly represented, in the tail, by the modified % 5
‘ parapophyses.’ ‘The seeming complexity of a fish’s ver- a =
tebra arises from the intercalation of bones appertaining
to the system of the dermo-skeleton : it would have been an
unusual exception to the general course of development if
the lowest of the vertebrate classes should have presented
the vertebral skeleton in its highest state of complication ;
and Geoffroy St. Hilaire was unfortunate in taking a fish’s
vertebra with its extrinsic evertebrate complications, as the Po
perfect type of that primary segment of the myelencepha- y:
lous skeleton (fig.16). He was still more unlucky in having
for the subject of his figure* a specimen from which two
of the pieces, had been accidentally lost, as Cuvier after-
Métapérial.
Neural spine
‘. Neurapophysis.
- Cyclopérial.
Cycléal.
Centrum.
wards pointed out ; yet Geoffroy’s mutilated caudal ver- . 2, |) s de
tebra of the plaice continues to be copied in some 2 eae
compilations of comparative anatomy, as the type ofa = & a 8
vertebra! To obtain the dermal spines (pro-epial and pro- oS 5 é
cataal) of the vertically extended caudal vertebre of fishes, a
Geoffroy had recourse to a hypothetical division length-
wise of the interneural and interhemal spines (which are -
represented as being single in his figure), and to as gra- q | 3
tuitous a displacement of one of the halves froin the side 8 \ 2
to the summit of the other t. Now the interneural and & 2
interhamal spines are actually double in relation to the om
neural and hzmal spines ; yet they coexist with a dermo-
neural and dermohzmal ray, which therefore needs no
imaginary change of place of either of its supporting :
spines to account for its existence. I subjoin in fig. g 3
16 an entire vertebra answering to the mutilated one g 8
figured by Geoffroy ; and for the better understanding of g e
the difference between his determinations of the vertebral 8
elements and those given in the present Report, the names
respectively indicating those different determinations are
added to the figure. In the description of the plate in Endo: and exo-ske-
the ‘ Mémoires du Muséum,’ Geoffroy explains that the caudal, vertelsa of)
‘ pro-épial’ is the left half or ‘épial gauche,’ and the en-épial 9, 7aice (Pleuro-
the right half or‘ épial droit’ : that the en-cataal is the right
half or ‘ cataal droit,’ and the pro-cataal the left half or ‘ cataal gauche,’ of his
imaginarily divided epivertebral and catavertebral elements (i. ep. 115)
* Mémoires du Muséum, t. ix. (1822), pl. 5, fig. 1.
+“ Lune de ces pieces monte sur l’autre”—‘ l'une se maintient en dedans, quand
l’autre s’élance en dehors,” id. p. 97.
ON THE VERTEBRATE SKELETON. 253
The trunk of fishes, in respect of its viscera and the degree of development
of the endoskeleton, answers to the lumbar and caudal regions of air-breath-
ing vertebrates, where the vertebra usually lose some of their elements, at
least as bones. The heart and respiratory organs are placed in the head of
the fish; and it is only in this region that the vertebral segments attain to
typical completeness in that class. Geoffroy, in studying the special and
general homologies of the bones of the head of fishes, blends indiscrimi-
nately, as in the supposed typical vertebra from the tail, elements of the
dermoskeleton (suborbitals and lacrymals, e. g.) with those of the endo-
skeleton ; and also presses the capsules of the special organs of sense into the
composition of the seven cranial vertebre of his system. It needs only to
compare the synonyms of the elements of these vertebre in Table III. to
perceive how impossible it would have been to have expressed the ideas
which I wish to expound and illustrate in this Report by the use of the names
for the vertebral elements proposed by Geoffroy, or of English equivalents.
The prefrontals, e. g. (no. 14), which I regard as the neurapophyses of the
nasal vertebra, are, according to Geoffroy, epials of the 2nd or labial vertebra
in the class of fishes; but are epials of the Ist or nasal vertebra in the cro-
codile, according to the tables given in the ‘ Annales des Sciences,’ t. iii. pl. 9,
and ‘ Atlas,’ p. 44; whilst they are the perials of the 2nd vertebra in the
scheme of 1825, cited in the fifth column of Table III.
I have deemed it requisite to enter the more fully into the grounds for
abandoning the analysis and nomenclature of the typical vertebra proposed
by Geoffroy, because they have received the sanction in this country of the
learned Professor of Comparative Anatomy at University College. Dr. Grant*
converts the French names into English equivalent phrases ; ‘cyclo-vertebral
element’ for cycléal, ‘perivertebral element’ for périal, &c.; and abandons
the advantage of a definite name, without remedying the disadvantages of
the double employment of the same names for two distinct elements, and of
the application of different phrases for the same element. If, for example,
the neural spine of the reptile or mammal be, in nature, the homologue of
the neural spine of the fish, then the latter is called an ‘ epivertebral element,’
whilst the former is called a ‘perivertebral element.’ If the dermo-neural
spines of the dorsal fin of a fish be, in nature, homologous with the fibro-
ligamentous tissue supporting the dorsal fia of the dolphin, then the term
‘ epivertebral element’ is applied to a spine of the exoskeleton in the fish, and
to a spine of the endoskeleton in the mammal, which spine co-exists with such
dermal spine in the fish (see fig. 16). If the parapophysis or inferior transverse
process in the fish be a distinct element from the diapophysis or superior
transverse process in the mammal, the same phrase, ‘ paravertebral element,’
is applied to each. Dr. Grant, moreover, gives the same name, ‘catavertebral
elements,’ to the free vertebral ribs in fig. 28, B. g. p. 58, op. cat., as he applies
to the hemapophyses in the tail of the reptile or cetacean, in fig. 28, C. g.
loc. cit.; whilst Geoffroy applies the name ‘cataaux’ to the sternal ribs,
and not to the vertebral ribs: and it is precisely with the sternal ribs that
the chevron bones in the tails of reptiles and cetaceans are homologous, and
both are, therefore, the ‘ hemapophyses’ in my system. The transference
of the term ‘ catavertebral elements’ (for cataaux), from the ‘ cdtes sternales’
to the pair of ribs extended from the ends of the parapophyses of the abdomen
of fishes, is a deviation from the original vertebral system of Geoffroy, which
seems to lead further away from nature. If it is meant that the outstretched
parapophyses in the diagram of the abdominal vertebra of a fish (fig. 28, B. f. f.
loe, cit.), and which are there called ‘ paravertebral elements,’ are the homo-
* Outlines of Comparative Anatomy, 1835, pp. 57-59.
954 REPORT—1846,
logues of the ‘ cdtes vertébrales’ of higher vertebrates, to which Geoffroy
assigned the name ‘ paraaux,’ this appears to be another misapprehension of
the relations in question.
Development of vertebre.—Before applying the idea of the archetypal
vertebra, or primary segment of the endo-skeleton, given in figs. 14 and 15,
to the elucidation of the modifications of those segments in the different ver-
tebrate classes, I shall premise a few observations on the mode of develop-
ment of the vertebrze in those classes.
The chief condition of the development of distinct vertebra in the trunk
is the conjunction of nerves with, or their progress from the spinal chord :
at least, this circumstance, with the concomitant exit of blood-vessels from
the neural canal, seems to determine the development of the neurapophyses :
and the vertebral bodies are not slow in coinciding in number with those im-
portant arches; and in determining with the regular primary pairs of (inter-
costal, lumbar, &c.) arteries, the inferior or hemal arches. We may learn how
much the development of the neurapophyses and vertebral bodies depends,
in the trunk, upon the conjunction of nerves with the spinal chord, by the
fact that, in the regenerated tails of lizards, the vertebral axis remains con-
tinuous and unjointed, because there is no co-extensive spinal chord giving
off pairs of nerves.
An extremely delicate fibrous band, with successively accumulated gelati-
nous cells, compacted in the form of a cylindrical column, and inclosed by a
membranous sheath, is the primitive basis, called ‘notochord’* (chorda dorsa-
lis seu gelatinosa, Lat., gallertsdule und ruckensaite, Germ.), in and around
which are developed the cartilaginous or osseous elements by which the
vertebral column is established in every class of Myelencephala.
The earlier stages of vertebral development are permanently represented,
with individual peculiarities superinduced, in the lower forms of the class of
fishest. In the Dermopteri or cyclostomous fishes, the neural and hemal
canals are formed by a separation of the layers of the outer part of the apo-
neurotic sheath of the gelatinous chorda: in the lancelet (Amphioxus) there
is no distinction of structure in the cranial part supporting the anterior end
of the neural axis, with which the trigeminal, optic and olfactory nerves com-
municate, and the rest of the rudimental vertebral column: a labial carti-
laginous arch supporting the tentacula is, at least, the only lineament of
development which sketches out the skull. In the myxinoids the skull in-
cludes a complex system of cartilages, but the vertebral column of the trunk
has not advanced beyond the gelatino-aponeurotic stage. In the lamprey
cartilaginous laminz are developed in the outer layer of the fibrous sheath,
and give the first indication of neural arches{. In the sturgeons (Sturio,
Polyodon) the inner layer of the fibrous capsule of the gelatinous notochord
has increased in thickness, and assumed the texture of tough hyaline carti-
lage. In the outer layer are developed distinct, firm, and opake carti-
lages, the neurapophyses, which consist of two superimposed pieces on each
side, the basal portion bounding the neural canal, the apical portion the
parallel canal filled by fibrous elastic ligament and adipose tissue; above this
is the single cartilaginous neural spine. The parapophyses are now di-
stinetly developed, and joined tugether by a continuous expanded base, form-
ing an inverted arch beneath the notochord for the vascular trunks, even in
the abdomen. Pleurapophyses are articulated by ligament to the ends of the
* Noros back, yopdn, string. We have hitherto had no English equivalent for this em-
bryonic keel or basis of every vertebrate animal: ‘dorsal chord’ or ‘chorda’ is liable to
be misunderstood for the ‘ spinal chord.’
+ Hunterian Lectures on Vertebrata, 1846, pp. 45, 46.
t Cuvier, Mémoires du Muséum d’Histoire Naturelle, t. i. 1815, p. 130.
Pa
2
~
ON THE VERTEBRATE SKELETON. 255
Jaterally projecting parapophyses in the first twelve or twenty abdominal ver-
tebre : in the anterior ones these ‘vertebral ribs’ are composed of two or
three distinct cartilages* : the posterior pleurapophyses are short and simple.
The parapophyses gradually bend down to form hzmal arches in the tail, at
the end of which we find hemal cartilaginous spines corresponding to the
neural spines above. The tapering anterior end of the notochord is con-
tinued forwards into the basal elements of the cranial vertebre. Vegetative
repetition of perivertebral parts not only manifests itself in the composite
neurapophyses and pleurapophyses, but in a small accessory (interneural ) car-
tilage, at the fore and back part of the base of the neurapophysis; and by a
similar (interheemal) one at the fore and back part of most of the parapo-
physes t.
Amongst the sharks (Squalide) a beautiful progression in the further
development of a vertebra has been traced out, chiefly by J. Millert. In
Heptanchus (Squalus cinereus) the vertebral centres are feebly and vege-
tatively marked out by numerous slender rings of hard cartilage in the noto-
chordal capsule, the number of vertebrz being more definitively indicated by
the neurapophyses and parapophyses; but these remain cartilaginous. In
the piked dog-fish (Acanthias) and the spotted dog-fish ( Scylliwm) the ver-
tebral centres coincide in number with the neural arches, and are defined by
a thin layer of bone, which forms the conical articular cavity at each end:
the whole exterior of the centrum is covered by soft cartilage, except at the
concave ends; the two thin funnel-shaped plates of osseous matter coalesce
at their perforated apices, and form a basis of the vertebral body like an
hour-glass ; the series of these centrums protecting a continuous moniliform
remnant of the gelatinous notochord. In the great basking-shark (Se/ache)
the vertebral bodies are chiefly established by the terminal bony cones, the
thick margins of which give attachment to the elastic capsules containing
the gelatinous fluid, which now tensely fills the intervertebral biconical spaces.
Four sub-compressed conical cavities extend, two from the bases of the
neurapophyses, and two from those of the parapophyses, towards the centre
of the vertebral body, contracting as they penetrate it. These cavities always
remain filled by a clear cartilage: the central two-thirds of the rest of the
vertebral body contain concentric, progressively decreasing, and minutely
perforated rings or cylinders of bone, interrupted by the four depressions:
the peripheral third of the vertebral body contains longitudinal bony lamin,
which radiate, perpendicularly to the plane of the outermost cylinder, to the
circumference ; these outer laminz lie, therefore, parallel with the axis of the
vertebra, and the intervening fissures, like those between the concentric cylin-
ders within, are filled by clear cartilage, which shrinks, and leaves them open
in the dry vertebra §.
In Cestracion, the intermediate part of the centrum between the terminal
cones is strengthened by longitudinal radiating plates only ; in Squatina by
concentric cylinders only. In the tope (Galeus) all the space between the
terminal bony cones is ossified, except the four conical cavities, the bases
of which are closed by the neur- and par-apophyses; so that the whole
exterior of the centrum appears formed by smooth compact bone.
In the osseous fishes | find that the centrum is usually ossified from six
points, four of which commence, as Rathke|| describes, in the bases of the
.. * Brandt & Ratzeburg, Medizinische Zoologie, 4to, 1833, t. ii. pl. iv. fig. 1.
+ Hunterian Lectures on Vertebrata, 1846, p. 53, fig. 12.
t See Agassiz, Recherches sur les Poiss. Foss. t. iii. pp. 361, 369.
§ Hunterian Lectures on Vertebrata, 1836, p. 55, fig. 13.
|| Abhandlungen zur Bildungs und Entwickelungsgeschichte, Zweiter Theil, 1833, p. 41.
256 REPORT—1846.
two neurapophyses and the two parapophyses ; but the terminal concave plates
of the centrum are separately ossified. They coalesce with the intermediate
part of the centrum, which is sometimes completely ossified, but commonly a
communicating aperture is left between the two terminal cones; and in
many cases, the plates by which calcification attains the periphery of the
body leave interspaces permanently occupied by cartilage, forming cavities
in the dried vertebra, especially at their under part, or giving a reticulate
surface to the sides of the centrum. ‘The expanded bases of the neur- and
par-apophyses usually soon become confluent with the bony centrum; some-
times first expanding so as wholly to inclose it, as, for example, in the tunny,
where the line of demarcation may always be seen at the border of the arti-
cular concavity, though it is quite obliterated at the centre, as a section
through that part demonstrates.
Miller correctly distinguishes a ‘central’ from a ‘peripheral’ (cortical) part
or seat of the ossification of the vertebral bodies of fishes. The peripheral
ossification which takes its rise from the outer layer of the fibrous sheath of
the notochord sometimes extends into broad plates beneath the anterior ver-
tebree of the trunk, and tends to fix or anchylose a certain number of them;
when they are commonly represented by the partially distinct central parts
of the bodies, together with the neur- and par- and pleur-apophyses.
The batrachia follow closely the stages above-cited in fishes ; the centrums
being arrested at the biconical stage in the perennibranchiates, but converted
into ball-and-socket vertebr by the ossification of the interposed gelatinous
ball* and its adhesion, either to the fore-part of the centrum (Pipa, Sala-
mandra), or the back part (Rana, Bufo). The mode of ossification of the
centrum varies somewhat in batrachia. Miullert describes annular ossifi-
cations in the sheath of the notochord of the Rana temporaria and R. escu-
lenta, which support, at first, the neurapophyses. Dugés, apparently in-
fluenced by M. Serres’ so-called ‘law of centripetal development,’ describes
two cartilaginous nuclei, side by side; but the more obvious and better-de-
termined development of the vertebrz of fishes gives no countenance to this
bilateral beginning of ossification of the centrum as a general law. The first
distinct bony nucleus in the centrum observed by Dugés was bilobed, and
afterwards cubical; but excavated before and behind, as well as beneatht.
The ossification of the centrum is completed by an extension of bone from
the bases of the neurapophyses, which effect, also, the coalescence of these
with the centrum. In Pelobates fuscus, and Pelobates cultripes, Miller found
the entire centrum ossified from this source, without any independent points
of ossification.
The vertebrz of the tail of the larve of the anourans are represented di-
stinctly only in the aponeurotic stage. Even when the change to cartilage
takes place, the tendency to coalescence has begun to operate, and only two
long neurapophyses are established on each side: the ossification of these
plates extends into the fibrous sheath of the remnant of the coccygeal noto-
chord, and they coalesce when the perishable parts of the tadpole-tail have
been absorbed, and the fore- and hind-legs developed, constituting the long,
often hollow, and inferiorly grooved coccygeal bony style.
In saurians, birds and mammals, the notochord is inclosed by cartilage
before ossification begins; which cartilage is continuous with the cartilagi-
nous neurapophyses§. In birds, the two histological processes, chondrifica-
* Duirochet, Mémoires pour servir a l’Histoire Nat. et Physiol. des Animaux, &c., t. ii.
p- 302. 1837.
+ Neurologie der Myxinoiden, 1840, p. 69.
t Recherches sur les Batraciens, 1835, 4to, p. 106.
§ Muller, Vergleichende Anatomie der Myxinoiden, Neurologie, 1840, p. 74.
ON THE VERTEBRATE SKELETON. 257
tion and ossification, do not precisely follow the same route. In the centrums
of the dorsal and cervical vertebra of the chick chondrification is centripetal:
it begins from two poiuts at the sides and proceeds inwards, the middle line
of the under surface of the primitive notochord resisting the change longest.
But, when the lateral cartilages have here coalesced, ossification begins at
the middle line and diverges laterally ; the primitive nuclei of the bony centres
‘appearing as bilobed ossicles, and its direction is centrifugal. The lobes
ascend to embrace the shrivelled remnant of the chorda, like the hollow ver-
tebral centres in fishes. Only in the sacral vertebrae has ossification been
seen to begin from two distinct points at the middle line. The bases of
the separately ossifying neurapophyses extend over much of the centrum,
and soon coalesce with it. In reptiles a greater proportion of the centrum
is ossified from an independent point, and the bases of the neurapophyses
often remain permanently distinct and united to the centrum by suture. In
mammals, as in fishes, the centrum is ossified from an anterior and posterior
centre, establishing the articular surfaces, as well as from an intermediate
point. This is considerably overlapped by the bases of the neurapophyses,
before they coalesce with the centruin. The three primitive parts of the
centrum remain longest distinct in the cetacea. The body of the human
atlas is sometimes ossified from two, rarely from three, distinct centres placed
side by side*. From these ascertained diversities in the mode of formation
of the central element of the vertebra, it will be seen how little developmental
characters can be relied on as affecting the determination of homologous parts.
General Characters of Veriebre of the Trunk.—The ossified parts of the
abdominal vertebre of osseous fishes answer to ¢, centrum; ”, neurapo-
physes ; 2 s, neural spine ; p, parapophyses; pl, pleurapophyses; and a, ap-
pendages (fig. 17).
The neurapophyses com- Fig. 17.
monly coalesce with their re-
spective centrums; except in
the case of the atlas, where the
neural arch is sometimes quite
separated from the centrum,
and wedged between those of
the occiput and second verte-
bra. I have found also the
neurapophyses of the two last
caudal vertebra unanchylosed
to their centrums in a large
sea-perch (Centropristis gigas,
O.) in which the five terminal
heemal arches and spines re-
mained similarly distinct, and
articulated with the centrums
below. In the carp and pike,
the primitive independence of
both neurapophyses and par-
apophyses is more general and : ; ;
longer maintained. In the le- Ossified parts of abdominal vertebra, hers
pidosiren the vertebral bodies are not developed, the notochord being per-
sistent; but the peripheral vertebral elements are well-ossified : the neur-
apophyses in this fish remain distinct from the neural spines ; and the hemal
spines are in like manner moveably articulated to the hemal arches. These
* Meckel, Archiv fiir die Physiologie, Bd. i. (1815) t. vi. fig. 1.
258 REPORT—1846.
are formed by the gradually bent-down ribs*, which are formed in the
abdomen either by unusally elongated ‘parapophyses’ (if they be inter-
preted by the condition of those elements in the cod-fish), or by pleurapo-
physes articulated directly to the fibrous sheath of the notochord; which
interpretation of the mode of formation of the hemalarches is supported by
Professor Miiller’s discovery of the nature of those arches in the Lepidosteus +.
Whether we adopt the analogy of the Anacanthini, or the Ganoidei (and
the general affinity of the Protopteri to the ganoids would incline the choice
to the latter), the constitution of the hzmal arches in the lepidosiren is
strictly piscine; at least if we take the skeleton of the tailed batrachia
(tig. 28) as our guide to the homology of the caudal inferior arches in
higher reptiles and mammals. The unusual size and length of the abdo-
minal parapophyses in the cod-tribe ( Gadide), the flat-fishes (Pleuronectide),
and the genus Ophidium, evinces the natural character of the order Anacan-
thini, in which they have been grouped together by Professor Miller: the
pleurapophyses are, conversely, very short and slender in this order. In all
bony fishes the costal arch in the abdomen is completed by the aponeurotic
septa between the ventral portions of the myocominatat, which there repre-
sent the ‘ hemapophyses’ (cartilagines coste, inscriptiones tendinee muse. recti
abdominis of anthropotomy). Indeed, when we reflect that the trunk of
the fish, by reason of the advanced position of the heart and breathing organs,
answers to the abdominal and caudal regions of the trunk of higher verte-
brates, we could hardly expect the typical vertebra to be there carried out in
osseous tissue; but rather be prepared to find the hemapophyses retaining
the same primitive histological state which they present in the abdomen of
mammals and man (fig. 25, h'’). ;
Immediately behind the coracoid arch, it is usual to find a long and slender
rib-like bone, sometimes composed of two pieces, on each side; it gives a
firmer implantation to the portion of the myocommata immediately behind
the pectoral fin; and is obviously the ossified serial homologue of the hema-
pophysial aponeuroses between the succeeding myocommata. It is usually
detached from its centrum and articulated superiorly to the inner side of the
coracoid: when it rises higher, as in the Batrachus, it becomes attached to
the atlas, and in the Argyreiosus vomer it meets and joins its fellow below,
forming a true inverted or hemal arch, parallel with, but more slender than
the coracoid arch. No other idea of the general homology of this arch pre-
sents itself than as a hemal one, completing the costal arch as an ossified
hemapophysis, differing from the typical vertebra (fig. 15) only by the non-
development of a sternum or hemal spine: and there appears to be as little
ground for hesitation as to the particular segment of the endoskeleton to which
to refer this costal or inverted arch; its immediate succession to the correspond-
ing arch attached to the occiput, as well as the occasional direct attachment,
indicating that segment to be the atlas or first vertebra of the trunk.
The best-marked general character of the vertebral column of the trunk in
the class Pisces is that which Professor J. Miiller first pointed out ; viz. the
formation of the hemal arches in the tail by the gradual bending down and
coalescence of the parapophyses ; the exceptions being offered by the ganoid
polypterus and lepidosteus and the protopterous lepidosiren. The pleurapo-
physes are, sometimes, continued in ordinary osseous fishes from the parapo-
physes after the transmutation of these into the hemal arches. The dory,
* Linn. Trans. vol. xviii. pl. 23, fig. 4, 2 2.
. + Remarks on the Structure of the Ganoidei, in Taylor’s Scientific Memoirs, vol. iv.
p. 551.
+ Lectures on Vertebrata, 1846, p. 163, fig. 44, h p.
oho
ON THE VERTEBRATE SKELETON. 259
tunny, and salmon yield this striking refutation of the idea of the formation
of those arches in all fishes, by displaced, curtailed and approximated ribs. In
some fishes, however (e. g. the cod), reduced pleurapophyses coalesce with the
parapophyses to form the heemal arches of the caudal vertebra. The meno-
pome, amongst the lowest or perennibranchiate reptiles, yields a clear disproof
of the formation of the hemal arch in the tail by the pleurapophyses (the
rts, viz. called by Geoffroy ‘ paraux, and by Dr. Grant ‘ catavertebral ele-
ments ’ in the abdomen of fishes)*. The vertebral ribs or pleurapophyses in
the menopome (fig. 27, p/) are short and simple and suspended to the extre-
mities of the diapophyses (d) at the beginning of the tail, where they coexist
with hzemal arches (A, h): these must be formed, therefore, by different ele~
ments, which, since no trace of parapophyses exists in any part of the spine,
I conclude to be the ‘hemapophyses.’ The young crocodile and the adult
enaliosaurs give the same evidence of the nature of the hzmal arches in the
tail, with which the corresponding arches or chevron-bones, in cetacea and
many other mammalia, are homologous.
_ Thus the contracted hemal arch in the caudal region of the body may be
formed by different elements of the typical vertebra: e. g. by the parapophyses
(fishes generally) ; by the pleurapophyses (lepidosiren) ; by both parapophy-
ses and pleurapophyses ( Sudis, Lepidosteus), and by heemapophyses, shortened.
and directly articulated with the centrums (reptiles and mammals)+. The
caudal vertebree of some flat-fishes (Pleuronectide, fig. 16), and the mu-
reenz, would seem to disprove the parapophysial homology of the hemal arches
in such fishes, since transverse processes. from the sides of the body coexist
with them, as they do in the cetacea. But, if we trace the vertebral modifi-
cations throughout the entire column in any of these fishes, we shall find that
the hzmal arches are actually parts of the transverse processes ; not independ-
ent elements, as in the cetacea ; but due to a progressive bifurcation : this, in
Murena Helena, for example, begins at the end of the transverse processes
of about the twenty-fifth vertebra, the forks diverging as the fissure deepens,
until, at about the seventy-third, the lower fork descends at a right angle to
the upper one (which remains to represent the transverse process), and,
meeting its fellow, forms the hzmal arch, and supports the antero-posteriorly
expanded hzmal spine. In the plaice a small process is given off from the
expanded base of the descending parapophysis of the first caudal vertebra,
which increases in length in the second, rises upon the side of the body in
the third, becomes distinct from the parapophysis in the fourth, and gradually
diminishes to the ninth or tenth caudal vertebra, when it disappears. These
spurious transverse processes never support ribs.
' The neurapophyses are often directly perforated by the nerves in fishes,
but are sometimes notched by them, or the nerves issue at their interspaces.
_ The neurapophyses, which do not advance beyond the cartilaginous stage in
the sturgeon, consist in that fish of two distinct pieces of cartilage; and the an-
terior pleurapophyses also consist of two or more cartilages, set end on end: and
this interesting compound condition is repeated in cases where the pleurapo-
physial element is ossified and required to perform unusual functions in the
bony state in other fishes. Amongst the more special or exceptional modifi-
cations of the vertebre of the trunk of fishes, which indicate the extent to
which their normal segmental character may be marked, I would cite those
-of the anterior vertebre in the pipe-fishes, in the loaches, and in certain
siluroids.
* Outlines of Comparative Anatomy, p. 58, fig. 28, B, g.
+ By a misconception of the sense in which I use the term ‘ hemapophyses,’ M. Agassiz
has applied it to the lamin of the inferior or hemal arches in fishes. ‘‘ Recherches sur les
Poiss. Foss.” tom. i. p. 95.
260 REPORT—1846.
In the Fistularia tabaccaria the four anterior vertebra are much-elongated;
the second one even to eight times the length of the ordinary abdominal ver-
tebree: and their centrums are firmly interlocked together, by very deeply
indented sutures, The parapophyses are co-extended with the centrums, and
overlap each other, forming a continuous outstanding horizontal ridge on each
side ; and the neural spines form a similar vertical continuous crest.
In the Cobitis fossilis and C. barbatula the par- and pleur-apophyses of
the second and third vertebrz coalesce and swell out into a large ‘ bulla ossea’
on each side, inclosing the small air-bladder of these fishes: they also lodge
the little ossicles which bring this vertebral tympanum into communication
with the prolongations or atria of the labyrinth *.
In a large South American siluroid fish, I found the fore-part of the verte-
bral column of the trunk apparently formed by one large vertebra, the body of
which sent a broad triangular plate outwards on each side, giving it a rhom-
boidal figure, viewed from below: these plates in this fish support and coalesce
with five parapophyses, which ascend and increase in breadth as they approach
the skull, where they join the paroccipitals, as they are, themselves, joined to-
gether so as to form a continuous broad oblique outstanding plate of bone.
Above these, the continuous bony neural arch is perforated for the exit of five
pairs of nerves; the dorsal and ventral roots escaping separately, as in the
sacrum of birds. The coalesced neural spines send up a lofty pointed plate
to the overhanging supraoccipital. On vertically bisecting this specimen, I
found the central parts of the bodies of five vertebrae, which had been deve-
loped in the notochord, distinctly marked out, and preserving in their an-
terior and posterior deep concavities the persistent gelatinous remains of the
notochord; although the rest of the circumference of such centrums were
anchylosed to the cortical or peripheral parts developed from the capsule of
the notochord, viz. to the continuous expanded plate of bone below, to the
parapophyses laterally, and to the neurapophyses above. The body of the
first vertebra, or atlas, presented the exception of being quite detached from
its elevated parapophyses, as well as from its neural arch ; it was anchylosed
only to the bony plate below. The body of the second vertebra was six times
as long as that of the atlas: yet the apices of the two deep terminal jelly-
filled cones extended to and met in its centre. The bodies of the third and
fourth vertebrz were elongated, but less so than that of the axis: the body
of the fifth vertebra was singularly modified; its anterior half presenting the
long and slender character of the antecedent vertebre ; whilst the posterior
half was suddenly shortened, but extended in depth and breadth so as to
adapt its shallow posterior concavity to that of the short and broad body of
the first free vertebra of the trunk, which is followed by others of similar
character. I have seen few better instances of adherence to type, irrespective
of obvious function, than the persistence of the biconcave articular cavities,
with the elastic capsules and contained fluid, in the centrums of these five
rigidly fixed anterior vertebrz of the siluroid fish.
The continuous bony plate supporting those centrums was perforated
lengthwise by the aorta, offering another mode of formation of a hzemal canal,
viz. by exogenous ossification in and from the lower part of the outer layer
of the capsule of the notochord: the carotid hamal canal in the necks of
birds seems to be similarly formed; and the neck of the ichthyosaurus derives.
additional strength and fixation from apparently detached developments of
bone in the lower part of the capsule of the notochord, at the inferior inter-
space between the occiput and atlas, and at those of two or three succeeding
cervical vertebre f.
* Weber, G. H., De Aure et Auditu Hominis et Animalium, 4to. 1820.
+ Sir Philip de M. Grey Egerton, in Geol. Trans. 2nd ser. vol. v. p. 187, pl. 14.
ON THE VERTEBRATE SKELETON. 261
_I am inclined to regard the ‘ odontoid process’ of the mammalian axis as the
homologue of one of these subvertebral wedge-bones, or peripheral develop-
ments of the outer layer of the notochordal capsule. It cannot be the pecu-
liarly developed anterior articular epiphysis of the second vertebra, since this
is represented by a distinct centre of ossification between the odontoid process
and the body of that vertebra, according to Professor Miiller’s observation
in a foetal foal *.
The diverging appendages of the hemal arch in the abdominal vertebre of
fishes present the form of long and slender spines (fig. 17, a a), usually at-
tached to, or near the head of the ribs, and extending upwards, outwards
and backwards, between the dorsal and lateral portions of the muscular
segments, to which they afford a firmer fulerum or basis of attachment ;
acting, therefore, asso many pairs of rudimental and concealed limbs. They
are termed the ‘obere rippe’ by Meckel, and at the fore-part of the abdomen
of the polypterus they are stronger than the pleurapophyses themselves.
As the vertebre approach the tail these appendages are often transferred
gradually, from the pleurapophysis to the parapophysis, or even to the cen-
trum and neural arch.
_ In the air-breathing vertebrata, in which the heart and breathing organs
are transferred backwards to the trunk, the corresponding osseous segments
of the skeleton are in most instances developed to their typical complete-
hess, in order to encompass and protect those organs. The thoracic hemapo-
physes in the crocodiles are partially ossified, and in birds (fig. 15, h, h) com-
pletely so; in which class the hzemal spines of the thorax (As) coalesce together,
become much expanded laterally, and usually develope a median crest down-
wards to increase the surface of attachment for the great muscles of flight.
This speciality is indicated by the name ‘sternum’ applied to the confluent
elements in question. The abdominal hemapophyses and spines retain their
primitive aponeurotic condition, though still preserving their characteristic
expansion+. In the crocodiles and enaliosaurs the abdominal hemapophyses
are also ossified; and, in the latter, they manifest the same composite character
which has been noticed in the pleurapophyses of the sturgeon, consisting of
three or more pieces, which overlap each other}. The abdominal hemal
spines, in the Plesiosaurus Hawhinsii, are transversely extended, they are
marked ¢ c in the figure quoted below: the compound hzemapophyses them-
selves are marked 6 6 in the same figure.
The typical thoracic vertebrze of most birds support diverging appendages
(fig. 15, a, a), either anchylosed or articulated, as in the penguin and apte-
ryx, to the posterior border of the pleurapophysis (pl). The function of the
appendages in this form of typical vertebra is to connect one hemal arch
with the next in succession, so as to associate the two in action, and to give
firmness and strength to the whole thoracic cage. (A portion of the next
rib so overlapped is shown at pl, a, fig. 15.)
With regard to the connections of the pleurapophyses, we have seen that,
in fishes, they may be directly attached to the centrum, or to the ends of the
parapophyses (fig. 17,p),or they may be quite detached from their proper seg-
ment, and suspended to the heemal arch of an antecedent vertebra, as in the
case of the clavicle or epicoracoid, no. 2s. In batrachians, ophidians, and
lacertians, the proximal end of the pleurapophysis is simple, as in fishes,
but is articulated to an exogenous tubercle or transverse process from the
is Vergleichende Anatomie der Myxinoiden. Abhand. Akad. der Wissensch. Berlin,
1834, p. 105.
T Myology of Apteryx, Zoological Transactions, vol. iii. pt. iv. pl. 35, g*, g*.
} Buckland, Bridgewater Treatise, vol. ii. pl. 18, fig. 3.
262 REPORT— 1846.
side of the centrum or the base of the neural arch, called ‘diapophysis,’a di-
stinet part from the autogenous parapophyses in fishes. The anterior verte-
bre of crocodiles have an exogenous inferior transverse process from the side
of the centrum, answering to the ‘parapophysis,’ as well as an upper transverse
process or ‘ diapophysis ’ developed from the base of the neurapophysis : and
the proximal end of the pleurapophysis bifurcates and articulates with both
transverse processes, circumscribing with them a foramen at the side of the
‘centrum. The same structure obtains in the cervical and anterior thoracic
vertebra of birds and mammals: thus the rib (p/) in fig. 15 articulates to the
parapophysis p and the diapophysis d. Very few, however, of the thoracic
ribs in the cetaceans offer this structure; the first or second may reach the
centrum, but the rest are appended to the ends of the long diapophyses, and
a character of affinity to the saurians is thus manifested. The cervical re-
gion is distinguished by the brevity of the pleurapophyses and the absence
of bony hemapophyses, in saurians, birds, and mammals ; but in the warm-
blooded classes the short floating vertebral ribs soon anchylose to the diapo-
physes and parapophyses, and constitute thereby the ‘anterior roots of the
perforated transverse process’ of anthropotomy*. ‘The cervical pleurapo-
physes are indicated diagrammatically at p/, in the neck of the embryo skele-
ton (fig. 25): those of the seventh cervical vertebree sometimes attain in
the human subject proportions which acquire for them the name of ‘ribs.’
The pleurapophyses retain their moveable articulation in the ninth, and
sometimes the eighth, vertebrae of the elongated neck of the three-toed
sloths f.
. The thoracic or dorsal vertebrze of mammalia are characterized by the free ar-
ticulations of the pleurapophyses (fig. 25, pl) : most of these are much-elon-
gated, and most, if not all, support hemapophyses (ib. /) ; which, in a greater
or less number of the anterior vertebree, articulate with beemal spines (ib. As),
completing the arch: these spines commonly remain distinct, and are called,
some ‘sternebers,’ others ‘manubrium,’ and ‘ xiphoid appendage,’ and to-
gether they constitute the ‘sternum.’ In most mammals the thoracic hema-
pophyses are cartilaginous: they become ossified in Dasypus, Myrmecophaga,
the megatherioids and monotremes. The hinder pleurapophyses, which pro-
gressively diminish in length, also, usually become simply suspended to the
diapophyses: all the ribs are so attached in Balena longimana, according
to Rudolphi. The lumbar vertebra, which in some mammals show, in the
foetal state, distinct rudiments of pleurapophyses more minute than those
in the neck, have them soon anchylosed to the extremities of the diapo-
physes, which are thus elongated; and the vertebra is characterized in anthro-
potomy as ‘ having no ribs, but simple imperforate transverse processes.’ The
hzemapophyses of these segments of the skeleton are represented by the
‘inseriptiones tendinex’ (fig. 25, h'') ; they do not advance even to the state
of cartilage, but retain the primitive condition which they presented in the
corresponding part of the trunk in fishes.
If a vertebra succeeding the lumbar or abdominal ones have its hemal
arch completed, as in the thorax, by pleurapophyses and hzmapophyses,
with diverging appendages, forming the ‘pelvic arch and hind or lower
limbs,’ it is called a ‘sacrum’ (fig. 28, p', H, A). If two or more vertebre
anchylose together, without such completion of the typical character, they
likewise are said to form a ‘sacrum,’ of which an example may be found in
* Meckel, Archiv fiir Physiologie, B. i. (1815) p. 594, pl. vi. fig. 12, e; and System der Ver-
gleichend. Anatomie, B. ii. p. 294. .
t+ Prof. Th. Bell, Trans. Zool. Society, i. p. 115. pl. 116, a, .
ON THE VERTEBRATE SKELETON. 253
the two or three anterior caudal vertebre of certain flat-fishes (Pleuro-
nectide*), characterized as usual by the simple parapophysi:l hzmal arch,
In most air-breathing vertebrates the sacrum is characterized by both modifica-
tions, which are carried out to their extreme in birds: in no other class is so
large a proportion of the vertebral column converted into a ‘sacrum’ by
coalescence (e. g. seventeen vertebrz in Struthio) : in none is the diverging
appendage developed to such enormous proportions (e. g. Apteryx, Dinornis).
The centrums of the middle sacral vertebre (fig. 27, ¢ 1-4) are expanded
transversely, but depressed, and converted into horizontal plates: the neur-
apophyses (ib. n 1-4) are lofty, expanded, and arch over the dilated part of
the neural canal, lodging the great sacral enlargement of the myelon, with
its ventricle. In the young ostrich, before the general anchylosis is completed,
the bases of these neurapophyses are found to cross the interspaces of the
centrums, and to rest equally upon two of those elements. This modifica-
tion was retained throughout life, unobliterated by anchylosis, in the sacrum
of the extinct dinosaurs (Jgwanodon, Megalosaurus, Hyleosaurus), and it
obtains in the dorsal vertebra of the chelonians. The adjoining portions
of the centrums and neurapophysis extend outwards into a short parapo-
physis, which affords an articular surface of three facets for the short pleur-
apophysis. One of these elements is figured iz situ at pl, fig. 27 ; it expands
at its distal end, and coalesces there with the contiguous pleurapophyses :
the long diapophyses (d, d) abut against the inner side, and the ilium applies
itself to the outer side of these expanded and anchylosed ends of the short
sacral ribs. The spinous processes of the sacral vertebrz (s, s) are developed
antero-posteriorly, and soon coalesce into a lofty longitudinal crest of bone.
In the chelonians, the dorsal spines develope horizontal plates from their ex-
tremities, which unite by suture to the similarly united and expanded pleura-
pophyses, forming with them the ‘carapace. The ‘plastron’ is formed of
the flattened and expanded hemal spines, which are divided in the middle
line, and have an intercalated bone (entosternal) between the halves of the
central pieces. Professor Miiller has noticed the sacral pieurapophyses in
the human and other mammalian embryost+.
_ As the segments of the endo-skeleton approach the end of the tail, in the
air-breathing vertebrates, they are usually progressively simplified ; first by
the diminution, coalescence and final loss of the pleurapophyses ; next by the
similar diminution and final removal of the hzmal and neural arches ; and
sometimes also by the coalescence of the remaining central elements, either
into a long osseous style, as in the anourous batrachia, or into a shorter
flattened disc “which has the shape of a ploughshare},” as in many birds.
The coalesced representative of the terminal vertebral centrums is developed
principally from the outer layer of the fibrous eapsule of the primitive noto-
chord. In fishes, however, the seat of the terminal degradation of the verte-
bral column is first and chiefly in the central elements, which, in the homo-
cercals §, are commonly blended together and shortened by absorption, whilst
both neural and hzmal arches remain, with increased vertical extent, and
indicate the number of the metamorphosed or obliterated centrums.
* Hunterian Lectures on Vertebrata, 1846, p. 65, fig. 22.
T ‘‘Selbst am Kreuzbeine mehrere Thiere giebt es noch abgesonderte Querfortsatze oder
Rippenrudimente.”—Anatomie der Myxinoiden, heft i. 1834, p. 239.
t “*La derniére de toutes (des vertébres de la queue), 4 laquelle les pennes sont attachées,
est plus grande et a la forme d’un soc de charrue, ou d’un disque comprimé :—dans le jeune
age, elle est évidemment composée de plusieurs vertébres.”—Cuvier, Lecons d’Anat. Comp.
2d ed. i. p. 208, and “ Lawrence’s Blumenbach’s Comparative Anatomy,” ed. 1827, p. 62.
§ M. Agassiz’ expressive name for the fish with a symmetrical bilobed tail.
264 REPORT—1846.
Summary of modifications of corporal vertebre.—To sum up the kind and
degree of modification to which the several elements of the primary segnients
of the endoskeleton of the trunk are subject, without masking their general
homology, we may commence with the centrum; and first, as to its existence.
It is wanting, as an ossified part, in the atlas of the wombat and koala*, in
which it remains permanently cartilaginous: in the petaurists, kangaroos,
and potoroos, ossification extends from the bases of the neurapophyses into |
this cartilage, but the neural arch or ring long remains interrupted by a me-
dian fissure below. In man the rudimental body of the atlas is sometimes
ossified from two or even three distinct centrest. The centrums at the oppo-
site extremity of the vertebral column in homocercal fishes are rendered by
centripetal shortening and bony confluence fewer in number than the per-
sistent neural and hemal arches of that part. The centrums do not pass
beyond the primitive stage of the notochord in the existing lepidosiren, and
retained the like rudimental state in every fish whose remains have been found
in strata earlier than the permian era in Geology, though the number of
vertebrz is frequently indicated in Devonian and Silurian ichthyolites by the
fossilized neur- and hem-apophyses and their spines}. The individuality of
the centrums is sometimes lost by their mutual coalescence without short-
ening.
‘Although the normal form of the centrum is cylindrical, it may be cubical,
conical, hour-glass shaped, like a longitudinal bar, like a transverse bar, like
a depressed or a compressed plate, like a ploughshare, &c. The co-adapted
terminal surfaces of the centrum may be flat, slightly concave, deeply con-
cave, cupped or conical, concave vertically and convex transversely at one
end and the reverse at the other end§; or the fore-end may be concave and
the hind-end convex||; or the reverse] ; or both ends may be convex**;
or both ends produced into long pointed processes with intervening deep fis-
sures, so as to interlock together by a deeply dentated sutural surfacet+-.
The centrum may be quite detached from its neural arch (atlas of siluroid
and many fishes), and from its hemal arch (atlas of most fishes).
The centrum may develope not only parapophyses but inferior median
exogenous processes, either single, like those of the cervical vertebre of
saurians and ophidians (which in Deirodon scaber perforate the cesophagus,
are capped by dentine, and serve as teeth {{); or double (atlas of Sudis gigas §§
and the lower cervical vertebra of many birds) ; or the fibrous sheath of the
notochord may develope a continuous plate of bone beneath two or more nuclei
of centrums, formed by independent ossification in the body of the notochord ;
these nuclei being partially coherent to the peripheral or cortical plate. The
vertebral centrum often shows the principle of vegetative repetition by its
partial ossification in the form of two or three bony rings, which answer to a
single neural arch (Heptanchus|\\|), or by three osseous discs, one for each
* Art. Marsupialia, Cyclopedia of Anatomy and Physiology, vol. iii. p. 277, fig. 99.
+ Meckel, Archiv fiir Physiol. i. taf. vi. fig. 1.
t See the admirable Monograph by Agassiz, Sur les Poissons Fossiles du Systeme Dé-
vonien, 4to, 1846. § Most birds.
|| Existing saurians and ophidians.
g Extinct saurian called ‘ Streptospondylus ;’ existing Salamandra, Lepidosteus.
** 4th cervical of Emys, Bojanus, Anat. Test. Europ., tab. xiv. fig. 51,4. Ist caudal of
crocodile.
+t Cervicals or anterior trunk-vertebre of Fistularia.
+t Jourdan, cited in Cuvier’s Lecons d’Anat. Comparée, ed. 1835, p. 340, and ‘ Odonto-
graphy,’ p. 179.
§§ Agassiz in Spix, Pisces Brasilienses, 4to, 1829, p. 6, tab. B, fig. 8.
\||| Miller and Agassiz, in Recherches sur les Poissons Fossiles, t. iii. tab. 40°, fig. 1.
ON THE VERTEBRATE SKELETON. 265
articular surface, and a thicker intermediate piece, as in all foetal mammals,
and throughout life in some cetaceans.
With respect to function, the centrum forms the axis of the vertebral
column, and commonly the central bond of union of the peripheral elements
of the vertebra: as a general rule it supports, either immediately or through
the medium of the approximated or conjoined bases of the neurapophyses,
the neural axis (in the trunk called myelon, or spinal marrow, and its mem-
branes); the terminal centrums being usually deprived of this function by
the withdrawal of that axis from them in the course of its centripetal or con-
centrative movement.
The newrapophyses are more constant as osseous or cartilaginous elements
of the vertebrz than the centrums; but they are absent, under both histolo-
gical conditions, at the end of the tail in most air-breathing vertebrates, where
the segments are reduced to their central elements. The neurapophyses lose
their primitive individuality by various kinds and degrees of confluence ; as
e. g. first, of the bases of each pair with their supporting centrum ; secondly,
of the apices of each pair with one another and with the neural spine,—the
lepidosiren affording a rare exception of the persistent individuality of this
element and of each neurapophysis throughout the trunk; thirdly, of two
or more neural arches with one another, as in the neck of some fishes, cetacea,
and armadillos, and in the sacrum of birds and mammals; where they also
often coalesce with the pleurapophyses, as they do in the neck of most mam-
mals and birds. The neurapophyses rarely depart from the form of plates,
either broad or high, or both ; sometimes they are straight, sometimes arched,
sometimes bent ; sometimes by the inward extension of their bases, they form
together a bony ring above the centrum, excluding both that and the spine
from the neural canal. The neurapophyses may develope, as exogenous pro-
cesses, either diapophyses or zygapophyses, and the latter are sometimes
double from both the anterior and posterior borders of the plates ; as e. g. in
the vertebrz of Mugil, in some serpents, and in the lumbar vertebrz of some
mammals. The observed extent of variation of position of the neurapophyses
_ is from the upper surface of their own centrum to above the next intervertebral
space, so as to rest equally on two centrums; or they may be uplifted bodily
from their centrum, and wedged or suspended between the two contiguous
neural arches, as e. g. in the atlas of ephippus and other deep-bodied fishes.
Except in the cartilaginous neurapophyses of the sturgeon, I am not aware
of any instance of the subdivision of this element into two pieces, placed
vertically upon each other. Some plagiostomes show the principle of vegetative
repetition in two or three star-like centres of ossification, side by side, in the
primitive basis of the neurapophysis, but the second of the two cartilaginous
_ plates on each side of the neural canal, coextensive with the single centrum,
in most sharks, which second piece has the form of a wedge with the small
end directed down over the intervertebral space, seems to answer, as Prof.
Miller has suggested, to the intercalary or interneural piece in bony fishes.
The most constant functional relation of the neurapophysis is to protect
the spinal nerve in its exit from the spinal canal, either by a direct perfora-
tion of the neurapophysis (many fishes, and some mammals), by a notch in
the margin, or by the interspace between two neurapophyses. This function
alone is performed, in reference to the nervous system, at the posterior part
of the vertebral column in many animals, where the place of the shortened
_ myelon is occupied by the lengthened roots of the nerves: in the rest of the
trunk the neurapophyses protect also the neural axis. The original relation
_ of each neurapophysis to the segments of that axis is determined by the place
_ of connection of the perforating nerve with the shortened myelon.
1846. T
266 © REPORT—1846.
_'The neural spine commonly retains in the trunk the form indicated by its
name ; but in the atlas of the crocodile, where it is distinct from the neur-.
apophyses, it isa depressed plate. In the thorax and abdomen of chelonians
it becomes still more expanded and flattened, and its borders unite by dentated.
suture to contiguous spines and to the similarly expanded pleurapophyses.
The neural spine is absent in the thin annular cervicals of the mole; it is
unusually developed and forms a thick square columnar mass of bone in the
cervicals of the opossum. It is double in the anterior vertebrze of some
fishes: in the barbel one stands before the other; in the tetrodon they
stand side by side: and various other minor modifications of this peripheral
element might be cited,
The parapophyses of the trunk-vertebre manifest their autogenous cha-
racter in fishes alone; andin most species the character is soon lost, the par-
apophyses becoming confluent with the centrum ; and, in the tail, either with
the pleurapophyses also, or with each other and the hzmal spine, thus comple-
ting the hemal canal (fig. 16). Amongst air-breathing vertebrates the par-
apophyses of the trunk-segments are present only in those species in which
the septum of the heart’s ventricles is complete and imperforate, and here.
they are exogenous and confined to thecervical and anterior thoracic vertebree,
or to the sacrum (as in the ostrich, figs. 15 and 27, p). The parapophyses are
subject to a certain extent of variation as to form: they are either mere
tubercles; or simple, shorter or longer, transverse processes ; or they may take
the form of long plicated laminz (in the tails of some pleuronectidz): they
are longer and broader than the pleurapophyses in the cod-tribe ; and are
sometimes much expanded in the anterior vertebre of fishes, where they
ascend in position, and in the siluroid species above described, coalesce to
iorm a broad outstanding ridge, directed outwards and a little upwards, and
rising as they approach the cranium, where they are joined by close suture to
the paroccipitals.
The normal function of the parapophyses is to give attachment to muscles
and articulation to ribs, and, occasionally, additional strength and fixation to
anchylosed portions of the vertebral column, As a rare and exceptional in-
stance, the expanded and excavated parapophyses of the second and third
vertebra in the genus Cobitis perform an office closely analogous to one of
those of the mastoid in man, since they inclose air-cells brought into com-.
munication with the acoustic labyrinth by a chain of small ossicles : and these
singularly modified rudiments of the swim-bladder seem to have no other func-
tion in the groveling loaches than that in connection with the sense of hearing.
The pleurapophyses are less constant elements than the neurapophyses ;
they exist as free appendages or ‘ floating vertebral ribs’ in the trunk, and
sometimes at the fore-part of the tail, in fishes, serpents, and certain batra-
chians (fig. 28, pl). The atlas has its pleurapophyses in most fishes, but they.
are often detached from their centrum, and sometimes joined to long bony
hzmapophyses, as is well-seen in the Argyrecosus, and other deep-bodied
scomberoids. Ossified heemapophyses are not present in any other vertebra
of the trunk in fishes. In batrachians the pleurapophyses of the single pelvic
vertebra are similarly connected with hamapophyses, and the costal arch is,
there completed.’ In the menopome, the pleurapophysial element of the sacrum,
ib. pl', is ossified from two centres. Such typical vertebrae are more common
in the higher air-breathing classes. Here the pleurapophyses have generally
the long and slender form understood by the word ‘rib ;’ but they expand into
broad plates in the thorax of the apteryx, in the anterior thoracic vertebra of
whales, and more especially in the carapace of chelonians, where they are
joined to each other by suture, and also to the expanded neural spines. These.
*
ON THE VERTEBRATE SKELETON. 267
broad pleurapophyses are occasionally ossified from two centres in the great
land-tortoises of India and the Galapagos isles. The free extremities of the
short cervical pleurapophyses of crocodiles and plesiosaurs are expanded and
produced forwards and backwards, like axe-blades, whence the name of
‘hatchet-bones,’ applied to them prior to the recognition of their true homo-
logy.
"The pleurapophyses are appended sometimes simply to the ends of par-
apophyses ; sometimes to the ends of diapophyses; sometimes by a head and
tubercle to both kinds of transverse processes ; sometimes directly to the
side of the centrum; and sometimes they are shifted backwards over the in-
tervertebral space, and are articulated equally to two centrums (human
thorax), and sometimes to two centrums, to a neurapophysis and to a long
diapophysis, as in the sacrum of the ostrich (fig. 27, pl). In the atlas of
some fishes the pleurapophysis is detached from its centrum, and is suspended,
with its heemapophysis, from the antecedent hzemal arch (scapulo-coracoid).
In some sturgeons the abdominal pleurapophyses are composed of two or
more cartilaginous pieces. I have observed some of the expanded pleurapo-
physes in the great Testudo elephantopus ossified from two centres, and the
resulting divisions continuing distinct but united by suture. The pelvic
pleurapophysis is in two pieces, as a general rule (fig. 28, pl’ attached to
D"); and the lower piece is the seat of that most common and simple kind
of modification, viz. increase of size with change of form from the cylindrical
to a flat bone (as indicated by the dotted line in fig. 27), whereby it comes
into connection with the pleurapophyses of other vertebre besides the proxi-
mal piece of its own; such pleurapophyses having their development stunted
so as not to exceed in size the proximal portion of the pelvic pleurapophysis,
whose expanded distal portion (62) receives the special name of ‘ilium.’ This
bone retains its rib-like shape however in the chelonians, as in the batrachians:
in most species it unites below with two hzmapophyses, called, on account
of their modifications of form and proportions, ‘ischium’ and ‘ pubis.’ The
pleurapophyses defend the hzmal or visceral cavity ; they are the fulcra of
the moving powers which expand and contract such cavity in respiration,
when its walls admit of those movements ; they frequently support ‘ diverging
appendages,’ and give origin to muscles moving such appendages, or acting
upon the vertebral column. In some exceptional cases the pleurapophyses
become, themselves, locomotive organs, as in serpents and the Draco volans.
The hemapophyses, as osseous elements of a vertebra, are less constant than
the pleurapophyses ; although they sometimes exist in segments, e. g. the
lumbar vertebra of certain saurians, and in the case of the ischium, or second
“pelvic heemapophysis, in which the corresponding pleurapophyses are absent,
or short, or anchylosed to the transverse processes. The only true bony
hzmapophyses in the trunk of fishes appear to be those of the atlas, forming
the lower piece of the epicoracoid ; and of the last (?) abdominal vertebra,
forming the ischial or pubic inverted arch supporting the appendages called
‘ventral fins.’ It is at least to the last abdominal vertebra solely that the
homologous arch and appendages are connected, by the medium of the
pleurapophyses (iliac bones) in the batrachians, and it needs but the removal
of the pleurapophysis, or of its second complementary portion (pl! in fig.
*28), to reduce that vertebral segment to the condition which it presents in an
abdorainal fish. The so liberated inferior (hemapophysial) portion of the
pelvic (last abdominal costal) arch is subject, in fishes, to changes of pesition
far more extensive than have been observed in the neurapophyses or pleur-
apophyses of the trunk-vertebra, without however preventing the recognition
of the segment to which such shifted hemapophyses actually and essentially
oe G Wa?
268 REPORT—1846.
belong. The homologous hzmal arch exists in the same free and detached
condition in cetaceans and enaliosaurs ; but in all other air-breathing verte-
brates it is connected with the iliac bones and completes the typical character
of the proper sacral vertebra. The bony hemapophyses of the lumbar vertebrae
are found suspended in the fleshy abdominal walls of certain saurians: but in
the region of the thorax in these and higher vertebrates, the heemapophysis
(fig 15, h) articulates by one end to the pleurapophysis (pl) and by the
other to the hzemal spine (sternal bone, fs) ; or its lower end is attached to a
contiguous hemapophysis ; or it is suspended freely from the pleurapophyses
(as in the ‘ floating ribs» of man and mammals), or it may be joined below
to the sternum, and have its upper end free, as in the seventh dorsal vertebra
of the Ciconia Argala. When the upper end of the hemapophysis articulates
with the pleurapophysis in birds, it is usually by a distinct condyloid joint,
with smooth articular cartilage and a synovial capsule.
Where hemapophyses exist in the tail, they articulate directly to the
under part of the centrum, or to two centrums at the intervertebral space ;
and are either free at the opposite end, as in some caudal vertebre of ser-
pents and in those of the enaliosaurs, or they are confluent with each other
at their distal ends; when each pair of hemapophyses forms the so-called
V-shaped or chevron-bone. The changes of position of that detached ‘ pubic
arch’ or ‘chevron-bone’ which supports the ventral fins in fishes afforded
Linnzeus the characters of the orders ‘ Abdominales,’ ‘ Thoracici,’ and
‘Jugulares’ in the ‘ Systema Naturz’; and its immortal author, in giving the
name ‘ Apodes’ to those fishes in which the ventral fins were absent, con-
cisely indicates his perception of their relation to the hind-legs of batrachia
and the lower limbs of man. If, then, mere change of relative position,
however extensive, failed to conceal the special homology of the detached por-
tion of the pelvic arch and its appendages from the keen-sighted naturalist,
still less ought such a character to blind the philosophic anatomist to the
general homology of such detached vertebral elements, or prevent his tracing
them, wherever he may find them, to the remainder of their proper segment;
especially when its place is so clearly and beautifully indicated, as it is by the
condition of the pelvic arch in the perennibranchiate reptiles (fig. 28).
The function of the hemapophyses is to complete, with or without a hemal
spine, the hemal arch of the vertebral segment ; and, in so far to protect the
hzemal or visceral cavities and support their contents. They give attachment
to the lower or ventral portions of the primary muscular segments ‘myo-
commata’*, called ‘intercostals’ in the thorax, and ‘recti abdominis’ in the
abdomen of the higher vertebrata; and they thus serve as fulcra to the
muscles that expand and contract the abdominal or thoracic-abdominal cavity :
and sometimes more directly aid in these movements by the elasticity resulting
from an arrest in their histological development at the cartilaginous stage, e.g.
in the thorax of most mammals. Hzmapophyses may support or aid in sup-
porting diverging appendages; and in giving attachment to the muscles of
those appendages. The hemapophyses are usually slender, longer, or shorter
simple bones; but are broad and flat, overlapping each other in the thorax
of monotremes: they become broader and shorter in the expanded and fixed
thoracic abdominal bony case of chelonians, and are still broader where they
close the pelvic arch in the plesiosaurs. Inthe abdominal region of these ex-*
tinct saurians and in crocodiles, the freely suspended heemapophyses are com-
pounded of two or more overlapping bony pieces.
* See the description of these segments, usually confounded under the name of the ‘ great
lateral muscle’ or ‘ longitudinal muscles’ in fishes.—Hunterian Lectures on Vertebrata, 8vo,
pp. 163-165.
ON THE VERTEBRATE SKELETON. 269
» The hemal spine is much less constant as to its existence, and is subject
to a much greater range of variety, when present, than is its vertical homo-
type above, which completes the neural arch. Long, slender, and ‘ spinous’
in the tail, the hemal spine is reduced to a short and thick bone, often
flattened, in the thorax of mammals, a series of thirteen such modified spines
forming the so-called ‘sternum’ in the two-toed sloth: the thoracic hemal
spines are few in number, and are expanded and perforated in the whales:
the horizontal extension of this vertebral element is sometimes accompanied
by a median division, or in other words, it is ossified from two lateral centres ;
this is seen in the development of parts of the human sternum: the same vege-
tative character is constant in the broader thoracic hemal spines of birds ;
though, sometimes, as e. g. in the struthionide, ossification extends from the
same lateral centre lengthwise, ¢. e. forwards and backwards, calcifying the
connate cartilaginous homologues of halves of four or five hzemal spines,
before these finally coalesce with their fellows at the median line. In some
other birds, however, there are two or more lateral centres, and usually,
also, a median one, from which the ossification of the keel extends down-
wards, prior to its confluence with the rest of the ‘sternum. In the thorax
of chelonians four hemal spines are established, each by two lateral centres
of ossification, forming four pairs of sternal bones with a ninth ‘ entosternal’
piece between the first and second pairs. ~The ‘ plastron’ is the result of
this extreme development of the hemal spines :—the modified moieties of
which, remaining permanently distinct and united by suture, have received
from Geoffroy St. Hilaire* the convenient special names of ‘ episternals,’
‘hyosternals,’ ‘ hyposternals’ and ‘xiphisternals,’ respectively, as they suc-
ceed each other from before backwards.
The diverging appendages are, as might be expected, of all the elements
of the vertebral segment, the least constant in regard to their existence, and
the subjects of the greatest amount and variety of modification. Simple
slender spines or styles in fishes (fig. 17, aa), simple plates retaining long
their cartilaginous condition in crocodiles, short flat slightly curved pieces in
birds (fig. 15, a a), in some of the lowest species of which, e. g. Aptenodytes,
they become expanded, like their homologues in the crocodile ; such, with
one exception, is the range of the variety of form to which these parts are
subject in the segments of the trunk. But that exception is a remarkable
one: even under its normal ichthyic condition, as a simple style or filament,
the diverging appendage of the insulated heemapophysial portion of the pelvie
arch in the protopterust and lepidosiren{ is composed of many cartilaginous
segments, and projects freely from the surface, carrying with it a smooth
covering of integument. In other fishes similar filaments or jointed rays are
progressively added to the sustaining arch, which cause a progressive expan-
sion of the common investing fold of skin, forming the organ called the
‘ventral fin,’ which is accordingly described by the ichthyologist as having
two rays (Blennius), three rays (Zoarces), up to more than twenty rays, (as
Acipenser in the sturgeons).
When we quit the piscine class we find the diverging appendage of the pel-
. * Du Sternum considerée dans les Oiseaux et dans les Poissons. Anatomie Philoso-
phique, p. 69. pl. 2, fig. 21. Here Geoffroy contends that the parts of the hyoid arch (39,
40 and 43) are the homologues of the modified hzmal spines which he calls episternals, hyo-
sternals and hyposternals in the plastron of the turtle: but these names may well be retained,
that of ‘ hyosternal’ being used in an arbitrary sense, without reference to the hypothesis
which first suggested it.
_.¥ Linn. Trans. vol. xviii. pl. 23, fig. 4, z. Lectures on Vertebrata, p. 79, figs. 27, 66.
~ = Bischoff, op. git. pl. 2, fig. 5, c.
e
270 - REPORT—1846.
vic arch resuming its primitive unity, and with fewer joints than in lepidosiren,
but manifesting the principle of vegetative repetition by a bifurcation of the
distal segments. Such is itsform in the Proteus anguinus and in the Amphi-
uma didactylum : in another species of amphiume, the radiated type is more
strongly marked by the subdivision of the last segment into three rays, the
homology of which with certain of the five terminal rays, called toes or
digits in the human foot, is signified by Cuvier’s specific name ‘ tridactylum’
applied to this species ; the middle segment of the appendage is bifid, the
first one is undivided. In the menopome (fig. 28), the proximal segment
(65) is likewise single, the second segment (66, 67) double, and a mass of carti-
lage (6s) separates this from the last segment which branches into five jointed
rays (cv). In the frog two styliform bones are developed in the position of
the cartilage (6s in fig. 27), forming a fourth segment of the division: they
are replaced by more numerous and shorter ‘bones in higher vertebrates, in
which it will be unnecessary to pursue the metamorphoses of the appendage
as itis adapted for swimming, steering, balancing and anchoring, for explora-
tion, for burrowing, creeping, walking and running, for leaping, seizing;
climbing, or sustaining erect the entire frame of the animal. Its parts under
these endless and extreme modifications have necessarily received special
names: the first segment (65) is the thigh, femur ; the second is the leg, and
its two rays or bones are called-¢bia (66) and fibula (67): the segment (6s)
is called ankle or tarsus, each of its component ossicles having its proper
name ; and the last radiated segment (69) includes the metatarsus and pha-
langes: the segments 6s and eo are termed collectively, the foot, pes*.
The primitive function of the simple diverging appendages (fig. 17, a, a)
of the abdominal vertebre in fishes is closely analogous to that of the more
developed appendage of the pelvic vertebra, viz. to aid in locomotion, as
fulcra to the muscles concerned in that act. In crocodiles and birds they
serve to connect one costal arch with the next arch in succession, associating
them in action or giving fixity and strength to the whole thoracic cage.
Any given appendage might, however, have been the seat of such develop-
ments as convert that of the pelvic arch into a locomotive limb: and the true
insight into the general homology of limbs leads us to recognise many poten-
tial pairs in the typical endo-skeleton. The possible and conceivable modi-
fications of the vertebrate archetype are far from having been exhausted in
the forms that have hitherto been recognised, from the primeeval fishes of
the palzeozoic ocean of this planet up to the present time.
The beneficent Author of all, who has created other revolving orbs, with
relations to the central source of heat and light like our own, may have willed
that these also should be the seat of sentient beings, suited to all the condi-
tions of animal enjoyment existing in such pianets; basking, perhaps, in the
solar beams by day, or disporting in the soft reflected light of their earth’s
satellites by night. The eyes of such creatures, the laws of light being the
same, would doubtless be organized on the same dioptric principles as ours;
and, if the vertebral column should there, as here, have been adopted as the
basis of the higher animal forms, it may be subject to modifications issuing
in forms such as this planet has never witnessed, and which can only be con-
ceived by him who has penetrated the mystery of the vertebrate archetype,
aud recognised the kind and mode and extent of its modifications here.
_ It is, for example, by no means essential to that organic type that it should
be ‘tetrapodal’: although it best accords with the force of attraction and other
* A remarkable example of the extent to which an early or low form of such segment
may be regained by adnormal development in a higher species is given by Kerkringius,
Opera Omnia, 4to. 1717, p. 55, tab. viii. : : : r
ON THE VERTEBRATE SKELETON. 271
conditions of our globe, that not more than two pairs of the latent limbs or
appendages of the vertebral segments should be developed to react, as loco-
motive instruments, upon its waters, its atmosphere and its dry land.
The views of the essential relations of such limbs to the vertebrate type
which suggest these and similar reflections, may not be accepted by all anato-
mists: some may be disposed to regard the parts 62 and 64 in fig. 28 as pecu-
liar superadditions, rather than a reappearance of normal elements completing
the costal or hemal arch of a segment of the endo-skeleton and restoring it
to its typical condition: and, in the same spirit, they may deny the special
homology of the radiated appendage A, with the hinder filamentous fin of
the lepidosiren, and the ventral fins of other fishes, and consequently, will re-
pudiate its general homology as the diverging appendage of such hemal
arch, and its serial homology with the simple diverging appendages of the
thoracic-abdominal vertebra of fishes, crocodiles and birds.
Tam sensible how large a demand is made on the most philosophic faith in
general laws of organization, by seeking acquiescence in the view of the parts
of the hind-limb, so variously and definitely modified for special functions, as
having for their seat the homologues of segments and rays, which are the
result in the first instance of the common course of vegetative repetition of a
single vertebral element—an element under all circumstances compounded
teleogically, and, therefore, essentially one bone.
~ But here I must explain what I mean by ‘ teleological ne Indi-
vidual —— of a skeleton,—what are commonly “called < bones,’—are fre-
quently ‘ compound’ or composed vf the coalescence of several primarily
distinct osseous pieces: In human anatomy every single and distinct mass
of osseous matter entering into the composition of the adult skeleton is called
‘a bone’ ; and Soemmerring, who includes the thirty-two teeth in his enumera-
tion, reckons up from 259 to 264 such bones. He counts the os spheno-
occipitale as a single bone, and also regards, with previous anthropotomists,
the os temporis, the os sacrum, and the os innomiratum, as individual bones ;
the sternum, he says, may include two or three bones, &c*. . But in birds
the os occipitale is not only anchylosed to the sphenoid, but they both very
soon coalesce with the parietals and frontals ; and, in short, the entire cranium
proper consists, according to the above definition, of asingle bone. Blu-
menbach, however, applying the human standard, describes it as composed
of the proper bones of the cranium consolidated, as it were, into a single
piecet. And in the same spirit most modern anthropotomists, influenced by
the comparatively late period at which the sphenoid becomes anchylosed to
the occipital in man, regard them as two essentially distinct bones. In direct
ing our survey downwards in the mammalian scale, we speedily meet with
examples of persistent divisions of bones which are single in man. Thus it
is rare to find the basioccipital confluent with the basisphenoid in mamma-
lian quadrupeds ; and before we quit that class we meet with adults in some
of the marsupial and monotrematous species, for example, in which the supra-
occipital, ‘ pars occipitalis proprie sic dicta,’ of Soemmerring, is distinct from
the condyloid parts, and these from the basilar or cuneiform process of the
os sccipitis: in short, the single occipital bone in wan is four bones in the
opossum or echidna ; and just as the human cranial bones lose their indivis
duality in the bird, so do those of the marsupial lose their individuality in the
ordinary mammalian and human skull. In many mammals we find the
Pterygoid processes of anthropotomy permanently distinct bones; even in
SUPT * De Corporis Humani Fabrica, t. i. p. 6.
+ Manual of Comparative Anatomy, by Lawrence, ed. 1827, p. 56.
272 REPORT— 1846.
birds, where the progress of ossifie confluence is so general and rapid, the
pterygoids and tympanics, which are subordinate processes of other bones in
man, are always independent bones.
In many mammals, the styloid, the auditory, the petrous, and the mastoid
processes remain distinct from the squamous plate of the temporal, through-
out life ; and some of these claim the more to be regarded as distinct bones,
since they obviously belong to different natural groups of bones in the skeleton ;
as the styloid process, for example, to the series of bones forming the hyoi-
dean arch.
The artificial character of that view of the os sacrum, in which this more
or less confluent congeries of modified neural arches is counted as a single
component bone of the skeleton, is sufficiently obvious. The os innominatum
is represented throughout life in most reptiles by three distinct bones, answer-
ing to the iliac, ischial, and pubic portions ir anthropotomy. The sternum
in most quadrupeds consists of one more bone than the number of pairs of
ribs which join it ; thus it includes as many as thirteen distinct bones in the
Bradypus didactylus.
The arbitrary character of the definition of a bone, as ‘any single piece of
osseous matter entering into the composition of the adult skeleton,’ the com-
plex nature of many of such single bones, and the essential individuality of
some of the processes of bone in anthropotomy, are taught by anatomy, pro-
perly so called, which reveals the true natural groups of bones, and the modi-
fications of these which peculiarly characterise the human subject.
It will occur to those who have studied human osteogeny, that the parts of
the single bones of anthropotomy which have been adduced as continuing
permanently distinct in lower animals, are originally distinct in the human
foetus: the occipital bone, for example, is ossified from four separate centres;
the pterygoid processes have distinct centres of ossification ; the styloid, and
the mastoid processes, and the tympanic ring, are separate parts in the foetus.
The constituent vertebra of the sacrum remain longer distinct ; and the ilium,
ischium, and pubes are still later in anchylosing together, to form the ‘ name-
less bone.’
These and the like correspondences between the points of ossification of
the human fcetal skeleton, and the separate bones of the adult skeletons of
inferior animals, are pregnant with interest, and rank among the most stri-
king illustrations of unity of plan in the vertebrate organization.
The multiplication of centres from which the ossification of an ultimately
single bone often proceeds has especially attracted the attention of the philo-
sophical anatomists of the present century with reference to the right or
natural determination of the number of the constituent parts of the verte-
brate skeleton. Geoffroy St. Hilaire, in his memoir on the skull of birds, in
1807, says, “ Ayant imaginé de compter autant d’os qu'il y a de centres d’os-
sification distincts, et ayant essayé de suite cette maniére de faire, jai eu
lieu d’apprécier la justesse de cette idée*.” Cuvier adopted and retained
the same idea to the last. Commenting in the posthumous edition of the
‘Lecons d’Anatomie Comparéet’ on the character of some of the defini-
tions of single bones in anthropotomy, he, also, concludes that, in order to
ascertain the true number of bones in each species, we must descend to the
primitive osseous centres as they are manifested in the foetus. But according
to this rule we should count the humerus as three bones and the femur as four
* Annales du Muséum, t. x. p. 344.
+ Tom. i. 1835, p. 120. “ Mais ces distinctions sont arbitraires, et pour avoir le véritable
nombre des os de chaque espéce, il faut remonter jusqu’aux premiers noyaux osseux tels
qu’ils se montrent dans le foetus,”
ON THE VERTEBRATE 8KELETON. 273
bones, in the human skeleton ; for the ossification of the thigh-bone begins at.
four distinct points, one for the shaft, one for the head, one for the great
trochanter, and one for the distal condyles: such deference, however, to the
judgment of the great Comparative Anatomist has been withheld by the most
devoted of his admirers; whose disinclination to regard these parts and pro-
cesses as distinct bones is justified by the fact that in birds and reptiles the
femur is developed from a single centre.
The rule laid down by the French authorities above-cited fails in its appli-
cation to the difficult question of the nature and number of bones in a skeleton,
because they did not distinguish between those centres of ossification that
have homological relations, and those that have only teleological ones ; 2. e.
between the separate points of ossification of a human bone which typify
vertebral elements, often permanently distinct bones in the lower animals; and
the separate points which, without such signification, facilitate the progress
of osteogeny and have for their obvious final cause the well-being of the grow-
ing animal. The young lamb or foal, for example, can stand on its four legs as
soon as it is born; it uplifts its body from the ground and soon begins to
run and bound along. The shock to the limbs themselves is broken and
diminished at this tender age, by the divisions of the long bones, and by the
interposition of the cushions of cartilage between the diaphyses and epiphy-
ses. And the jar that might affect the pulpy and largely developed brain of
the immature mammal, is further diffused and intercepted by the epiphysial
articular extremities of the bodies of the vertebre.
We thus readily discern a final purpose in the distinct centres of ossifica-
tion of the vertebral bodies and the long bones of the limbs of mammals
which would not apply to the condition of the crawling reptiles. The dini-
nutive brain in these low and slow cold-blooded animals does not demand
such protection against concussion; neither does the mode of locomotion in
the quadruped reptiles render such concussion likely : their limbs sprawl out-
wards and push along the body which commonly sweeps the ground; there-
fore we find no epiphyses at the ends of a distinct shaft in the long bones
of saurians and tortoises. But when the reptile moves by leaps, then the
principle of ossifying the long bone by distinct centres again prevails, and the
extremities of the humeri and femora long remain epiphyses in the frog.
' . A final purpose is no doubt, also, subserved in most of the separate centres
of ossification which relate homologically to permanently distinct bones in
the general vertebrate series ; it has long been recognised in relation to faci-
litating birth in the human fcetus; but some facts will occur to the osteo-
genist, of which the teleological explanation is by no means obvious.
» One sees not, for example, why the process of the scapula which gives at-
tachment to the pectoralis minor, the coraco-brachialis, and the short head of
the biceps should not be developed by continuous ossification from the body
of the blade-bone, like that which forms the spinous process of the same
bone. It is a well-known fact, however, that not only in man, but in all mam-
mals, the coracoid process is ossified from a separate centre. In the mono-
tremes it is not only autogenous, but is as large a bone as in birds and reptiles,
in which it continues a distinct bone throughout life. Here, then, we have
the homological, without a teleological explanation of the separate centre for
the coracoid process in the ossification of the human blade-bone.
This distinction in the nature and relations of such centres is indispen-
sable in the right application of the facts of osteogeny to the determination
_ of the number of essentially distinct bones in any given skeleton.
7
_ All those bones which consist of a coalescence of parts answering to di-
stinct elements of the typical vertebra are ‘homologically compound.’
274 REPORT—1846.
All those bones which represent single vertebral elements are ‘ teleologi-
cally compound,’ when developed from more than one centre, whether such
centres subsequently coalesce, or remain distinct, or even become the subject
of individual adaptive modifications, with special Joints, muscles, &c. for par-
ticular offices.
In the human skeleton, the clavicles, the (thoracic vertebral) ribs, are in-
stances of simple and truly individual bones. The occiput, sphenoid, eth-
moid, temporal, superior maxilla, mandible, hyoid, scapula, the so-called true
vertebrae, the sacrum and coccyx, the sternum, and ossa innominata are
‘homologically’ compound bones.
The two parietals are essentially like the frontal and vomer, one ‘teleologi-
cally’ compound bone : so, likewise, are the two nasals. And, if the view of
the homology of the jointed filamentary skeleton of the rudimental ventral
fin of the lepidosiren with the simple diverging appendages of the costal
arches of the abdominal vertebrz be correct, then is not merely the mam-
malian femur a teleologically compound bone, but the whole skeleton of the
hind-limb from the femur to the distal phalanges inclusive must be regarded
as representing the essentially single vertebral element, here called ‘diverging
appendage, subdivided according to the law of vegetative repetition of centres;
which law is progressively overruled and masked by-the supervention of the
higher law of special modification and adaptation of such vegetative subdivi-
sions to the exigences and habits and sphere of life of the species.
In many animals all the parts of the skeleton of the limbs, and in all ani-
mals some of the parts, are simple bones, in the sense of being developed
from a single centre; but in none can they claim that essentially individual
character which the clavicles and osseous parts of the ribs are entitled to, as
being primary vertebral elements.
To trace the mode and kind and extent of modification of the same ele-
mentary parts of the typical segment throughout a large natural series of
highly organized animals, like the vertebrata ; and to be thus led to appreciate
how, without complete departure from the fundamental type, the species are
adapted to their different offices in creation, brings us, as it were, into the
secret counsels that have directed the organizing forces, and is one of the
legitimate courses of inquiry by which we may be permitted to gain an in-
sight into the law which has governed the successive introduction of ee ;
forms of living beings into this planet.
Vertebre of the Skull—Since it has been found that the bones of the trunk
maintain through every kind and degree of adaptive modification, whether as
‘thorax,’ ‘ carapace’ or ‘sacrum,’ an arrangement into segments in the con-
stitution and relative position of the parts of which the vertebral type has been
universally recognised—let us next examine, without bias, and, if possible,
without reference to or recollection of previous attempts, in the first instance,
whether such type be traceable through the remaining anterior part of the
axis of the endo-skeleton, which, like the thorax and pelvis, has received, on
account of its degree of coalescence and other modifications, the special col-
lective term of ‘ skull ;)—or, whether nature has, in this part of the endo-ske-
leton, so far departed from the pattern on which all the rest is constructed,
that we cannot, without manifest violence to her arrangements, demonstrate
the segmental composition ; or refer, without admitting modifications distinct
in kind as well as degree from those that mark the vertebral character in the
trunk, the constitution of such segments to the vertebral type.
Taking the conical skull of an ordinary osseous fish—that of the cod (Mor-
rhua vulgaris) for example,—if we detach the bones which form its hinder
extremity, or base, and which immediately precede and join the atlas, from
ON THE VERTEBRATE SKELETON. 275
those riext in advance, we have the-circle, or the base bone (1) and arch
(2,3, 4), represented in figure 1, and we also bring away, articulated therewith,
an inferior or inverted arch with its appendages, represented in profile outline
in fig. 5, 50-57: the arrow indicating the course of convergence, and its head
the point of union, of the two flanks or crura, forming the closing point or
crown of such inverted arch.
We have thus removed a segment of the skull, and with as little or even
less violence or disturbance to the other bones, than must have been used in
detaching a similar segment from the thorax or pelvis of a land-animal. If
we compare this cranial segment with the typical vertebra fig. 14, we recog-
nise in the single median bone (1, fig. |) the centrum, by its relative position
and its articular surface for the atlas, which retains, moreover, the concave
form characteristic of the vertebre in the piscine class: in the pair of bones
(2, 2), which articulate with the upper surface of the centrum, protect the
sides of the epencephalon, and are perforated by the ‘ nervi vagi,’ we have the
neurapophyses: in the single symmetrical bone (3) which completes the
arch, and terminates in a crest for the attachment of the uppermost or dorsal
portions of the vertebral muscles continued from the trunk, we have the newral
spine: and in the pair of bones.(4, 4), wedged between this spine and the
neurapophyses, which give attachment to the inferior arch of the segment
(fig. 5, H i), and terminate in a free crest or spine for the attachment of the
upper and lateral portions of the vertebral muscles, we have the parapo-
physes ; for whose elevated position we have been prepared by their gradual
ascent in the anterior vertebrz of the trunk. The rest of this natural segment
has undergone the same kind of modification as the thoracic vertebre present
in higher animals (fig. 15), and which consists in the great expansion of the
hzmal arch, the removal of the hemapophyses (fig. 5, 52) from the centrum
(ib. 1), and the interposition of elongated and deflected plewrapophyses (50, 51):
finally, the great inverted arch, so formed, enconipasses, supports.and protects
the heart, or centre of the hemal axis. The elements of this arch are open
to two interpretations according to the type of figure 15: either 50 may be
pl, 51, h and s2 hs; or 50 and 51 may be a divided (teleologically compound)
pleurapophysis, and 52 an unusually developed heemapophysis : and this latter
conclusion is more agreeable with the character of the vertebral segments of
the trunk in fishes, in which the hemal spines are absent, the hemapophyses,
when ossified, long and sometimes joined together at their lower ends, as é. g:
in the first trunk- vertebra of Argyreiosus vomer, and the pleurapophyses some-
times, as e. g. in the sturgeon, composed of two or more pieces, set end to
end. The condition of the pleurapophysis of the pelvic arch in the meno-
pome (fig. 28, 62, pl), which sustains a radiated appendage (ib. A) of the
_ chemal arch of the occipital vertebra, indicates the true character of the
_ pleurapophysis: and the modifications of this arch in the higher classes will
be found to establish the accuracy of the general homvlogy of the bone 52;
with the hemapophysial element, since the lower extremities of 52 are actu-
ally drawn apart and articulated to a hzemal spine, which completes the arch
_ below in reptiles and birds (fig. 22, Hs). boit |
Even should there be error in assuming the subdivision of the pleurapo-
physes and the absence of the hemal spine, in the particular determination of
the constituent elements of the arch in question, yet the alternative is still
within the recognised limits of the vertebral modifications of the trunk; and
the want of unquestionable proof of the precise elements forms no valid ob-
jection to its general homology as a hemal vertebral arch, expanded and modi-
fied after one or other of the types of those which, in the thorax of the air-
breathing vertebrates, encompass and protect the more backwardly placed
276 REPORT—1846.
centres of the vascular system (heart and lungs) ; according to which types,
for example, it may be either closed below by the meeting of the sternal ribs
one $i or by the intervention of a single or divided sternal bone
hemal spine). And, further, since in fishes, as the lowest class of vertebrata,
the vegetative character of repetition of forms, proportions and composition
in the successive segments of the skeleton prevails in a greater degree than
in any of the higher classes, so we may conclude that this hemal arch pre-
sents, by its articulation with the epencephalic neural arch, its normal position;
and that the whole occipital vertebra here manifests its veritable and typical
character.
As the hemal arches in the trunk of fishes commonly support diverging.
appendages, which project freely outwards and backwards, but are hidden and
buried in the muscular masses to which they give attachment, so the occipital
arch, also, commonly supports its diverging appendages. They are absent
in Gymnothorax and some other Murenide. The appendage is present in
the form of a single multiarticulate filament in the eel-like protopterus* and
lepidosirent ; it is modified by that mode of vegetative repetition which
results in adding to the number of similar filaments directly articulated to
the supporting arch; and is further complicated by the expansion or conflu-
ence of the proximal joints in different degrees as they recede from the sup-
porting arch, so as to constitute definable segments of the appendage}.
Such is the condition of the part in most osseous fishes, and such is shown
in the diagram of the base of the appendage in figure 5 ; where the proximal
segment consists of two broad and flat bones (54 and 55), the next segment of
five narrower and shorter but thicker bones (56), and the last segment of
more numerous bones of the primitive filamentary form and multiarticulate
structure, which bifurcate and radiate as they recede from the centre of at-
tachment.
We may connect the tendency to extreme and variable development in the
peripheral parts of a vertebral segment, with the freedom which is the neces-
sary consequence of their position: they are attached by one end only, they
have not, therefore, that physical restraint to growth which may arise out of
the fettering by both extremities, which characterizes the more central ver-
tebral elements entering into the composition of the neural and hemal arches.
Even in these we find the disposition to luxuriant growth or vegetative sub-
division greatest in the peripheral elements, viz. the neural and hemal spines :
much more, therefore, might it be expected in the less constant, diverging,
and commonly freely projecting appendages of the vertebral arches. Although
here the polarizing forces which tend to shoot out particle upon particle after
the pattern of dendritic corals, plants or crystals, are so controlled by the
antagonizing principle of adaptation, that the radiating growth is always
checked at that stage and guided to that form which is suited to the wants
and required by the mode of life of the species.
Since, however, we are able to retain firmly and with certitude our recog-
nition of the special homology of the diverging appendage of the occipital
hzmal arch, through all its modifications, from the single ray of the lepidosi-
ren to the hundred-fold repetition of the same elements with superadded
dichotomous bifurcations sustaining the enormous pectoral fins of the
broad and flat plagiostomous fishes thence called ‘ rays’ par excellence, so
we can retrace, with equal certitude, the serial homology of this appendage,
when it is so plainly manifested by its simple form as well as connections in
* Linnean Transactions, vol. xviii. pl. 23, fig. 4, w. ;
~ tT Bischoff, Lepidosiren paradora, Ato, pl. 2, fig. 4, ¢.
} Hunterian Lectures on Vertebrata, figs, 27, 40, 41, 42, 43, 75.
ON THE VERTEBRATE SKELETON. 277
the lepidosiren, the amphiuma or the apteryx, with the scarcely more simple
or less-developed appendage of the thoracic abdominal hzmal arches (ribs)
of birds and fishes (figs. 15 and 17, a, a) ; and thus we are led to determine
its general homology, under its manifold forms of fin, fore-limb, wing, or arm,
as the diverging appendage of the hzmal arch of the occipital vertebra.
_ Thenatural and typical vertebral segment above-defined cannot bedetached,
in every fish, hy the mere disjunction of sutures: in the lepidosiren, e. g. the
ossified part of the centrum has coalesced with that of the next segment in
advance and would require to be divided by the saw: the same coalescence
occurs in the human skull, and has led to the definition of the cranial bone,
called ‘os spheno-occipitale*.’ In osseous fishes, either by connation of 5
with 9, fig. 5, or by excessive development of bone in the notochordal capsule
extending forwards from the centrum 5, and producing 9, there results the long
bone (5,9) continuing the series of vertebral centrums forwards, and corre-
sponding in position with two segments or arches above. On the hypothesis
that it represents the central elements of both those arches, it must be divided
artificially, in order to separate that segment of the cranium which next suc-
ceeds the occipital one. And, further, either by a similar coalescence of the
proximal elements of two hemal arches, or by the undue extension of such
element of one of the arches, interposing itself between the next arch and
the rest of the vertebra to which that arch belongs, it happens, that unless the
proximal element or elements in question be artificially divided, as at 28a, 28a,
fig. 5, two hemal arches (H 1 and H 111) would be brought away, with the
neural arch detached by the separation of sutures and the division of the
bone 5,9. If neither that bone, nor 23a were divided, but were, with the
bones in superior connection with them, separated from the bones anteriorly
articulated to them by suture, then we should have the group of bones, in-
cluded by the curved lines marked N u1, N 111, Hut, H 111 in fig. 5. Two
vertebral segments are plainly indicated in this group by the distinct hemal
arches and their appendages, H 11 and H 111; but three pairs of bones, 16, 6
and 10, fig. 5, appear to be in neurapophysial relation with the single and
symmetrical median bone 5,9. If, however, what has been urged in the
chapter on ‘ Special Homology’ (pp. 188-196) respecting the petrosal cha-
racter of 16 be a true interpretation of that bone, then we must eliminate it
from our present inquiry, inasmuch as being a partial ossification of a sense-
capsule (and nature herself removes them, as such, in most fishes), it apper-
tains to.a category of bones (splanchno-skeleton), forming no part of the pro-
per neuro- or endo-skeleton, in which alone we seek for evidence of asegmental
disposition of parts corresponding with the segments of the nervous system.
