Two straight lines drawn from, or diverging from, the same point, may be conceived to be produced, until their distance becomes greater than any assignable magnitude;

as the straight lines AB, AC, diverging from the Point A,

By a straight line, we understand a line that preserves the same direction between its extreme points; as a crooked line is that which varies its direction, and a curve line that which constantly varies it.

H

G D

E

C

F A

B

It is evident, from Euclid, prop. 27, b. i., that if the straight line FD falling on the straight lines HE, FB, makes the alternate angles HDF, DFA equal, these straight lines are parallel; from which, it follows that the strait line GA, drawn through I, the middle of FD, perpendicular to HE, is also perpendicular to FB, (prop. 15 and 26, b. i., E.) It also follows, that if the straight lines EG, BA be each perpendicular to GA, they are parallel, for then the alternate angles EGA, GAF are equal, whence, &c. Now, let AC make with GA an angle less than BAG, in which case, the sum of the angles CAG, EGA, is less than two right angles; Euclid says, in his twelfth axiom, that these lines must then meet. But this not being evident, or being rather a proposition, leaves Euclid's, otherwise elegant system, imperfect.From the axiom which we have laid down, this proposition evidently follows. For AB and AC, both diverging from the point A, may be produced until their distance becomes greater than any assignable magnitude, and as the distance between the two parallels AB and GE must be an assignable magnitude, AC must, therefore, meet GE, when both are produced far enough.

Here then is an evident proof, not only of Euclid's axiom, but also, of what we have asserted in the beginning of this Review, that the simplest truths, and the easiest modes of arriving at them, are, generally, the last perceived.

We have now, we are persuaded, given an impartial review of a subject, which we deem of no little importance, and removed, we hope, a stigma from geometry, which has been long its disgrace. In the great analytic chain, it would be very desirable also, that its broken links could be repaired. To the analytic method, or rather the calculus, we are far from being inimical, We are too sensible of its value. We know that it has enlarged, and will more and more assist in extending that horizon of science, the boundaries of which will for ever recede as we advance; but when, like the parasite that clings to the stately oak, it attempts to destroy that from which it has received its

principal existence; then we think it right, we deem it even necessary, to curtail its lofty pretensions, and to point out its humble origin and dependence. We hope, however, that in this country as well as in the British Isles, and in Italy, both geometry and the calculus will be equally cultivated and encouraged.

ART. V.-1. Sur les Fonctions du Cerveau: et sur celles de chacune de ses parties: avec des observations sur la possibilité de reconnaitre les instincts, les penchans, les talens, ou les dispositions morales et intellectuelles des Hommes et des Animaux, par la configuration de leur Cerveau et de leur Tete. Par F. J. GALL. Paris, 1825. En 6 tomes. 8vo.

Of this work, the first and second volumes, are occupied "Sur l'origine des qualitès morales et des facultes intellectuelles de l'homme, et sur les conditions de leur manifestation.".

The third volume is, "Sur l'Influence du Cerveau sur la forme du Crane; difficultès et moyens de determiner les qualités et les facultès fondamentales, et de decouvrir le siege de leurs organes."

The fourth and fifth volumes are entitled, "Organologie, ou exposition des instincts, des penchans, des sentimens et des talens; ou des qualitès morales et des facultès intellectuelles fondamentales de l'homme et des animaux; et du siege de leur organes.

The sixth volume is entitled, "Revue critique de quelques ouvrages anatomo-physiologiques ; et exposition d'une nouvelle philosophie des qualités et des facultès intellectuelles.'

Such are the general contents of this work; which may be regarded as a supplement to the larger anatomical work of Dr. Gall, entitled, "Anatomie et Physiologie du Systeme nerveux en general et du Cerveau en particulier; avec des observations sur la possibilité de reconnaitre plusieurs dispositions intellectuelles et morales de l'homme et des animaux par la configuration de leurs tète. 4 tomes en folio, et 4 tomes en 4to. avec atlas de cent planches. Chez l'Auteur et chez N. Maze, libraire Rue Git-le-Cœur, No. 4. Par Gall et Spurzheim."

This larger work being too technical, and too expensive also, for general readers, a more popular exposition of Gall's opinions became necessary, for the purpose of enabling the public, generally, to become acquainted with them, and to judge of the facts and arguments on which they are based: hence the work now under review; which will enable us to give a brief outline of a system that has been, that still is, and for some years will continue to be, a subject of desperate controversy, until it becomes more generally known, explained and illustrated, than it has yet been, any where but in France. In England, notwithstanding the lectures of Spurzheim, and his exposition of the Physiognomical System, (large 8vo. London, 1815) it is generally considered little better than a branch of the pretensions of Lavater, Mesmer, and De Mainuduc; while men, who have no title to equal Gall in anatomical or physiological knowledge, speak of him, as Charles Bell does, with manifest contempt.* In Scotland, the brief exposition of Gall's system by Mr. George Combe, in his Essays on Phrenology, re-published in this country in 1822, has not saved the phrenologists from the very severe sarcasms of Mr. Jeffrey, in a late number of the Edinburgh Review; an essay, equally distinguished for its ingenuity, its severity, its flippancy, and its gross ignorance of the subject treated in it. It is one of those pieces, well calculated to illustrate the position, that ridicule is not the test of truth. Indeed, this is not the only instance in which that Review has been marked by a deplorable want of knowledge of anatomical facts, and just physiological views.‡ The French School of Anatomy, Physiology, and (of late years) of Medicine, is so

In "An Exposition of the Natural System of the Nerves of the Human Body," p. 163, of the Philadelphia edition, and yet the main idea of Bell's book, viz. that each system, each fasciculus of nerves, each nerve, and each separate filament of a nerve, is destined to its own peculiar functions, which no other can supply-was an essential part of Gall's system, long before Bell's papers were published in the Philosophical Transactions.