_ The bony petrosals (is) being removed, let us, then, with the view of ex-
_ amining the composition of the segment of the skull with which the occipi-
tal vertebra was articulated, saw across the bones 5, 9 and 28a, and separate
the bones 6, 7, s from their sutural connections with those in front of them.
In thus obtaining the segment in question, the opponents to the vertebral
theory of the skull are entitled to assert that violence is done to nature by
the sections of the single bones above-cited; the validity of which as an
objection to that theory will be afterwards inquired into. :
It is not, however, absolutely necessary to divide the basal bone 5,9: in
miany osseous fishes a symmetrical bone (fig. 5, 9’) supports the parial bones
10, and stands in the relation of a centrum tothem ; the neural arch or circle
of that segment would not, therefore, be broken by the removal with the
posterior segment of the whole of the bone s, 9. If the corresponding
* See Table I., Soemmerring. if
278 7 - REPORT—1846. me
development from the under part of the centrum of the second cervical ver-
tebra of the siluroid-fish (p. 260) were removed, with that segment, from the
atlas, the atlantal neural arch would still be completed by the rudimental body,
beneath which the ossification from the succeeding vertebrae had extended
itself.
Whether, however, we divide or not the bone 5, 9, those which rest upon
its posterior or basisphenoidal part present, after the removal of the petro-
sals, when viewed from behind, and slightly disarticulated from each other,
the arrangement exhibited in fig. 2. The bones 6,6 support and defend
the lobe of the third ventricle or the mesencephalic segment of the brain ;
they give exit to the trigeminal nerves (¢r), and thus, as well as by their con-
nections with the other bones of the arch, repeat the newrapophysial characters
of the bones 2, 2 in the occipital segment. The bones s,s, by their more ex-
ternal position, by affording an articular surface to the hemal arch (28a,
H 1), and their development of a strong transversely and backwardly pro-
duced process for muscular attachments, obviously repeat the parapophysial
characters of the bones 4, 4 in the occipital vertebra.
' The arch is not completed above in the cod-fish; the bones 7, 7 being se-
parated at the mesial line by the interposition of the produced spine of the
occipital vertebra s, which joins with 1. In some other fishes, however,
e. g. carp and pike, the bones 7,7 do come in contact and join each other by
a ‘sagittal’ ‘suture, thus completing the neural arch. It will afterwards be
seen, by tracing the homologues of these bones in other animals and their
homotypes in other segments, what value may be assigned to the objection to
their general homology as the crown or hemal spine of the mesencephalic
neural arch, founded upon the median division and occasional divarication of
the two halves of no. 7 in osseous fishes. I may so far anticipate the discus-
sion as to remark that, even in the present group of vertebrates, the spine of
the occipital vertebra; (3) is divided by a median suture in the lepidosteus ; so
that the condition of the epencephalic arch in that fish is precisely that of
the mesencephalic arch in the carp. and essentially the same as that in fig. 2,
and in most other osseous fishes. ak
- The remainder of the second or parietal segment of the skull, H 11, repeats the
expanded modification of the hemal arch of the occipital vertebra, and even
approaches nearer to the character of the thoracic vertebre of the higher
animals, by the development of single symmetrical bones at the crown of the
inverted arch. But the principle of vegetative repetition is still more mani-
fested in this arch than in the occipital one. If we regard the posterior half
of. the epitympanic, 2sa, as the proximal piece of the parieto-hemal arch,’
which has coalesced with the corresponding piece of the fronto-hzmal arch,
then the pleurapophysis of the parieto-hzmal arch will consist, in bony fishes,
of two pieces, esa and 3s, like the pleurapophysis of the occipito- haemal arch,
50ands1. Thebones, 39 and 40,represent the hemapophysis of the parieto-hzemal
arch. The two pairs of small bones (41) with the single median anterior (42)
and posterior (43) appendages, represent a still more subdivided spine or key-
bone of this inverted arch. ~
Beneath this mask of multiplication of bony centres, the broad characters:
of the inverted arch suspended to the parapophyses of the parietal vertebra,
as the hemal complement of that natural segment of the skull, stand boldly
Out: it encompasses, sustains and protects the branchial organs—the ana-
logues of lungs—the next great development of the vascular system anterior
to the heart ; and the subdivision of the piers of this expanded arch relates to .
the necessity for a combination of strength, with flexibility and elasticity, in
tlfe execution of the movements producing the respiratory currents.
ON THE VERTEBRATE SKELETON. ‘279
- The correspondence with the scapular, or occipito-hemal arch, is further
carried out by the presence of appendages (44) which freely diverge from it, but
the development of these appendages has not been observed to extend beyond
_ that second phase, marked by vegetative multiplication of the simple ray,
directly attached to the arch itself. The lepidosiren offers the simplest con-
dition of such ‘diverging appendage’ in the single slender bony piece con-
nected with the element 40*. Cuvier und other ichthyologists cite a series
of stages of this kind of development of the hyoidean appendage from a si-
nilar simple beginning up to a 30-fold repetition of the single ray (Zlops);
and the ‘ branchiostegal’ rays have been found in much greater numbers in
certain fossil fishes. Like the ‘ pectoral’ rays, they support a duplicature of
membrane, which plays freely backwards and forwards, reacting upon the
ambient medium, and forming, in short, a cephalic fin, but with its powers
so restricted and adjusted, as to propel the water through the branchial cham-
bers of the fish, instead of driving the fish through the water ; in which latter
action, indeed, the occipital appendages (pectoral fins)in most osseous fishes
can and do perform but a very small share.
If we next proceed to compare the frontal segment, N 111 and H 111, dis-
‘membered as above described from the parietal vertebra, and, by the separa-
tion of the sutures, from the bones terminating the skull anteriorly, we shall
find a neural arch (fig. 3) closely repeating the characters of that of the oc-
cipital vertebra. The centrum is sometimes represented simply by the forward
extension of ossification of the basisphenoid (11), which I regard as the ho-
motype of the ossification of the capsule of the notochord beneath the cen-
trums of the anterior trunk-vertebre in the silurus ; sometimes, also, of a di-
stinct superincumbent symmetrical ossicle (9, fig. 5), answering to the rudi-
mental (central part of the) body of the atlas supported by the inferior bony
plate, inthesilurus. This more complex condition of the centrum of the frontal
vertebra is well-seen in the sword-fish. The bones 10, 10, which directly rest
upono’, when it exists, which defend the sides of the, prosencephalon, and
which are either grooved by the optic nerves, or have tliose nerves perforating
the fibro-cartilaginous membrane close to the margin of the bone (10) from
‘which it is continued, are obviously the newrapophyses. They are, however,
small; inasmuch as the segment of the brain to which they relate is of inferior
size in bony fishes: and they are still smaller in comparison with the spine
-(11) which is enormously expanded, in relation to its accessory functions as
the chief contributor to and protector of the orbits. The bones 12, wedged
between the neurapophyses and spine, affording an articular surface to the
proximal piece of the hemal arch, and developing a transverse process for
muscular attachments, are the parapophyses. ‘The bones (17) have as little
essential connection with the typical neural arch above demonstrated, as the
bones 16, 16” had with the corresponding arch of the parietal vertebra: and
‘their more peculiar form in relation to the ball which they protect, and their
variable histological condition in the vertebrate series, have not only prevented
their ever being mistaken for parts of cranial vertebre, but-have led to the
opposite extreme of excluding them altogether from the bones of the skull,
with which they are as much entitled to rank as the petrosal (16) or the
turbinal (19) ; but always in the category of sense-capsules or ‘ splanchno-
skeletal’ pieces.
_ In regard to the inferior arch of the frontal segment, the subdivision of its
constituent elements, in subserviency to its special functions, is carried to as
great an extent as in that of the parietal segment. I regard the four over-
lapping and closely-connected pieces from the upper joint (2s) to the lower
Set ; * Hunterian Lectures on Vertebrata, p. 79, fig. 27, 37. ny
250 REPORT—1846.
joint (28d) inclusive, as the plewrapophysis: it is not so obvious whether
the bones 20-32 form a subdivided hemapophysis, or whether the terminal
bone (32), forming by symphysis with its fellow the crown of the inverted arch,
may not be the moiety of a mesially divided hemal spine. But the general
character of the inverted arch (H 111), as the hemal complement of the fron-
tal vertebra is unmistakeable, and its serial homology with the succeeding
arches (H 11 and H 1) is fully illustrated in fishes by its supporting diverging
appendages (31-37). These, in the series of fishes, manifest, in as many
permanent arrests, the ehief phases of development that the corresponding
appendages of the occipito-hzmal arch have been described to pass through.
The diverging appendage of the fronto-hemal arch is a single and simple
bony style in the lepidosiren ; it consists of three or four simple rays in the
monk-fish and some other plagiostomes ; it has one ray expanded into a broad
proximal piece in the conger, which sustains a distal segment of the appendage,
one member of which, the ‘subopercular,’ still retains the long and slender,
ray-like form, which is, also, clearly traceable in: the broader but long and
curved ‘opercular’; in the cod, as in most osseous fishes, the parts of the
second segment of the appendage (35, 36, 37, fig. 5) are metamorphosed, like
the proximal one (34), into broad and flat bones. The fin-like fold of inte-
gument, sustained and moved by means of this diverging appendage and its
muscles, reacts upon the surrounding water ; but, like the hyoid-fins, with
which the tympanic or opercular fins are closely connected, they are chiefly
subservient to the creation of the respiratory currents and their direction
through the gill-chambers. The weight of these appendages, and the con-
stant movements in connection with respiration, as well as those which the
hemapophysial portions of the arch, modified in subserviency to nutrition
have to perform, as jaws, explain the necessity of the subdivision of the sup-
porting pedicle into overlapping pieces allowing of a certain elastic yielding
with recoil, and thus diminishing the liability to fracture without affecting,
except by increasing, the strength of the arch. The trochlear joint between
- the two elements of this arch (at 28d and 29) with its cartilage and synovial
sac, repeats the complex structure of the articulation between the vertebral
and sternal portions of the ribs in birds. To the fore-part of the lower piece
(28d) of the pleurapophysis is usually articulated a bone (24) connecting it
with another bone (20) inadvance: the ground for regarding 24 as appertain-
ing to the arch (20, 21 and 22, H 1v) will be explained in the description of
that arch.
There remains, then, in the fish’s skull, to be considered, the group of
bones (N tv, H rv, fig.5) forming its anterior extremity; and we have to in-
quire, whether there can be traced in this easily separable group such a con-
cordance in its formation with the arrangement of the constituents of the
foregoing segments as will justify its being regarded as a natural segment of
the skull, and as still illustrating the type on which all the other segments of
the endoskeleton have been constructed. Fig. 4 gives the same view of the
bones of this group in vertebral relation with the rhinencephala as the views
in figs. 1,2 and 3 do of the bones having a similar relation to the three larger
segments of the brain: we perceive the single and symmetrical bone (13)
forming the basis of the arch, and sustaining the bones 14, 14, which more
immediately support the olfactory ganglicns and transmit their nerves, either
by grooves or foramina, to the olfactory capsules: the key of the arch is
formed by the single and symmetrical bone 15, which is articulated to and
chiefly sustained by the bones 14, 14: but 15 is expanded and deflected
anteriorly so as to rest directly upon 13 and completely obliterate the neural
canal ; the heemal canal being in like manner closed by the approximation of
ON THE VERTEBRATE SKELETON. 281
the hemal spine (22) to the nasal centrum (13), and by the upward develop-
nt of the processes of 22 which join the neural spine (15). Much modifi-
cation was to be expected in the segment which terminates the skeleton
anteriorly ; and yet the typical characters of the neural arch are more com-
pletely preserved here than at the opposite end of the vertebral column. If
the bones 4, s, 12, which I recognise as ‘ parapophyses’ in the cranial
segments 1, I, 111, must be viewed as superadded intercalations for the
special and characteristic expansion of the neural arches of those segments—
normal elements, indeed, of the typical vertebra, but with modified connections
for cranial functions—then the disappearance of their homotypes in the nasal
segment restores its neural arch (fig. 4.) to the more common condition, and we
recognise in 13 the centrum, in 14, 14, the newrapophyses, and in 15 the neural
spine of the nasal vertebra.
_ But the segment to be complete should exhibit a second arch, inverted ; and
we find such arch closed or completed by the symphysis of the bones 22,
fig, 5, and suspended to the sides of the centrum 13 and to the neurapophyses
145 14, by the bones 20, as the piers or crura of the arch ; these bones being
connected to the key-bones 22, by the intermediate bones 21. Now, the
modifications which these elements of the inverted or hzmal arch of the
nasal vertebra have undergone, are, also, much less than might have been
anticipated from the extent to which the segments are modified at the oppo-
site extreme of the endoskeleton. All the normal elements of the hemal
arch, for example, are. retained: 20 is the pleurapophysis, 21 the hemapo-
physis, and 22 the hemal spine, in most fishes divided at the middle line, but
sometimes confluent with its fellow e.g. Diodon. The essential (pleur-
apophysial) part of 20 extends in many fishes (e. g. percoids) like a short
straight rib from its articulation with 13 and 14 to the condyle at its opposite
end to which the hemapophysis 20 is articulated ; but it usually, also, de-
velopes a process from its hinder margin downwards and backwards, which
gives attachment to the diverging appendage of the arch Hiv, The de-
velopment of the other bones of the arch, 21 and 22, outwards, downwards
and backwards, is still more marked in relation to the protractile and retrac-
tile movements of the arch in most osseous fishes; and some anatomists,
influenced by the form and proportions rather than the connections of those
‘bones, have described them as independent parallel arches: but, as such,
they must be regarded as being suspended by their apices or key-stones to
the axis of the skull, and as having their haunches hanging freely downwards
and outwards—a position the reverse of that of the foregoing inferior arches
of the skull and of every typical hemal arch. The reduction of that di-
-vergent development, characteristic of the bones 21 and 22 in fishes, is ef-
fected in a great degree within the limits of the piscine class: already we
_ find one of the spurious arches abrogated in the salmonoid fishes by the short-
ening of 22, and its more direct continuation from 21, which now forms the
larger part of the upper border of the mouth and supports teeth: the con-
fluent maxillaries and premaxillaries send down only a single divergent
process from their point of suspension to the palatine condyle in the plecto-
hig gnathic fishes; and the consolidation of all the elements of the palato-maxillary
arch into its normal unity is effected in the lepidosiren*. The palatines (20)
always form the true bases or suspensory piers of the inverted hemal arch
at their points of attachment to the prefrontals (14) ; the premaxillaries, 22,
_ constitute the true apex or crown at their symphysis or point of confluence,
_ H41v; the approximation of which to the anterior end of the axis of the skull
is rendered possible, in fishes, by the absence of any air-passage or nasal
z * Hunterian Lectures, Vertebrata, p. 81, fig. 29.
_ 1846. U
282 REPORT—1846.
canal. The diverging appendage, sometimes single and anchylosed to the
arch (lepidosiren); sometimes single and detached like a long, narrow bone
(some murenoids); more commonly consists of two bones (23, 24), which
extend outwards, downwards, and backwards from the pleurapophysis (20) ;
but the more constant and better ossified bone of the two, no. 24, articulates
posteriorly with the succeeding pleurapophysis (23) and combines its move-
ments with those of its own arch, just as the diverging appendages of one
thoracic hemal arch in the bird associate the movements of that arch with
those of the next in succession (as in fig. 15, pl, a, pl). The hemapophyses
here, as at the opposite end of the body, begin so far to dissociate themselves
from the pleurapophyses as to articulate also directly with the centrum (13)
as well as with the pleurapophyses. I regard this as a very interesting ap-
proximation to that condition of the typical vertebra which is illustrated by
the diagram (fig. 14), and which is seen in nature in the caudal vertebre of
the crocodiles, enaliosaurs and menopome (fig. 28, H).
From the foregoing analysis it appears, then, that in osseous fishes the
endoskeletal bones of the head are arranged, like those of the trunk, in seg-
ments; that these are four in number, and that they closely conform to the
. character of the typical vertebra. ,
Thus we have four centrums and neural arches : viz.
N 1. Epencephalic arch (figs. 1 and 5, 1, 2, 3, 4);
N 1. Mesencephalic arch (figs. 2 and 5, 5, 6, 7,8);
N 1. Prosencephalie arch (figs. 3 and 5, 9; 10, 11, 12);
N iv. Rhinencephalic arch (figs. 4 and 5, 13, 14, 15).
As a collective name for the sum of these immoveably articulated arches
would be as convenient as the anatomist finds the names ‘sacrum’ and ‘cara-
pace,’ applied to similarly consolidated portions of vertebral segments in the
pelvic and abdominal regions of certain air-breathing vertebrates, that of
‘cranium’ may well be retained for the neural arches of the skull: but it
should be understood to signify, in all animals, the bones 1 to 15 inclusive ;
whereas it has, hitherto, been applied variably in different species; some-
times including sense-capsules and facial bones, intercalated to expand the
walls.of the cavity for a large brain; and more frequently excluding true
cranial bones, those of the rhinencephalic arch, for example, which encompass
as essential a part of the encepbalic chamber, as the sacral vertebre do of the
neural canal at the opposite end of the vertebral axis ; although in both in-
stances the extremities of the neural axis may have been withdrawn, in the
course of its concentrative change and movement, from their original seat.
The hemal arches indicated by the arrows in fig. 5, the heads marking
the point of junction or crown, are,—
H 1. Scapular arch (50-52) ;
H 11. Hyoidean arch (3s—a3) ;.
H ur. Mandibular arch (28-32) ;
H tv. Maxillary arch (20-22).
The diverging appendages of the hemal arches are,—
1. The Pectoral (54-57) ;
2. The Branchiostegal (44) ;
8. The Opercular (34-37) ;
4. The Pterygoid (23-24).
The bones or parts of the splanchno-skeleton which are intercalated with
or attached to the arches of the true vertebral segments, are,—
The Petrosal (16) or ear-capsule, with the otolites, 16";
The Sclerotal (17) or eye-capsule ;
The Turbinal (19) or nose-capsule ;
The Branchial arches ;
ON THE VERTEBRATE SKELETON. 283
.) The Teeth.
_. The bones of the dermo-skeleton are,—
The Supratemporals ;
_. The Supraorbitals ;
. The Suborbitals ;
The Labials.
Such appears to be the natural classification of the parts which constitute
the complex skull of osseous fishes.
As the object of the present report relates chiefly to the endoskeleton, I
have only added the osseous parts of the sense-capsules to the cranial vertebrae
in fig. 5; omitting the branchial arches and dermal bones: the hemal arches
and their appendages are given in diagrammatic outline.
Reptiles—In proceeding with the inquiry into the natural arrangement of
the skull-bones, I have selected from the Zeepétilia the crocodile, as a typical
example of that class, and one most likely to facilitate the inquiry on account
of the characteristic persistence of the primitive cranial sutures.
Pursuing the same mode of investigation as in the case of the fish, let us
disarticulate the hindmost segment of .
the skull and so detach the four bones, Fig. 18.
represented in fig. 18. The dotted ;
circle indicates the points at which
these bones are joined together, in
order to encompass the epencephalon,
or hindmost segment of the brain.
No.1 is the centrum ; 2, 2 are the neur-
apophyses with the coalesced par-
apophyses (4, 4); and 3 is the neural
spine. This element differs but little
in size and shape from the similarly
detached and depressed neural spine
of the atlas of the crocodile. The Bn: ; ;
single convex condyle at the back part _Disstticulated epencephalic such, viewed from
of no. 1 makes that centrum resemble
the posteriorly convex bodies of the
trunk-vertebre in as striking a manner as the repetition of the articular
concavity in the basioccipital of the cod (fig. 1,1) marks its serial homo-
logy with the succeeding vertebral centrums of the same animal. In the
descending process from the under part of the occipital centrum of the
crocodile (fig. 18, 1), we see a second character of the cervical centrums in
that reptile repeated, viz. their inferior exogenous spine. The neurapo-
physes (2,2), like those of the atlas, meet above the neural canal: they give
exit to the vagal and hypoglossal nerves, and protect the sides of the me-
5 dulla oblongata and cerebellum, The neural spine (3) protects the upper
Rn surface of the cerebellum: it is also traversed by tympanic cells, and assists,
with the bones 2, 2, in the formation of the chamber for the internal ear.
The special homology of the outstanding processes (4,4) in the crocodile
and serpent (fig. 10), with the similarly situated but distinct ‘ paroccipital’
bones in the cod, is confirmed by their resuming their independency in the
hinder segment of the skull of the chelonian reptiles; and the occipital neural
_arch of the crocodile is reduced by their confluence with the neurapophyses
to the condition of those of the trunk-vertebre, as composed, viz. of four
instead of six elements. <
The epencephalic arch offers the same simple condition not only in the
ophidians but in most saurians: the chameleons however retain, like the
u2
:
.
ae BX
284 REPORT— 1846.
chelonians, the ichthyic independence of the parapophyses (4, a)... In batra-
chians the epencephalic arch is reduced to the two important elements, the
reurapophyses ; which meet and join each other below as well as above the
foramen magnum, and develope the exogenous zygapophyses, or two occipital
condyles, for articulation with the corresponding processes of the neural arch
of the atlas. The basioccipital, if it exists in batrachians, is rudimental and
confluent with the basisphenoid, and the supraoccipital is in like manner
recognisable only as the posterior border of the hackwardly produced parietal.
The parapophyses are short exogenous processes of the neurapophyses of this
much simplified epencephalic arch in all batrachian reptiles.
‘The chief modification that distinguishes the above-described segment of
the crocodile’s skull from its homologue in the fish, is the absence of an
attached inverted or hemal arch. We recognise, indeed, the special homo-
logues of the piscine constituents of that arch in 50, 51 and 52, fig. 22. The
upper suprascapular piece (50) is however free, disconnected from any seg-
ment, and retains, in connection with the loss of its proximal or cranial
articulations, its cartilaginous state : the scapula (51) is ossified, as is likewise
the coracoid (52), the lower end of which is separated from its fellow by the
interposition of a median, symmetrical, partially ossified piece called ‘epister-
num’ (As). The power of recognising the special homologies of 50, 51, and
52 in the crocodile, with the similarly numbered constituents of the arch H1
in fishes (fig. 5), though masked not only by modifications of form and pro-
portion but even of very substance, as in the case of 50, depends upon the
circumstance of these bones constituting the same essential element of the
archetypal skeleton: for although in the present instance there is superadded
to the adaptive modifications above cited the rarer one of altered connections,
Cuvier does not hesitate to give the same names (suprascapulaire) to 50
and (scapulaire) to 51, in both fish and crocodile: but he did not perceive or
admit that the narrower relations of special homology were a result of, and
necessarily included in, the wider law of general homology. According to
the view of this law here taken, we discern in 50 and 51, fig. 22, a teleologically
compound pleurapophysis, in 52 a hemapophysis, and in hs the hemal
spine, completing the hemal arch.
The general relations of the scapulo-coracoid arch to a hemal or costal
one have been long recognised, but the vertebral segment to which it apper-
tains seems not hitherto to have been suspected, and has certainly not been
satisfactorily determined. Oken, who had observed the free cervical ribs in
a specimen of the Lacerta apoda, Pallas (Pseudopus), deemed them repre-
sentatives of the scapula, and this bone to be, in other animals, the coalesced
homologues of the cervical pleurapophyses*. In no animal are the conditions
for testing this question so favourable and obvious as in the crocodile: not
only do cervical ribs coexist with the scapulo-coracoid arch, but they are of
unusual length and are developed from the atlas as well as from each suc-
ceeding cervical vertebra: we can also trace them beyond the thorax to the
sacrum, and throughout a great part of the caudal region, as the sutures of
the apparently long transverse processes of the coccygeal vertebrae demon-
strate in the young animal; the lumbar pleurapophyses being manifested
at the same period as cartilaginous appendages to the ends of the long dia-
pophyses.
* “ Auch die Scapula nicht ein Knochen, sondern wenigstens eine aus finf Halsrippen
zusammengeflossene Platte ist.”—Programm, &c., 4to, 1807, p. 16. He reproduces the
same idea of the general homology of the scapula in the ‘ Lehrbuch der Natur-philosophie,’
1843, p. 331, § 2381. Carus also regards the scapulo-coracoid arch as the reunion of seve-
ral (at least three) protovertebral arches of the trunk-segments. ‘ Urtheilen des Knochen
nnd Schalen gerustes, fol. px.
See.
a ney
2
Mi
4
:
4
a
“A
:
4
ON THE VERTEBRATE SKELETON. | 285
-“The scapulo-coracoid arch, both elements of which retain the form of
‘strong-and thick vertebral and sternal ribs in the crocodile, is applied in the
skeleton of that animal over the anterior thoracic hemal arches. Viewed
as a more robust heemal arch, it is obviously out of place in reference to the
rest of its vertebral segment. If we seek to determine that segment by the
‘mode in which we restore to their ceutrums the less displaced neural arches
‘in the sacrum of the bird (fig. 27, m 1-7 4), we proceed to examine the verte-
bre before and behind the displaced arch with the view to discover the one
which needs it in order to be made typically complete. Finding no centrum and
neural arch without its pleurapophyses from the scapula to the pelvis, we give
‘up our search in that direction ; and in the opposite direction we find no verte-
“bra without its ribs until we reach the occiput: there we have centrum and
neural arch, with coalesced parapophyses—the elements answering to those
included in the arch N 1, fig. 5—but without the arch H1; which arch
can only be supplied, without destroying the typical completeness of antece-
dent cranial segments, by a restoration of the bones 50-52, to the place which
they naturally occupy in the skeleton of the fish. And since anatomists
“are generally agreed to regard the bones 50-52 in the crocodile (fig. 22)
as specially homologous with those so numbered in the fish (fig. 5), we
must conclude that they are likewise homologous in a higher sense ; that in
fig. 5 the scapulo-coracoid arch is in its natural or typical place, whereas in
the crocodile it has been displaced for a special purpose. Thus, agreeably
with a general principle, we perceive that as the lower vertebrate animal
‘illustrates the closer adhesion to the archetype by the natural articulation of
the scapulo-coracoid arch to the occiput, so the higher vertebrate manifests
the superior influence of the antagonising power of adaptive modification by
the removal of that arch from its proper segment.
The scapula retains the more common cylindrical long and slender rib-
like form of the pleurapophysis in the chelonian reptiles, where, from the
- greater length of the neck, it has retrograded further than in the crocodile
‘from its proper centrum, and is placed not upon, but within, an anterior
thoracic hemal arch, the pleurapophysis of which has, on the other hand,
been expanded like a scapula. 5
If the arguments founded upon the relations of the scapulo-coracoid arch
to the segments of the skeleton in osseous fishes and crocodilians be admitted
“to sustain the conclusion here drawn from them, that arch must be held to
form the hemal complement of the occipital vertebra in all animals. Bojanus,
in illustrating his vertebral theory of the skull by the osteology of the Eimys
. Europea, thus defines the
g J “ VERTEBRA OCCIPITALIS, SIVE CAPITIS PRIMA.
' “Basis occipitis, seu corpus hujus vertebra,
~~ Pars lateralis occipitis, sive arcus,
“Crista occipitalis, processus spinosi loco,
“ Cornu majus hyoidis, coste vertebre occipitalis comparandum *,”
He adds a dotted outline of the hyoid arch to complete the vertebra oc-
cipitalis, in tab. xii. fig. 32, B. 1 of his beautiful Monograph.
Supposing the special homology of the middle cornua of the hyoid of the
chelonian, so represented and compared to ribs by Bojanus, with the stylo-,
epi- and cerato-hyals of the fish (fig. 5, 38, 39,40) to have been correct, which
the metamorphoses of the hyoid and branchial arches in the batrachians dis-
» prove, the singular and highly interesting change of position as well as shape
of the true ceratohyals, during the same metamorphosis, prepares us to expect
_aretrogradation of the hyoid arch in respect to its proper centrum, in the
* Anatome Testudinis Europzz, fol, 1819, p. 44.
286 REPORT—1846. 3
skulls of the air-breathing vertebrates. In the young tadpole the thick car-
tilaginous hyoidean arch * is suspended, as in fishes, from the tympanic pedicle :
the slender hyoidean arch of the mature frog is suspended from the petrosal
capsule +. The mandibular arch has, also, receded ; and the scapular areh
which, at its first appearance, was in close connection with the occiput, further
retrogrades in the progress of the metamorphosis to the place where we find
it in the skeleton of the adult frog.
The argument, therefore, may be summed up as follows. The position of
the neurapophyses in the dorsal vertebra of chelonians and in the sacral ver-
tebrze of dinosaurians and birds, -shows that a change of relative position in
respect of other elements of the same vertebra may be one of the teleological
modifications to which even the most constant and important elements are
subject. Instead of viewing such shifted arches as independent individual parts,
we trace their relation to the stationary elements of the vertebral segments—
the centrums. Thus, commencing, for example, with the anterior of the
sacral vertebre of the ostrich, A in fig. 27, we observe that, besides sup-
porting its own neural arch, it bears a small portion of that of the next ver-
tebra: the third neural arch (” 1) has encroached further upon the centrum
of the vertebra in advance ; and thus, in respect to the neural arch ( 2), if
it were viewed with the centrums, ¢2 and ¢1, upon which it equally rests,
apart from the rest of the sacrum, it would appear to appertain equally to
either, and be referable to the one in preference to the other quite gra-
tuitously. Nevertheless 72 is proved, by the intermediate changes in ante-
cedent neural arches, to belong actually, and in no merely imaginary or trans-
cendental sense, to ¢ 2 altogether, and not to the segment of which ¢ 1 is the
centrum ; and in tracing the modifications of those sacral vertebrae which
follow ¢ 2, we find 2 4 to have regained nearly the whole of its centrum, ¢ 4,
and the normal relations of the elements are quite restored in the sueceeding
vertebra.
Now let us suppose the habits of the species to have required a more
extensive displacement of the arch (7 2) and its appendages: if its formal
characters as a neural arch were still retained beneath the adaptive develop-
ment superadded to the adaptive dislocation, and if the segments before and
behind the centrum ¢ 2 were found complete, and that centrum alone wanting
its neural arch; would the mere degree of modification in respect of relative
position nullify the conclusion that the shifted arch appertained to such in-
complete segment, and forbid that restoration to the typical condition, which
no anatomist, it is presumed, will dispute in the case of m 2, ¢2, fig. 27? No
anthropotomist hesitates in pronouncing the exact vertebra to which the
sixth ribs belong in the human skeleton. But, separate that costal arch
with the two bodies and neural arches of the vertebrae with which it articu-
lates, and to which of them it belonged would be as questionable as in the
instance of the displaced neural arch in the bird’s sacrum. The head of each
rib is applied half to the upper centrum, half ‘to the lower one: the upper
border of the neck of the rib articulates with the upper neural arch, the tu-
bercle with the diapophysis of the lower neural arch. Ifa naturalist, not
conversant with the definitions of human anatomy, were shown this detached
part of the human skeleton and were pressed to determine the proper centrum
and neural arch of the hypothetically displaced costal element, the attempt
might seem to him gratuitous: and to the question, to which of such
centrums the rib exclusively (as to the pre-existing pattern) belonged ? he
* Cuvier, Ossem. Foss. v. pt. ii. pl. 24, fig. 23, a.
+ Ib. fig. 27, a:—an intermediate stage is shown at fig. 25. Dugés and Reichert confirm
and further illustrate this change of position of the hyoidean arch.
i
:
ON THE VERTEBRATE SKELETON. 287
might reply, to neither. And such, doubtless, would be the matter-of-fact
answer most congenial to the character of mind which would limit its views
to the specialities of the ribs as parts independent of any ideal archetype, or
be unable or unwilling to push the consideration of their connections beyond
the purposes apparently subserved thereby. A second anatomist might see
in the more constant articulation of the costal tubercle with the transverse
process, a character which would incline the balance in favour of the vertebra
to which the transverse process belonged. A third anatomist might extend
his comparisons to other ribs and centrums, and finding the lower centrum
obtaining by degrees a greater proportion of the head of the rib, until the
first and last ribs respectively wholly articulated to the centrum answering to
the lower one in the case of the hypothetically detached sixth pair, he would
conclude that such pair of ribs belonged essentially to the lower and not
to the upper supporting centrum, and he would count accordingly such
lower centrum with its neural arch, as the sixth of those vertebrze which are
characterized as supporting ribs. The anthropotomist, in fact, in so counting
and defining the dorsal vertebre and ribs, admits unconsciously perhaps, an
important principle in general homology, which pursued to its legitimate
consequences and further applied, demonstrates that the scapula is the modi-
fied rib of that centrum and neural arch which he calls the ‘ occipital bone,’
and that the change of place which chiefly masks that relation (for a very
elementary acquaintance with comparative anatomy shows how little mere
form and proportion affect the homological characters of bones) differs only
in extent and not in kind from the modification which makes a minor amount
of comparative observation requisite in order to determine the relation of the
shifted sixth 1ib to its proper centrum.
With reference, therefore, to the occipital vertebra of the crocodile, if the
comparatively well-developed and permanently distinct ribs of all the cervical
vertebre prove the scapular arch to belong to none of those segments, and,
if it be wanting to complete the occipital segment, which it actually does
complete in fishes, then the same conclusion must apply to the same arch in
other animals, and we must regard the occipital vertebra of the tortoise as
«completed below by its scapulo-coracoid arch, and, not as Bojanus supposed,
by its hyoidean arch*.
With these views of the general homology of the scapulo-coracoid arch,
the embryologist will observe with less surprise its constant appearance in
the first instance close to the occiput, and its equally constant primitive ver-
‘tical position; however far back it may be subsequently removed, or to
whatever extent it may be rotated, in the same progress to maturity, out of
its original parallel direction with the more normal pleurapophyses.
Returning to.the study of the crocodile’s skull in reference to the verte-
brate archetype, if we proceed to dislocate the next segment in advance of
the occipital, we bring away in connection with the long base-bone, 5 and 9,
fig. 22, the bones connected by the double lines N11, N 111, and by the
* Geoffroy St. Hilaire selected the opercular and subopercular bones to form the inverted
arch of his seventh (occipital) cranial vertebra (Table III. and note 11), and took no account
of the instructive natural connections and relative position of the hyoidean and scapular
varches in fishes. With regard-to the scapular arch, he alludes to its articulation with the
_skull:in the lowest of the vertebrate classes as an ‘ amalgame inattendue’ (Anatomie Philo-
sophique, p..481); and elsewhere describes it as a ‘‘ disposition véritablement trés singuliére,
et que le manque absolu de cou et une combinaison des piéces du sternum avec celles de la
téte pouvoient seules rendre possible.”—Annales du Muséum, ix. p.361. A due appre-
ciation of the law of vegetative uniformity or repetition, and of the ratio of its prevalence
and power to the grade of organization of the species, might have enabled ‘him ‘to discern
the true signification of the connection of the scapular arch in fishes.
288 REPORT—1846.
curved arrows H 11 and Hu. The relations of the superior series of bones
as neural arches to the optic lobes and cerebrum are even less doubtful than
in many fishes, by reason of the much smaller degree of independent ossifi-
cation of the proper capsule of the acoustic labyrinth. Taking, then, the
bones forming the arch N 11, we find them, viewed from behind, to present
the general arrangement shown
in fig. 19. The hinder (basisphe-
noidal) portion of the bone s and
9 forms the centrum, and imme-
diately supports the floor of the
mesencephalon, or lobe of the
third ventricle, being’ excavated
for the pituitary prolongation of
that cavity: it also sends a pro-
cess downwards, repeating, like
the basioccipital, the inferior
exogenous spine of the centrums
of the cervical vertebra. The
bones 6, 6 protecting the sides
of the mesencephalon, and notch-
ed for the transmission of the
trigeminal nerve, manifest the Pie : ; {
neurapop hysia i characters of the rete ae mesencephalic arch, viewed from behind :
segment. As accessory func-
tions they contribute, like the corresponding bones in fishes, to the forma-
tion of the ear-chamber. They have, however, a little retrograded in posi-
tion (see fig. 9), resting below, in part, upon the occipital centrum, and sup-
porting more of the spine of that centrum (3) than of their own (7); which
is, however, formed of a single bone, and in so far manifests more of the
normal character of the element completing the neural arch, as its crown or
key-bone, than does the homologous divided and often divaricated bone in
fishes. This and other analogous facts show that although the lowest ver-
tebrate class adheres most, as a whole, to the archetype, yet that it can be
recognised clearly and unequivocally only by patient study of its modifica-
tions in all classes: for even the lowest have special exigencies arising out
of their sphere of existence calling for modifications of the type which are
not present in other and higher classes. We shall find, indeed, that the con-
nation of the basi- and pre-sphenoids ceases in mammals, and that they only
coalesce in that class, being primitively distinct ; so that the second cranial
centrum (5) may be removed with its neural arch, in the foetal quadruped
(fig. 24) or human subject (25), without doing violence to nature by the use
of the saw. The bones s, s, fig. 19, wedged between 6 and 7, here, also, ma-
nifest more of their parapophysial character than in fishes, inasmuch as they
are excluded from the inner walls of the cranium, whilst they retain and
manifest broadly their characters as outstanding processes for muscular at-
tachment. But, besides affording ligamentous attachment to the hyoid arch
(29, 40), they articulate largely with the proximal element (1s) of the man-
dibular arch, whose backward displacement, in comparison with its more
normal position in the fish’s skull (fig. 5), is as clearly illustrated in the meta-
morphosis of the anourous batrachia, as is that of the hyoidean or scapular
arches.
Referring, then, to the side view of the cranial vertebra of the crocodile
(fig. 22), we see the hemal arch of the second or parietal vertebra in the
hyoid (39, 40, 41) retaining so much of its embryonic dimensions as is required
P
e
‘ON THE VERTEBRATE SKELETON. 289
by ‘its restricted functions, and having no call for progressive growth in sub-
serviency to a branchial respiration. It consists of a ligamentous stylohyal,
its plewrapophysis, retaining the same primitive histological condition which
obstructs the ordinary recognition of the same elements of the lumbar hemal
arches. The hemopophyses and hemal spine are, however, here as there,
more advanced in respect of their tissue. The hemapophysis is ossified like
the so-called ‘abdominal ribs,’ and usually, like them, consists of two portions,
having the special names of epihyal (39) and ceratohyal (40): the hemal
spine (41) retains its cartilaginous state like its homotypes in the abdomen:
there'they get the special name of ‘ linea alba’ or abdominal sternum, here
of * basihyal.’ With respect to formal modification, this element is chiefly
remarkable in the crocodile for its broad expanse: it sustains the ascending
valvular ridge at the base of the tongue, which, applying itself against the
descending ‘ palatum molle,’ constitutes an effectual barrier against the entry
of water into the glottis from the mouth, whilst the crocodile is engaged in
overcoming the struggles of a submerged and drowning prey.
There being no need of diverging appendages from the hyoidean arch in
‘the crocodile, brauchiostegal rays are not developed. The scapular arch is
similarly simplified in Anguts and other serpentiform lizards ; but, to those
who recognise its true homology, its presence without a trace of its appen-
dages, the fore-limbs, will create no more surprise, than the presence of the
hyoidean arch without the branchiostegal fins or of the mandibular arch without
the opercular fins.
On removing the neural arch of the parietal vertebra, with or without the
section of the connate centrum (5), the bones completing, with the part (9),
the corresponding arch of the frontal vertebra present the general arrange-
ment shown in fig. 20.°
The compressed produced
bone, 9, shown in natural con-
nection with the bone 10 in
fig. 9, notwithstanding its mo-
dified form, presents all the
essential characters of the cen-
trum of the arch: although it
may have been developed ex-
clusively from the capsule of
the notochord, like the coa-
leseed inferior parts of the cer-
vical centrums in the silurus:
there is no distinct ossicle an-
swering to the central part of
the centrum of the frontal ver-
tebra, likeo', fig.5,in certain
bony fishes. On the other hand,
awefindthe neurapophysial cha-
racters of the orbito-sphenoids
(10, 10) more largely and typi-
cally manifested in the croco-
dile: they are smoothly excavated within by the sides of the prosencephalon :
they dismiss the great special-sense nerves of the eye by the notch (fig. 9, op),
and the motor nerves by the notch s: they show, however, the same ten-
dency to change of position as the succeeding neurapophyses; for though
Disarticulated prosencephalie arch, viewed from
behind: Crocodile.
_ they support a greater proportion of their proper spine (11), they also sup-
port part of the succeeding spine (7), and rest below in part upon the pa-
290 REPORT—1846.
rietal centrum (5). The newral spine of the frontal vertebra (11) retains its
normal character as a single symmetrical bone, like the parietal spine, which
it partly overlaps. It is much developed longitudinally, but more in the
anterior, and less in the lateral direction than in most fishes,
One cannot contemplate the relative position of the frontal to the parietal
and of the parietal to the supraoccipital, which is overlapped by the parietal
and itself overlaps the flattened spine of the atlas, without a conviction of the
serial homology of these single, median, imbricated bones, all completing
arches above the neural axis, and each permanently distinct from tie piers
or haunches of the arch of which it forms the key-stone. In like manner
the serial homology of those piers or neurapophyses, viz. the lamine of
the atlas, the exoccipitals, the alisphenoids and the orbitosphenoids, is equally
unmistakeable. Nor can we close our eyes to the same serial relationship
of the postfrontals (fig. 20, 12, 12) as parapophyses of their vertebra, with
the mastoids (s) and the coalesced paroccipitals (4). The frontal parapo-
physis, 12, is wedged between the back part of the spine, 11, and the neur-
apophysis, 10: its outward process extends backwards and joins the next
parapophysis (s); but, notwithstanding the retrogradation of the mandi-
bular arch, it still receives a small part of its own plewrapophysial element
(28). This element now manifests its typical unity: vegetative subdivision,
much reduced in the batrachian reptiles, no more prevails in the develop-
ment of the frontal pleurapophysis in any higher vertebrate. The serpents
exhibit this element under the common form of a rib; longer, indeed, than
are any of the pleurapophyses in the batrachian order; but it has so far
retreated in serpents as to be exclusively attached to the parietal parapo-
physis, which is remarkably elongated and produced backwards, and sus-
pends the long, slender, straight and simple frontal pleurapophysis (tympanic
pedicle) vertically from its posterior extremity. In lacertians no. 2s is ver-
tically suspended from no. s, and, commonly also, from no. 27, which is con-
tinued from the backwardly produced parapophysis of the frontal vertebra
(12) to that of the parietal vertebra (s) in most of this division of the Cu-
vierian order Sauria. In chelonians and crocodilians the diverging appen-
dage of the maxillary arch (27) descends and applies itself to a large propor-
tion of no. 2s, down to its lower articular end, and contributes to fix and
strengthen that bone, as well as the modified costal arch from which it di-
verges.
The condition of the shortening, expansion and fixation of the frontal
pleurapophysis in crocodiles and chelonians is exemplified in the uses to
which the modified heemapophyses, completing that' costal arch, are put.
Tortoises crop the grass by the application of the trenchant horny plates of
the under to those of the upper jaw: turtles equally need a fixed suspensory
joint of the under jaw in the act of biting and dividing the tough sea-weeds.
Crocodiles have the frontal hemapophyses (mandibular rami) unusually
long; supporting numerous large laniary teeth, and requiring a fixed and
firm point of suspension in the violent actions to which they are put in re-
taining, and overcoming the struggles of their prey.
The teleological complication of the lower or distal elements of the arch
in question (29-32, fig. 22) is carried further than in fishes: there was more
need, in fact, for a combination of the greatest elasticity and strength with
the least weight of bone* in the frontal hamapophysis of the crocodile than
in the frontal pleurapophysis of the fish (2s a—2s d, fig. 5).
There, lastly, remain then in the skull of the crocodile the bones inter-
* Conybeare, Geol. Trans. 1821, p. 565. Buckland, Bridgewater Treatise, 1836, vol. i.
p. 176. This author well illustrates the final purpose of the subdivision of the mandibular
“cephalic prolongations traversing
“spine of the nasal vertebra was
‘cies of alligator I have observed
ON THE VERTEBRATE SKELETON. 291
‘sected by the lines N rv and the arrow H rv, with those numbered 26, 27,
and 73, and we have to inquire whether through all the modifications which
their extreme position subjects them to, we can still trace any evidence of their
arrangement according to the vertebrate type.
A long and slender symmetrical grooved bone, like the ossified inferior
half of the capsule of a notochord, is continued forwards from the centrum
of the foregoing vertebra, and stands in the relation of a cenérum (13) to the
vertical plates of the bones 14, which expand as they rise into the broad and
thick triangular plates with an ex- :
posed horizontal superior surface. Fic. 21
The arch of which these form the My Sar
piers, and to the anterior rhinen-
which arch they stand in the re-
lation of neuwrapophyses, is com-
pleted by the two bones(13): which
I, therefore, regard as a divided
neural spine. In fishes we have
seen that the corresponding ele-
ment of the parietal vertebra was
similarly divided, whilst the neural
single: in the crocodile the re-
verse conditions prevail. In a spe-
the bone 13 continued further for-
ward, expanded, and divided at the
middle line, the two divisionsform-
ing a small disc on the bony palate.
The centrum of the nasal vertebra
‘a divid ed longitudinally ue the ane Disarticulated rhinencephalic arch, with the anchylosed
‘dian line in batrachians, ophidians, pterygoids (24) viewed from behind : Crocodile.
and most lacertians; it is single in
‘chelonians, but retains its carti-
Jaginous ‘state in some species (Emys expansa, e.g.). The neurapophyses
(14, 14) transmit the olfactory nerves in all reptiles; but the ganglions are
usually withdrawn backwards into the prosencephalic neural arch, leaving
ramus in the recent and extinct saurians by pointing out the similarity of the structure to
that adopted in binding together several parallel plates of elastic wood, or steel, to make a
cross-bow; and also in setting together thin plates of steel in the springs of carriages. Dr.
Buckland-adds, ‘Those who have witnessed the shock given to the head of a crocodile by
the act of snapping together ‘its thin long jaws, must have seen how liable to fracture the
lower jaw would be, were it composed of one bone‘only on each side.”’—Jb. p. 177. The
same reasoning applies to the composite condition of the long tympanic pedicle in fishes.
In each case the splicing and bracing together of thin flat bones of unequal length and of
varying thickness affords compensation for the weakness and risk of fracture that’ would other-
wise have attended the elongation of the snout. Inthe abdomen of the crocodile and plesi-
osaur the analogous composition of the hemapophyses (abdominal ribs) allows of a slight
change of length in the expansion and contraction of the walls of that cavity: and since
amphibious reptiles, when on land, rest the whole weight of the abdomen directly upon the
ground, the necessity of the modification for diminishing liability to fracture further appears.
‘But what we are here ‘chiefly concerned in is the evidence that ‘the general homology of
elementary:parts of a natural segment is not affected by the modification of teleological
composition of such parts. What happens to the hemapopbysial or inferior elements of
the inverted arch in the abdominal segments of the crocodile also affects the same elements
of a cranial hemal arch; and the subdivision of the pleurapophyses of the trunk in the
“stutgeon is repeated in the same elements of the cranial vertebrz in osseous fishes.
292 REPORT—1846.
only the nerve-trunks to be protected by the nasal neurapophyses. These
are, therefore, more approximated, and the antericr termination of the neural
canal is much contracted; and, in the tailless batrachia, the nasal neur- ’
apophyses coalesce together.
We recognise in that element (20) of the fourth or foremost inverted arch
of the crocodile’s skull, which is in connection with the body (vomer, 13) and
descending plates of the neurapophyses (prefrontals, 14) of the nasal vertebra,
the proximal or pleurapophysial element of such arch; and the same repe-
tition of the characteristic connections of the bone, 20, which enabled Cuvier
and Geoffroy to recognise its special homology with the palatine bone in the
fish, establishes its claim to be equally regarded in the crocodile as the pleur-
apophysis of its vertebral segment; although it now affords but a partial at-
tachment to the bone 21, which forms the next element of the inverted arch.
This bone, the hemapophysis, has undergone a striking change in its propor-
tions by development both in length and breadth: it is connected not only with
no. 20 behind and with no. 22 before, but with the elongated spine, no. 15, of its
own vertebra, and with the lacrymals, 73, above ; with its fellow of the opposite
side below, and with a well-developed proximal element, no. 26, of a strong
diverging appendage behind. The hemal spine, no. 22, is divided, and the
arch is completed by the symphysial junction of the two halves at Hiv. The
nasal aperture or entry to the air-passages forms the span or area of the
much-modified inverted arch constituting the upper jaw of the crocodile.
The two proximal elements of the arch, nos. 20 and 21, continue to send
outwards and backwards exogenous diverging processes; but they consti-
tute a smaller proportion of the bones than in fishes, and both processes di-
rectly support distinct bones representing the diverging appendage of the
arch, and serving to fix and attach it to the succeeding arch. The pleurapo-
physial appendage (pterygoid, 24) soon coalesces, however, with its fellow
and with the centrum of its own vertebra (vomer, 13), and then expands to
unite by a broad sutural surface with the coalesced centrums of the frontal
and parietal vertebre (9 and 5). A second osseous piece (ectopterygoid,
24’) diverges from the pleurapophysis external to the preceding and attaches
it to the hemapophysis, to the heamapophysial appendage, and to the par-
apophysis of the frontal vertebra. The strong diverging ray from the hem-
apophysis is teleologically subdivided into nos. 26 (malar) and 27 (squamosal),
and firmly attaches the maxillary arch to the pleurapophysis (28) of the man-
dibular one.
In the chelonian reptiles the modifications of the nasal segment of the
skull adhere pretty closely to the type of those in the crocodile; the centrum
is more independent and better developed, but the divisions of the neural
spine have coalesced with their neurapophyses: the diverging appendages,
a6 and 27, are usually developed into broad and flat bones. In many lizards
we find the nasal centrum divided but the neural spine single: the hemal
spine is, also, single, as a general rule, and sends upwards and backwards a
process to join the neural spine, divide the area of the hemal canal, and
terminate the vertebral series anteriorly. The hemapophysial diverging ap-
pendage commonly resumes its long and slender ray-like proportions, and joins
the parapophyses of both frontal and parietal vertebre as well as the prox-
imal end of the pleurapophysis of the mandibular arch. In serpents both
divisions of this appendage are absent (indicating the inferior character of
the bones 26 and 27 in general homology), but the two parts of the pleurapo-
physial appendage, 21 and 24', are retained and serve as levers in the move-
ments of the maxillary arch. The spine of that hemal arch is single, and
commonly united only by lax and elastic ligaments with the hemapophyses,
Se
ernst
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ON THE VERTEBRATE SKELETON. 293
which may be divaricated like the halves of the mandibular arch, so as to
widen the mouth laterally ; and this free suspension and incomplete closure
of the principal costal arches of the cranium in serpents repeats in an inter-
esting manner the characteristic free and open condition of all the costal arches
of their trunk. In the genus Tythlops the diverging appendage of the
palato-maxillary arch is reduced to the primitive condition of a long and
slender ray. In anourous batrachians a long and slender backwardly pro-
duced exogenous process of the hzmapophysis (maxillary) joins a shorter
advancing exogenous process of the distal division of the next pleurapo-
physis (tympanic): but in the tailed species the maxillary arch is fixed only
by a broad (pterygoid) appendage; and both maxillary and premaxillary retain
only their essential connections as forming the inferior arch of their segment.
In the proteus and siren the pleurapophysis (maxillary) is almost obsolete.
The bones nos. 24, 24', 26 and 27, being shown to be the least constant
members of the group forming the nasal segment, and to form by their posi-
tion and direction, the diverging appendages of the hzmal arch H tv, there
remains in the skull of the crocodile only the bone 73, which by its position
in front of the orbit and its relation to the lacrymal duct, is to be referred
like the great anterior suborbital mucous bone in fishes to the dermal skele-
ton. In like manner the palpebral or supra-orbital scale-bones are to be ex-
cluded from the category of the pieces of the endoskeleton. The small and
inconstant ossifications in the capsule of the organ of smell, together with the
scarcely ossified sclerotals (17), the small petrosal, is, and the columelliform
stapes, 16, are intercalated portions of sense-capsules and appendages re-
ferable to the system of the splanchnoskeleton.
Thus the endoskeletalsystem of bones of the head of the crocodile are natu-
rally arranged in four segments, each composed of a centrum with a neural
and a hemal arch. The hemal arches have been subjected, as in the trunk,
to most modification ; that of the occipital vertebra having been displaced;
that of the parietal vertebra detached from its segment and arrested in its
development ; whilst that of the frontal vertebra is articulated in a very small
proportion to the parapophysis of its own segment, but chiefly to that of the
parietal segment, with paroccipital connections also; it is immensely de-
veloped, the hemapophysial portion being the chief seat of extension. The
heemal arch of the nasal segment is also very large, but shows as much
excess of development in breadth as that of the frontal vertebra in length.
‘The diverging appendage is more complex than in fishes: one piece indeed,
no. 25, fig. 5, is absent, but three others, 24’, 26 and 27, have been superadded.
The diverging appendages of the frontal and parietal vertebree cease to be
developed in every class above that of fishes ; but that of the occipital hemal
arch, though it no longer shows the luxuriant profusion of rays that distin- ~
guishes it in fishes, begins to assume a more fixed and definite character with
more special powers and independent movements of its constituent parts.
The first segment (53), doubtfully and obscurely recognizable in any fish, is
henceforth a constant and important bone, and is always single: the next
segment consists as exclusively of two bones, connate, indeed, in batra-
chians: the distal segment presents two jointed rays (digits) in the Amphi-
‘uma didactylum ; three rays in Amph. tridactylum and the proteus and four
‘rays in the Siren lacertina ; it branched into as many as nine rays in the ex-
tinct ichthyosaurs ; but they never exceed five in the existing saurians, which
number is presented by this appendage in the crocodile (57, fig. 22.)
Birds.—The cranium of the bird offers the extremest instance of a homo-
logically compound bone, and its development the clearest evidence of that
principle of unity of composition which lies at the bottom of all the modifica-
294 REPORT—1846.
tions of the cephalic division of the vertebrate endoskeleton. Although, as a
general rule, the separate cranial bones can be discerned only at a very early
period, yet in those birds in which the power of flight is abrogated the indi-
cations of the primitive centres of ossification endure longer, and in the
species here selected for the illustration of the cranial segments (fig. 23) the
constituent bones of the skull, though figured of their natural size, have, with
the exception of the basioccipital, 1, and basisphenoid, 3, and the two bones,
6 and s, which coalesce with the petrosal, 16, been separated by maceration
merely. I may remark, however, that in all birds, certain bones, which
coalesce with others in the cranium of most mammals, always retain their
primitive individuality ; the tympanic (2s) and the pterygoid (21) for ex-
ample.
The hindmost segment of the cranium (N 1, fig. 23) so closely repeats the
characters of the epencephalic neural arch of the crocodile (fig. 18), as to
render a separate and full view of it unnecessary for the illustration of its
vertebral character. The basioccipital (1) still developes the major part of
the single articular condyle, and sends down a process, more marked in the
struthious genera, and especially the dinornis, than in most other birds: in
all respects this primitively distinct bone retains the character of the centrum
of its vertebra.
The exoccipitals, 12, contributing somewhat more to the occipital condyle
than in the crocodile, develope, as in that reptile, the paroccipital (24) as an
outstanding exogenous ridge or process: but it is lower in position than in
the crocodile: the proper newrapophysial characters of no. 2 are fully main-
tained. The supraoccipital (3) now begins to manifest more strongly the
flattening and development in breadth, by which the spinous elements lose
the formal character from which their name originated, and are converted
from long into flat bones. We saw the first step in this most common of the
changes to which one and the same endoskeletal element is subject, in the
detached neural spine of the atlas of the crocodile: that of the occipital
vertebra of the same animal presented another stage in the metamorphosis:
we have a third degree in the bird, and the extreme of expansion is attained
in the human subject (fig. 25, 3), where the spine is sometimes developed,
like that of the parietal vertebra, from two centres. But the arrested steps
in this strange change of form and proportion demonstrate the essential
nature of the part, as the neural arch, whilst the constancy of the characters
of connexion is shown by this crown of the arch of the occipital vertebra
having the exoccipitals as its piers or haunches from the fish to the human
subject. It always protects the cerebellum; is absent in the frog where this
organ is a mere rudiment; and is present in the crocodile in the ratio of
the superior size of the cerebellum. The further development of the cere-
bellum is the condition of the superior breadth of the spine or crown of
the epencephalic arch in the bird.
The arguments that determined the nature and displacement of the hemal
arch of the occipital vertebra in the crocodile apply with equal force to that
in the bird. The extent of the displacement, it is true, has been greater:
not seven, but seven-and-twenty vertebre may intervene between the place
of the scapulo-coracoid arch and the remainder of its proper segment con-
stituting the occipital region of the simple cranial box in the bird. But this
difference of extent ought no more to mask the real relationship of such
costal arch to its centrum, than the degree of development of the spine of
the: occipital vertebra affects the general homology of that element.
In the ostrich, and other struthious birds, the hemal arch of the occipital
vertebra has retained much of its embryonic proportions. The pleurapo-
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ON THE VERTEBRATE SKELETON. 295
physial part (51) has, also, retained its slender rib-like form* ; it has coalesced
with the hemapophysis (sz), and the inverted arch is completed, as in the
crocodile, by a hzemal spine, as much modified in form by flattening and ex-
pansion as is the neural spine represented by the supraoccipital (3). The
diverging appendage of the occipito-hemal arch also retains much of its
primitive simple character: a long and slender bone (53) supports two rays
(4, 55), and there is an attempt at three at 57, of which one is short, atrophied
and anchylosed to the rest. In the two small bones (s6, 56) interposed be-
tween this and the preceding segment, we recognise the special homologues
of the carpal series in the crocodile and fish: in 51 we have the ulna, in 55
the radius, in 53 the humerus, in 57 the metacarpus ; in d 3 and da the rudi-
ments of the digits so numbered in the crocodile (fig. 22) and the mammal
(fig. 24). The evidences of the unity of plan in the construction of the
scapular limb, whether it be an arm with the prehensile hand, a hoofed fore-
leg, a wing, or a fin, are admitted by all; the same scapula, humerus, anti-
brachial, carpal, metacarpal and phalangial bones are readily recognised by the
tyro in comparative osteology in the ape, the horse, the whale, the bird, the
tortoise and the crocodile. The beautiful simplicity of the fundamental basis
of all these adaptations of structure is descanted upon in all our popular
teleological treatises. But the higher law governing the existence of these
special homologies has attracted little attention in this country. Yet the
inquiry into that more general principle of conformity to type according to
which it has pleased the Creator of organic forms to restrict the manifesta-
tions of the variety of proportion and shape and substance and even relative
position of the limbs requisite for the various tasks assigned to the vertebrate
species, is one that by no means transcends the scope of the comparative
anatomist. And the conclusion to which my comparisons have conducted
me is, that one and the same element, viz. the diverging appendage of the
occipital vertebra, forms the seat or substratum of all the adaptive modifica-
tions of the’ part called ‘anterior’ or ‘ superior extremity.’
The second segment of the skull has for its central element a bone (fig.
23, 5), which in the bird, as in other ovipara, is connate with that (9) which
stands in the same relation to the third cranial segment; the proof of the
natural distinction of these segments is given by the neural, N 11, N 111,
and hemal, H 11, H 111, arches. Probably the circumstance of the bodies
of those vertebré being formed by ossifications of the fibrous capsule of the
‘notochord, representing the external or cortical parts only of such centrums,
may be the condition, or a favourable physical cause of such connation.
The neural arch of the parietal vertebra retains the same characters which
it first manifested in fishes. Besides the neuwrapophyses (6) impressed by the
mesencephalic ganglia and transmitting the trigeminal nerves, besides the
vastly expanded and again, asin fishes, divided neural spine (7), the parapo-
physis (a) is independently developed. It is of large proportional size ; and,
owing to the raised dome of the neural arch, is relatively lower in position
than in the crocodile; it sends downwards and outwards an unusually
long ‘mastoid’ process, and forms a large proportion of the outer wall of
the chamber of the internal ear with the bony capsule of which it speedily
coalesces. :
The hzmal arch of the parietal vertebra (H 11) is more reduced than in
the crocodile, and owes much of its apparently typical character to the re-
tention of the thyrohyals (46, 47) borrowed from the branchial arches of the
* The very common modification of form which this element undergoes in becoming ex-
panded into the broad scapula of man and other mammalia, appears to have influenced Oken
in his idea of that bone being the homologue of a congeries of ribs,
296 REPORT—1846.
visceral system, which are feebly and transitorily manifested in the embryo
bird. These spurious cornua project freely or are freely suspended, and are
the subjects of singular and excessive development, as has been exemplified
in the chapter on Special Homology. -
The bones (10) of the third neural arch protect a smaller proportion of the
prosencephalon than in the crocodile, but maintain their newrapophysial rela-
tion to it and to the optic nerves: the neural spines (11) cover a larger proportion
of the hemispheres, and, with their homotypes (7), exhibit a marked increase
of development in conformity with that of the cerebral centres protected by
their respective arches. The parapophysis of the frontal vertebra (12) is
relatively smaller in the bird than in the cold-blooded vertebrates, and is
rarely ossified from an independent centre ; but I have seen this in the emeu,
and it appears to have been constantly an autogenous element in the dinornis.
The hemal arch of the frontal vertebra has been transferred backwards to
the parietal one; its plewrapophysis (28), which is simple, as in the crocodile,
articulating exclusively with the parietal parapophysis (s), though this in
some birds unites with that of the frontal vertebra. In the ycung ostrich
and many other birds traces of the composite character of the hemapophysis
are long extant; and bear obviously a homological relation to the teleologi-
cally compound character of the element in the crocodile: for the pieces,
nos. 29, 29/, 30/ and 31 ultimately, and in most birds early, coalesce
with each other and with the hemal spine (32), the halves of which are con-
fluent at the symphysis.
The centrum (13) of the nasal vertebra is always single, and, when it does
not remain distinct, coalesces with the neurapophyses, 14, and pleurapophyses,
20, of its own segment, and sometimes, also, with the rostral production of the
frontal centrum (9): it is elongated and pointed at its free termination, and
deeply grooved above where it receives the above-named rostrum ; indicating
by both its form and position that it owes its existence, as bone, to the ossi-
fication of the outer capsule of the anterior end of the notochord. In the
ostrich the long presphenoidal rostrum intervenes between the vomer (13)
and prefrontals (14). These latter bones manifest, however, as has been
shown in the paragraph on their special homology (p. 214), all the essential
neurapophysial relations to the rhinencephalon and olfactory nerves: but
they early coalesce together, or are connate, as in the tailless batrachians.
The neural spine (15) is divided along the middle line ; but in most birds the
suture becomes obliterated and the spine coalesces with its neurapophyses,
with the frontal spine and with those parts of the hemal arch of the nasal
vertebra with which it comes in contact.
The pleurapophyses (fig. 23, 20) of this inverted arch retain their typical
connections with the nasal centrum and neurapophyses at one end, and with
the hemapophysis (21) at the other end, and they also support the constant
element of the diverging appendage of the arch, no. 2. The hemapo-
physis (21) resumes in birds more of its normal proportions and elongated
slender form: but the hemal spine (22) is largely developed though undi-
vided, and sends upwards and backwards from the part corresponding to the
symphysis of the spine, when this element is divided, a long pointed process
(22'), which joins and usually coalesces with the neural spine (15) and divides
the anterior outlet of the hzemal canal into two apertures called the nostrils.
The modification of the inferior arch of the nasal vertebra in the lizard tribe
is here repeated. The pleurapophysial appendage, 24, connects the palato-
maxillary arch with 2s, and in the ostrich and a few other birds, also with s:
the second or hemapophysial ray of the diverging appendage is deve-
loped in all birds, as in the squamate saurians ; combining the movements
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ON THE VERTEBRATE SKELETON. 297
of the hemal arch of the nasal vertebra with that of the frontal vertebra,
and consisting of the two styliform ossicles (26 and 27) which extend from the
hemapophysis, 21, 21’, to the pleurapophysis, 28 : the essential relationship of
the compound ray, 26 and 27, with the nasal vertebra, is indicated by their
becoming confluent with its hemapophysis (at 22”), whilst they always main-
tain an arthrodial articulation with the pleurapophysis (2s) of the succeeding
vertebra.
The bones of the splanchno-skeleton intercalated with the segments of the
endoskeleton in the bird’s skull are the petrosal (16), between the neural
arches of the occipital and parietal vertebra, early coalescing with the ele-
ments of those vertebre with which it comes in contact: the sclerotals (17),
interposed between the frontal and nasal neural arches: and the thyro-hyals
(a7), retained in connection with the debris of the hemal arch of the parietal
vertebra, H u. The olfactory capsule remains cartilaginous. The dermal
bone (73) is well-developed and constant: a second supraorbital dermal bone
is occasionally present. All the endoskeletal bones manifest, under every
adaptive modification, the segmental arrangement, and it is difficult to con-
template the repetition of the arrangement of the cranial bones around the
primary segments of the encephalon in the series of arches closed respectively
by the bones N 1, N 11, N 111, N tv, together with that of the corresponding
number of arches closed below, at H rv, H 111, H 11 and H1, without a con-
viction that the type illustrated in fig. 15 is that upon which these seg-
ments of the skull have been constructed. ‘This conclusion might seem
forced, in respect to the occipital vertebra, were its displaced hemal arch
and appendages to be viewed without reference to their relative position and
connections in the lower vertebrate classes; but it will be confirmed and
shown to be agreeable to nature and to the recognised kinds and grades of
modification to which the elements of one and the same vertebra are subject,
by observing in the young bird the distinct pleurapophysial elements of those
cervical vertebrae, beyond which the corresponding elements of the occiput
have retrograded, in obedience to the functions which the hemal arch of
that vertebra and its appendages are destined to perform in the feathered
class.
Mammals.—ltf the foregoing views of the general homology of the bones
of the skull be agreeable to their essential nature, we should expect that the
new and additional modifications, in the mammalian class, which tend to
obscure those relations would be seated in the appendages and peripheral
elements of the endoskeletal segments, or in the capsules and appendages of
the special-organs of sense.
I have selected with a view to testing such anticipation the skull of a young
pachyderm*, and, after successively disarticulating the segments in the order
in which they have been previously described, I have given a side view of
them arranged in correspondence with the figures 23, 22, and 5. (Fig. 24.)
The neural arch of the occipital vertebra, N 1, agrees with that of the bird and
crocodile in the coalescence of the parapophysis, 4, with the newrapophysis,
2; but the process, 4, now descends from the lower part of the arch, and,
as in many other mammals, is of great length. An articular condyle is also
developed from each neurapophysis which articulates with the concave an-
terior zygapophysis of the atlas, and is the homotype of the posterior zyga-
pophysis in the trunk-vertebre. The centrum (1) is reduced, like that of
_ the atlas, to a compressed plate, and its hinder articular surface is not more
is
* The skull of the ruminant is perhaps still better adapted to demonstrate the vertebral
relations of the cranial bones: that of the sheep is the subject of the diagram for this pur-
pose in the concluding volume of my ‘ Hunterian Lectures.’
1846. x
298 REPORT—1846.
developed than is the front one of the centrum of the atlas, with which, in-
deed, it is loosely connected by ligament. The expanse of the occipital
‘spine, 3, has been governed, agreeably with a foregoing remark, by the su-
perior development of the cerebellum. :
The hzemal arch of the occipital vertebra is represented, like those of the
cervical vertebra, by the plewrapophysial elements only (51); but these, in
most mammals, are developed into broad triangular plates with outstanding
processes: that called ‘spine’ and ‘acromion’ is exogenous ; but that called
‘coracoid’ is always developed from an independent osseous centre (a rudi-
mental representative of the hemapophysis, 52), which coalesces with the
pleurapophysis in mammalia, and only attains its normal proportions, com-
pleting the arch with the hemal spine (episternum) in the monotremes.
In many mammals the arch is completed by bones, which are, apparently,
the hemapophyses of the atlas, e. g. in man (fig. 25, 52’), which have followed
the occipital heemal arch in its backward displacement, but not quite to the
same extent.
The diverging appendage, though retaining the general features of its
primitive radiated form, has been the seat of great development and much
modification and adjustment of its different subdivisions (53-57) in relation
to the locomotive office it is now called upon to perform.
With the exception of this excess of development of the appendage, the
defective development and displacement of the hzmal arch, and the coales-
cence of the parapophyses in the neural arch, there are few points of resem-
blance which are not sufficiently salient between the segment N1, H1 in the
mammal, and that so marked in the fish (fig. 5). And, if the interpretation
of the more normal condition of this segment in the lower vertebrate, ac-
cording to the archetypal vertebra, fig. 15, be accepted, then the explana-
tion of the nature of the modifications of the special homologues of the con-
stituents of the occipital segment by which that archetype is masked in the
mammal, may be confidently left to the judgement of the unbiassed student
of homological anatomy.
In commencing his comparisons of the second segment of the skull with the
typical vertebra, he will be unexpectedly gratified by finding, in the immature
mammal, the centrum, 5, naturally distinct, and the hemal arch, H.1, retaining
its natural connections with the rest of the segment, and by means of a more
complete development of the pleurapophyses (3s) than in any of the inferior
air-breathing vertebrates. He may now separate, without artificial division of
any compound bone, the entire parietal segment, but he brings away with it
the petrified capsule of the acoustic organ, and the anchylosed distal piece (27)
of the maxillary appendage, which more or less encumbers and conceals the
typical character of the neural arch of the parietal vertebra in every mammal :
least so, however, in the monotremes and ruminants. The newrapophyses (6)
of the parietal vertebra, like the mesencephalic segment of the brain, are but
little more developed in mammals than in the cold-blooded classes: they are
notched in the hog and perforated in the sheep by the larger divisions of
the trigeminal, and they send down an exogenous process, which articulates
and sometimes coalesces with the appendage (24) of the palato-maxillary
arch. The neural spine (7), always developed from two centres, often vastly
expanded, and sometimes complicated with a third interealary or inter-
parietal osseous piece, is occasionally uplifted and removed from its neur-
apophyses by the interposed squamous expansion of the bone 27; but this,
which reminds one of the occasional separation of the neural arch from the
centrum of the atlas in fishes, is a rare modification in the mammalian class.
A still rarer one is the separation of the halves of the parieto-neural spine
ON THE VERTEBRATE SKELETON. 299
‘from each other by the extension and mutual junction at the median line
of the occipital and frontal spines. A specimen of this, in a species of
Cebus, which repeats the common modification of the parts in fishes, is pre-
served in the museum of the Royal College of Surgeons. The parapophysis
(s) always commences as an autogenous element by a distinct centre of ossi-
fication, as shown in the human feetus, fig. 11,8; it speedily coalesces with
the petrosal, but otherwise retains its individuality in some of the lower mam-
mals, as e.g. in the echidna (fig. 12,8): or it coalesces with the curtailed
frontal pleurapophysis 2s, or with the maxillary appendage 27, or with both
‘these and the pleurapophysis of its own vertebra (38), when the complex
‘temporal bone’ of anthropotomy is the result. In most mammals the pleur-
apophysis (38) retains its primitive independency and rib-like form, with
usually the ‘head’ and ‘tubercle’; but by reason of its arrested growth it
has been called ‘styloid’ bone or process. Sometimes it is separated from
the short hemapophysis, 40, by a long ligamentous tract, sometimes it is imme-
diately articulated with it, or by an intervening piece. The hemal spine, 41,
is usually small, but thick and alwayssingle. The rudiments of hypobranchial
elements (46) are retained as diverging appendages of the parieto-hzmal arch
in all mammals, and have received the special names of ‘ posterior cornua,’
or ‘ thyrohyals,’ from their subservient relationship to the larynx.
In the frontal segment the centrum, 9, and neurapophyses, 10, very early
coalesce. ‘Two separate osseous centres mark out the body (fig. 26, C, 9),
and each neurapophysis has two distinct centres (7b. 10, 10), the optic foramina
(op) being first surrounded by the course of the ossification from these
points. The superior development of the neurapophysial plates (10), as com-
pared with those of the parietal vertebra (6), in most mammals, harmonizes
with the greater development of the prosencephalon ; but the chief bulk of
this segment of the brain is protected by the expanded spines of the frontal (11)
and parietal(7) vertebrae, and by the intercalated squamosals (27). And the ap-
pendicular piece (27) not only usurps some of the functions of the proper cranial
neurapophyses, but, likewise, the normal office of the frontal pleurapuphysis
(2s), in the support, viz. of the distal elements of the hzmal arch (29, 32),
which now articulate directly with 27, in place of 2s as in all oviparous verte-
brates. The true pleurapophysis of the frontal vertebra (2s) is almost re-
stricted in the mammalian class to functions in subserviency to the organ
of hearing, is sometimes swollen into a large bulla ossea, like the parapophyses
and pleurapophyses of the cervical vertebra of Cobitis ; it is sometimes pro-
duced into a long auditory tube, and sometimes reduced to the ring supporting
‘the tympanic membrane. Yet, under all these changes, since its special ho-
mology is demonstrable with 2s in the bird (fig. 23) and crocodile (tig. 22) as
well as with the teleologically compound bone, 2s a, b, c, d, in the fish (fig. 6),
so likewise must its general homology, which is so plainly manifested in
the fish, be equally recognised. The frontal hemapophysis (fig. 24, 29, 30),
and the corresponding half of the hemal spine (ib. 32) are connate on each
side in all mammals, and become confluent at H 111, in most. The hemal
arch of the frontal segment of the skull, as in other air-breathing vertebrates,
has no diverging appendage, unless the tympanic otosteals be so regarded,
an idea which is not borne out by their development.
The nasal segment (N rv, H rv) is chiefly complicated by the confluence of
parts of the enormously developed olfactory capsules (1s) in the mammalian
class, and its typical character is masked by the compression and mutual coa-
lescence of the neurapophyses, 14. The centrum is usually much elongated,
as at 13, and socn coalesces with both newrapophyses (14) and nasal capsules
in the hog. The newral spine (15) is usually divided, but is sometimes single,
x2
300 REPORT—1846.
e.g. in Simia. In the rhinoceros it supports a dermal spine or horn. The
pleurapophysis (20) or proximal element of the hzmal arch of the nasal ver-
tebra has its real character and import almost concealed by the excessive
development of the second element of the arch (21), which resumes in mam-
mals all those extensive collateral connections which it presented in the cro-
codile ; and to which are sometimes added attachments to the expanded spine
of the frontal vertebra, as well as to that of its own segment. The pleurapo-
physis however, besides its normal attachment to its centrum, 13, sends up a
process to the orbit, in order to effect a junction with its neurapophysis which
sometimes appears there, as the ‘ os planum’ of anthropotomy. The hemal
spine (22) is developed in two moieties, which never coalesce together, al-
though, in the higher apes, and at a very early period in man, each half
coalesces with the hzmapophysis, and repeats the simple character of the
corresponding elements (rami) of the succeeding (mandibular) arch.
The appendicular element (24) which diverges from the pleurapophysis
(20), contributes to fix and strengthen the palato-maxillary arch by attaching
it to the descending process of the parietal centrum (s) ; with which, in most
mammals, it ultimately coalesces. The other elements of the diverging mem-
ber of the arch correspond in number and in the point of their divergence
with those in birds, chelonians and crocodiles. They are two in number, suc-
ceeding each other, and both become the seat of that expansive development
which is followed by the multiplication of their points of connection ; thus
the proximal piece (‘ malar’ 26) articulates in the hog not only with the
heemapophysis (21) from which it diverges, but likewise with the mucc-dermal
bone, 73. The distal piece of the appendage (squamosal, 27) expands as it
diverges, and fixes the naso-hemal arch not only to the frontal pleurapo-
physis (2s), but also to the frontal, parietal and occipital neurapophyses and
spines: it also affords, in the hog, as in other mammals, an articular surface
to the frontal hemapophysis (29).
The development of an osseous, centre in the cartilage of the snout of
the hog, and the homologous’£ prenasal’-ossicle in certain fishes, the carp,
e.g might be regarded as rudiments ‘of terminal abortive segments more
anterior than the nasal vertebra. The multiplied points of ossification in the
vomer have been, also, deemed indications of that bone being, like the vome-
rine coccygeal bone in birds, a coalescence of several vertebral bodies. Of
course, @ priori, the segments in the cranial region of the endoskeleton
might as reasonably be expected to vary in number in different species, as
the segments in the thoracic or sacral regions. I have not, however, been
able to determine clear and satisfactory representatives of more than four
vertebrz in the skull of any animal ; and the special ossifications in the nasal
cartilages appear to me to belong to the same category of osseous parts, as
the palpebral bones in certain crocodiles and the otosteals.
Man.— Arriving, finally, in the ascensive survey and comparison of the
archetypal relations of the bones of the vertebrate skull,at Man, the highest and
most modified of all organic forms, in which the dominion of the controlling
and specially adapting force over the lower tendency to type and vegetative
repetition is manifested in the strongest characters, we, nevertheless, find the
vertebrate pattern so obviously retained, and the mammalian modification of it,
as illustrated in the preceding paragraph and diagram, so closely adhered to,
as to call for a brief notice only of those developments of the common
elements which impress upon the human skull its characteristic form and
proportions.
The neural arch of the occipital vertebra differs from that of the hog by
a much greater development of the newral spine (fig. 25, 3) and a much less
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ON THE VERTEBRATE SKELETON. 301
development of the parapophysis. This, as in other mammals, is not only an
exogenous process of the neurapophysis, 2, but is commonly reduced to a
mere “ scabrous ridge extended from the middle of the condyle towards the
root of the mastoid process” (Monro, J. ¢. p.’72)—the “ eminentia aspera
musculum rectum lateralem excipiens” of Soemmerring: the knowledge of
its general homology, however, makes quite intelligible and gives its true
interest to the occasional development of this ridge into a ‘ paramastoid’
process, which now, however, projects, like the true ‘ mastoid,’ downwards
from the basal aspect of the cranium (ante, p. 204).
The occipital plewrapophysis, pl, 51, shows the same displacement as in
other mammals, but is still more expanded in the direction of the trunk’s
axis, and its exogenous (acromial) process is still more developed. The hem-
apophysis (52), originally distinct, has its development checked and speedily
coalesces with the pleurapophysis.
If the bone 52! be the special homologue of the bone, ss, in the fish,—and
considering the backward displacement of 51 and 5, its anterior position to
them in man is no valid argument against the determination,—then we may
adopt the same general homology, and regard the clavicle, in its relations to
the vertebrate archetype, as the displaced hemapophysial element of the
atlas, to which segment its true relative position is shown in the same low |
organized class in which the typical position of the scapular arch is likewise
retained.
The adaptive developments of the radiated appendage of the occipital
hemal arch reach their maximum in man, and the distal segment of the ap-
pendage constitutes in him an organ which the greatest of ancient philoso-
phers has defined as the “ fit instrument of the rational soul ;” and which
the first of modern physiologists has described “as belonging exclusively to
man—as the part to which the whole frame must conform”*. And these ex-
pressions give no exaggerated idea of the exquisite mechanism and adjust-
ment of its parts.
It is no mere transcendental dream, but true knowledge and legitimate
fruit of inductive research, that clear insight into the essential nature of the
organ, which is acquired by tracing it step by step from the unbranched
pectoral ray of the protopterus to the equally small and slender but bifid
pectoral ray of the amphiume, thence to the similar but trifid ray of the
proteus, and through the progressively superadded structures and perfec-
tions in higher reptiles and in mammals. If the special homology of each
part of the diverging appendage and its supporting arch are recognisable
from Man to the fish, shall we close the mind’s eye to the evidences of that
higher law of archetypal conformity on which the very power of tracing the
lower and more special correspondences depend ?
Until the alleged facts (p. 285) are disproved, demonstrating change of
position to be one of the modifications by which parts of a natural and re-
cognisable endoskeletal segment are adapted to special offices, and until
the conclusions (p. 286) deduced from those facts are shown to be fallacious, I
must retain the conviction that, in their relation to the vertebrate archetype,
the human hands and arms are parts of the head—diverging appendages of
the costal or hemal arch of the occipital segment of the skull+.
* Bell (Sir Charles), ‘“ The Hand.” Bridgewater Treatise, 1833, pp. 16, 18.
Movoy 6é kai augoézvoy yiyverat Tw Gdd\wy Cowy avOpwros.— Aristotle.
+ As another example of the new light and interest which a knowledge of general homo-
logy gives to the facts of abnormal anatomy in the human species, I may cite the remark-
able case described by Sir C. Bell (op. cit p. 52), of the boy ‘ born without arms,’— but who
had clayicles and scapule.’ Here development was arrested at the point at which it is normal
302 : REPORT—1846.
The centrum, 5c, of the parietal vertebra gives, in the human fcetus, the
same evidence of its essential individuality, by the same absence of the mask
of connation which somewhat concealed it in the oviparous classes, as
we have already noticed in the lower mammal (fig. 24). The newrapo-
physes (6) rise higher to reach their proper spine (7) in the lofty cranial dome
of man, of which that divided and enormously expanded element forms the
greatest part of the roof: but the base of the neurapophysis continues to be
perforated by the homologous divisions of the nerve (¢r) that notches it in
the cod-fish (fig. 5, 6 ér). The parapophysis (s) retains its autogenous or
independent character in relation to its proper neural arch, the ‘ additamental’
suture by which it manifests its normal relations to the neural spine (7) being
persistent; but it speedily coalesces with the acoustic capsule, 16 (from
which it is artificially separated in fig. 25), and with the modified plewrapo-
physis, 28, as has been already explained in the chapter on ‘ Special Homo-
logy’ (Mastoid, pp. 197-210).
The proper pleurapophysis (3s) of the parietal vertebra ordinarily becomes
confluent with contiguous and coalesced portions of the parapophysis, s, and
acoustic capsule, 16; and the ossified portion of the hemapophysis, a0 h, is
separated from it by a long ligamentous tract, and becomes confluent with
the hemal spine, 41hs. The entire inverted arch exhibits the usual arrested
growth characteristic of the air-breathing vertebrates, and its appendages
are represented by the still retained ‘hypobranchial’ elements, 46, of the
splanchnic arches, which are so voluminously developed in the fish.
The centrum and neurapophyses (9, 10) of the frontal vertebra manifest the
same speedy coalescence as in other mammals. The spie, 11, though developed
from two lateral moieties, regains its normal unity, as a general rule, in man
by the obliteration of the median suture: its transverse and vertical expanse
here attain their maximum. The parapophysis (12) is developed, as in the
occipital segment, as an exogenous process, called ‘external angular or or-
bital’ in anthropotomy, but from the neural spine instead of the neurapo-
physis. This element is perforated by its characteristic nerve (op). The pleur-
apophysis, 28, is now separated from its parapophysis, 12, by both parts, 27 and
26, of the diverging appendage of the maxillary arch ; but yet it is interesting
to note that it is still connected through the medium of these with the same
element to which, agreeably with the greater retention of the vertebrate
archetype, it directly articulates in the fish (fig. 5, 12, 2s a-d). The inter-
calated piece (27) further interposes itself, as in other mammals, between
the pleurapophysis, 2s, and heemapophysis, 29, of the frontal segment, directly
articulating with the latter and leaving the proximal element of the arch (2s )
reduced in man to its subordinate function of sustaining the ear-drum. The
hemapophysis,29,and hemal spine, 32, are connate, and soon coalesce with their
in the Anguis, Pseudopus, and some other limbless and snake-like lizards. The usual pre-
dominating development of the scapular appendage has bred so prevalent an idea of the sub-
ordinate character of the supporting arch, that the existence of the arch minus the append-
age, is adverted to not without a note of surprise in the above-cited and other excellent works.
General homology, however, teaches that a vertebral arch is a more constant and important
part than its appendages ; and, that, being anterior in the order of development, it may be
expected, in cases where development is arrested, whether normally in accordance with the
nature of the species or abnormally as an individual defect, to be present when the diverging
appendages are absent. Sir Charles Bell, well recognising the primary function of the modi-
fied occipital rib in relation to breathing, observes, in reference to the above-cited case, ‘“‘ We
would do well to remember this double office of the scapula and its muscles, that, whilst it is
the very foundation of the bones of the upper extremity, and never wanting in any animal
that has the most remote resemblance to an arm, it is the centre and point d’appui of the
muscles of respiration, and acts in that capacity where there are no extremities at all!”
p. 52.
ON THE VERTEBRATE SKELETON. 303
opposites at the symphysis menti; and the whole distal portion of the inverted
arch of the frontal segment is then formed by a continuous bar of bone, modi-
fied in its form and articulation, and by its dental appendages, in subserviency
to mastication and other subordinate functions in relation to the human mouth.
We recognise the centrum of the nasal vertebra in the human skull by the
position and connections of the bone, 13, notwithstanding it has undergone
as extreme a divergence from the ordinary cylindrical shape of such elements,
as its homotype at the opposite extreme of the vertebral column in birds,
which Cuvier compares to a ‘soc-de-charrue’: it is, in fact, more compressed
and vertically developed than in the hog (fig. 24, 13); but it is shorter, and
commonly retains its original individuality. It directly supports the similarly
modified compressed, and also, coalesced newrapophyses, 14, which termi-
nating in like manner the series of their vertebral homotypes anteriorly, have
-undergone the extremest modification. But the arguments which show the
coalesced prefrontals of the frog, the bird and the mammal to be the special
homologues of the bones so called in the fish, establish, as a corollary, their
general homology with those bones, which retain in so much greater a degree,
and unmistakeably, their neurapophysial characters in that lowest class of
cold-blooded vertebrates. The nature of the additional complication by
which those vertebral or archetypal characters are further masked in mam-
mals, has been already explained in relation to the nasal neurapophyses of
the hog. The olfactory nerves are transmitted in man, as in that and most
other inferior mammals, by numerous foramina, 14, ol. The nasal spine, 15, is
divided, but much-restricted in its growth, and presents a singular contrast
in that respect to its homotypes, 11, 7, 3, in the succeeding cranial vertebre.
The development of the neural arch of the nasal vertebra is so modified in
man, so contracted as well as retracted, that the orbits, instead of being
pushed apart and directed laterally, have approximated by a kind of reci-
procal rotation towards the median plane, and have thus gained a directly
anterior aspect.
General homology perhaps best explains the import of the continuation
of the small and seemingly insignificant bones (20, pl) from the roof of the
mouth “up the back part of the nostrils to the orbit,” where they are
connected “to the ossa plana and cellule ethmoidee by the ethmoid suture.”
That the connection is the best possible for the functions of the bone we
may feel assured, without the sentiment being damped by discerning in it,
at the same time, the attempt to retain the type, and repeat those constant con=
nections of the plewrapophysis in question, not only with its centrum (vomer),
but also with the modified neurapophyses of its proper segment (prefron-
tals with coalesced olfactory capsules constituting the compound ‘ ethmoid
bone’ of anthropotomy). The connections of the pleurapophysis, 20, with its
hzemapophysis, 21, in front, and its diverging appendage, 24, behind, are also
retained in man ; and in short, all those characters that, depending on the
essential nature of the palatine bone as the pleurapophysis of its vertebral
segment, have served to indicate its special homology from man to the fish,
without doubt or difficulty, to all anatomists (see Table I.).
The hemapophysis (20) has the usual mammalian expansion, but is unu-
sually short in man, and coalesces unusually early with the corresponding
moiety of the hemal spine (22). Besides the normal and constant connec-
tions with 20 and 22, the hemapophysis, 21, articulates with its fellow, with
the centrum (13), neurapophysis (14, os planum), and spine (1s), of its
own vertebra, with the spine of the frontal vertebra (11), with the detached
portion of the olfactory capsule (19), and with the muco-dermal bone (73).
It also affords a large surface of attachment to the proximal piece of
304 REPORT—1846.
its diverging appendage (26), which, in addition to the more constant con-
nections with 21 and 2, articulates in man with the neurapophysis (10)
and parapophysis (12) of the frontal vertebra. The distal extremity of the
second bone (27) of the diverging appendage attains its maximum of expan-
sion in man, and besides its connection with 26, and the glenoid articulation
for the hemapophysis, 29, it joins the parietal neurapophysis, 6, and spine, 7,
and sometimes also (in the melanian race) the spine (11) of the frontal: ver-
tebra: and it speedily coalesces with the reduced pleurapophysis, 2s, of the
frontal vertebra, and with the parapophysis (s) of the parietal vertebra, to-
gether with a portion of the capsule of the acoustic organ.
In reviewing the general characters of the human skull in reference to the
vertebrate archetype, we find the occipital segment simplified by the atrophy
and connation of its parapophyses and hemapophyses; and modified chiefly
by the excessive growth of its neural spine and pleurapophyses, and by the
backward displacement of the latter element, as in all other air-breathing
vertebrates. The parietal segment, retaining, like the occipital one, the more
normal proportions of its centrum and neurapophyses, is still more remark-
able for the vast expanse of its permanently bifid spine. As in most cold-
blooded vertebrates, the parapophysis preserves its independence in respect of
the neural arch of its own segment. The hemal arch retains its almost foetal
proportions, but is less displaced than in some of the inferior air-breathing
vertebrates. The primitive individuality of the centrum of the parietal vertebra
is a feature by which the human subject, together with all other mammals,
manifests a closer adhesion to type than is observable in this part of the skull
in any of the oviparous vertebrates, and it shows the necessity of extending
comparisons over the entire series, and not deducing the vertebrate arche-
type exclusively from those inferior forms: for although it may be upon the
whole best retained in them, yet the modifications superinduced in subser-
viency to their exigences, and by which they diverge to that extent from the
common plan, and, as a series of species, from the common vertebrate stem,
may affect a part which the conditions of existence of higher forms do not
require to be so masked. The early ossification and large proportional size
of the hyoidean arch in the human embryo is very significant of its true
nature and importance, in relation to the archetypal vertebrate structure,
i.e. as being the hemal complement of a primary segment of the skull.
Exogenous processes descend, like the pair from beneath the lower cer-
vical vertebrae of some birds, from the body of the parietal vertebra; but
the true transverse processes are the mastoids, which always articulate with
a corner of the parietals.
The centrum and neurapophyses of the frontal segment retain their ordi-
nary proportions, and the spine is again the element which, by its extreme
expansion and its modification in subserviency to the formation of the orbits,
chiefly masks the typical features of the neural arch. The parapophysis is
connate and reduced in size, and its vertebral relations with the pleurapo-
physis of its segment interrupted by the interposition of the diverging appen-
dage from the antecedent hemal arch: the unusually expanded distal end
of the same appendage also intervenes between the frontal pleur- and hem-
apophyses ; the pleurapophysis (2s) being more atrophied in man than in
most inferior mammals. The hemapophysis and spine are on the other
hand much developed and modified as above described, for the business of
mastication, though relatively shorter than in other mammals.
The compression and extension, both vertically and longitudinally, of the
centrum (13), the compression and coalescence of the neurapophyses (14),both
with each other and the nasal capsules (1s), and the corresponding proportions
ON THE VERTEBRATE SKELETON. 305
_ of the divided spine (13), mainly characterize the neural arch (N rv) of the
terminal or nasal segment of the human skull. The early coalescence of each
heemapophysis(21) with the corresponding half of the divided hzemal spine (22),
and the unusual expansion of the bones, especially the second (27), which
diverge from the hemapophysis, form the chief characteristics of the hzemal
arch (H 1v) of the nasal segment. The hemapophysial portions of both the
nasal and frontal vertebre are much less elongated than in most other
animals.
It may serve to test the accuracy of the general homologies here assigned
to the bones of the human skull, if we notice the degree to which they have
been subject to modification in connection with such determinations.
According to the general character of the vertebral elements in the rest of
the frame, we should be prepared to expect that the hemal arches would be
subject to a greater variety in respect of development and relative position
to their segments than the neural arches; and that in the latter the parts
determined as centrums and neurapophyses would retain more of the or-
dinary proportions of such parts in other segments or in other animals, than
the peripherally situated spines. If new bones are added, we should expect
to find them in the relative position of appendages to the normal vertebral
arches: or should these be homologous with similar superadditions in the
skulls of lower animals, they will probably be the seat of more extensive
changes of form, proportion and connections, than the elements of the verte-
bral arches themselves. :
Now if the reader will glance at fig. 25 and compare the bones forming
the segments of the skull with those in figs. 24, 23, 22 and 5, he cannot but be
struck with the remarkable degree of uniformity in the dimensions of the
bones 2, 6 and 10: no. 14 being the terminal neurapophysis, has been the seat
of mere variety ; but the general steadiness of this series of bones in regard
to their dimensions and connections accords with the characters assigned to
them, as-neurapophyses, which are always the most constant and important
of the ossified vertebral elements.
The bones 1, 5, 9 and 13 equally conform in the kind and degree of their
modifications with their determination as the bodies of the vertebre.
The increasing capacity of the neural canal of the head, demanded for the
lodgment of the progressively expanded encephalonas the vertebral scale rises,
is chiefly acquired by the expansion of the bones, 3, 7, 11, which, being deter-
mined as ‘neural spines’ in the fish, might be expected to be subject to greater
deviations from their typical form and proportions than the more central
and essential parts of the neural arches. ‘The terminal neural spine, 15, is
subject to still greater varieties in the range of species, as might also be ex-
pected from its position. In one mammal, e.g. the porcupine, it is more
expanded than any of its succeeding homotypes in the cranium; in man its
proportions are so much reduced as greatly to mask the homotypal relation.
Tn one mammal, e.g. the orang, the nasal spine is not only diminutive but
single: in another mammal, e.g. the manatee, it is also diminutive but di-
vided, and the halves completely separated by the intervention of part of the
succeeding spine.
The abnormal conditions of the human skull give further illustration of the
truth of these general homologies of the cranial bones, and reciprocally re-
ceive light from such determinations. In the case of idiots from defective
growth or development of the brain, where the cavity of the cranium is re-
duced to half or less than half its normal capacity, as e. g. in the skull described
and figured in my ‘ Memoir on the Osteology of the Chimpanzee*,’ it might
* Zoological Transactions, vol. i. p. 343, pl. 57 and 58.
306 REPORT—1846.
have been expected from the anthropotomical ideas of the cranial bones,—
according to which no one bone is deemed either more or less important
than another in its essential nature, and where the squamosal is as little re-
garded in the light of a superadded or intercalary piece as the alisphenoid,—
that all would be reduced in the same proportion in forming the parietes of
the contracted brain-chamber. But this is by no means the case. In the
instance above-cited the basioccipital and basisphenoid have been developed
to their usual size, and the distance from the posterior boundary of the bony
palate to the anterior border of the foramen magnum is as great as in any
normal skull. The exoccipitals (condyloid portions of the occiput), the
alisphenoids and the orbitosphenoids retain in like manner their full dimen-
sions. The distance between the frontal and temporal bones is as great as
in the average of fully developed Caucasian skulls, and is greater than in
most of those from the Melanian race, in which the direct junction of the
frontal with the temporal, as in the chimpanzee, is by no means rare. The
contraction of the capacity of the brain-chamber is due chiefly to arrested
development of the frontals, parietals, supraoccipital and squamosals. By
the reduction of the supraoccipital and the retention of the centrums of the
cranial vertebra of their normal proportions, the foramen magnum becomes
situated nearer the back part of the basis cranii than in the normal skull.
In a still smaller cranium of a female idiot, who reached the age of twenty-
one years, which is preserved with the male idiot’s skull above-mentioned in
the anatomical museum of St. Bartholomew’s Hospital, the contrast between
the normal proportions of the basioccipital, basisphenoid, exoccipitals, ali-
sphenoids and orbitosphenoids, on the one hand, and the reduced dimensions
of the supraoccipital, parietals, frontals and squamosals on the other, is still
more striking and significant of the true nature of those bones. The normal
growth of the centrums, indeed, might be explained by the concomitant nearly
normal size of the medulla oblongata, base of third ventricle and optic chi-
asma, in the brain of the same idiot: but it is not so obvious from the con-
dition of the brain itself why the alisphenoid should not have shrunk in the
same proportion as the parietals, frontals and squamosals. To the homologist,
however, the recognised difference of subjectivity to modification presented
by the neurapophyses, spines and diverging appendages of the typical seg-
ments, renders very intelligible the partial seats of arrested growth in the
bones of these idiots’ crania.
In reference to disease, also, one sees not why the alisphenoid should have
a minor attraction for the morbid products deposited, or be less subject to
the destructive actions excited, during syphilitic or mercurial disease, than
the parietals, or the orbitosphenoids than the frontals, or the exoccipitals
than the supraoccipital: yet it needs but to examine any series of such
morbid skulls in our museums of pathology to be convinced that the variable
and peripheral elements of the neural arches, viz. their expanded spines, are
almost exclusively so affected: the frontal and parietal being the most
common seats of the disease ; the supraoccipital a less frequent one, concomi-
tantly with its minor deviation from the typical standard of the element. I have
yet seen no example in which either a cranio-vertebral centrum or neura-
pophysis was so affected ; but the nasal bones are notoriously attacked.
It would be easy to multiply such instances of the new light—new eyes,
so to speak,—with which human anatomy, normal and abnormal, is viewed,
after the essential nature or general homology of the parts have been appre-
ciated.
If the bones 4, 8, 12, fig. 5, have been correctly determined as the parapo-
physes of the cranial vertebra, they might be expected to be subject in the
——
ON THE VERTEBRATE SKELETON. 307
course of adaptive modification to the loss of their individuality, and from
autogenous elements to be reduced to the condition of exogenous processes.
Now this is exactly what we trace in the series of vertebrate skulls ; and we
are further prepared to expect that the simplification of the segment forming
the anterior extremity of the vertebral series will be in part effected by the
total disappearance of its least important elements, the parapophyses. These
are, in fact, absent in the nasal vertebra in all animals; they become con-
fluent with the occipital vertebra in most reptiles and all warm-blooded ani-
mals ; and in the latter, we find, with the exception of a few birds, that the
parapophyses of the frontal vertebrae have likewise lost their individuality.
The first endoskeletal bones which plainly disappear from the skull in
tracing its modifications upwards from fishes are those which, in the present
vertebral theory, have been referred to the category of diverging appendages;
viz. the entopterygoid (fig. 5,23), the operculars (7b. 34-37), and the branchi-
ostegals (ib. 41). The first bones that we discover to be plainly superadded
to those that remain after the above subtraction, in the skull of the reptiles,
for example, are, also, referable, in the present vertebral theory, to the same
variable and inconstant class of elements: they are the ectopterygoids (fig.
22, 2a’), the malars (figs. 22 to 25, 26) and the squamosals (#6. 27) ; and are,
in general homology, diverging appendages of the palato-maxillary arch.
They are subject to more inconstancy as to their existence than the more
regular and normal elements of the skull: some reptiles, for example, have
the malar and squamosal, whilst others want them; most reptiles have the
ectopterygoid, but this, which is not present in fishes, is again taken away in
the warm-blooded vertebrates. With reference to inconstancy of form and
connections no bone of the cranium exceeds the squamosal, and it is precisely
this distal element of the diverging appendage, which, through its inordinate
development, most masks the archetypal character of the human cranium
(compare 27, fig. 25, with 27, fig. 23).
Classification of Skull-bones.—A knowledge of the special homologies of
the bones of the skull is essential to that of their general homology, and a know-
ledge of their general homology is indispensable to their natural classification.
Cuvier divides the bones of the head in all animals into bones of the cra-
nium and bones of the face.
The bones of the cranium are those of the cavity containing the brain:
all the rest are bones of the face and contribute to form the cavities for the
organs of sight, smell and taste*. But these primary divisions do not in-
clude the same bones in all animals: the nasal (fig. 5, 15) and vomer (éb. 13)
are cranial bones in fishes, but not in mammals: the squamosal (fig. 25, 27) is
a cranial bone in mammals and not in birds or reptiles, &c. And this dis-
erepancy in the Cuvierian classification of cranial bones is due, not only to a
non-appreciation of their essential nature, but partly to mistakes of special
homologies: thus the nasal is called ethmoid in the fish, and the squamosal
is called jugal in the bird.
In all anthropotomical classifications the bones of the cranium are reckoned
eight in number: four single, viz.—
The frontal (fig. 25, 11) ;
The ethmoidal (2d. 14 and 18) ;
The sphenoidal (5, 6, 9, 10 and 24) ;
The occipital (1, 2 and 3): and
four in pairs, viz.—
The two parietal (7), and
The two temporal (2, 16, 27, 23 and 3s).
* Lecons d’Anat. Comp. t. ii. (1837) p. 159.
308 REPORT—1846.
The bones of the face are reckoned as fourteen in number, viz.—
The two malar (26) ;
The two maxillary (21, 22) ;
The two palatal (20) ;
The two nasal (15) ;
The two turbinal (19) ;
The vomer (13), and
The mandible (20-3).
The detached portion of the hyoid arch (40, 41) and its appendages (47),
together with the whole of the scapular arch and its appendages, are excluded
from the category of the bones of the head.
The natural classification of the bones of the human skull appears to me
to be, first into those of
The EnDo-sKELETON,
The SPLANCHNO-SKELETON, and
The Exo-sKELETON.
The primary division of the bones of the endo-skeleton is into the four seg-
ments, called
Occipital vertebra, N 1, H1;
Parietal vertebra, N 11, H 11;
Frontal vertebra, N 111, H 11;
Nasal vertebra, N tv, H tv.
These are subdivided into the neural arches, called
Epencephalic arch (1, 2, 3) ;
Mesencephalic arch (5, 9, 7, 8);
Prosencephalic arch (9, 10, 11 and 12) ;
Rhinencephalic arch (13, 14, 15) :
and into the hemal arches and their appendages, called
Maxillary arch (20, 21 and 22) and appendages (24, 26, 27) ;
Mandibular arch (28, 20-32) (no appendage) ;
Hyoidean arch (3s, 40, 41) and appendages (46) ;
Scapular arch (51 and 52) and appendages (53-58).
The bones of the splanchno-skeleton, are
The petrosal (16) and otosteals (16')* ;
The turbinals (1s and 19) and teeth. (The sclerotals retain their primitive
histological condition as fibrous membrane.)
The bones of the exo-skeleton, are
The lacrymals (73).
* These ossicles are described by most anthropotomists as parts of the ‘temporal bone.’
‘Os temporum infantis magnopere ab osse temporum adulti differt ; labyrinthi et ossiculorum
auditis fabrica absoluta est,” says Soemmerring in the classical work before cited (t. i.
p- 132). The signification of the differences between the foetal and adult human temporal
bone, which the great anthropotomist truly regarded as so remarkable, is made plain by
anatomy ; which shows the bone to be an assemblage of several essentially distinct ones, and
at the same time exposes the character of that singularly heterogeneous assemblage and
coalescence of osseous elements to meet the exigences of the peculiarly developed frame of
man. What the ‘ossicula auditis’ are, is a problem which still awaits careful additional
research in the embryonic development of the hemal arches of the cranium, for its satis-
factory solution. The question is not, of course, whether they are dismemberments of the
‘temporal bone,’ since this has no real claim in any animal to an individual character; but
whether the ossicles of the ear-drum in mammals are to be regarded, like the pedicle of the
eye-ball in the plagiostomous fishes, as appendages to a sense-organ, and thereby as develop-
ments of the splanchno-skeleton ; or whether they are, like the tympanic ring, modifications
of the tympano-mandibular arch. The reasons are adduced in the Chapter on ‘Special
Homology’ (p. 235) which have led me to view them as peculiar mammalian productions
in relation to the exalted functions of a special organ of sense.
ON THE VERTEBRATE SKELETON. 309
The course of coalescence reduces the epencephalic arch (fig. 25, N 1) to
one bone, the scapular arch to one bone (the arch is apparently completed
by the connexion of an element (s2') not appertaining to the skull). The
centrums 5, (9) and neurapophyses (6, 10) of the parietal and frontal vertebra
coalesce together and with the diverging appendages (21) of the maxillary arch
to form one bone, the ‘sphenoid’ of anthropotomy, and this ultimately coa-
lesces with the epencephalic arch and constitutes the ‘os spheno-occipitale’ of
Soemmerring. The expanded halves of the parietal spine (7) remaining
usually distinct are reckoned as two bones. The expanded halves of the frontal
spine (11) usually coalescing together form asingle bone. ‘The halves of the
nasal spine (13) rarely coalescing are counted as two bones. The mastoid (s)
coalescing with the petrosal (16) and this with the tympanic(2s), squamosal (27)
and stylohyal (ss), the whole is reckoned a single bone, which thus combines
a parapophysis and pleurapophysis of one vertebra with a pleurapophysis of
another and a diverging appendage of a third vertebra, and all these parts of
the endo-skeleton become confluent with a sense-capsule belonging to the
splanchno-skeleton: such is the heterogeneous compound character of the
‘temporal bone’ of anthropotomy. The neurapophyses of the nasal vertebra
(14) coalesce with each other and with a considerable part of another ossified
sense-capsule (1s), to form the single bone called ‘ethmoid.’ The maxillary
bone includes the superior maxillary (21) and premaxillary (22) of the lower
animals. The hyoid bone includes the basihyal (41), with the ceratohyals (40)
and the thyrohyals (46). The scapula includes both the pleurapophysis (51)
and the hemapophysis (52) of the occipito-hemal arch. The signification of
the separate points of ossification of the human fcetal skull is made plain by
the foregoing applications of the ascertained general homologies of the bones
of that part of the skeleton.
Objections to the Cranial vertebre considered—The latest and most formal
objection to the fundamental idea on which the general homologies of the
bones of the head have been worked out in the present Report, is also
the most formidable in respect of the great and deserved eminence of the
objector. In a manuscript left by Baron Cuvier, entitled, “ Le crane est-il
une vertébre ou un composé de trois ou quatre vertébres?” appended to
the posthumous edition of the ‘Lecons d’Anatomie Comparée*,’ he admits
that “the analogy of the basilar and two condyloid parts of the occiput with
the body and two halves of the annular part of the atlas is very appreciable.
The basioccipital and the body of the atlas serve equally to support the
myelon ; the exoccipitals and the two halves of the ring of the atlas to cover it.
The condyles are represented by the articular processes by which the atlas is
joined to the dentata. The condyloid foramen, which gives passage to the
nerve of the ninth pair, has some relation with the hole in the atlas which
gives passage to the first cervical nerve and to the first bend of the vertebral .
artery. Some have also found a certain relation between the mastoid process,
which in most animals appertains to the occipital bone, and the transverse
process of the atlas and the other vertebree ; upon which it must be remarked
that these relations are less in man, in some respects, than in the quadrupeds,
since the atlas has commonly only a notch for the passage of the artery, and
the mastoid belongs in man entirely to the petrosal”}. “‘ We may even com-
- * Tome ii. p. 710. (1837) par MM. F. G. Cuvier and Laurillard, who hold the arguments
of their author to be conclusive. The criticism in the ‘ Histoire des Poissons,’ t. i. p. 230,
bears only upon the @ priori cranio-vertebral theory of Geoffroy, and does not concern us
here.
+ “L’analogie de ces trois piéces, Je basilaire et les deux condyloidiens, avec les trois
piéces de l’atlas, son corps et les deux moitiéy de sa partie annulaire est trés sensible. Le
basilaire et le corps de l’atlas servent également 4 supporter Ja moélle épiniére ; les condy-
310 REPORT—1846.
pare,” Cuvier says, “the supraoccipital to the spinous processes which in
certain animals originate by special points of ossification and remain for some
time distinct from the rest of the vertebra: nevertheless, there is already here
a great difference of structure and function*.” With regard to the points in
which Cuvier is willing to admit an ‘ analogy’ between the occiput and the
atlas, he subjoins, agreeably with his idea of the law which governed such
correspondences,—“ These resemblances might naturally be expected in the
part of the head placed at the extremity of the vertebral column, and the
functions of which are, in fact, analogous to those of vertebra, since it gives
passage, like them, to the great neural axis+.”
With regard to the feature of resemblance (quelque rapport) which some
had seen between the mastoid process and a transverse process, Cuvier founds
his objection to its application to the vertebral character of the occipital
bone on a false homology. Concluding that the mastoid in man (fig. 25, s)
was homologous with the paroccipital in the hog (fig. 22, 4){ and some
other quadrupeds, he deems the determination of the paroccipital as the
transverse process of the occipital vertebra to be invalidated by the fact
that the ‘ mastcid’ belongs, in man, not to the occipital but to the petrosal.
There were cases, however, not unknown to the able Editors of the posthu-
mous edition of the ‘Lecons d’Anatomie Comparée,’ where the true trans-
verse processes of the occipital vertebra, though exogenous, like those of the
succeeding trunk-vertebree in man, had become developed to an equal extent
with such transverse processes ; the abnormality of the human occipital thus
repeating its normal condition in the quadruped. They however do not cite
these instances, or notice the confusion by their author of the true mastoid
with the paroccipital in reference to this his first objection to the vertebral
homology of the occipital segment. But it might further have been re-
marked, in respect of the segment of the skull to which the mastoid really
stands in parapophysial relation, that although the mastoid belongs in man to
the petrosal in the sense of being anchylosed with it, it articulates with the
parietal ; and the persistence or obliteration of a primitive suture is too vari-
able a phenomenon to determine to which of two bones a third connected with
both essentially belongs. The constant existence of the paroccipital either
as an autogenous element or an exogenous transverse process in all the
oviparous vertebrate classes, its common existence in mammals, and occa-
sional, though rare, development in man, establish that additional, though
by no means essential vertebral character in the occipital segment, which
loidiens et les deux moitiés de l’anneau de V’atlas 4 la couvrir. Les condyles sont repré-
sentés par les facettes articulaires au moyen desquelles l’atlas s’unit 4 axis. Le trou con-
dylien qui laisse passer le nerf de la neuviéme pair, a quelque rapport avec le trou de l’atlas
qui laisse passer le premier nerf cervical, et la premiére courbure de l’artere vertébrale. On
a aussi trouvé quelque rapport entre l’apophyse mastoide qui, dans la plupart des animaux,
appartient a l’occipital, et l’apophyse transverse de l’atlas et des autres vertébres; sur quoi
il faut remarquer que ces rapports sont moindres dans l’homme 4 certains égards que dans
les quadrupédes, puisque V’atlas n’y a ordinairement qu’une échancrure pour le passage de
Vartére et que l’apophyse mastoide y’appartient entiérement au rocher.”—1. c. p. 710.
* “Qn pourrait méme comparer l’occipital supérieur aux apophyses épineuses qui, dans
certains animaux, naissent par des points d’ossification particuliers, et restent quelque temps
distincts du reste de la vertébre; cependant il y aurait déja ici une grande différence de struc-
ture et de fonction.” —/. c. p. 711.
+ “Ces resemblances étaient naturelles 4 attendre dans la partie de la téte placéé a l’extré-
mité de la colonne vertébrale, et dont les fonctions sont en effet analogues a celles des ver-
tébres puisqu’elle laisse passer comme elles le grand tronc medullaire.”—. ¢. p. 711. i
t Cuvier, e. g. describes this element as “ L’apophyse mastoide, qui est trés-longue, trés-
pointue et ae de l’occipital,” in his elaborate Ossemens des Cochons, Oss. Fossiles, t. ii.
pt. i. p. 117.
ON THE VERTEBRATE SKELETON. 311
Cuvier seeks to obscure by the normal absence of its proper transverse pro-
cesses in man, and the assumed transference of them to another part of the
skull.
_ Cuvier in the next place objects to the comparison of the supraoccipital
with the neural spine of a trunk-vertebra, ‘“ because of its vast difference of
structure and function.” He does not specify the nature of the difference :
he admits that the neural spines have distinct centres of ossification in certain
animals; and all will allow that, in most of the trunk-vertebre of such, the
neural canal is closed by the coadapted ends of the neurapophyses to which
the spine articulates or becomes anchylosed : that therefore such spine does not
directly cover the neural axis, but, retaining the shape signified by its name,
performs exclusively the function in relation to muscular attachments. At
first view the contrast seems conclusive against all homology between such
‘mere intermuscular spine and the broad thin convex plate applied over the
cerebellum and posterior cerebral lobes in man. And it must be confessed
that the determination of their general homological relations could not have
been satisfactorily demonstrated by the mere relations of the parts to the
laminz supporting them, in so limited a range of comparison. - But, if we
descend to the fish, we shall find the supraoccipital equally excluded from
the neural canal by the meeting of the exoccipitals beneath its base; we
shall, also, see it still retaining the spinous figure, indicating its function in
relation to muscular attachments to predominate over that in subserviency
to the protection of the epencephalon. If we next ascend to the crocodile,
we shall find the neural spine of the atlas to be one of those examples alluded
to by Cuvier, where the ossification proceeds from an independent centre:
and it not only thus manifests its essential character as an autogenous ver-
tebral element, but maintains its permanent separation from the neurapo-
physes: and it further indicates the modifications of form to which the cor-—
responding elements will be subject in the more expanded neural arches of
the antecedent cranial segments by having already exchanged its compressed
spinous for a depressed lamellar form. Here indeed Cuvier might not only
have objected to recognise it as a vertebral spine by reason of its change of
form and function, but also by its continuing a distinct bone, which is
not the case with the expanded ‘spine’ of the mammalian occipital vertebra.
But returning to the crocodile, we observe in the segment anterior to the atlas
that both the form and connections of the supraoccipital (fig. 22, 3) are
so closely similar to those of the neural spine of the atlas that the recog-
nition of their serial homology is unavoidable; and we have a repetition
of the same characters of the vertebral element in question in the small and
undivided parietal (ib.7). Now Cuvier makes no difficulty in admitting the
‘occipital supérieur’ in the crocodile to be the homologous bone with its
more expanded namesake in the bird; or this with the still more expanded
‘partie grande et mince de l’occipital’ in mammals and man: he is also
disposed to admit the special homology of the supraoccipital under all
its variations of form and function in the above-cited air-breathing animals
with the bone 3 in fishes, which he sometimes calls ‘ occipital supérieur,’
sometimes ‘interpariétal.’ If then the special homology be admitted on the
‘ground of the constancy of the connections of the part, with what show of
reason can its general homology be rejected which forms.the very basis or
condition of the characters determinative of such admitted special homology ?
But Cuvier is not consistent with himself in his grounds of objection to the
essential nature of the human supraoccipital as the neural spine of its seg-
ment ; for he does not hesitate to call the atlas of the crocodile a vertebra,
312 REPORT—1846. q
although its ‘annular part’ is closed above by a transverse plate*. instead of
by a vertical spine, of which, indeed, there remains hardly more vestige than _
is presented by the tubercle or rudiment of the spinous process in the supra-
occipital of man. It must also be remembered, that the human supraoccipital
does retain to a certain extent the same function in relation to the attach-
ment of the proper vertebral muscles (splenii capitis, complexi, and the modi-
fied interspinales called ‘recti capitis postici maj. et min.) as the succeeding
vertebral spines; and combines this with the same place of completing, as
the key-stone, the neural arch; although by reason of the more voluminously
developed segment of the neural axis protected by that arch the peripheral ele-
ment is chiefly modified for the acquisition of the required increase of space.’
Cuvier next proceeds to comment on Oken’s endeavour to represent the
basisphenoid and the two alisphenoids with the two parietals as forming a ver-
tebra: and he admits that there is some analogy, though this is much more
feeble than the differences. ‘The basisphenoid, having another function,
takes on a different form from the basioccipital, especially above, by virtue :
of the posterior clinoid processes: and in the embryo it is composed not of
a single nucleus, but of twot+.” With respect to the objection from the
modification of form alluded to, it may be remarked that the same element
in other vertebral segments of the body undergoes much greater change
of shape; the centrums of the lower cervical vertebra in many birds send down
two processes as well-marked as the ascending ones called ‘ clinoid’ in that
of the parietal vertebra, not to speak of the ‘soc de charrue’ of the coccy-
geal vertebre of the bird, for example, without any difficulty having been felt
or expressed by Cuvier in their recognition as modified vertebral bodies, the
more essential characters of their general homology being as plainly retained
as in the case of the basisphenoid ; in its relation, e. g. to the neur-
apophyses and the support of the mesencephalon. With regard to the
objection from the two centres of development, if this be valid against the
general homology of the basisphenoid (6, fig. 25) as a vertebral centrum, it
equally tells against the body of the atlas (¢), which, as Cuvier well knew,
was ossified sometimes from two, and sometimes from three centres{. And
I may further observe that, although Cuvier affirms the two ossifie centres of
the basisphenoid to retain for a long time between them simple cartilages,
my observations bear out the accuracy of the remark of Kerkringius, (whose
figures Cuvier cites,) touching the “ dua ossicula distincta” (tab. xxxiv. fig.
iii. c, c), viz. “que celerrimé in formam figure apposite K coalescunt”:
and the figure of the coalesced rudiments of the basisphenoid given by Kerkrin-
gius closely resembles the bilobed rudiment of the vertebral centrums in the
sacrum of the chick.
Cuvier next objects to the neurapophysial character of the alisphenoids,
that the ‘foramen ovale’ is rarely a notch, more often a complete hole.
* “ Tes vertébres. L’atlas est composé de six pieces, &c.—La premiere, a, est une lame
transverse qui fait le dos de la partie annulaire. Elle n’a qu’une créte 4 peine sensible pour
toute apophyse épineuse.’’—Ossemens Fossiles, t. v. pt. ii. p. 95.
+ En avant du basilaire se trouve le corps du sphénoide postérieur, aux cdtés duquel ad-
hérent les deux ailes temporales ou grandes ailes. On a aussi cherché areprésenter ces trois
pieces comme formant une vertébre avec les deux pariétaux. II reste en effet encore quelque
analogie, mais beaucoup plus faible, tandis que les différences deviennent plus fortes. Le
corps du sphénoide a bien l’air d’une répétition du basilaire, mais ayant une autre fonction il
prende aussi une autreforme, surtout en dessus,au moyen des apophyses clinoides postérieures ;
et dans les premiers temps du fcetus il n’est pas composé d’un seul noyau, mais de deux, qui
ont long-temps entre eux de simples cartilages.’’—/. c. p. 712.
t Legons d’Anat. Comparée, t. i. (1836) p. 174. Meckel has figured the variety of three
ossific centres in this element of the human atlas in the Ist vol. of his Archiv fir die Phy_
siologie, taf. vi. fig. 1.
A
ON THE VERTEBRATE SKELETON. 313
“Now,” he urges, “vertebra properly so called give passage to the nerves only
by the intervals that exist between them and the other vertebra, and not by
particular foramina*.” Therefore the young anatomist must conclude that
the dorsal vertebree of the ox, the abdominal vertebrz of the lophius, and
every other segment of the trunk whose neural arches are directly perforated
by the spinal nerves, are to be rejected from the vertebral category !
_ Ithas been shown in the generalities on the corporal vertebra (p. 265), that
the neurapophyses in relation to the passage of their governing nerves may
be either untouched, notched or perforated by them, without prejudice to
their neurapophysial character. Viewed in the entire series of vertebrata
the cranial neurapophyses are more frequently perforated than notched, those
of the trunk more frequently untouched or notched by the nerves in passing
through their interspaces.
The penetration and sagacity of Cuvier nowhere shine forth more brightly
than in his bold and true determination of the bone 6, fig. 5, in the cod-fish t
as the homologue of the temporal wing of the sphenoid in the human skull.
To any less-gifted comparative anatomist the relation would have been masked
by the coalescence of the homologous part in man, by its connections with the
squamosal and frontal, and its comparatively small proportions under the
guise of a subordinate process; none of which characters exist in the ali-
sphenoid of fishes: it still retains, however, in that class, as in man, its most
essential connevtions in relation to the bones of its own segment and to the
brain and nerves; and Cuvier availing himself of these in the determination
of its special homology, was little likely to be swayed by so unimportant a
variety as the transmission of the characteristic nerve by a foramen instead
of by a notch. No sooner, however, has the time arrived and the call been
sounded for an advance to a higher generalization, which includes and ex-
plains the minor proposition, than Cuvier interposes the least important
difference of the alisphenoid to check the progress. It will be obvious to
the anatomist that the foregoing explanation of the value of the nerve-
notch or hole in the homological character of a neurapophysis has been’
called forth by the weight of the name of the ebjector rather than by the
force of the objection.
. Cuvier directs his next argument against the vertebral character of the
(neural arch of the) parietal segment generally. “Its composition,” he avers,
“is different from that of other vertebra, since the ring (he had just before
denied its annular form) would be composed of five pieces or even of six, inclu-
ding the interparietal.” Yet Cuvier does not hesitate, in his Article V., ‘Les Ver-
tébres’ (Ostéologie des Crocodiles), to reckon as the first vertebra, the atlas
notwithstanding its composition of six pieces.
_ If,indeed, Cuvier had subscribed to Geoffroy’s assertion, that “ Nature repro-
duces the same number of elements, in the same relations, in each vertebra,
only she varies indefinitely their form,’—his objection to the vertebral charac-
ter of any given segment that might deviate from the assumed normal number
of pieces would have been intelligible. But even, then, he would not have
been guided consistently by his own principle; for the objection founded
upon the supposed abnormal number of pieces in a cranial segment weighs
' ¥* “ Ses ailes different beaucoup plus encore et des deux condyliens, et des deux piéces qui
forment la partie annulaire des vertébres. A'la vérité, le trou ovale n’est quelquefois qu’une
échancrure ; mais le plus souvent il est entouré d’os, et par conséquent un vrai trou. Il-en
est de méme du trou rond toutes les fois qu’il est distinct du sphéno-orbitaire ; or les verté-
bres proprement dites ne laissent passer les nerfs que par les intervalles qui existent entre
elles et les autres vertébres, et non par des trous particuliers.”—/. c. p. 712.
" F Régne Animal, 1817, pl. viii. fig. 2,0, p. 184.
t “‘L’atlas est composé de six piéces qui, a ce qu’il paroit, demeurent pendent toute la vie
distinctes.’’—Ossemens Fossiles, t. v. pt. ii. p. 95.
1846. x5
314 REPORT—1846.
not at all against the recognition of a corresponding segment of the trunk,
though similarly composed. ©
In fact, throughout this attack upon the vertebral theory of the skull, it -
will be seen that it is based upon the @ priori assumption that all the endo-
skeletal segments of the trunk, however modified, are vertebre, and all those
situated in the head, are not vertebre. The essential character of a vertebra
is thus deduced from its position, not its composition. It needs only to com-
pare any of Cuvier’s objections to the vertebral character of the cranial seg-
ments, with the modifications of the corporal segments admitted by him to
be vertebrz, previously enumerated in this Report (pp. 264-270), to see that
the characters of the cranial vertebra objected to by Cuvier differ in degree not
in kind, and become valid arguments against the admittance of natural seg-
ments into the vertebral category, only when they happen to be situated at or
near the commencement of the series.
It has been abundantly proved, I trust, that the idea of a natural segment
(vertebra) of the endoskeleton, does not necessarily involve the presence of
a particular number of pieces, or even a determinate and unchangeable ar-
rangement of them. The great object of my present labour has been to
deduce, by careful and sufficient observation of Nature, the relative value
and constancy of the different vertebral elements, and to trace the kind and
extent of their variations within the limits of a plain and obvious maintenance
of a typical character.
In reference to the neural arch, the variation in the number and disposition
of its parts, illustrated in the figures 1, 2, 3,4, 18, 19, 20, 21, do not seem to
me, nor will they I apprehend to any unbiassed anatomist, to obliterate the
common typical character of that part of a vertebra. Those elements which
are furthest from the centrum are the chief seat of the changes. Ifthe reader
will compare figure 2 with figure 19, he will see for example that the crown of
the arch is formed by a single bone(7) in the crocodile, but by two bones (7,7)
in fish ; nay, in most fishes the halves are even pushed apart by the interposi-
tion of athird bone. Yet the sagacity of Cuvier led him to determine the di-
varicated moieties of the divided parietal in such fishes to be the same (homo-
logous) bone with the single parietal of the crocodile. With what consistency,
then, can the general homology of the segments be rejected, which sufferno
other change in their composition than that resulting from the single or bifid
character of the same bone in each? Is the single frontal of the human
adult regarded as a distinct bone from the bifid frontal of the foetus? If,
therefore, the neural arch of the parietal vertebra (mesencephalic arch) of
the crocodile be free from the objection, raised by Cuvier to the vertebral
character of the homologous arch in man, on the score of the number of its
elements; neither can that objection be allowed to have any force when it
rests upon the mere division in the human mesencephalic arch of the recog-
nised homologue of the single spinous element in the crocodile.
In the sheep, the arch which encompasses the epencephalon is formed by
only three elements, the neural spine resting upon the conjoined upper ends
of the neurapophyses. In the dog these elements are divaricated and the
epencephalic arch is closed above by the neural spine. Now Cuvier does
not allow this difference of arrangement of the latter element (3) to affect his
recognition of the ‘ suroccipital’ in both mammals; and, therefore, one is at
a loss to discover the consistency of the ideas which would repudiate the
general homology of the bones or of the entire arches which they surmount,
because, as Cuvier would say, “ the composition of the arch is different, being
of three pieces in the sheep and of four pieces in the dog.” Yet this is pre-
cisely the kind of objection which he has directed against the mesencephalic
arch, viz. because it may be composed of five or even six pieces, in certain
ON THE VERTEBRATE SKELETON. 315
animals, In the fish, in fact,—by reason of the parietal parapophyses (8, s)
being subject to the same variation in their relative position to the other
elements, which has been illustrated in respect of the neural spine in the
epencephalic arch of the dog and sheep,—the mesencephalic arch is com-
posed of seven pieces, or, including the interposed supraoccipital, of not less
than eight bones. Yet even here we clearly and easily trace the kind and
degree of modification to which the fundamental plan of the neural arch
has been subject. The archetype is nowise obliterated: the general homo-
logies of the modified elements are not less recognisable than their special
homologies. The centrum and neurapophyses are the steadiest elements:
the spine is not only subject to great diversity of size and shape, but to some
variety of position, and, moreover, to be either single or bifid: the parapo-
physes have less range of variety in point of dimensions, but may be more
or less interposed between spine and neurapophyses, or may become con-
fluent with either element. Thus the epencephalic arch of the crocodile
(fig.18) differs essentially, in a Cuvierian sense, from that of the tortoise or the
fish (fig. 1), because it is composed of four pieces in the first and of six
pieces in the latter; the difference of composition merely depending, how-
ever, on the more exterior position and connation of the parapophyses, 4, 4, in
the crocodile.
The independency of the parietal and frontal bones is next urged by
Cuvier as militating against the idea that they complete a vertebral arch
formed respectively by the alisphenoids and orbitosphenoids as the piers or
haunches: and the more so, inasmuch as they are separated from those bones
in some animals by the intercalation of the squamosals*. By parity of reason
we must reject the general homology of the neural arch and spine of the
atlas in the Ephippus and some other fishes, because that part of the verte-
bra is not only distinct, but uplifted and removed from the piers or base of
the arch by the intercalation of the articular processes of the neural arches
of the occiput and axis. According to Cuvier such separated atlantal arch
must. be regarded as a new bone, and the centrum ought therefore equally
to be viewed as ‘une piéce particuliére qui a une destination particuliére ’:
but the general homology of vertebral elements may be determined not only
by their relations to their own segment, but by those which they maintain
with their less modified homotypes in contiguous segments.
The centrum of the atlas in the Ephippus directly sustains other neur-
apophyses than its own, and so far has a new or particular function ; but,
since it continues to unite the centrum of the axis with that of the occiput,
we still regard it as their homotype, and as standing in the relation of the
centrum to its uplifted and shifted neurapophyses. So, likewise, although
these elements now aid in strengthening the joint between the zygapophyses
of the neural arches of the occiput and axis, and thus perform a new and
very peculiar function, their relation to these and other neural arches in the
series of vertebre renders it impossible to overlook the serial homology of
the separated ‘ laminz’ of the atlas and that of its spine with the other and
larger vertebral laminz and spines.
* “ Tans tous les cas, on ne pourrait regarder cette vertébre comme annulaire, ni supposer
ane Jes pariétaux en forment le complément ; d’une part, ce serait une composition différente
e celle des autres vertébres, puisque l’anneau serait formé de cinque piéces et méme de
six, en comptart l’inter-pariétal; de autre, il arrive dans plusieurs animaux que les ailes
temporales du sphénoide n’atteignent pas au pariétal, parceque le temporal va toucher au
dessus d’elles, soit au frontal soit au sphénoide antérieur. Ainsi les pariétaux sont des
piéces indépendantes du sphénoide postérieur, des piéces particuliéres qui ont une desti-
nation particuliére, celle de servir de bouclier 4 la partie moyenne et postérieure des hémi-
_ sphéres, tout comme les grandes ailes ont celle de servir de support aux lobes moyens dans
a we
lesquels ces hémisphéres se terminent vers le bas.”—I. e. p. 713.
y@2
316 REPORT—1846.
The new functions which the uplifted and independent spines of the pari-
etal and frontal vertebrae perform in man and many mammals are, with
respect to the parietal bones, to shield the upper surface of the middle and
posterior parts of the cerebral hemispheres, whilst the frontal is confined to
covering the anterior lobes of the same hemispheres.
Hereupon it may be asked whether such relations and offices are the rule
or only the exception; and, if the latter, whether it occurs in the lowest or
the highest of the vertebrate series ; whether in that class where the arche-
typal arrangement of parts is most, or in that in which it is least departed
from? All these considerations are felt to be indispensable by the homo-
logist in quest of the true signification of the parts of the animal frame,
before drawing his conclusions from the first modification that may present
itself. They are neglected by Cuvier in the objection to the vertebral cha-
racter of Oken’s ‘kiefer-wirbel,’ founded upon the relations which the parietal
bones present to the encephalon in the mammalian class. Yet the more
normal relations of those bones, both to the encephalon and to the alisphe-
noids, seem to have been present to the mind of Cuvier, and to have been
duly appreciated by him when he defined, in 1817, the second cranial cine-
ture as constituted by the parietals and sphenoid*.
With regard then to the first of Cuvier’s arguments for viewing the human
and mammalian parietals as ‘ des piéces particuliéres qui ont une destination
particuliére,’ viz. that they are separated from the alisphenoids by the tem-
poral bones. If we commence our consideration of it by the question, whether
this separation be the rule or the exception, the reply which Nature sane-
tions will be that they are not so separated in any of the three great classes of
oviparous vertebrata, nor in the majority of mammalia, nor even, as a general
rule, in man himself. With regard to the second objection founded on the
interposition of the enormously and backwardly developed prosencephalon
between the mesencephalic spines (fig. 25, 7) and the mesencephalic segment
of the brain, to which the parietal vertebra essentially relates,—-its value will
depend on the choice made by the homologist between the function of the
parietals as immediate shields to the optic lobes (mesencephalon) in the cold-
blooded classes, and their function as mediate ones through the interposed
mass of the prosencephalon in the warm-blooded classes, as that which best
manifests adhesion to the ideal archetype. What to me has ever appeared one
of the most beautiful and marvellous instances of the harmony and simplicity
of means by which the One great Cause of all organization has effected every
requisite arrangement under every variety of development, is the fact, that
the protection of the enormous cerebrum peculiar to the higher mammals
has not been provided for by new bones: by bones, e. g. developed from
centres so numerous or so situated as to render any determination of their
homologies as vague and unsatisfactory as would result from the attempt to
determine those of the dermal ossifications upon the head of the sturgeon, in
reference to the endoskeletal epicranial bones in fishes and reptiles. We
might well have expected, had conformity to type not been a recognizable
principle in the scheme of organized beings, to have had so many ‘ particular
bony pieces’ and so situated in the expanded human cranium as would have
baffled all our endeavours to reduce them to the type of the epicranial bones
of the reptile or fish. Yet the researches of the great comparative anatomists
of the present century, and more especially those of Cuvier himself, have
proved that there is no such difficulty: and a glance at the Table of Special
Homologies, No. 1, will show that the bones (3, 7, 11) most modified in rela-
tion to the expanded cerebrum and cerebellum of man and mammals are
* Reégne Animal, i. p. 73.
“gaa7
ON THE VERTEBRATE SKELETON. 317
precisely those of which the determination has been easiest, and respecting
‘the names and nature of which there has been the least discrepancy of opi-
‘nion. It is with pain and a reluctance, which only the cause of truth has
‘overcome, that I am compelled to notice the inconsistencies into which the
great Cuvier fell, when his judgement became warped by prejudices against
a theory, extravagantly and, perhaps, irritatingly, contended for by a con-
temporary and rival anatomist. After having established by the clearest
evidence and soundest reasoning in his great and immortal works that the
‘bones (7) in the fish (figs. 2 and 5) and reptiles (figs. 9, 10, 13, 19, 22) were
homologous with those in birds (7, figs. 8 and 23), mammals (7, figs. 12 and
24), and even in man (7, figs. 11 and 25); and, after contending that they
ought to bear the same name—under which, indeed, we find him describing
them in the ‘ Lecons d’Anatomie Comparée’ from man down to the fish—
Cuvier comes at last to declare that, in those animals in which they are
‘separated from the alisphenoids and mesencephalon, they are “ particular
pieces which have a particular destination !”
~The relation of the mastoids (s,s), as parapophyses, to the parietal or
sphenoidal vertebra not having been detected in Cuvier’s time, he supposes
that the pterygoids, in the system which makes a vertebra of the sphenoid,
‘ean be compared to nothing else than the transverse processes of such. As,
according to my views, they are recognizable in General Homology as quite
_ distinct elements of another cranial vertebra, the arguments which Cuvier
advances in disproof of what he thought they must be called, do not concern
the subject of the present Report. The inferior exogenous processes, in-
deed, of the basisphenoid in mammals are not unlike those developed from
the under surface of the centrum of the atlas in Sudis gigas, or from some
‘of the cervical centrums in birds. The argument founded by Cuvier on the
autogenous development of the true pterygoid (figs. 24 and 25, 21) would
weigh little against its parapophysial nature, if other characters concurred
‘to prove it a ‘ parapophysis;’ but its connections and position show it to be
-a ‘diverging appendage.’
‘With respect to the anterior sphenoid, Cuvier affirms that its composition
is totally different from that of the posterior sphenoid and occipital, and from
‘that of any vertebra. By the term ‘ sphénoide antérieure’ is meant the
“eoalesced presphenoid and orbitosphenoids (figs. 24 and 25, 9 and 10); and the
two bones referred to in the comparison signify, the one, the basi- and ali-
sphenoids (i. 5 and c), and the other the basi- and ex-occipitals (#b. 1 and 2).
‘With respect to 9 and 10, Cuvier remarks that it is never, in mammals, formed
“of three pieces, but only of two; and that these are properly the bony rings
‘for the optic nerves, which in course of time approximate and coalesce with
each other: but so long as the median suture divides them, no distinct or
“third bony nucleus is developed in the intervening cartilage*.
» Since, however, we see that the homologues (recognised as such by Cuvier)
of the orbitosphenoids are something more than rings surrounding the optic
nerves in the bird (figs. 8 and 23, 10) and crocodile (figs. 9 and 22, s)—that
they are merely notched by the optic nerves, and are chiefly developed in
* “Ton a voulu aussi considérer le sphénoide antérieur comme une vertébre dont les
_frontaux compléteraient la partie annulaire, et ou la position du trou sphéno-orbitaire entre
les deux sphénoides repondrait assez aux trous inter-vertébraux ordinaires. Mais la compo-
“sition du sphénoide antérieur lui-méme est toute différente de celle des deux os, dont nous
avons parlé avant lui, et de celle d’aucune vertébre. Il n’est jamais, dans les mammiferes,
formé de trois piéces, mais seulement de deux; ce sont proprement des anneaux osseux pour
les nerfs optiques, qui par suite du temps se rapprochent et se soudent entre eux; la suture
est toujours au milieu, et tant que V’ossification n’est pas complete, il n’y a entre les deux
anneaux que du cartilage, dans Jequel il ne se forme pas de troisicme noyau.”—/. ¢. p. 714.
318 REPORT—1846.
neurapophysial relation to the sides of the prosencephalon,—we are led to
carry our inquiries into an earlier period of their development than that ad-
duced by Cuvier, as contravening their vertebral characters. Cuvier cites
the figure 2, in pl. xxxv. of the ‘Osteogenia Foetuum’ of Kerkringius, as evi-
dence of his statement of the developmental characters of the ‘ sphénoide
antérieur.” That figure, however, exhibits the condition of the bone, when,
although the median suture remains, each orbital ala has become anchylosed
with the posterior sphenoid, and is likewise directly perforated by the optic
nerve. The gelatinous cells of the anterior extremity of the notochord very
early retrograde to the basioccipital region of the basis cranii, and the noto-
chordal capsule alone is continued to the anterior extremity of the basis.
This is converted into cartilage,
and the osseous particles which Fig. 26.
ultimately constitute the anterior
sphenoid are deposited as follows :
first a centre or nucleus appears,
in each orbital ala, external to the
hole by which the optic nerve
passes through the primitive carti-
lage (fig. 26, A, 10); soon after a
second nucleus (76. B, 10) is esta-
blished at the inner or mesial side
of each optic foramen : these cen-
tres form the foundation of the
neurapophyses or orbitosphenoids,
and ultimately coalesce around the
optic nerve, as Kerkringius has
depicted. Buta third pair of ossi-
fic centres (ib. C, 9) is established
behind the optic foramina between
poe te oe henna (s). Phases of deyclapmeas the a Sphenoid bone:
a single transverse bar (2b. D, 9),
before coalescing with the orbitosphenoids in front, or with the basisphenoid
behind, and that bar transitorily represents the centrum of the frontal vertebra.
To the objection that such supposed centrum is developed from two points
instead of one, the same reply may be made that was made before to a similar
objection raised by Cuvier against the general homology of the basisphenoid ;
which objection, as was then shown, would be equally valid against the uni-
versally admitted homology of the body or centrum of the atlas.
The frontal neurapophyses manifest in their development, each from two
centres (fig. 26, B, C, 10), a transitory mark of vegetative repetition analogous
to that which permanently characterizes the neurapophyses of the trunk-verte-
bre in the sturgeon.
Thus the evidence of development, when complete, tells for, rather than
against the serial homology of the ‘sphénoide antérieur’ of Cuvier with the
centrum and the neurapophyses of other vertebre ; and the more obvious
and important characters of relative position to the other bones of their own
segment, and to their homotypes in the contiguous segments, as well as to
prosencephalic segment and characteristic nerves,—which characters have
served to determine the special homologies of the coalesced bones in ques-
tion (9,10) from man down to the fish,—concur with the developmental
characters in establishing their general homology as centrum and neur-
apophyses.
ON THE VERTEBRATE SKELETON. 319
_. Cuvier affirms, however, in support of his argument, that, although the
orbitosphenoids are never separated from the frontals, as the alisphenoids are
from the parietals, in the mammalia, they are almost always separated from
the frontals in the other classes, so that the vertebral ring is again inter-
rupted *. But, were even the frontals commonly uplifted above the orbito-
sphenoids in birds, reptiles and fishes, which does not accord with my ex-
perience, the objection, on that score, to regarding them as ‘neural spines,’
would as little apply, as it does to the universally recognised general homology
of the separated and uplifted neural arch of the first vertebra of the trunk
of the Ephippus and some other fishes.
Cuvier finally regards the connection of the frontals with the prefrontals,
which he calls ‘ ethmoid’ in mammals, ‘l’enchdssement de l’ethmoide,’ as a
function quite remote from any of a vertebral character, “ relative 4 toute
autre chose.” This objection only shows the necessity of a right apprecia-
tion of special homologies, in order to form a true judgement respecting
general homology ; and, with respect to the ‘ ethmoide,’ I must refer to the
section on the prefrontals in the chapter on ‘ Special Homology (p.214). If
the arguments there adduced be held to prove the crista galli and cribriform
plate in the human skull to be the homologues of portions of the coalesced
prefrontals and olfactory capsules, we may next remark that these portions
are not merely wedged between the orbital plates of the frontal, but articu-
late behind by a persistent suture with the orbitosphenoids. As neurapo-
physes, the coalesced prefrontals of the terminal vertebra of the skull thus
articulate with their next succeeding homotypes; and, by virtue of the ex-
cessive development of the spine of the frontal vertebra, as well as from their
being contracted and drawn backward in the human skull, they articulate
with such spine (the frontal) as well as with that of their own proper seg-
ment (the nasals). But, in the crocodile (fig. 9), we have seen a similar
relation manifested not only by the more normal neurapophyses (14) of the
nasal vertebra, but likewise by those (10) of the frontal, those (6) of the
parietal, and those (2) of the occipital vertebra.
All the objections raised by Cuvier to the general homology of the cranial
bones as modified vertebral elements, equally apply to elements of vertebree
in the trunk, which Cuvier himself has admitted to be vertebra, notwith-
standing such modifications. The repetition of the perforated character of
the human alisphenoid and orbitosphenoid in the neurapophyses of the trunk-
vertebrze of many inferior animals, requires only a passing notice. The
flattening, expansion and sutural union of the human supraoccipital, parietal
and frontal bones, are matched by the neural spines in the carapace of the
tortoise. If the basioccipital, basisphenoid and presphenoid are broad and flat,
instead of cylindrical, so likewise are the bodies of the sacral vertebre in the
broad-bodied megatherioids and in many birds. If the basioccipital and
basisphenoid are lengthened out and firmly united together by deeply in-
dented sutural surfaces in most fishes, so likewise are the bodies of the four
anterior vertebre of the trunk in the pipe-fish (fistularia). If the basi-
sphenoid and presphenoid be developed each from two ossifie centres, as in
man, so likewise may the body of the human atlas be ossified; and even should
the moieties of that centrum not coalesce at the median plane, they would
» * “Ce que j’ai dit des pariétaux s’applique aux frontaux, considérés comme compléments du
sphénoide antérieur ; leur fonction est relative 4 toute autre chose, la protection des lobes
antérieurs du cerveau et 4 l’enchassement de l’ethmoide; et quoique le sphénoide antérieur
n’en soit jamais séparé dans les mammiféres comme le postérieur l’est souvent des pariétaux,
il Pest presque toujours dans les autres classes, en sorte qu’alors V’anneau vertébral serait
aussi interrompu.”—/. c. p. 714.
320 REPORT—1846.
nevertheless still retain their essential characters as divisions of a single ver-
tebral element: just as does the vomer in the salamanders, salamandroid
fishes and serpents, which begins to be developed from two lateral points,
like the body of the human atlas occasionally, without the development end-
ing, as it always does in such atlas, by confluence of the resulting halves. It
would be more reasonable to repudiate the general homology of the body of
a whale’s dorsal vertebra with the centrum of the typical vertebra, because
it consists of three pieces set end to end, than to deny the general homology
of the vomer because it may consist of two pieces set side by side, or that
of the anterior trunk-vertebrz of the silurus because they consist of two
pieces set one upon the other. These are examples of a principle of varia-
tion which Cuvier never permitted to blind his perception of the special ho-
mology of certain bones, the mandibular ramus, for example ; though vege-
tative or teleological subdivision is carried out to a much greater extreme
there than in any vertebral centrum; unless, indeed, the number of points
from which the whale’s vomer be ossified may equal those in the crocodile’s
lower jaw. But if the differences in this developmental character, viz. of ossi-
fication from a single ossifie point as in the vomer of the cod, or from two
points as in that of the lepidosteus, or from three or more points as in the
human vomer, interpose no obstacle to the determination of the special homo-
logy of the bone 13 from man to fish, it can as little avail as an argument
against its general homology, which is determined not by the development of
the vomer but by its relations to the other constituents of the segment of the
skeleton to which it naturally belongs. ‘
The great difficulty which the anthropotomist may naturally experience in
forming an idea of the vomer as the body of a vertebra, will arise from ‘its
extremely modified form in the human subject: but he must bear in mind
that it is an extreme part, the last of its series counted forwards; and if he
should desire some higher and better established authority than the present
Report before yielding assent to the vertebral character of the bone, under
its characteristic ‘ ploughshare’ mask in man, I know no name more influen-
tial than that of Cuvier himself, in regard to the equally and similarly modi-
fied centrum at the opposite end of the vertebral series in the bird. For
although the mask of coalescence is superadded to that of strangeness of
shape in the bone which Cuvier there compares to a ploughshare [ vomer, or
‘soe de charrue’ ], the great anatomist and cautious generalizer does not hesi-
tate to affirm that it is “ composed of many vertebre ” (see ante, p. 263).
It may, perhaps, be said that the coccygeal vomer must be vertebral in its
nature because it is situated in the tail; but the ‘ petitio principii’ in this
argument will be transparent, if we transpose the locality, and say that ‘the
cranial vomer must be vertebral in its nature because it is placed in the
head.’ For what are ‘head,’ ‘tail,’ ‘ thorax,’ or ‘ pelvis,’ but so many di-
versely modified portions of a great segmental whole? These localities do not
determine the nature of the segments composing them ; such knowledge can
only be acquired by a study of the composition of the segments ; andit is the
modifications of the segments that determine the nature of the localities or
divisions of the endoskeleton, to which such special names as ‘ head,’ ‘ tho-
rax,’ &c. are applied.
Yet Cuvier himself, perhaps, little suspected how much his ideas of the
essential nature of a segment of the endoskeleton were governed by the part
of the body in which it happened to be placed. Whenever the young ana-
tomist finds a difficulty from the peculiar form or development, division
or coalescence, of a cranial bone, in recognising or admitting its vertebral
ce a
xray
ON THE VERTEBRATE SKELETON. 321
character, Jet him compare the results of his own observations with those
summed up in pp. 264-266, and see whether the same kind of modification
may not'be’repeated in the homologous element of a vertebra of the trunk
in one or other of the species of vertebrate animals.
» The latest direct objection to the cranio-vertebral system is from the pen
of the celebrated ichthyotomist of Neuchatel. M. Agassiz represents the
current ideas respecting this system at the period when he published his
objections to it, in the following graphic passage of his invaluable and
splendid work :—“ It was M. Oken who had printed the first programme on
the signification of the bones of the skull. The new doctrine which he set forth
was received with extreme enthusiasm in Germany by the school of physio-
philosophers [Natur-philosopher]. The author at that time required three
cranial vertebrz, and the basioccipital, the sphenoid and the ethmoid were
viewed’as the central parts of these cranial vertebra. Upon these pretended
bodies: of vertebree were raised the arches enveloping the central parts of the
nervous system (our ‘protective plates’) ; whilst to the opposite side were at-
tached the inferior pieces which should form the vegetative arch destined to
embrace the intestinal canal and the great vessel (the ‘ facial arches’ of which
we'shall presently speak). It would be tedious to enumerate here the changes
which each author has rung upon this theme in modifying it agreeably with
his notions. These contented themselves with the number admitted by Oken;
those raised the number of cranial vertebre to four, six, seven, or even more:
some'saw nothing but ribs in the branchial arches and jaws ; others took the
latter for limbs of the head, analogous to arms and legs. If they could not
agree about the number of the vertebrz, still less were they at one in regard
to’ the part assigned to each bone. The most bizarre nomenclatures have
been* proposed by different authors who thus sought to generalize their
ideas. Some have gone so far as to pretend that the vertebre of the head
wereas complete as the vertebre of the trunk, and by means of dismember-
ments, with divers separations and combinations they have reduced all the
forms of skull to vertebre, assuming that the number of pieces was in-
variable for every form of skull, and that all vertebrate animals, whatever
their definitive organization, bore, in their respective crania, the same number
of points of ossification *.”
-» And thus it is that a great truth in nature has been endeavoured, and
* “(C’est M. Oken qui fit imprimer le premier programme sur la signification des os du
crane, La nouvelle doctrine qu’il exposait fut accueillie en Allemagne avec un enthousiasme
extreme par l’école des philosophes de la nature. L’auteur postulait alors trois vertébres
du crane, et Voccipital basilaire, le sphénoide et l’ethmoide étaient envisagés comme les
parties centrales de ces vertébres craniennes. Sur ces prétendus corps de verteébres s’élevaient
des’ arcs enveloppant les parties centrales du systéme nerveux (nos plaques protectrices) ;
tandis. que du. coté opposé étaient attachées des piéces inférieures qui devaient former l’are
végétatif destiné & embrasser le canal intestinal et les gros vaisseaux (les arcs de la face dont
nous traiterons plus tard). Il serait trop long d’énumerer ici les changements que chaque
auteur apporta 4 ce travail en le modifiant 4sa maniére. Les uns se contentérent du nombre
admis par Oken, les autres élevérent le nombre des vertébres craniennes jusqu’a quatre, six,
sept et méme plus ; les uns voulurent voir des cotes dans les arcs branchiaux et les machoires ;
les autres prirent ces derniéres pour des membres de la téte, analogues aux bras et aux
jambes. Sil’on n’était pas d’accord sur le nombre des vertébres on l’était encore moins sur
le réle qu’on assignait & chaque os. Les nomenclatures les plus bizarres ont été proposées
par les différens auteurs, qui cherchaient ainsi 4 généraliser leurs idées. On alla jusqu’a
prétendre que les vertébres de la téte étaient aussi complétes que les vertébres du tronc, et
au moyen de démembremens, de séparations et de combinaisons diverses, on ramena toutes
les formes du crane 4 des vertébres, en admettant que le nombre des piéces etait invariable-
ment fixé pour toutes les tétes; et que tous les vertébrés, quelle que soit d’ailleurs leur
organisation définitive, portaient dans leur téte le méme nombre de points d’ossifications.”
—Recherches sur les Poissons Fossiles, t. i. (1843), p. 125.
322 REPORT—1846.
too successfully in regard to the rising generation of anatomists; to be
obscured. Ideas and statements are misquoted, unintentionally, doubtless,
and through neglect of reference to the original work (as in the citation of
the bones representing the bodies of the cranial vertebra in the Okenian
theory): or they are misunderstood (as where the arches, neurapophyses or
‘ bogentheile,’ composed as Oken truly said by the alisphenoids and orbito-
sphenoids are held to be synonymous with the ‘ plaques protectrices’ of M.
Vogt): the most extreme and least defensible views are selected out of each
tentative step in the inquiry, and are clubbed together to represent the
general result, which is of course dismissed with as sweeping a condemnation.
The specific objections raised by Cuvier are deemed well-founded and un-
assailable ; and to these M. Agassiz adds the following. Premising that,
“the formation of vertebrae presupposes as a first condition the existence
of a notochord* ;” and, arguing upon this basis, and on the assumption
that the cephalic extension of the ‘ chorda dorsalis’ as it is permanently
manifested in the Branchiostoma is not so great in the embryos of other and
higher fishes, but is arrested at the region of the alisphenoid from the com-
mencement of its development, M. Agassiz concludes: —“ Now, the application
of this principle to the composition of the skull demonstrates at once that there
exists but one cranial vertebra, the occipital vertebra, and that the rest of
the skull is foreign to the vertebral system+.”
At the period of development described and figured by M. Vogt in the em-
bryo of the Coregonus, which period M. Agassiz conceives to represent the very
earliest condition of the anterior extremity of the notochord, the pointed ex-
tremity of the gelatinous central cells of this part terminates at the posterior
boundary of the hypophysial space: but the peripheral capsule of the notochord
extends over that space and forwards to the obtuse anterior extremity of the
embryonal ‘ basis cranii’: and it is in the expanded aponeurosis, directly con-
tinued from the chorda along the basis cranii, that the thin stratum of carti-
lage cells are developed, arching along the sides of the hypophysial. space,
from which the ossification of the basisphenoid, presphenoid and vomer
proceeds {.
The superaddition or the later continuation of the cylindrical gelatinous
‘chorda’ in the aponeurotic basis of the cartilaginous and osseous growths of
the vertebral centres in the trunk, seems to relate chiefly to their more or
less cylindrical form in that region : the notochord regulates, asa mould, the
course of ossification, disappearing by absorption as the bony lamelle of the
vertebral bodies encroach upon it in their centripetal progress: the notochord
plays an important part also in the establishment of the elastic jelly-filled
capsular joints in the back-bone of fishes; and therefore it might well be
dispensed with, or be early and rapidly removed, in the development of the
flattened, expanded and anchylosed or immoveably articulated bodies of the
cranial vertebra. And, besides, the notochord is immediately concerned in
the development of only one of the elements of the typical segment of the
endoskeleton. It is obviously, therefore, an unwarrantable and erroneous
application of a developmental character, to conclude, from a modifica-
tion of this one character in respect of a single element, the ‘ centrum,’ that
every other character establishing the general homology of such element, as
* “La formation des vertébres suppose, comme premiére condition, l’existence d’une
* corde dorsale.’’’—Op. ci¢. tom. i. p. 127, livr. xviii. (1843.)
+ “Or, V’application de ce principe 4 la composition de la téte nous montre d’entrée qu’il
n’existe gwune seule vertébre crdnienne, la vertébre occipitale, et que le reste de la téte est
étranger au systéme vertébrale.”—Jb. p. 127.
+ Hunterian Lectures on Vertebrata, 1846, p. 71.
ON THE VERTEBRATE SKELETON. 323
well.as every character determining that of the surrounding vertebral elements,
are to be nullified and set aside! M. Agassiz, moreover, seems not to have
suspected that the notochord may have other and more immediate and import-
ant functions than even those relating to the vertebral column. The peculiar
elective attraction of its component cells for the gelatinous principle may be es-
sential to the due operation of those neighbouring cells which form the basis of
the neural axis, and which as exclusively assimilate the albuminous principle :
and this reciprocal antagonism in the selection of particular proximate prin-
ciples from the common primitive blastema may explain the contemporaneous
origin of notochord and myelon in the embryonic trace, when all development
is as yet the work of cell-assimilation and metamorphosis, without any supply
from a vascular system, this being a later formation in the building up of the
organic machinery. By confining, however, his views of the notochord to one
of its functions in relation to a single vertebral element, and by extending his
conclusions from this to the entire vertebra, M. Agassiz, though recognising
more absolutely than Cuvier, the vertebral character of the neural arch of
the occipital segment, concludes that Nature discards that type in the con-
formation of the cinctures that precede it and which successively girt the
mesencephalon, prosencephalon and rhinencephalon.
Assuming a gratuitous explanation of the hypothetical absence of the bodies
of the cranial vertebre (Poissons Fossiles, t. i. p. 128), M. Agassiz asks,
“ Ainsi, que seraient dans cette hypothése, le sphénoide principal, les grandes
ailes du sphénoide, et l’éthmoide, qui forment pourtant le plancher de la
cavité cérébrale ?— Des apophyses ?—Mais, les apophyses ne protégent les
centres nerveux que du cdté et d’en haut ?—Des corps des vertébres ?—
Mais ils se sont formés sans le concours de la corde dorsale ; ils ne peuvent
done pas étre des corps des vertébres.” (1b. p. 129.) To this it may be
replied, first that the bodies of the cranial vertebra are not absent; they
are represented, as above explained, by their cortical portions in the vomer
(fig. 5, 13), presphenoid (2b. 9) and basisphenoid (2. 5), and by both cortical
and central portions in the basioccipital (2d. 1): nay, the central part of the
body of the frontal vertebra is represented in some fishes by the entosphenoid
(2b. 9'), which remains distinct from the cortical part below, as does the central
part of the body of the atlas in the siluroid fish. If it were true, indeed,
that the entosphenoid was pierced by the canals transmitting the olfac-
tory nerves*, Bojanus’ idea of its general homology as the centrum of the
‘vertebra optica’ must be abandoned. But the parts called ‘olfactory
nerves’ by M. Agassiz, pass from the prosencephalic to the rhinencephalic
compartments of the cranium not merely above the bone called ‘ cranial
ethmoid ’ by the same author, but, also, through the upper part of the inter-
space between the bones (orbitosphenoids) which the entosphenoid (9')
sustains: and the true olfactory nerves perforate the neurapophyses (14)
which Bojanus called ‘ ethmoid’ and which Cuvier and M. Agassiz have
termed ‘frontaux antérieurs’ (see ante, pp. 214-226). The alisphenoids, being
notched or perforated by their proper intervertebral nerves, are ‘ apophyses’
(neurapophyses), and accordingly do protect the sides of their proper nervous
centre, the mesencephalon. The central jelly-cells of the notochord appear to
be withdrawn into the occipital region before ossification of the basisphenoid
commences, and that modified vertebral body is therefore developed at the
expense of the fibrous sheath of the notochord, and is represented by its
‘cortical’ part only. But its general homology is determined by its con-
* M. Agassiz has described this bone under the name of ‘ éthmoide cranien’ as “un os
impair, court, de forme presque carré dans lequel sont percés les canaux servant aux nerfs
_ olfactifs.”—Recherches sur les Poissons Fossiles, t. i. p. 120.
<
324 REPORT—1846.
nections with the basioccipital (admitted by Agassiz to be a vertebral body)
behind, and with the alisphenoids above.
In many fishes the basisphenoid unites with the basioccipital by a deeply
indented sutural surface, like that which unites together the elongated bodies
of the anterior trunk-vertebre in the Fistularia. In mammals the basioc-
cipital and basisphenoid join each other by flat surfaces, also like the bodies
of the trunk-vertebre, until the period when, in most of the class, the
joint is obliterated by anchylosis. These and similar repetitions of class-
characters of vertebral elements in the regions of the head and trunk are not
so wholly devoid of signification, as they must seem to be to the opponents
of the cranio-vertebral theory.
In his new and elaborate classification of the bones of the skull of fishes,
M. Agassiz divides them primarily, like Cuvier, into bones of the cranium,
or ‘ box which envelopes the brain and the organs of sense’: and into bones
of the face, ‘which is composed of the moveable pieces subservient to nutrition
and respiration’ (/. c. p. 110).
This division is open to the objection that the bony or cartilaginous cap-
sules which immediately envelope the organs of sense are always originally,
and most of them permanently, separate from the box or capsule that enve-:
lopes the brain. The independent character of the ear-capsules, for example,
is manifest on their first appearance in the ammocete ; and, although they
subsequently lose their distinctive features by the accumulation of cartilage-
cells around them in which the foundations of the neurapophyses and parapo-
physes, contributing to the otocrane, are laid, one centre of ossification is
commonly established, even in fishes, in special relation to the immediate
protection of the vascular and nervous parts of the labyrinth.
As to the proper bony envelope of the eye, M. Agassiz does not enumerate
it amongst the cranial bones of fishes: but admits into that series only the
accessory protecting pieces which form the orbit ; or rather only those that
at the same time form the brain-case: for, the suborbitals, the entopterygoids
and palatines are placed amongst the ‘ facial’ bones : whilst the supraorbi-
tals are transferred to another category of osseous pieces, the natural Oy
here prevailing over the artificial one.
Subjoined* is an outline of the arrangement of the two primary classes of
‘cranial’ and ‘facial’ bones, founded upon the embryological researches of
* CRANIAL BONES. (OS CRANIENS.)
A, EMBRYONIC BASIS (‘ BASE EMBRYONALE, Vogt).
a. Nuchal plate (‘ Plaque nuchale,’ V.). Basioccipital, Exoccipitals, Paroccipitals,
Supraoccipital, Petrosals.
b. Lateral loops (‘ Anses latérales,’ V.). Alisphenoids, Orbitosphenoids.
c. Facial plate (‘ Plaque faciale, V.). Entosphenoid (l’ethmoide cranien, Ag.).
B. PROTECTIVE PLATES (‘ PLAQUES PROTECTRICES,’ V.).
a. Superior plates. Parietals, Frontals, Nasals.
b. Lateral plates. Prefrontals, Postfrontals, Mastoids (temporaux, Ag.).
c. Inferior plates (‘ Plaque buccale,’ V.). _Basi- pre- sphenoid, Vomer.
FACIAL BONES. (OS DE LA FACE.)
1. Mazillary arch. Suborbitals (jugaux, Ag.), Maxillary, Premaxillary.
u1. Palatine arch. Palatines, Entopterygoids, Pterygoids (transverses, Ag.).
111. Mandibular arch. Pretympanics (‘ caisses,’ Ag.), Mesotympanics (‘tympano-mal-
leaux,’ Ag.), Hypotympanics (‘ os carrés,’ Ag.), Mandible.
tv. Hyoidean arch. Epitympanics (‘ mastoidiens,’ Ag.), Preoperculars, Stylohyals, Epi-
hyals, Ceratohyals, Basihyals (‘1’os lingual,’ Ag.).
y. VI. vil. vimt.. Branchial arches. ‘ Composes chacun de deux ou trois piéces et reunis
sous le gorge par le corps de l’hyoide.’
1x. Pharyngeal arch. ‘Composé d’une ou de plusieurs pieces,’ &c.—Op. cit. t. i.
pp. 124, 130.
4
ON THE VERTEBRATE SKELETON. 325
Vogt. With regard to the series of nine arches into which the facial
‘bones are distributed, it may be remarked that the independence of the maxil-
Jary from the palatine, which is more apparent than real in the osseous fishes,
ceases to be manifested in any degree in the plagiostomes and lepidosiren :
that the first and second arches are suspended by their crowns with their
haunches projecting freely outwards, whilst the third and fourth arches are
‘suspended, in the reverse position, viz. inverted, with the crowns or key-stones
‘downwards: the four next arches are rather complete cinctures, their sum-
‘mits meeting and being loosely suspended to the basis cranii, or, in pla-
giostomes and cyclostomes, to the under part ef the vertebral column of the
trunk. Although professing to base his classification upon developmental
characters, M. Agassiz owns with regard to the posterior branches of the
maxillary arch, e. g. the suborbitals, “that they appear to be rather formed
by the dermal system.” And this is unquestionably true: whilst the pala-
tines, which are the true piers of the arch, are developed from the blastema
‘of the same visceral arch as the maxillaries and premaxillaries.
The error in regard to the special homology of the suborbital bones, deter-
mined by M. Agassiz as the malars, and which is so clearly exposed by the
structure of the skull of the Psittacide (ante, p- 209), has misled him in re-
spect to the natural and typical constitution of the maxillary arch.
_ The mistake in reference to the Se ee homology of the epitympanic (2sa),
determined by M. Agassiz as the ‘ mastoid,’ has, in like manner, influenced
him in dissociating it from the other dismemberments of the tympanic pedicle,
and referring it to a different arch.
With regard to the hyoid and branchial arches, it will be observed that
M. Agassiz makes no distinction between the systems of the neuro- and
splanchno-skeleton. An arch constant and ossified in all vertebrates where
the rest of the endoskeleton is ossified, and which, even admitting M. Agassiz’
special homology of the preopercular as the styloid process of the temporal,
‘would still be suspended in the inverted position, like a true hemal arch, is
‘placed in the same category as the branchial girdles, which are often cartila-
ginous when the hyoid is osseous, in bony fishes ; and which disappear, in the
‘metamorphosis of the tadpole, with the evanescent respiratory viscera for
the support of which they are exclusively developed.
The constitution of a distinct 9th facial arch for the posterior pair of bran-
chial girdles, which retain their gills in lepidosiren, though modified in sub-
servience to mastication in most osseous fishes, appears to be giving undue
importance to an artificial or adaptive character. Finally, the natural con-
nections of the scapulo-coracoid arch in osseous fishes are totally disregarded,
and it is left out of the enumeration of the bones of the head.
The unbiassed anatomist may find an element for judging of the natural
character of the cranio-vertebral system propounded in the present Report,
by contrasting the classification of the bones of the fish’s skull to which it
leads, with that proposed by M. Agassiz, and with nature*.
Having thus responded to the objections advanced by Cuvier and M.
Agassiz to the interpretations of the segmental constitution of the bones of _
the head which were open to the criticism of those great authorities in
anatomy, I proceed briefly to explain the segmental constitution of the bones
~* Tam bound here to say that in the discussion of the subject of this Report with M.
Agassiz, which, amongst other advantages of the meetings of the British Association, I en-
joyed at Southampton, he admitted, with his characteristic frankness, that some points of
his classification of the bones of the head in fishes would require reconsideration. One of
‘the eminent physiologists who was present at the debate which followed the reading of the
Report, has recorded the impression it produced upon him in a review of my ‘ Hunterian
— on Vertebrata’ in ‘The British and Foreign Medical Review,’ No. xlvi. p. 490.
pi. ssc
326 REPORT—1846.
of the trunk of the human subject according to the archetype with which the
segments in the head have been illustrated.
The first seven segments of the trunk consist each of centrum (fig. 25, e),
neurapophyses(z), neuralspine (s), and rudimental pleurapophyses(p/), which -
coalesce, in each segment, into one bone, called ‘ cervical vertebra’ in anthro-
potomy. If the hemapophyses (s2') have the same relation to their centrum
which those of the seventh dorsal vertebra, in the Ciconia Argala, more ob-
viously bear to theirs,—that is, being attached below and disunited at theirupper
ends from their pleurapophyses, which are short, stunted and anchylosed to the
centrum,—and if, as the apparent homologues of 52’ in fishes would indicate,
the atlas be actually the centrum to which such detached and shifted hema-
pophyses belong, then the first wilkbe the sole segment of the cervical region of
the trunk in which those elements are ossified.
In the seven vertebra which succeed the cervicals the pleurapophyses (p/)
are progressively elongated; they are shifted from their proper centrum to the
interspace between it and the next segment above, or in advance, and retain
their moveable joints. The hemapophyses (/) are cartilaginous and articulate
with the ends of the pleurapophyses and with the hemal spines (As), which are
flattened, slightly expanded, and ultimately blended into one bone called ‘ ster-
num. The hzmal spine of the first typical segment remains longest distinct :
it receives, also, the extremities of the displaced heemapophyses (s2’) and has
been called ‘ manubrium sterni.’. The hemal spine of the seventh segment
commonly continues longer distinct, and is later in becoming ossified, whence
it is called ‘ ensiform cartilage’: it probably includes the rudiments of some
succeeding hzmal spines. In the four succeeding segments the pleurapophyses
become progressively shorter, and the hemapophyses, still cartilaginous, are
severally attached by their lower attenuated ends to the pair in advance ;
leaving the hemal arch incomplete below. In the next vertebra (19th from
the skull) the still shorter pleurapophyses resume the exclusive articulation
with their proper centrum ; and the correspondingly short and pointed hem-
apophyses terminate freely.
Those pleurapophyses and hemapophyses which directly articulate with
hemal spines (sternum) are called collectively ‘true ribs’ (cost vere), the
proximal element being ‘the bony part of the rib’ (pars ossea coste), the distal
one the ‘cartilage of the rib.’ The rest of the hemal arches which are in-
complete through the absence of the hemal spine, are called ‘false ribs’
(costz spuriz); and the last, which terminates freely in the origin of the
diaphragm, is a ‘ floating rib.’ The centrum, neurapophyses and neural spine
of each segment with freely articulated pleurapophyses coalesce into one bone,
called ‘ dorsal vertebra’ in anthropotomy : these vertebre are twelve in
number. Each of the five succeeding segments is represented by the same
elements (centrum and neural arch) coalesced that constitute the so-called
dorsal vertebre : they are called ‘lumbar vertebre ' (fig. 25,L.): they have no
ossified pleurapophyses ; and the hemapophyses of these segments are repre-
sented only by the aponeurotic ‘inscriptiones tendinez musculi recti’ (”).
Certain elements of the five succeeding segments (7b. S.) coalescing together
in the progress of growth form the bone called ‘sacrum’: and are described in-
dividually as sacral vertebra. The first four of these each combine the same
elements, coalesced, as in the neck; viz. centrum, neurapophyses, neural spine,
and short but thick pleurapophyses*: in the fifth sacral vertebra there are no
* J. Miiller notices the rudimental ribs in the first and second sacral vertebre of the
human foetus in his Anatomie der Myxinoiden, heft i. 1834, p. 240. Mr. Carlile has
described (Report of British Association, 1837, p. 112), and Dr. Knox has figured (Lancet,
1839, p. 191) these ribs and their homotypes in the third and fourth sacral vertebre.
ON THE VERTEBRATE SKELETON. 327
osseous rudiments of pleurapophyses ; and the neural spine is commonly un-
developed. One or more typical segments are obviously completed by the
meeting of the broad sides of the inverted arch (62, #3, 61) at the ‘ ischio-
pubic symphysis’ forming the ‘pelvis’ of anthropotomy. Before, however,
entering upon the difficult inquiry into the general homology of the pelvis,
I would beg to refer the reader to the analysis of the sacrum of the ostrich
given at p. 263: and I here subjoin a figure of seven of those vertebre,
from an immature specimen, the pleurapophyses being removed from all
_ save the last (pi), in order to show the change of place of the neurapophyses
m1—4,in relation to their centrums, c 1 to 4: dd are the long diapophyses ;
the short parapophyses. The sacral spines, s s, are enormously developed.
In the bird the modification of the vertebral segments at the posterior
region of the trunk in relation Fie. 27
to the transference of the whole Reels
weight of the body and fore-
limbs (wings) upon the hind-
limbs, is greater and more ex-
tensive than in the ‘bipes im-
plume,’ and the essential nature
of the pelvic arch is still more
masked in the bird than in man.
In order to obtain an insight
into the model according to
which it is constructed, we must
descend still lower, even to the
humblest of the vertebrated
creatures that crawl upon the 7 sacral vertebree of a young ostrich (Struthio camelus),
_ earth. The example which is here selected for that purpose is the perenni-
branchiate amphibian calleq Menopome Alleghanniensis.
The three anterior ver- Fig. 28.
tebrz which answer in po-
sition to the ‘lumbar’ in
_ fig. 25, differ chiefly in ha-
_ ving rudimental pleurapo-
physes (P/) articulated to
_ the ends of the diapophyses
(D). In the next vertebra
thediapophysis(D')andthe
_ rudimental pleurapophysis
(Pl) are thickened and
_ enlarged: a second pleur-
_ apophysial rib-like piece(62)
__ is joined by one end to the
4 pleurapophysis, and by the Sacral vertebra and appendage with contiguous vertebrze. Menopome.
other to a broad partially ossified cartilage (61) which meets and joins its
fellow, completing a hemal arch and restoring the vertebra in question to
the typical character. A radiated appendage, moreover, diverges on each
side from the articulation between 62 and 641, and forms the hind-limb. Now
the special homology of this limb with the undivided filamentary appendage
similarly situated in the lepidosiren, and with the ventral fins of fishes, ‘jn
the descending series ; and with the hind-limb of other reptiles, of birds and
of mammals in the ascending series, is unmistakeable, and, I believe, is gene-
_ rally admitted: so that comparative anatomists have not hesitated to call
_ the rib-like bone, 62, ‘ilium,’ and the part, 61, ‘ pubis” in the menopome.
=
328 _ REPORT—1846. 7
?
The special homologies of these elements of the pelvis being thus deter-
mined, it follows, that their general homology, as ‘it may be revealed by the
simple condition of the pelvic arch in the species in which the pelvis, as
complete and fixed to a sacrum, makes its first appearance in the animal
kingdom, will be equally applicable to the parts under all their metamor-
phoses in the higher air-breathing vertebrates.
The correspondence of the segment of the endoskeleton in the menopome
D’, Pl’, H, A, with the typical vertebra, as illustrated by fig. 15, is such,
that any other explanation of its essential nature than as a representative or
repetition of such fully developed segment or vertebra seems contrary to ~
nature. The chief modification has its seat in the most peripheral part or
appendage A. as compared with its simple homologue in the thoracic segment
of the bird (fig. 15). If 62 and 61 are to be regarded as strangers to the
vertebral system, new parts introduced for special purposes, and not as
normal elements modified for special purposes, I am at a loss to know on
what principles, or by what series of comparisons we can ever hope to attain
to the higher generalizations of anatomy, or discover the pattern according
to which the vertebrate forms have been constructed. It may be said thatthe
arch which they constitute performs a new function, inasmuch as it sustains
a locomotive limb which reacts upon the ground. But this new function
arises in the menopome, rather out of the modifications of the appendage
than of the arch itself. In so far as the mere support of the appendage is
concerned, the inverted or hemal arch Pl’, H, performs no new function, but
one which is common to such arches inthe thorax of birds, and to the less com-
pletely ossified homologous arches in the abdomen of fishes, where moreover
the simple diverging appendages do give attachment to the muscles of locomo-
tion. Comparing, then, the hemal arch in question with that of the typical
vertebra (fig. 15), we find that, like the scapulo-coracoid arch in fishes
(fig. 5, H 1), its parts are open to two interpretations. The upper piece of
Pl' may be thewhole pleurapophysis, the lower, 62, the heemapophysis, and the
part, 64, the half of an expanded and bifid hemal spine: or Pl’ with 62, may
be two portions of a teleologically compound pleurapophysis, and 64 the heem-
apophysis, which would join with its fellow without, or with a mere rudiment
of, a hemal spine intervening. From the analogy of the scapulo-coracoid
arch in fishes, which is proved by its modifications in higher animals to
want the hemal spine, it is most probable that such is the condition and
true interpretation of the correspondingly simple pelvic arch under considera-
tion. But the genera] relation of this arch to the hemal one of the typical
segment is not affected by the alternative. ~
I regard, therefore, Pl’, 62, as two portions of a fully developed pleurapophy--
sis; and the pleurapophyses, Pl’, P/ of the contiguous vertebree as answering
only to the upper portion of the pelvic one. In ascending from the meno-
pome to the crocodile, we find the homologue of 62 broader than it is long,
and articulated to the thickened proximal portions of the pleurapophyses of
two segments ; and we observe, likewise, the pelvic arch completed below
by two pairs of hemapophyses: for the anterior pair the name of ‘ossa
pubis’ is retained ; to the posterior pair that of ‘ischia’ is given. In general
homology these bones complete, as hemapophyses, the two vertebral seg-
ments modified to form the sacrum of the crocodile; and the intermediate
connecting piece (ilium) may be interpreted, as either the confluent distal
portions of the pleurapophyses of both vertebree, or as an expansion of one
such portion, answering to 62 in the menopome, and intruding itself between
the stunted pleurapophysis and distant hemapophysis of the second sacral
vertebre in the crocodile.