We have not yet seen Dr. Combe's reply to the anti-phrenological article in the Edinburgh Review, noticed in the 13th Number of the Edinburgh Phrenological Magazine; but we have read with great pleasure, a very severe and complete refutation of Mr. Jeffrey's attack on Gall's System, by Dr. C. Caldwell, Professor in the Medical School of Lexington, Kentucky. It is reponse sans replique. Dr. Caldwell has done himself much credit, and the cause much service; though we are inclined to think, he has burthened the subject unnecessarily, with an antiquated hypothesis, that no physiologist of note, at the present day, would be inclined to support.

In a review, October 1806, p. 159, these gentlemen laugh outright at the absurdity of a sensation and an idea, being motions in the brain, perceived. In the Review, for June, 1815, p. 227, they give what they are pleased to call, an account of the doctrines of Gall and Spurzheim, in which, it is hard to say, whether unjustifiable abuse, or ignorance of the subject, be most apparent. In a review of Sir Everard Home, on the Functions of the Brain, these sage physiologists give it as their opinion, (Review, Feb. 1815, p. 450) that the brain has no share in the operations that give rise to sensation! and Edinburgh! has the honor of this notable discovery.

decidedly superior to those of London and Edinburgh, that the jealousy of the anatomists and physiologists of Great Britain, has induced them to shut their eyes against the Continental discoveries, which leave them almost half a century behind the established knowledge of the day.

Dr. Gall began to lecture on his Craniological System, in Germany in 1805. He associated himself with Dr. Spurzheim; and they visited Paris soon after, and publicly lectured on their system in that city, conjointly. In 1808, they presented a Memoir to the Institute, entitled, "Recherches sur le Systeme nerveux en general, et sur celui du Cerveau en particulier." The physical class of the Institute, appointed Mess. Tenon, Portal, Sabatier, Pinel, and Cuvier, to report on this Memoir, which they did on the 14th March, 1808. The report is purposely confined to the anatomical doctrines, and the practical methods of developing the structure of the brain, which Drs. Gall and Spurzheim claimed as new. The novelty is disputed by these reporters, excepting a reluctant kind of acknowledgment of merit, in relation to the practical methods of demonstrating some parts of the brain, which the committee could not withhold. It is a report that seems to carry on the face of it, a jealousy of discoveries not originating in the French school; and it is, by no means, such as we should expect from a committee, of which Cuvier was an active member. This esprit de corps, or rather this esprit nationale, is a great obstacle to science. An Englishman can hardly allow any merit in the French contributions to physiological and medical knowledge, nor from reading the English publications, can we find proof that they know what the French have been doing for the last dozen years. Excepting the late compilation of Dr. Bostock,* it is almost a century since an elementary book of physiology has been produced in England: the students of this country, have resort to French books, almost exclusively. Haller and Blumenbach are now little read: Richerand, Bichat, Majendie, Adelon, and Broussais, some, or all of them, are found in almost every student's library.

As Dr. Spurzheim seems to lay claim to no discovery of his own; differing from Dr. Gall only in his enumeration of the primitive faculties, whose seat is to be found in the encephalon, and marked on the cranium; and as he appears only as the earliest and most active disciple of Gall, and his most zealous coadjutor, we shall consider the treatise before us, and the opinions detailed in' it, as belonging exclusively to Dr. Gall, so

* Dr. Roget's recent work has not yet reached this country.

far as they differ from the views of the same subjects before taken by other anatomists and physiologists. Indeed, the book now reviewed is published by Gall alone, and the doctrines contained in it are claimed by him as his own. Dr. Spurzheim has published in London, (2d edition, 1815, large 8vo.) his own views of the "Physiognomical System," differing little from those of Gall. The system of Dr. Gall may be regarded as threefold; anatomical, physiological, and physiognomical: and under these three aspects, we shall consider it.

It may be worth while to premise, that, throughout this treatise, Dr. Gall purposely rejects all metaphysical considerations respecting an independent soul or mind, distinct from the body, and to which bodily impressions are supposed to be transmitted. On this subject, the reader is left to his own reflections; it does not enter among Dr. Gall's investigations, who professes to adhere strictly to those phenomena which are the manifest result of the functions belonging to the nervous apparatus of the animal body. How perception or sensation arises, he does not pretend to know, or to explain.

On examining the Anatomical part of the book now before us, we are disposed to conclude, that Dr. Gall has rendered highly probable in most cases, and has completely established in others, the following points, which previous investigations had left in great obscurity.

1. That the brain, including in that term the cerebrum, the cerebellum, and the medulla oblongata, and excluding the nerves of the senses and the spinal marrow,* is not one organ, but a nervous apparatus-an assemblage of organs distinct from each other, and each destined to its peculiar function: and that one organic part of the brain, one nerve or set of nerves, cannot perform the office of another. See vol. vi. pp. 296 and 313, and his treatise on the difference of nerves, and the function of the senses in vol. i. of his great work. M. Cuvier seems to accede to this opinion, (see Gall, vol. vi. p. 313) and Mr. Charles Bell has applied it to each nerve of a fasciculus, and each filament of a nerve, in his treatise already cited.

2. That there is no common sensorium, or centre of sensation or perception, but each distinct organic portion of the brain, having its peculiar function, possesses its own. This is a point adhuc sub judice. M. Broussais differs in opinion from Gall hereon; adopting Gall's descriptive anatomy of the brain, he considers the centre of sensations and volitions to be placed in the medulla oblongata or rather more particularly, at the

VOL. I.-NO. 1.

:

* 2. Gall. 67.

18