Saag
ON THE VERTEBRATE SKELETON, 329
ie bird the expansion of the element 62 proceeds to a further extent,
1 besides the proximal piece of the pleurapophysis of its own segment o2,
is rought. into connection with the homologous stunted or proximal ends
pl pleurapophyses of several contiguous segments, in the manner indicated
the dotted line in fig. 28. Now, if the ilium, so expanded, were inter-
tg as the coalesced complementary portions of all the short pleurapo-
physes with which it articulates, its condition would be very similar to that
which Oken has attributed to the scapula. But its ossification radiates, as
in the simple rib-like ilium of the menopome, from a common centre: there
are no corresponding multiplications of haemapophyses below; these are
restricted in the pelvis of all animals to the number which they present in
the crocodile. And since the scapula has been proved to be, under its most
expanded form, the homologue of a single pleurapophysis, so also I am dis-
posed to regard its homotype, the ilium, as maintaining under every variety
of form and proportion, the same fundamental singleness of character, as it
presents on its first appearance in the perennibranchiate batrachian.
The first sacral vertebra, then, in man is complete; but its pleurapo-
physis i is. divided, and the lower portion expanded to form the so-called
‘ilium’ (62). The heemapophysis (6a) coalesces with that of the succeeding
yertebra (63), and with its own pleurapophysis (62).
_ The second sacral vertebra has its hemapophysis (63, called ‘ ischium ’)
gssified, but separated from its proper pleurapophysis by the expanded (iliac)
portion of that of the preceding vertebra, with which it coalesces, as well as
with the preceding hemapophysis (pubis). The short and thick pleurapo-
physes of the third sacral vertebra also articulate in the adult with the ex-
panded distal portions of those of the first sacral vertebra: but these (iliac
bones) are restricted in infancy and early childhood to their connections
with the first and second sacral vertebre, which connections are permanent
in most reptiles.
The fourth sacral vertebra consists of centrum, neurapophyses, and rudi-
mental pleurapophyses; the fifth sacral vertebra of centrum and rudimental
neurapophyses, which rarely meet above the neural canal.
_ In each sacral vertebra the elements of the neural arch and rudimental
ribs first coalesce together; and afterwards the vertebrae unite with each
ether and form the anthropotomical bone called ‘ sacrum.’
The first coceygeal vertebra in man consists of a centrum and of stunted
eR wide apart above, but developing zygapophyses, which join
those of the last sacral vertebra, and diapophyses which extend outwards
further than those of the same vertebra. The neurapophyses are represented
exogenous tubercles of bone in the second coccygeal vertebra ; and the
ird and fourth vertebre are reduced to the centrums only.
ae The cartilaginous deposits in the primitive blastema of this extremity of
the. trunk indicate a greater number of caudal vertebre, and the rudimental
tail i is proportionally longer in the embryo than in the adult. It is shortened,
however, by absorption prior to the commencement of ossification, and but
four segments are indicated by depositions of the earthy salts in the situa-
tions proper to the above-specified elements of a typical vertebra: these
finally coalesce into a single bone “ of a crooked pyramidal figure,” which
got its name of ‘os coccygis’ from its supposed resemblance to a cuckoo’s
beak +.
The early recognition of these and other specialities arising out of the va-
rious adaptive modifications of the typical segments of the human skeleton
found its expression, necessarily, in special terms, the convenience of which
* “ Shoulders of the os coccygis.”-—Monro, J. c. p. 142. t i. p. 141.
1846. Zz
330 REPORT—1846.
will ensure their permanence ; but the course of anatomical science having
unfolded the primary form which is the basis of those modifications, there
arises the same necessity for giving utterance to ideas of the generie cha-
racter of the parts by general terms.
Inasmuch, however, as the different segments of the human skeleton de-
viate in various degrees from the common archetype, and as the different
elements of such segments differ in their modifiability, anthropotomy has at
no period wanted also its ‘ general terms’ expressive of the recognised ex-
tent of such conformity: such terms also, indicating, obscurely indeed, so
much perception of the pre-existing model as could be obtained from the
study of one form, at a period when that form—the human frame—was
viewed as something not only above, but distinct from, if not antithetical
to the structures of the brute creation, and when it was little suspected
that all the parts and organs of man had been sketched out, in anticipation,
so to speak, in the forms of the inferior animals. Thus the word ‘ vertebra’
shows, by the number of the segments or parts of segments to which it is
applied in anthropotomy, the recognition of the obvious extent to which the
archetype is retained in such primary constituents of the human endoskeleton.
And, inasmuch as in some regions (the cervical, e.g.) the ‘ vertebra’ includes
all the elements of the typical segment, there developed, it has been retained,
but, with a more definite meaning, as the technical term of the primary
constituent segment of the endoskeleton in all vertebrate animals.
The ‘true vertebra’ of anthropotomy are those segments which retain the
power of moving upon each other ; and the term is applied in a peculiar and
empirical sense very different from the meaning which the anatomist at-
taches to a true or typical vertebra. ‘The ‘ false vertebre’ of anthropotomy
are those segments or parts of segments forming the lower or hinder extreme
of the endoskeleton, and which do not admit of reciprocal motion at their
joints. And Monro, admitting that the condition of even the human os
coccygis sometimes militates against the definition, meets the objection by
arguing for the speciality of that bone, and with as good or better reason
than those who have subsequently contended against admitting the cranial
segments into the category of vertebra. “From the description of this bone ”
(os coccygis), “* we see how little it resembles vertebre ; since it seldom has
processes, never has any cavity for the spinal marrow, nor holes for the pas-
sage of nerves*.”
Embryology has since demonstrated that the parts of the os coecygis are
originally in vertebral relation with the neural axis; and that this is subse-
quently withdrawn by a concentrative movement, which in like manner
withdraws it from the terminal segment at the opposite extreme of the endo-
skeleton. The homology of the divisions of the sacrum with the true ver~
tebre is admitted by Monro, because of the perforations for the nerves : and
this character is still retained in the nasal vertebra in the form of the cribri-
form foramina, although its neurapophyses, like those of the sacrum, have
lost their primitive relation to the neural axis.
Homological anatomy, therefore, teaches, that the term ‘ vertebra’ should
not only‘be applied to the segments of the human skeleton in the technical
and definite sense illustrated by figs.14 and 15, but be extended to those
modified and reciprocally immoveable segments which terminate the endo-
skeleton superiorly, and are called collectively ‘ skull.’
The term ‘ head,’ then, indicates a region of specially modified vertebra, like
the terms ‘ neck,’ ‘ chest,’ ‘loins,’ &c. ; and amongst the species of the primary
segmeuts characterized by specific modifications, the ‘ cranial’ vertebrae must
* Monro, /.c. p. 143.
ON THE VERTEBRATE SKELETON. 331
be added to the ‘ cervical,’ ‘thoracic or dorsal,’ ‘ lumbar,’ ‘ sacral,’ and ‘ coccy-
geal or caudal.’
Such, with reference to the ‘general’ term ‘ vertebra,’ seems to be the
advance of which anthropotomical science is susceptible, in order to keep
progress and be in harmony with anatomy.
As to the elements of the typical vertebra, anthropotomy has also its gene-
ral phrases (see Table II. column vi. ‘Soemmerring.’), some of which are
equivalent to the clearly defined technical terms of such elements in anatomy
_ properly so called.
The serial homology of the centrum (corpus vertebre) has been recognised
in all the so-called ‘true vertebra,’ and in some of the ‘ false vertebre :’ thus
Monro says, “ The fore-part of the os sacrum, analogous to the bodies of the -
true vertebre, is smooth and flat*.” But their smooth and flat homotypes in
the skull have only the special names of ‘basilar’ and ‘cuneiform’ processes ; of
‘processus azygos’ and ‘vomer.’ The ‘neurapophyses’ are recognised as re-
petitions of the same part under the definitions of ‘a bony bridge produced
backwards from each side of the body of the vertebra,’ of ‘ areus posterior
- vertebre,’ of « vertebral laminz’ or ‘ pedicles.’ Monro describes these rudi-
mental elements in the last sacral vertebra as ‘ knobs,’ and in the first coccy-
geal vertebra as its ‘shoulders.’ In the skull they receive the special defini-
tions of “ the pieces of the occipital bone situated on each side of the great
foramen ; from which nearly the whole condyles are producedt+ ” (partes late-
rales seu condyloidee, Soem.); ‘great’ or ‘ temporal wings of the sphenoidal
_ bonet;’ ‘ orbitar wings’ or ‘ processes of the sphenoidal bone ;’ ‘ nasal” or
‘ vertical plate’ and ‘ cristi galli’ of the ethmoid (‘pars media ossis ethmoidei,’
_ Soem.).
The neural spines are called generally ‘ spinal processes’ in every segment
of the trunk: in the head they are known only by the special names of ‘oc-
cipital plate,’ ‘ parietal bones,’ ‘ frontal bone,’ ‘ nasal bones.’
The pleurapophyses, when free, long, and slender, are called ‘ ribs,’ ‘verte-
_ bral ribs,’ or ‘bony parts of the ribs’; when short and anchylosed, they are
, called, in the neck, “the second transverse processes that come out from the
_ sides of the body of each vertebra§ ;” (radix prior processus transversi ver-
7 tebre, Soem.;) in the sacrum ‘transverse processes’ and ‘ilium’; in the skull,
* scapula’, ‘styloid process of the temporal bone,’ ‘ external auditory or tym-
i panic process of the same bone’; ‘ palatine bone.’
_ In like manner the serial homology of the hemapophyses is recognised in
the thoracic region by the general term ‘ cartilages of the ribs’ or ‘ cartilages
_ of the sternum’ there applied to the same elements of twelve successive seg-
_ ments. When ossified in other vertebre they have received the special names
_ of ‘ischium,’ ‘ pubis,’ ‘ coracoid process of the scapula,’ ‘clavicle,’ ‘ appendix *
_ or lesser cornua of the hyoid bone,’ (‘ crwra superiora,’ ‘os linguale superius,’
_ Soem.), ‘lower jaw’ or mandibula, ‘ upper jaw’ or mazilla.
' The exigences of descriptive anthropotomy and its highly important ap-
_ plications to Medicine and Surgery necessitate such special nomenclature, and
the reform which that nomenclature chiefly requires is the substitution of
names in the place of phrases for the parts of the human body.
_ But the retention and use of specific names for specially modified elements
in the different segments by no means precludes the entertainment of general
_ ideas and the necessity of expressing them by generic names for the homo-
4 logous elements in the entire series of vertebre.
If anthropotomy is to make corresponding progress with anatomy, and
_ to derive the same light from the generalizations of zootomical science which
, * Monro, J. c. p. 138. + L. c. p. 76. t L.c, p. 86. § L. ae 126,
Zz
332 REPORT—1846.
medical botany has done from general botanical science, its nomenclature
must expand to receive those generic terms which express the essential
nature of the parts, heretofore named and known only according to the
results of particular and insulated observation. A term which truly ex-
presses the general homology of a part enunciates the most important and
constant characters of such part throughout the whole animal series, and
implies therefore a knowledge of such characters in that part of the human
body, when used and understood by the human anatomist. Before the eunei-
form process of the occipital bone could be defined as the ‘ occipital cen-
trum,’ the modifications and relations of the homologous part in all classes of
vertebrate animals had to be accurately determined. The generic homo-
logical term expresses the sum or result of such comparisons, and the use of
such terms by the anthropotomist implies his knowledge of the plan or pattern
of the human frame which lies at the bottom of all the modifications that
raise it to an eminence so far above those of all other vertebrate animals.
In no species, however, is each individual segment of the endoskeleton
so plainly impressed with its own individual characters, as in Man ; the prac-
tised anthropotomist, for example, will at once select and name any given
vertebra from either the cervical, the dorsal, or the lumbar series. During
that brilliant period of human anatomy which was illuminated by a Fabricius,
an Eustachius, a Fallopius, and a Laurentius, the terms expressive of the
recognition of such specific characters were more numerous and often more
precise than in our modern compilations. Pleurapophyses were indivi-
dualized in the thorax as well as in the head: the ‘antistrophoi,’ ‘stereai’
and ‘sternitides,’ for example, were distinguished from the other ‘ pleurai
gnesiai’*.
General anatomical science reveals the unity which pervades the diversity,
and demonstrates that the whole skeleton of man is the harmonized result
of essentially similar segments, although each segment differs from the other,
and all vary from their archetype.
Part III.—SeriaL Homo oey.
Since, then, we are led by the observations, comparisons and reasonings re-
corded in the preceding parts of this Report, to recognise, as the fundamental
type of the vertebrate endoskeleton, a series of segments repeating each
other in their essential characters, it follows that, not only the power of de-
termining the homologous bones throughout the vertebrate series, but also
throughout the vertebral segments of the same individual, is included in
such generalization.
The recognition of the same elements throughout the series of segments
of the same skeleton I call ‘the determination of serial homologies.’ This
kind of study appears to have been commenced by the gifted Vieq d’Azyr,
in his ‘ Mémoire’ entitled “ Paralléle des os qui composent les extrémités,”
printed in the Mémoires de l’Académie des Sciences for the year 1774, and
Condorcet, in his Report on this ingenious Essay, speaks of it as “ un essai
d’une autre espéce d’Anatomie comparée, qui jusqu’ici a été peu cultivée.”
Vicq d’Azyr compares, or points out the serial homology of, the scapula
with the ilium, the humerus with the femur, the two bones of the fore-arm
with the two bones of the leg, the small bones of the carpus with those of
the tarsus, the metacarpus with the metatarsus, and the fingers with the toes.
He is not so happy in his particular as in his general determinations: his
* Anatomica Humani Corporis, &c., multis controversiis et observationibus novis illustrata.
Andr. Laurentio, fol. 1600, p. 95.
ay
t
.
E.
ON THE VERTEBRATE SKELETON. 333
choice in the leg, for example, of the homotypes of the radius and ulna in
the fore-arm, is erroneous ; but the whole memoir is an admirable example
of the appreciation of correspondences which later researches in the same
direction have proved to flow from a higher and more general law of uni-
formity of type. It is, indeed, a striking instance of the secret but all-pre-
vailing harmony of the vertebrate structure that serial homologies should be
determinable to such an extent in the parts of the diverging appendages,
which are the seat of the greatest amount and variety of deviations from the
fundamental type.
Tt will, of course, be obvious that the humerus is not ‘the same bone’ as
the femur of the same individual in the same sense in which the humerus
of one individual or species is said to be ‘the same bone’ as the humerus of
another individual or species. In the instance of serial homology above-cited,
the femur, though repeating in its segment the humerus in the more advanced
segment, is not its namesake, not properly, therefore, its ‘homologue’. I
propose, therefore, to call the bones so related serially in the same skeleton
‘homotypes,’ and to restrict the term ‘homologue’ to the corresponding bones
in different species, which bones bear, or ought to bear, the same names.
In the skull those bones are homotypes, or repetitions of the same essential
part in the series of vertebral segments, which succeed each other length-
wise, as in the last four columns of the subjoined Table :—
VERTEBRE. OcciPiTaAL. PaRIETAL. FRONTAL. NASAL.
Centrums ..........++- Basioccipital ....|Basisphenoid...... Presphenoid ....|Vomer.
Neurapophyses.... ..|Exoccipital ..../Alisphenoid ...... Orbitosphenoid. . |Prefrontal.
Nasal spines..... ..|Supraoccipital ..|Parietal .......... Frontal ......., Nasal.
Parapophyses ......:...|Paroccipital ....|Mastoid.......... Postfrontal...... None.
Pleurapophyses ........ Seapula ........ Stylohyal ........ Tympanic ...... Palatal.
Hemapophyses ........ Coracoid........ Ceratohyal........ Articular ...... Maxillary,
Hemal spines .......... Episternum ....|Basihyal.......... Dentary ........ Premaxillary.
Diverging appendages ..|Fore-limb or fin|Branchiostegals ..|Operculum ....|Pterygoidand Zygoma.
Thus the basioccipital, basisphenoid, presphenoid and vomer are homo-
types with the centrums of all the succeeding vertebra. The exoccipitals,
alisphenoids, orbitosphenoids, and prefrontals, are homotypes with the neur-
apophyses of all the succeeding vertebra. The paroccipitals, mastoids and
postfrontals are homotypes with the transverse processes of all the succeeding
vertebre. The supraoccipital, parietal, frontal and nasal are homotypes
with the vertebral neural spines.
The petrosals, sclerotals, and turbinals are homotypes of each other, as
being respectively sense-capsules of the splanchno-skeleton.
The suprascapula and scapula are together the homotypes of the stylohyal
and epihyal; of the tympanic, whether simple or subdivided, and of the
palatal: and all these are the homotypes of the pleurapophyses collectively,
whether modified as ribs, hatchet-bones, or iliac bones, in the rest of the
vertebral segments.
The coracoid is the homotype of the ceratohyal, this of the articular di-
vision of the mandible (with its subdivisions called angular, sur-angular and
coronoid, in cold-blooded animals), and this, again, of the maxillary bone: all
four being homotypes of the heemapophyses of the remaining vertebral seg-
‘ments, whether modified to form clavicles, pubic bones or ischia, chevron-bones,
‘sternal ribs, abdominal ribs, cartilages of ribs, abdominal cartilages or tendi-
nous intersections of the modified intercostal muscles called ‘recti abdominis.’
The entosternal, when present, is the homotype of the basihyal, of the
dentary or premandibular, and of the premaxillary bones ; and these collec-
tively are homotypes of the hemal spines of the rest of the vertebral seg-
334 REPORT—1846.
ments, whether retaining their spinal shape as in the caudal hamapophyses,
or flattened as ordinary ‘ sternal bones,’ or expanded and subdivided, like the
neural spines in the cranium, in order to complete below the thorax of the
bird or to form the plastron of the turtle.
There reigns a beautiful parallelism in the kind and degree of modification
of the parts of the neural with the corresponding parts of the hzmal arch of
the same vertebral segment: and as the serial homologies which have just
been enunciated succeed each other longitudinally (horizontally in beasts,
vertically in man) in the axis of the vertebral column, so these manifest them-
selves in a direction perpendicular to that axis.
The manubrium sterni of the bat developes a spine downwards, as the
supraoccipital of the fish sends a spine upwards: the expanded manubrium
sterni of the whale repeats the condition of the supraoccipital in birds and
mammals. The form of the ordinary sternal bones in mammals is repeated
by the parietal and supraoccipital bones of the crocodile. The divided sternum
of the young ostrich, before the two lateral ossifications have coalesced
at the median suture, repeats the condition of the divided parietal in most
mammals. The development of the crista from the obliterated suture of
the lateral halves of the expanded hemal spine in the thorax of birds is
paralleled by the development of the crista from the obliterated suture of
the expanded neural spine in the cranium of carnivores. The interposition
of the entosternal piece in the chelonian carapace parallels below the inter-
position of the interparietal bone in the rodent cranium above.
Thus modifications and developments of the same kind and degree manifest
themselves in the upper (neural) as in the lower (hemal) peripheral elements
of the vertebra ; and though not always in the same vertebra, nor in the
same animal, yet they are sufficiently exemplified in the myelencephalous series
generally, to establish the conclusion that the hemal spines under all their
modifications are vertical homotypes, not of the centrums, as Oken, Meckel
and De Blainville have supposed, but of the neural spines of the same verte-
bre. In the composition of the neural arch of the occipital, parietal and
frontal vertebre, we find the neurapophyses repeating the pleurapophyses of
the hemal arch, and the parapophyses repeating the heemapophyses in their
relative positions to the centrum and the spine or key-bone of such arches.
Symmetry or serial homology of parts of the same vertebral segment is
usually still more strictly preserved in the transverse direction, and is so
obvious, as to have immediately led to the detection of the homologous parts,
which are accordingly distinguished as ‘ right’ and ‘ left.’
To return to the consideration of those serial homologies with which Vicq
d’Azyr commenced the study of these relations, | may remark that the bones
of the fore- and hind-limbs of some of the marsupial quadrupeds best illus-
trate the true relations which my revered Preceptor in Anatomy, Dr. Barclay*
was, I believe, the first to enunciate in respect of the bones of the fore-arm
and leg.
The skeleton of the Phalangista or Phascolomys plainly demonstrates that
the tibia is the homotype of the radius, and that the fibula is the homotype
of the ulna. In both wombat and ornithorhynchus the fibula assumes those
* In his explanations of Mitchel’s Plates of the Bones, 4to, 1824, pl. 24, figs. 3 and 4,
Dr. Barclay, without referring to Vicq d’Azyr’s Memoir, simply enunciates the correct
view of the serial homology of the bones of the fore-arm and leg, as follows :—* On com-
paring the atlantal (pectoral) and sacral (pelvic) extremities, the fibula is found to be the bone
corresponding to the ulna; and accordingly, upon extending our researches to Comparative
Anatomy, we perceive it exhibiting the like variety and unsteadiness of character, sometimes
large, sometimes small, and sometimes merely a process of the tibia,” &c. He does not push
his comparison to the bones of the distal segment of the limbs.
ON THE VERTEBRATE SKELETON. 335
proportions*and developes that process from its proximal end, the want of
_ which in'man and most mammals deceived Vicq d’Azyr, as it has misled,
more recently, M. Cruvelhier. The complex explanation of the serial homo-
logies of the bones of the upper and lower extremities proposed by the last
named pains-taking anthropotomist*, involves more unnatural transpositions
and combinations of the parts than those of the D’Azyrian hypothesis, which
its ingenious author could not but admit seemed paradoxical ; viz. that the
anterior member of one side of the body repeated or corresponded with the
posterior member of the opposite side. Cuvier, however, seems to sanction
this idea by repeating the statement of Vicq d’Azyr, “C’est la droite d’une
paire, qu'il faut comparer 4 la gauche de l'autret.”
M. Flourens has exposed in detail the fallacies of this view in an excellent
memoir in the ‘Annales des Sciences’ for 1838 (t. x. p. 35); in which he
arrives at the same conclusions as Dr. Barclay, and from similar considera-
tions from Comparative Anatomy, as to the serial homologies of the bones of
the fore-arm and leg ; and he confirms those of the carpal and tarsal bones,
which had been so truly and acutely discerned by Vicq d’Azyr.
In mammalian quadrupeds generally the fore-limb takes the greater share
in the support, the hind-limb in the propulsion of the body. The manus is
accordingly-commonly shorter and broader than the pes ; this may be seen in
the terminal segment of even the monodactyle hand and foot of the horse.
Consequently the transverse direction prevails in the arrangement of the
carpal bones and the longitudinal in that of the tarsal bones.
The difference is least in the carpus and tarsus of the long and slender fore-
and hind-hands of the quadrumana. If the carpus of the chimpanzee, for
example, be compared with that of man, the first difference which presents
itself is the comparatively small proportion of the scaphoid which articulates
with the radius, as compared with that in man, in whom the distal articu-
lation of the radius is equally divided between the scaphoides and lunare
-which are on the same parallel transverse series. In the chimpanzee and
orang, on the contrary, the scaphoid is elongated, and extends, almost as much
from the os lunare as from the radius, along the radial side of the carpus, to
reach the trapezium and trapezoides; it is, as it were, interposed between the
lunare of the proximal row and the trapezium and trapezoid of the distal row
of the carpal bones. The similarity of its connections, therefore, in the carpus
with those of the scaphoid in the tarsus (fig. 25, se.){ is so close that the
serial homology of the two bones is unmistakeable. The astragalus (2. a),
then, in the foot, repeats the os lunare (/) in the hand, but usurps the whole
of the articular surface of the tibia, and presents a larger proportional size,
especially in man, whose erect position required such exaggerated develop-
-ment of the astragalus, or homotype of the lunare. The prominent part of
the calcaneum obviously repeats the prominent pisiforme (p), and the body
of the calcaneum (cl) articulates with the fibula as the cuneiforme (cz)
articulates with the ulna. The strain upon the homotype of the pisiforme to
produce the required effect in raising the back-part of the foot with its super-
incumbent weight upon the resisting ends of the toes, required its firm
coalescence with the homotype of the cuneiforme ; in other words, the cunei-
* “T/extrémité supérieure du tibia est représentée par la moitié supérieure du cubitus,
et la moitié inférieure du tibia par la moitié inférieure du radius ; tandis que le péroné est
représenté par la moitié supérieure du radius et par la moitié inférieure du cubitus.”—Anato-
mie Descriptive, t. i. p. 315.
+ Lecons d’Anat. Comp. t. i. 1836, p. 342.
= The carpal and tarsal bones are indicated diagrammatically in fig. 25 ; their ossification
has not commenced at the period of the embryonic skeleton there represented.
336 REPORT—1846.
forme and pisiforme of the carpus represent together the os calcis of the
tarsus. With regard to the other bones there is no difficulty ; the cuboid
(b) supports the two ulnar digits, iv, v, of the foot, as the unciform bone (w)
does those of the hand: the ecto-cuneiform supports the digitus medius, iil,
of the foot as the os magnum (m) does that of the hand: the meso-cunei-
form supporting the toe ii is the homotype of the trapezoid supporting the
finger 2, and the ento-cuneiform (ci?) is the homotype of the trapezium (¢).
It is no unusual exception that of two essentially distinct bones in one
segment being represented by a coalesced homotype—a single bone—in an-
other segment, as in the explanation above given of the serial homology of
the caleaneum. The scaphoides and astragalus in the tarsus of the lion are
represented by the single scapho-lunar bone in the carpus. The seaphoid
and a cuneiform bone in the tarsus of the sloth and megatherium are repre-
sented by the single scapho-trapezium in the carpus.
I have long entertained the opinion that an appreciation, vague and indi-
stinet, perhaps, of certain serial homologies, may have been associated with,
if it did not suggest the epithets “scapula of the head,” “femur of the head,”
&c. applied to certain cranial bones by Oken and Spix.
To Cuvier this language seemed little better than unintelligible and mystical
jargon, and he always alludes to it with ill-disguised contempt*. It has beer
commonly cited by those who have followed the great palzontologist in de-
preciating the cranio-vertebral theory, as a sufficient instance, needing no
comment, of the extravagances essentially inherent in such attempts to recog-
nise and explain the fundamental pattern to which the modifications of the
cranial bones are subordinated. And it must. be confessed that the expres-
sions by which the philosophical anatomists of the school of Schelling have
endeavoured to illustrate in the animal structures the transcendental idea of
-*the repetition of the whole in every part,’ have operated most disadvan-
tageously and discouragingly to the progress of calm and dispassionate
inductive inquiry into that higher law or condition upon which the power
of determining the special homologies of the bones of the skeleton depends.
Nevertheless the utterances of gifted spirits to whom the common intellectual
storehouse is indebted for such original and suggestive generalizations as those
contained in the “ Program tiber die Bedeutung der Schadelknochen” are
entitled to some, and we will hope to respectful consideration, even when
they happen to be least intelligible or most counter to the conventional ex-
pressions of the current anatomical knowledge of the day; nor will the at-
tempt to detect their latent meaning be wholly unproductive.
With regard, for example, to the term ‘scapula capitis’ applied by Oken
to the tympanic bone in birds (fig. 23, 28), it is quite possible that some ap-
preciation of its serial homology with ribs and other modifications of the pleur-
apophysial element, besides that exhibited by the blade-bone, may have lain at
the bottom of the expression. And, we may ask, whether the error here be not
rather inthe mode of expressing the relationship than in the relationship itself?
Had Oken, for example, said that the tympanic bone of the bird was a modified
‘ pleurapophysis,’ or expressed by any other equivalent general term his idea of
its standing in such general relation to its proper cranio-vertebral segment, his
language would not only have been accurate, but might have been intel-
* “ Quant 4 M. Oken—il déclare les piéces en question les parties écailleuses des temporaux,
ou, selon son langage mystique, ‘la fourchette du membre supérieur de la téte.’ ””—Ossem.
Foss. v. pt. ii. p. 75.—“ Cet humérus de la téte de M. Oken devient pour M. Spix le pubis
de cette méme téte; ou, pour parler un langage intelligible, un des osselets de 1’ouie,
‘savoir, le marteau.””—‘‘ M. Spix croit aussi qu’il répond a la partie écailleuse du temporal,
quwil décore du titre d’iléon de la téte."—&c. Ib. pp. 85, 86.
Se ee
PSL SS eM aS
ON THE VERTEBRATE SKELETON. 337
ligible to Cuvier. When Oken called the ‘tympanic’ a ‘cranial scapula’ he
unduly extended the meaning of the term ‘scapula,’ and converted it froma
specific to a generic one. The tympanic is the homotype of the scapula,
both being modified pleurapophyses, but each has an equal claim to its proper
or specific name indicative of their respective modifications.
I am aware that Oken meant more than mere serial homology when he
called the tympanic the ‘ blade-bone of the head’: it is part of the phraseology
of the hypothesis of the head being a repetition of the whole body, &c. But
at the time when that anatomist wrote it was not known or suspected that
the head already possessed the scapula, and that the modified pleurapophysis
so called, actually appertained to a segment of the skull (fig. 5, 50, 51). In
the terms ‘femur capitis,’ ‘tibia,’ ‘fibula,’ « pes capitis,’ applied by Oken to the
parts of the teleologically compound mandibular ramus, and in those of ‘ wlna’
and ‘ manus capitis, applied to the distal segments (21, 22) of the maxillary
arch, we have not only instances of the attempt to express general relations of
repetition or homology by special terms, but these modes of expressing the
serial homologies of nos. 29, 30, 32, and of 21 and 22, betrays the misappre-
ciation of the general homologies of the locomotive extremities, and their
relations to the vertebral arches supporting them.
To gain an insight into whatever proportion of truth may be involved in
the ideas signified by the phrases above cited, it is necessary to determine
the essential nature of the parts called ‘femur,’ ‘tibia,’ ‘ humerus,’ ‘ ulna,’
‘manus,’ ‘ pes,’ &c., or the general homology, in short, of locomotive members,
and the attempt to master this problem has been not the least difficult part
of the present inquiry. Cuvier has offered no opinion, nor does he appear
to have ever troubled himself with the attempt to decipher the significa-
tion of the locomotive members of the vertebrate animals; 7. e. of what
parts of the primordial or pre-existing vertebrate model they are the
modifications.
_ Oken’s idea of the essential nature of the arms and legs is, that they are no
other than ‘liberated ribs’: “ Freye Bewegungsorgane konnen nichts anderes
als frey gewordene Rippen seyn *.”
Carus, in his ingenious endeavours to gain a view of the primary homologies
of the locomotive members, sees in their several joints repetitions of vertebral
bodies (¢ertiar-wirbel)—vertebre of the third degree +—a resultof an ultimate
analysis of a skeleton pushed to the extent of the term ‘ vertebra’ being made
to signify little more than what an ordinary anatomist would call a ‘ bone.’
But these transcendental analyses sublimate all differences, and definite
knowledge of a part evaporates in such unwarrantable extension of the mean-
ing of terms.
it has been, however, I trust, satisfactorily demonstrated that a vertebra
is a natural group of bones, that it may be recognised as a primary division
or segment of the endoskeleton, and that the parts of that group are definable
and recognizable under all their teleological modifications, their essential
relations and characters appearing through every adaptive mask.
According to the definition of which a vertebra has seemed to me to be sus-
‘ceptible, we recognise the centrum, the neural arch, the hemal arch, and the
appendages diverging or radiating from the hemal arch. The centrum,
though the basis, is not less a part of a vertebra than are the neurapophyses,
hzmapophyses, pleurapophyses, &c.; and each of these parts is a different
part from the other: to call all these parts ‘vertebra’ is in effect to deny
* Lehrbuch der Natur Philosophie, p. 330, 8vo, 1843.
t Urtheilen des Knochen und Schalengeriistes, fol. 1828.
338 REPORT—1846.
their differential and subordinate characters, and to voluntarily abdicate the
power of appreciating aud expressing them. The terms ‘secondary’ or
‘tertiary vertebra’ cannot, therefore, be correctly applied to the parts or
appendages of that natural segment of the endoskeleton to the whole of
which segment the term ‘ vertebra’ ought to be restricted.
So likewise the term ‘ rib’ may be given to each moiety of the hzemal arch
of a vertebra; although I would confine it to the pleurapophyses when they
present that long and slender form characteristic of the thoracic abdominal
region, viz. that part of such modified hzemal or costal arch to which the term
‘vertebral rib’ is applied in comparative anatomy and the term ‘ pars ossea
coste’ in anthropotomy : but, admitting the wider application of the term
‘rib’ to the whole hemal arch under every modification, yet the bony di-
verging and backward projecting appendage of such rib or arch is something
different from the part supporting it.
Arms and legs, therefore, are developments of costal appendages, but are
not ribs themselves liberated: although liberated ribs may perform analo-
gous functions, as in the serpents and the Draco volans.
If then the arms or pectoral members be modified developments of the
diverging appendage of the scapulo-coracoid arch, and if this be the hzmal
arch of the occipital vertebra, it follows that the pectoral members are
parts of the head, and that the scapula, coracoid, humerus, radius and ulna,
carpals, metacarpals and phalanges, are essentially bones of the skull.
The transcendentalism, therefore, which requires for its illustration that
the maxillary arches be the arms and hands of the head, meets its most direct
refutation in the fact of the diverging appendages, properly called arms and
hands, belonging actually to one of the modified segments of which the head
itself consists.
The head is, therefore, in no sense a summary or repetition of all the rest
of the body: the skull is a province of the whole skeleton, consisting of a
series of parts or segments essentially similar to those of which the rest of
the skeleton is constituted.
Most of the phrases by which Spix attempted to systematize and carry out
the repetition-hypotheses of Schelling and Oken, as applied to the osteology
of the vertebrate skull, may be similarly explained, and when well-winnowed
some grains of truth may be recovered.
In denominating the palatine bone the ‘hyoid bone of the f. face,’ Spix en-
deavours to express a relation of general homology by a term which should
be confined to the enunciation of a special homology: but he adds “ cornui
ossis hyoidei anteriori analogum,” which shows an almost correct appreci-
ation of the serial homology of the palatine bone. It answers, however, in
the maxillary arch to the stylo-hyal or proximal element of the hyoidean
arch, not to the cerato-hyal or hemapophysial element ; and it needs only to
recognise the palatine as the ‘ pleurapophysis’ of its vertebral segment, to
. eS
appreciate all its true serial homologies. It might as well have been called the | |
‘tympanic pedicle of the face,’ the ‘styloid process,’ the ‘scapula,’ the ‘vertebral
rib,’ or the ‘ilium—of the face’, according to Oken’s and Spix’s faulty method
of expressing serial homological relations, since it holds in its vertebral segment
the same place which each of the above-named bones respectively does in its
segment.
So also, with regard to the term ‘ os faciei iliacum’ applied by Spix to the
mastoid (s), the error lies not only in the application of a special term to ex-
press a general homological relation, but in the supposed serial homology so
expressed. Had Spix detected, in a cranial vertebra, the precise element
answering to that called ‘iliac bone’ in a post-abdominal vertebra, yet it
[Insert at, the end of the Report.]
SOEMMERRING*.
Names. Nos.
; Pars prior sive basilaris partis occipitalis ossis 1.
z spheno-occipitalis.
: Pars lateralis sive condyloidea, &¢. ...++-.-+++++++ 2.
¥ Pars occipitalis stricte sic dicta, &C. ....+-++-se0+++ a
a
A Eminentia aspera musculum rectum lateralem 4.
it excipiens, &c.
Mi Basis sive corpus partis sphenoidalis ossis sphe- 5.
; no-occipitalis.
1° (in|, | Ala media sive major partis sphenoidalis, &c. ... 6.
i
¢ Dol SERRE {6b Se ee nee ee 6!
le); iq, | Os bregmatis sive parietale ........:seeessesereeees i:
. al 9% | Processus mastoideus ossis temporis ---+- seseees 8.
tosphé, | Pars prior sive rostrum basis partis sphenoidalis ae
; ossis spheno-occipitalis.
7 ae oe DPE on acsivehaconjiecccdpeiaesenesssancdssee Berackan fone nate 9!
' (in er, | Ala superior sive minor partis sphenoidalis, &e. | 10.
fronta, | Os frontis ...... La ee eee Se ase ae pe eee 11.
19.&20 (i) | Apophysis orbitaria externa .....s6+..:0++++s00 my (ea
hérissé{, | Vomer....... Bee eee BUN Sle uct sacadaeceasnanseenue: th ndiaea
ophysa|, | Pars media ossis ethmoidei .........+++-++-++eeeee 14.
le); nal. | Os nasi ...... ee Se ese Resear 15.
mpéal (. | Pars petrosa partis pyramidalis ossis temporis... | 16.
“
eexacss . | Ossicula audittis .......-..cceesescoeerseeneneeees atenwa 16’.
a3 p.. . | Tunica sclerotica opaca oculi ......- seaebweaen 17.
i 2 ......\.. | Partes laterales. seu cellule et conch ethmoidei | 18.
Fy f the “i 30 “Schuppentheil des Schlafenbeins” (in fishes, reptiles and
%) ertains birds); hintere Abtheilung des Schlafenfliigels (in monotremes),
.. ii. p. 10 Késtlin ; “ Felsentheil desselben (os petrosum),” Bojanus.
- the ty 31 “ Kleine Fligel des Keilbeins,” Bojanus ; “‘ Vordere Schla-
3 4 applied fenfliigel,”’ Kostlin.
pet os. 28a 32 Siebbein, K6stlin.
rof horr 33 Mastoideum, Bojanus and Kostlin.
Ss. V. PD 34 « Os transversum,” Kostlin.
hyals. 35 « Gelenktheil des Schlafensbein,” Késtlin; ‘ Paukenring-
2 Osseus knochen,” Bojanus.
je total 36 Gaumenflugel des Keilbein, Bojanus.
\oides’ 37 Jochfortsatz, Késtlin; Fligelbein, Bojanus.
nian g¢ 38 Recherches sur les Poissons Fossiles, 4to, t. i. 1843.
1 plus 39 De Corporis humani Fabrica, 8vo, 1794.
Selerotal .
Keio
moturbinal,
‘Turbinal
Palatine
Maxillary
Premaxillary
Entopterygoid,
Prerygoit
Eetoptery
Malar
Squamosal
‘Tympanie
Bpihyal
Ceratoliyal
Basi-hyal
Glosso-hiyal
Uroliyal
Brunchiostegal
Hasibranchial
Hypobranchial (in
‘ishes) : Thyro-
hyal (in other
vertebrates™),
Corato-branchial...
Lpibranchial ss.
rh
haryngo-branchinl
Suprascapula ..
Seapula
Coracoidl
Clavielo
P
\upratern por
Suborbitals
Lachrymal
Labial...
Mastoidien
Noval (in fivbs
Palatin
Maxillais
Tot
r
‘Transverse
pitee
siren").
Os phas
Sune i
Sur-orbitaire
Sur-temy
Colomelle (in
Pariétal
repoiles) ; temporal
Sphénoide principal (in fishes)
ip! peels oc. fr
Sphénoide antérseur (im fishes) 5
Aile orbitaire (in fisbes, birds and mammals); aile texsporale et une grande partie de
Vaile orbitaire (in erocexfile?).
Lngrassial (in Bisbes); ptéreal™ in crocodile); rocher (in binds)"; pl.
Frontal (in fishes and birds); frontal unique (in ervcodile) ...
Temporal (in fishes)"; jugal™** (in erocodile),
eed (im fishes)"; Bériméal (partly, in crocodile); yomer (in
Hone fishes)"; ethmophysal (in crocodile); nasal ethmordal (in
Frontal principal (in fisbes and reptiles); frontal ow frontal unique (in birds snd mam-
reptiles); borde externe ou posténicur de V'arcade
)
).
Frontal powtérieur (in fishes and
sourciliére du frontal
Vomer were
Provtal anténeor (i
Jews batrachians'
mals).
Ethmoule (im fi
saurians, bil
Rocher (in fishes, birds and mammals)
Onselets de Voreille
* Viteos it
Partie ersniente
(in mammals),
crorodiles) ; os en ceinture (in tail~
fishes, tailed batrachians and
o ni }}; ethmoide (im birds and rnam-
");, comets inféniears (in ephidians|
); fromtal antérieur (in tail-Lexs batrachians) ; nasal (in opbidians, | Nasal (in fishes and crocodile); nasal maxillaire (ia binls) .
irds wad maxmmals)-
Tn-rupéal (in fishes)"; post-nipéal (in part, in crocodile)™
Ethmophyxal (in fishes)"; rhinosphénal (in crocodile)™ -s-sscyensssiee
Palatal (in fishes and crocodile); palatin antéricur (in bints)* ....
Addental (in fishes! and. crocodile)”,
iasal (in flies and crocodile)”
Wérisaéal (in fishes)".
Adgustal (in fishes)"; hérisséal (in crocodile
birds),
maxillaire aupérieur (in birds)".
maxilinire™ inter-taxillaire (in birds) #4 ,
sidicn interne (in flahes")
verse (in fhea?), prérygoidien (in batrachians and saurians
terne (in ophidians*),
‘Transverse (in ophidians*, # in lizards’, d in crocodiles") ..
crocodiles", f, We in mammals*).
#
} ptérygoidien in- Palatin postéricur (in
Adgustal (in erocodile)®
Gavier includes the squa- | Adorbital (in crocodile)”; pidee antéricure de Vos jugal (in birda)".
‘Temporal, ou partic feailleuse (in lizards’, p in crocodiles, ¢, &e. in mammals); jugal | Cotyléal (in crocodile)"; pitee postéricure do I'os jugal (in binds)".
(in birds and monotremer
Enostéal (in crocodile); tympano-styloide (ia birds). ....
Le ean (n ophidinns and i eo) ro ympanique (in Tard); ox ar (in
1 partic tympanique dix tem
panique (in batrachians Serval (in fishes). .
mpanitad Uroservial (in fishes)
Epicotyléal (in fishes)
Hypocotyléal (in fishes).
Submalléal (in fishes);
Subjugal (in crocodile)
Subcotyléal (in fishes)
piras!), cai
‘Temporal ({n fis
Sympleetique (in
‘Tympe (in fishy
wubrupéal (in crocodile)".
gabtewsporal (in erocodile)”
Subvoméral (in fishes); sublachrymal (in crocodile)
Subpalpicbral (in crocodile). x
Subdental (in fishes and crocodile)!
Styl-lyol (in fishes and mammals).
Gs styloidien (in lizards”
branche’ suspensoire, al),
on come antérieure
jéee de In corne nntéricure (in
‘and mammals); petit of
ilice cartilagineux (in crocodiles*).
pitee de la corve nntérieure
(in lzards* and mammal
térieure (in crocodiles
remibre pidce impaire de I'os hyo
~Wyatrachia)*; carps de V'ox hyoide (in sau-
Hyposternal (in fishes); cernto-hyal (in mammals)...
Grunile pidee Intérale
(in fishes);
Fone moyenne (in Hyo-sternal (in fishes); glomo-byal (in birds); npo-hyal (in mammals)*
Grande pido latérale
‘some chelonians™);
(in fishes);
Petites pices latérnfen (in faite Apo-byal ad cerato-hyal (in fishes); basi-hyal (in binds and mammals)*
paira de Vox hyoide (1n ot)
rinns and some ebelanians™, in W
Os Lingo (i fishes und binks?); ew
particulier dle In langue (in ehel
Queue de Mos hydide (in falies?
al (in fishes and some birds); ento-hyal andl uro-hyal (in mam-
Episternal (in fishes) ¢ uro-hyal (in bia) Moose
Cotes sternales™sees.cees
Basi-hyal and uro-hyal (in fishes)
‘ui soutient la langue (in batrachians’}; ox
Virds)) seconde pidee iunpaire de Vor hyoide (in
Tayon branchioatégal +.
Chafne intermédiaire d'omelets
ythenéal (in fishes) =; apo-hyal and cerato-hyal (in
Piteo interne ie inferieure de Varceau brancbiale (in fishes); branche latérale
FET pete : Vinls}*; glosso-hyal (in mammals) *.
‘unl come postéricur* de l'os hiyoide (in batrachinns); la deuxieme paire de comes
nde come and corne moyenne (in some chelouians); corne anté-
rheure (in binds’); came postéricure (in mainmals).
(in Tiare);
Piteo externo de la partic inféricure de Marceau branchiale, and pharyngien inférieur | Plural inférieure and ericéal (in fishes)*.
(in fishes). ‘
Partio nupdricurs do Vareeau branchiale «
nygien superie f :
re? (in fishest); laine cartilagincuse du bord spinal de Vomoplate
‘dies nnd saurians); yuirtie spinale de omoplate {in anourans)s
petite os particuliers dans le ligament de Yomoplate (in cheloninn
Scaplilaire® (in fishcs); col de l'omoplate (in proteus); l'autre partie, b, de l'omoplate
(io anourans).
Tuméat (in fsbo) ox comesitien (reptiles and hinds); apophyse ou tubercule | Furculaire (in fshes); coraccide (in reptiles, binds and mammals)
coracoide (in
Clavicule arromion de Vomoplate* (in chelonians®) ; clavicule (in other reptiles, birds | Furculaire (in reptiles, birds snd mammals) *
= anil mammals).
Troinme om de Varna
yptiles, binds and rat
Headial! in Hohes}; cubitus (Wi reptiles, binds and mammals).
Cubital” (in fishes); radii (iu reptiles, birds and mammals) .
J Op da earpe? osssse
| ARayons de In peetorale? (in fishes); métacarpicns and phalanges (in other vertebrates)
porte la nageoire pectorale® (in fiahes); humérus (in | Humérus (in reptiles, birds andl mammala)*4* ...
cubitus (in reptiles, birds and mammals)?
vrua® (in fishes); radius (in reptiles, birds and mammals)
and cubitus™ (in some fishes); ox du carpe in reptiles,
gea™ (in some fishes); os du métacarpe and phalanges
(in reptiles, birds and mammals)*.
Os caracaidien® (in fishes) Coracoisde ™ (im fishes)
Sous-orbitaire®
a
‘MECKEL” —WAGNER®.
News,
(Corps oni Oceipitissanenseten
Ooxpinks baerie ee
(i H
sqibenodSei (in fabes and rep=
magna
tiles); ala parva (un birds and mam
Pr ams :
Prontalle sessserssorserenvenssvenvessavecssseene
birds and mammals)
ficula auditos
One turbinata superior
Nasale (in fishies) se-secsscsarseres
Palatinum ...
Maxilla superior
Totermaxillare
Pterygoideum interaum
Pterygoideum externutn (in fishes!
+ rygoideum (in other vertebrates
‘Transversum
Zyomaticun
Quadrato-jugale ani quadrato-maxillare
(in reptiles and birds); squats tem
poralis (in maummals™),
Os quadratum seu tyrpanicum...
‘Os quadratum seu tympanicam (in fishes).
‘Os sympleeticum (in fishes)
Pterygoideum posterius (in fishes)
Or quadrata-jugale (in fishies)
Os articulare
‘Os dentale
Macxilla inferior
Preoperculum...
Operculum
Subaperculum
Jnteroperenlum
Processus styloideus
Das vierte doppelte Seteustick ios Zan:
gen-beinbogens (in fishes), |
* | purposely depart,
name (o the bomologo:
pedantic to persist in extendiog a
special function in one class, which
in that sense to the bom
have substituted,
hypoliranchials in
acconls with ite constant
‘lasses, and which harmonises in its termi
of the other parts of tbe hyoid apparst
arngoty from Eta Oe aalen
real” and “come
™thyro-byal" has occurred to me
for No. 46, that of = thyro-hyal Y his Soi omen
‘os the root a} eb with wie it is
lature adopt
us part i
herefore, for ie depe
te, and as agree!
for the parts of the hyuid
lying the same
here, from the rule of applying the same
associated. have the less hesitation in thus deviatin ® Not reckoned as part of the
‘ince the metamorpboses of © The term “*intermaxillare™
"is bunks, or “os
Wlstoire Naturelle des Possaons,¢.&. (182%)
4 Rigoe Animal, t. iii. (1830.) pp 431,432. In this work the
indicated by letters: the sumbers cited are thove used
Possoca”
“Vapophyse_mastoide
‘oecipital.” The same
the
Razrachians, whieb, with those
Agaaniz, will he found after Nat. 236 to 28d.
1 Cavier salds, that this pase of borns ix “ celle qui représent
Jes on styboidiens"—Onx Fog x. part ii. p.19%, Bot they
The epi-hyal of thie Chee
them by Geoffroy and
‘Omemens Fousiles, 410, tip. 23;
(9e ek courte, et sppartient
‘of the par-eccipital with tbe true mastoid process per-
* Lesons d’Amatomie Conaparée, t. fi. 1837.)
2 Onernens Fensiles, ¥-
vorbitaire (in Lizard)
* Owemens
answer to the epi- and .
yn he describes as “ane pitch
sayenne."—Ibd. p 194. The
sometimes called
76. Aile temporale et Iaile
Cavier.
= ‘genera in which the “corps
Ato, & ¥. part fh (1824.) prices”
© Cuvier specifies the
Ge Vow bryoide™ is ™ subelivise
the pharyngeal bones (1
Physiologie, iv. (1618.) p. 240. Cavier these parts
hyold as “ cornes onseuses fieures,” in the *Legous
a Avatowle Comparte,’ ii. (1805.) p-252, bot afterwards adopt
Meckel's view of 1 aod that “ile ponr.
that
the hypo-branchials.
1s To oot regard this howe as part of a cranial vertebra.
& Die Verglachende Osteologie dea Schiifeabeios, 4t0, 137,
: ee =
aS a
Nenes. sn
a
‘Squamsa Qeeipitalis wassererecessssceenneece |
a r
Occipital exterme cress
Sphénoide principal, snnece
Grande aile du xphéngide ccs:
‘Seitlichen obern Hinterhauptbein vss.ss
“Roeilbeinklirper ssesesnssesnessseeessesen
‘Febmateia™ (0, fhe and
‘mararmals)™, Lo
‘Schlifbeinschuppe oder vonlere do. ....+-
nasal (in sau |
nians, birds and mammals).
Oe iegomarem ts ‘petrosum (in
fishes); wntere Muscheln
Maxillaire supéricur
Tntermaxillairo®..,
Peérygoiilien interne
Zwischenkieferbei
Auserer Fligelfortaats (in reptiles)
Jochbein Ceenaion binls and mam-
mals),
Tlintere Schlif beinsehuy
Cartilage mobile du Her... | Ox xpongiosim sive turbinatum inferius .., 1.
On palati srescoee 20.
‘Maxilla nyperior al.
Thre incisive maxillon 2.
23.
Y ory
rygolilet partis sphouoiilalis ossis spheno-
bevipitalis
Pte 26,
Ox jugale seu inalio 26.
Pare squamosa oasis tomporie ....). 7,
.. | Lamina omen omix tomporis © qui ineatus mudi | 28,
Obere Gelenkbein™ ...,. orn
Griffelfurniges Stick des Schlifebeins.
‘aixse, oF ox tympani,
Unteres Geleakbein®.... earré, of of quailraturn.
Gelenstiick dos Unterkiofers ..
Kronenstiick dex
‘Zahstiick des Unter
Varkicmendeckelstiick
Higontlich Kiemendeckelstiick ,.
Unterkiomendeckelstuick
‘svisohenkiomendeckelstiick
Kleine stilotfirmigo Knochen dos Zun-
nbein (in fishes); Griffelfortsite
des Schtifenbeins (in maimtnals),
Zungen-hor, oder...
Zungen-bogen. Drittes, vorderstes weit
Jeiner Hornerpuar (in chelonians).
Branche latérale -....+00
Mittlero Stick der Zangenbein Tite glénoidlale s.....5.0+
Zungenkerne (W.) v0»:
Tlintore mittlore Stick dor Zungenbein,
Kiemenhautetrablen sae
Unpaare Kuochen in der Miteli
Queue de Vos hy
jimnerpanr (in batruchians) 5
tem nilaseren Zungenbeinhirner
res Hornerpaar (in.
Pitee orticolaire ...
hintern Horner (in
Stick der Kiesnenboger
Pitco branchial, et
Pharyngien inféricure,
Pigs branchialo «sere»
veh
hen der Sehulterthell (in
Obere Knochen deswelb, oder Schulter-
Schulterblate (io
Unterste Knochen der Sebultertheil.
Vordere Schliimelbein (in fishes);
Tlintere Schliisselbein (in other ver-
.
Vordere Behl teeth (in reptiles, birds
Oberummknochen seers
Vorderarmknochen.
Mandwurselknochen
Brusttlowenstrable (in fishes) ; Mittel~
handkoochen und Phalangen (i
Jugal et apophyse rygomatique
7 ™ Kthmoldeam erit
™ Aonales des Sciences
de VAead. Royale des Sciences, t. xii, (1833).
® Annales da Muséom, t. x. (1807.) pp. 42—360.
Anstomeps 1818; p. 196: pl: 3 4.
ie, Bo, Ths fe il. 121,
144,
batrachia, Vergl. Anat.’
sa
«|
ar pra ave rstr nase rte coals a
torius externiis oritur,
\iliformis parti pyrninidne
a roceen
is tomporia,
Tis onal
Ligomentumn ov lingoalo suporius inter et pro | 9.
comsun atiliformem.
Os lingualo auperins vel pisiforme esses | 40,
Os linguale modtiumn so.
(QM LSpraul Ns rseresszocecavoronthl | Pasratinratecre OMTERUENSTT econ ante! | AY
Corps de Whyaiile
Oven lateralia lingualia
Os lnerimale «.
ot
ila Schlafembein,” Kénilin * Paukenting»
a ercnendigal dex KelTbin,Bojanas
2 Jochorvatr, Konllin, Wigelbein, Bojanus.
™ Recherches eur les Poissons Powsiles, 4to, t. i. 1843.
® Te Carports homaui Fabric, HY0, 1794.
[Insert at the end of the Report.]
SOEMMERRING®.
jo ph coceschrseceredeed dncince Corpus vertebree. ;
ut lames vertébrales ...... Areus posterior vertebra, seu radices arcus
posterioris.
ls roche Scer Seasechagencerene Radix prior seu antica processus tramsversi ver-
tebree.
Mee Meerian cage ch sk'se,c dee sue Processus transversus vertebr cervicalis. Costa,
seu pars vertebralis, seu ossea, costz.
thorax); cétes abdomi- Cartilago cost seu pars sternalis coste; (in
ges ventraux (in abdo- the abdomen) inscriptiones tendinex mus-
é en chevron (in tail). culi recti.
| Spoccaccososuernegnennedces Processus spinosus vertebra.
Eee aeeeasenteecthsctsucuss Ossa sterni et processus ensiformis; (in the ab-
domen) linea alba.
S[2 GBP oc ee*an- ConeBEBBEDOe Radix posticus processus transversi vertebre,
(and) processus transversus.
Processus obliquus vertebree.
der Wissenschaften zu Berlin, 1834. The terms adopted in
-ind anal fins * most of the recent works of the German zootomists correspond
ataaux”’ by with those of John Miller. ;
7 Lecons d’Anatomie Comparée, t.i. edit. 1835.
‘ol. 1828. 8 De Corporis Humani Fabrica.
TasLte I].—SYNONYMS or tue ELEMENTS or toe TYPICAL VERTEBRA: [Insert at the end of the Report.]
OWEN'. GEOFFROY®. CARUS®. MULLER®. CUVIER?. SOEMMERRING*.
Autogenous Dlements.
Centrum (kévrpov, CONG) apmreeevsstenvsirctsnects Cycléal .. Tertiar-wirbel ......... Wirbel-kérper «..... Corps! deivertebreverscsccssssssesnexteses Corpus vertebrie.
Neurapophysis (vedpov, nerve, and dndpuors, a Périal «.... Deckplatten and Grundplatten . Oberer Wirbelbogen.. Partie anmulaire, on lames vertébrales Arcus posterior vertebrae, seu radices arcus
process of bone). pan
Parapophysis (apd, across, and dmdduats) «+++ Paraal (in the tail of fishes) ...... Querfortsatz ... Unterer Querfortsatz. Apophyse transverse . Rad cRnoF seu anticn processus transversi ver-
tebree.
Pleurapophysis (wAevpa, a rib, and drrddvuots) «+ argaltsccccesacversss sorsavonseesens Riickentheil and Ober-sternal-theil des | ..... sovenceasecesansnsnans Cotes vertébrales ...sscccscccccescesscceeeseees Processus transversus vertebrae cervicalis. Costa,
Urwirbelbogens. seu pars yertebralis, seu ossea, costa.
Haemapophysis?; by syncope for hamato-apo- Cataal ... Unter-sternal-theil des Urwirbelbogens... Unterer Wirbelbogen Cotes sternales (in thorax); edtes abdomi- Cartilago coste seu pars sternalis cost; (in
physis (from Gr. alya, Wood, and dréuars) nales, ou cartilages ventraux (in abdo- the abdomen) inscriptiones tendines: mus-
men); os ployé en chevron (in tail). euli recti.
Neural spine ...... sonsensecesssensne feveveretvexsesee Périal (in fishes); épial (in other (Its base is the) Oberer Tertiar-wirbel, Oberer Dornfortsatz.. Apophyse €pimeuse sscseeeeesssseereeensaeens Processus spinosus yertebra:.
vertebrates). (its apex is the) Oberer Dornfortsatz.
Homal spine ......006+ muvetee dcetece OASLOCCELECO EDD Paraal (in fishes); cataal (in other Sternal-wirbel Korper .....ssseeceeeees cco Unterer Dornfortsatz syabonataavdenccan?darssansuvaddeavaudeasiah maaerenccey Ossa sterni et processus ensiformis ; (in the ab-
vertebrates) *. domen) linea alba.
Exogenous Parts.
Diapophysis (8:4, across, and drdcbuats) ......0. Paraal (in reptiles and mammals) Querfortsatz ..... SACRED CORDON EOCUCC CCL Oberer Querfortsatz.. Apophyse transverse ........++ Mrtaddccccth Badle osticus processus transversi vertebrae,
and) processus transyersus.
Zygapophysis (Cvyds, junction, and drduats)... * én Seitlicher Tertiar-wirbel .. Gelenk-fortsatz ...... Apophyse articulaire ........ Eccceeerepnsnscenee riosuend obliquus vertebra.
' Description of the Plesiosaurus macrocephalus (April1838), apophyses.” Dr. Stannius, it seems, would abrogate the useful 3 Mémoires du Muséum, 4to, t. ix. 1822, p.89. der Wissenschaften zu Berlin, 1834. The terms adopted in
‘Geological Transactions,’ 2nd series, vol. v. p. 518. license of the grammarian’s syncope and apocope: but how 4 The dermal spines which sustain the ‘dorsal and anal fins most of the recent works of the German zootomists correspond
’ The accurate and laborious coadjutor of Prof. von Siebold, many current scientific terms must be expanded into sesquipe- of fishes are called respectively “épiaux” and “‘cataaux” by with those of John Miiller. é
the second part of a recently published compendium of Com- dalian longitude, if such “ purism”’ should prevail! See‘ Lehr- Geoffroy. 7 Lecons d’Anatomie Comparée, t.i, edit. 1835.
rative Anatomy, adopting in part my Nomenclature of the buch der Vergleichenden Anatomie,’ yon V. Siebold und Stan- 5 Urtheile des Knochen- und Schalen-geriistes, fol. 1828. ® De Corporis Humani Fabrica.
ticbral Elements, corrects this word, and writes “ hemato- uius, Zweiter Theil, p. 5. ® Vergleichende Anatomie der Myxinoiden: Abhand. Akad.
jaRCLEITE
{
OWEN (1846)?
|
} OKEN (1807)*.
Taste III.—SYNONYMS or tue BONES or tue HEAD, accorptnc ro THEIR GENERAL HOMOLOGIES.
| [Insert at the end of the Report.)
SPIX (1815)',
Occipital Vertebra.
1. Occipital centrum «+-+++ee+06
neurapophyses «+++...
} diverging appendage ...
Splanchno-skeleton.
16
| Capsules of f sens f
18. Japs! ie3 0! organs of sense . |
Radius capit
Humerus capitis
Corpus vertebra.
is
Koprwirpex oder KoprsiNNESWIRBEL.
Ohrwirbel.
oder Korper der Ohrwirbel
Processus transyersi et obliqui oder Seiten- und Schiefenfortsiitze do.
pia bests ecs tsi vaate Processus spinosus - oder Stachelfortsatz do. Pars superior processus spinosi
F yertebree prime,
Ei Partes inferiores spi-
4. FAPOPLYSCS ss eeeereeree Undetermined *:. -.:s..s5-cusesstiettercnssuvapsdaprcucsr scans { : Processus s ‘}
‘ parapophyse s ; ; nosi vertebra: prima.
50, 51. plewaponbyses Line aus finf Halsrippen zusammengeflossene Platte Notiracopuinedinsteleniantarcn he
52. hemapophyses : Rae Tt yasteham Tee ees Ossa extremitatis thoracic «++
53-57. diverging appendages «
Parietal Vertebra. Kieferwirbel. Vertebra Cents seu parie-
iy Parietal centrum. Corpus vertebrie ...- : ; oder Korper des Kieferwirbels Corpus vertebrae secundie ..-+++
6. 7 Processus transyersi et obliqui oder Seiten- und Schiefenfortsit Processus transyersi vert. 2de.
ii. spine Processus spinosus . oder Stachelfortsatz do. tae media processus spina
4 vertebrae secunds.
8. parapophyses Undetermined ...... Os facie iliacum .........2000+
38 leurapophyses
39, 40. izemapophyses . Se
41-43. escalate 5 Sacrum capitis... Ossa extremitatis cervicalis ...
44. diverging appendage...
Frontal Vertebra. Augwirbel. Vertebra tertia, seu frontalis.
9,9" Frontal centrum.. . s ee . E ? Corpus vertebra tertie
10. neurapophyses . Corpus et processus transyersi oder Korper nebst den ised [oan des Augwirbels. { ae Bansvetoertl inti
11. spine ... Processus spinosus . . oder Stachelfortsatz nebst seinen Seitentheilen Processus spinosus vert. tertiee
12, parapophyses .....+.000 Undetermined... Os faciei scapulare
28. pleurapophyses «.......+ Scapulz capitis (in birds)...... oder Schulterblatt des Kopfes ............ seswaeseseneesersenseese Os faciei ischiale.........0.2000+
Femur capitis
29, Tibia capitis Femur, tibia, fibula, tarsus, faciei
a Fibula capitis
Slee |Ueavexvcree seeeesenees tye
ay nuenee })_ Pes capitis Phalanges pedis faciei seers»
34-37. diverging appendage... Os pubis faciei
KoprruMPFSINNESWIRBEL.
Nasal Vertebra. Nasenivirbel*.
13. Nasal centrum Corpus vertebrale ...........-... oder Korper der Nasenwirbel Os mediastino-faciale.
14. “Das Siebbein mit seinen Windungen (18) fiir das zu Gefassen metamorphosirte Hirn. Ossa thyreoideo-facialia.
15. Processus spinosus ....-.--..-- oder Stacheltheil der Nasenwirbel Os faciei sternale
pleurapophyses ......... Costa capitis fixe ...-...... s+ oder Verwachsene Kopfrippe «sessessscressereeetssesetseenesees Os secundum hyoideo-faciale ..
hemapophyses ... Ulna capitis ....-20.secseseeseee oder Ellenbogenbein des Kopfes -.:....::00:sseesseeseeeeeeeeeee Os ulmare faciei «..........c00e8 :
hamal spine ... Manus capitis -....-es210+ee00+ oder Hand des Kopfes® ...sc+cesersssesscerseestensensseseereereee Os radiale faciel ...........c00008
ader Schliisselbein des Kopfes ....:sssccssscseeeeesseeesseeeereee Os hyoideo-faciale ..........0.0+
. oder Speiche des Kopf
Sinnorgan
45,
ASAT Branchial arches....-.s.s0++e++
48, 49.
Dermo-skeleton,
71. Supra-orbital sealebone ...... Undetermined .......... Prod FrlOLEr Hon cer Ps pPLEAP CCCOSEC RSD) CLDF PLE ECE PEECEE PEPE Cer EPE PEP EEE EE PPRCELDS
Supra-temporal do. Undetermined.
Lacrymal do. Processus transyersus
Suborbital do. Undetermine
Labial do. Undetermined.
. oder Oberarm des Kopfes (in birds); seapula capitis (in man)
BOJANUS (1818)7.
GEOFFROY (1824).
Vertebra prima, seu occipitalis.
Corpus vertebrae primm ...++++++
Processus transversi yert, 1a--
Undetermined
Os erico-arytenoideo-faciale
Os coracoideum faciale .
Undetermined
v
Javiculare faciei .
Os humerale facie:
Ohrwirbel (Vertebra acus-
Ohr-Grundstiic
Bogenstiicke «.
Dornfortsatz .
Undetermined....--:..6-+-01--«
{ Not
Schmeckwirbel (Vertebra
recognised as elements
of cranial yertebrax.
ae vertebrae primm, seu
occipitalis *.
{ Cost:
Sehwirbel (Vertebra optica).
Undetermined...
Seh-Bogenstiicke
Dornfortsatz
Undetermined
Undetermined ........6000
Undetermined ........cceree é
Undetermined scccsscsereesseees
Undetermined
Riechwirbel ( Vertebra olfac-
Riech-Grundstiick
Bogenstiicke
Dornfortsatz
vertebrae 4ta,
wthmoidalis *.
Undetermined...
Undetermined..
Coste vertebra:
seu sphenoidales *.
Undetermined
Undetermined ;
Grundstiick der Sehw
Undetermined
Processus zygomaticus sae
frontis.
Undetermined .
Ossa jugalia
tica).
Vileme vertébres
Périaux du Viléme yertébre
Epial du Viéme vertébre ...
Epiaux du VIléme vertebre.
Not recognised as elements
of cranial vertebrae,
gustatoria).
Schmeck-Grundstiick. Cyeléal du Véme yertébre” .
Bogenstiicke ... Epiaux du TVeme yertebre .,
Dornfortsatz Epiaux du Véme yertébre ...
Périaux du Vieéme vertebre..
Not recognised as elements
of cranial vertebrae,
Cyeléal du TVéme vertébre ”
Périaux du 1Veme vertébre .
Epial du I1leme vertébre ...
Périaux du Véeme vertébre...
Anneau inférieure du Véme
vertébre,
Undetermined........:.0:s0+0+
Undetermined ..
34. Anneau inférieure du
37. Viéme vertébre.
35, Amneau inférieure du
36, f Vleme vertébre".
toria).
Cycléal du Ide vertébre ”..,
Périaux du IIde vertébre®.
Epial du Ide vertébre ......
Cataaux du T1Iéme yertébre
seu }
Cataaux du Tere vertébre ..
yertebre.
Cataaux du IVéme vertébre.
Paraaux du Ide vertébre -
we et Stire, }
Undetermined
Epiaux du Tere yertébre:
Cataaux du Ide vertebre
Pleureaux, ou Cotes de ln
poitrine
me vertdbre!*
me yertebre.
‘aranux du Ter
Paraaux du IVéi
dieters des Viéme oh
Heras and Paraaux du pa
}
}
Nos,
Grundbein oder Wirbelkérper (Unterer paral-
{ dele eras ‘bel) fice I, Schiidelwir- if
els,
Bogenstiicke oder Grundplatten des I, S. W. 2.
Obere Deckplatten des I. S. Wirbels......-.. 3.
Untere Deckplatten des I. S. Wirbels ..... 4
Oberer Sternantheil.. “
{ Unterer Sternantheil, } der Halsrippen
Glieder der Brustflosse ......0.0..202005
Wirbelkorper des Il. Schadelwirbels 5.
Bogenstiicke des II. S. Wirbels 6.
Deckplatten des IT. S. Wirbels co 7.
Obere Bogenstiicke des I. Zwischenwirbels. 8.
Riickentheil der Eingeweide-rippe .. 38.
Sternantheil der Eingeweide-rippe
Eingeweide-wirbelkorper ......... 4143.
Auswarts gekehrte Ausstrahlungen des Kopfs- 44.
eingeweidskelettes.
Wirbelkorper des ITT. Schiidelwirbels . pate
Bogenstiicke des IIT. S. Wirbels 10.
Deckplatten des III. S. Wirbels . i.
Vordere Abtheilungen d. obern Grundp! Heal 12.
{ des I. S. W.
a. Obere Riickenstiicke der I. Zwischenrippe
6, Unterer Rickentheil der I. Zwischenrippe 23,
c. Rudiment der I. Schadelrippe 3
d. Oberer Sternaltheil der I. Zwischenrippe.
Hintertheil des untern Kopf-gliedmaasses oa
{ 30.
| Vordertheil des untern Kopf-gliedmaasses «..{ 33°
Obere-hintere Kopf-gliedmaasse . 34-37.
Wirbelkérper des IV, Schiidelwirbels - 13.
Grundplatten des IIT. Zwischenwirbels 14.
Deckplatten des IV. S. W. 15.
Ite. Antlitz-rippenpaar 20.
2te. Antlitz-rippenpaar .. 21.
3te. Antlitz-ripperpaar .. 22.
Schadel-rippenpaar des IIT, S. W. ..-- 23.
Unterer Sternaltheil der I. Zwischennppe re
‘ 26.
27.
5 16
. 17.
: 18.
Grundplatten des V. Schadelwirbels. . 19.
Bauchwirbelkérper . 45.
Unterer Theil der Eingeweiderippe - 46, 47
Oberer Theil der Eingeweidenippe 48, 49
CARUS (1828),
' These are the numbers by which the bones of the
head are indicated throughout the present ‘Report’ and
in the subjoined work.
Fs Hunterian Lectures on Vertebrata, 8vo, 1846.
. Ubere die Bedeutung der Schiidelknochen, 4to, 1807.
This vertebra is not formally admitted in the Pro-
gramm of 1807; but in a subsequent essay (Esquisse
d'un Systéine de l’Anatomie, de Physiologie, &c., Paris,
1619), Oken admits this as a vertebra of the face, and
calls it “vertébre nasale;” and in the ‘ Naturphiloso-
phie,’ 1843, p. 304, it receives the name above cited,
* “Toh halte die Zihne fur die Finger.” ({ regard the
teeth as digits.) Oken, 1. c. p- 14; and those of the pre-
pay he regards as more particularly representing
e thumb (/bid. p. 14), and deems it worthy of remark,
that the thumbless mammals likewise want premaxil-
lary teeth: not considering, or at that time not know-
ing, that the thumbless ateles has premaxillary teeth,
whilst certain bats (Taphozous perforatus, Geoff, for
example), and seyeral Edentata, have the homologue of
the pollex but no teeth in the premaxillaries,
© Cephalogenesis, fol. 1815.
7 Versuch einer Deutung der Knochen in Kopfe der
Fische, Isis von Oken, 1818,
vi Anatome Testudinis Europem, fol, 1819-1821,
p. 44.
® Tableau de la Composition de Ja téte osseuse de
V'Homme et des Animaux, cited by Cuvier (Hist, des
Poissons, t. i. p. 230) as being the Jast which Geoffroy
published, and of the date of December 1825. It differs
in many respects from the “ Tableau" given in the An-
nales des Sciences Naturelles, t. iii 4
W Body of cranial vertebra.
Comp. Anatomy, 8vo, 1835, p. 62.
41“ The number of distinct osseous pieces in the com-
position of the skull is greatest in fishes, aud they cor-
respond nearly with the theory of this part of the skele-
ton, being composed of seven vertebrie, each consisting,
as usual, of a body with four elements aboye and four
elements below. ....- The arches, which hang down
from the sides of the yertebral column, are more like
ribs in fishes than in higher classes, as the lower jaw,
the os hyoides, the scapular arch, and that of the pel-
vis.’—Grant, doc. cit. pp. 63, 65. It does not appear
that the scapular any more than the pelvic arch is recog-
rant, Outlines of
nised as essentially a part of a cranial vertebra, In the
Lectures (Lancet, 1833-34), the lower jaw is described
‘as “the first of these inferior arches”; the hyoid as “the
second arch."—p.572. And, with regard to the poste-
rior cranial vertebra, “* the two external and two lateral
occipitals form the upper arch, and the two opercular
and two subopercular bones constitute the lower arch.
—p. 543. This is the view taken hy Geoffroy of the
posterior (his seventh) cranial vertebra. e
12 The prefrontals of fishes, being called “lacrymauxy
are the “ épiaux”” of the second cranial vertebra; whilst
those of the crocodile form the “épiaux” of the first
cranial vertebra in the ‘Tableau’ of 1824. J
18 Philosophie Anatomique, 1818, p. 217, “The
branchial arches are connected with the os hyoides,
Lectures, Lancet, 1833-34, p. 573.
which, by extending backwards behind these arches, pro-
duces a true thoracic sternum, considering the branchial
apparatus as analogous to ribs for respiration. *—Grant,
Tn the ‘ Outlines”
(p. 65) the branchial arches are stated to be “ the ana-
Jogues of tracheal rings,”” which is likewise a view pro-
pounded by Geoffroy. ae 4
4 The lacrymals of the crocodile (adorbitals) are the
‘ périnux”” of the third vertebra in the ‘Tableau’ of
1824.
1 Urtheile des Knochen- und Schalen-gerustes, fol.
1828. ie
16 Carus views the modified centrum of the occipital
vertebra of the carp as including also the whole hemal
arch of that vertebra,
4
J »
ON THE VERTEBRATE SKELETON. 339
‘would have been more proper to have signified such serial homology by giving
the general term applicable to such parts, as abstract vertebral elements.
The fact is, however, that the mastoid (s) is the parapophysis of its verte-
bra, whilst the ilium is a portion of the pleurapophysis of its vertebra; and
the mastoid is serially homologous with the transverse process (parapophysis)
of a sacral vertebra (fig. 27, p), not with the pleurapophysis or ‘ilium’; it
is not, therefore, a repetition of the ilium in the skull. The true expression
of the ideas which suggested the terms ‘ ilium of the head,’ ‘scapula of the
head,’ &c., will be found in the true enunciation of the serial homologies of
the vertebrate skeleton.
It finally remains for inquiry, admitting the explanation of the endoskeletal
archetype given in this Report to be the true one, whether such is the
ultimate attainable generalization, or whether we may not also gain an in-
sight into the nature of the force by which all the modifications of the
vertebrate skeleton, even those subservient to the majesty of man himself,
are still subordinated to a common type.
We perceive in the fact of the endoskeleton consisting of a succession
of segments similarly composed,—in the very power, in short, of enunciating
special, general and serial homologies,-—an illustration of thatlaw of vegetative
or irrelative repetition which is so much more conspicuously manifested by
the segments of the exoskeleton of the invertebrata, as, for example, in the
rings of the centipede and worm, and in the more multiplied parts of the
skeletons of the echinoderms.
The repetition of similar segments in a vertebral column, and of similar
_ elements in a vertebral segment, is analogous to the repetition of similar cry-
stals as the result of polarizing force in the growth of an inorganic body.
Not only does the principle of vegetative repetition prevail more and more
as we descend in the scale of animal life, but the forms of the repeated parts
of the skeleton approach more and more to geometrical figures; as we see,
for example, in the external skeletons of the echini and star-fishes: nay, the
calcifying salt actually assumes in such low-organized skeletons the very
crystalline figures which characterize it when deposited, and subject to the
general polarizing force, out of the organized body. Here, therefore, we
have direct proof of the concurrence of such general and all-pervading polar-
_ izing force with the adaptive or special organizing force in the development
_of an animal body.
The marvellous phenomena of this development have, hitherto, been ex-
plained by two hypotheses or forms of expression, as the result, viz. of ‘ vital
properties’ either peculiar to living matter or common to all, but latent in
dead, matter ; or, as due to the operation of one or more ‘vital principles,’
vital forces, dynamies or faculties, answering to the idéac of Plato, deemed
by that philosopher to be superadded to matter and mind, and which he de-
fined as a sort of models, or moulds in which matter is cast, and which
regularly produce the same number and diversity of species*.
Now besides the i¢éa, organizing principle, vital property, or force, which
produces the diversity of form belonging to living bodies of the same materials,
which diversity cannot be explained by any known properties of matter, there
appears also to be in counter-operation during the building up of such bodies
_ the polarizing force pervading all space, and to the operation of which force,
or mode of force, the similarity of forms, the repetition of parts, the signs
_ of the unity of organization may be mainly ascribed.
The platonic i¢éa or specific organizing principle or force would seem to
: * See Barclay, Life and Organization, 8vo, 1822. ©
*
340 REPORT—1846.
be in antagonism with the general polarizing force, and to subdue and mould
it in subserviency to the exigences of the resulting specific form.
The extent to which the operation of the polarizing or vegetative-repeti-
tion-force is so subdued in the organization of aspecific animal form becomes
the index of the grade of such species, and is directly as its ascent in the scale
of being. The lineaments of the common archetype are obscured in the same
degree: but even in man, where the specific organizing force has exerted its
highest power in controlling the tendency to type and in modifying each
part in adaptive subserviency to, or combination of power with, another part,
the extent to which the vegetative repetition of segments and the archetypal
features are traceable indicates the degree in which the general polarizing
force may have operated in the arrangement of the parts of the developing
frame: and it is not without interest or devoid of significance that such
evidence should be mainly manifested in the system of organs in whose tissue
the inorganic earthy salts most predominate.
On Anemometry. By Joun Putuuirs, F.R.S., F.G.S.
ANEMOMETRY, or the registration of wind, is a process of recording certain
effects of the (horizontal) pressure or movement of the atmosphere. Ac-
cording to the kind of effect which is subjected to observation, and to the
process of measuring, weighing or counting which is adopted, the anemo-
metrical instruments vary, and it is required to determine the forms of these
instruments which are best adapted for accurate meteorological inquiries.
Correct anemometers may be applied with advantage as auxiliaries in a variety
of important problems not meteorological, but they are of primary import-
ance in meteorology, and derive their value in other branches of knowledge
from their proved adaptation to this.
A complete anemometrical register should give on a scale of time the
direction of the wind, and its pressure or velocity in a continuous series, or
at very frequent intervals, for days, weeks, months or years. We may for
particular inquiries be desirous of learning the total space traversed by the
aérial movement, or be satisfied with knowing the maxima and minima of
pressure, in a given period of time, or in other ways simplify the problem,
which in its general form cannot be solved without adding a clock or other
register of time to the apparatus for measuring wind.
Mechanical Effects of the Movement of the Atmosphere.
The (horizontal) movement of the air over any given point on the earth’s
surface, one of the most important desiderata in meteorology, can only be
observed directly in the phenomena of the clouds. The velocity of these
light bodies may be measured trigonometrically, by their change of position,
or when the sun shines, by observing the progress of their shadows on the
ground. But these are rather experiments than observations, and when we
attempt by instrumental means to register the velocity of the wind, some
considerable difficulties at once appear. The air moves because it is pressed :
machines to be influenced by wind must be made to receive and yield to its
pressure. If this pressure be received on a machine so contrived that it has
a resisting power, which rises with the increase of pressure till equilibrium
is gained, the displacement of the spring, the elongation of the lever, the
augmentation of the weight, &c. may be taken as proportioned to the
ON ANEMOMETRY. 341
Pressure. Many such instruments have been invented, the most famous
_ being M. Osler’s anemometer, first erected at Birmingham.
But if the pressure (P) be received on an instrumental contrivance, which
(its inertia being overcome) is set into a continuous motion (as the various
sorts of windmills), the rate of this motion goes on increasing till the resist-
ance which the motion generates balances the wind-pressure on the sails.
This resistance consists of two parts, one caused by the displacement of the
air in the path of revolution of the sails, and consequently proportioned to
the square of the velocity of revolution (or to v'?); the other caused by the
ordinary friction of machinery, which being a uniformly retarding force (db),
destroys the power P exerted on the machine a quantity proportioned
to the space moved over*, and consequently to v'. P then is prop. to
av'+bv', the coefficients a and b requiring to be separately determined for
each instrument.
If we conceive friction to be very small, so that the second term almost
vanishes, the velocity of revolution becomes nearly proportioned to V, the
velocity of the wind; but if friction be very large, the velocity of revolution
i of the machine becomes nearly proportioned to P or V%. The former is the
case on a windmill in heavy wind-pressures ; the latter of the same machine
when the wind-pressure is light t.
Hence all machines of this kind have a rate of revolution proportional to
the movement of the air, retarded by quantities which are proportioned to
something else. The smaller we can make this retardation, the nearer to
perfection is the instrument. Such an instrument is Whewell’s anemometer.
Whewell’s Anemometer.— Assuming in respect of this instrument that its
general action is like that of a windmill, we see with low velocities of wind,
the term 6 v! is not only greater in proportion to av’? than with high veloci-
ties, but may acquire a higher numerical value than it.
Coulomb found with a windmill (the load being constant), the following
proportions of wind’s velocity and revolutions of sail :—
Wind Vel. | Revolutions.
Vi. v.
7:0 3:0
125 75
20:0 13°0
28:0 22°0
We may with these data compare the following calculation :—
Wind Vel. | Revolutions. || ________ Calculation, Vv :
Vv. v. av?+ bv = | Sum.— v®. \calculatea.| PHference-
; 7-0 3-0 9-04 44:3 53:3 730 | +030
12°5 75 55°3+100°6 165°9 12-88 +0°38
20-0 13°0 169:0+191°8 360°8 18-99 —1:01
28-0 22:0 484:04+-324°6 808°6 28°43 +0°43
_ * This is not strictly the case with varying pressures of wind, if these act unequally on
the bearings of the axles.
+ Mr. Harris’s experiments with Whewell’s anemometer (Reports of the British Asso-
ciation, 1844, p. 245) confirm this view. He had previously observed (Reports of the
Association, 1842, p. 33) in one limited set of experiments with low velocities of wind, the
_ space described by the pencil to be proportional to the square of the velocity of the wind.
_ But in a larger series of trials, in strong and steady breezes, the spaces passed over by the
pencil came nearer the simple ratio of the wind’s velocity. In strong winds the ratio be-
tween the revolutions of the fly and the velocity of the wind is [nearly] constant.
342 REPORT— 1846.
In this calculation a is taken at 1:0 and 4 at 14°75. The small differences
are quite within the range of errors of observation.
Mr. Harris has furnished us with experiments* in which the revolutions
of the vane of Whewell’s anemometer were compared directly with the
wind-pressure on Lind’s well-known instrument, and to these the same form
of calculation is equally applicable. In the subjoined Table the observed
values of v! and V2 are first given, and then a column of values of V®, cal-
culated from the formula P = av'?+ 6v', the values of a and 6 being taken
at 1 and 10.
v. V2, v2.
Observation.| Calculation. | Difference.
|
* . i“ . “ut . t
Se ah mts 7 These differences of V? are
2-0 -080 -081 +001 much within the possible
2-5 -100 “106 +006 errors of observations. Those
3-0 “130 132 4-002 marked ” examined by differ-
355 “160 “160 asta ences, appear to be the least
4-0 ‘190 -190 i in harmony with the rest,
aoe -290 297 +007 and it is from these that the
5:0 “270” O54 _ 016 greatest deviations occur in
Be -290 -288 _-002 the calculation. Similarly
6:0 330 396 —-004 compared, V as deduced from
65 +350” 360 4-010 Lind and V as deduced from
7-0 “400 +1) hee hae age Whewell,are almost identical.
By this very simple calculation, then, any one rate of revolution of the vanes
of Whewell’s anemometer may be made to indicate the corresponding velo-
city of the wind. But we cannot from the sum of these rates, obtain by this
calculation the corresponding sum of the velocities of the wind; since the
relation of these sums to each other depends on the individual values of v’,
and these are not recorded. They may be recorded, in a form fit for the cal-
culation, by adding a clock-movement, which shall cause the instrument to
register the series of values of v', but the machine then loses its simplicity.
An approximation to the individual values of v' may be had by a process
suggested by the inventor, but not (it is believed) put into constant use by
any observer. It consists in simply turning round the cylinder, on which the
wind register is written, after regular intervals of time by hand. The shorter
these intervals, the nearer the approximation.
If we knew precisely the Jaw according to which the wind’s velocity rises
and falls with the lapse of time, the correction of the record in Whewell’s
anemometer might become more complete ; and it seems no small recommen-
dation to observers for practising the hourly rotation of the instrument, that
this process would speedily furnish data for the determination of that law.
The conversion of the register effected by Whewell’s anemometer into
pounds of pressure or miles of air-movement may perhaps be sufficiently
easy and accurate, if only two things are attended to :—first, the values of
the constants a and 6 in the previous formula must be determined by obser-
vationt; and secondly, the register scale should be read and the results re-
corded sufficiently often to obtain an adequate number of values of 2’.
* Reports of the British Association, 1844, p. 263.
+ The observation must be a comparison of Whewell’s registration with some experimental
contemporaneous determination ; the simple pressure of wind may be obtained by Lind’s
ON ANEMOMETRY. : 343
__ Anemometers on the principle of Dr. Whewell’s, almost perfectly fulfil the
intention of the inventor at high velocities, and also give results capable of
satisfactory interpretation at all velocities down to a certain low rate of
wind movement, but below that the instrument ceases to be sensibly affected.
Its sensibility to light winds might be perhaps augmented by a change of
_ construction—especially by substituting wheel-work for the screw, and the
sails should probably be set to the angle of maximum effect*. This instru-
ment appears applicable tu a variety of problems in which the air-movement
enters as an element. Among the results which have been already obtained
for meteorology by the diligent use of it, Mr. Harris’s demonstration of the
_ path of the air over Plymouth is very conspicuous. Were such records con-
_temporaneously kept at only three selected stations in the British Islands, for
a few years, or even one year, and accurately discussed and compared, how
great and how valuable would be the accessions to our knowledge of the
winds !
Osler’s Anemometer.—The pressure of the wind on Osler’s anemometer is
resisted by the equable force of a spring, and by the friction of the machinery
_ for registration. The pressure of the wind is well-known to be subject to fre-
_ quent and great pulsations, all of which (except the very quickest and feeblest )
the instrument registers. By enlarging the scale, every the minutest variation
of the wind’s force has been traced during the flow of the minutes and seconds,
_ so that in one minute twelve conspicuous (besides many smaller) undulations
of the wind’s direction, and twice as many notable risings and fallings of its pres-
_ sure have been graphically recorded by the pencils of the anemometert.
Thus the machinery is kept in continual and sometimes quick motion, and the
friction which it generates is considerable. The pressure of the wind then is
balanced by two forces, one of which is proportional to itself, the other to the
_ frequency and extent of the fluctuations of strength and direction of the wind.
Each of these fluctuations is a function of the pressure ; they are not necessa-
ily similar functions; but from Osler’s experiments in November and De-
-cember 1846, they seem to be proportionate to one another.
_ It is of importance to the theory of this instrument to obtain a correct ex-
pression for these functions, since if they determine movements whose extent
is simply proportioned to the pressure, the instrument, properly set to an
adapted scale, would register exactly for all winds the continually varying
pressure of the atmosphere down to some certain small pressure, below which
there will be no record. But if the movements in the machinery caused by
these pulsations and fluctuations are in extent not simply proportional to the
-wind’s pressure, but to something else, as for instance to the wind’s velocity,
the forces balancing the wind’s pressure would then be of two kinds, or
P=aP'+6¥P’; a similar form of expression to that for Dr. Whewell’s
anemometer ; and this instrument, like Dr. Whewell’s, would require a com-
‘puted correction, and in small wind-pressures this might become important.
_ Mr. Osler’s latest inventions have so greatly increased the sensibility of
his apparatus to light winds, that it may be seen working freely, when
_the wind-pressure is no more between half a pound per foot and0. This on
tube, of the deviation of a falling body from a vertical line, or the recession of a fine spring.
The simple velocity of wind may be measured by the transference of clouds, the shadows
of clouds, or the movement of light bodies near the surface of the earth.
__ * Since these remarks were written, the Association has received from the Rev. Dr.
Robinson a notice of the construction of an anemometer with a different mechanism, which
appears to satisfy the much-desired object of a direct registration of the wind’s velocity.
_ ¥ Report of the Philosophical Society of Birmingham. -
344 : REPORT—1846.
Lind’s anemometer corresponds to the space from 0:0 to 0°10 inch, and to a
velocity of from 0 to 15 feet per second, that is to say, 0 to 10 miles per
hour*,
Except the instrument be very carefully constructed, this degree of accu-
racy is unattainable, and pressures less than 1b. per foot, and velocities of
several miles per hour, may not be recorded at all. One of the most inter-
esting of the powers connected with the use of this instrument has been
already noticed,—the power of studying the momentary phases of air-move-
ment at the observatory. This is peculiar to the principle of Mr. Osler’s
invention ; another result of great importance has been derived from the study
of its tracings. The force of the wind for every hour of the day and night
has been determined not only for the whole air-movement, but for each direc-
tion of wind, and in each season of the year. Mr. Osler’s conclusions on
this subject, supported by Harris, Brewster and Sabine, go directly to deter-
mine a law of the wind’s daily pressure and to connect it with the progress
of diurnal heat. In fact the curves of daily wind-force and of daily mean
temperature are almost identical, as may be seen in Col. Sabine’s Observations
on the Meteorology of Toronto.
The same registration gives data for investigating what may be called
curves of storm pressure, the law according to which wind-pressure rises to
a maximum and sinks to a minimum, a subject of great interest and import-
ance. From some data which may be found in Mr. Osler’s Report, in the
volume of the Association for 1840, I have obtained the following Table of
pressures during a strong wind of 96 hours’ duration.
* Tt may be useful to give here Smeaton’s Table of Wind Velocity in relation to Pressure
in Ibs. (Phil. Trans. 1759.)
Velocity of Wind. Pressure on
Ta VE ACI comes | hance omg
} . avolr- .
— bet pe ae Se-| ™ pats
1 1:47 005 Hardly perceptible.
2 2°93 020 Taat tibl
3 4-40 044 ust perceptible.
: 0 mee } Gentle pleasant wind.
10 14°67 *492 .
15 22-00 1107 | Pleasant brisk gale.
20 29°34 1:968 a as
25 36°67 3-075 a
30 44:01 4:429 3
35 51°34 6-027 } Bigh wind.
40 58°68 7°873 ;
45 66-01 9-963 } Very high.
50 73°35 12:300 Storm or tempest.
60 88-02 17°715 Great storm.
80 117°36 31°490 Hurricane.
100 146°70 49-200 Destructive hurricane.
913°6 1340* | One atmosph.
Vh atmosphere in feet x 83, = feet per second,
ON ANEMOMETRY. 345
4 Table of Mean and Minimum and Maximum Wind-pressures during 96
hours.
. Maximum.| Minimum. Mean.
First twelve hours ...........+ 25 0°5 1°5 lb.
Second twelve hours ......... 2:0 1:0 1:5416+
Third twelve hours ........- 3°5 20 2°5
Fourth twelve hours ......... 4°5 3:0 3°5416-+-
Fifth twelve hours........... | 45 25 3°29164
Sixth twelve hours ......... 25 2:0 2°125
Seventh twelve hours ...... 2:0 1:0 1:54
Eighth twelve hours ......... 2:0 05 1:0
The regularity of the results is conspicuous when represented by curves.
_ The central ordinate of pressure is seen to occur two hours before the middle
hour of time. It occurs in a lull of the wind.
It is much to be wished that the numerous observations which have been
made with Osler’s anemometer under the direction of the Association, should
_ be reduced and tabulated so as to determine from them the annual air-move-
_ ments over the place of observation, for comparison with the result given by
Mr. Harris at Plymouth. The registers for Inverness, Edinburgh, Dublin, Bir-
- mingham, Greenwich and Plymouth, thus brought together, would afford a valu-
able basis for reasoning on the leading vicissitudes of British climate. This will
probably be included in the reductions on which Mr. Harris is now engaged.
It is neither an obvious nor an easy thing to obtain correctly the mean
velocity of air-movement, or the total horizontal transference of the air in a
given period, from the register of wind-pressure. The momentary velocity
‘is a constant function (the square root) of the momentary pressure ; but the
‘mean velocity is not a constant function of the mean pressure; the total air-
“movement is not a constant function of the sum of the pressures. The larger
the range of these pressures, the more variable is the relation of the mean
velocity and the mean pressure ; the duration of the several values of pres-
‘sure influences the calculation of the total air-movement, so that to obtain it
even approximately from a register of momentary pressures a great number
of these must be separately valued and reduced to velocity, and this is a great
arithmetical labour. It might be diminished if we could assume as sufficiently
known, the Jaw of the variation of the pressure, from 0 to the maximum, and
calculate corrections in conformity with the successive swellings and sub-
sidings of the wind; but this would still leave the result unsatisfactory.
ressure in ~ Velocity in
8. per foot miles per
iquare. hour.
meee > ~~~ ~~ ~~~ ~~ ~~ | - - - - - - - ~~ +--+ ~~ ~~~ ~~ - + --) - -- i} - - - - o - -
Mee
ETE:
| nt
Il ili y a Mu a
- aaa WE SES
_ A mechanical process may be substituted with evident advantage. If on
1846. P =
$ lhour }
BSE)
346 REPORT—1846.
the register paper now ruled for a scale of momentary pressure, we rule
another scale, that of momentary velocity, or copy the register on a paper
prepared with such a scale, the ordinates of velocity may be measured off
with nearly as much accuracy as those of pressure, and the mean velocity
and total air-movement be approximately obtained with great facility. It is
obvious that the paper in Mr. Osler’s apparatus may be ruled, as in the speci-
men, p. 345, both for velocity and pressure, with very little additional expense.
The pressure lines may be continuous, the velocity lines dotted. Such a
table shows how imperfectly the registration of wind-pressure to one pound,
or even one-tenth of a pound per square foot, satisfies the question of the
velocity of the wind. In many cases winds of several miles an hour have been
left entirely unnoticed.
Lind’s Anemometer.—In Lind’s anemometer, the pressure of wind is ba-
lanced by the weight of a column of water, + the force due to the friction of
its movement. Owing to the facility of liquid movements, this instrument, if
made with a siphon of large diameter, is very quick in its indications, and
prettily exhibits what Mr. Osler’s pencils record, the continual fluctuations
of the wind. Pressures which move the water to a difference of level of less
than one-twentieth of an inch, can scarcely be noted accurately, but may he
estimated to one-fortieth or one-fiftieth. ‘This gives as the limit of wind-ve-
locity really measurable five or seven miles an hour.
Lind’s anemometer may be rendered self-registering, but not without
some sacrifice of its quickness and accuracy *. -
It is possible to arrange apparatus which shall allow of the flowing of a
liquid under the pressure of the atmosphere with the velocity due to that
ressure ; it is also possible so to regulate the direction of this flowing that the
direction shall be known of the wind to which the efflux is due; and in other
ways the apparatus may be varied; but it does not appear that by these pro-
cesses any real advantage can be gained over the instruments of Whewell
and Osler, when these are properly attended to. I proceed therefore to an-
other view of the subject.
Molecular Effects of the Movement of the Atmosphere.
The class of phenomena to which attention is now requested depends on
the molecular condition of the air, and on its rate of movement; if it can
* Table for Lind’s Anemometer.
Difference The Vel. in
feelin | renee, | mals Pet
0°25 13 18-0
0°5 2°6 25°6
1:0 iy 36:0
20 10°4 50°8
3:0 15°6 62°0
4:0 20°8 76:0
50 26:0 80°4
60 ald 88:0
7:0 36°5 95°2
8:0 41:7 101°6
9:0 469 108°0
10°0 52:1 113°6
11:0 57°3 119-2
12:0 62°5 124°0
ON ANEMOMETRY. 347
be made the basis of wind-registration, there will be no mechanism required
_ for recording the measures of air-movement or pressure, and the scale of re-
_ sults will increase in accuracy as the wind-force grows less, and may be in this
_ direction more and more trusted as we approach to zero; a circumstance which
would confer upon this mode of anemometry a peculiar value, and render it
_ almost a necessary complement to the mechanical processes now in use, for
_ these take but little notice of very light winds, which yet it is of much im-
portance to record.
One of these joint effects of the molecular constitution of the air, com-
bined with its rate of movement, is seen in the rapidity with which objects
exposed to wind acquire the temperature of the atmosphere.
If a thermometer whose temperature differs from that of the atmosphere
_ by m degrees be exposed in the open air, it instantly begins to undergo
change of temperature, and loses or gains heat continually until it has be-
come sensibly of the same temperature as the surrounding medium. This
_ effect, a mixed result of radiation and conduction of heat, is in the open air
very nearly in simple proportion to m; but in closed vessels, where conduc-
tion is impeded and radiation influential, the changing temperature of the
surrounding bodies complicates the experiment, and the wet thermometer
- does not in this case lose or gain heat in the same simple proportion to m.
Exposure of the thermometer to a current of wind accelerates the process
by which its temperature is made sensibly equal to that of the surrounding
medium, and thus by careful experiments the momentary velocity of the
current may be estimated, as Sir John Leslie has proposed*.
_ If we maintain a continual moisture on the bulb of the thermometer, a
new element of change of temperature is introduced, the force of vaporiza-
_ tion, the effect of which is finally to reduce the thermometer to the tempera-
_ ture of evaporation, where it remains.
_ If we commence the experiment with the temperature of the wet bulb
raised by the quantity m above that of the surrounding atmosphere (¢), it will
_ sink under the operation of two forces, the cooling power of air, proportioned
to m, and the force of vaporization. (The movement of the air is not now
considered.) By the swm of these forces it approximates to ¢, at which point
_m being =0, the cooling power of the air ceases. By the force of vaporiza-
tion it is depressed below this point to ¢’, but between ¢ and @' the air exerts
a heating power proportioned to m. The rate of cooling in air of a wet-bulb
thermometer is thus found to be complicated with two quite distinct functions,
at every point but one, viz. at the temperature ¢ of the atmosphere; at this
‘point it depends solely on the force of vaporization, modified by the move-
‘ment of the air. If then we perform a series of experiments on the rate of
cooling of a wet-bulb thermometer exposed in the open air, from ¢+4° to
t—+°, under the influence of winds of very unequal velocity, and under the
influences of very unequal degrees of dampness in the air, we shall be able
to distinguish the effects of these influences, and assign to each its proper
functional expression, But if one of these can be determined theoretically,
fewer experiments will be required. It appears that the cooling influence of
evaporation at different temperatures and in different hygrometrical states of
the atmosphere can be thus determined.
The rate of evaporation of water in the atmosphere depends upon the force
of aqueous vapour at that temperature, diminished by the force of the aqueous
vapour actually present in the atmosphere. Thus if f’ represent the force of
vapour at the temperature of evaporation, and f" the force of vapour at the
temperature of the dew-point, f’—/" is the unbalanced and active force
* Professor Forbes in Reports of the British Association for 1832.
2a2
348 REPORT—1846,
which determines the rate of evaporation into the open air. Now by Dr.
Apjohn’s researches f!—f" is exactly proportional to e x where d is the
difference in,degrees between the temperature of the air and the tempera-
ture of evaporation, and / the barometric pressure. Water undergoing eva-
poration takes up for each unit of weight a certain measure of heat from the
substances in contact ; its cooling effect on them is therefore proportioned to
the quantity of water evaporated in a given time, which again is proportional
piles ‘ hi enh
to the force f'—f", that is, to a * 30°
A convenient mode of experiment to obtain separately the cooling power
of evaporation from that of air currents and radiation, is to note the times of
cooling of one thermometer first dry and then wet, other circumstances being
similar, as in the following experiment, made in the calm air of a large room
(air 55°, evaporation 4:7°8, dew-point 38°6).
Temp. of Time of cooling 5°
‘Thermometer, in seconds,
dry. wet
105 0 0
100 45 18
95 52 21
90 60 23
85 70 29
80 85 36
75 102 42
70 125 54
65 168 70
60 257 93
DD) oy rith : nebees ve 137
50 Gaunehier 253
The reciprocals of these times (=) correspond to the cooling powers ex-
erted on the two instruments and appear in the following table (column A
and B). The difference between them obviously corresponds to the cooling
power of evaporation exerted on the wet bulb (column C). Column D con-
tains the numerical values of the forces of evaporation due to the successive
temperatures of the bulb in the existing state of the air; and column E a
series of numbers proportioned to these, and representing the successive
cooling powers as they ought to be found experimentally if the theory
already advanced be true. F shows the difference between theory and
experiment.
Mean Temp. A. B. Cc. D. E. F,
wet.
1025 | 293 | 555 | 333 | 1-758 | 352 | 419
975 | 192 | 476 | 284 | 1-458 | 292 | +8
925 | 166 | 435 | 269 | 1-208 | 242 | —28
875 | 143 | 344 | 201 | 1014 | 203 | +2
s25 | 117 | 279 | 162 | -a31 | 166 | +4
775 98 | 237 | 139 | -673 | 135 | — 4
70°5 80 | 185 | 105 | +535 | 107 | +2
67°5 59 «| «(143 84 | -418 | ‘84 0
62-5 38 | 107 69 | -316 | 63 | —6
57°5 20 73 53 | 229 | 46 | —7
50.5 eo ed: Aiwidy A SPN 155 | 31
arp \eenieds Sen eee. 091 18
LAD ERE BR! ASL Wet DN 000 0
ON ANEMOMETRY. 349
_ The truth of the theory may therefore be regarded as established, the
small differences being quite unimportant.
On regarding attentively the columns A, B, it will be seen that the pro-
gression of each is nearly similar, from which it follows that C, their differ-
ence—representing their cooling power of evaporation—contains a series of
numbers nearly proportioned to B. Ranging these columns side by side, and
reducing to the same mean values, we have
B. Cc. E.
83 84. | 82
62 69 61
43 53 45
From which it follows, that for temperatures of the wet bulb above
_ that of the atmosphere, we may disregard the correction in column A, and
take the whole cooling effect of air and vapour, as proportioned to the va-
porizing force. The problem is thus simplified for practical use.
To judge if the same rule applies when the temperature of the wet bulb is
below that of the atmosphere, the following sets of experiments were made
in the open air, with variable differences between the temperature of the air
and that of the wet bulb (air 75°, evap. 63°):—
Temperature of I. Il. Ill. IV.
air above that | Thermometer | Thermometer | Thermometer {Mean of observed)
of wet bulb. at rest. swung slowly. | swung faster. times.
10” 17” 13” 12” 14:0”
9 18 13 11 14:0
8 19 14 15 16:0
7 20 20 16 18°6
6 26 24 17 22:3
b) 30 26 24 26°6
The numbers in columns I. II. IIL. TV. represent the seconds of time in cooling 1° of the wet
__ thermometer.
With the mean of the times we may compare a series of numbers propor-
‘tioned to the vaporizing force due to the temperatures, in the given condi-
tion of air, as under :— .
Tempera f Mean of
air asore tit observed Cepigied
of wet bulb. times.
10 14:0 13°0
9). 14:0 14°4
8 16:0 16°3
7 18°6 18°6
6 22:3 21°6
5
26°6 ° 26°1
_ From which it appears that the rate of cooling of the wet bulb is still
nearly proportional to the force of vaporization, until the temperature of the
wet bulb deviates much from that of the atmosphere.
350 REPORT—1846.
For determining the influence of the rate of air-movement on the rate of
cooling of the wet bulb, several processes have been employed, both in the
open air and in the house.
1. In the first place, choosing a day when the air was considered nearly
calm, (%.e. moving so gently that only leaves with very flexible petioles were
swayed by it,) the wet bulb was first suspended at res¢ in this gentle current
(A); secondly, it was carried across it ( B) at the rate of 2°75 miles an hour;
thirdly, it was swung across it at the rate of 6°18 miles an hour (C). The
effects are recorded in the table below.
Experiment of 22nd Aug. 1846. Temperature of air 75°, of evaporation 63° (€d=12).
. B. Cc.
Time of cooling 1° ...... 16° 12: 9°
Reciprocals of these numbers, which represent the cooling powers of the air
in the several conditions, appear below :—
A. B. Cc.
625 833 TLE
and are obviously not in simple proportion to the velocity of the air-move-
ment in the several cases. If we suppose the so-called ‘calm’ air to move
two miles an hour (which the movement of smoke at the time seemed to in-
dicate), the velocities, obtained by calculating the diagonals of the air-move-
ments combined with the thermometer-movements, would be as under :—
A. B. Cc.
2:00 3°40 6:48,
and their square roots, viz.—
1-41 184 2:55
approach nearly to the ratio of the cooling powers.
2. Experiments of this kind however being unsusceptible of much preci-
sion, recourse was had to railway movement in a ‘calm’ day. Temperature
of air 70°, of evaporation 64° (d=6). Time of cooling 1°, at 3 inches from
the carriage window, 14''; at 18 inches, 10"; at 24 inches, 9”.
Again, on another occasion, temperature of air 69°5, of evaporation 64°
(d=5'5). Time of cooling 1°, at 20 inches distance from the window, 10".
In each of these cases the real velocity of the train was believed to be
about 36 miles an hour.
These experiments are sufficiently in accordance with those already dis-
cussed to allow of our applying the formula a = VV toall; where T is
the observed time of cooling 1° and C a constant peculiar to the instrument.
By taking C = 300, and employing this value for the several experiments,
the estimated and calculated results appear thus :-—
ae gC velocity | Calculated velocity
in miles. in miles,
Calm air! deehetecectstee 2-00 2-44
Thermometer carried ... 3°40 431
Thermometer swung ... 6:48 771
Railway movement...... 36°00 30°86
Railway movement...... 36:00 29°75
As all these experiments are complicated with the uncertain and variable
influence of what is called ‘calm’ air, their accordance with one general for-
mula appears quite as great as could be expected. The drag of air, which
the unequal rates of cooling at different distances from the carriage indicate,
ON THE CRYSTALLINE SLAGS. 351
-may perhaps not be wholly eliminated at even 20 or 24 inches distance.
Perhaps no better mode of experiment on this peculiar transportation of the
_ atmosphere by railway trains could be devised than the trial of its cooling
_ power. In the first of the above experiments the air-displacement appeared
to be about 13 miles an hour at 3 inches from the carriage ; about 24 miles
_ at 18 inches, and 30 miles at 24 inches.
The result now arrived at must, however, be regarded as only a first ap-
proximation, and requires to be tested and corrected by more rigorous pro-
cesses. For this purpose the cooling of the wet bulb has been observed
when carried round by a lathe movement, and when subject to the vibrations
of a pendulum. The results are yet incomplete, but may be offered for the
consideration of the Association on a future occasion.
Report on the Crystalline Slags. By Joun Percy, M.D.
_ We have pleasure in now presenting to the Association the results of our
investigation of the crystalline slags. It is obvious that such an investiga-
_ tion must be limited by the opportunity of obtaining specimens, which re-
quire to be diligently sought for at the various metallurgical works; and
that, consequently, it is impossible for us at present to offer anything like a
complete report upon this interesting subject. We have however been for-
tunate in procuring already an extensive series of beautifully crystallized
slags, several of which we have not yet had time to examine. We are espe-
cially indebted to Mr. John Dawes, of West Bromwich, and to Messrs.
Blackwell and Twamley, of Dudley, for many valuable contributions. In
_ the present Report we have confined our attention to the slags produced in
_ the smelting and manufacture of iron. We shall adopt the following ar-
rangement :—
1. The crystallographic and mineralogical description by Professor Miller.
2. The analysis*.
3. Special remarks.
The first series is composed of six specimens. Nos. 1 and 2 were ob-
tained from hot-blast furnaces in the vicinity of Dudley ; Nos. 3 and 4 from
_ Messrs. Blackwell's hot-blast furnaces at Russell’s-hall, near Dudley; No. 4
_ from one of Mr. Philip Williams’s cold-blast furnaces, at the Wednesbury
_ Oak Works, near Tipton; No.6 was brought by Mr. Samuel Blackwell from
a hot-blast furnace named La Providence, at Marchienne, Charleroi, Bel-
‘gium. No. 3 was produced when the furnace was considered to be work-
ing unsatisfactorily, from some interruption to the free course of the blast.
The crystals of the slag No. 3 are square prisms, terminated by planes
perpendicular to the axis of the prism. Many of the prisms have their
angles truncated by planes, making equal angles with the adjacent faces of
the prism.
Al ., Specific gravity of slag |
Hardness = 6. At 19°1 specific gravity of water =2°9242.
_ _ The crystals of slag No. 4 are square prisms, having the angles truncated
like No. 3.
Hardness = 5°5. At 18°-2 C Ue? Beno OF SIRS eat) oF sins,
specific gravity of water
* Tam happy to state that I have had the assistance of my friend Mr. David Forbes,
_ brother of Professor Edward Forbes. To the analyses made by myself I shall append my
_ Own initials, and to those made by Mr. Forbes the initials of that gentleman.
=2'9187.
352 REPORT—1846.
The crystals of No. 5 are square prisms, having the angles truncated like
No. 3. Hardness = 5°7.
No. 1. Square prisms like No. 3.
specific gravity of slag
— 9, —O-
Hardness = 6. At 19°2 C specific gravity of water =2°9052.
No. 2. Square prisms like No. 3.
f :
Hardness = 6. At19°2C ~~ bel alt =2°9152.
specific gravity of water
Analysis——The slags composing the first series were found to contain
silica, alumina, lime, magnesia, protoxides of manganese and iron, potass in
small quantity, and sulphur as sulphuret. Phosphoric acid was also found
in some of them. They are readily decomposed by digestion with dilute
hydrochloric acid. The following method of analysis was adopted.
Method of Analysis —1. The fine powder obtained by trituration in an
agate mortar was digested with dilute hydrochloric acid. The whole was
evaporated to dryness. The dry mass was treated with hydrochloric acid,
and left fora few hours. Nitric acid was added sometimes before and some-
times after evaporation to peroxidize the iron. The silica separated by fil-
tration was washed with boiling water until nitrate of silver ceased to pro-
duce the slightest turbidity, dried, incinerated at a bright red heat, cooled
under a glass shade containing sulphuric acid, and then weighed.
2. To the acid solution was added a slight excess of ammonia. Filtration
was conducted as rapidly as possible, the funnel being covered with a glass
plate.
3. The precipitate (2) was boiled with potass. The solution was treated
with an excess of hydrochloric acid, and the alumina then precipitated by
carbonate of ammonia.
4, The insoluble residue (3) was dissolved in hydrochloric acid, and the
iron was precipitated by succinate of soda or ammonia with the usual pre-
cautions.
5. The lime was precipitated by oxalate of ammonia from solution (2),
after treatment by ammonia. The precipitate, which consisted of oxalate of
lime mixed with oxalate of manganese, was incinerated at a bright red heat,
and then digested with dilute acetic acid, which dissolved the lime and left
the brown oxide of manganese. A slight excess of sulphuric acid was added
to the solution of acetate of lime; the whole was evaporated to dryness, and
heated to redness; from the sulphate of lime thus obtained the lime was
calculated.
6. The solution (4), after separation of the iron, was added to solution (5)
after separation of the lime. The manganese was precipitated by hydrosul-
phate of ammonia in a close vessel, and in every instance at least twelve
hours were allowed for precipitation. The sulphuret of manganese was dis-
solved in hydrochloric acid, and precipitated as carbonate by carbonate of
potass. The carbonate of manganese was incinerated at a bright red heat
for a considerable time. The oxide of manganese thus produced was esti-
mated as MnO-+ Mn? O3.
7. The solution (6), after precipitation of the manganese, was digested
with excess of hydrochloric acid until the sulphur separated by decomposi-
tion of the excess of hydrosulphate of ammonia had completely separated.
The magnesia was precipitated by phosphate of soda and excess of ammonia.
Generally twenty-four or forty hours were allowed for complete precipita-
tion. The precipitate was washed with ammonia-water until no sensible
residue was left by evaporation on a plate of glass. When dry, generally
as much of the magnesian salt as possible was detached from the filter, and
ON THE CRYSTALLINE SLAGS. 353
slowly heated to redness; the filter, with what adhered to it, was then intro-
duced into the crucible and incinerated as usual. ;
8. To determine the potass, the slag was digested as usual in hydrochloric
acid, the iron was peroxidized by nitric acid, and the solution was then
treated with excess of carbonate of ammonia. The filtrate was evaporated
to dryness, and the ammoniacal salts were expelled by heat. The residue
was treated with boiling water, and the solution filtered from the brownish
residue. The filtrate was evaporated to dryness after the addition of excess
of sulphuric acid. The residue was dissolved in water, acetate of baryta
was added in excess, the sulphate of baryta was separated'with the usual
precautions by filtration; the filtrate was evaporated to dryness, and after-
wards heated to redness. The solution contained the potass as carbonate;
hydrochloric acid was added, and from the amount of chloride obtained by
evaporation and heating to low redness, the potass was estimated. Berze-
lius’s method of separating potass from magnesia by oxide of mercury was
also occasionally resorted to.
9. The sulphur was determined either by oxidizing with strong nitrous
acid, or by fusing with nitrate of potass and a mixture of carbonate of potass
and soda. Chloride of barium was added to the acid solution. From the
_ sulphate of baryta produced the sulphur was estimated.
_ 10. The method resorted to for the detection of phosphoric acid will be
described in each case.
The actual quantities of the substances found by analysis will always be
given, in order that the calculations may be corrected in the event of any
errors in the received atomic weights being corrected by future observers. .
The calculations have been made from the tables in the French translation
of Rose’s work by Peligot (Paris, 1843).
1. Anatysis. By J. P.
1. Weight of slag employed 27°57 grains, after having been gently heated
over a spirit-Jamp.
2. Silica 10°49.
8. Alumina 3°89.
4. Sulphate of lime 24°35.
5. Phosphate of magnesia (2MgO, P? O*) 5°74.
6. Oxide of manganese (MnO + MnO? 03) 0:12.
7. Sesquioxide of iron 0°39.
8. Potass. Weight of slag employed 50°47 grains. Chloride of potas-
sium 1°48. A minute quantity of precipitate was produced by the addition
of antimoniate of potass to the solution. The quantity of chlorine was de-
termined by nitrate of silver. The chloride of silver obtained weighed 2°814
grains, which correspond to 0°694 of chlorine. 1°48 of chloride of potassium
by the tables, contains 0°702 of chlorine. Difference 0°702—0°694=0°008.
The chloride may therefore be estimated as nearly pure chloride of potassium.
__ 9. Sulphur. Hydrosulphuric acid was liberated by the action of hydro-
ehloric acid. Weight of slag 22°68. The nitrous acid process was em-
ployed. The sulphate of baryta weighed 0°59. It was ascertained that the
slag did not contain sulphuric acid. The sulphur is admitted to exist as
sulphuret of calcium.
10. Phosphoric acid was not detected. Weight of the slag employed
51°38 grains. It was digested with hydrochloric acid, and the silica sepa-
ted as usual. The precipitate obtained by the addition of ammonia in
light excess was dissolved by hydrochloric acid; tartaric acid was added,
354 REPORT—1846.
and then chloride of magnesium and excess of ammonia; no trace of the
characteristic precipitate of phosphate of magnesia and ammonia appeared
after several days.
Analysis tabulated. Oxygen.
Gilson. a!s2'.'. - Can. teens SBMS wleNiiee. vest 19°76
Alumina ........ i. ake oo ee ne a 6°59
RAMOS i iesie', M6 ooees & SEO vices’ 1008
Magnesia.......... Cece PGLiwwa 4 29% (
Protoxide of manganese... 040.... 0°09 oe
Protoxide of iron........ LAT cease O29
Potassiii honors om POSS aih s covese OD]
Sulphuret of calcium .... 0°82
Error of loss.......... ie OLD
100°00
2. ANALysIs. By J. P.
1. Weight of slag employed 25°41 grains, after having been gently heated
over a spirit-lamp; the odour of free sulphur was distinctly remarked.
2. Silica 9°85
- Alumina 3°68.
. Sulphate of lime 22:04.
. Phosphate of magnesia 4°76.
. Oxide of manganese 0°07.
. Sesquioxide of iron 0°34.
- Potass. Weight of slag employed 46°93. Chloride of potassium 0:82.
By treatment with nitrate of silver 1:51 grain of chloride of silver was ob-
tained, which corresponds to 0°372 of chlorine. 0°82 of chloride of potas-
sium contains 0°389 of chlorine.
9. Sulphur. Hydrosulphurie acid was evolved by the action of hydro-
chloric acid. Weight of slag 20:06. The nitrous acid process was em-
ployed. The sulphate of baryta weighed 0°63.
10. Phosphoric acid was not sought for.
COnF OH TS Oo
Analysis tabulated. & Oxygen.
SICA erect teeatis mee te ae 38°76" .is. einielcsinele }) COne
Alumina ..... stole als 1 LAB i cc dtrentew ee, 4: GNTbe
Laimesc. oon. ae Pig tea MSO GOL mate.) O02
WTRETNCRIA! o's. 'o ntoiatniaha Bits 684 c.06 2°56 12°89
Protoxide of manganese... 0°23 .... 0°05
Protoxide of iron...... oes DIRS Fildes O87
POtass 'x> viddebdes » = DEES Si’ <'s oh esl olde’ 8 0:19
Sulphuret of calcium .... 0°98
Error of loss,......... «» =O°74
100°00
3. Anatysis. By J. P.
1. Weight of the slag employed 25°27, after having been gently heated
over a spirit-lamp.
2. Silica 9°51.
3. Alumina 3:23.
4, Sulphate of lime 20°68.
5. Phosphate of magnesia 4°58.
6. Oxide of manganese 0°72.
7. Sesquioxide of iron 1°18.
4
ON THE ORYSTALLINE SLAGS. 355
8. Potass. Weight of slag 50°47. Chloride of potassium 1°53. By the
addition of bichloride of platinum to the solution a copious yellow granular
precipitate was produced. Carbazotie acid also occasioned a copious pre-
cipitate. Antimoniate of potass occasioned a minute quantity of precipitate.
9. Sulphur. Hydrosulphuric acid was evolved by the action of hydro-
chloric acid, and the odour of free sulphur was also observed on the appli-
_¢ation of heat. Weight of slag, after gently heating over a spirit-lamp, 20°13.
_ The nitrous acid process was employed. Sulphate of baryta 0°58.
Analysis tabulated. Oxygen.
BIMOB cress nieirerne cans £688) SCO nev eee seas ee MOD
BYGMING. 0). soe scene dd Hal 1298. s doo
U0 ae er voce S346 20... 9°40
Warmest Yih. 28s scree Sete ¢ | GG4 concn 248 13-46
Protoxide of manganese... 2°64 ...... 0°67
Protoxide of iron........ 3°91 ...... O91
Potiies ides SPR cate eae s - 032
Sulphuret of calcium .... 0°68
Error of loss........%++: 0°34
100-00
4, AnALysts. By D. F.
1. Weight of slag employed 25°38 grains.
2. Silica 9°62.
3. Alumina 3:30.
4, Sulphate of lime 21°43.
5. Phosphate of magnesia 5°09.
6. Oxide of manganese 0°76.
7. Sesquioxide, of iron 0°35.
_ 8. Potass. Weight of slag employed 75°68. The weight of the chloride
was lost after the calculation of the potass.
9. Sulphur. The process by fusion with nitrate of potass and a mixture
of carbonate of potass and soda was adopted. Weight of slag 20°83. Sul-
phate of baryta 2°45.
_ 10. Phosphoric acid was not detected by the process resorted to in No. 1
- (sup. Pp. 353).
Analysis tabulated. Oxygen.
PUMOlr 6 eae .n. sk 6 Rak bh Oe he sales ree er 19°69
AAD ii: ee ef) 0) ra Sakis tra, OO
TGMO. . cig Weck Nad». 2.0 BRA bias oc 8°73
Magiesiat a osc tis ong) TRA, cae os 281 | 19.97
Protoxide of manganese.. 2°79 ...... 0°52
Protoxide of iron........ OB acini an) OF
Protas Fs. . 4s ae ihe Klaha ACD sik wh ace an Hn a, 1), OPE
Sulphuret of calcium .... 3°65 .
Error of loss....... icaee . O44
100-00
5. Anatysis. By D. F.
J. Weight of slag 25°76 grains.
Q. Silica 10°18.
3. Alumina 3°89.
_ 4, Sulphate of lime 21:23.
356 REPORT—1846.
5. Phosphate of magnesia 2°45.
6. Oxide of manganese 0°80. ©
7. Sesquioxide of iron 0°61.
8. Potass. Weight of slag 27°52. Chloride of potassium 0°46.
9. Sulphur. The fusion process was adopted. Weight of slag 22°63.
Sulphate of baryta 1°54.
10. Phosphoric acid was sought for by the process previously mentioned,
but not a trace was detected even after standing a week.
Analysis tabulated. Oxygen.
LLIGH Ye ele ras ve tebeeeholohars Sey Oy Mabie eidaloncdeidvssis 20°50
Alumina atiete VORL pitied 7:06
Eames F.O042 cn: fon Eee S2BE) scans tie 9°60
DMienegigie 22... 2 aie ince steele Pao cuenee 135 | 10.05
Protoxide of manganese... 2°89 ...... 0°64 f
Protoxide of iron........ 2:02 ...... O46
bthss 3S ee <4 2.61206) 5. Ueeiws tai OT
Sulphuret of calcium .... 2°15
Error of lone oni cs, Sy 1:24
100°00
6. Anatysis. By J. P.
1. Weight of slag employed 19°78 grains, after drying i vacuo over sul-
phuric acid for twenty-four hours.
2. Silica 8°32.
3. Alumina 2°62.
4. Sulphate of lime 15°9.
5. Phosphate of magnesia 0°57.
6. Oxide of manganese 0°48.
7. Sesquioxide of iron 1°09.
8. Potass. Weight of slag, after drying im vacuo during twenty-four
hours over sulphuric acid, 20°44 grains. Chloride of potassium 0°87.
9. Sulphur. Hydrosulphurie acid was evolved by the action of hydro-
chloric acid. Weight of slag 20°01 grains. The fusion process was adopted.
Sulphate of baryta 0°65. 4
10. Phosphoric acid. The alumina and oxide of iron obtained in the pre-
ceding analysis were fused for a considerable time with bisulphate of potass.
The mass was digested with hydrochloric acid; some flocculent matter re-
mained undissolved. To the solution tartaric acid was added, and after-
wards chloride of magnesium and excess of ammonia. Two days afterwards
minute crystalline particles were observed adhering to the glass. On exa- —
mination with a simple microscope, the well-known star-shaped crystals of
phosphate of magnesia and ammonia were immediately recognised. The solu-
tion was allowed to stand several days afterwards. The minute quantity of
crystals was collected on a filter, and washed with cold ammonia-water, until
no sensible residue was left by evaporation on a plate of glass. After in-
cineration the phosphate of magnesia weighed 0°06. The phosphoric acid is
admitted to exist in combination with the alumina.
ON THE (CRYSTALLINE SLAGS, 357
Analysis tabulated. Oxygen.
ICR Pathe lore. Gi Sa ROG) eiev ee ore e's veee 20°81
AlUmEM Ay eee aie Saved OOS "sol. oe red 6:05
Dene wae ello PLE 32°53 .... 6. O14
Gy le ar 1:06 ...... O41 U iy4¢
Protoxide of manganese... 2°26 ...... 0°51
Protoxide of iron ...... 4°94 ...... 1°12
POtaRsii ye see te eee ay DOR oe oewee ee §=O'46
Phosphoric acid .. 0°19 ‘
Alumina ........ O12 O31"
Sulphur ........ O45 Y
Calcium ........ age 2?
Error of loss .......... 0:19
100-00
From an examination of the preceding analyses, it is evident that the fol-
lowing formula is the correct expression of the composition of this series: —
Al?03, Si0’+2 (3(Ca, Mg, Mn, Fe) 0, SiO®).
The formula differs from that of Vesuvian, in containing two equivalents of
the silicate of lime series instead of one. Ivanov however has described a
mineral from Slatoust, identical in composition with the preceding slags
_ (Rammelsberg, Part 2. p. 258, and first supplement, p. 151); but Professor
_H. Rosé informs us that the analysis of Ivanov has been clearly proved
erroneous. Berthier has given the results of several analyses of slags
from blast furnaces of nearly the same composition, but has incorrectly de-.
duced the formula “(Ca, Mg, M, f)S+ AS,” which is that of Vesuvian.
He has also omitted in his analysis of a slag from Dudley, protoxide of man-
_ganese, potass and sulphur, which were found in all the preceding analyses
_ of slags from the same locality.
7. ANALysiIs. By J. P.
__ This slag was obtained from one of Mr. Dawes’s hot-blast furnaces at
Oldbury. It was found mixed with coke and other matters; it contains
globules of iron, and sulphur may be readily observed deposited here and
_ there upon the crystalline plates.
__ The crystals are thin square plates, the lateral faces of which are perpen-
dicular to each other, and to the terminal faces. They appear to belong to
the pyramidal system. They are white, and when very thin transparent.
# Hardness =5°7.
7. ANALysis a. By J. P.
__ 1. Weight of slag, after heating carefully over a spirit-lamp to expel the
free sulphur 20°19.
2. Silica 5°71.
_, 8. Alumina 4°89.
_ 4. Sulphate of lime 20°97.
_ 5. Phosphate of magnesia 1°64.
_ 6. Oxide of manganese 0°016.
_ 7. Sesquioxide of iron 0:06.
__ 8. Potass. After heating to expel the free sulphur, weight of slag 14°74.
‘Chloride of potassium 0:15. The presence of soda in minute quantity was
also clearly detected, as follows :—
a, By heating before the blowpipe a platinum wire, and making a com-
* Estimated as 2Al? 03, 3PO05 (51°44 x 2+55°44 x3).
358 REPORT—1846.
parative experiment with platinum wire alone, a decided yellowness
indieative of soda was observed.
b. By the addition of the solution of antimoniate of potass to a few
drops of the solution on a watch-glass, a minute quantity of preci-
pitate appeared.
9. Sulphur. Hydrosulphuric acid was copiously evolved by the action
of hydrochloric acid. Sulphur existed in three states, free, combined as sul-
phuret, and also as sulphuric acid. The free sulphur was not estimated.
The nitrous acid process was adopted. 14°74 grains, weighed after expul-
sion of the sulphur by heat, furnished of sulphate of baryta 1°71. By a
second determination of sulphur 13°01 grains, heated as before, and treated
with nitrous acid, gave of sulphate of baryta 1°58. By the first total sul-
POU...) WOR eee eww TGA. Gs cee we 1°60 per cent.
Bythe weeontd ai «esses jes 3 22 1°67
Sine ince ucarict qe ae EPR” 1°63
phur, were digested with hydrochloric acid. Evaporation to dryness was
omitted, and the solution was immediately filtered; baryta water was added
to the filtrate. The sulphate of baryta weighed 0:104, This, by tables,
corresponds to 0°37 per cent. of sulphuric acid, and to 0°15 of sulphur.
The whole amount of sulphur is 1°63. Therefore 1°63—0°15=1°48 is the
sulphur combined as sulphuret,.
10. Phosphoric acid was not sought for.
7. Anatysis &. By J. P..
1. Weight of slag, after treating as before, 20°31 grains.
2. Silica 5°76.
8. Alumina 4°93.
An accident occurred in the determination of the lime.
7. Anatysise. By J. P.
1. Weight of slag, after heating as before, 20°23 grains.
2. Sulphate of lime 20°77.
3. Phosphate of magnesia 1°44,
Analysis tabulated.
a.
b. eC Mean Oxygen.
Silica, eee Pts sens QSOS SLO sO teen. s« QBS evn Aone a aieg
AM NAMI NS Weed Se DE OD . QMaOTIRES. 2 ye 4 BAW Se he 11°33
DB Sy i a sie ous 5 ahd geo A390 shah ale 39°96.. 40°12.. 11°27
IBERIA eis oe es we DQ aier 11°18
Protoxide of iron........ PED A k O85
Sulphuret of calcium .... 1°76
Error of loss............ 0°55
100°00
Without attempting to extort from the preceding analytical results a pre-
cise atomic expression, we may state that probably the formula of Hum-
boldtilite, as deduced from the analysis of Von Kobell (Rammelsberg, 2nd
part, p. 308), nearly represents the constitution of this slag. The formula
in question is
3R2Si+ R Si.
_ We introduce Von Kobell’s analysis (Rammelsberg, Ist part, p. 314) :—
Oxygen
Sei Gi dbe sis voile, x .- aed bv. 6 AB OG jniycs)- deny 44>» 21°83
Die | nea Siri ta 31°96 .... 897
BEEN Mul slp cats GLO peice) OO 11°86
Protoxide of iron........ 232 .... 0°53
MA | os ey 120. awd d- aael-, 228
ee ee Peele fh 3 ADS vie adh whi Pibgiae 4 1:09
en oe elena tahictngs,< 0°38 ‘ 0:06
: 10020 | -
‘The per-centage composition calculated from the formula would be,—
rite Lem 52) th 45°37
Alumina.......... 1262
Lime ............ 41°99 99°98
Damour assigns a different formula for Humboldtilite, which he believes
© be identical with Mellilite*; and this formula is precisely that which we
lave given for the first series of blast-furnace slags. For the sake of com-
arison we subjoin Damour’s analyses.
Mellilite. Humboldtilite.
nig Oxygen.
Memied ek. SF eetites wee ss SOO... Ye 21°13
welumina...-....... 6°42 .. 2:99 610 443 .. 2:06 5
Sesquioxide of iron.. 10:17 .. 311 10°88 .. 3:33 f 99
Se 82-47 ., 312 162 81°81. 8921 1,
_Magnesia.......... 6°44 .. 2-50 5°75 .. 222
ra oS ESG Ae eatatet ae Dei caries 0 (6) a Bsa ade 0°06
ae SARA SURO REE 2c. SOE 112
' 98°18 98-35
1846. 2B
362 REPORT—1846.
Berzelius remarks that “in designating by 7 the bases with 1 atom of
oxygen, and by R the bases with 3 atoms of oxygen, the formula 27S+RS
will be obtained, which expresses a somewhat rare kind of composition.”
9 and 10.
The two following specimens were communicated by M. Krantz, the
well-known mineralogist of Berlin. They were labelled, Olsberger Fur-
naces, on the Rhine.
No. 9 contains a drusy cavity with projecting crystals, which are not suf-
ficiently bright for measurement with the reflective goniometer. They
appear to belong to the oblique prismatic system. They have a single end-
face which is not at right angles to the axis of the prism. Hardness = 5,
No. 10 is a mass exhibiting a radiated crystalline structure, the individuals of
which are too small for measurement. Hardness = 5°7.
To one side of each of these specimens are attached minute scales of
graphite.
9. ANALYSIS a. By J. P.
The three following slags not being decomposable by hydrochloric acid,
the method of fusion with a mixture of equal parts of carbonate of potass
and soda* was resorted to.
1. Weight of slag 20°16 after heating over a spirit-lamp and cooling over
SO’. Being extremely hard, it was broken between writing-paper on an iron
plate, further reduced in a steel mortar, and finally triturated in an agate
mortar, and levigated until the whole piece detached was reduced to im-
palpable powder. It was fused with 80 grains of the carbonate of potass-
soda mixture. The fused mass had a blue-green colour.
. Silica 10°74.
. Alumina 1°02.
. Sulphate of lime 14°88.
. Phosphate of magnesia 5°21.
. Oxide of manganese 0°31.
. Sesquioxide of iron 0°23.
. Potass. Weight of slag 50°51 grains. Fused with 200 grains of car-
bonate of baryta and proceeded in the usual way. This alkali was distinctly
recognised by the following tests :—
a. Bichloride of platinum produced the characteristic yellow granular
precipitate.
b. Carbazotic acid, after the lapse of a short time, produced the charac-
teristic crystals of carbazotate of potass.
c. No indication of the presence of soda was furnished by antimoniate
of potass.
A source of error occurring, the weight of the chloride of potassium was not
determined ; however, it is certain that the quantity must have been very
small, less than in any of the preceding analyses.
9. Sulphur existed combined as sulphuret in minute quantity. By the ac-
tion of hydrochloric acid a slight evolution of gas was occasioned, but it had
the odour of hydrogen (from particles of iron detached from the steel mor-
tar ?), obtained by the aetion of an acid on iron; the odour of hydrosulphurie
acid could not be distinctly recognised; yet on suspending for some time a
piece of moistened acetate of lead-paper at the top of a test-tube containing
M~I™MDM-S ov
* Prepared by calcination of pure tartrate of potass and soda.
ON THE CRYSTALLINE SLAGS. 363
some of the powder of the slag and hydrochloric acid, blackening was slowly
produced. No quantitative determination of sulphur was made.
10. Phosphoric acid. The precipitate obtained by ammonia (8 in the
potass examination) was dissolved in hydrochloric acid, tartaric acid was
added, and then excess of ammonia, and finally chloride of magnesium. After
standing many days not a trace of crystalline precipitate could be detected.
9. Anatysis &. By J. P.
1. Weight of slag 20°21 grains. Fused with 100 grains of the carbonate
_ of potass-soda mixture.
2. Silica 10°81.
3. Alumina 1°05.
4. Sulphate of lime 14°97.
5. Phosphate of magnesia 5°26.
6. Sesquioxide of iron 0°20.
Analysis tabulated. a. b. Mean. Oxygen.
|S) CCE Ya A A er 8 BROT Me. | DRAB eben OO AL coin cele cie le
Alumina............ 506 .. 519... Ir) AA ee 2°81
Oy) Ua Se BR Rr 3065 .. 30°78 .. 30°71 .. 8°62
Magnesia’ ..........- aT ts. feo, dint. 9 OG? . selon
Protoxide of manganese 1°41 .. iB AS TA ok 0°31
Protoxide of iron .... 1°02 .. Oso .. O95 .. 0:21
101:06
10. Anatysis. By D. F.
1. Weight of slag 17:54 grains. Fused with 80 grains of the carbonate of
potass-soda mixture. :
2. Silica 9°43.
_ 3. Alumina 0°84.
4, Sulphate of lime 12°43.
5. Phosphate of magnesia 4°70.
6. Oxide of manganese 0-24.
_ 7. Sesquioxide of iron 0°29.
8. Potass. The slag was decomposed by digestion with fluoride of calcium
nd sulphuric acid. Potass was not detected.
Analysis tabulated. Oxygen.
Silica: is DP ad oe e's SRT RG eae 27°93
Adem as ob. 5» 5%, 2 AcE Wiehe s\alate 2:29
Line. 2 sop eae Ws «) o!olalg 29°48 ss eee 8:28
Magnesia: ictas 2.3: O82) ne args) ) O80,
Protoxide of manganese .. 1°30 ...... 0°29
Protoxide of iron........ TAB Oise OBE
100°60
ith the exception of a few small crystals in a drusy cavity in No. 9, the
rystallization of the two preceding slags is confused, so that we could scarcely
ope to deduce from their composition a satisfactory formula. The oxygen
the acid being nearly double that of the bases, the slag is formed of bisili-
and evidently approximates very nearly in composition to some varieties
ugite (pyroxene) containing alumina. Several analyses of augite giving
yout the same per-centage of alumina may be found in the first part of
2B2
364 REPORT—1846.
Rammelsberg’s admirable work previously referred to. The silicate of alu-
mina exists probably as an accidental constituent, and does not enter into
the formula (Vide ‘ Handbuch der Chemie,’ von L. Gmelin, Zweiter Band,
p- 383).
W
This specimen was brought by Mr. Blackwell from the hot-blast furnaces
called L’Espérance, at Seraing, near Liége, in Belgium.
This slag is brown, porous, and confusedly crystalline.
1]. Anatysis. By D. F.
1. In the first analysis an accident happened, and the lime only was de-
termined. Weight of slag 23°63. Fused with the carbonate of potass-soda
mixture. Sulphate of lime 15°04.
2. Weight of slag 17°34.
3. Silica 9°95.
4, Alumina 2°48.
5. Phosphate of magnesia 1°02.
6. Oxide of manganese 0°49.
7. Sesquioxide of iron 0°42.
8. Potass. Weight of slag 30°40. Fused with 120 grains of carbonate of
baryta. Chloride of potassium 0°86.
9. Sulphur was present in very minute quantity.
Analysis tabulated. Oxygen.
Silica; 2 cash sey hs Ga FAA cikh dive 28°97
ARIUS ‘ase {taailae oe ADM est. bora 8 649
WEROIEG ca here ee ah mle ahs a) > 22°22 624
DMB Rneaia. 7/35 ee as ce 210 O81 $09
Protoxide of manganese... 2°52 0°56
Protoxide of iron........ 212 0°48
GEARS yt. naeiota sie See Els, eevee | hats Ral cst 0°30
100°41
As the crystallization was very confused, and as the analytical results do
not point satisfactorily to a formula, we do not attempt to deduce any rational —
expression of the composition of this slag.
12.
This specimen of “ Refinery Cinder” was produced in the Bromford Iron
Works, near Birmingham, and was communicated by one of the proprietors,
our friend Mr, John Dawes. The process of refining, which is not now ex-
tensively practised in Staffordshire, consists in exposing the surface of melted
cast iron to the action of a blast. The products are refined or white iron,
and “ refinery cinder” or slag.
12. AnAtysis. By D. F.
Method of Analysis —25:178 grains were fused with 80 of the carbonate
of potass-soda mixture and 30 of nitrate of potass. The fused mass was de-
composed by hydrochloric acid, and the solution evaporated to dryness. The
dry mass was digested with hydrochloric acid and filtered. The silica on the
filter not being white, it was again fused with 40 grains of the carbonate of
ON THE CRYSTALLINE SLAGS. 365
_ potass-soda mixture and LO of nitrate of potass. The fused mass was digested
as before with hydrochloric acid; but even then the silica did not appear
_ perfectly white, and, accordingly, it was again fused and treated as before,
_ when it was obtained beautifully white. The alumina was determined in the
usual way. The iron and manganese were separated by the succinate plan.
_ On redissolving both the oxides of iron and manganese, a small quantity of
_ silica was left, which was collected and added to that previously obtained.
_ The solution from which the alumina was separated, was precipitated by a
little chloride of barium, and the sulphur determined from the sulphate of
baryta: the excess of chloride of barium was removed from the filtrate by
_ the addition of 20 grains of strong sulphuric acid diluted with 6000 grains
_ of water; a liquid which does not precipitate lime. The lime was deter-
mined, as usual, after separation of some oxide of manganese by acetic acid.
_ The remaining manganese (the greater part having been precipitated with
_ the alumina and iron by ammonia) was thrown down by hydrosulphate of
ammonia. The magnesia was then determined by ammonia and phosphate
of soda.
1. Weight of slag employed 25:18 grains.
2. Silica 5°73.
3. Alumina 1°84.
4, Sulphate of lime 2:07.
5. Phosphate of magnesia 0°49.
6. Oxide of manganese 0°98.
7. Sesquioxide of iron 17:19. The iron must be estimated as protoxide,
as will be evident from the results of the analyses.
8. Sulphate of baryta 0°89.
Analysis tabulated*.
RIGA. eee ale Gs eet OnE So Sas 11°83
Protoxide of iron........ Lo.) Sure Re et 13:95
Protoxide of manganese .. 3°58 ...... 0°70
it gt al Ie ae lela iD aati ino! ite Aa cla 3°41
1 ii ial ed cl cageue We Rae ets ae Ory,
Hs Co 2 a ae ee Lf ee 0°29
21). ee I a ee OD
Error of loss... /......... 0°45
100-00
From the identity in crystalline form of this slag with the one succeeding,
_ we are inclined to regard it as a mixture of silicate of protoxide of iron with
_aconsiderable amount of impurity, represented especially by the alumina.
_ This view would also appear to receive confirmation from an inspection of
_ the slag itself. We need scarcely refer to the numerous instances of well-
formed crystals containing much foreign matter, so that there seems to be
nothing improbable in this view respecting the composition of the crystals of
4h: . .
' this slag, which are certainly not perfectly formed.
13.
q ‘The following beautifully crystallized specimen was presented by Mr.
Dawes. It was found in the flue of a puddling furnace, where it had pro-
bably been exposed to a high temperature for a considerable time.
_* T have no doubt that phosphoric acid and sesquioxide of iron existed in this slag in
small quantity.—J. P.
366 REPORT—1846.
The surface of this slag is covered with bright black crystals, exhibiting
occasionally an iridescent tarnish. The crystals belong to the prismatic
system. The normals to the faces make the following angles with each
other :—n 2! = 49° 24', nt = 65° 18’, kk! = 98° 24', ht = 40° 48’. They
cleave readily parallel to a plane p, which is perpendicular to the faces
t,n,n', and makes equal angles with the faces f, h'.
Hardness = 6. At 186 C. specific gravity of slag
specific gravity of water
fT
= 4°0805.
om
mi Ra Tene. ts
pe
Ny a ee
13. AnaLysis. By J. P.
This slag was found to contain silica, protoxide and sesquioxide of iron,
protoxide of manganese, alumina, lime, magnesia, sulphur as sulphuret, and
phosphoric acid. It was decomposed by long digestion with dilute hydro-
chloric acid. The silica, however, obtained by this means was more or less
gray; and in order to obtain it perfectly white, it was fused with the car-
bonate of potass-soda mixture, and the fused mass, which had a bluish-green
colour, was decomposed with hydrochloric acid. The solution was treated
with nitric acid to peroxidize the iron ; ammonia was then added in slight
excess, and the analysis continued in the manner formerly described. The
proportion of the two oxides of iron, the phosphoric acid and the sulphur,
were determined by separate analyses, as will be described in the sequel.
1. Weight of slag 20°20 grains, after drying in vacuo over SO8 during 48
hours.
2. Silica 5°98. Repeated by Mr. Forbes; 20:14 grains of slag gave 5:99.
3. Total amount of iron obtained as Fe? O3, 14°63. The oxide of iron
contained a minute quantity of P?O°, which was not removed by boiling
with potass; for on redissolving the iron in hydrochloric acid, adding excess
of tartaric acid and afterwards excess of ammonia, and lastly, chloride of
magnesium, a few minute crystalline grains appeared after standing some days.
However, this error of excess must be very small.
4. Oxide of manganese 0°256.
5, Alumina 0°53. As the alumina was precipitated from its solution in
presence of P? O°, and as only a minute quantity of this acid was retained by
the iron, the whole amount of P? O05 may be subtracted from the alumina.
The total P? O° obtained (vide sequel) was 1°34 per cent.
20:2 (slag) : 0°53 :: 100 : 2°62.
2°62 — 1:34 = 1:28 alumina.
Taking the phosphate alumina as 4Al*O%, 3P205 (see Rappert Annuel,
ON THE CRYSTALLINE SLAGS. 367
Berzelius, 7#™¢ année, p. 127, and Graham’s Chemistry), 2°62 of the salt
would contain 1°28 of alumina.
6. Sulphate of lime 0°23.
7. Phosphate of magnesia 0°19.
8. Sulphur. This determination was made by Mr. Forbes by fusion with
nitrate of potass and the carbonate of potass-soda mixture. 20°14 grains
gave of sulphate.of baryta 0°87. The odour of hydrosulphuric acid could
not be'detected by the action of hydrochloric acid upon the powder of the
slag; but on suspending for some time a slip of moistened acetate of lead
paper in a test tube containing some of the powder of the slag and hydro-
chloric acid, it became slightly brown. Now, as the slag contains sesqui-
oxide of iron, the hydrosulphuric acid liberated by the action of hydrochloric
acid upon any sulphuret which may be present, would evidently be imme-
diately decomposed, with the separation of free sulphur, by the sesqui-
chloride of iron which would be formed at the same time; and, accordingly,
free sulphur was always distinctly recognised by its odour in drying the silica
obtained from slags of this group. It may perhaps appear somewhat remark-
able that sulphuret of iron and sesquioxide should exist together in the same
slag; the fact however is certain. It may be that the sulphuret is irregu-
larly diffused, and is, as it were, entangled in the mass. No trace of sul-
phuric acid could be detected by the addition of baryta water to the solution
of the slag in hydrochloric acid, even after standing 24 hours.
9. Sesquioxide of iron. About 10 grains were digested in dilute hydro-
chloric acid in a well-stopped flask over the water-bath. The necessary
precaution of previously filling the flask with carbonic acid was carefully
observed. The clear supernatant liquor was decanted rapidly into a stoppered
phial containing excess of the solution of chloride of gold and sodium. The
phial was well-closed and left for several days. The metallic gold weighed
3°93, which by the tables corresponds to 4°16 FeO. The filtrate was deprived
of the excess of gold by digestion with oxalic acid. The iron was precipi-
tated by hydrosulphate of ammonia; redissolved in hydrochloric acid; per-
oxidized by chloride of potass, and precipitated by ammonia ; the precipitate
was boiled with potass, redissolved in hydrochloric acid, and precipitated by
succinate of soda with the usual precaution. The sesquioxide of iron weighed
5°76, but from this must be deducted 4°16 FeO, estimated as Fe? O3=4:°63 ;
5°76 —4°63=1°13 iron existing as Fe?O%. The ratio of FeO to Fe? O3 is
4°16: 1:13. The total amount of iron estimated as Fe® O8 is 72-42 per cent.
5°76 : 1°13 :: 72°42: 14°20. But 0°60 of S, as sulphuret, was present, which,
by tables, gives 2:91 Fe? O%. The total amount of Fe?O* per cent. is
1420+ 2:91 =17°11 . 72°42—17:11=55'31 Fe? O3=49°73 FeO, from which
must be subtracted a quantity of Fe proportionate to 0°60 S. This quantity
is 1:01—1-01 +0°60=1:61=quantity of FeS. 1-01 corresponds to 1°30 FeO.
49°73 —1-30=48'43=total FeO per cent.
Fe as FeO 48°43
Fe as Fe? O3 17-11
Fe as FeS 1°61
10. Phosphoric acid. Weight of slag 20°10. Proceeded to obtain asolu-
tion in hydrochloric acid free from silica in the usual way. The tartaric acid
_ process was adopted. The whole was allowed to stand several days. The
ammoniaco-magnesian phosphate was washed with cold ammonia water.
Phosphate of magnesia 0°42. Colour pale brown from a trace of manga-
hese. Every trace of carbon was burnt out.
368 REPORT—1846.
Analysis tabulated. Oxygen.
ST OA ier ee aaa CTE) nies «02. ASH
Protoxide of iron ........ BSNS Gel», », 0,0 11°02
Sesquioxide of iron........ 1h eee 5:24
Protoxide of manganese*.. 1°13 ...... 0°25
RTI... nd: ti0 ns hela asl SI dal bs, ohn 0°59
PLING 5. xiniin'b Seven wks sca REEL Golkeaus ¥ 013
Dp gnesih .:.5.cieips tie ducetdn Da a aiaas Son 0°13
Phosphoric acid.......... Dein atti, 0°75
Sulphuret of iron ........ 1°61
101°32
These crystals closely resemble olivine in their form. The faces of the
crystals are denoted by the same letters as the faces of olivine in Naumann.
t, k, n of Naumann correspond to p, e, 5, of Phillips respectively.
Crystals similar to these in form, composition and mode of occurrence, were
described by Mitscherlich in the Annales de Chimie, t. xxiv. Measurements
of crystals of the same form, and a comparison of their angles with those of
olivine, were given by one of the authors (W. H. M.) of the report in the ©
third volume of the Transactions of the Cambridge Philosophical Society.
Estimating the whole of the iron as protoxide, the composition would be
nearly that of Fe’ Si, the formula assigned by Thomson to the mineral from
Ireland, named “ Anhydrous silicate of iron.” Now, this slag had evi-
dently been in a position favourable to the absorption of oxygen, namely,
the flue of a puddling furnace; and we shall probably be justified in sup-
posing that, after crystallization as silicate of protoxide of iron, oxygen may
have been absorbed, and that the crystal may consequently be regarded
to a certain extent pseudomorphous. In the case of the following slag,
which is similar to the one in question, it was found by experiment that the
powder of the slag readily absorbed oxygen by calcination in the air. If
this view be admitted, the slag will in constitution as well as form resemble
olivine, the magnesia of the latter being replaced by protoxide of iron.
14.
This slag was found by Mr. Twamley at the Bloomfield iron-works, Tip-
ton, in a heap of calcined puddling furnace slag, technically called “ tap
cinder.” The proprietors of these works have secured by patent the appli-
cation of calcined tap cinder for the beds of puddling furnaces. It is stated
that, by the process of calcination, which is conducted in large kilns similar
to brick-kilns during a fortnight or three weeks, the slag is rendered much
less fusible, and is therefore well-adapted to the purpose to which it is ap-
plied. The analysis will probably explain this fact. The heat of the kilns
appears, from an examination which one of us has made (J. P.), to be suffi-
cient to soften and agglutinate the pieces of slag together, but not to effect
perfect fusion.
This slag is a mass of large iron-gray crystals, the faces of which though
even are much too dull to be measured with the reflective goniometer. The
general resemblance of their forms, however, to those of No. 12 is so close
as to leave no doubt of their crystalline identity.
At 182°C. Specific gravity=4°1885.
It attracts the magnetic needle strongly.
* Probably a portion existed as a superior oxide.
ON THE CRYSTALLINE SLAGS. 369
14. Anatysis. By J.P.
This slag was found to contain the same constituents as the one preceding,
and the analysis was conducted in a similar manner.
1. Weight of slag 21:00 grains.
2. Silica 5°01 grains.
3. Total amount of iron obtained as Fe? O% 14°44.
The oxide of iron in this case after boiling with KO twice, was redissolved
in HCl and precipitated by hydrosulphate of ammonia.
4. Oxide of manganese 1°39. The manganese was precipitated as MnO?
_ by chlorine and ammonia.
5. Alumina with phosphoric acid 1°87. The Al? O° was precipitated from
a solution containing much more P? O than required for saturation, for the
greater part of the P? O° had been dissolved out of the iron precipitate by
KO. This fact was confirmed in another case by dissolving the oxide of
iron after treatment by KO in HCl and digesting with excess of hydro-
sulphate of ammonia, and testing the filtrate for P?O%. Admitting the
phosphate of alumina, as precipitated by ammonia, to be 4Al? O3, 3P2 05
(Rammelsberg, Rapport Annuel, Berzelius, 7*™¢ année, p. 127), the calcu-
lated proportion of alumina is 0°91.
6. Sulphate of lime 0°136.
7. Phosphate of magnesia 0°139.
8. Sulphur. The observations upon this element in the preceding analysis
exactly apply to the present. 26:14 grains of slag were fused with 50 of
nitrate of potass and 100 of the carbonate of potass-soda mixture. Sulphate
of baryta 0°44.
9. Sesquioxide of iron.
1. By chloride of gold and sodium process. Weighed roughly 10 grains.
Proceeded precisely as in the former analysis. Metallic gold 3:32.
Total quantity of iron as Fe? O, 5°85.
2. By Fuchs’s method with pure copper. The necessary precautions
concerning the exclusion of air during solution, &c. by carbonic
acid, were carefully attended to. The copper was left in the solu-
tion during several days, until the latter had become colourless.
Weight of slag 25°83 grs. A piece of electrotype sheet-copper was
used; before immersion it weighed 18-176, afterwards 15°815 grs.
Fe? O83 per cent. by the first method ...... 22°65
Ditto second versa cay eae
But the slag contains 0°23 per cent. of sulphur, which corresponds
to 1:12 per cent. of Fe O%. From the preceding data the following
results are obtained :-—
Peas. Pe Ors ales 39°83
Fe as Fe? OS8 .......... 23°75
Feas FeS............ 0°62
10. Phosphoric acid.
1. By the tartaric acid process. Weight of slag 25:83. The solution
used in the Fe* OS determination by Cu was employed. The
phosphate of ammonia and magnesia having a brown colour, it
was redissolved and reprecipitated by ammonia. Phosphate of
magnesia 2°76.
2. The solution obtained in the sulphur determination was also em-
ployed. Weight of slag 26:14. Phosphate of magnesia 2°66.
P? O° per cent. by the first method .... 6°40
Ditto second cece G45
Wears asin igias S96 Mbs eee ye Le eae GMD
-
370 REPORT—1846,
11. Our friend T. H. Henry, Esq. of London, determined the proportions
of several of the ingredients of this slag, and has communicated to us the
following results :—
Si O° 23°77 per cent. Fe O 40:07. Fe*® O08 22-68 (quantity corresponding
to sulphur not added). Al*O% with P?0* 1:6. P?0O® 6°40.
Analysis tabulated. Oxygen.
Pes sais ns. 5 aia ote union fc ar 12°41
Protoxide of iron........ a ie 9°07
Sesquioxide of iron ...... 2k ot ce mG 2
Protoxide of manganese .. 6°17 ...... 1:38
VANES, OF cra are 2 oon ania a a a 0°42
ASAE «0 chute a sbaeclala wis cole. b'e O25 her iaers ; 0:08
WeHCRIARE 0 3p i0's = = ny 6 RE AS ine 0:09
PRGepHOTiG BENG Fo 5iy aie, ORE pomp at 3°60
Sulphuret of iron,....... 0°62
102-08
We regard this slag as similar in constitution to the preceding, the alumina,
some of the sesquioxide of iron, and the phosphoric acid being present as
impurity. The presence of so large a quantity of sesquioxide of iron in this
slag is probably to be explained by its long exposure in the kiln, during
which it was in a condition favourable to the absorption of oxygen. The
powder of the slag, when heated to redness in a platinum crucible, changes
colour, acquiring a brown tint, and increases in weight. The quantity of
phosphoric acid is also remarkable, and is well-deserving of the attention of
those engaged in the smelting of iron. Berthier has given the analysis of a
refinery slag from Dudley (Traité des Essais, t. 2. p. 289), containing 7-2
per cent. of phosphoric acid. It is found that when puddling furnace slag
(tap cinder) is worked with the ordinary ores of iron, such as argillaceous
ore and hematite, the iron is liable to be “cold short,” or possess that
property which is known to be dependent upon the presence of phosphuret
of iron. Now it is evident that in smelting tap cinder, which will probably
always be found to contain a sensible amount of phosphoric acid, the manu-
facturer will be introducing into the furnace the very element, in a concen-
trated form, which it is one object of the puddling furnace to remove, namely,
phosphorus. An immense quantity of iron slag, far richer than many iron
ores, is annually thrown away, and it may be that the presence of phos-
phorus in sensible quantity is one of the causes which prevents the resmelting
of this slag with advantage. This fact has not yet sufficiently attracted the
attention of those engaged in the manufacture of iron. The discovery of a
method of extracting economically good iron from these rich slags would be
of great advantage to the country, and could not fail amply to reward its
author.
ioe
The history of this slag is doubtful; though it is probable that it was
produced in a puddling furnace. It has not yet been analysed; yet we in-
troduce the results of its crystallographic examination in order to illustrate a
new process of admeasurement of crystals of this kind, by W. H. M.
One side of this piece of slag is bounded by a plane smooth surface, on
which are traced the outlines of a number of crystals packed close together,
separated by a lighter-coloured slag. Some of the outlines of crystals are
rectangles, others rhombs, haying their obtuse angles cut off by parallel lines,
ON THE CRYSTALLINE SLAGS. 371
An attempt was made to measure approximately the
acute angle of the rhomb in the following manner :— fn
_ By means of a stout branch with an universal joint like
that of Wollaston’s goniometer, the slag was attached
to a common six-inch circular protractor graduated to A B
half degrees, with its plane surface upwards, and parallel
to the plane of the protractor. The protractor was
placed upon a table, having traced upon it a fine straight
line longer than the diameter of the protractor. A com-
pound microscope, having a spider line in the focus of
the eye-piece, was firmly fixed with its axis perpendi-
cular to the table, and at such a distance from it as to
command distinct vision of the plane surface of the
slag. By moving the protractor with the slag attached to it till the images
of the sides of the rhomb formed in the microscope successively coincided
with the spider line, and reading off the degrees and minutes at which the
protractor met the line traced on the table, the angle is obtained through
which the protractor has been turned between the two observations; or, the
angle of the rhomb. The values of the angle ACB thus observed were,—
77°-0, 79° 45', 81° 30’, 80°, 78° 15', 79° 15’, 77° 45', 78° 20', 82° 6’, 80° 50’,
77° 30', 80°, 80° 15’. Such a method of observation is obviously insuffi-
cient for the identification of a crystalline species; yet renders it probable
that these crystals are the same as No. 13, a section of which, by aplane
perpendicular to £', would produce a rhomb of 81° 36’.
At 181 C. specific gravity of slag = 3°9984,
We conclude our present report by the cry- Crystal in profile.
stallographic description of an interesting slag
obtained from the gold and silver refinery of
Messrs. Betts of Birmingham. The matrix is
very heavy, and probably differs considerably in
composition from the minute crystals in question,
which appear to be, as it were, sublimed upon the
surface, and of which it is impossible to obtain
sufficient for analysis. mW /m
The surface of this is studded with numerous
extremely small black bright crystals belonging End of crystal. | m' | m
Cee rr ea ee eR
all
=
-to the oblique prismatic system. The angles
between normals to the faces are mm! 73° 10’,
pp! 86°, mp 29° 42’. The edge in which pp!
intersect makes an angle of nearly 46° 30! with
the intersection of m,m!*. For a portion of the
slag having crystals adhering to it, at 19%1 C.
specific gravity of slag = 6°3802.
We have remaining an extensive series of slags from various metallurgical
works, which we have not yet had time to investigate, but we hope to be able
to continue our labours in this department, and to present to the Association
a second report at no distant period. We have several specimens of beauti-
fully crystallized octahedral or magnetic oxide of iron, and many other
erystals from the copper furnaces. We take this opportunity of publicly
thanking those gentlemen who have obligingly contributed to our collection,
and of inviting any others, who may have the opportunity, to further our
views in a similar manner by the contribution of specimens.
* I cannot find any mineral having the same or nearly the same angles.—W. H. M,
Addenda to Mr. Birt's Report on Atmospheric Waves.
The following table exhibits the distribution of pressure on the transit of
the crest of the great wave, Nov. 18, 1842, with especial reference to the
wave, crest No.4, including St. Petersburgh as a station.
Tasre XVII. | parom. Phase. Station. Altitude. Wave Phase.
Min. The Orkneys ... 30°18
COM ccrnabrt hes ags 30°18
EWASt. scscecacsee 30°37 Posterior
Shields {35 .0..08e 30°42 Slope.
Bristol. sez. cate. 30°42
Plymouth.....-..« 30-47
Max. ponege ee beer A < 30°53... | . Crest.
AUIS: Waadaps aun ae5 30°38 .
Christiania ...... ig it Nir pecs
Min. St. Petersburgh.. 29°85 ope:
A the highest reading at these stations on this day.
Altitude of anterior slope. St. Petersburgh to London *68
(A very oblique section.)
Altitude of posterior slope. Cork to London *35
(The posterior trough was doubtless some distance north-west of Great Britain and Ireland.
November 22. Trough between waves 7 and 9.—The trough now trans-
its St. Petersburgh, crest No. 9 now transits Christiania. We have already
noticed that crests 7 and 11 were small waves ; abstracting them, we have this
succession of large waves thus, Nos.1, 3, 5, 9. When crest No.1 traversed
England on the Ist, its anterior trough extended beyond St. Petersburgh ;
when crest No.3 traversed England on the 10th, its anterior trough also ex-
tended beyond St. Petersburgh; when crest No. 5 passed the Orkneys on the
15th, its anterior trough passed St. Petersburgh; and when crest No. 9 passes
Christiania (this day), its anterior trough passes St. Petersburgh. These facts
clearly show the gradual contraction of the waves or oppositely directed beds
of parallel currents.
General Conclusion.
It will be readily apparent from the collation of Mr. Brown’s with the St.
Petersburgh observations, that the results arrived at in the preceding discus-
sion have been fully confirmed, and there appears to be but little doubt that
the waves as determined in the first instance by a discussion of observations
from the stations announced in my first report (Report, 1844, page 267), and
further identified and illustrated by the observations collected by Mr. Brown,
as well as those which have been brought to light by means of Mr. Brown’s
observations, and confirmed and illustrated by the St. Petersburgh observa-
tions, had a real existence; an individuality has been attributed to certain
arrangements of aérial currents and distribution of pressure in connexion
with such currents, the aggregate pheenomena forming an atmospheric wave.
Of the waves thus brought to light, two occupy very prominent positions ;
they stand out as it were from the others; the individuality of each is very
striking, and the velocities with which they traversed the area isolate them
from their predecessors and exhibit them not as gregarious, but solitary waves.
These waves are B° and crest No. 4, the first occurring just previous to the
setting-in of the great wave, and the last forming its crown. The wave, crest
No.4, appears from its elevated position on the symmetrical or normal wave,
admirably adapted to crown our investigations with success, especially in so
far as its amplitude, velocity and path are concerned, we are now, I appre-
hend, in possession of materials to determine with a considerable approxima-
tion to accuracy, these elements. Its longitudinal direction appears to have
been very extensive. This element would receive considerable elucidation
by means of observations from the south of France, Spain, Portugal and the
north of Africa. It is highly probable that this wave in the direction of its
length stretched from the extreme south to the very north of Europe.
NOTICES
AND
ABSTRACTS OF COMMUNICATIONS
TO THE
- BRITISH ASSOCIATION
FOR THE
ADVANCEMENT OF SCIENCE,
AT THE
SOUTHAMPTON MEETING, SEPTEMBER 1846.
rig:
ADVERTISEMENT.
Tue Epirors of the following Notices consider themselves responsible
only for the fidelity with which the views of the Authors are abstracted.
CONTENTS.
NOTICES AND ABSTRACTS OF MISCELLANEOUS
COMMUNICATIONS TO THE SECTIONS.
‘MATHEMATICS AND PHYSICS.
Page
Professor Youne on the Principle of Continuity in“reference to certain Results
Of Analysis ....cscccsceeceeeeeereee Reskicsiiawaebent = ways epak «= ded Sandia evpleerhemerian cave 1
Professor OrrsTED on the Deviation of Falling Bodies from the Perpendicular 2
Professor PowEuu on certain Cases of Elliptic Polarization of Light by Re-
fleXION ........sceceeeee 5 Pere Becondet see Reais easeneean aicee Seneesicsbe nang esunaaee 3
— on the Bands formed by partial Interception of the Pris~
Matic Spectrum ......ssceeeseeeees Rcltuadantedelcabicbiesnieesae seats tataawendoss=veeusecsdens 4
SS SSS on attempts to explain the apparent projection of a Star on
the Moon ............. ppiddakouhaas oe siddsoupenmasus selene reataeandecs Mhatdsaney es Sepisinpenin teen a
Mr. Daze on Elliptic Polarization ..........ssscsesesseeceneccueeeees iSvadtada sesh tieeas 5
Sir Davip BrewstTeEr’s Notice of a New Property of Light exhibited in the
Action of Chrysammate of Potash upon Common and Polarized Light ....... i
Dr. Greene’s Description of a Portable Equatorial Stand for Telescopes with-
out Polar Axis........ Hpeaeo serene ce = Andee dualaalcobloubvuriceabeehoweciee ea ee 8
Mr. Henry Lawson on an easy pat of contracting the Aperture of a
Mare Telescope’! Lis.) idec bes ties cdeaede ecaeateasweevecevevedwewesvivaneses dan cel eteads 9
on the Arrangement of a Solar Eye-piece .........sseeeeees 9
Mr. F. Ronatps on the Meteorological Observations at Kew, with an Account
of the Photographic Self-registering Apparatus ...ccc..ecesscseeeseeasees peepee 10
Professor WARTMANN on some Meteorological Pheenomena ............+..40+ Se re illp!
Dr. Banks on a New Anemometer ...........ccccesseeeceersetneeseeveseeeesees ery 12
Capt. W. W. CuitpErs’s Meteorological Observations ...........sseeeeeee ecactis 13
Rev. T. Ranxrn’s Notices of a Halo, Paraselene and Aurore Boreales ......... 15
Rev. W. WHEWELL’s Method of Measuring the Height of Clouds ............... 15
Capt. SHoRTREDE on the Force Of Vapour.......,.csssecsseenessesessenceecececesecees 16
Mr. G. Dottonp’s Account of an Atmospheric Recorder.......cssecereesessecseeee 17
Mr. C. Brooxe on the Construction of a Self-registering Barometer, Thermo-
meter, and Psychrometer ......+ Bdsddacs vide pda sewed wae Rowine 4 ad asia a bicdvwcacsee 17
Mr. J. F. MituEr’s Table of the Fall of Rain in the Lake Districts of Cum-
berland and Westmoreland, &c. in the Year 1845 ..........06 eean Seah Uidadaeee 18
——— Readings of Mountain Gauges, June, July and August -
1846........ Peeeeeeeseeeseesesesee @eeersesseree SCeeeeseeseseseeesese eeeeeetsesaseses COC CCC eeeeee 21
Lt. Colonel Syxzs on the Fall of Rain on the Coast of Travancore and Table
Land of Uttree, from Observations of M. General Cullen .........ssececoeesssees 22
_ Mr. E. J. Dent on a New Portable Azimuth Compass............ Sescntheoecnande (EE
lV 4 CONTENTS.
Mr. Tuomas Hopxrns on the Relations of the Semi-Diurnal Movements of the
Barometer to Land and Sea-Breezes..........ssseeeeseeeees eaels- sateen athabte douse
Mr. Witx1am Mayes’s Abstracts of Meteorological Observations made at Aden
WINS oto reseemaeecetet «sac ce -eszsevceeue Sbewseenemeelsteleaeisinsele s0ccecbesemeusehee seeeee
Mr. Witi1am Mayes’s Meteorological Observations taken at Fort George Bar-
racks, Bombay, in July, August, September and October 1845 ......es0...00-
Prof. WartmMann’s New Experiments on Electro-Magnetism ........scssseeees she
Prof. Matrrucci’s Summary of Researches in Electro-Physiology...............
Dr. Josspu Buxtxar on the Identity of certain Vital and Electro-magnetic
LAWS .....c00000 se nssesege sees e SpE A Oy 18 ech Poe Seer Sobte Paces cts dusassscns cubes ay oooh
Prof. SVANBERG on a new Multiplying Condenser............. cud cUalodamaheenessae <
Mr. J. A. Broun on some Results of the Magnetic Observations made at General
Sir T. M. Brisbane’s Observatory, Makerstoun ......scscsesesesesereceseereeeesens
Mr. G. Tow Ler on Magnetic Causation .........ssseccsscssssscececescesseeees en
Mr. We Petrie on the Results of an extensive Series of Magnetic Investiga-
tions, including most of the known varieties of Steel ............seseceseeeecneeees
Rev. W. Scoressy on the Mode of Developing the Magnetic Condition.........
Dr. Laine on the Constitution and Forces of the Molecules of Matter.........
Mr. W. R. Brrr on Atmospheric Waves....c.secseseseseceeceversenes RE as tas be Se ¥
i
CHEMISTRY.
Prof. OzRsTED on the Changes which Mercury sometimes suffers in Glass
Vessels hermetically sealed ............04. wowesossjasiaacdegterths conaten anaeeaeenn en
Prof. H. Rosz on a second new Metal, Pelopium, contained in the Bavarian
Tantalite ..........4. ade aa dein ees pem anche gecesine ata aoiedees wae. dceskagnaugonadeneeten aeeee
Prof. Dauseny on Cavendish’s Experiment respecting the production of
INTERIGEACIO} cc 3h emcee Acero dan enasisapeibmapeecscacy sacha nencee clin a nus dente Doge immer
Dr. Gzorer WIxson on the extent to which Fluoride of Calcium is soluble in
Water at 60°F. ............00- senassiessiesnsmeDheddeteseshosciees cus eectaO tans ebm eheeweas
Prof. ConnELL’s Analysis of the American Mineral Nemalite .,...........0:0000+
Observations on the Nature of Lampic Acid ..........6. sseeeees
Mr. James Buaxe on the Connexion between the Isomorphous Relations of
the Elements and their Physiological Action .....0....:ssssssscesceseeeeeceeneeenee
Mr. H. Letuesy on the Action of Oxalic Acid upon the Dead Tissues of the
Animal Body *......2.0s---acedusssenses epnie ae seeee ata de aad nesis pas os «=~ sc dae eee eenaee
Dr. R. D. THomMson on an important Chemical Law in the Nutrition of Ani-
MUA S dain cm a sies aneassicas sees acieisceteteaacansnancesvaadatuemeneners sss caclesscvncessacnwe dadenwe ee
Mr. H. Leruesy on the Difference in the Physiological Actions of the Yellow
and Red Prussiates as an evidence of their containing dissimilar Radicals ....
Mr. W. West on the use of stating, with the results of Analyses, the nature of
the Methods employed: a. .s.5scoassncesaneae¥ecaneaisdncensieansiees ses doscacucenanguecns
Mr. Henry Ossorn on the presence of Atmospheric Air, uncombined Chlo-
rine, and Carbonic Acid found in the Water of some of the Wells in the
suburbs of Southampton, and their Action on Lead.......ccccsseeeserecnecneeeaee
Professor DausEny on the Rationale of certain Practices employed in Agricul-
Professor Way on the Fairy-rings of Pastures .......... Sao scnnccescscscousarsnasnape .
Mr. Wiii1am Cuarves Spooner on certain Principles which obtain in the
application of Manures.......cccsseccsecererseceecstescascascenscstscecsssccsevenecnes gs
Page
25
26
26
27
28
29
31
32
33
33
35
35
35
37
37
38
38
39
40
CONTENTS.
_ Dr. G. Kemp on the application of the Principles of a Natural System of Or-
ganic Chemistry to the Explanation of the Phenomena occurring in the
Missased Potato WUDelnas ihe sccvecsesseoathantniadeiataldcuiiicecnseasceevecectcou succes de
Mr. J. PripEaux’s Inquiries into the Extent, Causes and Remedies of Fungi
destructive in Agriculture........ solves ou susan saeeeeetnee tenes cdaisace vosee ccs Racretcae
Professor Dauseny’s New Facts bearing on the Chemical Theory of Volcanoes
Dr. Reape’s Notices of Experiments in Thermo-Electricity............cccsesseeees
Professor Marrrvcci on the Electrization of Needles in different Media.........
ses
PY Re
Dr. Lexson on Crystallography and a new Goniometer..,........++5 pie Uta els he's *
Rey. T. R. Rosinson on the Influence which finely-divided Platina exerts on
the Electrodes of a Voltameter..........sesscsscsesenscereececsseses He Es seidehemads's
Mr. John P. Gassior on the Electricity of Tension in the Voltaic Battery ......
Prof. W. R. Grove on the Decomposition of Water into its constituent Gases
by Heat...... eveveees Beek esuaee Seansisiatrat ap wiaiesabicatele cle oisih cthinwcicsmeatibsiaies cs cistalenel
Dr. Percy’s Notice of a Gas Furnace for Organic Analysis....c...sesesssceessesee
Sa ae
#
h
é
Mr. E. R. J. Knowzzs on an extraordinary appearance in the Flame of a
Commonatouldcandlerpiisisle.iiesscseces Uusscevectaetsseatavecare codtieadeaatacncds
GEOLOGY AND PHYSICAL GEOGRAPHY.
EE SEP E
Professor GOprert on the Origin of the Coal of Silesia............sccseeceveseeeeees
Professor ForcHHAMMER on Sea Water, and the Effects of Variation in its Cur-
_ M. Agasstrz on the Fishes of the London Clay...........c:sseccseeeeeeeeeceneeeeeeees
_ Mr. J. R. Keezxz on the Artesian Well on the Southampton Common...........
Rev. W. Buckiawp on the applicability of M. Fauvelle’s mode of boring Arte-
sian Wells to the Well at Southampton, and to other Wells, and to Sinkings
for Coal, Salt, and other mineral beds... scccccccccecscssacseccenccecsccccsescsevsvens
Mr. JosspH Prestwicu, Jun. on the occurrence of Cypris in a part of the
Tertiary Freshwater Strata of the Isle of Wight.............scsesscsseseecreeeecees
_ Dr, Firron on the Arrangement and Nomenclature of some of the Subcretaceous
POEM GAN es sin shtedvicsele oe sna saa -LOUU Spr Gageb6r UR AS BSC CUE ECU n Sep RuH OnE ne SRA Se pases soecreee. =
_ Mr. W. Hopxrtwns on certain Deviations of the Plumb-line from its Mean Di-
rection, as observed in the neighbourhood of Shanklin Down, in the Isle of
_ Wight, during the progress of the Ordnance Survey................ See ep eae acdsee
. Mr. W. Sanpzrs on Railway Sections made on the Line of the Great Western
Railway, between Bristol and Taunton ............scsscsssesvescecseceeeserseeensenes
t Captain IpBETSON on three Sections of the Oolitic Formations on the Great
Western Railway at the West end of Sapperton Tunnel...................seseee0
. Mr. James Buckman on the Age of the Silurian Limestone of Hay Head,
near Barr Beacon, in Staffordshire ..............0c00s See endees Ha aaa eS aE
——=».
oo ’s Notice of the Discovery of a new Species of Hypantho-
crinite in the Upper Silurian Strata..........ccccceceecscsccececeensceeececaecececesees
Mr. Rozzrr Baxp on the Mushet Band, commonly called the Black-band
Tronstone of the Coal-field of Scotland...............cscssceseeseeccecssceceeeasensans
Mr. G. Wareinec Ormerop on the extent of the Northwich Salt-field.......s.
_ Professor AnsTEp’s Notice of the Coal of India, being an Analysis of a Report
_ communicated to the Indian Government on this subject
SO reece ecerese eee seceseses
Prof. OweEn’s Notices of some Fossil Mammalia of South America.......s.ses0+
vi CONTENTS.
Mr. J. B. Juxes’s Notice of some Tertiary Rocks in the Islands stretching from
Java to Timor...... poateceds Mtaeres Sparignoseanacess eaRT ERE on vas computer te panbsitde x
Sketch of the Geological Structure of Australia ............++
Mr. J. Duncan’s Notes on Geological Phenomena in Africa ........ se eonaaee is
Mr. A. C. G. Jopert’s Note on Graphic Granite ..,......0.sseecsecreserees ft opee he
Prof. E. Forsxs’s Notices of Natural History Observations Bhi since last
Meeting bearing upon Geology .......ssssscsssereesseeesenseceeceeressneseneseanesenees
Dr. Cuartuezs T. Bexe on the Physical Character of the Table-land of Abes-
Mr. W. Desporoven Coorzy’s Synopsis of a proposal respecting a Physico-
Geographical Survey of the British Islands, particularly in relation to Agri-
CUILUTE .....cccecccscencscccccccceccncccccesencseceseseeseesseesenssosccsecensseeseseseucoage
M. GuErRIn on the Georama .........seeesssees weeee SoA ee its See EL A ies
ZOOLOGY AND BOTANY.
Prof. Royiz’s General Observations on the Geographical Distribution of the
Flora of India, with Remarks on the Vegetation of its Lakes............ decades
Mr. Joun Hoae’s Synopsis of the Classification of the Genera of British Birds
Mr. Joun Buackwa.Lw’s List of the Names of Periodical Birds, and the dates
of their appearance and disappearance, at Llanrwst, in North Wales .........
Mr. J. Bonomi on the Figures of Birds observed on a Tomb at Memphis ......
Dr. H. Fatconer and Mr. W. Toompson on the Crania of two species of
Crocodile from Sierra Leone .........sscsseccssecsscecscsssssssecssesenseesesscescvesces
Dr. R. Knox’s Recollections of Researches into the Natural and Economic
History of certain Species of the Clupeadz, Coregoni, and Salmonide .......
on the Application of the Method, discovered by the late Dr.
Thibert, of Modelling and Colouring after Nature all kinds of Fishes .........
Mr. J. Coucu on the Egg-purse and Embryo of a Species of Myliobatus ......
Prof. Taomas Bxrxu on the Crustacea found by Prof. E. Forses and Mr.
McAnprew in their Cruises round the coast .........ssssseeeee sana ak as ae Rabe sans
Dr. CarPENTER on the Structure of the Pycnogonided..........secsssecssesecceeees
Mr. L. Reeve on the Dissimilarity in the Calcifying Functions of Mollusks,
whose organization is in other respects Simla’: syacactetc.: ccc snas a. caeeee
Prof. ALLMAN on certain Peculiarities in the Anatomy of Limax Sowerbii......
Messrs. Jospua ALDER and Atpany Hancocx’s Notices of some new and
rare British species of naked Mollusca...........-+++++ i dh ona sihedeira dace Sete ddias 0 tela
Rev. T. Rankin on the Hybernation of Snails .........scceeecesesseseseeseenes pases
Mr. W. Tuompson’s Notes on the Land Mollusca, Zoophytes, and Algz of the
[ste tof, Wight: s1.<::ctsesceeuttewedsssssasn deer nesamveasuns sects siecsssdeeseaneemdetaestee
to that of Dritaim sic tiie cece aes eebaes tobe cesecs eecet es cebseecaecesc@enee se: tae ae
on the Zoology of Lough Neagh, compared with that of the
Takes of Geneva: vas.cocsstietesecustubs ss nss tates cettecescpecectocseeetecdencee pecans
Captain Portiocx’s Notes on the Natural History of Corfu ...............ce0eee
Prof. E. Forszs on the Pulmograde Medusz of the British Seas..................
Mr. C. W. Peacu on the Marine Zoology of Cornwall .........sessecessceseeeeces
Mr. Joun Price on the Embryogeny of Pulmogrades and Ciliogrades ..........
on the Quasi-osseous System of Acalephz.......... Siesta “i
Mrs. Wurtsy on the Cultivation of Silk in England..........csscsssseeseeeene Ravesk
Page
CONTENTS,
_ Prof. ALLMAN on the Structure of Cristatella mucedo .........e0ss00 Src,
Dr. T. Beit Satter’s Observations on the true Nature of the Tendril in the
BD RCUCUMDEL ..,.cesseveeceeerereres onda Meee Aa i Pea ie Nesisitslepp'cap ean v dy Yeates
_ Professor ALLMAN on an undescribed Alga allied to Coleochete scutata ....... si
Mr. W. Hoean on the means of obviating the ravages of the Potato Disease,
by raising fully-grown healthy Potatoes from seed in one season............4..
Mr. T. D. Morriss-Stirxine on proposed Substitutes for the Potato .........
Mr. A. Henrrey on the Development of Cells ..........ccsseecceceeeseceenecseuscees
Mr. W. Tuompson’s Comparison of the Periods of the Flowering of Plants in
the early spring of 1846, in the Botanic Garden of Belfast, and the Jardin
CHM IARICGS AEE AUIS! 125 cede ccdcdowcedoddscidaddactes tease edema daigeeacntdeatets tauatceres
Mr. B. Crarxe on the Foliage and Inflorescence of the genera Phyllanthus
and Xylophylila........ Sc pUSSICE CoRR bch ated ganmigdgdenricsog cancer capepncencass” Savon aaa
MEDICAL SCIENCE.
_ Dr. Carpenter on the Physiology of the Encephalon....... nde secgneetateee se tocass
Dr. Fow.er on the Relations of Sensation to the Higher Medical Processes....
q Dr. SeaRze on the Cause of the Blood’s Circulation through the Liver....... dee
_ Dr. Laycocx on some Diseases resulting from the immoderate use of Tobacco.
—’s Diagrams showing the Mortality of Diarrhcea concurrently with
progressive Increase of Pemperature in London..........2c0sesseeeee ceecaccecsecccs
| Dr. Benner ona peculiar form of Ulceration of the Cervix Uteri............00000
STATISTICS.
’ Licut.-Colonel Syxxs’s Statistics of Civil Justice in India for four years, from
_ 1841 to 1844, both inclusive .....e.cececssececeee EabawaWars ees SPARRO HES CHEE AARAE
. Statistics of the Criminal Courts of India..............+
Statistics of the Government Charitable Dispensaries
_ Of India.........seseeseeereeeenes Betees rs Sfbacc CadoctUcerRCARAaae aritdach Lnoceeade anasaceed
| Professor Axison on the Medical Relief to the Parochial Poor of Scotland under
the Old Poor Law.............seseseess be aevease str csestece. tesseasuat uae aesias ebb aduhala -
Mr. Nrewp’s Crimina! and Miscellaneous Statistical Returns of the Manchester
_ Police for the year 1845......... PRE AA aay AEE EE SE eteeeeanaaes dees been ois
| Mr. James Heywoop’s Oxford University Statistics.......-.... pelea ara deg
NOTICES AND ABSTRACTS
OF
MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS.
MATHEMATICS AND PHYSICS.
On the Principle of Continuity in reference to certain Results of Analysis.
By Professor Youne, Belfast.
Tue principal object of this paper is to examine into the influence of the law of
continuity, as it affects the extreme or limiting values of varying functions, and to
exhibit some remarkable verifications of the mathematical axiom that “ what is true
up to the limit is true a¢ the limit.”
Much error and confusion exists in the writings of analysts, more especially in those
of Cauchy and Poisson, in consequence of the imperfect views generally entertained
in reference to the principle of continuity, whenever extreme or ultimate values of a
"variable come under consideration. In certain infinite series where the condition
of continuity avowedly prevails, it is the common practice to neglect this principle in
_ the limiting cases, and to treat such cases as if they were entirely isolated and un-
connected with the general forms to which they really belong; whilst in other classes
of series, those namely that have been called periodic, as also in definite integrals
involving periodic quantities, it is a practice equally common to introduce the condi-
tion of continuity where in fact it has no legitimate existence. Many false conclusions
have thus obtained currency in analytical writings, and it is the aim of the paper, of
which this is a very brief abstract, to inquire into the sources of these errors, and to
supply the requisite corrections,
As respects series, for instance, it is shown that the limiting cases of
2
v1 +5 += +..... ad inf., corresponding to#= 1land«= —1,
are very different from what Cauchy and other writers affirm them to be. Cauchy
says, that when these limits are reached, the series will be divergent in the first case,
and convergent in the second: but it is proved in the paper adverted to, that “if x
ascend from an inferior numerical value (that is from a fractional value either positive
‘or negative), up to =1 or x = — 1, the limiting cases will both be convergent,
like all the preceding cases; but if the same limits be reached through descending
values of the variable, the extreme cases will then, on the contrary, be divergent.”
bs In like manner the limit of the series
os lt+oet2a2?4+ 2.3234 2.3. 424+ &c. ad inf.
when x arrives at zero, and which is said by Cauchy to be equal to 1, is proved to be
reality equal to a quantity infinitely great.
‘The errors of Cauchy arise from his neglecting the influence of continuity in these
miting cases: the errors of Poisson, in his researches into the theory of periodic
series and definite integrals in the ‘ Journal de |’Ecole Polytechnique,’ and in his
Théorie de la Chaleur,’ are of a directly opposite character: they arise from his
arbitrarily introducing continuity where no such principle exists. Poisson admits
that periodic series and periodic integrals are in themselves indeterminate; but
he considers himself at liberty to overrule this indeterminateness, by introducing
into the series the ascending powers of a quantity infinitely little different from unity,
and by introducing into the integral the arbitrary multiplier e—47. By means of this
unwatrantable artifice the periodicity is in both cases destroyed: the series is ren-
—~«(1846. B
2 REPORT—1846.
4
dered convergent instéad of periodic, and the integral is rendered determinate instead
of indeterminate.
To avoid the recurrence of these errors, it is proposed to divide infinite series and
definite integrals into two classes, those which are dependent upon some condition of
continuity, and those which are altogether independent, or neutral. Hutton restricted
the term neutral series to the form 1 — 1 + 1 —14, &c., because of its being neither
convergent nor divergent. It is here proposed to extend the signification of this
term, so as to have no especial reference to convergency or divergency: a strictly
neutral series may be either convergent, divergent, or periodic.
Some controversy has arisen of late respecting Poisson’s theory of definite integrals,
and certain forms have been condemned as erroneous which are really correct. Thus
the integrals ;
% sin ax 2 COs ax
Eis z dwand J 9 Tha dx
have been recently affirmed to be indeterminate, which they arenot. The second of
these however has been investigated by Legendre, Gregory and others, by methods
altogether objectionable, as is fully shown in the present paper. A correct process
for obtaining the proper determinate result, has been given by Sir W. R. Hamilton
in his paper on Fluctuating Functions, in the nineteenth volume of the Transactions
of the Royal Irish Academy. The ordinary investigations of the first of the pre-
ceding forms are correct, although objected to in a paper in the recently published
per of the Cambridge Transactions, yet the conclusions obtained by Euler, Fourier,
oisson, and indeed by analysts generally, in reference to this integral, are affected
F Cy :
with error: the values of the integral are always stated to be A ops 2 according
as the constant a is positive, zero, or negative.
It is easily shown however, by a reference to the law of continuity, that the
middle one of these values, viz. 0, has no existence; for if « become zero by vanish-
ing positively, the value of the integral is still 7 ; and if it become zero by vanishin
8 Pp y: 8 5 y g
negatively, the value is — a i
Among the collateral topics discussed in the present paper, notice is taken of the
method proposed by Deflers, and so often quoted by Poisson, for verifying the well-
known integral theorem of Fourier; this method has been properly objected to by Mr.
De Morgan, as involving an inadmissible principle: by.a little modification, sug-
gested by the theory unfolded in this paper, the defect is removed, and Deflers’ short
and ingenious proof of Fourier’s remarkable theorem rendered conclusive.
The paper terminates with some observations on what is called discontinuity, a term
which it is thought is often injudiciously and unnecessarily employed in analysis.
It is suggested that expressions called discontinuous may generally be contemplated
with advantage, as consisting of distinct continuities embraced in a single form. An
instance of this is shown in the consideration of definite integrals of the form
A tm a which are treated by Poisson, ‘in the eighteenth cahier of the Journal of
—™m «
the Polytechnic School, but whose conclusions are, by this mode of viewing the —
integral, shown to be erroneous. The entire paper will probably be published in the
Cambridge Transactions.
Letter, on the Deviation of Falling Bodies from the Perpendicular, to
Sir Jonn Herscuet, Bart., from Prof. OERsTED.
The first experiments of merit upon this subject were made last century, I think in _
1793, by Professor Guglielmini. He found in a great church an opportunity to
make bodies fall from a height of 231 feet. As the earth rotates from west to east,
each point in or upon her describes an are proportional to its distance from the
axis, and therefore the falling body has from the beginning of the fall a greater ten=
dency towards east than the point of the surface which is perpendicularly below it;
thus it must strike a point lying somewhat easterly from the perpendicular. Still, the i
P b'|
i
TRANSACTIONS OF THE SECTIONS. 3
_ difference is so small, that great heights are necessary for giving only a deviation of
some tenth-parts of an inch. The experiments of Guglielmini gave indeed such a
deviation; but at the same time they gave a deviation to the south, which was not in
accordance with the mathematical calculations. De la Place objected to these expe-~
riments, that the author had not immediately verified his perpendicular, but only some
months afterwards. In the beginning of this century, Dr. Benzenberg undertook new
experiments at Hamburg from a height of about 240 feet. The book in which he de-
scribes his experiments, contains in an appendix researches and illustrations upon the
subject from Gauss and Olbers, to which several abstracts of older researches are added.
The paper of Gauss is ill-printed, and therefore difficult to read; but the result is,
that the experiments of Benzenberg should give a deviation of 3:95 French lines.
The mean of his experiments gave 3-99; but they gave a still greater deviation to
_ the south. Though the experiments here quoted seem to be satisfactory in point of
re the eastern deviation, I cannot consider them to be so in truth; for it is but right to
state that these experiments have considerable discrepancies among themselves, and
i that their mean therefore cannot be of great value. In some other experiments made
_ afterwards in a deep pit, Dr. Benzenberg obtained only the easterly deviation; but
_ they seem not to.deserve more confidence. Greater faith is to be placed in the ex-
periments tried by Professor Reich in a pit of 540 feet at Freiberg. Here the easterly
a
SIS EN
deviation was also found in good agreement with the calculated result; but a con-
i siderable southern deviation was observed. Iam not sure that I remember the num-
_ bers obtained; but I must state that they were means of experiments which differed
( much among themselves, though not in the same degree as those of Dr. Benzenberg.
Professor Reich has published his researches, an abstract of which is to be found in Pog-
gendorff’s ‘ Annalen der Physik.’ After all this there can be no doubt that our know-
ledge upon this subject is imperfect, and that new experiments are to be desired; but
these are so expensive, that it is not probable that they would be performed with all
means necessary to their perfection without the concurrence of the British Associa-
tion. I will here state the reasons which seem to recommend such an undertaking.
1. The art of measurement has made great progress in these later times, and is here
exercised in great perfection. 2. All kinds of workmanship can be obtained here in
the highest perfection. I think it would not be impossible to have-an air-tight cylinder
of some hundred feet high made for the purpose. This would indeed be expensive,
but it would present the advantage that the experiments could be made in the vacuum
and in different gases. 3. With these experiments others could be connected upon
the celerity of the fall and the resistance opposed to it by the air and by gases. Pro-
_ fessor Wheatstone’s method for measuring the time would here be of great use.
_ 4. If the southern deviation should be confirmed, experiments could be undertaken in
_ order to discover in how far this could be effected by magnetism in motion. For this
purpose balls of different metals might be tried. Very moveable magnetical needles,
_ well-sheltered, but placed sufficiently near to the path of the falling bodies, would
_ indicate magnetical effects induced in them.
On certain Cases of Elliptic Polarization of Light by Reflexion.
By the Rev. Professor Powett, V.P.B.A.
__ From the principle investigated by Fresnel, that polarized light changes its plane in
_ reflexion, by a certain law dependent on the incidence, for transparent media, and the
__ extension of a similar law to the reflexion from the second surface by Sir D. Brewster
- (Phil. Trans. 1830), other formule were obtained by the last-named philosopher to
_ express the varied phenomena observed by himself (Phil. Trans. 1841), in the re-
_ flexion of polarized light from thin jilms, in extension of those previously investigated
_ by Mr. Airy and M. Arago. The whole subject was reduced to the principles of the
| undulatory theory by Dr. Lloyd (Brit. Assoc. 1841, Sect, Proc. p. 26), who pointed
_ out the further theoretical result, that owing to the difference of phase or retardation,
_ thus produced in the two portions into which the reflected light is divided, polarized
_ light reflected by a thin plate will in general become elliptically polarized*.
_ * This deduction, though stated in the report given in the Atheneum, is omitted in the
volume of the Association, SR
: BQ
4 REPORT—1846.
It is certain however that in a great number of cases of thin plates examined by
the author of this communication no ellipticity can be detected. Glass superficially
decomposed and giving brilliant tints produces no ellipticity, except in those instances
where it has a decided metallic lustre. Vapour condensed on soaped glass (in the
manner described by Sir D. Brewster), oils of turpentine, cassia, &c. between glass
plates (the upper being slightly prismatic to separate the reflexions), are equally de-
void of any indication of ellipticity. 4
The theory therefore clearly needs some further modification to express the condi-
tions under which the effect may be sensible. _
There are doubtless many cases of thin plates in which elliptic polarization is pro-
duced (as in the films formed by Nobili’s process and by heat, as investigated by the
author of this communication, or again, as in mica which has become laminated, &c.),
but in these cases the modus operandi is well understood; the former arising from the
enormous refractive power, in the latter from the crystalline structure.
In the instance of China ink observed by the author, the ellipticity appears equally,
whether it be in the form of a film or in a solid mass; but it is only seen in the
purest specimens.
In the numerous other cases examined by Mr. Dale it does not appear that any-
thing like films can be supposed; the only condition seems to be the high refractive
ower.
It may still be a question, then, whether the theory proposed independently by M.
Cauchy and by Mr. Tovey be not more easily applicable; since it requires nothing
but the very simple and admissible hypothesis, that the molecules of ether, for a minute
depth within the surface, are unsymmetrically distributed*,
In various substances containing but a very small proportion of metal, ellipticity
has been detected, in addition to those enumerated by the author on a former occa-
sion. Among these are prussian blue, and a specimen of the meteorite from the Cape
of Good Hope, 1839, which contains only about 33 per cent. of protoxide of iron, very
small portions of oxides of nickel and chrome, and a minute trace of metallic iron.
On the Bands formed by partial Interception of the Prismatic Spectrum.
By the Rev. Professor PowEtt, V.P.B.A,
In the discussion} relative to these bands one or two points suggested themselves
which appear to need further remark.
The principal objection was, that according to the theoretical formula, a contrac-
tion of the aperture of the eye or telescope should produce an enlargement of the in-
tervals between the bands, which is not confirmed by experiment.
The author finds that with a contraction down to the twentieth of an inch, though
there is no sensible enlargement of the intervals, yet the bands become greatly more
vivid and distinct, while they extend only over a smaller portion of the spectrum at a
time §.
With the same plate, the enlargement of the intervals appears to depend solely on
the increase in the angular extent of the spectrum subtended at the eye, whether pro-
duced by a greater distance from the origin, a greater prismatic angle, higher di-
spersion, or greater power in the telescope.
The formula involves the ratio of the semieaperture to the distance of an assumed
point on the retina from the geometrical image of the point of light; and this “ dif-
fusion” being no arbitrary supposition, but a direct portion of the theory, it seems un-
reasonable to pronounce it “ untenable” and “ quite inadmissible,’ when the question
at issue is, whether the theory as a whole will apply to the phenomena.
Apart from all theory, when under certain conditions bands are formed equally
whether the plates be applied at one end of the spectrum or at the other, “ polarity”
seems an improper term by which to describe the effect,
* See the author’s Treatise on the Undulatory Theory, &c., p. 33.
+ See Phil. Trans. 1839, i. 86.
t See Brit. Assoc. 1845, Sectional Proceedings, p. 7.
§ Both these results have since been shown to be in perfect accordance with theory by
Mr. Airy.—Phil. Mag. Nov. 1846.
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TRANSACTIONS OF THE SECTIONS. 5
_- On attempts to explain the apparent projection of a Star on the Moon.
By the Rev. Professor PowEti, V.P.B.A.
Some remarks having been brought forward at the last meeting* relative to the sin-
gular phenomenon above named, in which “ diffraction” was referred to as at least
in a general sense likely to afford an explanation, the author of this communication
conceived that some observations he has made might have a bearing on the question.
“< Diffraction” has often been appealed to in cases apparently of the same class,
but in the more strict and limited sense of the term it cannot apply, since both the
conditions and the resulting phenomena appear essentially different.
The phenomena properly ascribed to “ diffraction” exhibit fringes, and suppose the
edge of the intercepting body to be within the area of the rays.
But there are some effects of a concomitant kind which have been less attended to.
One of the most remarkable of these is that described by Newton (Opt. bk. iii. pt. 1.
obs. 5, 6, 7), in which the light admitted through a hole a quarter of an inch in dia-
meter, falling on the edge of an opake body, besides the phenomena since called
“diffraction,” gave rise to long streaks or “trains” of light darting into the shadow
perpendicular to the edge and shown on a screen; or, when the eye was substituted,
producing a /uminous line running along the edge, between it and the first fringe.
The author has repeated this experiment in a different manner, and though in the
original experiment the edge is within the area of the rays, yet a part of the same phe-
nomenon (viz. the line of light along the edge) is seen, even when the edge is beyond
the rays, by the naked eye, or with a telescope.
When the origin of light is reduced to a mere point (as by using the sun’s rays re-
flected from a very small globule of mercury) and the rays are wholly intercepted by
a small circular opake disc at the distance of about 2 inches, so that both the luminous
point and the disc may be seen at once in focus by a small telescope about 12 feet dis-
tant, the bright line is reduced to a luminous patch on the edge of the disc at the part
nearest the luminous point which appeared to extend to a small distance inwards, and
then the rays converging crossed and diverged again faintly. This might possibly be
regarded as affording some experimental imitation of the case of the star: the origin
is not an absolute point; but if it were, the patch of light on the disc might appear
like a projection of its image.
Another explanation has been proposed of the phenomenon of projection, on the
principle that owing to aberration, the star being seen out of its true place, a screen
placed in its érue direction, as the moon, would exhibit the star projected on its disc
(Royal Astron. Soc. Reports, vol. vi. p. 246) ; and taking into account the proper mo-
tions of the stars, this would explain the appearance of the phenomenon in one instance
_ and not in another, on the supposition that those proper motions are in opposite direc-
tions in the two instances. But this will not apply in the very instance to which re-
ference has been made, of the two stars 119 and 120 Tauri, which have proper motions
both in the same direction ; also, the principle of this explanation is rendered ques-
tionable altogether from what has been lately suggested by Prof. Challis on the theory
of aberration.
The whole subject is perhaps not yet ripe for explanation, since the first astro-
nomers are so much at variance as to the facts, the appearance having been frequently
seen by one observer and not by another; while it is believed by some to occur or
not, according as the attention is directed to the moon or to the star; which, if true,
would seem to point to some ocular cause. Hence a further accumulation of in-
stances is much wanted, any statements of which the author of this paper would be
thankful to receive addressed to him at Oxford.
On Elliptic Polarization. By Mr. Date.
The paper which I have to read to the Section relates to some new observed facts
in the subject of elliptic polarization, which appear to point out the physical element
on which depends the different action of metals on light, as compared with transparent
substances in general. They have already been communicated to the Ashmolean
_ Society at Oxford, but I have been induced to bring them forward at present, with a
* Brit. Assoc. Report, 1845, Sect. Proc. p. 5.
6 REPORT—1846.
view of more readily gaining for them the notice of those interested in optics. This
peculiar action, it will be remembered, is of this kind: first, that the metals (and
metallic sulphurets, &c.) have no angle of complete polarization for common light ;
and secondly, that a plane polarized ray becomes elliptically polarized after reflexion
from their surfaces, whereas it remains plane polarized after reflexion from glass and
such like bodies. Endeavours have naturally been made to account for these phzeno-
mena on the principles of the undulatory theory ; and always, apparently, on the suppo-
sition that the laws of reflexion from transparent (uncrystallized) bodies were already
rigorously given by Fresnel’s formulz, but that a new and distinct theory was required
for metallic reflexion: thus assuming that the two classes of phenomena were ab-
ruptly separated, without any intermediate links of connexion. It has, indeed, long
been known that several transparent or translucent substances have no angle of com-
plete polarization. Thus Biot (Traité de Physique, iv. 288) has excepted sulphur
and the diamond; and Sir John Herschel (Optics, Art. 845 ; see also 831) excludes
from the general rule, besides the metals, those substances which have the adamantine
lustre; which term is applied, in Mohs’s system of crystallography, to several of the
minerals to be presently spoken of, as resembling the metals in another respect. I
do not know that any writer, except Mr. Green (in Camb. Phil. Trans. vol. vi.), has
stated this exemption to be general for all substances having a high refractive index;
but it is important to recall this experimental fact to our attention, on account of its
coincidence and harmony with the new result which I have now to state. It consists
in this: that these same highly refractive substances resemble the metals also in a
second respect—that they confer elliptic polarization on a plane polarized ray reflected
from them. The following list of substances, in which this property was observed,
will be found to contain most of those at the top of Sir D. Brewster's list of refractive
indices :-—
Indigo—which is remarkable for possessing the metallic lustre without con-
taining any metal.
Artificial realgar.
Diamond—of which three specimens were tried.
Sulphuret of zine in transparent crystals.
Glass of antimony—translucent.
Sulphur—melted on a polished slip of zine foil.
Tungstate of lime—transparent.
Carbonate of lead in crystals, clear and limpid as glass.
Hyacinth, or zincon—translucent.
Arsenious acid.
Garnet.
Idocrase.
Helvine.
Labrador hornblend.
Of which the last five possess the property in a very slight degree only. The test
used in every case was the dislocation of the rings of a plate of cale spar; of which a
very good specimen was used, capable of exhibiting eight or nine red rings: and all
the experiments were made by candle-light, which is indispensable, It will secure
greater confidence in these results to say, that all the specimens which I submitted to
Prof. Powell’s examination, in a different instrument, were found by him to produce
the above effect; and from his published observations several more cases may be
quoted in confirmation of the general result: such are—chromate of lead, litharge,
plumbago, and Indian ink. The natural conclusion from these facts appears to be,
that in a perfect mathematical theory of reflexion, both cases should be embraced in
one set of formule, of which some terms or coefficients should be insensibly small,
except when the refractive index was very large ; that, strictly speaking, no substances
completely polarize common light at any angle, but that the residue of unaltered light
is too feeble to affect the eye, when the refractive index is below a certain limit;
and that plane polarized light always becomes elliptically polarized, but that the vir-
tual difference of paths of the two compact vibrations parallel and perpendicular to
plane reflexions is insensibly small, except the refractive index surpass a certain value
greater than the refractive indices of felspar and sapphire, which I found to produce
no dislocation of the rings. It is remarkable, that such formule have some time
TRANSACTIONS OF THE SECTIONS. 7
since been deduced from a very profound mathematical investigation by Mr. Green,
in the Cambridge Philosophical Transactions, vol. vii—whose results, however, do
not seem to have met with much attention. Now, however, that they have met with
the above undesigned general confirmation, it seems very desirable that they should
be compared with the numerical results of experiments of Sir D. Brewster and Prof.
Powell. Mr. Green adopts, as part of the basis of his calculation, the original view
of Fresnel,—that the vibrations of a polarized ray are perpendicular to the plane of
polarization ; but as this point is a matter of dispute amongst mathematicians, I have
thought of an experimental method by which this point might, as I think, be decided,
independently of all theory. Itconsists in the observation of the shifting of the fringes
produced by two pencils of light polarized in the same plane on interposing in their
paths a piece of compressed glass. This last apparatus is to be constructed in the
following manner :—A strip of clear plate, 4 or 5, inches long by half an inch broad,
is to be provided; and its narrowest faces (or narrowest long sides of the parallelo-
piped) are to be carefully polished, and rendered perfectly plane and parallel to each
other,—at least, in the middle part of their length, through which the light is to pass,
And the glass must be so well annealed and so free from striz as to allow of the for-
mation of fringes by interfering pencils which have traversed it. It is to be provided
with a wooden frame and screw, capable of compressing it in the middle, [A similar
apparatus has already been employed by Brewster, Ling, and Pouillet, to show that
glass under pressure possesses double refraction.] We may now proceed to the ex-
periment itself. Let us suppose, then, that the arrangements have been made in a
darkened room for producing the interference of two pencils of light, which are to be
polarized in the same plane, by passing, for example, through the same tourmaline
plate. This arrangement might, in fact, be that of Fresnel, in which a slender beam
is reflected from two glass plates very slightly inclined, provided that the light were
incident at the polarizing angle of glass. And, for the sake of clearness, let us suppose
the two foci, or virtual foci, to be vertically one above the other, the plane of polari-
zation to be vertical, and the glass to be interposed with its length horizontal, Then,
in its natural state, it will produce no displacement of the fringes, if made carefully
after the above description. But let us consider what will be its effect if interposed in
its bent state. The elasticities on its convex and concave sides are different in this
respect, that the particles are dilated or compressed parallel to the length of the glass ;
whereas little or no alteration of elasticity is produced in a plane perpendicular to the
length of the glass. Hence if the vibrations of the two polarized pencils are really
executed perpendicularly to the plane of polarization, or parallel to the length of the
glass (according to the arrangement above agreed upon), they will be propagated
with different velocities, and the fringes will be displaced paralle] to the length of the
glass, in a direction which might be inferred from some statements of Sir D. Brewster,
but which is quite unimportant to the present purpose. If, however, on the other
hand, the vibrations be executed in the plane of polarization, or perpendicular to the
length of the glass, the two rays will traverse the glass with almost, or quite the same
velocities, and the fringes will either not be displaced at all, or to a far less amount
than in the preceding case.
Notice of a New Property of Light exhibited in the Action of Chrysammate
of Potash upon Common and Polarized Light. By Sir Davip BREewsTER,
KL, FRS. .
The Chrysammate of Potash, which crystallizes in very small, flat rhombic plates,
has the metallic lustre of gold, whence it derives its name of golden sand. When the
_ . sun’s light is transmitted through the rhombic plates it has a reddish yellow colour,
and is wholly polarized in one plane. When the crystals are pressed with the blade
of a knife on a piece of glass, they can be spread out like an amalgam. The light,
transmitted through the thinnest films thus produced, consists of two oppositely polar-
ized pencils,—the one of a bright carmine red and the other of a pale yellow colour,
With thicker films, the two pencils approach to two equally bright carmine red pencils,
It is to the reflected light, however, and its new properties, that I wish to direct the
attention of the Section. Common light, reflected at a perpendicular incidence from
the surfaces of the crystals, or of the films, has the colour of virgin gold, It grows
less and less yellow as the incidence increases, till it becomes of a pale bluish white
8 REPORT—1846.
bs
‘
colour at very great incidences. The compound pencil, thus reflected and coloured,
consists of two oppositely polarized pencils,—one polarized in the plane of reflexion,
and of a pale bluish white colour at all incidences; and the other polarized perpendi-
cular to the plane of reflexion, and ofa golden yellow colour at small incidences, passing
successively into a deeper yellow, greenish yellow, green, greenish blue, blue, and
light pink, as the angle of incidence increases. This very remarkable property, which
I have discovered also in some other crystals, is not caused by any film of oxide formed
upon the natural surface of the crystal, nor is it the result of any change produced
upon the surface by external causes. It is exhibited, under the usual modifications,
if the surface of the chrysammate is in optical contact with fluids, and, by pressure, with
’ glass :—and when the crystal is in the act of being dissolved, or when a fresh surface is
exposed by mechanical means, the superficial action of the crystal upon light is in both
cases the same. When the chrysammate is re-crystallized from an aqueous solution, it
appears in tufts of prisms of a bright red colour, the golden reflexion being overpowered
by the transmitted light ; but when these tufts are spread into a film by pressure, the
golden yellow colour reappears. When the crystals of chrysammate are heated with
a spirit lamp, or above a gas burner, they explode with a flame and smoke like gun-
powder ; and, by continuing the heat, the residue melts and a crop of colourless amor-
ee th is left. I have found the same explosive property in the Aloetinate of
otash,
Description of a Portable Equatorial Stand for Telescopes without Polar
Axis. By Ricwarp Greene, M.D.
All previous attempts to produce equatorial motion have (the author believes) been
based upon the notion that the telescope should revolve upon a material axis, which
of course must be adjusted parallel to the axis of the earth. The principle also is
bad, inasmuch as the telescope is supported near the centre, and the moving power is
applied to that point, instead of the extremity of the tube.
In following any of the heavenly bodies either to the east or west of the meridian
with the common stands mounted with altitude and azimuth movements, the observer
is obliged to keep them both continually in action to prevent the object getting out of
the field of the telescope. As the effect of these two powers acting at right angles to
each other is to cause the tube to move in the diagonal between them, it occurred to
the author that it would be more simple and equally efficacious to employ only one
moving power in the direction of that diagonal, and thus obtain the same motion by
one screw, which before was obtained by the two screws worked together. He also
remarked that when the object is passing the meridian, for a certain time it will re-
main in the field of view by moving the azimuth screw alone.
The essential principle of the invention is simply to be able to place the horizental
or azimuth screw in all situations of the heavenly bodies in a position similar to that
in which it is placed when an object is passing the meridian, viz. parallel to a tangent
of the circle the body is describing and touching the circle at the point where the body
then is. The common azimuth screw fully answers the purpose when the body is on
the meridian, as the tangent is then horizontal. When the body observed is to the
east of the meridian, as it is then rising higher every instant, and at the same time
moving westward, all that is required is to point the adjustible screw, which the author
calls the equatorial screw, upwards from the observer to such an angle as appears to
be parallel to the path the body is describing, which, from its altitude and distance
from the meridian, can be pretty nearly guessed by an astronomer. If he has ele-
vated the screw to the proper angle, the body will remain very nearly in the centre
of the field of view during the time he is following it through the length of the screw.
Tf, however, it appears to sink in field, it shows that the screw is not sufficiently ele-
vated, and that it rises faster than the axis of the telescope, and he must raise the
remote end of the screw a little more; if the star rises in the field, of course it shows
that the screw is too much elevated. By two or three trials the angle may be found
in less than a minute. If the body viewed be to the west of the meridian, the remote
end of the equatorial screw is of course to be depressed, pointing downwards from the
observer.
The principle of this equatorial movement is easily applied to many of the stands
now in general use, as well as to the Herschel stand, on which the author first tried it.
TRANSACTIONS OF THE SECTIONS. 9
Having no stands of his own, except the Herschel stand, (and this certainly defec-
tive in stability, in consequence of the great mirror being unsupported except by the
tube, upon which it acts through a long and powerful lever of agitation,) Dr. Greene
turned his attention to the construction of some simple stand based upon the principle
of stability which the triangle affords, and presented a model of his first attempt to
attain that object.
In this arrangement the heel of the telescope hangs by two pivots upon two Ys
fixed to the upper surface of a flat circular disc, which revolves upon another similar
disc, by means of a pin in the centre; the lower disc stands upon three very low feet to
ensure its stability. The upper or eye-end of the telescope is attached by a pin to an
equatorial slide. ‘The pin is united to a slide which moves parallel to the tube of the
telescope at its under side, and being moved by a rack and pinion, gives the slow
elevation movement. The equatorial slide is supported by a pair of shears, capable
of being lengthened or shortened at pleasure, to effect the quick motion in altitude.
The legs of the shears rest upon the two extremities of a sliding piece moving by rack
and pinion in the groove of a piece of mahogany or other hard wocd in the shape of
the letter T, supported by three very low feet to ensure its steadiness. The sliding
piece is moved by a long handle attached to the pinion, and gives the slow azimuth
motion to the entire stand. To unite the different parts into one system, the piece
which supports the shears, and the lower circular disc which supports the heel of the
telescope, are attached by two bars with hooks at each extremity, the bars being
themselves bound together by two diagonal braces.
It will be seen at a glance, that the telescope and its stand form one great triangle,
while each of its parts is a minor triangle; that the great mirror is solidly supported,
having no tendency to disturb any part of the fabric by its disposition to be moved by
any slight external force.
On an easy Method of contracting the Aperture of a Large Telescope.
By Henry Lawson, .RS., FRAS., &e.
It is well known to the practical astronomer, that in using a telescope of large
diameter it is needful to contract the aperture of the object-glass when measuring
binary stars, &c., and also when the haziness of the atmosphere demands such con-
traction. The mode adopted is the adaptation of a brass tube, 6 to 12 inches long, to
the eye-end of the telescope tube, in such a manner that it may slide out and in with
facility. Into one end of this tube the eye-pieces of the telescope must screw (or
what is better, slide). Within this tube is to be placed a moveable diaphragm, made
to slide up and down the tube by means of a slit and stud. The diaphragm is to be
pierced with an aperture of such size as just to let the whole cone of rays proceeding
from the object-glass pass through it towards the eye-glasses, when the diaphragm is
drawn down or stands near to the eye-piece. When the aperture of the object-glass is
required to be contracted, the diaphragm must be slid towards the object-glass, and it
wiil have the effect of circumscribing the cone of rays to any required diameter. The
benefits resulting from the above-described plan are the following: that the astro-
nomer can with the greatest facility and without moving from the eye-end of his tele-
scope, adjust or contract the aperture of the object-glass to any required diameter ;
he can vary the magnifying power without shifting or deranging the aperture; and,
lastly, he can produce these benefits without fear of altering the adjustments, or
turning the telescope from the object in view.
On the Arrangement of a Solar Eye-piece.
By Heyry Lawson, F.RS., F.R.AS., &c.
This arrangement does away with the inconvenient and dangerous breaking of the
dark glass when viewing the sun through telescopes of large size, and enables the
astronomer to view the sun with the whole aperture of his telescope, however large it
may be; thus giving an immense advantage when scrutinizing the wonderful and
most interesting appearances of the solar disc. The method consists in placing the
dark-glass or glasses within the telescope, by means of a brass tube supported between
the object-glass and the eye-glass of the telescope, the tube being from 3 to 18 inches
(according to the length of the telescope), measured from the eye-piece, to which
10 REPORT—1846,
it is to be attached. By this means the cone of rays proceeding from the object-glass
towards the eye-glass is intercepted by the dark glass at a considerable distance from
its focus, or most heating point, and thus the heating power of the rays, being spread
over a large surface of the dark glasses, passes through without injuriously heating
them, and enters the eye in a cool and agreeable temperature. Another benefit de-
rived by this arrangement is, that the cell holding the dark glass may be made to con-
tain several glasses; and those may be of different colours; whereby an opportunity
is afforded of repeating the valuable experiments of Sir John Herschel on transmitted
light through different coloured media; and also attempering or adjusting the inten-
sity of the light entering the eye to the sensibility of the retina. Another benefit is
obtained, that of using various magnifying powers with the same dark glass arrange-
ment with the greatest facility.
On the Meteorological Observations at Kew, with an Account of the Photo-
graphic Self-registering Apparatus. By F. Ronaups, F.RS.
Mr. Ronalds, on presenting his third annual volume of observations and experi-
ments made at the Kew Observatory, described his experiments on the photographic
self-registration of the electrometer, the barometer, the thermometer and the declina-
tion magnetometer ; explained his existing apparatus for these purposes, and exhibited
the resulting photographs, but first briefly adverted to his previous proposals in 1840
and 1841, and experiments in 1844, relative to the subject. The principal charac-
teristic of his improved system is a peculiar adaptation of the lucernal microscope.
An instrument of this kind was employed in July 1845 to register the variations of
Volta’s atmospheric electrometer. The pair of straws were properly insulated and
suspended within the body of the microscope and towards its object-end. A con-
densing lens was placed at the end itself, and a good lamp stood beyond it. A strong
light was therefore projected upon those sides of the straws which were turned towards
the condensing lens, and the other sides were in deep shade. The light also impinged
upon a little screen fitted into the back of a case about two feet long, fixed to the eye-
end of the microscope at right angles with it, and vertically. Through this screen
was cut a narrow curved slit whose chord was horizontal and radius equal tothe length
of the straws, Between the electrometer and the screen a combination of achromatic
lenses by Ross was adjusted to produce a good chemical focus of the electrometer, at
a distance as much beyond the external surface of the screen as the thickness of one
of the plates of glass to be presently mentioned. In the long vertical case was sus-
pended a frame about half the length of the case, provided with a rabbet, into which
two pieces of plate glass could be dropped, and these brought into close contact by
means of six little bolts and nuts. The frame could be removed at pleasure from the
line by which it was suspended, and the line, after passing through a small hole stopped
with grease at the top of the long case, was attached to a pulley about four inches in
diameter on the hour arbor of a clock. Lastly, counterpoises, rollers and springs
were used for ensuring accurate sliding of the frame, &c. A piece of Mr. Collen’s
photographic paper was now placed between the two plates of glass in the moveable
frame ; the long case was closed so as to prevent the possibility of daylight entering it,
the clock was started, and the time of starting was noted. All that part of the paper
which was made to pass over the slit in the screen by the motion of the clock, became
now therefore successively exposed to a strong light, and was consequently brought
into a state which fitted it to receive a dark colour on being again washed with the
usual solution, excepting those small portions upon which dark images of the lower
parts of the straws were projected through the slit. These parts of course retained
the light colour and formed the long curved lines or bands, whose distances from each
other, at any given part of the photograph, i. e. at any given time, indicated the
electro-tension at that time. Sometimes daylight was used instead of the light from
a lamp, and in that case, during the process, some appearances of the sky were occa-
sionally noted, by which it was evident that in serene weather, when the sun’s light
and heat varied, and the paper became consequently either more or less darkened,
the electric tension, as shown in the photograph, varied also, increasing with the in=
. crease of light, &c. This fact has not perhaps been before observed, but as the dark-
ening effect on the paper could not be always depended upon, separate notes were
taken of the intensities of light and the same results obtained. At the suggestion of
TRANSACTIONS OF THE SECTIONS. ll
the Astronomer Royal, a distinguishing electrometer, formed on the dry pile system,
was afterwards employed, which exhibited in the photograph, not only the tension,
but the kind of electricity possessed by the electrometer at any given time. The dry
thermometer was next tried. It was of the horizontal kind, had a flat bore, and its
tube was introduced through the side of the microscope. The tube had a diaphragm
of very narrow aperture fixed upon it, and the slit in the screen, at the eye-end of the
microscope, was now of course straight and horizontal. The image was a little mag-
nified, and the breadth of the dark band or line in the photograph became the mea-
sure of temperature inversely at any given time*. ~The barometer employed was of
the siphon kind. The microscope was turned in order to bring the long case and its
sliding frame into a horizontal position. The clock was placed at one end, and a
little weight, sufficient to keep the frame steady, was suspended by a line passing over
a pulley at the other. The lower leg of the barometer was introduced through the
now bottom of the microscope; it was provided with a similar kind of diaphragm to
that on the thermometer, and of course the slit in the screen was now vertical. A
light blackened pith-ball rested on the surface of the mercury, and its image was
slightly magnified, but will in future be much more so. The declination magnet was
one of two feet, lent to Mr. Ronalds by the Astronomer Royal. It was provided with
a damper, and its mode of suspension was essentially similar to that of the Greenwich
declinometer. In order to adapt it for self-registration, a light conical brass tube,
projecting six inches beyond its north end, was affixed to the lower side of the spur
which carried it, and to the north end of that tube a small wire, called the index, was
attached at right angles. This index descended through little slits in the bottoms of
the two cases which enclosed the magnetic, and took the place of the electrometer
in the lucernal microscope, which was placed below the cases, and was now required
to be much longer than before, in order that the image and motion might be suffi-
ciently magnified, yet a flat field retained. Everything was firmly fixed upon the two
pillars which formerly carried the transit instrument of His Majesty George III, A
great many photographs were obtained and sent for inspection to Greenwich. Con-
cerning some term-day impressions, Mr. Glaisher, the Magnetical and Meteorological
Superintendent of the Greenwich Observatory, says, in an official note, that “the
beautiful agreement of the results with these at Greenwich is highly satisfactory.”
On some Meteorological Phenomena. By Professor WARTMANN.
Although many attempts have been made of late to extend our knowledge of ‘the
electrical phenomena of the atmosphere, it must be confessed that much remains to
be done. The frequency of the flashes of lightning, according to the latitude to the
seasons, is a subject of inquiry which has been recommended.by M. Arago. It
would also be interesting to record the duration of thunder-storms, the number of
flashes of each of the three classes which have appeared, the height and general
appearance of the clouds, and the hygrometric state of the atmosphere. ’
I shall take the liberty to point out some facts which I had occasion to witness on
the evening of the lst of August last. After many hot days, clouds appeared on
the south-west part of the horizon of Lausanne, and when over the town they began
to become illuminated almost without interruption. I counted more than forty flashes
in twenty-two minutes, two-fifths of which were of the first class, and all going
eastward.
A flash, of such a white byilliancy that the eye could not bear it, but the appear-
ance of which was perfectly definite, did not disappear suddenly, but left a florescent
trace of a dark red colour, like to the illusions of the dissolving views and the trainées
or trails of certain shooting stars which I observed on the night of the 10th of
August 1838.
Another flash of the first class appeared at the under part of the clouds, and after
a rather long course, it vanished at the very edge of it: no thunder was heard.
Two flashes were bicuspidated ; three others were tricuspidated at some distance from
their origin, two of which appeared together, one over the other, in the same hori-
* Tn order to convert this into the wet bulb hygrometer, nothing of course is necessary but
the application of the usual cup of water and the capillary threads.
12 REPORT—1846.
zontal position. Are those flashes as scarce as it is generally believed? Are they pro-
duced by a particular state of humidity which makes the state of the air better
conductors in many given directions simultaneously than in others? This I am not
able to decide; but I think that the quantity of rain which happens to fall during a
thunder-storm has a great influence upon the falling of the electric fluid. Indeed, in
a recent instance, a thunderbolt fell in a low part of a vintage near Lausanne,
burning all the stems on an area of more than eighty feet square, during a shower of
the most tremendous character, and without being attracted by more elevated con-
ductors which were at a short distance; and, on the contrary, two years ago, during
a storm which was accompanied by no rain, the thunder fell on a neighbouring situa-
tion, and burned by ricochets, stems here and there, upon a surface of more than
four acres.
Dr. Lee presented the following tables to the Section :—
1. Meteorological Observations for the year 1845, made by J. R. Crowe, Esq., the
British Consul-General of Norway, residing at Christiana. These tables are a con-
tinuation of others made in 18438, and presented to the British Association at York,
and of similar tables made in 1844, and presented to the Association at Cambridge,
and which are noticed in the volume of the Proceedings for 1545, at page 19 of the
abstracts of communications to the Section of Mathematics and Physics. They con-
sist of observations of the barometer and thermometer, and of the direction of the
wind, made on nearly every day in the year 1845, at the hours—7 a.m., 9 a.M., 2P.M.,
4 p.m., and 10 p.m., with the means of each column for each month, and the mean tem-
perature of each month. The depth of snow is given for the months of January,
February and March, in cubic inches; and the quantity of rain in cubic inches for each
of the other months of the year.
2. Meteorological Observations made at Alten in West Finmark, at the Kaafjord
Meteorological Observatory, in the years 1844 and 1845, by J. F. Cole, Esq. and
J. H. Grewe, Esq., of the Alten Mining Company. These tables are a continuation
of others for the year 1848, presented to the British Association at York, and which
have been deemed worthy of notice by Colonel Sabine, who has referred to them in
a note on his paper on the Meteorology of Bombay, at p. 80 of the Report of the Pro-
ceedings at Cambridge, in the volume published in 1845. These tables contain the
height of the barometer and thermometer, in shade, at 9 a.m., 3 p.M., and 9 P.M., with
the maxima and minima of the thermometer at 3 p.m.; the quantity of rain or melted
snow; the force and direction of the wind, and of the clouds, and the description of
clouds, and the proportion of clear sky at the same hours. To which are added,
tables of the half-hourly results of all the above observations on the 21st and 22nd of
each month in the year.
3. Observations on the Aurora Borealis during the year 1845, made at the Kaaf-
jord Meteorological Observatory at the Alten Copper Works, by J. F. Cole, Esq. and
J. H. Grewe, Esq. These tables contain observations upon the position and the
degree of intensity, and the forms of the aurora, which have been made by these zeal-
ous amateurs of meteorology during the months of January, February, March and
April, September, October, November and December; no observations being practi-
cable during the summer months, on account of the brighiness of the daylight during
this portion of the year.
On a New Anemometer. By Dr. BAnks.
The instrument is worked by a vane supported on a hollow wooden shaft about
two inches diameter and three feet long, whose upper end is supported by slight
friction rollers, and the bottom rests on a steel point.
Each of two levers holds a pencil, one for the direction of the wind, working
in a spiral of three turns, which by a very simple contrivance returns to its position
if the wind moves round the compass with frequency. The other lever is acted upon
by the force-board attached to the vane, and which, in its retirement from an in-
creasing wind, raises a series of weights together with a disc, upon which, by a roller,
the lever rests. ‘The instrument is about 24 feet long by 2 feet high, exclusive of the
vane, which is attached to a tin tube of length according to circumstances.
EFS
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TRANSACTIONS OF THE SECTIONS. 13
Meteorological Observations. By Capt. W. W. CHILDERS.
Taste A.—Meteorological Observations, Saint Helier, Jersey, deduced from Hourly
Observations taken by William Walbanke Childers, late Captain in the 42nd Royal
Highlanders, assisted by Mr. John B. Le Roy, Optician; from the Mean of four
barometers and three thermometers. The extremes noted by a perpendicular Self-
Registering Thermometer eighty-five feet above the mean level of the sea. Soil
gravelly clay. Latitude 49° 11’ N., Longitude 2°06’ W.
Height of Thermometer Daily prevailing Wind. Barometer.
2 &
Joie] lel-ldi@] og | 4 : g
Jel JEL IE > = 2
silulalalelejeleia| 2 | g@ | 38 | 4
inches. inches.| inches.| inches,
52|50/49/48)45| 4¢ g| 2] 4| 5] 3\..}..| 2] 30 | 29°65 | 30°15 | 28°30 | 29°40
39|41)40139|39|36) 39°0|49|24| 36°5| 4}15| 4] 5)..]..)..]..|..| 3] 31 | 29°65 | 30°05 | 28°65 | 29°35
42|44)49/41/41|39] 41°5|/49|32] 40°5| 3] 3] 3) 5] 1} 7] 3] 3] 1) 2] 31 | 20°55 | 30°00 | 98°60 | 29°30
38]41/38/38/38/35| 38°5|49|26] 37°5| 2/19] 1] 2! 1] Q)..| 4] 2| 2) 28 | 29°60 | 30°25 | 29°35 | 29-80
39]42)39|38/36/35| 38°0|55|25] 40°0| 5]12]..|..| 2] 3] 2} 1) 5) 1) 31 | 29°65 | 30°35 | 29°05 | 29°70
46}44| 49°0}65|39] 52°0| 1|12/..] 4!..] 4] 4) 3] 2)..) 30 | 20°45 | 29°90 | 28°65 | 29°95
49|46| 51°7|70/41| 56°0) 5} 6)..) 1] 1} 4] 2} 8] 4)..}) 31 | 29°70 | 30°30 | 29°25 | 29°75
56/54] 60°0|77/40| 58°5) 2) 6} 1) 2) 1] 4] 8} 5] 1)..] 30 | 29°90 | 30°45 | 29°30 | 29:90
57|55| 61°0/79|48} 63°5)..}..| 6) 5]..|10) 4} 4] 2)..} 31 | 29°70 | 29°90 | 29°30 | 29°60
58|56/54| 59°5|69|43| 56°0) 3] 2) 1) 2)..| 4/11} 8). 31 | 29°70 | 30°20 | 28-90 | 29°55
56/55/53] 58°0|72/44] 58°0)..|11) 1) 2]..| 8} 5} 2} 1)..) 30 | 29°60 | 30°00 | 29:00 | 29:50
55|58/54/52/51|40| 53°5/68/41| 54°5| 2] 6] 1| 7) 1] 3) 5} 3) 1] 2] 31 | 29°90 | 30°35 | 29°05 | 29°70
51/54151/49|48)45| 50°0|79|24| 51°5/31187/26|37/11|54|47/41\19]12|365 | 29°65 | 30°45 | 28°30 | 29°35
50)54/51/49|48/46} 49°5/58/37] 47°5). .
'46)40147|46)45/43] 46°0|56)31]43°5) 1) 1|..
45]49]45|45|44/43] 45'0/54|32/ 43°0|..
46/48]46/45]44)43) 45°0/57|31| 44°0} 2) 5
'46|50|47/45144|42! 45°5|54|/32/ 43'0) 2) 3}..
50/53/51/48/47|44) 49°0/59/34) 46°5| 2) 5
Taste B.—Meteorological Observations, Saint Helier, Jersey, taken by Captain
William Walbanke Childers, for the year 1846, with a Comparative Table ot’ the
difference in Temperature between that place and the Horticultural Gardens at
Chiswick, as reported in the Gardeners’ Chronicle. St. Helier, 49° 11! N. Chis-
wick Gardens, 51° 20'N.
Comparative Table.
‘Thermometrical Observations. Direction of Wind. a eee eee
fey Difference between
Ghiswicie | Tesey as Ohlawitie
23 Sper e lh Sis
23) ¢ 3 : glsis] ¢|/ $$] 8] 4
ololslalulel & eel 2 |e lSielai.. JE) 3/4) S)el2] 3] S| 2) 8
4] 4 EA] & 14) a) ala Elazlelol a |e/S] S| Be] a] 4
1846. |o}ololololol o
Jan, |45/49/45/45/44/43 45-0|5al32 43:0)... al vAe 5] 1 5| 31 {56/21 44-3|— 21401 +07
Feb. |46/48/46)45/44/43) 45°0/57/31| 44°0/ 2] 5) 1) 8]. 3) 5 1} 28 |64/24| 40°2!|— 7/+ 8] +4'8
Mar, |46/50|47/45|44/49] 45°5/54|32/ 43°0/ 2] 3}..| 7]... peyl3 31 (62/20] 43'°4)— 8}-+12) +2°1
Apr. {50 salsilssla7|44 49°0|59|34| 46°5| 2 |. 5]..] 9}... 217 30 |65/29|47°8) G/+ 5) +12
May { Giga ere ae a 13] 2} 5]. 2] 1 31 |g1/34] 52°3
June 68|73\70|68|65 63 68°0)80]57} 68°5]..|15)..] 2).. ++|--| 2} 1] 30 93/43] 70°0}—13/+14] —2°0 |.
July |66)69|68|65)\62'59) 65°0/81\49| 65°0}..|..) 4) 5).. 3}... | 2)..| 31 |92/44) 66°4)—11/4+ 5} —1°4
Aug, 65\6a\66\63|61150 63°8/79] 2] 65°5|..| 8} 1] 1] 1 1} 6} 2] 1] 31 (92/44) 61°6}—13/+ 8] +22
Sept. |63/67/64/61 sols8 62°0|74|50} 620}, . |16]..} 1).. 4} 1) 3} 2} 30 |78)40| 60°0}— 4)+10| +2°0
Oct, {54}57|55/53/52/50) 53°8/64/41) 52°5}..} 4/ 1] 2) 1 6] 3} 4] 1] 31 |67\29] 49°5|— 3)+12| +3°0
Noy. |47/49|48)46/46/44] 46'3/61/31| 46°0}..|10] 1] 7) 1 1} 1] 1} 30 |61/16| 39°4)+ 0)/+15] +8°0
Dec. |31/49/39/38|38/35] 38°5/50)25 |37°5| 1116)..|..|.. 1] 7} 1)..{ 31 44/11] 31°0)+ 6]+14) +6°5
Aver. |53|57|55)52/51/49| 53'0/61/25 |52°5| 7/95/10|54| 3/107 |27|35\15|13/365 g3\11| 51°6|—19|-+14 +1'0
14 REPORT—1846.
From the above comparative table, it appears that Jersey, although within a comparative
short distance of London; enjoys a far more equable temperature, neither undergoing so great
a degree of heat nor exposed to so extreme cold. This ina great measure arises from its
position, and the great rise and fall of the tide, upwards of forty feet between the levels at
high and low water, spring tides and the nature of its soil; a rich loomy clay with gravelly
subsoil. In June and July, for instance, the temperature in London reached 93°, in Jersey only
81°; whereas in December the thermometer in London fell to 11°, in Jersey no lower than 25°.
Jersey is a very moist climate, §.W. winds having prevailed: 107 days during the year, and
the quantity of rain fallen being nearly double that at Chiswick.
Taste C.—Meteorological Observations, Saint Helier, Jersey, for the year 1844,
commencing in November 1843, before taking the Observations hourly, by Captain
Childers.
Direction of Wind.
5 GI Pe a) Ss Oe Sains hae PE er a nee Se rar ee eee ee ee
Thermometrical Observations.
|e
9)2}5]s\n a
1843, }o}/olOlolojola jolo|lo inches.| inches.| inches.| inches.
Noy. |48|52|49]48)47|44| 48+4]58|29) 43°5}..| 5] 1] 2] 1] 8) 3) 4) 6|..| 30 | 99-40] 30°10 | 28°80 | 29°45
Dec. |46/49|47]46,45/43| 45°5|53/39) 42°5|..| 5] 2} 6|..| 4] 1] 4) 3] 6) 31 | 30°10] 30°30 39°80 30°05
ood 145}47|46|46145/41| 45°0|54/31| 42°5| 3] 9] 1] 3|..} 4] 1] 8) 1] 1} 31 | 29°00 | 30°00 | 28°70 | 20°35
Feb. |42/44/42/4)/41/38] 41°5|52/26) 39°0| 3) 6j..] 1] 1) 5) 6) 5) 2}..| 29 | 29:00 | 29°65 28°15 28°90
- |Mar, |46}49/47|45/44/40| 45°3/62/26] 44-0] 1} 6) 5] 2] 2) 5) 4! 6)..]..| 31 | 99°95 | 30°10 98°50 29°30
April |54]59}56)51/48/44] 51°7|75|36) 55°5| 4/11) 3] 1) 2) 2) 3) 2) 1) 1) 30 | 99°70 | 30°15 29°10 29°60
May. |54|57/55|52)49}45| 52°5|67\40| 53°5| 6/20] 1)..}..|--|..| 3) 1]..] 31 | 29°60 | 29°95 | 29°30 | 29°65
June |59|62|61|59/57/53] 58°3/71/46] 58°5|..| 3] 4] 1] 1/14] 4) 1) 2)..) 30
July |63|67\66 63160 57| 62-6\e7\5a| 70-0] 1) 5| 2] 5| 1| 6| 5| 5| 1|..| a1 | Observations not to be de-
‘Aug. |62\67|64/61|59|55] 61-3|76|51| 63°5| 4| 5) 3]..| 1] 6] 5) 3) 4)..| 31 pendetupin, Wea
Sept. |63168167|64\62|57| 63-s|79\50| 64-s| 5{12| 6 2|..| 2|..| 2 1}..| 30 |/y taken during my absence,
Oct. |56)59/57|55|54/51| 55°2/65/40| 52°5] 1) 5; 2} 3) 6) 8) 1) 4)..] 1] 31 | 29°10 | 20°85 | 28°25 | 29°05
Aver. |53/57|55/53/51|47| 52°6/87/26) 54°7/28/92/30/26)15|64 33/47/22 9/366 sie 28°15 | 29°40
Taste D.—Comparative Temperature Table for the years 1843, 1844, 1845. and
1846, taken by Captain Childers at St. Helier, Jersey, Latitude 49° 11’ N.
1843. 1844, 1845. 1846,
a ie 2 3 a|¢ zs] ¢ :
o o =| o — | . o 3S | 5 o 2 os
BIE E/ 81 S| EF) #1) 8 [Sl El a] EL Sl Ears
gixlal|<] & 8 a 4 j|/m)/A} a 4 - | | apes 4
° ° °
March} 60) 32] 46°0)42°0) 62 26 44°0|} 45°3| 55} 25) 40°0| 38°0; 54] 32) 43°0] 45°
April | 58] 37)47*5|}49°0) 7 36 55'5| 51°7| 65) 39] 52°0| 49°0| 59] 34) 465} 49°0
June 68} 48)58°0|60°0| 71 46 58'5| 58°3| 77) 40} 60°0| 60°0| go} 57| 68°5| 68°0
July 74| 56) 65:0) 63°0| 987 53 70°0| 62°5| 79| 48] 63°5| 61°0| 81} 49] 65:0] 65°0
Aug. 81} 60) 70°5| 660} 76 51 63°5| 61:3| 69| 43) 56°%0| 50°5| 79| 52) 65°5| 63'8
Sept. | 79} 47) 63°0| 65-0) 7 50 64°0| 63:5] 72| 44| 580| 58°0| 74] 50) 62°0| 62°0
Oct. 70| 30\ 50:0] 56°0) 69 40 52°5| 55°2| 68] 41) 54°5| 53°5| 64) 41] 52°5} 53°8
Nov. 58| 29) 43°5|}48'5| 59 32 45°5| 48'7| 58] 37| 47°5} 49°5| 61] 31) 46:0) 46:3
Dec. 53} 32) 43°5} 45°5| 49 24 36°5| 3970] 56) 31) 43:5] 46°0| 50) 25) 37°5) 38'S
Ayer. | 65] 40 38 0| 52'°3 52'7
Differ.|- 1|+ 1
i
be
ie
f
We
tm
a
=<
TRANSACTIONS OF THE SECTIONS, 15
Taste D. (continued).
REMARKS.
B)el|.:
=| &| &| 8 | Hottest day, 23rd July 1944. Ther. 879,
Hi] Al =| < | Coldest day, 5th March 1845, Ther. 25°,
i heal Ue 2. . HOTTEST MONTHS.
Sie August 1843...... 66°
Feb. |52'2|28°2/41'0/40°0 September 1844 .. a
58'0|290 149"2 |49° July 1845 ........ 1
eset i anal June 1846........ 68
April 64°5 |36°5 |50°0 |46°5
May |69°0|410|53"0 [520 COLDEST MONTHS,
+0 140°0 |61°0 |62* February 1843.... 37°
“he vaiee Verb tae Hitete December 1844 .. 39
July |78°0|51°5|64"0 |63°0 March 1845 ...... 38
Aug. |76:0/52*5 |63°5 |63-0 February 1846.... 45
. |76°0|47°0/61'0 \62°
Ga ae Bar Hottest year ..........05 1846,
pete 68°0 |37°0 |53°0 |65°0 Coldest year .......+...5 1845.
| ° “0 |33°0 |45° ‘
Pays (678 a id 52° Average Mean Temperature. May 1843,
Dec. |63°0 |31°0 |42°0}44°0) April and May 1844, and May 1845, repre-
——|——|—|-_ | sent the Mean Temperature,
Aver. |64°0|39°0 |52°0 |52°0
Taste E.
From a series of observations, commenced in 1826 and continued to the present
period, it is observed that the most rain falls in November, the least quantity in April.
The ratio of the year is as follows :—
November, July, September, October, December, January Rainy months,
August, February, March, June, May, April ..... seseeeseee Dry months.
The observations which complete the record for 1846, have been forwarded by the
Author since the Meeting.
Notices of a Halo, Paraselene and Aurore Boreales. By the Rev. T. RANKIN.
The halo occurred on Sunday, October 12, 1845, at 5 p.m., at Huggate in York-
shire; it formed a portion of an ellipse above the sun, which was in a focus of the con-
jugate diameter of the ellipse. The inner part of the are was most luminous.
In the evening of the same day occurred a paraselene, from 7 to 10 p.m.; its dia-
meter was about 20°, and the inner part of the arc was most luminous.
On the evening of October 6, 1837, January 3, 1840, and August 29, 1845, aurorz
were noticed at Huggate.
Method of Measuring the Height of Clouds.
By the Rev. W. Wuewe 1, D.D., F.R.S.
I do not know whether it has been observed how easily the height of clouds ma
be measured when the reflexion of them can be seen in a lake from a station above it.
In that case the angle of elevation above the horizontal plane for any selected point
of a cloud is not equal to the angle of depression of the image ; for the latter angle is
the angle of elevation of the cloud at the point of the take where reflexion takes place,
and is therefore greater than the former. The difference of these two angles gives us
the means of finding the height of the cloud. If « be the angle of depression of the
image of the cloud-point, 6 the angle of elevation, and h the vertical height of the
station of observation above the level of the lake, it is easily shown by trigonometry
that the height of the cloud above the level of the lake is
h sin (w + #)
sin(« —#)
The angles « and 3 may be measured by any contrivance for measuring elevations
and depressions; for instance, a graduated quadrant with a plumb-line, or hanging
alidade, and plain sights. No great accuracy is attainable or is needed in this inquiry
Hence a table of double entry (there being two elements, « and @) would be a conve-
16 REPORT—1846.,
nient mode of determining the multiplier of %. But the multiplier varies rapidly
with variations of « — 6; more slowly with variations of « + 6. Hence it would be
convenient that a table should be arranged for small intervals of « —@ (say 1°, or be-
low 1° to 15!), while larger intervals for « might suffice, as 5°. Hence this might be
the form of the Table (or rather these the numbers to be calculated :—
And for intermediate values, the multipliers would be given by interpolation. But since
the result depends so much upon the value of « — 8, it would be desirable to observe «— 6
directly, rather than by taking the difference of two observations. This may be done
thus: take a dark cup full of water, and place it so that the surface of the water in it
is seen at the cloud-point reflected in the lake. Also place it so that the boundary of
the water in the cup when it falls upon the cloud-speck is in the vertical plane passing
through the speck. Then the horizontal edge of the cloud-speck, seen in the lake andin
the water-cup, will be dislocated, and the amount of dislocation subtends the anglea—f
at the eye. Hence a— may be measured directly on the limb of the quadrant; or a
micrometer affixed to the alidade of the quadrant for the purpose of measuring 2—8
may easily be devised. The same formula and process may obviously be applied to
measure the height of a mountain when h is known. If the height of the mountain
be known, # may be deduced by the same formula. Without knowing 4, the formula
will serve for comparing the height of a cloud with that of a mountain, when both can
be seen in the lake. The arc a— will usually be very small, and will vary as its
sine ; and in this case a+ will be 2« nearly. Hence, in comparing clouds and moun-
sin2 «
a— p
seen very near the mountain top are inversely as the dislocations in reflexion. If the
mountain image be dislocated three times as much.as the cloud-image, the cloud is
three times as high as the mountain. If the altitude be different—for example, if the
mountain be 15° and the cloud 45° elevated, and the dislocation still as 8 and 1, the
height of the cloud is six times the height of the mountain (for, sin 2x 15°=%,
sin2x45°=1). The same is the case of different strata of clouds. When seen in
the same quarter, their heights are inversely as the dislocation of their images.—N.B.
Perhaps a piece of glass ruled with parallel equidistant lines held at a given distance
from the eye would be a good way of comparing dislocations of images.
tains, their height will be as Hence the heights of a mountain and of a cloud
On the Force of Vapour. By Captain SHorTREDE.
The author adopts the experiments of the French Academy at high temperatures,
and those of Magnus at low temperatures, as being the most carefully performed
and the most extensive of all yet available. In the Academy’s experiments, the in-
dications of the smaller thermometer in the steam are preferred to those of the larger
thermometer in the water; because the temperature of the water increases with its
depth, and always exceeds that of steam formed at its surface, besides the heat
which may be necessary to overcome the cohesion of water in passing into vapour.
TRANSACTIONS OF THE SECTIONS. 17
It is probable, also, that the temperature of the steam in the manometer was, from
exposure to the air, less than that of the steam in the boiler, so that the small ther-
mometer may be expected to give the temperature too high rather than too low.
An Account of an Atmospheric Recorder. By G. Dotionp, F.R.S.
It having appeared to be desirable at the last meeting of the British Association
that a correct self-registering apparatus should be constructed, by which the various
changes of the atmosphere should be recorded upon paper, in such manner that they
might be referred to at a future period, I have the pleasure to describe an apparatus
which records the indications of the following eight instruments, viz. the barometer,
the thermometer, the hygrometer, the electrometer, the pluviometer, the evaporator,
the force-board, and the anemometer, in relation to time. I have found it answer the
purpose for which it was intended, in every way satisfactorily, 1st. The barometer
registers the change which takes place in the weight of the atmosphere at every half-
hour, and the line may be traced from one point to the next without any difficulty.
2nd. The thermometer registers the various changes from cold in the night or morn-
ing, to the greatest heat in the afternoon, continuously. 3rd. The hygrometer is
adjusted to show the changes from dryness to extreme saturation of moisture to every
hundredth of the scale, and is extremely steady in action, 4th. The electrometer is
acted upon by a conductor, and registers each flash of lightning which comes within
the range of the conductor, 5th. The pluviometer registers the drops of rain which
fall upon the surface of the receiver, and shows the continuation of the falling quan-
tity until an inch is received; this is then discharged and the process recommences
for another inch, and so on continually. 6th. The evaporator is so constructed as to
retain a quantity of water with the surface exposed, and so guarded that rain cannot
enter into the vessel. The surface gradually evaporates, as shown by a diagonal line
upon the paper until an inch is evaporated, when a discharge takes place and another
line commences. 7th, The force or power of the wind acts upon a board one foot
square, whose movement is registered in pounds and ounces avoirdupois, from one
ounce to thirty pounds. 8th. The direction of the wind is shown in circles, which
immediately upon inspection show the direction of the course or change which has
taken place, for instance, if it has passed through the south or the north, from east to
west, and the point from which it started and that to which it returned. All these
eight varieties have their scales about half an inch from the marking-points, and can
be very easily read or referred to. There are markers on each edge of the paper for
time, the paper being carried forward by a clock.
Mr. Dollond gave an account of the storm, as shown by this instrument, at Cam-
berwell on the 1st day of August 1846, during his absence :—
The barometer changed from............... 30°03 inches to 29°82 inches,
The thermometer FFOM.......000002s+- 69° to 98°
during the day, or twenty-four hours.
The hygrometer ranged from 39° to 80° of moisture.
At two o'clock the electrometer was affected by the lightning, and registered fifteen
discharges or flashes in one hour.
At 35 23! the rain commenced falling, and in two minutes the pluviometer dis-
charged an inch, which had previously stood at 11°90 for several days. At 4° 3!
"another inch was registered, and at 55 25!’ a third inch was marked upon the regis-
tering paper ; and so tremendous was the fall of rain and hail, that at 5% 35! a fourth
inch was marked upon the paper, making on the whole 3°12 inches in 25 17’.
The force of the wind was equal to one pound four ounces, and the direction
changed from east to west, through the south at 3" 20'.
On the Construction of a Self-registering Barometer, Thermometer, and
Psychrometer. By C. Brooxe, MB.
"Mr. Brooke remarked that he had been induced by the want of efficient means of
automatic registration of the variation of meteorological instruments, and especially
of magnetometers, which was so generally expressed at the last meeting of the British
—«*1846. c
18 ‘ REPORT—1846.
Association at Cambridge, to bestow some attention to the subject, and was enabled
to report to the meeting that he had succeeded in devising a method of continuous
registration with as much accuracy as the purposes of science require.
Various mechanical means have been proposed for the registration of all meteoro-
logical instruments except the magnetometers ; but the amount of magnetic force is
so small, that the variations of its intensity and direction are incapable of actuating
any mechanism, and therefore can only be expected to be recorded by the aid of
photography ; and by these means the proposed object had been accomplished: as
however a detailed description of the apparatus by which magnetic variations have
been registered is already in the hands of the Royal Society, Mr. Brooke did not con-
sider himself authorized to enter into a description of it, further than is necessary to
explain those modifications of the apparatus which formed the subject of the present
communication. A piece of prepared photographic paper is placed between two con-
centric cylindrical glass surfaces, which are carried round their common axis, placed
horizontally, by the hour-hand of a time-piece movement. The paper consequently
passes vertically behind a horizontal slit in a case of suitable form in which the
cylinders are enclosed to protect the prepared paper from the influence of diffused
light. A cylindrical refractor, the axes of whose surfaces are parallel to the slit, is
placed in front of the slit, and at such a distance from it that the rays of light falling
on it may be refracted to a focus on the paper. In the case of the magnet, a sphe-
rical concave reflector is attached to a stem by which the magnet is suspended, and a
camphine lamp having a vertical narrow slit in the chimney is placed at such a dis-
tance from it that an image of the slit may be formed at the distance of the paper ;
a portion of the image is condensed vertically by the cylindrical refractor, and im-
presses the photographic paper. Some registers obtained by this apparatus were
exhibited to the Section, from which the position of the declination magnet might be
determined by a scale with a probable error not exceeding 10", and in some, not ex-
ceeding 5".
In obtaining the register of the barometer, a lamp is placed in front of the appa-
ratus, and a screen with a narrow vertical slit attached to the end of the long vertical
arm of a lever is interposed between the refractor and the horizontal slit before de-
scribed. This lever is balanced, anda short horizontal arm rests on a float supported
by the mercury in the shorter tube of a siphon barometer; the lengths of the arms of
the lever having been taken as 10 to 1, the variation of the height of the column will
be magnified 5 times, and the light passing through the point at which the two slits
cross, will trace out a line sufficiently distinct to indicate the height of the barometer
at any period to the =4,th of an inch.
The registration of the thermometer and psychrometer was obtained by interposing
the stem of these instruments with a flat bore, wide enough to exclude the light, be-
tween the slit and the refractor ; as however this expedient is not new, it need not be
more particularly described; the only novelty in Mr. Brooke’s apparatus was in
placing the stems of the two instruments on opposite sides of the cylinder, so as to
obtain a register of both on the same paper, and in making the bulbs long narrow
cylinders instead of spheres, in order to increase the surface and consequently the sus-
ceptibility of changes of temperature. By having each degree about 3th of an inch
long, the temperatures may be obtained at any time to jth or oth of a degree.
Table of the Fall of Rain in the Lake Districts of Cumberland and West-
moreland, &e. in the Year 1845. By J. F. M1Luer.
The writer exhibited a series of registers in a tabular form, from which it resulted
that at Seathwaite there have been 31 days in which the fall was between 1 and 2
inches, five days between 3 and 4 inches, one day between 4 and 5 inches, and one
day between 6 and 7 inches. ;
On the 27th of November, 1845, there was measured at Seathwaite 6:62 inches,
and on the 26th and 27th nearly 10 inches, being the greatest quantity of rain which
has ever been measured in the same period in Great Britain. At Langdale Head in
Westmoreland, the fall on the 27th was 6:28 inches, and on the 26th and 27th nearly
9 inches.
TRANSACTIONS OF THE ‘SECTIONS, 19
The consequence was the heaviest flood which had occurred at these places for at
least sixty years past.
Windermere Lake had not been so high for the last fifteen years; on the night be-
tween the 26th and 27th it rose 2 feet in perpendicular height; the quays along the
banks of the lake were immersed in water, and much wood was carried away by the
current and lost. Keswick Lake had not been so high since November 30th, 1838.
Of the total quantity of rain, measured in the vale of Borrowdale in 1845, 106-58
inches fell in the months of January, March, August, October, November and De-
cember; and nearly 46 inches in the two latter months.
Such was the violence of the storm on the night of the 28th of December in the
lake districts, that a number of fish were found next day on the margin of Bassen-
thwaite Lake, which had been thrown up by the waves in the course of the night by the
force of the wind,—a circumstance wholly without a parallel, except on the night of the
memorable 6th of January, 1839. The rain which fell in the preceding twenty-four
hours amounted to 4:22 inches; at Whitehaven the quantity was °323, or nearly one-
third of an inch.
Through the kindness of various gentlemen I am enabled to add returns of the rain
in 1845, from several places throughout Great Britain, by way of comparison with the
quantities measured in the lake districts.
inches.
Allenheads, Northumberland ......ssseeeseseesseeerseee S6'411
Kendal, Westmoreland ............. See daae seereveee 00'S46
Cartmel, ditto.....++.s+.- ar eeaadnae's Seba ita cla aes tad sala 3 53°665
Rampside, ditto ...ssescseeeeeeseeees Rae ete tale vaciae’d 40-289
Tivil, ditto ...ssecccceceees aeiaaesene errors Soaenitsbdalels eee 40°000
Bolton-le~Moors......+++ seaawevaadeus Sacekgevan waa deeoenae 48:110
Carlisle, Cumberland..........s.+0+ Bi scala ca tiorsta S08 hea ees. 31°280
Brougham Hall, ditto .....ssesseeseeeee iia Wan aheaawenuas 35:000
Manchester...... seh geste eas arial site aah eats tea socevece: 44°415
Doncaster. .........000s pita usledha tists bydeicpangene he vaunres 29198
Highfield House, Nottinghamshire ......... Sunde neice va 29°595
Girencesten)sdo.cassccony ccsernasenadatedeasaace NM ieevadaesatali 251 OO
Leeds ........ Settee desadess ius dane sundae aa esscarpeederene 25°586
North Shields............ i sear da lea Sane pW iedvavadcemaese 26:200
Culloden, Inverness, N.B....... de Migtet od: ub ivideadvess < 27°632
Applegarth Manse near Lockerby, N.B. .......c2c00e . 30°32
Arbroath, Co. Angus, N.B. ......s0esee0 eis gees Maas 28-211
Liverpool ........4+ Aree arch ac cotener er core apie Rearherrree 34:06
*)| pStratton, Cornwalhi.icsdelevcidesaccvacsane Me Weces aware 40°89
Uckfield, Sussex........se000+ Betis atin caieny cacteitscsaeatas 25:08
Empingham, Rutlandshire ...........secsesesscseeeneees 24°61
Helston, Cornwall ............:sceeecessseeeeees bce ceases goeSD
Kelso, Roxburghshire, N.B.......... BS Sod caeeteseet 24°42
Makerstoun, near Kelso ......sceccscancesseceenscnsenses 21:27
The fall at Seathwaite is more than 3 times the quantity measured at Whitehaven,
one of the wettest éowns in the kingdom. It exceeds the fall at Leeds by 6 times; at
_ Culloden by 53 times; at Doncaster and Highfield House, N ottinghamshire, by 5 times;
__ at Cirencester and Arbroath by 54 times; and at Makerstoun near Kelso, the seat of
Sir Thomas Brisbane, Bart., by more than 7 times.
Seathwaite exceeds Doncaster, in January, by 15 times ; in November by 21 times ;
and in December by 9 times. It exceeds the quantity at York, in January, by 16
inches, or 20 times; in March by 9 times; and in November by 20 times. It ex-
ceeded Dublin, in March, by 14 times; in April by 13 times; in October by 5 times;
and in November by 7 times.
The quantity measured at Seathwaite and Langdale Head, in the month of De-
_ eember (24-02), is more than falls at some places in Great Britain during a year.
_ Mr, Miller said, “ It is much to be regretted. that the meteorology of our lake and
- mountain districts should have been so long neglected. Prior to the establishment
of these gauges, there were none stationed in the lake district of Cumberland, and, so
_ far as I am aware, only two among the lakes of Westmoreland, viz. one at Esthwaite
. c2
20 REPORT—1846,
Lodge, and the other at Grasmere; and the largest quantities measured in any year
were 86 inches, and 90 inches respectively. And so startling did these results appear
to meteorologists, when first made known, that many were led either to doubt their
authenticity, or to suspect the accuracy of the instruments employed.
“ But subsequent investigation shows that these values are exhibited in some por-
tions of the lake district of Cumberland only in the very driest years. Thus, in the
period from July 1844 to June 1845 (which for drought has only found a parallel in
the memorable 1826), the fall at Gatesgarth and Wastdale Head amounted to 83°96
and 88°42 respectively, and at Grasmere in Westmoreland to 74 inches nearly. But we
suspect that meteorologists will hardly be prepared for the discovery, that we have
localities in our own country, which, even in average years, exceed the amount of rain
annually deposited in many tropical climates; yet such is the almost incredible fact.
At Grenada, lat.12°5', the average fall is 126 inches; at St. Domingo, lat. 18° 20’, it is
120 inches; and at Calcutta, in lat. 22° 35’, it is 81 inches. In the past year the
quantity measured in the vale of Borrowdale exceeds the largest of these amounts by
25°87 inches. An inspection of a map of the country in connection with the table
will show, that the wettest portions of the lake district are those situated at the head
or eastern extremity of those valleys formed by our highest mountain ridges, amongst
which are the Great Gabel, Sca Fell, Glaramara, Red Pike and Honister; the first
being apparently the grand central point of attraction and condensation for the warm
vapour atriving in a south-westerly current across the Atlantic; and it is a remark-
able coincidence that nearly all our lakes bear in the direction of Gabel, so that if ex-
tended onward in a direct line, they would all converge at the base of this noble
mountain.
“‘ Immense as is the deposit of rain at Gatesgarth, Grasmere, Wastdale, and in other
portions of the lake district, even these enormous quantities sink into comparative in-
significance when compared with the fall at Seathwaite, a small hamlet at the head of
the vale of Borrowdale, which exceeds the wettest of the other localities by 27°74 inches,
or by one-fourth nearly. Now it is chiefly the deposit in the vale of Borrowdale which
supplies the majestic river Derwent and the extensive and picturesque lakes of Der-
went and Bassenthwaite, so that we might @ priori have expected to find the greatest
amount of rain in this section of the district.
“ The great difference in the fall between places closely contiguous to each other is
very remarkable: the proportion which obtains between Ennerdale lake, and a farm-
house about 11 mile distant, is as 2 to 1 nearly. x
“« Loweswater, Buttermere and Gatesgarth are all in the same line of valley, sur-
rounded by the same ridges of mountains, and are each distant about 2 miles from the
other. Buttermere exceeds Loweswater by 18 inches or one-fourth; but Gatesgarth,
at the head of the valley, exceeds Buttermere by 36°65 inches, or nearly one-half. Here
the difference between the head and foot of the valley, in a distance of 4 or 5 miles, is
54°588 inches.
“ But the great increase in the fall towards the head of the valleys is appreciable at
much more limited distances. At Wastdale Head I have two gauges of precisely the
same size and shape, and within a quarter of a mile of each other, yet the difference
of the receipts in a single month sometimes amounts to half an inch.
“ The annexed statement will show that the excess is always in favour of the higher
gauge marked No, 1.
1845. No. 1. No, 2. Diff.
October ......| 12°35 | 11-89 | -46
November ...| 12°31 11:90 “41
December ...| 16°18 15°78 40
1846.
January ...... 12°97 12°47 50
February ...| 6°60 658 | :02
March ...... 10°35 10:07 28
April ....... | 659 | 616 | -43
May sec] 3°65 3:44 | -21
TRANSACTIONS OF THE SECTIONS. 21
“ The current of vapour is apparently only partially decomposed in passing over a
flat or even an undulating country; it aims at once for the loftiest heights, passing
over the less hilly districts with little diminution of its original weight or volume. But
on reaching the mountain peaks, the sudden change of temperature causes a rapid and
continuous condensation in the form of vast torrents of rain, whilst comparatively
little descends on the adjacent plains.
“« As an instance of the low temperature on our mountain tops, I may mention that
on making the ascent of Skiddaw, on the 5th of September last year, the thermometer
on the summit, at noon, stood at 41°; sky overcast, the sun gleaming out at intervals.
The temperature of a strong spring, about 2 miles from the summit, was also 41°.
The temperature of the air at the foot of the mountain, at 35 30™ p.m., was 58°.
“« Snow not unfrequently continues on Sca Fell till the middle or end of June; we
remember seeing a patch on the 15th of June, 1843; and on the neighbouring moun-
tains the air was so intensely cold that we think it could not be more than 2°or 3° above
the point of congelation. That the rapid increment in the fall of rain in approaching
mountainous districts is owing to the causes above alluded to, and not to the greater
number of wet days, is evident on an inspection of the table, where it will be found
that we have as many wet days at Whitehaven near the level of the sea; indeed it
rarely rains in the lake districts, that the day is not also wet, more or less, at the coast.
“« And in comparing the number of wet days at various places, we not unfrequently
find them to obtain in the inverse ratio to the fall of rain; thus, in 1845, they range
from 195 to 211 in the lake district; but at Manchester, with a fall of 41 inches, they
amount to 235; at Culloden, with a fall of 27 inches, to 237; but at Kendal, where
the quantity of rain is 53 inches, the wet days are only 178.
“ At Carlisle the wet days are the same as in the lake district, where the fall is four
times as much.
‘© We are informed by a gentleman recently returned from India, who was many
years medical attendant to the Rajah of Sattarah, that he seldom measured more
than 40 inches of rain in the plain, but among the hills 30 miles distant, the annual
cal reached 350 inches; and as much as 9 inches has been known to fall in 24
ours.
“ The utility and beauty of this arrangement is obvious, since the mountain torrents
afford a continuous supply of water to the lakes and rivers, which otherwise could
scarcely have an existence, The rivers thus called into being aid the efforts of the
husbandman by carrying off the superfluous moisture from the plains, which, without
such a provision, would be in danger of stagnating into pestilence.”
Readings of Mountain Gauges, June, July and August 1846.
By J. F. Mitier.
Feet above Sea. June, July. August,
inches. inches. inches,
Whitehaven * ........006 100 2°311 9-061 4:066
Scilly Banks, near ditto.. 500 27103 8626 | 3-465
Sea Fell Pike............ Fis 3166 5:000 | 14-380 7°050
Great Gable ..... a ecreded 2925 7:60 16°870 § 650
Sparkling Tarn....... ase 1900 6°55 22°730 | 12-030
Stye Head Pass ...... vee 1250 6°26 17°760 | 11:080
Valley (Wastdale)... .. oee 160 5°33 16820 | 8-960
Seatollar (Borrowdale) ... 1850 5°79 18°350 8:150
Valley (Seathwaite) ...... 300 6:29 22°125 | 10°480
In March, April and May, the higher gauges received less rain than the lower; in
June the reverse of this is the case, owing doubtless to the greater elevation of the
nimbi or rain-clouds in the warmer months, and especially when the air is highly
charged with electricity, as was the case last month.
* On the spire of St. James’s Church, eighty feet above the street, 1°680.
22 REPORT—1846.
The number of gauges in the lake districts, in addition to the above, is twelve,
most of which are read off daily.
It would appear from the average results since April last, that the amount of rain
increases from the valley upwards, to an altitude of about 2000 feet, and gradually
decreases above that elevation; thus the gauge at Sparkling Tarn (1900 feet) almost
invariably receives more than any other of the gauges; much however depends upon
the position of the mountain with respect to the prevailing wind; thus the gauge on
Seatollar (nearly the same elevation as Sparkling, but bearing nearly due north) in-
variably receives Jess rain than the valley at the end of a month; nevertheless, mea-
surements made at short intervals, when a north or north-west wind had prevailed,
show that it sometimes receives considerably more.
Fall of Rain on the Coast of Travancore and Table Land of Uitree, from Ob-
servations of M. General Cullen, Resident in Travancore. By Lt.-Colonel
Sykes, F.R.S.
At former meetings of the British Association I have had the means of submitting
to the Physical Section facts illustrative of the meteorology of portions of Western
India, particularly at great elevations, such as at Mahabuleshwur, near Sattarah,
at the height of 4500 feet above the sea, and at a distance of about 30 or 40 miles
inland. It was shown that the fall of rain in one monsoon was of the prodigious
amount of 302°21 inches, or more than 25 feet depth of water. At a similar height
at Merkara in Coorg, about 5° of latitude S. of Mahabuleshwur, and in about the
same longitude, and at 65 miles from Cananore on the coast, the mean fall of rain
for the years 1838, 1839 and 1840, was 143-35 inches. Communications from my
friend General Cullen, the British minister at the Travancore court, enable me to ex-
tend the meteorological observations, at least as far as relates to temperature and the
fall of rain, to Cape Comorin, supplying also data for a comparison of the fall of rain
on the coast and at short distances inland, at a considerable elevation. I may state
that we are indebted for the present communication from India to the stimulus oc-
casioned by the publication of the Mahabuleshwur and Merkara observations in the
volumes of the Association. General Cullen’s letter to me is dated Cochin, the 27th of
July 1845, and he states that he had been in the habit for many years past of observing
the meteorology of his location, wherever that might be, but that the pressure of his
public duties had disabled him from reducing and arranging the observations, parti-
cularly the barometrical. He had, however, been enabled to transmit to the govern-
ment of Madras, statements of the fall of rain along the western or Malabar coast of
Hindoostan, from Cape.Comorin in Travancore, lat. 8° 4!, to the town of Cochin and to
Panlghatcherry, in lat. 10° 45’, as well as at several inland stations in the provinces of
Cochin and Travancore; and in the Company’s district of Tinnevelly, on the east side
of the Ghats, for the years 1841, 1842 and 1843. These statements were accompanied
with explanations which I shall shortly notice. In the year 1841 the stations selected
in Travancore were 5; but the observations did not commence at Nagercoil, Trevan-
drum and Quilon, before the month of May; and at Allepy and Cochin in the month
of June. The stations on the east side of the Ghats were 3; at Vaurioor the obser-
vations commenced in June, at Shenkotah in July, and at Palamcottah not before
October. As the observations are not for equal periods, I shall confine myself to ob-
serving that both the Malabar and Coromandel coasts appear to have been subjected to
both monsoons, the S.W. and N.E. rain having fallen at all the stations in the months
of October, November and December, as well as in the usual S.W. monsoon months of
June to September inclusive. In the year 1842 the stations in Travancore and Cochin
were extended to 8, and the observations were for the whole vear, with the exception of
Tritchoor and Chittoor, where they did not commence until May, and at Koravantava-
lum, where they did not commence until August. At the three former stations in Tin-
nevelly the observations were for the whole year. In this year, although both mon-
soons appear to have operated upon both coasts in the months of August, September,
October and November, yet in the month of December rain only fell on two days on the
Travancore coast, and only five times at Palamcottah on the opposite coast. The same
discrepancies exist with respect to the months of January, February and March, rain
having only fallen on thirty-eight days at all the eleven stations together, on both coasts,
TRANSACTIONS OF THE SECTIONS. 23
during those three months. In the year 1843 Cape Comorin is added to the eight stations
in Travancore, and the observations at all the stations are for the whole year. AtCape
Comorin, at an elevation of fifty feet above the sea, we have the singular fact of not a
single shower having fallen in the months of February, March, April, August and No-
vember, months belonging to both monsoons; and the fall for the whole year at Cape
Comorin was only 19:2 inches. At Palamcottah, on the Coromandel side, there was
not a single fall of rain in the months of June, July, August and September, and only
1 and 3 and 1 and 4 falls respectively in the months of February and March, at all
the stations in Tinnevelly. The total fall at each station exhibits a rapid increase in
quantity, in increasing the latitude, as is shown by the annexed tabular statement.
TRAVANCORE.
Cape Comorin,| Nagercoil, | Treyandrum, Quilon, Koravantava- Allepy,
50 feet 150 feet 130 feet 30 feet lum, 300 feet 30 feet
above sea. above sea, above sea. above sea. above sea. above sea.
Ce ee ee EO
From May
only, 1841j ... | .... | 73 | 46:8 |103 | 86:07 | 124/ 94-76] ... | ... 1140) 96:8
1842)... | ... | 63 | 385°7 | 97 |57-7 |131| 81:06] tmecomplete | 168} 104:5
1843 | 32 | 19:2 | 71 | 42:6 124 85°45 | 121 |105-7 2 129-0 | 184 | 131-85
CocuHIn. TINNEVELLY.
Cochin, Tritchoor, Chittoor, Shenkotah, | Palamcottah,} Vaurioor,
20 feet 60 feet 400 feet 600 or 700 feet 200 feet 60 feet
above sea. above sea. above sea. above, sea, above sea. above sea.
From May From Oct.
28 | 3)-48)} 20 | 14:57} 29 | 18-05
only, 1841}124| 77:3
Incomplete.
Incomplete.
1842 | 119} 105-27} 129| 104-4 | 82 | 52-3 | 51 | 39:45) 71 | 23:1 | 60 | 20:27
1843 | 138 | 124-49) 115} 80-15/108} 68:6.| 68 | 48:1 | 58 | 26:9 | 66 | 25-75
It exhibits also the fact of the total fall on the Coromandel side bearing no compari-—
~ son to that on the Travancore side. or instance, at Shenkotah, at the east base of
the Ghats, sixty miles from the sea coast of Travancore, and about eighteen miles due
east of Koravantavalum on the west side of the Ghats, and forty miles from Quilon, the
fall of rain at Shenkotah was 48-1 in. in 1843, and at Koravantavalum 129 inches,
both places being at a considerable elevation. Palamcottah again is in the latitude
of Quilon, is sixty miles from the western coast, and thirty miles east of the chain of
Ghats. Here the fall of rain was 26-9 inches in 18438, while at Quilon, on the western
coast, the fall was 105-7 inches. Cape Comorin and Vaurioor are placed in the same
category, but the former is in Travancore and the latter in Tinnevelly, the latter
being only three miles N. and a little E. from the former; but the difference is 63
inches of rain in favour of Vaurioor. The next feature is the singularly limited
fall of rain at Cape Comorin and Vaurioor, both of them situated at the extremity of
the peninsula of India, and both freely expesed to the first action of both monsoons,
N.W. and S.E., and yet the amount of rain is not one-fifth the amount of that which
falls at places on the Travancore coast, a few miles N.W. Nagercoil is the next sta-
tion to Cape Comorin and comes into the same category, but it is nine miles inland,
and though so near to Cape Comorin, has a fall of rain more than double that of the
Cape. The next feature is the great and progressive increase in the fall of rain which
takes place at the respective stations as they lie north-westward from Cape Comorin,
along the western coast. Trevandrum, Quilon and Allepy, are apparently under nearly
similar physical circumstances on the coast, yet the first in 1843 had only 85 inches,
the second 105, and the last 131 inches of rain. Chittoor, which is fifty-five miles in-
94. REPORT—1846.
land E. from Quilon, and in the gorge of the great gap in the Ghats at Palghat, which
opens to the Coromandel coast of ‘Tinnevelly, and on the high road it might be said
of the aqueous vapour of both monsoons, had only 68 inches, while Allepy, on the
open coast, had 131 inches, and Cochin 124 inches. The fall is greatest on the sea
coast, diminishes at stations inland to the foot of the Ghats, but, as I shall have oc-
casion to show, increases enormously on ascending the Ghats to their plateaus or table-
lands. u
General Cullen says it is difficult to attempt explanation of the differences in the
amount of rain exhibited in his tables; but he offers some remarks on the winds and
physical structure of the country as necessarily influencing the distribution of rain.
The peninsula of India, as is known, is in a triangular form, the apex of which is Cape
Comorin. The western Ghats in maps appear to run continuously without break from
Cape Comorin to the 24 or 25° of latitude N.; but such is not the case. The land
within the apex of the triangle to Palghat, a distance of 150 miles, rises precipitously
into a table land 2000 or 3000 feet high, with peaks and masses attaining an elevation
of 5000 or 6000 feet. It has at its sides a narrow low tract of land on both coasts. In
the latitude of Palghat, this table land suddenly terminates in a chasm or gap forty
miles long by thirty miles broad, without a single hill or ridge. There are other gaps,
but of less marked character; in one of these stands Shenkotah. It might be supposed
the continual passage of aqueous vapour through these gaps would continually drench
them; but such is not the case, as the vapour passes through only partially condensed ;
for Chittoor, which is at the western gorge of the Palghat gap, has only 68 inches of
rain and Shenkotah only 48 inches; both however have rain in every month of the
year, excepting February at Chittoor, and in the month of November, at both places,
there was only one fall of rain. The paucity of rain at Palamcottah, General Cullen
attributes to the intercepting of the vapour of the western monsoon by the table lands
of Travancore. But this does not explain the paucity of rain at Cape Comorin and
Vaurioor, which are open to both monsoons; and why should they not be deluged at
least by the S.W. monsoon as well as Allepy or Cochin?
General Cullen made the observations which I have adverted to without a view to
the illustration of any particular meteorological phases or phenomena ; but observing
the publication in the annual volume of the Association of the extraordinary fall of
rain at high elevations, as at Mahabuleshwur and Merkara, he was induced to ascer-
tain whether a similar fact obtained on the high lands of Travancore. He therefore,
on the 23rd of June 1844, established a pluviometer at a spot called Uttree Mullay.
thirty miles E.N.E. of Trevandrum, at an elevation of 4600 feet above the sea
(about that of Mahabuleshwur), and continued his observations simultaneously with
others at Trevandrum and Quilon on the coast until the end of December. The fall
of rain on the table land was 164 inches, while the fall at Trevandrum and Quilon
respectively was only 36 and 363 inches. The variation of the monthly mean tem-
perature at Uttree Mullay was only from 64° to 67° Fahr., and at Trevandrum from
772° to 782° Fahr.
Temperature. Rain.
Uttree Mullay, | Trevandrum, | Uttree Mullay, | Trevandrum, Quilon,
4600 feet. 130 feet. 4600 feet. 130 feet. 30 feet.
1844, TEE A. A oe :
June 23 to 30 66 78h 73 Y3
July <..ccusccess 67 78 263 53
August.......+ 64 782 23 63
September ... 66 783 24
October ...... 66 784 41% 14
November ... 65 774 363 3}
December ... 64 78 23 3+
Total...... 653 78k 164 36
SE
SEP.
==
TRANSACTIONS OF THE SECTIONS. 25
have been much greater; but as it is, it is sufficiently remarkable*. Above 100 inches
of the rain which fell at Uttree Mullay occurred in the months when the $.W. mon-
soon is considered to have ceased on the western or Malabar coast, and may there-
fore be said to belong to the N.E. monsoon of the Coromandel coast, There appear
to have been two occasions when the fall of rain was remarkable in twenty-four
hours. On the 10th of October there fell 9 inches, and on the 26th of November
there fell 7°35 inches; but there also fell from the 6th to the 10th of October inclu-
sive, 29°4 inches, averaging nearly 6 inches daily, or more than falls in most of the
counties in England in a twelvemonth. Iam glad to communicate the assurance of
General Cullen, that not only will he continue these interesting observations throughout
the year, but that he has also established two pluviometers in the central table land of
Travancore, which is about thirty miles across to the Coromandel side; one at Perre-
gaar at 2300 feet, and another on the eastern or Coromandel edge at an elevation of
3600 feet. General Cullen considers the area of this table land to be about 2000
square miles, much of it at an elevation of 4000 feet. He states that it is lost to
civilization, from the Travancore government drawing only cardamoms from it, and
rigorously prohibiting culture to protect their cardamom monopoly. ‘The main fea-
tures of these observations correspond with those of Mahabuleshwur and Merkara, and
testify to one of those benevolent provisions of nature which the inquirer always
meets with, of the continuous impingement of aqueous vapour upon mountain masses,
occasioning very great condensation, and furnishing the perennial sources of springs and
rivers. The apparent discrepancy of the comparatively small fall of rain at Chittoor,
situated in the midst of the great gap of Palghat, confirms this view ; for though the va-
pour is constantly driving through the gap, it does not meet with any impediment to
force it up into a much lower temperature than its own, and it is therefore only partially
condensed. The paucity of rain however at Cape Comorin and Vaurioor, both open
more or less to both monsoons, does not admit of a ready solution. If,as General Cullen
asserts, the S.W. moonsoon beats rather from the N.W. and westerly points than from
the 5.W., it eannot be said that Ceylon intercepts the vapour from Cape Comorin;
and then, why is there a fall of 131 inches and 124 inches respectively at Allepy and
Cochin on the open coast, and only 19 inches at Cape Comorin? With respect to the
N.E. monsoon, some of its vapour may be cut off from Cape Comorin by shoulders
or peaks from the table land of Travancore, and yet the whole mass of the table land
does not prevent Trevandrum and Quilon from receiving a portion of the N.E. mon-
soon, as is shown in the preceding table. A closer attention to local physical circum-
stances is evidently necessary before a rational account can be given of these discre-
ancies ; but General Cullen is too zealous an observer not to work out the question ;
and I look to being enabled, at a future meeting of the Association, of laying before
this Section a continuation of General Cullen’s observations and a satisfactory solu-
tion of the existing difficulties.
On a New Portable Azimuth Compass. By E. J. Dent, F.R.A.S.
Mr. Dent exhibited this instrument. The magnetic needle was suspended in an
inner case, and that again fitted in an outer case in such a manner as to admit of
having either its ends reversed so as to eliminate errors of centring ; or its faces re-
versed so as to eliminate the error of collimation.
On the Relations of ihe Semi-Diurnal Movements of the Barometer to Land
and Sea-Breezes. By Tuomas Horxins.
Mr. Hopkins exhibited diagrams, drawn up from Col. Sabine’s paper ‘ On the Me-
Pa teorology of Bombay,’ of the diurnal temperature curve, total pressure curve, and ga~
‘seous pressure curve; with a diagram representing the, swelling and sinking of the
land and sea-breezes ; and endeavoured to show that these were inconsistent with the
_ explanation given by Col. Sabine, but harmonized with alternations of pressure caused
_ by the alternate extrication of heat and absorption of it during the alternate evapora-
_ tions and depositions of water, in the state of clouds and dew.
_ * Since this paper was read it has been ascertained that the fall of rain for the whole year
was 290 inches,
26 REPORT— 1846.
Abstracts of Meteorological Observations made at Aden in 1845.
By Wii.1am Mayes, Serjeant in 7th Regiment.
I. Hourly Means, for the Month of February, of the Temperature of a Thermometer
observed in the Sun.
Time, Mean of Therm. Readings. Max. Min.
8 a.m. 83°9 — 90°0 — 80:0 —
9 88-5 — 93°2 — 80-0 —
10 91:9 + 97°38 + 8270 —
11 95:1 + 99°2 + 90°0 +
12 96°9 + + max. 100°2 + + max. 90°0 +
lr... 9671 + 99°3 + 92°0 + + max,] °
2 94-4 + 98:2 + 90:0 +
4 91°5 + 94:0 — 86°0 +
4 87-9 — 91-2 — 84-0 —
5 82°5 — 86:0 — 79°0 —
einai een | 90-9 Sa aks ‘mam { 85°3
The readings above the average are marked + (the maxima being marked + +),
and those below the average —.
II. Means of Dry and Wet Bulb Thermometers, in February 1845, at the following Hours.
Hour. Dry Bulb. Wet Bulb. Diff.
2 A.M. 76°9 BET hese 3-2
as 76°6 73°9 27 #8
6 76-4" 73°8 26
8 78°4 74:4 a 4-0
9 79°9 74°7 su 7)
10 80°8 (Appelt 55
12 81:9 74-9 4 7-0
2 P.M. 81°5 (o-4 6-1
4 79°9 74:7 + 5-2
6 78°8 74:3 4:5
8 78°3 74:2 4:1
9 77°8 74-3 3-5
10 717-9 74:8* 3:8
12 77°9 73°9 4:0
ediop nie oes ibe 74:3
co tcome ee eee 44
III. The barometric curve at Aden on the 24th and 25th of March 1845, corrected
for temperature, had two maxima, viz. a principal one at 10 a.m. and a lesser one at
10—11 p.m.: it had two minima, viz. at 2—3—4p.m. and 4a.m. The extreme
diff. from the lowest min. (2—38 p.m. on the 24th) to the highest max. (10 a.m. on
the 25th) is 30°074 — 29°859 = 0°215. The author appends a column of corrections
for the moisture of air.
Meteorological Observations taken at Fort George Barracks, Bombay,
in July, August, September and October 1845. By WitL1am Mayss,
Serjeant in 7th Regiment.
The instruments observed are dry bulb thermometer, wet bulb thermometer, and
* In the MS. this is written 74°8, but the correct mean is 74:1.
TRANSACTIONS OF THE SECTIONS. 27
(for part of the time) rain-gauge. The wind is recorded in direction and estimated
in force; and the state of the sky and character of weather are noticed several times
daily.
‘The hours for registration of instruments are sunrise, 9 a.m., 2 P.M., sunset, 9 P.M.
The max. min. and range of the daily observations are entered, with the several ob-
servations in tables. [After the 7th of October the observations were taken at Calabar
Barracks.] We extract the following general results :—
; i Extreme
Extreme | Extreme Mean diff.
Mean Mean diff. of Dry
Mean Temp. s A of Dry and
P-| Max. Temp.|Min. Temp-|Max. Temp.|/Min. Temp. Wet Bulb. ae 4
— | ——— | | SS | Le, |
August .....} 81:3 83°8 78°8 86°5 77:0 4°1 75
September..| 81-7 84:7 78°8 89:0 76°8 5:0 9-0
October.....| 85°0 89°9 80°1 97-2 74:0 79 10°6
New Experiments on Electro-Magnetism. By Prof. WARTMANN.
Since the discovery made last year, by Dr. Faraday, of the action of magnets upon
polarized light passing through different media, it became interesting to ascertain
whether this influence is limited to the rotation of the plane of polarization of the ray.
Numerous experiments have shown that no change whatever is undergone by the
fixed lines of the spectrum, either in position, or in quantity or visibility, when they
are produced by rays of natural or artificial light, common or polarized, which have
_ been made to go through different substances, such as air, nitrous acid gas, water,
_ alcohol, oil of turpentine, syrup of sugar, a solution of ferruginous alum, or a long
prism of flint glass, put in the sphere of action of powerful electro-magnets. As
far as those researches have been brought, they lead to the conclusion, that neither
light nor the medium suffers any constitutional derangement which could alter the
_ property of the ray to be partially absorbed when it is refracted through a prism.
The view generally entertained by foreign philosophers as to the real action of the
magnet being one upon the material substance which gives way to the luminous ray,
_ it became necessary to test whether the new magnetical state of molecular equilibrium
_ would not be concordant with some new properties of chemical affinity. Indeed, it
has long ago been asserted by Ritter, Fresnel, Hansteen, Murchmann, Lodeck, Mur-
ray and others, and more recently by Mr. Hunt, that the magnets have a decided in-
fluence upon chemical phenomena. I have taken advantage of powerful electro-
_ magnets, which are put in action by sixty pairs of Bunsen’s battery, to make some
_ fresh trials upon the subject, convinced that such means would afford me an oppor-
tunity of witnessing, if any, far more decisive actions than those which have been
described. But all my attempts have proved unsuccessful to produce any difference
in the electrolysis of acidulated water of ferruginous dissolutions, or in the electro-
chemical decomposition of sulphate of copper, or of acetate of lead by soft iron. All
the results have been carefully and repeatedly tested by accurate weighings; and in
the case of the electrolysis of water, 1 employed electrodes of soft iron gilt by elec-
trical process, and supported by the very poles of the magnets, with the interposition
of a film of mica as thin as possible. The apparatus have been placed in all direc-
tions relative to terrestrial magnetism, and the poles of artificial magnets have been
made to act both separately or together, without any different result whatever. But
_ in expressing this my opinion, I must add that I mean not to say that magnetism is
not able to interfere with molecular disposition, which is quite a different view of the
_ subject, though it has not perhaps been sufficiently distinguished from the former one.
Indeed we have ample evidence that this is the case under favourable circumstances,
‘These experimental inquiries have led me to ascertain two facts which it may perhaps
not be improper to state here. Ifa chemical action is produced by the immersion of
two pieces of soft iron into a liquid which is able to corrode them, or to be decom-
posed by the metal, and if the poles of a magnet be applied upon these cores, an elec-
u
.
28 REPORT—1846.
tro-magnetic rotation takes place all round each, which is in the sense of the hypo-
thetic currents of Ampére. Prof. Grove has just pointed out to me that such an action
had been stated by Dr. Christie, though, as far as I know, it had been referred to
by no treatise on electro-magnetism, and that he himself had witnessed the phzeno-
menon many times. ‘The other fact seems to be of a higher interest, since it declares,
as it were, to the eye, what may be called the lines of chemical affinities. I shall now
content myself by merely describing what I have been able to witness and to show to
many scientific men, reserving for a future occasion to complete this communication
and to dwell upon the theoretical part of the subject. Common sulphate of copper is to
be dissolved in water, and a cylinder of soft iron dipped into it; as soon as the first
deposit of copper has taken. place, it is easy to perceive all round the cylinder light
films of a blue matter which are extending themselves as diverging rays from the very
centre of the cylinder which may be thought to represent the centre of the chemical ac-
tion. I suppose this substance to be a subsulphate of copper, and Prof. H. Rose is of
the same opinion; but from want of time and scarcity of matter, I have not yet been
able to submit it to analysis. During the progress of its manifestation, the nature of the
liquid is always varying, sulphate of iron taking the place of a corresponding quantity
of sulphate of copper. When this change has reached a certain extent, the phenome-
non ceases to spread. It is then like to a large passion-flower, with slender stamina
terminated by a continuous circular and opake ridge of thick anthere. Its figure,
which is altogether independent of the nature and the form of the vessel, is very geome-
trical. After halfan hour, more or less, this extraordinary design fades by the deposition
of the matter at the bottom of the trough. When two cylinders are used in the same
plate, two of the rays meet each other perpendicularly on the line of shortest distance of
the centres. Others join in direction more and more oblique, and being totally deprived
of the faculty of entering their relative dominions, they incurve themselves in hyperbolic
arches. Thus a perfectly straight line is formed which cuts into two halves the line
of shortest interval. It is scarcely necessary to add that the rays which are not to
meet others, extend as in the first case described. With three centres situated at the
summits of an equilateral triangle, the lines of separation intersect each other in a
point which is at equal distance from the summits, and thence run perpendicular to the
three sides of the triangle. The diverging rays, opposite in two directions, are much
inflected. The whole of the figure is perfectly regular. These rays are not affected
in their development by the magnetization of the cylinders; at least, if one observa-
tion made on this point suffices for deciding the question. If there are but two cylin-
ders, and if they are lifted up in the liquid by means of an appropriate horse-shoe
magnet, it is possible to move them very slowly without any disturbance of the figure,
and particularly without the least incurvature of the line of separation, which follow
the cylinders backwards and forwards, as if firmly tied together. But a shock loosens
all those particles geometrically adherent ; they fall down, and all the design vanishes.
Summary of Researches in Electro-Physiology. By Prof. Martevucct.
In the first place he described the experiments which prove that the development of
electricity in living animals is a phenomenon appertaining to all organic tissues, and
principally to muscular fibres, and that it is a necessary consequence of the chemical
processes of nutrition. He particularly wished to prove that the development of elec-
tricity in the muscles can never produce electric currents which circulate either in the
muscular mass or in the nerves. It is only by a particular arrangement of the expe-
riment that we succeed in obtaining a muscular current.
Further, all experiments contradict the opinion of an electrical current existing in
the nerves. M. Matteucci proved that the current said to be proper to the frog is
on the contrary a general phenomenon which exists in all the muscles that have ten-
dinous extremities unequally distributed, and that this current, supposed to be peculiar
to the frog, is only a particular instance of muscular current. In the second place,
the Professor laid before the Section his last researches on electrical fishes. He showed
that the laws of the electrical shock of these animals are a necessary consequence of
the development of electricity, which is produced in each cell of the electrical organ
under the influence of the nervous power. In the third place, he showed the relation
which exists between the electrical current and nervous power, and proved that mus-
TRANSACTIONS OF THE SECTIONS. 29
eular contraction is always pence by a phenomenon analogous to the electrical
_ spark, and that the electrical current does but modify the nervous excitability. On
_ these facts M. Matteucci establishes a simple theory of electro-physiological pheno-
- mena. In the last part of his communication he treated of inducted contraction; and
after having demonstrated that these phenomena cannot be explained in supposing
an electrical discharge of any kind indiscriminately, he concluded that inducted con-
traction is an elementary phenomenon of the nervous power, which acts in muscular
contraction, and is analogous to all the actions of induction of physical forces.
On the Identity of certain Vital and Electro-magnetic Laws.
By JosEru Butiar, M.D.
The object of this paper was to show that the direction and formation of bleod-
vessels and the capillary circulation through them, which is independent of the pro-
pulsive power of the heart, are in accordance with laws of the vital force, identical in
their direction and relation to each other with those of the electro-magnetic force.
In such an investigation the forms of bodies were considered of the highest import-
ance, Growth is invisible, but the forms it produces are the evidence of the unseen
vital force, and by announcing its direction, determine its law. To seek therefore the
primary forms of which others are mere varieties, and to ask, “ From what direction
of the living force does such a form derive its shape?” is a legitimate step towards the
discovery of the cause of that form, the “formal cause” of Bacon, or the law in mo-
dern language. The formation of blood and blood-vessels in the germinal membrane
which grows round the embryo during the incubation of a hen’s egg, was taken as a
simple type of this process. The small whitish disc on the yolk-bag (the cicatricula),
is the spot where the vital changes begin. The embryo occupies the centre of this
spot, and becomes the centre of the vital force excited by the mother’s warmth. From
this centre the force is communicated to the yolk-bag. The disc enlarges, still keep-
ing its circular form, and marked by concentric circles more or less perfect. The disc
is produced by the conversion of the yolk into cells, which adhere as a thin circular
layer. The circular form of this disc and the general concentric arrangement of the
cells, were considered to indicate that the lines of vital force which arranged and pre~
served that form were circular. The next step is:the conversion of a portion of these
cells which form the disc into blood and blood-vessels, The trunks pass in the direc-
tion of radii of the original disc and central germ. The main trunks unite at the
central heart, which is at first only a bent portion of the common trunk. The capil-
laries inosculate at the circumference; thus the vessels form a complete circle. This
circular arrangement of the vessels as radii indicates a second circular force at right
angles to the plane of the former one. The vessels are formed thus. Those called
by Harvey “ vasa lutea” are coarse, and the stages in their formation are more easily
watched, They are formed in the substance of the disc, and out of the same mate-
rial,—the cells of the yolk, These cells continuing to accumulate, some are arranged
as cylinders, then in succession as half-circles, circles, net-work, and trunks conver-
_ ging to the central embryo. At this stage each vessel is a coarse yellowish cylinder,
' with a red streak down its axis. Externally it is composed of cells of various sizes,
which can easily be brushed off from the semi-transparent tube which they cover, and
_ which is composed of smaller cells, and contains the red blood flowing towards the
' centre. The inference drawn was, that this tube, formed of cells around the current,
is the evidence of a circumferential force around the current, arranging the cells as
- atube. It was next shown that such a direction and relation of the vital force in
_ arranging the disc and its vessels were in accordance with the direction and relation of
_ the electro-magnetic force. The law of this double force, which bears on the present
inquiry, is, that in order to act both currents must circulate, that is, each must return
into itself. That the galvanic force must circulate, is evident from the construction
_ of a galvanic cell. The magnetic force accompanying the galvanic obeys the same
law. It also circulates, but in a plane at right angles to the galvanic. Dr, Wollaston
called it, in consequence of its cireulation, verfiginous magnetism. These two cur--
_ xents are inseparable. They are directive forces, or carrying, according to the con-
| dition of matter on which they act. What is true of the magnetic current circulating
' round a single wire conyeying the galvanic current, applies to two or more wires if
30 REPORT—1846. .
put together as a ribbon, or to a slip of metal, the only difference being the increase
of force in the latter instances, If the galvanic wire be bent in a circle, or if several
wires are arranged so as to form a series of concentric rings, or if, which is the same
thing, a spiral coil of wire be made, the magnetic force still retains the same direc-
tion as in the straight wire; but as the whole of the wire acts upon the circle of mag-
netic force, its direction is through the centre of the ring or coil. If such a spiral
coil be placed on iron filings, they arrange themselves in lines, passing through the
centre parallel to its axis, and then folding up on either side as radii round the edge,
where they meet. These experiments were quoted from Dr. Faraday. Such a spiral
coil, through which galvanic force circulates, was considered to represent the disc
around the embryo; and the iron filings to represent the direction of the capillary
vessels, arranged circularly in a plane, at right angles to the disc, by the magnetic
force accompanying the galvanic. From comparing the two, the conclusion was drawn,
that in both cases the force at work obeys the same laws; that the formation of a
circular living disc, by a central force constantly acting, proves the existence of a
circular force around that centre, and is analogous to a flat spiral or disc, through
which the galvanic force is circulating; and that this vital force in the disc is neces-
sarily attended by a second circulating force in the direction of radii to it, such as is
indicated by the vessels. The actual movements of the cells in this living process
are invisible, as it is one of growth; but the forms produced are explicable on the
hypothesis that the living force acts in accordance with the laws of a force the direc-
tion and relation of which have been ascertained. This analogy is rendered still more
probable by the connexion between heat and galvanism discovered by Seebeck. If
a current of heat instead of a current of galvanism be made to circulate through the
spiral coil of wire, it will, like galvanism, develope magnetic currents in the direction
of radii to the centre. Now as the mother’s heat is the source which supplies force
to the embryo, in both instances, in the metal coil of wire and in the disc the force is
in the form of heat. In both there is a primary concentric arrangement of matter
for the transmission of this force; and in both there is the evidence of a second cir-
cular force in a plane at right angles to the first.
If, instead of the arrangement of the galvanic wire as a flat spiral coil, the rings are
arranged side by side, as a spiral tube or helix, then the second or magnetic force
would be through its axis. It would be a tube, which, if placed in water, would carry
one pole of a magnetic needle, floated on cork, through it; and iron filings would
arrange themselves in a circular line, going through the helix, round on the outside,
returning into itself (Faraday). The spiral galvanic force here is attended by the
current through the tube. The converse would be the case. The steps in the forma-
tion of vessels are, that blood is first formed, and when it circulates a tube is formed
around it. The current of blood indicates a force through the axis of the tube; the
tube itself indicates a circumferential force around the current to arrange its materials
as a tube. The tubes are arranged circularly, meeting at the heart in the centre, and
at the capillaries in the circumference. The living tube, if it followed electro-mag-
netic laws, would have (like the helix of wire through which the galvanic force was
circulating) a circular force through its axis; and conversely, this current would tend
to form a tube around itself—supposing always appropriate materials. The vital
force has evidently appropriate materials in the form of cells. Those cells, which
exposed to oxygen become converted into red globules, are moved in a current; thus
showing that they are fit matter for the influence of vital force in one direction, and
that such a force is moving them; whereas the smaller cells are arranged round the
current as a tube; thus showing a second force at work around the first. There is a
current in one direction, and a tube around it; neither tube nor current can be ex-
plained without the assumption of a moving power: both are readily explained by
two circular forces having the same relation to each other as the electro-magnetic.
The cells out of which the disc and vessels are built have been regarded so far as
under the influence of a force external to them. But each cell has a vital force of its
own, similar in kind to the central force, but less in degree. The central force sub-
ordinates all lesser forces and makes the disc one. Embryologists have shown that
the earliest appearance of organization in the ovules of plants and ova of animals is a
cell, and that such cell has a nucleus, and each nucleus a nucleolus, or central spot,
which is the essential part of each cell, and which has the power of forming cells and
of arranging them round it. Dr. Barry has shown that each secondary cell becomes
‘a vented from touching by plates of glass
_ cemented to them, and a little larger for
- an instance of its use, suppose the first
' condenser has received a small positive
with the finger, D will become negative
TRANSACTIONS OF THE SECTIONS. 31
in its turn the centre of a similar action, smaller ones being generated and arranged
round the larger ones. Prof. Goodsir finds that the inner membrane of the tubes of
glands is formed of cells, and that nucleated cells are found among them, which he
calls centres of nutrition, as if these nucleated cells were the parents of successive broods
of young cells passing off from them, and arranged round them as centres. These
centres of nutrition are here called centres of force; and according to the law of this
force, there would be a common centre, bringing all these isolated and secondary
centres into one comprehensive whole. The blood corpuscles are also nucleated
cells, each having its own central living force, and thus their relation to the vital force
whilst circulating is analogous to that which a magnet holds to the electro-magnetic
force moving it. Both are bodies containing within themselves these forces.
The vascular disc of the yolk-bag had been taken as a central fact, the right com-
prehension of which would explain other facts of the same kind, but more complex.
Its application to some few facts in physiology was then shown,—such as the formation
of new blood-vessels; the tubular form of vessels and ducts among cells; the circu-
lation through capillaries independently of the contraction of their coats, or of the
propulsive power of the heart; and of that universal fact, that wherever there is a
central heart, there are powers at work which neither its propulsive power nor capil-
lary action can explain,—of forming new vessels in connexion with the old ones. Such
a universal fact becomes a law, when the cause is shown. This cause or law, now
proposed as the solution of these living processes, is, that the vital force circulating
in two directions, one circle being in a plane at right angles to the other,—thus iden-
tical in direction and relation with the electro-magnetic force,— will explain the phe-
nomena; or, in other words, that wherever there is a central moving force there is
a power at work around, and to and from that centre, capable of arranging fit matter
as tubes, and of circulating fluid to a certain extent through them, and that the tubu-
lar formation is owing to a vital power identical in its direction with the galvanic;
and the radiated arrangement of these vessels, and the circulation (to a certain ex-
tent) of fluid through them, are dependent on a power accompanying the former, and
identical in its direction with the magnetic force. The conclusion was not drawn that
the vital and electro-magnetic forces were the same, but that the direction and rela-
tion of both forces were identical.
On a new Multiplying Condenser. By Prof. A. F. SVANBERG.
The author was led by the process used by M. Pfaff of Kiel, in his researches on the
electricity of contact between metals and fluids, to construct a new instrument, which,
by asingle contact of zinc and copper, can be charged by manipulation, requiring only
a minute of time, to an intensity sufficient to give a brilliant spark and strong shock.
It consists of two ordinary condensers, whose plates are of copper, the two lower con-
nected by a copper wire. They are pre-
the sake ofinsulation. The lower plates
are supported by insulating stems, and
the upper have insulating handles. For
charge ~ a. Raising A and touching C
and C positive by induction, Remove
_ the finger from C to D, the electricity of this last is retained by that of C; and at the
same time replacing A, which had not lost its electricity during the preceding opera-
tions, that of B can be transported to D by a repetition of the process. By three such
_ operations the tension of D’s electricity is tripled, and this can be transferred to B by
_ raising C and touching A. In this way it is obvious that by 3” manipulations the
final electricity=3".a; it is easily seen that there is a certain number of transfers
before changing, which gives the greatest result. ‘Thus with two transfers and three
changes 2”. a=4096 a, while 3 (which is the best number of transfers) give with the
amount of manipulation 5°.a—=6561 a; 4 transfers give 4°.a=4096a@, Such an in-
strument made for the Cabinet de Physique at the University of Upsal, of six inches
32 REPORT—1846.
Santis gives by twenty-four manipulations a strong spark and shock felt in the
elbows.
On some Results of the Magnetic Observations made at General Sir T. M.
Brisbane's Observatory, Makerstoun. By J. A. Broun.
1st. Magnetic Declination.—The annual diminution of westerly declination at
Makerstoun is 5'"8, When proportional parts of this have been added to the monthly
means, from January 1844 till August 1846, their whole range is only 2"1; that is
to say, the mean position of the magnetic needle for any month, freed from secular
change, has not been above 2'1 further west than the mean position for any other
month. Mr. Broun conceives that he has found the annual period of westerly decli-
nation to consist of a minimum at the vernal, and of a maximum at the autumnal
equinox; the mean range being under 1/2. From the observations for 1843, Mr.
Broun has concluded that there is a maximum of westerly declination when the sun
and moon are in opposition, and a minimum when they are in conjunction ; that there
is a maximum of westerly declination when the moon has its greatest north, and also
when it has its greatest south declination, minima occurring when it crosses the
equator, In the diwrnal period, the double maximum and minimum have been found
to exist in eachJmonth of the year. In the Transactions of the Royal Society of
Edinburgh, Mr. Broun has given certain results relating to the horizontal and vertical
components of the earth’s magnetic force; but these results were obtained in scale
divisions corrected for temperature by his method. In order to deduce the variations
of magnetic dip and of the total magnetic force from the variations of these compo-
nents, it was necessary to determine the values of the scale divisions in known units.
Mr. Broun had previously shown* the inapplicability of the method given by the
Committee of Physics of the Royal Society of London for the balance magnetometer.
He now described a method by which the value of the micrometer divisions may be
satisfactorily determined. This method will be found in the Introduction to the
Makerstoun Observations for 1843. He has applied the same method to the bifilar
magnetometer, and has found that the value of the scale divisions, obtained in the way
recommended by the Committee of Physics, is also inaccurate for this instrument.
With the aid of the values obtained by the new method, the following results have
been deduced.
2nd. Magnetic Dip.—tThe dip is a minimum when the sun and moon are in con-
junction, and a maximum when they are in opposition. In the mean diurnal period
for the year,
The principal maximum occurs at 10° 10™ a.m.
Me minimum is 5 40 pm.
A secondary maximum ,, Bit AOU Asis
o minimum —,, 5 40 a.m.
Makerstoun mean time being always used. These periods vary to some extent
throughout the year, the principal minimum occurring at 6 a.m. in winter; the two
minima being nearly equal at the equinoxes, and the diurnal curve being single in
summer. Mr. Broun has found that there is a maximum of dip about four hours and
a half before the moon’s passage of the superior meridian ; a minimum about half an
hour after that passage; a secondary minimum about three hours after it; and a se-
condary maximum about eight hours after it.
8rd. Total force of the Earth’s Magnetism.—A minimum occurs when the sun and
moon are in opposition, equal maxima near the quadratures, and a secondary mini-
mum at the time of conjunction. In the mean diurnal period for the year,
The principal maximum occurs at 55 40™ p.m.
oa minimum se, 2 10 a.m.
A secondary maximum _,, 7 10 a.m.
> minimum ,, 10 10 a.m,
The periods of maxima and minima shift about two hours in the course of the year,
and in summer the principal minimum occurs at 10" 30" a.m, The variations of
force with reference to the moon’s hour angle were found by Mr. Broun as follows :—
* Transactions of the Royal Society of Edinburgh, vol. xvi.
TRANSACTIONS OF THE SECTIONS. 33
The principal maximum occurs about two hours after the moon’s passage of the infe-
rior meridian ; a secondary minimum about four hours before the passage of the su-
| perior meridian ; a secondary maximum about one hour after the superior passage ;
and the principal minimum about six hours and a half after that passage.
Curves were exhibited illustrating these results, and also the diurnal motion of a
magnetic needle freely suspended in the direction of the magnetic force. From the
: latter some curious results have been deduced, which will be found elsewhere, It will
be enough to mention, at present, that in the mean for the year, the motion from 6 p.m.
till 6 a.m. is very trifling ; between midnight and 6 a.M. the needle is almost stationary,
nearly the whole motion occurring between 6 a.m., Noon, and 6 p.m. The end of the
needle describes an ellipse whose major axis is at right angles to the magnetic meridian ;
but the direction of this axis varies throughout the year.
Magnetic Causation. By G. TowLer.
Magnetic phenomena are due to two distinct classes of forces, which, in the absence
of more appropriate terms, may be called the “intrinsic” and “contingent.” It is to
the consideration of the intrinsic forces that this paper is directed. The “intrinsic”
forces of the magnet are due, first, to the mechanical structure of the bodies in which
magnetical phenomena are displayed, the capacity of the interstices of which bears a
given ratio to the dimensions of the particle of fluid constituting atmospheric air, by
and through which such interstices become highly sensitive conductors of atmospheric
air; and, secondly, to the fluxion through and circulation round a magnetic bar of the
particles of atmospheric media.
The following are among the propositions which the author regards as established :—
Each extremity of a magnet perpetually exercises the same power over the other
that each does over indifferent masses of iron; in other words, one-half of a magnet
is constantly magnetizing the other.
The “intrinsic” attribute, or sine qua non of a magnet, is the extreme sensibility
of the fluid particles in its interstices to motion, from minute forces, arising from the
mechanical conformation of magnetical substances; and the extremities, or opposite
forces of the body, being within that distance of each other, whereby the forces gene-
rated by such action are sufficient to reproduce it.
On the Results of an extensive Series of Magnetic Investigations, including
most of the known varieties of Steel. By W. PETRIE.
On the Process of Manufacture to produce permanent Magnets having the greatest
_ fixity and capacity conjointly secured.—\st. The original iron—should be the purest
soft iron charcoal made (not coke) ; the Swedish from the Dannemora mine is better
than any other. 2nd. Converted—with pure charcoal; it should be carbonized
lightly, the process to be stopped when the bars, of the usual size, are scarcely steel
through, yet so that it will harden with certainty without an undue heat. 3rd. Sorted
_ —with attention to homogeneous conversion, &c., according to the ordinary rules.
_ 4th. Melted—the pot kept covered, and not longer than necessary in fusion. 5th.
__ Cast—into a large ingot, so as to allow of its being weld rolled out singly, before it
_ becomes reduced to the requisite thinness. 6th. Rolled—while hot from casting, to
| save a second heating. It should not be doubled over nor sheared and faggofed.
_ The rolling should be conducted at as low a temperature as convenient, as it thereby
_ acquires a harder and closer texture and finer grain. 7th. In cutting—into shape,
the substance (if large or of varied form) should not be strained, as by boring with
rimers, or straightening (oftener than is unavoidable) with the hammer, as it is
then apt to warp and to have unseen commencements of cracks on becoming subse-
quently hardened.
_ More carbonization than that previously described as best is of little injury to the
_ magnetic goodness of the steel, provided it be so prepared as to preserve a homo-
geneous and white appearance of fracture when hardened, which is not so easily ma-
_naged as with that of lower carbonization ; but if it be again carbonized more than
“usual (as razor steel, or above that) it rather improves; and again, an increase dete-
‘Tiorates it as in cast iron, and a further increase again improves it. In short, in the
1846. D
Se ate
D?
‘
.
34 REPORT—1846.
scale of carbonization there is a succession of continually decreasing maxima of
advantage.
On the Physical Properties which the Steel should possess.—The fineness of grain is
affected by many adventitious circumstances, which must be considered and allowed
for in judging of it; and the most important fact is the difference between the appear-
ance in the hard and sofé states ; for in the general properties, both optical, mechanical
and magnetical, their order, in’any set of samples, is reversed in the hard state, inde-
pendently of the absolute change in each property.
The steels should be examined by breaking with a single bend at a file notch
(notching with a chisel, bending back, &c. changes the appearance). A microscope
of six or ten lineal power is better than any other power for examining it.
The general properties, without going into detailed description, should be as follows,
the terms being comparative with other samples of less value, and not at all with the
hard or soft states of the same steel.
IN A SOFT STATE. IN A HARD STATE.
General appearance, uniform darkish gray ... Uniform white.
Rather a large grain, compared with razor
steel (or finer if much rolled). ............
Rather irregular in size and shape of Bie? } Rather more regular than before ;
Unless LINE ...crrceacceesercaeensscenregenesens rounded crystallization disappears.
Grains individually distinct with good
metallic lustre.
Close texture without cavities .........0.see... Not particularly close.
Rather tough for steel .,.......s.eseseeseeeeseee+ Brittle and very hard.
Attracted considerably before magnetizing ... Ditto.
Loses induced magnetism more freely Retains magnetism well and abun-
than other steels ..........s000 antchecedche } dantly.
Care must be taken to discriminate between real cavities and indentations arising
from the crystals being torn up by the breaking; pure iron often appears porous
from this cause.
The author added some peculiar considerations on the chemical constitution and
molecular arrangement of certain sorts of steel; and on the molecular peculiarities
of iron and other metals, in connexion with their magnetic capacity, illustrated by a
tabular arrangement.
On Hardening, &c.—In the ordinary process there is much risk and difficulty for
large work, owing to unequal heat, unnecessary time and heat applied, especially to
fine edges, decarbonization, scaling, &c.
These are obviated by a process, which is new as applied on a large scale, namely,
heating in melted lead. It will be observed that the precise heat is imparted quite
uniformly in half a minute or so, and the finest edge is heated momentarily no higher
than the thickest part (rendering this process incomparable for all instruments where
it is the edge or smaller parts that are of importance). No scale is formed, the finest
polish or sharpest edge being preserved through the hardening; the previous prepa-
ration of the steel and some other points are described ; and particularly the manner
of refrigeration in water (salt), and for securing hardness and great evenness, are
also detailed.
The process has been applied to steel sheets of 10 inches by 20, obtained quite flat,
and as hard as a file throughout, even at the middle parts, which has hitherto been
found very difficult, we may say impossible. Magnets prepared by these means only
differ generally in magnetic power by jth part, many being absolutely equal.
Particulars are then given of the advantage of certain high powers for magnetizing
bars, and of an apparatus constructed weighing 2 cwt. and possessing nearly as great
aggregate power as the colossal magnet in possession of the Royal Society (weighing
we believe 2 tons).
A method is suggested for verifying the constancy of magneto-meteorologic instru-
ments, by means of the terrestrial magnetism itself; independently of its own varia-
tions, or of the comparison of the mutual action of three or more bars.
A smaller grain than it was before.
Rounded crystallization ......s.sseeeessesees {
TRANSACTIONS OF THE SECTIONS. 35
On the Mode of Developing the Magnetic Condition.
By the Rev. W. Scoressy, D.D., F.RS.
Dr. Scoresby stated that he had, at York, shown a new and superior mode of deve-
loping the magnetic condition in properly prepared and hardened steel bars, by inter-
posing a thin plate of soft iron between the operating magnet and the bar of steel to
be magnetized. He had, at that time, supposed it to be necessary to extend the thin
plate of soft iron the entire length of the bars of steel to be magnetized. But he had
since found this to be by no means the case; since by laying any number of unmag-
netized bars of steel in a long line, and passing along them a horse-shoe magnet with
its poles connected with a thin polished plate of soft iron (he used common hoop iron),
the ends being slightly bent upwards to cause it to pass more freely over the steel
bars, and then turning them over and renewing the process on the other face, he found
he could communicate to the bars the full charge which they were competent to re-
ceive. The author exhibited this experiment: and by simply passing a horse-shoe
magnet thus armed with an interposed piece of sheet iron, once over each face of
twelve previously unmagnetized bars of steel, he communicated to them so much
power as that they sustained their 6wn weight, when held up as a chain.
F 7
On the Constitution and Forces of the Molecules of Matter. By Dr. Laminc.
In this paper the author applied a theory of the molecular constitution of matter in
forty-two distinct propositions to the explanation of gravitation, temperature and spe-
cific heats of gases, cohesion, affinities, latent heat, volume, disturbances of electrical
equilibrium, and other electrical phenomena, with electro-motion and electro-chemical
decomposition. In this theory, matter is regarded as constituted of atoms; each of
which consists of three sorts of spherical atoms, distinguished as basic, calorific, and
electrical. The only force it recognizes is attraction. The basic atoms do not attract
one another, neither do the calorific; but the electrical attract each other with a force
reciprocally as the square of their distances. ach electrical atom attracts calorific
atoms around it, and each basic atom attracts calorific in unlimited numbers; whilst
it also attracts around it electrical atoms, in some large but definite number. This
number is in each case unchangeable, but the basic atoms differ one from another in
attracting around them a greater or less number of electrical atoms. The force be-
tween basic and electrical atoms is much greater than that between the electrical
_ atoms mutually; hence one of these is termed the major, the other the minor
electrical force. The attraction of the basic for the calorific atoms is intermediate
between these. The attraction of the electrical for the calorific atoms is the greatest
of all the mutual forces. The immediate consequence of these forces is to cause
_ each electrical atom to be surrounded by calorific atoms, and each basic atom to be
then enveloped with these electrical atoms, in greater or less number according to
_ its chemical nature, but in each case definite. One of these basic atoms so sur-
rounded is the elementary molecule of matter, or the simple atom of the chemist.
_ Each basic atom thus surrounded by its sphere of electrical atoms constitutes an elec-
_trosphere ; but a change of the calorific atomospheres of the electrical atoms of this,
_ may cause a change of their arrangements about the central basic atoms, so that some
_ of the electrical atoms may be thrown out on the surface of the electrosphere and
thus become complementary ; and it is upon the mutual actions and relations of these
complementary atoms that all electrical and other phenomena involving change are
“supposed to depend. One remarkable consequence of this theory is, that pravitation
_ depends on the electrical atoms alone; and that hence a positively electrified body must
_ be heavier, and a negatively electrified body lighter, than the same body with its elec-
tricity in the ordinary undisturbed state. This the author proposed to prove experi-
' mentally to the Section.
On Atmospheric Waves. By W. R. Birt.
In introducing his report, the author noticed the steps he had taken during the last
autumn for observing the great symmetrical wave of November. Instructions de-
tailing the instruments to be observed, times of observation, &c., were drawn up and
forwarded by him to gentlemen interested in meteorological research, and also other-
D2
36 REPORT—1846,
wise circulated*, In accordance with these instructions, about thirty sets of inter-
esting and valuable observations had been made; the stations extending in one
direction from the west of Ireland to Heligoland, and in the other from the Scilly
Isles to the Orkneys. These observations Mr. Birt had subjected to a very careful
comparison, especially those made at his own residence near London, with those
which he made in the autumn of 1842 at Leicester Square. The result of this com-
parison was such as clearly to show that there was a most striking coincidence between
the barometric movements of October and November 1845, and those of a portion of
September, October and November 1842. So close did this coincidence appear to
the author, that during the period from October 1 to November 21 in 1845, the baro-
metric movements of October 23 to 26 were the only oscillations that appeared to
have no corresponding movements in 1842. It appeared that the great wave com-
menced in 1845, near midnight, between the 6th and 7th, that it culminated on the
14th, and terminated on the 21st; during the 10% days previous to the setting in of
the wave, the movements in 1842 and 1845 were almostidentical. Mr. Birt observed
that in 1845 the great wave, in all its essential features, was very distinctly marked ;
that it was completely separated from all the preceding barometric movements, and
that the individuality that was thus given to it, induced the strong belief that we haye
obtained the type of the barometric oscillations during the middle portion of No-
vember. This type he proposed to express in the following language :—
“‘ That during fourteen days in November, more or less equally disposed about the
middle of the month, the oscillations of the barometer exhibit a remarkably symme-
trical character, that is to say, the fail succeeding the transit of the maximum or
highest reading, is to a great extent similar to the preceding rise; this rise and fall is
not continuous or unbroken; in three out of four of the occasions on which it has
been observed, it has been found to consist of five distinct elevations. The complete
rise and fall has been termed the great symmetrical barometric wave of November,
and as such has been considered to result from the transit of a large wave, but there
is great reason to believe that while it may be due to the transit of a normal wave
of about fourteen days’ amplitude, it also exhibits the transits of five secondary super-
posed waves. At the setting in of the great November wave the barometer is gene-
rally Jow, sometimes below 29 inches. This depression is succeeded by éwo well-marked
undulations, varying from one to two days in duration. The central undulation, which
also forms the apex of the great wave, is of larger extent and longer duration, occu-
pying from three to five days; when this has passed, two smaller undulations, corre-
sponding to those at the commencement of the wave, make their appearance, and at
the close of the last the wave terminates.”
Mr. Birt exhibited curves of observations that had been made during November at
Dublin, from 1829 to 1845 inclusive, which he had received from Capt. Larcom of
the Royal Engineers. From these curves, it appeared that the great wave had been
observed at Dublin in twelve out of seventeen years, and that with two exceptions in
eleven years of distinct and well-marked transits of the great wave, the epochs of the
maxima were confined to five days, near the middle of the month, namely from the
12th to the 17th+.
The author then proceeded to notice the comparison he had instituted between the
curves he had obtained from various stations, and exhibited curves from twelve stations
in Ireland, England and Heligoland. From a consideration of these curves (which
were so arranged as to show the departure from symmetry in certain directions), he
argued that while the posterior slope of a wave of considerable magnitude was passing
off towards the E.N.E., the front of another was approaching from the N.W., and that
it was the interference of the two that produced the symmetrical arrangement of the
curves. In that portion of the area covered by the advancing wave the barometer
rose; in that covered by the receding wave it fell; while in that in which the two
waves interfered, the atmosphere as regarded these waves was quiescent, and the
smaller secondary waves passed on uninfluenced by them. He also showed that
* These instructions, with a short notice of the wave, were published in the Atheneum
of Sept. 6, 1845. No. 932, pp. 880, 881.
+ While exhibiting these curves, the author invited the attention of the Section to a very
remarkable and apparently constant depression of the mercurial column which occurred about
the 28th of November. It had been observed in fifteen out of the seventeen years’ observa~
tions, and appeared to be unconnected with the great wave.
ie
“
TRANSACTIONS OF THE SECTIONS. 37
these lines of symmetry or interference varied in different years ; in the year 1842 the
line of greatest symmetry passed from Dublin through Brussels to Munich; in 1845
it appeared to be confined to the south of England.
Mr. Birt next proceeded to notice the arrangements of the aérial currents or winds
with regard to the distribution of pressure. He stated that the observations on the
winds in November 1842, clearly established Prof. Dove’s theory of parallel and
oppositely directed currents, and he showed by diagrams that if these currents are
shifting ones, as the Professor suggests, as they passed over any tract of country in
a direction transverse to those in which the wind was blowing in each, all the phe-
nomena of an atmospheric wave would be produced. He remarked that if there was
only one set of these parallel currents passing over a line of country, then the exa-
mination of the phenomena of an atmospheric wave would be comparatively easy.
The discussion of the observations had however shown that there were two sets of
parallel and oppositely directed currents at right angles to each other, one set from
the N.E. and 8.W., with a lateral motion from the N.W., and the other from N.W.
and S.E., with a lateral motion from the S.W.; and also that when these currents are
referred to the wave, the N.E. and N.W. currents, in their respective systems, re-
present anterior slopes with the direction of the aérial currents at right angles to the
axis of translation directed towards the left-hand; and the S.W. and S.E. currents
represent posterior slopes, the direction of the aérial currents still at right angles to
the axis of translation, but directed towards the right-hand*. ‘Vhe author considered
that these rectangularly posited currents explained several phenomena, such as the
barometric wind-rose, the revolution of the vane in one uniform direction, &c., and
concluded his report with pointing out several important desiderata that it was desi-
rable should be made the subjects of future inquiries.
CHEMISTRY.
On the Changes which Mercury sometimes suffers in Glass Vessels hermeti-
cally sealed. By Prof. OrrstTep.
Ir has been frequently noticed that. mercury inclosed in glass tubes, even when
those tubes were hermetically sealed, undergoes a remarkable change. It first be-
comes covered by a thin film of a yellow colour, which adheres to the glass, and
becomes eventually nearly black. This has been attributed to oxidation, but the
oxidation which would arise from the exceedingly small quantity of atmospheric air
which could be contained within the bulbs exhibited by Professor Oersted was too
small to account for the formation of such a quantity of dark and yellow powder as
many of them exhibited. Professor Oersted referred the change on the mercury to
the action of that metal on the glass of which the bulb was formed. It appears that
sulphate of soda is frequently employed in the manufacture of glass, and it is thought
that a sulphuret of mercury is formed by the decomposition of the glass itself. This
is not however satisfactorily proved, and the subject has only been brought forward
that attention might be directed to a subject which appeared to involve some remark-
able conditions.
On a second new Metal, Pelopium, contained in the Bavarian Tantalite.
By Prof. H. Rose.
In a former communication it had been shown that the so-called tantalic acid
which occurs in the Bodenmais in Bavaria, consisted of two acids, one of which
' differed materially from all known acids. To this Professor Rose gave the name of
Niobium, regarding it as a new metallic oxide. After a most elaborate investigation,
- Professor Rose has found that the other acid contains another oxide of a metal dif-
* These directions are in close accordance with that of the rotation of the air in revolving
_ Storms, and appear strongly to support Sir John Herschel’s suggestion, that such storms may
_ be produced by the crossing of two large atmospheric waves moving in different directions.
See Sir John’s Report on Meteorological Reductions, Report, 1843, p. 100.
38 REPORT—1846,
fering from niobium, and to this metal he has given the name of Pelopium, from
Pelops the son of Tantalus and the brother of Niobe. The tantalite of Bavaria is
therefore now shown to contain three metals—tantalium, niobium and pelopium.
These differ from each other in specific gravity, and they exhibit different and pecu-
liar chemical properties.
On Cavendish’s Experiment respecting the production of Nitric Acid.
By Prof. Dauseny, M.D., F.RS.
Dr. Daubeny stated the result of some experiments he had instituted with the
view of ascertaining whether the production of nitric acid by electricity, as was first
effected by Cavendish, really arose from the direct union of oxygen with nitrogen, or
was produced indirectly through the presence of minute portions of ammonia. For
this purpose he deprived the air, through which the electrical sparks were to be
passed, of water, and of any traces of ammonia that might have been contained in it,
by allowing it to stand in contact with concentrated sulphuric acid for some time
previous to the commencement of the experiment. Even in this case, although the
air had been in contact with no liquid except the mercury over which it was con-
fined, the usual diminution of volume took place after the electrical sparks had been
passed through it, and solution of litmus, when introduced into the tube, became
sensibly reddened. Hence the author infers that nitrogen does combine directly
with oxygen, as it is now known to do with carbon, but he still questions whether
it can do so with gaseous hydrogen, since ammonia cannot be formed, as nitric acid
is, by means of electricity ; and, as in all the cases in which ammonia has been pro-
duced artificially, one of the elements appears to have existed in what is called a
nascent state. But if nitrogen can be made to combine directly with oxygen, how
comes it that through the operation of thunder-storms the composition of the whole
atmosphere has not before this time been changed by the production in it of con-
siderable quantities of nitric acid? This the author explains by the small amount of
heat generated by the union of the two gases, owing to which only those particles
combine which lie contiguous to the line of the electrical spark ; whereas in other
cases, as in that of the union of oxygen with hydrogen, so much heat is elicited
by the union of those particles which are affected by the passage of the electrical
spark, that a condensation of other portions of the mixture results, whence will arise
a union of more of the particles, and an extrication of a larger amount of heat. In
this way the explosion propagates itself through all parts of the mixture with a ra-
pidity which causes it to be considered by us as instantaneous. In all cases however
in which gaseous elements that can remain together without acting upon each other
are made to unite, the modus operandi, whether it be by electricity, by heat, or (as in
the case of porous bodies) by adhesive affinity, appears to be the same, that is, such
a condensation of the respective gases as shall bring their particles within the sphere
of their mutual affinity.
On the extent to which Fluoride of Calcium is soluble in Water at 60° F.
By Grorce Witson, M.D.
In April of this year, 1846, Dr. Wilson read a paper to the Royal Society of
Edinburgh announcing the solubility of fluoride of calcium in water, and stating
that in consequence of observing this fact, he had been led to seek for that salt in
milk, in blood, and in sea-water, where it had not been previously detected, but in
all of which he found it. He also mentioned that he was able to confirm the re-
sults of previous observers as to the presence of fluoride of calcium in natural waters,
in plants and in animal remains, as well as in the urine of man.
Since that paper was read, Dr. Wilson ascertained the extent to which fluoride of
calcium is soluble in water at 60° F. ; and as it is a point of some interest in connexion
with geological and mineralogical, as well as with chemical speculations, he brought
it before the Chemical Section of the Association. The experiments recorded below
were performed with a solution of native well-crystallized fluor spar, prepared by
boiling distilled water upon the powdered fluor, which had been previously purified
by digestion with warm aqua regia, so as to remove any trace of metallic oxides,
lime-salts or the like, which might be present. The solution at 212° F., was filtered
TRANSACTIONS OF THE SECTIONS. 39
whilst warm, and left at rest for some days in stoppered bottles at a temperature of
about 60°, till it deposited the excess of fluor soluble above that temperature. It was
then filtered a second time. A certain volume of the solution measured at 60° was
evaporated to dryness on the vapour-bath, in a counterpoised platina basin, and the
weight of the residue ascertained.
Twenty-four pints of the solution were thus made use of. In six experiments,
one imperial pint of the solution (16 fluid ounces, or 7000 grains) was taken at each
trial. In four trials three pints were evaporated at each experiment. In one case
six pints were employed. The following are the results :—
Per pint.
Expt. I. evap. 1 pint of solution. Residue 0°27 grs.
Il. ” ”» ” 0°28
Ii. ef ” par Oe
IV. ” ”» ” 0°24
Ve a3 2? a> 0°27
VI. 2 » 9 0°25 Average 0°265 per pint.
+ Per pint.
Expt. VII. evap. 3 pints of solution. Residue 0°79 = 0°263
Vill. » » » 0°78 = 0'260
IX. ” 2” ” 0°78 = 0°260
Xx. ” » ” 0°77 =0°257 Average 0°260 per pint.
Per pint.
Expt. XI. evap. 6 pints of solution. Residue 1°62=0°27 Average 0°270 per pint.
Twenty-four pints of distilled water thus dissolved 6-330 grains of fluor spar; so
that the average amount dissolved in one pint will be 0°2637 grains. One grain
therefore of fluor will requrie 26°545 grains of water at 60° F. to dissolve it, or water
at that temperature will take up seuagths of its weight of the salt.
The solubility here indicated must be considered great for a salt hitherto reputed
quite insoluble. It is still more soluble in water at a high temperature, as the de-
posit left by warm solutions on cooling shows. These facts will now be connected
with the appearance of fluoride of calcium in plants and animals, as well as in mineral
veins and elsewhere, and may perhaps prove sufficient to explain these hitherto per-
plexing phenomena.
Analysis of the American Mineral Nemalite. By Prof. Conne.z, P.RSE.
This mineral bears a striking resemblance to asbestus, so that by the eye it can
hardly be distinguished from it. It was first chemically examined by Mr. Nuttal,
who ascertained that it differs entirely in constitution from asbestus, and concluded
from his experiments that it consists essentially of magnesia and water with a little
oxide of iron and lime. It was subsequently examined by Dr. Thomson, according
to whom it also contains 12 per cent. of silica. The constituents found by the
latter were—
Magnesia ......seseeeee . 51°721
Silica ....cs0s Ditapvess s.. 12°568
Peroxide of iron...... ase D874
Water ........ seca seseee 29°666
99°829
The result which I have obtained differs somewhat from both the preceding.
According to both the previous experimenters, the mineral is soluble in acids without
effervescence. But I have found that even perfectly fresh portions of the specimens
(which I have) of the mineral from Hoboken in America sensibly effervesce when
dissolved in acids, showing some carbonic acid to be contained in it. I have also -
_ found only a very minute quantity of silica, the mineral leaving scarcely any residue
when dissolved.
__. The amount of water was determined by ascertaining the quantity of water col-
lected by ignition in a tube of German glass twice bent, and containing at one end
40 REPORT—1846.
fused chloride of calcium. The carbonic acid was estimated by the loss of weight on
treating a portion of the mineral with dilute acid in a little bottle connected with a
tube containing chloride of calcium.
The solid constituents were determined by ordinary methods. The result was, in
100 parts,—
Magnesia ......ssccsensecee 57°86
Protoxide of iron......... 2°84
SillGbcesccertatecttesSaneene. 0°80
Water 7%, cctecaedaae cess cate 27°96
Carbonic acid .........00. 10°00
99°46
Considering the protoxide of iron to replace a little magnesia, the mineral appears
to be a combination of hydrate of magnesia and hydrated carbonate of magnesia.
The formula 5MgO, HO + MgO, CO?, HO will nearly express its constitution, and
gives—
Magnesia ...sssssceeeeeeees 61°67
IV SECT nc 'csr sinre Seaaeate 27°24
(CAaTbDONICACIA secescesenss 11°09
100°00
The native hydrated carbonate of zinc (zinkbliithe) is a mineral of analogous con-
stitution.
Observations on the Nature of Lampie Acid. By Prof. Conn 1, F.RS.E.
The author had shown some years since that a large quantity of formic acid and
a little acetic acid exist in lampic acid as prepared in the ordinary way. Marchand
and others, admitting the presence of these acids, maintain that in addition it con-
tains aldehydic acid. It appears however to Professor Connell that the mere reduc-
tion of oxide of silver without effervescence, the formation of resin with alkaline
solutions, the blackening of the lampic salts on evaporation and by the action of sul-
phuric acid, are insufficient to support this view; and these facts are all explained
on the idea of aldehyde being associated with the acetic acid present in the liquid.
Further, the atomic weight of lampic acid, 50°35, is much too high to belong to an
acid, containing aldehydic acid, associated with much formic acid. But if we sup-
pose a foreign body, such as aldehyde, associated with the acetic portion of the
liquid, and entering for the time into the constitution of its salts, we can easily ex-
plain the high atomic weight and chemical reactions.
On the Connexion between the Isomorphous Relations of the Elements and their
Physiological Action. By James Buaxe, MB. F.R.CS.
In a paper read before the Academy of Sciences at Paris, the author remarked
“that when introduced directly into the blood, the salts of the same base appear to
exert the same effect on the animal ceconomy.”’ Since that time further researches
have led to the discovery of a law, equally interesting under a chemical as under a
physiological point of view. The law alluded to is that, when introduced into the
blood, all isomorphous substances produce analogous effects and give rise to the same
reactions in the animal ceconomy. This law has been verified by an extended series
of experiments with the salts of magnesia, lime, manganese, iron, cobalt, nickel, zinc,
cadmium, copper, bismuth, lead, baryta, strontia, soda, silver, potash, ammonia,
palladium, platinum, osmium, iridium, antimony,—the acids of phosphorus, arsenic,
bromine, chlorine, iodine, sulphur, and selenium. One of the facts observed is the
connexion which exists between the physiological action of these substances, and
their isomorphous relations to the elements of the blood. It is found that those
substances which exist in the blood, or which have isomorphous relations with its
elements, give rise to the least marked reactions: thus phosphoric and arsenic acids
can be introduced into the veins without producing any marked phenomena, whilst,
on the other hand, those elements which are most distinct in an isomorphous point
aa
TRANSACTIONS OF THE SECTIONS. 41
of view, from the constituents of the blood, are those which give rise to the most
marked phenomena. Two drachms of arsenic acid injected into the veins will pro-
duce no marked effect on any organ; but a grain of chloride of palladium, or two
grains of nitrate of baryta, are sufficient instantly to arrest the movements of the
heart. Several other instances analogous to those quoted were pointed out.
On the Action of Oxalic Acid upon the Dead Tissues of the Animal Body.
By H. Letuesy, WB.
It has been stated by Dr. Coindet, Dr. Christison and others, that oxalic acid does
not appear to have any corrosive action on the stomach like the mineral acids. Dr.
Letheby however remarks that these statements are opposed to the observations
which he has made. In every case which he had examined of poisoning by oxalic
acid, the stomach soon after death was found to be completely corroded, so that it
would scarcely hold together. Numerous experiments were made with various
animal tissues, such as submitting skin, stomach, intestine, muscle and tendon to
the action of solutions of oxalic acid of different strengths. After standing about
twelve or fourteen hours at a temperature of 60° Fahr., it was found that the cel-
lular and mucous tissues of each underwent either complete solution, or else were so
softened that they broke down under the pressure of the thumb and fingers; the
albuminous and muscular tissues were also softened and looked as if they had been
scalded.
On an important Chemical Law in the Nutrition of Animals.
By R. D. Tuomson, M.D.
This paper was a recapitulation of the results obtained by Dr. Thomson when
engaged on the Government Commission, and published in the Report presented to
Parliament, and also in Dr. Thomson’s ‘ Researches on the Food of Animals.’
On the Difference in the Physiological Actions of the Yellow and Red Prus-
siates as an evidence of their containing dissimilar Radicals. By H.
Letuesy, MB.
In the course of his inquiries into the actions of the various compounds containing
cyanogen on the animal ceconomy, the author was particularly struck with the great
dissimilarity in the effects produced by the yellow and red prussiates of potash, and
was led to think it might furnish some evidence upon the side of Liebig’s doctrine,
that the two salts contain radicals which are dissimilar. To prepare himself for this
inquiry, however, he thought it necessary to ascertain what would be the effects of
the simple and the double cyanides, and then to experiment with the yellow and red
prussiates of similar bases. Of the simple cyanides, he chose those of potassium,
sodium, ammonium, mercury, lead, iron, zinc and silver ; and, to provide against any
fallacy which might arise from the action of the gastric juice, injected them into the
veins or peritoneal cavity. Contrary rather to his expectations, it was found that
_ they were all poisonous ; the soluble ones generally acting as quickly as prussic acid,
_ while the others required a little longer time for the development of the symptoms ;
but in all cases death followed their administration, from two to five grains being
sufficient to produce such a result. Of the double cyanides, he chose those of po-
tassium and zinc, potassium and silver, potassium and nickel, and a mixture of
cyanide of potassium with cyanide of iron. These also were found to be most poi-
_ sonous, proving fatal in doses almost as small as the preceding. Now, these in-
quiries clearly established two facts,—that neither the simple nor double cyanides
_ could be given even in five-grain doses with impunity. The author was therefore
_ much astonished to find that a class of salts regarded by some chemists as double
_cyanides should have little or no action upon the animal ceconomy, and that they
might be administered in doses of half an ounce without their exhibiting any un-
pleasant symptoms whatever. This was found to be the case with the ferrocyanides,
experiments having been made with those of potassium, sodium, ammonium, barium,
lead, iron and silver.
42 - REPORT—1846,
He next examined the effects of the red prussiates; and here again, contrary to
what would have been surmised from the want of action in the preceding compounds,
it was found that they constituted a class almost as poisonous as the simple cyanides.
The experiments were made with the red prussiates of potash and lead, and with a
crystalline acid obtained by the action of muriatic acid and ether upon the former
of these compounds. Each of them was quickly fatal in doses of from ten to forty
grains.
On the use of stating, with the results of Analyses, the nature of the Methods
employed. By W. West, F.R.S.
The author of this communication pointed out the necessity which existed for
knowing, not merely the results to which chemists might arrive, but the processes
by which these results were obtained. It was shown that many of the discrepancies
found to exist in analytical results would thus be satisfactorily explained, and all
doubt as to the correctness of an analysis removed.
On the presence of Atmospheric Air, uncombined Chlorine, and Carbonic Acid
found in the Water of some of the Wells in the suburbs of Southampton,
and their Action on Lead. By Henry Osporn.
The principal object of this paper was to caution persons residing in the neigh-
bourhood of Southampton against the use of leaden pipes for conveying water, and
to induce them to avoid the use of lead in any form for that purpose without having
the water previously examined, in order to ascertain whether it possessed the property
of acting upon the metal and holding it in solution. The author brought forward
several instances of the serious consequences which had resulted from the use of
water impregnated with lead, and pointed out the different solvent principles found
in the water, one of which was uncombined chlorine discovered in a spring in the
New Forest. This water possessed the property of bleaching Brazil paper and redden-
ing litmus paper after concentration. The amount of uncombined chlorine was esti-
mated as chloride of silver by deducting the amount of the latter contained in twenty
ounces of water from that of the chlorine contained in the solid contents, the former
weighing 1°2 more than the latter; thus indicating 0°296 of uncombined chlorine
which is capable of uniting with 0°864 of lead, forming 1°16 of chloride of lead in
the imperial pint. The lead held in solution by carbonic acid and the oxygen of
atmospheric air was converted into chromate of lead, and estimated as chloride of
lead, which indicated 0°25 or 0*2 of the oxide in twenty ounces of water. The solid
contents in an imperial pint were found to vary from one to three grains, and to be
composed of the chlorides of sodium, calcium and magnesia, sulphate of lime, silica
and vegetable matter. Notwithstanding the preservative property which the salts
contained in spring-water are said to possess by forming an insoluble crust in the
interior of the pipes, it was found that the leaden pipes had been in use for some
years and the action of the water on the lead still continued with as much energy as
when they were first laid down, thus showing the presence of the above solvents, and
that they met with no resistance from the presence of the saline matter.
On the Rationale of certain Practices employed in Agriculture.
By Prof. Dauseny, M.D., FBS.
The Professor instanced among other practices the use of quicklime and of gypsum
as fertilizers to the land.
The former of these substances he supposes to act in part by rendering those in-
organic substances which are present in the soil more soluble, or, in accordance with
the views laid down by the author in a memoir which he has published in the Phi-
losophical Transactions of last year, by converting the dormant constituents of the
soil into active ones, or into a state in which they become immediately available.
He appealed to the authority of Professor Fuchs, confirmed by that of Mr. Pri-
deaux of Plymouth, as showing that the alkali may be extracted from granite readily
by water after the rock in a pounded form has been heated together with quicklime ;
TRANSACTIONS OF THE SECTIONS. 43
and he stated that a soil exhausted by long-continued cropping was found by him-
_ self to yield to water twice as much alkali, after having been mixed with quicklime,
as it had done before.
Hence the frequent application of lime tends to produce exhaustion in the land,
not only because it supplies in itself no fresh alkali, but likewise because, by ren-
dering that which the soil contains more soluble, it causes it to be washed away
more readily by atmospheric water.
Ploughing, and other mechanical methods of pulverizing the soil, appear to act in
the same way; and so also may we suppose to do the sprinkling of the soil with
sulphuric acid, as is practised in some parts of the continent.
The author then alluded to the various modes of explaining the advantage attri-
buted to gypsum which certain leading agricultural chemists had proposed; one
ascribing its virtues to the direct influence of the salt; another to the indirect good
resulting from it, owing to its property of fixing ammonia; a third regarding its acid
constituent as of the principal utility ; and a fourth its base.
Dr. Daubeny gave reasons for rejecting the third and fourth of these hypotheses,
but considered that the use of gypsum may be in part attributable to the first and in
part to the second of the causes pointed out; supposing that this substance is gene-
rally useful to all plantssfrom its property of fixing ammonia, and also especially
serviceable to certain species, by supplying them with a salt which they require for
their development. He was principally anxious however to bring forward this sub-
ject, in the hope of inducing chemists to institute fresh experiments for the purpose
of setting the question at rest.
On the Fairy-rings of Pastures. By Prof. J. T. Way.
A description of these patches, with which most persons are familiar, was given ;
and it was stated that the grass of which such rings are formed is always the first
to vegetate in the spring, and keeps the lead of the ordinary grass of the pastures
till the period of cutting. If the grass of these fairy-rings be examined in the spring
and early summer, it will be found to conceal a number of agarics or “‘ toad-stools”
of various sizes. They are found situated either entirely on the outside of the ring
or on the outer border of the grass which composes it. The theory of DeCandolle,
that these rings increase by the excretions of these fungi, being favourable for the
growth of grass but injurious to their own subsequent development on the same
spot, was remarked on, and shown to be insufficient to explain the phenomena. A
chemical examination of some fungi (the true St, George’s Agaric of Clusius—Agaricus
graveolens) which grew in the fairy-rings on the pasture around the College at Ciren-
cester was made. They contained 87°46 per cent. of water, and 12°54 per cent. of
dry matter, The ashes of these were found to contain—
Silicas.sssunsssssecdevessass.. “1°09
Lime ....cecece phedintdeiouka® (1°35
Magnesia. ......escsecsesees 2°20
Peroxide of iron ......... trace
Sulphuric acid ............ 1°93
Carbonic acid ........ sexe 3°80
Phosphoric acid ......... 29°49
VOtAGE) sancisnmenpurpasesacs 00:10
SOdA dsp asesateanccadeaceadne a a2
Chloride of sodium ...... 0°41
98°69
The abundance of phosphoric acid and potash, existing no doubt as the tribasic
phosphate of potash (3KO, PO5), which is found in these ashes is most remarkable.
The author’s view of the formation of these rings is as follows :—A fungus is deve-
loped on a single spot of ground, sheds its seed and dies: on the spot where it grew
it leaves a valuable manuring of phosphoric acid and alkalies, some magnesia, and a
little sulphate of lime. Another fungus might undoubtedly grow on the same spot
again; but upon the death of the first the ground becomes occupied by a vigorous
_ crop of grass, rising like a Phoenix on the ashes of its predecessors. It would thus
44 REPORT—1846.
appear that the increase of these fairy-rings is due to the large quantity of phosphated
alkali, magnesia, &c. secreted by these fungi; and whilst they are extending them-
selves in search of the additional food which they require, they leave, on decaying, a
most abundant crop of nutriment for the grass. :
On certain Principles which obtain in the application of Manures.
By Witt1aM CHARLES SPOONER.
This was a paper by a practical agriculturist, who has paid attention to the re-
commendations of chemists as to the application of manures. It was pointed out
that many of the recommendations of chemists were nearly valueless to the practical
farmer on account of the expense involved in their employment. The direct appli-
cation of sulphuric acid and silicate of potash were adduced as examples, the expense
in both cases rendering their use impracticable, however valuable these ingredients
may otherwise prove. Many other examples were given enforcing on chemists the
necessity of connecting with their experimental inquiries the practicability of their
agricultural applications, both with reference to economical use and the ease with
which they may be employed.
On the application of the Principles of a Natural System of ‘Organic Che-
mistry to the Explanation of the Phenomena occurring in the diseased
Potato Tuber. By G. Kempe, M.D.
At the meeting of the Association last year at Cambridge, Dr. Kemp introduced
to the notice of the Society an outline of the results of two years’ investigation into
the nature of the changes effected by vital and physical agents on organized bodies,
his principal aim being to suggest an arrangement founded upon natural affinities,
and capable of interpreting the results of organic analysis, consistently with the phe-
nomena which natural or artificial agents have effected.
At an early period of the ravages committed last year by what is called the potato
disease, Dr. Kemp was induced, by the application of elementary analysis, to attempt
the removal of some of the difficulties in which the explanation of the subject was
involved. The results of those analyses are recorded in the abstracts of the Cam-
bridge Philosophical Society. By the application of the principles of the natural
system of organic chemistry which he has suggested, the author arrived at the con-
clusion, ‘‘ that the true nature of the affection is an abnormal tendency to premature
germination,” and that the changes which the diseased tuber undergoes are identical
with those which had three years previously been discovered by Erdmann, Marchand
and Scharling to take place during the normal germination of seeds and tubers.
Some remarks followed which all bore on the importance of autumn planting.
Numerous striking instances were adduced in which healthy potatoes had been grown
from diseased tubers planted in the autumn.
Some Inquiries into the Extent, Causes and Remedies of Fungi destructive in
Agriculture. By J. PRIDEAUX.
lst. Extent.—DeCandolle’s theory of injurious excretions having been opposed
by many arguments and experiments, particularly those recently published by Dr.
Daubeny ; that of Liebig, of specific exhaustion of the soil by plants of one species,
leaving it fit for another which required different ingredients, had been generally
substituted. Some however had taken a middle course, and supposed plants to breed
animalcules ; which they left in the soil, and which would feed upon other plants of
the same species, but not upon those of different ones. The writer also, unsatisfied
with the theory of specific exhaustion of inorganic ingredients, from the occasional
unaccountable efficacy of ashes and soot, and the inconsistent effects of inorganic
manures ; had investigated the organic residues on the soil,—after wheat, barley, tur-
nips and potatoes; compared them with the premature decay of wheat (where too
often cultivated) in patches, expanding from centres, like fairy-rings; and with the
notoriety of fungus in the potato disease; and had thence been led to inquire how
far such fungous parasites might be the general representatives of DeCandolle’s sup-
ae
TRANSACTIONS OF THE SECTIONS. 45
posed injurious excretions. To what extent this may be true, the microscope will
best decide, by examining the roots and contiguous soil of plants after harvest, espe-
cially those which have ripened seeds.
2nd. Causes.—Fungi and mucors were supposed to bear somewhat the same re-
lation to vegetable, as mites and the like to animal, life—a sort of debased or degraded
vitality, produced when the organizing vital power was not enough predominant over
the disorganizing tendency to decomposition, to effect due assimilation of the nutri-
_ tious matter presented ; but still sufficiently so to prevent decomposition or decay.
The constant struggle between the organizing vital force, and the decomposing power
of chemistry, was described ; and instances were adduced to show that the invigora-
tion of the vital force by solar light, and abundance of proper nourishment, enabled
it effectually to repress the decomposing action; whilst, on the contrary, gloom,
warm damp, and stagnant electrical air, assisted the disorganizing force, and often
produced predatory fungi, which might thus be considered a sort of retarded disor-
ganization. So ripening plants, as their vital powers decay, might generate such
parasites, which would explain how they weaken the soil so much more than green
crops, in proportion to the contents of their ashes. Such fungi, though not the
cause of disease or decay, are effectual promoters of both, and probably the chief
means of infection, where that also exists.
3rd. Remedies.—If further investigation prove fungi thus generated to produce
such generally injurious effects, the remedies will be of practical importance. These
should be cheap and antiseptic, as well as destructive to fungi. Sulphate of copper
with salt, which had been successfully used for seed potatoes, was too costly for
spreading over the soil. Fresh lime, the general destroyer of noxious vermin, roots
and seeds, would probably answer till rendered inert by carbonic acid. Salt, which
appeared more promising, he had found, in some experiments, rather promote than
destroy fungi. Lime and salt digested together would eliminate caustic soda, a very
active destroyer; and soda ash, with or without lime, would have a somewhat like
effect ; and ammoniacal gas liquor is perhaps a still more destructive application.
But none of these alkalies can be regarded as antiseptic; and the ammonia, when
neutralized in the soil, might even promote disorganizing fermentation where already
too strong; and therefore, though they might do after seed crops, more antiseptic
dressings must be used where there is putrescent tendency. Chloride of lime, in
solution, he had found useless on diseased potatoes; the powder had been said to
answer better, but either would soon be rendered inactive in the soil by the humous
matters. Sulphuric acid, diluted, might succeed, where farmers had the means of
applying it; and alum, which is of easy application, is a cheap and powerful anti-
septic.
Dressings of this kind, intended to kill the fungi and check the disorganizing
action, would be turned under in the first ploughing after harvest, independent of the
usual manure for nourishing and exciting vital action.
New Facts bearing on the Chemical Theory of Volcanoes.
By Prof. Dauseny, MD., F.RS.
This communication detailed the views formerly promulgated by the author in
support of that at one time entertained by Sir Humphry Davy, that volcanic phe-
nomena are due to the oxidation of the metallic bases of the earths and alkalies by
the access of water and atmospheric air to the interior of the earth.
After alluding to the hypothesis of central heat, and pointing out in what respects
it fails to account for the phenomena presented by volcanoes, Dr. Daubeny particu-
‘larised two new facts which lend countenance to the chemical theory. The first of
these is the chemical composition of volcanic products, which, according to recent
researches, is such as to lead to the inference that they are derived from granitic
materials, by the super-addition of those alkaline and earthy ingredients, which would
arise from the supposed oxidation of the inflammable bases assumed to exist in the
interior of the earth.
The other new fact was the emission of flames from the orifices of Vesuvius and
other volcanoes, attributable apparently to the combustion of hydrogen in some of its
combinations, this disengagement of hydrogen being an immediate consequence of
the supposed process,
46 REPORT—1846.
Notices of Experiments in Thermo-Electricity. By J. Reaper, M.D.
Some experiments were shown by which a brass bar covered with paper, placed
in the focus of a reflecting sheet of copper bent into a semicircular form, and at a
short distance from a spirit-lamp, was made to revolye. This Dr. Reade thought to
be due to the influence of thermo-electricity.
On the Electrization of Needles in different Media.
By Prof. C. Matreucct.
Professor Matteucci has found that needles electrized in air, in oil, or in water,
were differently affected by the current, the magnetism varying with the nature of
the medium in which the needles were placed. The materials employed were the
oil of turpentine, olive oil, alcohol and water, and also plates of mica. The discharge
of a Leyden jar was then passed near the needles suspended in these fluids, and the
amount of magnetization ascertained.
On Crystallography and a new Goniometer. By H. B. Lerson, M.D.
This new system of crystallography was, during the last session of the Chemical
Society, brought under the notice of that body, and illustrated by models and instru-
ments, Dr. Leeson’s goniometer consists in adapting to a microscope a polarizing
prism ; the crystal observed through this polarizing eye-piece of course presents two
faces instead of one, but by turning the eye-piece until these two angles are made to
correspond, the true angle of inclination from the axial line is obtained, and its value
is read off from a graduated circle within which the polarizing arrangement moves.
On the Influence which finely-divided Platina exerts on the Electrodes of a
Voltameter. By the Rev. T. R. Rozinson, D.D.
Having occasion some years ago to construct a small voltaic battery on Daniell’s
principle, and wishing to make it as powerful as was consistent with a limited size,
I was led to determine its constants by Ohm’s theory. Using the voltameter, and
grouping observations by the means used in astronomy, I succeeded in this; and
when Mr. Wheatstone’s paper on the ‘ Rheostat’ appeared, wished to confirm by
that instrument my results. The facility of its application led me to other examina-
tions, one of which I have ventured to lay before the Section, as it seems to me im-
portant in its bearing on a matter lately brought before the scientific world by Grove
and Faraday, namely the intimate connexion of all or nearly all the molecular forces,
The galvanometer used by me, being intended to measure powerful currents, con-
sisted of a simple needle suspended in the centre of a massive rectangle of copper.
I was in hopes that this simplicity of construction might give some simple relation
between the deflection and force, but it was not so; the denominator of Ohm’s ex-
pression of the force of the current is
R+=r Veo taagd B cos* 6 }.
as given by careful interpolation; but I have not tried whether this can be deduced
from theory. The needle’s magnetism was constantly examined and kept at satura-
tion. The rheostat was of Mr. Wheatstone’s second kind slightly modified, its wire
copper 7;th of an inch, and 100 turns of it are 70 feet. The value of E, the elec-
tromotive force of Ohm, or rather the infensity of the sum or difference of the che-
mical affinities exerted in the cells is, as in Wheatstone’s memoir, expressed by the
number of turns of the rheostat required to bring the needle from 45° to 40°. The
determinations of it are very consistent, provided that the magnetism of the needle is
constané and all the apparatus in given positions *.
* The author adds the value of E in the following cases :—
Copper, zinc, dilute sulphuric acid .........seseeeeeeeee peunaaae FEE conssosscsesesecs 2 = oL'U
Platina, zinc, dilute sulphuric acid ..........sesecscecessnversesreveeors oawd soa sesame ane .. E = 43°0
Daniell’s cell ....... to seeaccenecerccedcarerstocccgscsnsccsesesrsoncs osegenescecsenadnestane® cote = OF
Ditto, with mur. acid and ammonio-chloride of COpper .sccsseseceeseceeeeeecsceereceee . E = 539
Zinc in dilute mur. acid, copper and a mixture of sulph. of copper and nitr.ofammon. E = 68°0
Groye's)cell, .i3. Wukesssiecscecedéacess sederseseeseecvean edad. Gdssasen tacdbbecncvocccoscabedes Mules Oma
These values neither change with the concentration of the fluids nor with the temperatures.
TRANSACTIONS OF THE SECTIONS. 447
When one of these cells is connected with a voltameter, no decomposition takes
place that is sensible, though a feeble current passes. With two a slight extrication
of gas takes place at first and ceases, though it may be made continuous by reversing
the direction of the current. Three act steadily: the inactivity of the others is owing
to what has been called polarization of the electrodes, but which I would rather name
electrolytic resistance. It may be measured as E in turns of the rheostat, and was,
with the particular charges which I then used, 2°5 E. Obviously, therefore, two cells
could not decompose it, for in that case by Ohm’s theory the energy of the current
pu2E—e5E
~“2R+rt+y
(y being the resistance of the voltameter) is negative.
This antagonist force is, I believe, referred to the accumulation of nascent hydrogen
and its peroxide on the electrodes; and it seemed likely that the evolution of these
substances might be promoted by coating the platina with that metal in a state of
fine division. This was performed by filling the voltameter with chloride of platina,
immersing in it a positive platina wire, and making the electrodes negative. The case
was now altered; one cell decomposed feebly with chlorine compounds as charges,
but decidedly with sulphates; two give 1*1 cubic inch of the mixed gases in five
minutes. With higher numbers the difference is also decided. The quantities given
by 3 cells had been 2°5,now 5°5
6 a3 ? 9°9 o> I 1 8
6 double ,, 185 ,, 25:3
My first impression was that the electrolytic resistance must have been lessened, for
the fact of decomposition implies that n E is greater than e in the formula; but on
examining it I found that e=E x 2°49. Therefore J infer that the force which thus
assists the battery in subverting the affinity of oxygen for hydrogen is of such a
nature that the galvanometer does not take cognizance of it, and therefore is not elec-
tric. What then is its nature? The only explanation which occurs to me is, that
the energetic capillary attraction which appears to exist at the surface of this platina
coating may be, like heat or electricity, convertible into chemical attraction, or that
the film of water in contact with it being decomposed, the heat evolved by its con-
densing a new one (for the intensity of this capillary force is very great) may, as in
Grove’s recent discovery, aid the separation of the gases. I may add that this pe.
culiar action is more energetic at the positive electrode than the other. I removed
the coating from one of the plates by filling the voltameter with muriatic acid, and
making it positive. The surface retained however some of it which could not be re-
moved. When this was the negative electrode, more gas was evolved than when it
Was positive. With 2 cells the quantities are 2°18 and 2°68, with 6 cells 8°60 and
9°12. It maybe added, that in all these cases the resistance of the voltameter itself
appears to have been the same, the different measures varying from 38 to 35.
On the Electricity of Tension in the Voltaic Battery.
By Joun P. Gassiot, F.R.S.
_The author, referring to a paper presented to the Royal Society in December 1843,
remarks that the water battery he then used, which with 3520 pairs gave a continued
series of sparks, is at this time nearly as energetic in its action as at first, merely re-
quiring to be refilled with water from time to time as it evaporates.
This was the only arrangement of the voltaic battery by which he was then en-
abled to exalt the effects of tension so as to obtain the electrical spark before contact
of the terminals; although with the assistance of an exceedingly delicate gold-leaf
electroscope, he at that time elicited distinct signs of tension in a single cell of Grove’s
nitric acid battery, and subsequently in one of copper and zinc charged with sul-
phuric acid. But in all the different series of experiments described in the paper
‘referred to, he invariably found that the higher the chemical affinities of the elements,
the greater was the development of the effects of tension, For instance, to produce
a certain extent of tension with the gas battery of Grove when charged with oxygen
and hydrogen, ten or twelve pairs of cells were required; with hydrogen and chlo-
rine, six pairs ; with chlorine in a single tube and amalgamated zinc as the positive
48 REPORT—1846.
~
element, two pairs; and while it took sixteen cells of the water battery to produce a
_ given effect on the electroscope, ten of the same cells when charged with dilute acid
produced the same effect in the same instrument.
The static effects of a voltaic battery are very feebly developed, except when the
battery is insulated, and the difficulties of insulation in an extended series are at all
times great. In the battery excited by acid solutions these difficulties are much in-
creased, in consequence of the conducting power of the liquids ; still they are not
insurmountable; and as of all the batteries hitherto constructed, the nitric acid battery
of Grove is composed of elements of the highest chemical affinity, the 13 in.
author determined on constructing one, in which the effects of tension
should be heightened to the extent of exhibiting the spark before the
circuit was completed, which he hoped to accomplish without being
compelled to extend the series to any extraordinary number, as he had
done in the water battery previously described.
For this purpose he had 100 glass cells constructed three inches deep,
with stems seven inches long; the zinc of each series was attached to
a slip of platinum foil; each cell was carefully charged in the usual
manner (but only half-full), with strong nitric and dilute sulphuric
acid, and great care was taken that the outside of each cell with the
stem was perfectly dry. To the terminals of this battery were attached
the copper plates of the micrometer electrometer described in a former
paper (Phil. Trans. 1840). On approximating the plates of this in-
strument to about 555th of an inch, a series of minute sparks took
place, and in a few seconds the usual voltaic are was produced ; this arc
could then be elongated to the extent of half an inch, in consequence of
the particles of the copper having passed between the plates.
If, in lieu of the copper plates, pieces of charcoal be similarly ap-
proximated to z2,5ths of an inch, the arc is at once produced, instead
of the sparks as from the discs ; the loose particles of the carbon being
more easily detached by the force of tension, and consequently at once
producing the are.
The author believes that this is the first instance in which a ¢rue spark
has been obtained from so small a series of the voltaic battery.
‘soul ¢
‘soqouy £
On the Decomposition of Water into its constituent Gases by Heat.
By W. R. Grove, F.R.S.
Mr. Grove called attention in the first place to the fact, proved by Cavendish
and the French philosophers, that oxygen and hydrogen being exposed to a high’
temperature the electric spark immediately combined to form water. He stated his
belief that the explosion of the mixed gases by the electric spark was due only to the
heat of the spark, and not to any specific electrical effect. He then announced his
discovery that similar processes to those by which water may be formed are capable
of decomposing water. Priestley’s method for decomposing gases by passing them
through heated tubes was described, and the advantages of using a form of eudio-
meter devised by Mr. Grove, in which an incandescent platina wire was employed
to effect combination and decomposition, were pointed out. By an apparatus of this
kind, ammonia, camphor, the protoxide and peroxide of nitrogen were readily de-
composed. It was stated that hydrogen gas exposed to the ignited wire always
showed the presence of oxygen, and that it is impossible to pass hydrogen gas
through water without its taking up so much oxygen as to acquire the power of
giving luminosity to phosphorus in the dark.
It was found that if equal volumes of hydrogen and carbonic acid were exposed to
the action of the ignited wire, there was a contraction to one volume, leaving a resi-
due of carbonic oxide. If carbonic oxide alone was exposed to the wire over water,
the gas expanded in volume, and the carbonic oxide, taking oxygen from the water,
was converted into carbonic acid. Here we have two dissimilar results produced by
the same cause. By means of hydrogen we take oxygen from carbonic acid, leaving
carbonic oxide ; and by means of carbonic oxide we take oxygen from water, leaving
hydrogen. If steam is formed in the eudiometric tube and acted on by the ignited
r, . TRANSACTIONS OF THE SECTIONS. 49
wire, on cooling a small bubble of gas is formed, which is found to be mixed oxygen
and hydrogen in the proportions in which they form water. This is the result of the
first action of the heated wire: in a few seconds a small bubble of gas is formed ;
but if the action be indefinitely continued, the gas does not increase in quantity.
It is however easy to remove the bubble after it is formed, and bring a fresh supply
of steam under the influence of the heated wire, and thus to collect a sufficient
quantity of gas for an eudiometric examination.
_ Numerous forms of apparatus were described by which this result can be ob-
tained. It might be objected that, as the wire was ignited by a voltaic battery, the
_ decomposition was not due to the heat of the wire, but to an electric action. This
_ objection would not indeed be maintained by those who were well acquainted with
electrical phenomena. With the view, however, of removing all doubt, the use of
_ the battery was entirely done away with, and all the results obtained by the agency
' of heat alone, in the following manner :—
Into a silyer tube a narrow tube of platina is soldered ; and this is again connected
_ with a bent tube which admits of the removal of any gas formed. The tubes being
filled with distilled water, and the open extremity immersed in a vessel of water, the
_ flame of an oxyhydrogen blowpipe is made to act upon the narrow tube of platina,
by which this is brought to a white heat. The water is of course instantly con-
verted into steam, and this steam is decomposed by the agency of the heat alone.
By apparent boiling, we thus convert steam into mixed oxygen and hydrogen gases ;
and this operation may be continued for any length of time by bringing a fresh
_ supply of steam under the influence of the ignited platina. Ifa fused or intensely-
| heated globule of platina is plunged into water, bubbles of oxyhydrogen gas imme-
| diately ascend from it, which may be collected in an inverted tube.
Prof. Grove went on to show the probable connexion between this phenomenon
of decomposition, and the spheroidal state of fluids when projected on capsules of
| heated platina; this had been referred to a repulsive action of a coating of steam
_ enveloping the spheroid of fluid; but in all probability the spheroidal drop was
_ made to assume a state of tension approaching decomposition by the agency of the
_ heat to which it was exposed. He also entered into several considerations suggested
_ by the above facts as to the relation of heat to chemical affinity, as well as their
geological bearings and possible practical applications.
Notice of a Gas Furnace for Organic Analysis. By Joun Percy, M.D.
In this arrangement, gas burnt, mixed with air through wire-gauze, is substituted
for charcoal. The advantages are its extreme cleanliness, and the power which the
operator possesses of regulating at will the heat, which is not practicable in the or-
dinary furnace for organic analysis with charcoal.
Extraordinary appearance in the Flame of a common mould candle.
By E. R. J. KNow es.
The writer’s attention was suddenly attracted by the light of the candle flitting,
as though a moth had flown into the flame, when to his surprise instead of an insect
struggling he saw a bright spot revolving with great rapidity in the flame; on exa-
“mining it, the bright spot was found to be the end of a very fine filament attached to
the side of the wick about half-way up the ignited part, and thus held to it, while
_ the extremity with the bright spot of light revolved in a circle like a ‘‘ Catherine
_wheel,””—the circle described being about 4th or 33,ths of an inch in diameter. It
moved with a velocity of about three or four revolutions in a second, and ceased
revolving in about three seconds. As stated, when it commenced it was a very small
- luminous point, and it increased visibly in size as it revolved, becoming eventually a
ball or aggregation of carbon, suspended by a single thread like a very fine hair.
| Experiments on the Expansion of Salts. By Messrs. Joure and PLAYFAIR.
[This paper will be published elsewhere in extenso. ]
1846. E
50 REPORT—1846., .
GEOLOGY AND PHYSICAL GEOGRAPHY.
On the Origin of the Coal of Silesia. By Professor GoprEert of Breslau,
Communicated by Sir R. I. Murcuison, G.C.St.S., PRS,
Tue Society of Sciences of Holland at Haarlem, proposed in the year 1844, the
following prize questions :—
Ist. To point out by accurate investigation of the different coal-measures, whe-
ther the beds of coal derived their origin solely from the vegetables which once lived
upon their present locality, or whether they originated from plants which had been
floated thither from other places.
2nd. To inquire whether different coal layers have had a different origin.
At the session of that Society of the 23rd of May, 1846, a paper sent in by me
was honoured with both prizes : the suggester of the questions, Professor Von Breda,
received a silver medal.
Regretting very much that I am unable to attend the present meeting of the
British Association, I beg to submit to the Society’s indulgent criticism some ex-
tracts from the before-mentioned paper, the materials for which were derived from
the coal formations of Silesia. I am now about to extend this inquiry, at the re-
quest of the Prussian authorities, to the other coal strata situated in the Rhenish
provinces of Westphalia. : ;
Geologists had rarely found in former years any well-preserved plants in the coal
itself, and had inferred its composition from the plants that lie in the shale,
&c. associated with the coal: my observations in Upper and Lower Silesia prove
the correctness of this inference, as I have met with extended coal layers in
which the plants (Sigillaria, Stigmaria, Calamites, Lepidodendra, Nogyerathia) are
still so well preserved that we can distinguish with the naked eye the individual spe-
cies. Thesestems, or more properly their barks, lie pressed flat one upon the other,
commonly without the inner parenchyma (yet sometimes the latter is preserved
and converted into coal), in such a manner that we are able still to recognise, under
the microscope, the cells of the parenchyma. Besides this, the so-called mineral
charcoal, or fibrous anthracite, does not occur here in single little fragments as it
is found elsewhere in the coal, but in broad compressed stems a foot long, which
offer the structure of the Araucariz of our present period (Araucarites carbonarius,
mihi).
According to the predominance of one or the other genus of plants, I distinguish
at many places in Upper Silesia, coal of Sigillaria, Araucarian coal, and Lepido-
dendron coal, of which the last is far the rarest.
In consequence of these observations I can now give a very simple explanation
of the way in which coal has been formed. The Sigillariz (Stigmaria), Lepido-
dendrez, Calamitez, containing a softer parenchyme, soon began to be decomposed
and disaggregated ; but when this process of decomposition was terminated, by early
depositions covering the vegetable mass, and the formation of coal was rendered
possible, the Araucariz, which were much harder, and therefore not equally ad-
vanced in decomposition, were introduced into the mass in longer fragments, in
which the ligneous structure, viz. the parenchymatous wood, cells and medullary
rays, are still clearly discernible even under a simple lens. By a more detailed re-
search into the situations which are occupied by all the species of plants detected in the
coal itself (which species amount to eighty in number), compared with those plants
which occur in the slate-clays and sandstonesof the Silesian coal-pits (which produce
about four millions of tons a-year), certain positive relations, or modes of distribu-
tion, became apparent, such as could not be overlooked. I observed a separation
into groups, or the consociated occurrence of certain species; the failing of one
species and the substitution of another of the same genus in one and the same coal
stratum ; and also a different condition of the vegetables in the strata superimposed
one on another.
Besides this, the mode of preservation of the fossil plants (ferns with flexible but
browned leaflets, &c.), the uniform continuity of many strata with the same thick-
ness over a space of many German miles, the multitude of upright stems, of which
as many as 200 have already been observed, with other conditions not noticed here, ~
are proofs of tranquil deposition over the present localities,
TRANSACTIONS OF THE SECTIONS. 51
On the other hand, calculation shows, that to form such thick strata of coal as
occur in our country (to the thickness of from thirty to sixty feet), the plants which
could grow upon the same area, even in their most luxuriant condition, would never
have sufficed. I therefore cannot but suppose that a large part of our layers of
coal have been formed after the manner of our peat moors, during a long course
of time; and certainly in the humid way, as I have formerly attempted to show,
and as I have more recently exemplified satisfactorily by experiments. If, for in-
_ stance, we keep vegetables in boiling water for a long time (for three months to a
year), they are converted into brown coal (lignite), and they acquire at last a totally
black coal-like condition, if we add a small quantity of sulphate of iron, in the
proportion of half a drachm to six ounces of plants; no one will doubt that this
salt, which occurs so commonly in coal, has largely cooperated in the formation of
the mineral.
I may state that many spherosiderites of the coal haye been produced just as
_ our marsh iron ores (Limonite, Rasenerz) now are.
On Sea Water, and the Effects of Variation in its Currents.
By Prof. Forcunammer of Copenhagen.
The author, referring to a chemical examination of sea water in different latitudes
and currents, tried to show the influence which a change in oceanic currents might
have had upon the climate of the North of Europe, The inquiries of Prof. Steenstrup
and Lovén respecting the changes in the forest- trees and marine animals indicated a
slow increase of the mean temperature of Northern Europe. To account for this, Dr.
_ Forchhammer supposed the British Channel to have been closed, and a polar current to
haye passed over the lower partsof Northern Russia into the Bothnian Gulf, and thence
into the German Ocean. The separation of England from France was supposed to
have taken place in recent times ; and without quoting the zoological evidence col-
lected by British naturalists, he would refer to physical features,—such as the va-
_ rious changes which the Rhine and the Scheldt suffer at their mouths, and which even
the smallest rivulet on the western shore of the Cimbrian Peninsula undergoes.
These rivers turn their mouths towards that side from which the tide comes,—one ha-
Ying, in historical times, changed its mouth more than thirty miles to the south. The
mouth of the Rhine has been known for about 2000 years; and since the time of
the Romans, when it flowed straight towards the north, where at present the Zuy-
der Zee is, it has been seen constantly turning towards the west. From this change,
he inferred a change in the direction of the tide, which he supposes to have arrived
formerly at the coast of Holland from the north, instead of from the west, as at pre-
sent, The marshes on the southern and eastern sides of the German Ocean become
| broader in proportion as they approach the mouth of the present channel ; a circum-
tance the very reverse of what might have been expected under present circum-
stances, since the clay is never deposited when there is any considerable motion in
the water. On the contrary, if the Channel were shut up, then the present locality
of the marshes would be that best adapted for their formation: from which he infers
that the principal marshes were formed before the opening of the Channel. The
) earliest accounts of the Channel date from the fourth century 8B.c., and at the time
f Alexander the Great we find that news of a very great inundation in the north-
ern countries (the Cimbrian flood) had reached Greece; and a tradition still ex-
isting in Jutland connects such a flood with the opening of the Channel. Along
all the western part of the Cimbrian Peninsula occurs a bed of pebbles, and in some
jlaces occur rolled pieces of the clay of the marshes, which must be ascribed to an
undation washing away the lighter materials. This inundation the author regards
‘as that of which both history and tradition speak ; and he thinks it was occasioned.
by the first opening of the Channel. These changes were in close connexion witha
depression of the greater part of Northern and Western Europe ; which is indicated
ong the coasts of Denmark and England by submerged forests and peat-mosses.
In the shore of the dukedom of Sleswig a tumulus has been found in a submerged
st ; it contained knives of flint, and shows that the subsidence took place after
the country-was inhabited. The continuous elevation of the North of Europe would
d to this result,—that the White Sea would flow over the lower parts of Russia
EZ
52 REPORT—1846.
and Finland, bringing cold water and masses of ice into the German Ocean, which
being at that epoch a bay receiving waters also which had flowed round the northern
coast of Scotland, must have been materially influenced in its climate, so as to have
been colder than it is now. f
On the Fishes of the London Clay. By M. Acassiz.
The Professor stated that since his last report the number of species known from |
the Paris basin increased; whilst few new forms had been obtained in the London
clay. He had however been interested in the examination of specimens of the teeth
of the saw-fish (Pristis) ; and had noticed some curious changes which they under-
went during the growth of the animal. The young teeth were covered with enamel,
and had a notch in their posterior margin; whilst in old tusks the bony material
alone existed and the margin was entire. On these grounds he considered the
three species of Pristis described by Shaw (P. semi-sagittatus, microdon and cuspi-
datus) as constituting in reality only one. Widely as these teeth differed in appear- _
ance from the flat, pavement-like teeth of the Sting-rays (Myliobatis), their micro-
scopic structure was identical; and Prof. Miiller of Berlin had lately shown that
the Pristis was not a shark, but belonged to the family of Rays. The Professor
then pointed out a peculiarity in the construction of the ventral fins of the Medi-
terranean Goby, a fish which fixes itself to the bottom by its fins; that act also like
springs in enabling the fish to rise from the bottom. He expected soon to be able
not only to discriminate every individual bone of any importance in the skeleton of
a fish, but also to distinguish the separate fin rays. M. Agassiz then made some
general remarks on the geographical distribution of recent fishes. There were many
families—of which the flying-fish (Exocetus) was an example—which were found
equally in the Indian, Pacific, and Atlantic Oceans. Others, like the Sharks and
Rays, were found in every sea from the Arctic circle to the tropics, but the species
differed on each coast; whilst some families were confined to the Indian seas, and
co-extensive only with the great land animals of that region. The Goniodontes
were peculiar to the freshwaters of South America; but these were connected with
the Ganoides of North America ; and these again closely allied to the Sturgeon, whose
affinities have hitherto been little understood. We have here, confined to the New
World, all the representatives of an order widely dispersed over the ancient strata.
Looking at the distribution of a particular species, like the Silurus, confined to the
Danube, Rhine, and a few other freshwaters of Europe, it might be asked by what
means it had wandered from one locality to another; to which he would reply that
these freshwater fish must have been created in the very streams in which they now
live, and in the same proportion as now. They leave the egg in so short a time, that
it was quite impossible they should be transported by birds or otherwise. The fishes
in the Paris basin appeared to have lived on a coral reef or rocky bottom, whilst
those of the London clay were such as in existing seas are found in shallow seas
and muddy waters.
On the Artesian Weil on the Southampton Common.
By J. R. Keerz, M.R.CI.
It will be seen on reference to the map that Southampton is situated about the
middle of a tertiary basin, and in its geological position is not very different from
London or Paris. The supply of water hitherto obtained has chiefly been from
private wells: almost every house in the town of any pretension as to size or value
has one, varying in depth from 10 to 25 feet. It is not known that any well
in the town exceeds that depth, since beyond that point, in most parts of the
town, we enter the bed of London clay, which lies under the whole district. There
is also a fluctuating supply obtained from the Common, about a mile-and-a-half
or two miles from the town. The extent of the Common is about 360 acres, and
its elevation varies from 100 to 200 feet above the sea-level of the town; the
quantity of water got from this quarter has been gained by intersecting the Common
in various directions by drains of varying depth from 10 to 20 feet: the water
thus collected flows into three reservoirs, from whence it is conveyed into the town
by iron pipes. This supply is variable according to the season; in the winter
TRANSACTIONS OF THE SECTIONS. 53
there is abundance ; and in the spring it affords 19,000 or 20,000 cubic feet per diem :
in the summer it has fallen as low as 3600, as in September last. Under these
circumstances it became necessary to seek for a larger supply. The town is situ-
ated on a tongue of land with the rivers Itchen and Test on each side discharging
their waters into the estuary called the Southampton Water. The inhabitants
would gladly have availed themselves of a supply from the waters of the Itchen,
but the late owner of that part of the river which would have been most suitable
for this purpose would not grant the supply but upon terms that were unsatis-
factory to the rate-payers. This mode of supply was therefore abandoned; and the
greater distance of the River Test being an objection on account of the expense it
would have entailed upon them, it was also given up; the commissioners were thus
thrown back upon their own resources, and determined to ascertain the practicabi-
lity of forming an Artesian Well. For this purpose an experimental boring was
made on the Common, asa preliminary step, in Nov. 1835, and was continued till
the chalk formation was reached, in January 1836, at the depth of 480 feet.
In this experiment the diluvial gravel and sand, and upper tertiary strata, over-
lying the London clay were found to be about 80 feet in thickness, the bed of London
clay about 300 feet, and the plastic dlay, resting on the chalk, another 100 feet ; the
boring was continued 50 feet further, when it having been reported that an ample
supply of water was to be found at that depth, an act of parliament was soon after
obtained for providing the means necessary ; and a plan having been fixed on, the
undertaking commenced by sinking an iron shield made in segments, which, bolted
together, formed as a whole a cylinder of 13 feet in diameter ; this shield the con-
tractor purposed sinking to the depth of 160 feet, and from that point to bore to
the depth of 400 feet, commencing with a hole of 30 inches, diminishing gradually,
and ending with one of 20 inches in the chalk formation.
The work began in July 1838. Two steam-engines were provided, each of
twenty-horses power. The estimate and contract for the performance of the work
was 10,180/., for which the contractor undertook to supply from the well 40,000
cubic feet of water per diem, and provided four gentlemen as securities for the due
performance of the work. », exported to France from 1831 to 1844,
118.
++—, estiniated quantity of, required for the
construction and putting into operation
each mile of railway, 119.
in 1839, quantity of made in,
Jessop (William), production of iron in Great
Britain in 1840, as ascertained by, 116.
Light on the growth of plants, influence of,
33.
Lindley (Prof.) sixth report on the vitality of
seeds, 20.
Madder, on the colouring matters of, 24.
Man, on the bones of the skull of, 300.
Mastoid, on the, 197.
Medicines, on the physiological action of, 27.
Mushet (David), quantity of iron made in
Great Britain in 1839, as stated by, 116.
Orbitosphenoid, on the, 211.
Osler’s anemometer, on, 343.
Owen (Prof.) on the archetype and homolo-
gies of the vertebrate skeleton, 169; table
of synonyms of the bones of the head ‘of
vertebrata, according to their special ho-=
mologies ; of the elements of the typical
vertebrata; of the bones of the head, ac-
INDEX I.
cording to their general homologies. See
Tables I. I. and III.
Pachyderm, on the skull bones of a young,
297.
Percy (Dr. John) on the crystalline slags,
351.
Phillips (John) on anemometry, 340.
Plants, influence of light on the growth of, 33.
Porter (G. R.) on the progress, present
amount, and probable future condition of
the iron manufacture in Great Britain, 99.
Railway, estimated quantity of iron required
for the constructing and putting into ope-
ration each mile of, 119.
Schunck (Dr.) on the colouring matters of
madder, 24.
Sea-water, comparative analytical researches
on, 90.
Seeds, on the vitality of, 203; table of expe-
riments, 21.
Skeleton, on the archetype and homologies
of the vertebrate, 169.
Skull of the vertebrate series, on the con
formity of structure of the, 176.
Skull-bones, classification of, 307.
Slags, on the crystalline, 351.
Steam-vessels, iron, being built. in the Clyde
during the spring of 1846, 117.
Stokes (G. G.) on recent researches in hydro-
dynamics, 1.
Strickland (H. E.) sixth report on the vitality
of seeds, 20.
Tides, theory of river and ocean, 9.
Transcendents, on algebraical, 43.
Vertebra, synonyms of, the elements of the
typical. See Tadle II.
Vertebre, development of, 254. a
, general characters of the, of the trunk,
257.
, summary of modifications of corporal,
264.
— of the skull, 274.
—, objections to the cranial, considered,
309.
Vertebrata, synonyms of the bones of the
head of, according to their special homo-
logies, 176, and see Table Il. ,
Vertebrate skeleton, on the archetype and
homologies of the, 169.
Water, comparative analytical researches on
sea, 90.
Waves, theory of long, 4.
, oscillatory, 5.
, solitary, 8.
——,, atmospheric, 119. iy
——, recurrence of symmetrical, 121:
——., stations at which observations of the,
were made, 122, :
—+4, comparison of observations made at
Cambridge Heath from Oct. 1 to Noy. 21,
INDEX II.
- 1845, with those made at Leicester Square
from Sept. 14 to Nov. 25, 1842, 123.
Waves, review of the great symmetrical baro-
metric, as observed at Dublin, during the
Novembers of 1829 to 1845 inclusive, 126.
——, comparison of contemporaneous obser-
. vations of the return of the great, Nov.
1845, 130.
123
Wave, definition and phenomena of an atmo-
spheric, 134.
——,, barometric differences arising from
anterior and posterior slopes of crest, No. 2,
146.
——, symmetrical commenced at London,
150.
Whewell’s anemometer, on, 341.
INDEX II.
TO
MISCELLANEOUS COMMUNICATIONS TO THE
SECTIONS.
ABESSINIA, on the physical character of
' the table-land of, 70.
Acalephz, on the quasi-osseous system of, 87.
‘ Acid, on the production of nitric, 38,
, on the nature of lampic, 40.
on the action of oxalic, upon the dead
tissues of the animal body, 41.
Aden, abstracts of meteorological observations
_ made at, in 1845, 26.
Africa, on geological phenomena in, 69.
, on the Shea Butter-tree growing in, 90.
Agassiz (M.) on the fishes of the London clay,
ec on the rationale of certain prac-
“tices employed in, 42.
sccm a the extent, causes and remedies of
' fungi destructive in, 44.
, Synopsis of a proposal respecting a
_ physico-geographical survey of the British
islands, particularly in relation to, 72.
Air, on applying atmospheric, to propulsion,
113.
Alder (Joshua) on some new and rare British
species of naked Mollusca, 83.
Alga, allied to Coleochzte scutata, on an un-
described, 89.
Alge of the Isle of Wight, on the, 83.
Alison (Dr.) on the medical relief to the pa-
ee BORE of Scotland under the old jnagr
law, 9
Allman (Prof.) on certain peculiarities in the
anatomy of Limax Sowerbii, 82.
on the structure of Cristatella mucedo,
88.
on an undescribed Alga allied to Coleo-
chete scutata, 89.
Alten, meteorological observations made at,
in 1844 and 1845, 12.
, observations on the Aurora Borealis,
during the year 1845, 12.
America, on some fossil mammalia of South,
65.
on the geology of North, 117.
American mineral nemalite, analysis of the,
39.
Analyses, on the use of stating with the results
of, the nature of the methods employed, 42.
Analysis, on the principle of continuity in re-
ference to certain results of, 1.
, on a gas furnace for organic, 49.
Andes, on new species of humming birds from
the, 79.
Anemometer, on a new, 12.
for measuring the velocity of the wind,
modification of Dr. Whewell’s, 111.
Animal body, on the action of oxalic acid upon
the dead tissues of the, 41.
Animals, on an important chemical law in the
nutrition of, 41.
Ansted (Prof.) on the coal of India, 63.
K2
124
Aquatice, 78.
Artesian wells, on Southampton common, on
the, 52.
, on the applicability of M. Fauvelle’s
mode of boring, to the well at Southampton,
and to other wells, 56.
Artesian springs, on a new method of boring
for, 105.
Ascidians, specimens of, discovered in the
links of the chain of the floating bridge at
Itchin, near Southampton, 83.
Atmospheric tube, on a new, 113.
recorder, on an, 17.
Aurora Borealis, observations on the, during
the year 1845, at Alten, 12.
at Huggate, on, 15.
Australia, on the geological structure of, 68.
Aves constrictipedes, 77.
inconstrictipedes, 78.
Azimuth compass, on a new portable, 25.
Bald (Robert) on the Mushet band, commonly
called the black-band ironstone of the coal-
field of Scotland, 62.
Banks (Dr.) on a new anemometer, 12.
Barometer, on a self-registering, 17.
, on the relations of the semi-diurnal
movementsof the, tolandandsea breezes, 25.
Beetle, on a specimen of a, found imbedded
in some artificial concrete, 82.
Beke (C. T.) on the physical character of the
table-land of Abessinia, 70.
Belfast, comparison of the periods of the
flowering of plants in the early spring of
1846, in the Botanic Garden of, and the
Jardin des Plantes at Paris, 90.
Belgium, on the mines and mining industry
of, 101.
Bell (Prof.) on the crustacea found by Prof.
E. Forbes and Mr. M°Andrew in their
cruises round the coast, 80.
Bennet (Dr. H.) on a peculiar form of ulce-
ration of the cervix uteri, 94.
Bessarabia, on the Nekrasowzers of, 115.
Bethuck Indians of Newfoundland, on a vo-
cabulary of the, 115.
Bevan (Dr.) on applying atmospheric air to
propulsion, 113.
Birds, synopsis of the classification of the ge-
nera of British, 76.
, new species of humming, from the
Andes, 79.
, on the figures of, observed on a tomb
at Memphis, 79.
, list of the names of periodical, and the
dates of their appearance and disappear-
ance at Llanrwst, 79.
Birt (W. R.) on atmospheric waves, 35.
Blackwall (John), list of the names of perio-
dical birds, and the dates of their appear-
ance and disappearance, at Llanrwst, 79.
Blake (James) on the connexion between the
isomorphous relations of the elements and
their physiological action, 40.
Blaps mortisaga found imbedded in some
artificial concrete, 82.
INDEX II.
Blood’s circulation through the liver, on the
cause of the, 93.
Bodies, on the deviation of falling, from the
perpendicular, 2.
Bodmer (Mr.) on long and short stroked
steam-engines, 113.
Bollaert (W.) on the Comanche Indians, 116.
on the Indian tribes of Texas, 117.
Bombay, meteorological observations taken
at Fort George Barracks, in July, August
and September, 1845, 26.
Bonny, the Africans of the neighbourhood
of, 117.
Bonomi (J.) on the figures of birds observed
on a tomb at Memphis, 79.
Boring for Artesian springs, on a new method
of, 105.
Botanists, directions for the guidance of, in
their excursion to the Isle of Wight, 86.
Botany, 74.
Bracklestone Bay, on the fossils of, 67.
Brewster (Sir David) on a new property of
light exhibited in the action of chrysammate
of potash upon common and polarized light,
7
Brian (Capt.) on the Africans of the neigh-
bourhood of Bonny, 117.
Bridge, tubular, proposed by Mr. Stephenson
for crossing the Menai Straits, on the, 108.
Brisbane (General Sir T. M.) results of the
magnetic observations made at his obser-
vatory, 32.
Bristol and Taunton, on railway sections made
on the line of the Great Western railway,
between, 59.
British islands, synopsis of a proposal respect-
ing a physico-geographical survey of the,
particularly in relation to agriculture,
72.
seas, on the pulmograde meduse of the,
84.
Brockedon (Mr.) on vulcanized caoutchouc,
113.
Brooke (C.) on the construction of a self-re-
gistering barometer, thermometer, and psy-
chrometer, 17.
Broun (J. A.) on some results of the magnetic
observations made at General Sir T. M.
Brisbane’s observatory, 32.
Buckland (Rev. W.) on the applicability of
M. Fauvelle’s mode of boring artesian wells
to the well at Southampton, and to other
wells, and to sinkings for coal, salt, and
other mineral beds, 56. ;
Buckman (James) on the discovery of a new
species of Hypanthocrinite in the upper Si-
lurian strata, 61.
on the age of the Silurian limestone of
Hay Head, near Barr Beacon, in Stafford-
shire, 61.
Bullar (Dr. Joseph) on the identity of certain
electro-magnetic laws, 29.
Butter-tree, on the Shea, growing in Africa, 90.
Calcium, on the extent to which fluoride of,
is soluble n water at, 60° F., 38.
INDEX II.
»Candle, extraordinary appearance in the flame
of a common mould, 49.
Caoutchouc, on vulcanized, 113.
Carpenter (Dr.) on the microscopic character
of shells, and on representing natural hi-
story objects by means of photography, 82.
on the structure of the Pycnogonidez,
82.
on the physiology of the Encephalon, 92.
Causation, magnetic, 33.
Cavendish’s experiment respecting the pro-
duction of nitric acid, Dr. Daubeny on, 38.
Cells, on the development of, 90.
Cervix uteri, on a peculiar form of ulceration
of the, 94.
Chemistry, 37.
, organic, on the application of the prin-
ciples of a natural system of, to the expla-
nation of the phenomena occurring in the
diseased potato tuber, 44.
Childers (Capt. W. W.) meteorological obser-
vations made at St. Helier, Jersey, in the
years 1843 to. 1846, 13.
Children, on the mortality of, 100.
Christiana, meteorological observations made
at, in 1845, 12,
Ciliogrades, on the embryogeny of, 87.
Clarke (B.) on the foliage and inflorescence of
. the genera Phyllanthus and Xylophylla,
91.
Clarke (Mr.) on increasing to larger dimen-
sions the model tubes for the proposed
Menai bridge, 109.
on a new atmospheric tube, 113.
| Clay, on the fishes of the London, 52.
Clouds, on measuring the height of, 15.
»Clupeade, on the natural and economic hi-
. story of:certain species of the, 79.
Coal-field of Scotland, on the black-band iron-
stone of the, 62.
‘Coal, on the applicability of M. Fauvelle’s
mode to sinkings for, 56.
of India, on the, 63.
of Silesia, on the origin of the, 50.
.—— on the annual consumption of, and the
probable duration of the coal-fields, 105.
Cole (J. F.) meteorological observations made
at Alten, in 1844 and 1845, 12.
observations on the Aurora Borealis
during the year 1845, at Alten, 12.
Coleochzte scutata, on an, undescribed Alga
«allied to, 89.
Compass, on a new portable azimuth, 25.
Connell (Prof.), analysis of the American
mineral nemalite, 39.
on the nature of lampic acid, 40.
Comanche Indians, on the, 116.
“—— vocabulary, on a, 117.
-Condenser, on a new multiplying, 31.
Continuity, on the principle of, in reference
to certain results of analysis, L.
_ Cooley (W. Desborough) on: a physico-geo-
graphical survey of the British islands, par-
ticularly in relation to agriculture, 72.
_ Corfu, on the natural history of, 84.
Cornwall, on the marine zoology of, 86.
125
Couch (J.) on the ege purse and embryo of a
species of Myliobatus, 80.
Coregoni, on the natural and economic history
of certain species of the, 79.
Crania of two species of crocodile from Sierra
Leone, on the, 79.
, on the ethnographical distribution of
round and elongated, 116.
Crime, statistics of, in England and Wales,
for the years 1842, 1843 and 1844, 102.
Criminal courts of India, statistics of the, 95.
and miscellaneous statistical returns of
the Manchester police for the year 1845, 98.
Cristatella mucedo, on the structure of, 88.
Crocodile from Sierra Leone, on the crania of
two species of, 79.
Crowe (J. R.) meteorological observations for
1845, made at Christiana, 12.
Crustacea found by Prof. E. Forbes and Mr,
M° Andrew in their cruises round the coast,
on the, 80.
Crystallography, 46.
Cucumber, on the true nature of the tendril
in the, 88.
Cullen (M. General) on the fall of rain on the
coast of Travancore and table-land of
Uttree, 22.
Cumberland, on the fall of rain in the lake
districts of, in 1845, 18.
Cypris, on the occurrence of, in a part of the
tertiary freshwater strata of the Isle of
Wight, 56.
Dale (Mr.) on elliptic polarization, 5.
Daubeny (Dr.) on Cavendish’s experiment re-
specting the production of nitric acid, 38.
on the rationale of certain practices em-
ployed in agriculture, 42.
» new facts bearing on the chemical
theory of volcanoes, 45.
Davies (H. B.) on the Tasmanians, 117.
Dent (E. J.) on a new portable azimuth com-
pass, 25.
Diarrheea, diagrams showing the mortality of,
concurrently with progressive increase of
temperature in London, 94.
Dispensaries of India, statistics of the govern-
ment, 96.
Dollond (G.) on an atmospheric recorder, 17.
Duncan (J.) on geological phenomena in
Africa, 69.
Duncan (J. F.) on the Shea butter-tree grow.
ing in Africa, 90.
Education in Glasgow in 1846, on the statis-
tics of, 101.
Edwards (Mr.) on the fossils of Bracklestone
Bay, Sussex, 67.
Egg-purse of a species of Myliobatus, on the,
80.
Electricity of tension in the voltaic battery, 47.
Electrization of needles in different media, on
the, 46,
Electrodes of a voltameter, on the influence
which finely divided platina exerts on the,
46. re
126
Electro-magnetic laws, on the identity of cer-
tain, 29.
Electro-magnetism, 27.
Electro-physiology, summary of researches
in, 28.
Elements, on the connexion between the iso-
morphous relations of the, and their phy-
siological action, 40.
Embryo of a species of Myliobatus, on the, 80.
Encephalon, on the physiology of the, 92.
England, on the cultivation of silk in, 87.
, on plate-glass making in 1846, con-
trasted with that in 1827, 101.
, Statistics of crime in, for the years 1842,
1843, 1844, 102,
Essington, on the inhabitants of port, 117.
Ethnological philology, on the present state
of, 115.
Eye-piece, on the arrangement of a solar, 9.
Eyton (Mr.) on a vertical steam-engine, 113.
Fairy-rings of pastures, on the, 43.
Falconer (Dr.} on the crania of two species of
crocodile from Sierra Leone, 79.
Fauna of Ireland, additions to the, 83.
Fauvelle (M.) on the applicability of his
mode of boring Artesian wells to the well at
Southampton, and to other wells, 56.
on a new method of boring for Artesian
springs, 105.
Finlay (G.) on the origin of the modern
Greeks, 117.
Fishes, on the, of the London clay, 52.
, on the application of Dr. Thibert’s me-
thod of modelling and colouring after nature
all kinds of fishes, 80.
Fitton (Dr.) on the arrangement and nomen-
clature of some of the subcretaceous strata,
58.
Flame of a common mould candle, extraordi-
nary appearance in the, 49.
Flora, on the geographical distribution of the,
of India, 74.
of Ireland, on additions to the, 90.
Forbes (Prof.) on the localities and geological
features of the Isle of Wight, 58.
on natural history, observations made
since last meeting bearing upon geology, 69.
, Prof. Bell on the crustacea found by, in
cruising round the coast, 80.
on the pulmograde medusz of the Bri-
tish seas, 84.
Forchhammer (Prof.) on sea water and the
effects of variation in its currents, 51.
Fort George Barracks, Bombay, meteorologi-
cal observations taken at, in 1845, 26.
Fossil mammalia of South America, on some,
65.
Fossils of Bracklestone Bay, Sussex, on the,
67.
Fowler (Dr.) on the relations of sensation to
the higher mental processes, 92.
Freeman (Rev. J.) on the inhabitants of
Prince’s island, 117.
Fungi, on the extent, causes and remedies of,
destructive in agriculture, 44.
INDEX Il,
Gases, on the decomposition of water into its
constituent, by heat, 48.
Gas furnace for organic analysis, on a, 49.
meters now in use, on the comparative
value of the different kinds of, 114.
Gassiot (John P.) on the electricity of tension
in the voltaic battery, 47.
Geneva, zoology of Lough Neagh compared
with that of the lake of, 84,
Geography, physical, 50.
Geological structure of Australia, on the, 68.
phenomena in Africa, on, 69.
Geology, 50.
, notices of natural history observations.
made since last meeting bearing upon, 69.
of N. America, on the, 117.
Georama, on the, 73.
Glasgow, on the statistics of education in, in
1846, 101.
Glass-making, plate, in England in 1846 con-
trasted with that in 1827, 101.
Goniometer, on a new, 46.
Géppert (Prof.) on the origin of the coal of
Silesia, 50.
Gould (John) on new species of humming
birds from the Andes, 79.
Grallatores, 78.
Granite, graphic, 69,
Great Western Railway, on sections made on
the line of the, between Bristol and Taun-
ton, 59.
, on three sections of the oolitic forma-
tions on the, at Sapperton tunnel, 61.
Greeks, on the origin of the modern, 117.
Greene (Dr. R.) on a portable equatorial
stand for telescopes without polar axis, 8.
Grewe (J. H.) observations on the Aurora
Borealis during the year 1845, at Alten, 12.
» Meteorological observations made at
Alten in 1844 and 1845, 12.
Grove (W. R.) on the decomposition of water
into its constituent gases by heat, 48.
Guerin (M.) on the Georama, 73.
Guy (Dr.) on the duration of life in the mem-
bers of the several professions, founded on
the obituary lists of the annual register, 99.
Haliday (A.H.), zoology of Lough Neagh,
compared with that of the lake of Geneva,
84,
Halo at Huggate, on a, 15.
Hancock (Albany) on some new and rare
British species of naked Mollusca, 83.
Hay ‘Head, on the age of the Silurian lime-
stone of, 61.
Heat, on the decomposition of water into its
constituent gases by, 48.
Henfrey (A.) on the development of cells, 90.
Herschel (Sir John, Bart.) letter to, from
Prof. Oersted, on the deviation of falling
bodies from the perpendicular, 2.
Heywood (James), Oxford University ‘statis-
tics, 99.
Hodgkinson (E.) on the tubular bridge pro-
posed by Mr. Stephenson for crossing the
Menai Straits, 108.
INDEX II.
- Hogan (W.) on the meatis ‘of obviating the
ravages of the potato disease, by raising
fully grown healthy potatoes from seed in
one season, 89.
Hogg (John), synopsis of the classification of
the genera of British birds, 76.
Hopkins (Thomas) on the relations of the
semi-diurnal movements of the barometer
to land and sea breezes, 25.
Hopkins (W.) on certain deviations of the
plumb-line from its mean direction, in the
neighbourhood of Shanklin Down, Isle of
Wight, 59.
Howard (H.) on plate glass-making in En-
gland in 1846, contrasted with that in 1827,
101.
Huggate, on a halo at, 15.
Hypanthocrinite, on ‘the discovery of a new
species of, in the upper Silurian strata, 61.
Ibbetson (Capt.) on the localities and geolo-
gical features of the Isle of Wight, 58.
on three sections of the oolitic forma-
tions on the Great Western Railway, at the
west end of Sapperton tunnel, 61.
Incrustation of steam boilers, on preventing,
114.
India, on the coal of, 63.
, on the geographical distribution of the
flora of, with remarks on ‘the vegetation of
its lakes, 74.
— —-, statistics of civil justice in, from 1841
to 1844, 94.
, Statistics of the criminal courts of, 95.
——, statistics of the government charitable
' dispensaries of, 96.
“Indian and Pacific oceans, on the three races
of men inhabiting the islands of the, 114.
Indians, on a vocabulary of the Bethuck, of
Newfoundland, 115.
,, on the Comanche, 116.
-Insessores, 77.
Treland, additions to the fauna of, 83.
—~, —— flora of, 90.
Tronstone, on the black-band, of the’ coal-field
of Scotland, 62.
Isle of Wight, on the occurrence of Cypris in
a part of the’ tertiary freshwater, 56.
on the localities and geological ‘features
of the, 58.
, on certain deviations of the plumb-line
* from its'mean direction, in the neighbour-
hood of Shanklin Down in the, 59.
directions for the guidance of botanists
‘in their excursion to the, 86.
Java to Timor, on some tertiary rocks in the
islands stretching from, 67.
»Jobert (A.C. G.)\on graphic granite, 69.
Joule (J. P.) on the expansion of salts, 49.
Jukes (J. B.) on some tertiary rocks in the
islands stretching from Java to Timor,
67.
+—— on'the’geological structure of Australia,
——, on the three races of men inhabiting
127
the islands of the Indian -and Pacific
oceans, 114.
Jukes (J. B.) on the Aborigines of vind is
land, 114.
Justice in India, statistics of civil, 94.
Keele (J. R.) on the Artesian well on South-
ampton common, 52.
Kemp (Dr. G.) on the application of the prin-
ciples of a natural system of organic che-
mistry to the explanation of the phzno-
mena occurring in the diseased potato
tuber, 44.
Kew, on the meteorological observations at,
10.
King (William) on some new species of ani-
mals found on the coast of ‘Northumber-
land, 838.
Knowles (E.R. J.) on an extraordinary ap-
pearance in the flame of a common mould
candle, 49.
on the annual consumption of coal and
the probable duration of the coal-fields,
105.
Knox (Dr.) on the natural and economic hi-
story of certain species of the Clupeade,
Coregoni and Salmonide, 79.
on the application of the method, dis-
covered by the late Dr. Thibert, of model-
ling and colouring after nature all kinds of
fishes, 80.
Lamb (Mr.) on mechanical apparatus em-
ployed for the purpose of preventing in-
crustation of steam-boilers, 114.
Laming (Dr.) on the constitution ‘and’ forces
of the molecules of matter, 35.
Lankester (Dr.) on' the woody fibres of the La-
vatera arborea, and suggestion that it'might
be of use in the arts and’ manufactures~of
the country, 90.
Latham (Dr.) on the’present ‘state of ethiié-
logical philology, 115.
on a vocabulary of the Bethuck Indians
of Newfoundland, 115.
on a Comanche vocabulary, 117. .
Lavatera arborea, suggested to be of use in
the arts and manufactures of ‘the country,
90.
Lawson (Henry) on an ‘easy*method of ‘con-
tracting the aperture’ofa large telescope, 9.
on the arrangement of asolar eye-piece, 9.
Laycock (Dr.) diagrams showing’ the morta-
lity of diarrhcea concurrently with progres-
sive increase of temperature in’ London, 94,
on some diseases resulting from the im-
moderate use of tobacco, 94.
on ‘the statistics of sickness’ and~mor-
tality in the city of York, 104.
Lead, on the action of atmospheric air, un-
combined chlorine, and carbonicacid on, 42.
Lee (Dr.)* tables of meteorological: observa-
tions made at Christiana and Alten, pre-
sented by, 12.
Leeson (Dr. H. B.) on crystallography and-a
new goniometer, 46.
128
Letheby (H.).on the action of oxalic acid upon
the dead tissues of the animal body, 41.
on the difference in the physiological
actions of the yellow and red prussiates as
an evidence of their containing dissimilar
radicals, 41.
Liddell (A.) on the statistics of education in
Glasgow in 1846, 101.
Life, on the duration of, in the members of
the several professions, 99.
Light, en certain cases of elliptic polarization
of, by reflexion, 3.
, on a new property of, exhibited in the
action of chrysammate of potash upon
common and polarized light, 7.
Limax Sowerbii, on certain peculiarities in
the anatomy of, 82.
Limestone of Hay Head, on the age of the
Silurian, 61.
Liver, on the cause of the blood’s circulation
through the, 93.
Llanrwst, in N. Wales, list of names of perio-
dical birds, and the dates of their appear-
ance and disappearance at, 79.
London clay, on the fishes of the, 52.
Lough Neagh, zoology of, compared with that
of the Lake of Geneva, 84.
Louisenberg, on the natural peculiarities of
the mountain so called, 91.
Lyell (Charles) on the delta and alluvial de-
posits of the Mississippi, and other points in
the geology of North America, observed in
the years 1845-46, 117.
Macassar, on the natives of, 115.
Macrauchenia, 66.
Magnetic causation, 33.
condition, on the mode of developing
the, 35.
observations made at General Sir T. M.
Brisbane’s observatory, 32.
Magnets, on the process of manufacture to
produce, having the greatest fixity and ca-
pacity conjointly secured, 33.
Mammalia of South America, on some fossil,
65.
Manchester police, criminal and miscellaneous
statistical returns of the, for the year 1845,
98.
Manures, on certain principles which obtain
in the application of, 44.
Marine zoology of Cornwall, on the, 86.
Mathematics, 1.
Matter, on the constitution and forces of mo-
lecules of, 35.
Matteucci (Prof.) summary of researches in
electro-physiology, 28.
on the electrization of needles in differ-
ent media, 46.
Mayes (William), abstracts of meteorological
observations made at Aden in 1845, 26.
, meteorological observations taken at
Fort George Barracks, Bombay, in 1845,
26.
M° Andrew (Mr.), Prof. Bell on the crustacea
found by, in cruising round the coast, 80.
INDEX II.
Mechanical Science, 105. ;
Medical Science, 92. :
Meduse of the British seas, on the pulmo-
grade, 84.
Memphis, on the figures of birds observed on
a tomb at, 79.
Men, on the three races of, inhabiting the is-
lands of the Indian and Pacific oceans, 114.
Menai bridge, on increasing to larger dimen-
sions the model tubes for the proposed, 109.
Menai straits, on the tubular bridge proposed
by Mr. Stephenson for crossing the, 108.
Mercury, on the changes which it undergoes
in glass vessels hermetically sealed, 37.
Metal, on a second new, contained in the Ba-
varian tantalite, 37.
Meteorological observations, on the Kew, 10.
made at Alten, at the Kaafjord Obser-
vatory, in 1844 and 1845, 12.
at Christiana, in 1845, 12.
at St. Helier, Jersey, in the years 1843
to 1846, 13.
at Fort George Barracks, Bombay, in
1845, 26.
at Aden in 1845, abstracts of, 246.
Meteorological phenomena, on some, 11.
Middendorff (Prof. Von.) on certain races of
Siberia, 115.
Miller (J. F.) on the fall of rain in the lake
districts of Cumberland and Westmoreland,
&c. in the year 1845, 18.
, readings of mountain rain gauges, in
June, July and August, 1846, 21.
Mineral beds, on the applicability of M. Fau-
velle’s mode to sinkings for, 56.
Mines and mining industry of Belgium, 101.
Mississippi, on the delta and alluvial deposits
of the, 117.
Mollusca of the Isle of Wight, on the land, 83.
, on some new and rare British ‘species
of naked, 83. ‘
Mollusks, on the dissimilarity in the calcify-
ing functions of, 82.
Moon, on attempts to explain the apparent
projection of a star on the, 5.
Morriss-Stirling (T. D.) on proposed substi-
tutes for the potato, 90.
Mortality, on the statistics of, in the city of
York, 104.
Murchison (Sir R. I.) letter to, from the Hon.
F. Strangways on the natural peculiarities
of the mountain now called the Louisen-
berg, 91.
Mushet band, on the, 62.
Myliobatus, on the egg-purse and embryo of
a species of, 80.
Natatores, 78.
Natural history observations made since last
meeting bearing upon geology, notices of,
69.
Needles, electrization of, in different media,
46.
Neeld (Mr.) criminal and miscellaneous sta-
tistical returns of the Manchester police for
the year 1845, 98. -
INDEX II.
Neison (F. G. P.), statistics of crime in Eng-
land and Wales, for the years 1842, 1843,
and 1844, 102.
Nekrasowzers of Bessarabia, on the, 115.
Nemalite, analysis of the American mineral,
39.
Nesodon, new species, 66.
Newfoundland, on the aborigines of, 114.
, on a vocabulary of the Bethuck Indians
of, 115.
Northumberland, on some’ new species of ani-
mals found on the coast of, 83.
Northwich salt-field, on the extent of the, 62.
Oersted (Prof.) on the deviation of falling
bodies from the perpendicular, in a letter
to Sir John Herschel, Bart., 2.
on the changes which mercury some-
times suffers in glass vessels hermetically
sealed, 37.
Oolitic formations on the Great Western Rail-
way, on three sections of the, at the west
end of Sapperton tunnel, 61.
Ormerod (G. Wareing) on the extent of the
Northwich salt-field, 62.
Osborn (Henry) on the presence of atmo-
spheric air, uncombined chlorine, and car-
bonic acid found in the water of some of
the wells in the suburbs of Southampton,
and their action on lead, 42.
Owen (Prof.) on some fossil Mammalia of
South America, 65.
Oxford University statistics, 99.
Paraselene at Huggate, on a, 15.
Paris, comparison of the periods of the flower-
ing of plants in the early spring of 1846, in
the Botanic Gardens of Belfast, and the
Jardin des Plantes at, 90.
Pastures, on the fairy rings of, 43.
Patterson (R.) on specimens of Ascidians dis-
covered in the links of the chain of the
floating bridge at Itchin, near Southamp-
ton, 83.
Peach (C. W.) on the marine zoology of
Cornwall, 86.
Pelopium, on a second new metal contained
in the Bavarian tantalite, 37.
Percy (Dr. John) on a gas furnace for orga-
nic analysis, 49.
Perpendicular, on the deviation of falling
bodies from the, 2.
Petrie (W.) on the results of an extensive
series of magnetic investigations, including
most of the known varieties of steel, 33.
Philology, on the present state of ethnologi-
cal, 115.
Phipps (Dr. J.) on the sailing powers of two
yachts, built on the wave principle, 112.
Photographic self-registering apparatus at
Kew, account of the, 10.
Photography, on representing natural history
objects by means of, 82.
Phyllanthus, on the foliage and inflorescence
of the genus, 91.
Physico-geographical survey of the British
129
islands, particularly in relation to agricul-
ture, 72.
Physics, 1.
Polarization of light by reflexion, on certain
cases of elliptic, 3.
, elliptic, 5.
Poor law, on the medical relief to the paro-
chial poor of Scotland under the old, 97.
Portlock (Captain) on the natural history of -
Corfu, 84.
Potash, chrysammate of, on a new property of
light exhibited in the action of, upon com-
mon and polarized light, 7.
Potato, on the application of the principles of a
natural system of organic chemistry to the
explanation of the phenomena occurring
in the diseased tuber, 44.
, on the means of obviating the ravages
of the disease in the, 89.
, on proposed substitutes for the, 90.
Powell (Rev. Prof.) on certain cases of ellip-
tical polarization of light by reflexion, 3.
on the bands formed by partial inter-
ception of the prismatic spectrum, 4.
on attempts to explain the apparent
projection of a star on the moon, 5.
Plants, comparison of the periods of the flow-
ering of, in the spring of 1846, in the Bo-
tanic Garden of Belfast, and the Jardin des
Plantes at Paris, 90.
Platina, on the influence which finely divided,
exerts on the electrodes of a voltameter,
46.
Playfair (Dr. Lyon) on the expansion of salts,
49.
Plumb-line, on certain deviations of the, from
its mean direction, in the neighbourhood of
Shanklin Down, Isle of Wight, 59.
Prestwich (Joseph, Jun.) on the occurrence of
Cypris in a part of the tertiary freshwater
strata of the Isle of Wight, 56.
Price (John) on the embryogeny of Pulmo-
grades and Ciliogrades, 86.
on the quasi-osseous system of Acale-
phe, 87.
Prideaux (J.) on the extent, causes and re-
medies of fungi destructive in agriculture,
44, g
Princes’ Island, on the inhabitants of, 117.
Propulsion, on applying atmospheric air to,
113.
Prussiates, on the difference in the physio-
logical actions of the yellow and red, as an
evidence of their containing dissimilar ra-
dicals, 41.
Psychrometer, on a self-registering, 17.
Pulmogrades, on the embryogeny of, 86.
Pycnogonidez, on the structure of the, 82.
Radicals, on the difference in the physiologi-
cal actions of the yellow and red prussiates
as an evidence of their containing dissimi-
lar, 41.
Railway sections made on the line of the
Great Western Railway between Bristol
and Taunton, 59.
130
Railway trains, on the law which governs the
resistance to motion of, at high velocities,
109.
» on a machine for registering the velo-
city of, 114. ‘
Rain, on the fall of, in the lake districts of
Cumberland and Westmoreland, in 1845,
18.
» readings of mountain gauges in June,
July and August, 1846, 21.
, on the fall of, on the coast of Travan-
core and table land of Uttree, 22.
Rankin (Rev. T.) on a halo, paraselene, and
Aurora Borealis, seen at Huggate, in York-
shire, 15.
: on the hybernation of snails, 83.
Raptores, 77.
Rasores, 78.
Reade (Dr. J.) experiments in thermo-elec-
tricity, 46.
Reeve (Lovell) on the dissimilarity in the
calcifying functions of Mollusks, whose or-
ganization is in other respects similar, 82,
Retzius (Prof.) on the ethnographical distri-
bution of round and elongated crania, 116.
Ricardo (M.) on a machine for registering the
velocity of railway trains, 114.
Robinson {Rev. Dr.) on the influence which
finely divided platina exerts on the elec-
trodes of a voltameter, 46.
» modification of Dr. Whewell’s anemo-
'.meter for measuring the velocity of the
wind, 111.
Rocks, tertiary, in the islands stretching from
Java to Timor, 67.
Ronalds (F.) on the meteorological observa-~
tions at Kew, with an account of the pho-
tographic self-registering apparatus, 10.
Rose (Prof, H.) on a second new metal, Pelo-
pium, contained in the Bavarian tantalite,
37.
Royle (Prof.) on the geographical distribution
of the flora of India, with remarks on the
_ vegetation of its lakes, 74.
Russell (Scott) on the law which governs the
__ resistance to motion of railway trains at high
_ velocities, 109,
Salmonidz, on the natural and economic hi-
story of certain species of the, 79.
Salt, on the applicability of M. Fauvelle’s mode
to sinkings for, 56-
, on the extent of the Northwich field, 62.
Salter (Dr, Bell), directions for the guidance
of botanists in their excursion to the Isle of
Wight, and list of flowering plants of in-
terest in various parts of the island, 86.
on the true nature of the tendril in the
~ cucumber, 88.
Salts, on the expansion of, 49.
Sanders (W.) on railway sections made on the
line of the Great Western Railway, between
Bristol and Taunton, 59.
Sapperton tunnel, on three sections of the
oolitic formation on theGreat Western Rail-
way, at the west end of, 61.
INDEX Il.
Scoresby (Rev. W.) on the mode of develop-
ing the magnetic condition, 35.
Scotland, on the black-band ironstone of the
coal-field of, 62.
, on the medical relief to the parochial
poor of, under the poor law of, 97.
Searle (Dr.) on the cause of the blood’s cir-
culation through the liver, 93.
Sea-water, and the effects of variation in its
currents, 51.
Sensation, on the relation of, to the higher
mental processes, 92.
Sharp, (J.) on the comparative value of the
different kinds of gas meters now in use,
114,
Shea Butter-tree growing in Africa, on the, 90.
Shells, on the microscopic character of, 82.
Short (Mrs.). on the natives of Timor and
Maeassar, 115.
on the inhabitants of Port Essington,
117.
Shortrede (Capt. ) on the force of vapour, 16.
Siberia, on certain races of, 115.
Sickness, on the statistics of, in the city of
York, 104.
Sierra Leone, on the crania of two species of
crocodile from, 79.
Silesia, on the origin of the coal of, 50.
Silk, on the cultivation of it in England, 87.
Silurian limestone of Hay Head, on the age
of the, 61,
Silurian strata, on the discovery of a new spe-
cies of hypanthocrinite in the upper, 61.
Snails, on the hybernation of, 83.
Solar eye-piece, on the arrangement of a, 9.
Southampton, on the presence of atmospheric
air, uncombined chlorine, and carbonic acid
in the water of some of the wells in the
suburbs of, and their action on lead, 42.
, on the Artesian well on the common at,
52.
, on the applicability of M. Fauvelle’s
mode of boring Artesian wells to the well
at, 56.
Spectrum, on the bands formed by partial in-
terception of the prismatic, 4.
Spooner (William Charles) on certain prin-
ciples which obtain in the application of
manures, 44.
Springs, on a new method of boring for Arte-
sian, 105. 1
Star, on attempts to explain the apparent pro-
jection of a, on the moon, 5,
Statistics, 94.
Steam boilers, on preventing: incrustation of,
114.
Steam-engine, on long and short stroked, 113.
+ on a vertical, 113,
Steel, on the physical properties which it
should possess in the manufacture of mag-
nets, 34.
Stephenson’s (Mr.) tubular bridge proposed
for crossing the Menai Straits, K. Hodg-
kinson on the, 108, i
St. Helier, Jersey, meteorological observations
made at, in the years 1843 to 1846, 13.
INDEX II.
Strangways (Hon. F.) on the natural pecu-
liarities of the mountain now called the
Louisenberg, in a letter to Sir R. I. Mur-
chison, 91.
Strata of the Isle of Wight, on the occurrence
of Cypris in a part of the tertiary fresh-
water, 56.
, on the arrangement and nomenclature
of some of the subcretaceous, 58.
Svanberg (Prof. A. F.) on a new multiplying
condenser, 31. '
Sykes (Lt.-Col.) on the fall of rain on the
coast of Travancore and table land of Ut-
tree, 22.
——— statistics of civil justice in India for four
years, from 1841 to 1844, both inclusive, 94.
statistics of the government charitable
dispensaries of India, 96.
Tantalite, on a second new metal, Pelopium,
contained in the Bavarian, 37.
Tasmanians, on the, 117.
Taunton and Bristol. on railway sections made
on the line of the Great Western Railway
between, 59.
Telescepes, on a portable equatorial stand for,
without polar axis, 8.
» on an easy method of contracting the
aperture of large, 9.
Terrestres (Birds), 77.
Texas, on the Indian tribes of, 117.
Thermo-electricity, experiments in, 46.
Thermometer, on a self-registering, 17.
Thibert (Dr.) on the application of his method
to modelling and colouring after nature all
kinds of fishes, 80.
Thompson (W.) on the craniaof two species
of crocodile from Sierra Leone, 79.
additions to the Fauna of Ireland, in-
cluding species new to that of Britain, 83.
on the land mollusca, zoophytes and
alge of the Isle of Wight, 83.
-—, zoology of Lough Neagh, compared
with that of the Lake of Geneva, 84.
on additions to the flora of Ireland, 90.
, comparison of the periods of the flower-
ing of plants in the early spring of 1846, in
the Botanic Garden, Belfast, and the Jardin
des Plantes at Paris, 90.
Thomson (Dr. R. D.) on an important chemi-
cal law in the nutrition of animals, 41.
Timor, on some tertiary rocks in the islands
stretching from Java to, 67.
, on the natives of, 115.
Tobacco, on some diseases resulting from the
immoderate use of, 94.
Towler (G.), magnetic causation, 33.
Toxodon, new species, 65.
Travancore, fall of rain on the coast of, 22.
Twining (Dr.) on the Nekrasowzers of Bessa-
rabia, 115.
Uteri, on a peculiar form of ulceration of the
cervix, 94.
131
Uttree, fall of rain on the table land of, 22.
Valpy (R.) on the mines and mining industry
of Belgium, 101.
Vapour, on the force of, 16.
Volcanoes, new facts bearing on the chemical
theory of, 45.
Voltaic battery, on the electricity of tension
in the, 47.
Voltameter, influence which finely divided
platina exerts on the electrodes of a, 46.
Wales, statistics of crime in, for the years
1842, 1843, and 1844, 102.
Wartmann (Prof.) on some meteorological
phznomena, 11.
on electro-magnetism, 27.
Water, on the decomposition of, into its con-
stituent gases by heat, 48.
Wave principle, on the sailing powers of two
yachts built on the, 112.
Waves, atmospheric, 35.
Way (Prof. J. T.) on the fairy rings of pas-
tures, 43.
Well, on the Artesian, on Southampton com-
mon, 52.
, on the applicability of M. Fauvelle’s
mode of boring Artesian and others, 56.
Westmoreland, on the fall of rain in the lake
districts of, in 1845, 18.
West (W.) on the use of stating, with the re-
sults of analyses, the nature of the methods
employed, 42.
Whewell (Rev. W.) on measuring the height
of clouds, 15.
, Modification of his anemometer for mea-
suring the velocity of the wind, 111,
Whitby (Mrs.) on the cultivation of silk in
England, 87.
Wigglesworth (Mr.) on the mortality of chil-
dren, 100.
Wilson (Dr. George) on the extent to which
fluoride of calcium is soluble in water at
60° F., 38.
Wind, modification of Dr. Whewell’s anemo-~
meter for measuring the velocity of the,
111.
Xylophylla, on the foliage and inflorescence
of the genus, 91.
Yachts, on the sailing powers of two, built on
the wave principle, 112.
Yates (James) on Zamia gigas, 62.
York, on the statistics of sickness and mor-
tality in the city of, 104.
Young (Prof.) on the principle of continuity
in reference to certain results of analysis, 1.
Zamia gigas, 62.
Zoology, 74.
Zoophytes of the Isle of Wight, on the, 83.
THE END.
wa?
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List of those Members of the British Association for the Advancement
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LIFE MEMBERS.
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Adams, John Couch, M.A.,St. John’s College,
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ter.
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non, Ireland.
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ton, Yorkshire.
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Graham, Thomas, M.A., Professor of Chemis-
try in University College, London, F.R.S.
L. & E., F.G.S., Hon. Memb. National
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ton.
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Together with Papers on Mathematics, Optics, Acoustics, Magnetism, Electricity, Chemistry,
Meteorology, Geography, Geology, Zoology, Anatomy, Physiology, Botany, and the Arts;
and an Exposition of the Objects and Plan of the Association, &c.
PROCEEDINGS or tue THIRD MEETING at Cambridge, 1833, 8s.
ContTENTS:—Proceedings of the Meeting ;—Mr. John Taylor, on Mineral Veins ;—Dr.
Lindley, on the Philosophy of Botany ;—Dr. Henry, on the Physiology of the Nervous Sy-
stem ;—Mr. Peter Barlow, onthe Strength of Materials ;—Mr.S8. H. Christie, on the Magnet-
ism of the Earth ;—Rev. J. Challis, on the Analytical Theory of Hydrostatics and Hydrody-
namics;—Mr. George Rennie, on Hydraulics as a Branch of Engineering, Part I. ;—Rev. G.
Peacock, on certain Branches of Analysis.
Together with papers on Mathematics and Physics, Philosophical Instruments and Mecha~
nical Arts, Natural History, Anatomy, Physiology, and History of Science.
PROCEEDINGS or rote FOURTH MEETING, at Edinburgh, 1834, 10s.
ConTEnTs :—Mr. H. D. Rogers, on the Geology of North America ;—Dr. C. Henry, on
the Laws of Contagion ;—Prof. Clark, on Animal Physiology ;—Rev. L. Jenyns, on Zoology ;—
Rev. J. Challis, on Capillary Attraction ;—Prof. Lloyd, on Physical Optics ;—Mr. G. Rennie,
on Hydraulics, Part II.
Together with the Transactions of the Sections, and Recommendations of the Association
and its Committees. ,
;
a
PROCEEDINGS or rue FIFTH MEETING, at Dublin, 1835, 9s.
ConTENTs :—Rev. W. Whewell, on the Recent Progress and present Condition of the
Mathematical Theories of Electricity, Magnetism, and Heat ;—M. A. Quetelet, Apercu de
VEtat actuel des Sciences Mathématiques chez les Belges ;—Captain Edward Sabine, on the
Phznomena of Terrestrial Magnetism.
Together with the Transactions of the Sections, Prof. Sir W. Hamilton’s Address, and Re-
commendations of the Association and its Committees.
PROCEEDINGS or tHe SIXTH MEETING, at Bristol, 1836, 8s.
Contents :—Prof. Daubeny, on the Present State of our Knowledge with respect to Mine-
ral and Thermal Waters ;—Major Edward Sabine, on the Direction and Intensity of the Ter-
restrial Magnetic Force in Scotland ;—Mr. John Richardson, on North American Zoology ;—
Rev. J. Challis, on the Mathematical Theory of Fluids ;—Mr. J. T. Mackay, a Comparative
View of the more remarkable Plants which characterize the neighbourhood of Dublin and
Edinburgh, and the South-west of Scotland, &c.;—Mr. J. T. Mackay, Comparative Geogra-
phical Notices of the more remarkable Plants which characterize Scotland and Ireland ;—Re-
port of the London Sub-Committee of the Medical Section on the Motions and Sounds of the
Heart ;—Second Report ofthe Dublin Sub-Committee on the Motions and Sounds of the Heart ;
—Report of the Dublin Committee on the Pathology of the Brain and Nervous System ;—
J. W. Lubbock, Esq., Account of the Recent Discussions of Observations of the Tides ;—Rev.
Baden Powell, on determining the Refractive Indices for the Standard Rays of the Solar Spec-
trum in various media ;—Dr. Hodgkin, on the Communication between the Arteries and
Absorbents ;—Prof. Phillips, Report of Experiments on Subterranean Temperature ;—Prof.
Hamilton, on the Validity of a Method recently proposed by George B. Jerrard, Esq., for
Transforming and Resolving Equations of Elevated Degrees.
Together with the Transactions of the Sections, Prof. Daubeny’s Address, and Recommen-
dations of the Association and its Committees. ,
PROCEEDINGS or tue SEVENTH MEETING, at Liverpool, 1837, 11s.
ConTENTs :—Major Edward Sabine, on the Variations of the Magnetic Intensity observed _
at different points of the Earth’s Surface ;—Rev. William Taylor, on the various modes of
Printing for the use of the blind ;—J. W. Lubbock, Esq., on the Discussions of Observations
of the Tides which have been obtained by means of the grant of money which was placed at
the disposal of the Author for that purpose at the last Meeting of the Association ;—Prof.
Thomas Thomson, on the Difference between the Composition of Cast Iron produced by the
Cold and Hot Blast ;—Rev. T. R. Robinson, on the Determination of the Constant of Nutation
by the Greenwich Observations, made as commanded by the British Association ;—Robert
Were Fox, Esq., Experiments on the Electricity of Metallic Veins, and the Temperature of
Mines ;—Provisional Report of the Committee of the Medical Section of the British Associa-
tion, appointed to investigate the Composition of Secretions, and the organs producing them ;
—Dr. G. O. Rees, Report from the Committee for inquiring into the Analysis of the Glands,
&c. of the Human Body ;—Second Report of the London Sub-Committee of the British Asso-
ciation Medical Section, on the Motions and Sounds of the Heart;—Prof. Johnston, on the
Present State of our knowledge in regard to Dimorphous Bodies ;—Col. Sykes, on the Sta-
tistics of the Four Collectorates of Dukhun, under the British Government ;—Eaton Hodgkin-
son, Esq., on the relative Strength and other Mechanical Properties of Iron obtained from the
Hot and Cold Blast ;—William Fairbairn, Esq., on the Strength and other Properties of Iron
obtained from the Hot and Cold Blast ;—Sir John Robison, and John Scott Russell, Esq.,
Report of the Committee on Waves, appointed by the British Association at Bristol in 1836 ;
—Note by Major Sabine, being an Appendix to his Report on the Variations of the Magnetic
Intensity observed at different Points of the Earth’s Surface ;—James Yates, on the Growth
of Plants under glass, and without any free communication with the outward Air, on the Plan
of Mr. N. J. Ward, of London.
Together with the Transactions of the Sections, Prof. Traill’s Address, and Recommenda-
tions of the Association and its Committees.
PROCEEDINGS or roe EIGHTH MEETING, at Newcastle, 1838,
10s.
ConTENTS :—Rev. W. Whewell, Account of a Level Line, measured from the Bristol Chan-
nel to the English Channel, by Mr. Bunt;—Report on the Discussions of Tides, prepared
under the direction of the Rev. W. Whewell ;—W. Snow Harris, Esq., Account of the Progress
and State of the Meteorological Observations at Plymouth ;—Major Edward Sabine, on the
Magnetic Isoclinal and Isodynamic Lines in the British Islands;—D. Lardner, LL.D., on the —
Determination of the Mean Numerical Values of Railway Constants ;—R. Mallet, Esq., First
Report upon Experiments upon the Action of Sea and River Water upon Cast and Wrought
Iron ;—R. Mallet, Esq., on the Action of a Heat of 212° Fahr., when long continued, on In-
organic and Organic Substances.
Together with the Transactions of the Sections, Mr. Murchison’s Address, and Recommen-
dations of the Association and its Committees.
PROCEEDINGS or tut NINTH MEETING, at Birmingham, 1839, 9s.
ConTEnTs :—Rev. Baden Powell, Report on the Present State of our Knowledge of Re-
fractive Indices, for the Standard Rays of the Solar Spectrnm in different media ;—Report on
the Application of the Sum assigned for Tide Circulations to Mr. Whewell, in a Letter from
T. G. Bunt, Esq. ;—H. L. Pattinson, Esq., on some galvanic Experiments to determine the
Existence or Non-Existence of Electrical Currents among Stratified Rocks, particularly those
of the Mountain Limestone formation, constituting the Lead Measures of Alston Moor ;—Sir
David Brewster, Reports respecting the two series of Hourly Meteorological Observations kept
in Scotland at the expense ofthe British Association ;—Report on the subject of aseries of Re-
solutions adopted by the British Association at their Meeting in August 1838, at Newcastle ;—
Richard Owen, Esq., Reporton British Fossil Reptiles ;—Edward Forbes, Esq., Report on the
Distribution of pulmoniferous Mollusca in the British Isles;—W. Snow Harris, Esq., Third
Report on the Progress of the Hourly Meteorological Register at the Plymouth Dockyard,
Devonport.
Together with the Transactions of the Sections, Rev. W. Vernon Harcourt’s Address, and
Recommendations of the Association and its Committees.
PROCEEDINGS or true TENTH MEETING, at Glasgow, 1840, 10s.
Contents :—Rev. Baden Powell, Report on the recent Progress of discovery relative to
Radiant Heat, supplementary to a former Report on the same subject inserted in the first vo-
lume of the Reports of the British Association for the Advancement of Science ;—James D.
Forbes, Esq., Supplementary Report on Meteorology ;—W. Snow Harris, Esq., Report on
Professor Whewell’s Anemometer, now in operation at Plymouth ;—Report on “ The Motions
and Sounds of the Heart,” by the London Committee of the British Association, for 1839-40 ;
—Professor Schénbein, an Account ef Researches in Electro-Chemistry ;—Robert Mallet,
Esq., Second Report upon the Action of Air and Water, whether fresh or salt, clear or foul,
and at various temperatures, upon Cast Iron, Wrought Iron, and Steel ;—Robert Were Fox,
Esq., Report on some Observations on Subterranean Temperature ;—A. Follett Osler, Esq.,
Report on the Observations recorded during the years 1887, 1838, 1839 and 1840, by the
Self-registering Anemometer erected at the Philosophical Institution, Birmingham ;—Sir David
Brewster, Report respecting the two Series of Hourly Meteorological Observations kept at In-
verness and Kingussie, at the expense of the British Association, from Nov. Ist, 1835 to Nov.
Ist, 1889 ;—William Thompson, Esq., Report on the Fauna of Isiand: Div. Vertebrata ;—
Charles J. B. Williams, M.D., Report of Experiments on the Physiology of the Lungs and
Air-Tubes ;—Rev. J. 8. Henslow, Report of the Committee appointed to try Experiments on
the Preservation of Animal and Vegetable Substances.
Together with the Transactions of the Sections, Mr. Murchison and Major Edward Sabine’s
Address, and Recommendations of the Association and its Committees.
PROCEEDINGS or tHe ELEVENTH MEETING, at Plymouth,
1841, 9s.
Contents :—Rev. Philip Kelland, on the Present State of our Theoretical and Experi-
mental Knowledge of the Laws of Conduction of Heat ;—G. L. Roupell, M.D., Report on
Poisons ;—Mr. Bunt, Report on Discussions of Bristol Tides, under the direction of the Rev.
W. Whewell;—D. Ross, Report on the Discussions of Leith Tide Observations, under the di-
rection of the Rev. W. Whewell;—W. S. Harris, Esq., upon the working of Whewell’s Anes
mometer at Plymouth during the past year ;—Report of a Committee appointed for the pur«
pose of superintending the scientific co-operation of the British Association in the system of
Simultaneous Observations in Terrestrial Magnetism and Meteorology ;—Reports of Commit-
tees appointed to provide Meteorological Instruments for the use of M. Agassiz and Mr.
M‘Cord ;—Report of a Committee to superintend the reduction of Meteorological Observations ;
—Report of a Committee for revising the Nomenclature of the Stars ;—Report of a Committee
for obtaining Instruments and Registers to record Shocks of Earthquakes in Scotland and Tres
land ;—Report of a Committee for making experiments on the Preservation of Vegetative
Powers in Seeds ;—Dr. Hodgkin, on Inquiries into the Races of Man ;—Report of the Com-
mittee appointed to report how far the Desiderata in our knowledge of the Condition of the
Upper Strata of the Atmosphere may be supplied by means of Ascents in Balloons or other-
wise, to ascertain the probable expense of such Experiments, and to draw up Directions for
Observers in such circumstances ;—Richard Owen, Esq., Report on British Fossil Reptiles;— -
Reports on the Determination of the Mean Value of Railway Constants ;—Dionysius Lardner,
LL.D., Second and concluding Report on the Determination of the Mean Value of Railway
Constants ;—Edward Woods, Report on Railway Constants ;—Report of a Committee on the
Construction of a Constant Indicator for Steam-Engines.
Together with the Transactions of the Sections, Prof. Whewell’s Address, and Recommen-
dations of the Association and its Committees,
PROCEEDINGS or tue TWELFTH MEETING, at Manchester,
1842, 7s.
ConTENTs :—Report of the Committee appointed to conduct the co-operation of the British
Association in the System of Simultaneous Magnetical and Meteorological Observations ;—
John Richardson, M.D., Report on the present State of the Ichthyology of New Zealand ;—
W. Snow Harris, Report on the Progress of Meteorological Observations at Plymouth ;—
Second Report of a Committee appointed to make Experiments on the Growth and Vitality of
Seeds ;—C. Vignolles, Esq., Report of the Committee on Railway Sections ;—Report of the
Committee for the Preservation of Animal and Vegetable Substances ;—Lyon Playfair, M.D.,
Abstract of Professor Liebig’s Report on ‘“‘ Organic Chemistry applied to Physiology and Pa-
thology ;’—Richard Owen, Esq., Report on the British Fossil Mammalia, Part I. ;—Robert
Hunt, Researches on the Influence of Light on the Germination of Seeds and the Growth of
Plants ;—Louis Agassiz, Report on the Fossil Fishes of the Devonian System or Old Red Sand-
stone ;—William Fairbairn, Esq., Appendix to a Report on the Strength and other Properties
of Cast Iron obtained from the Hot and Cold Blast ;—David Milne, Esq., Report of the Com-
mittee appointed at the Meeting of the British Association held at Plymouth in 1841, for re-
gistering Shocks of Earthquakes in Great Britain ;—Report of a Committee appointed at the
Tenth Meeting of the Association for the Construction of a Constant Indicator for Steam-En-
gines, and for the determination of the Velocity of the Piston of the Self-acting Engine at
different periods of the Stroke ;—J. S. Russell, Report of a Committee on the Form of Ships ;
—Report of a Committee appointed “ to consider of the rules by which the Nomenclature of
Zoology may be established on a uniform and permanent basis” ;—Report of a Committee on
- the Vital Statistics of large Towns in Scotland ;—Provisional Reports, and Notices of Progress
in Special Researches entrusted to Committees and Individuals.
Together with the Transactions of the Sections, Lord Francis Egerton’s Address, and Re-
commendations of the Association and its Committees.
PROCEEDINGS or tHe THIRTEENTH MEETING, at Cork,
1843, 8s.
ConTENTs:—Robert Mallet, Esq., Third Report upon the Action of Air and Water,
whether fresh or salt, clear or foul, and of Various Temperatures, upon Cast Iron, Wrought
Iron and Steel;—Report of the Committee appointed to conduct the co-operation of the
British Association in the System of Simultaneous Magnetical and Meteorological Observa-
tions ;—Sir J. F. W. Herschel, Bart., Report of the Committee appointed for the Reduction
of Meteorological Observations ;—Report of the Committee appointed for Experiments on
Steam-engines ;—Report of the Committee appointed to continue their Experiments on the
Vitality of Seeds ;—J. S. Russell, Esq., Report of a Series of Observations on the Tides of the
Frith of Forth and the East Coast of Scotland ;—J.S. Russell, Esq., Notice of a Report of the
Committee on the Form of Ships ;—J. Blake, Esq., Report on thie Physiological Action of Me-
dicines ;—Report of the Committee appointed to print and circulate a Report on Zoological
Nomenclature ;—Report of the Committee appointed in 1842, for Registering the Shocks of
Earthquakes, and making such Meteorological Observations as may appear to them desirable ;
—Report of the Committee for conducting Experiments with Captive Balloons ;—Professor
Wheatstone, Appendix to the Report;—Report of the Committee for the Translation and
Publication of Foreign Scientific Memoirs ;—C. W. Peach, on the Habits of the Marine Tes-
tacea ;—Edward Forbes, Esq., Report on the Mollusca and Radiata of the Aigean Sea, and
on their distribution, considered as bearing on Geology ;—M. Agassiz, Synoptical Table of
British Fossil Fishes, arranged in the order of the Geological Formations ;—Richard Owen,
Esq., Report on the British Fossil Mammalia, Part II.;—E. W. Binney, Report on the ex-
cavation made at the junction of the Lower New Red Sandstone with the Coal Measures at
Collyhurst, near Manchester ;—W. Thompson, Esq., Report on the Fauna of Ireland: Diy.
Invertebrata ;—Provisional Reports, and Notices of Progress in Special Researches entrusted
to Committees and Individuals.
Together with the Transactions of the Sections, Earl of Rosse’s Address, and Recommen-
dations of the Association and its Committees.
PROCEEDINGS or truz FOURTEENTH MEETING, at York, 1844,
13s. 4d.
Contents :—W.B. Carpenter, M.D.,F.R.S.,on the Microscopic Structure of Shells; —Joshua
Alder and Albany Hancock, Report on the British Nudibranchiate Mollusca ;—Robert Hunt,
_ ciation for Experiments on Steam-Engines ;—Report of the Committee to investigate the Va-
{ —Report of a Committee appointed by the British Association in 1840, for revising the No- |
(Researches on the Influence of Light on the Germination of Seeds and the Growth of Plants ;
menclature of the Stars ;—Lieut.-Colonel Edward Sabine, R.A., F.R.S., on the Meteorology }
of Toronto in Canada ;—John Blackwall, F.L.S., Report into some recent researches into the
Structure, Functions and CEconomy of the Araneidea made in Great Britain ;—the Earl of
Rosse, on the Construction of large Reflecting Telescopes ;—the Rev. William Vernon Har- |
court, F.R.S., Report on a Gas Furnace for Experiments on Vitrifaction and other Applica-
tions of High Heat in the Laboratory ;—Report of the Committee for Registering Earthquake
Shocks in Scotland ;—Report of a Committee appointed at the Tenth Meeting of the Asso-
rieties of the Human Race ;—Fourth Report of a Committee appointed to continue their
Experiments on the Vitality of Seeds ;—William Fairbairn, Esq., on the Consumption of Fuel
and the prevention of Smoke ;—Francis Ronalds, Esq., F.R.S., Report concerning the Observa-
tory of the British Association at Kew ;—Sixth Report of the Committee appointed to conduct
the Co-operation of the British Association in the System of Simultaneous Magnetical and
Meteorological Observations ;—Prof. Forchhammer, on the influence of Fucoidal Plants upon
the Formations of the Earth, on Metamorphism in general, and particularly the Metamorphosis
of the Scandinavian Alum Slate ;—H. E. Strickland, M.A., F.G.S., Report on the recent Pro-
gress and present State of Ornithology ;—T. Oldham, Esq., M.R.I.A., Report of Committee
appointed to conduct Observations on Subterranean Temperature in Ireland ;—Prof, Owen,
F.R.S., Report on the Extinct Mammals of Australia, with descriptions of certain Fossils
indicative of the former existence in that Continent of large Marsupial Representatives of
the Order Pachydermata ;—W. Snow Harris, Esq., F.R.S., Report on the working of Whewell
and Osler’s Anemometers at Plymouth, for the years 1841, 1842, 1843 ;—W. R. Birt, Report
on Atmospheric Waves ;—L. Agassiz, Rapport sur les Poissons Fossiles de I’Argile de Londres,
with translation ;—J. Scott Russell, Esq., M.A., F.R.S.E., Report on Waves ;---Provisional
Reports, and Notices of Progress in Special Researches entrusted to Committees and Indivi-
duals.
Together with the Transactions of the Sections, Dean of Ely’s Address, and Recommenda-
tions of the Association and its Committees.
PROCEEDINGS or tue FIFTEENTH MEETING, at Cambridge,
1845, 8s.
ConTENTS.—Seventh Report of the Committee appointed to conduct the co-operation of
the British Association in the System of Simultaneous Magnetical and Meteorological Obser-
vations ;—Lieut.-Col. Sabine, on some points in the Meteorology of Bombay ;—J. Blake, M.B.,
Report on the Physiological Action of Medicines ;—Dr. Von Boguslawski, on the comet of
1843 ;—R. Hunt, Esq., Report on the Actinograph ;—Prof. Schonbein, on Ozone ;—Prof.
Erman, on the influence of friction upon Thermo Electricity;—Baron Senftenberg, on the
Self-Registering Meteorological Instruments employed in the Observatory at Senftenberg ;—
W. R. Birt, Esq., Second Report on Atmospheric Waves ;—G. R. Porter, Esq., on the Pro-
gress and Present Extent of Savings’ Banks in the United-Kingdom ;—Prof. Bunsen, and Dr.
Playfair, Report on the Gases evolved from Iron Furnaces, with reference to the theory of
Smelting of Iron ;—Dr. Richardson, Report on the Ichthyology of the Seas of China and Japan;
—Report of the Committee on the Registration of Periodical Phenomena of Animals and
Vegetables ;—Fifth Report of the Committee on the Vitality of Seeds ;—Appendix, &c.
Together with the Transactions of the Sections, Sir J. F. W. Herschel’s Address, and Re-
commendations of the Association and its Committees.
LITHOGRAPHED SIGNATURES of the MEMBERS who met at Cambridge in 1833,
with the Proceedings of the Public Meetings, 4to. Price 4s. (To Members, 3s.)
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