now guides us along the steps of his advance. Under the heads of Physiology, Pathology, and Therapeutics, a detailed account is given of Cullen's system, in its common and in its peculiar doctrines. In this, the principal portion of the work, is exhibited, for the first time, (and chiefly from manuscript sources,) a comprehensive view of Cullen's services to medical science; much original information is supplied; new light is thrown upon points hitherto obscure; many prevalent misconceptions are rectified; and some unworthy, we are sorry to add, hitherto successful, plagiarisms are exposed. Cullen's reputation had suffered from misrepresentation, ignorance, and neglect; but never was the honour of an author more triumphantly vindicated by his biographer. We regret our inability to do any justice to this admirable survey; which is, indeed, not more valuable as an appreciation of Cullen's merits, than as a supplement to the history of modern medicine. An outline of its contents would be of little interest or value; and even an outline would exceed our limits.

To the history of Cullen's doctrines in relation to those of previous theorists, Dr Thomson subjoins an account,—and the best we have ever seen,-of the contemporary progress of medicine in the schools of Montpellier and Paris. On this, however, we cannot touch. Our limits also preclude us from following him in his important discussion on medical education. We warmly recommend this part of the volume to those interested in the subject. A curious letter of Adam Smith (prior to the publication of his Wealth of Nations) on Universities and Degrees, will be admired for its ability by those who dissent from his well-known doctrine upon these points. We regret that we cannot make room for this very characteristic production, which is now for the first time given to the public. Its praise of the Scottish Universities, and its opinion as to Visitations, are particularly worthy of notice. The results of the late Royal Commission of Visitation will by some, perhaps, be viewed as affording a good commentary on Dr Smith's text. "In the present state of the Scotch Universities, I do most sincerely look upon them as, in spite of all their faults, without exception the best seminaries of learning that are to be found anywhere in Europe." [Smith would not say this now; and he said it then, probably, in utter ignorance of the Dutch and German Universities.] "They are, perhaps, upon the whole, as unexceptionable as any public institutions of that kind, which

all contain in their very nature the seeds and causes of negligence and corruption, have ever been, or are ever likely to be. That, however, they are still capable of amendment, and even of considerable amendment, I know very well; and a Visitation is, I believe, the only proper means of procuring them this amendment. But before any wise man would apply for the appointment of so arbitrary a tribunal, in order to improve what is already, upon the whole, very well, he ought certainly to know, with some degree of certainty, first, who are likely to be appointed visitors; and, secondly, what plán of reformation those visitors are likely to follow." Besides the medical matters we have been able to notice, this volume contains various other topics of general interest. The letters alone which it supplies of distinguished individuals form an important addition to the literary history of Scotland during last century. David Hume, Adam Smith, Lord Kames, Duhamel, William Hunter, Black, Senac, Fothergill, are among Cullen's most frequent correspondents.

We look forward to the concluding volume with no little curiosity. It will trace of course the influence of Cullen's speculations on the subsequent progress of medicine, and, we hope, continue (what Dr Thomson has already proved himself so well qualified to execute) the history of this science to the present day.

EDUCATION.

I-ON THE STUDY OF MATHEMATICS,

AS AN EXERCISE OF MIND.*

(JANUARY, 1836.)

Thoughts on the Study of Mathematics as a part of a Liberal Education. By the Rev. WILLIAM WHEWELL, M.A., Fellow and Tutor of Trinity College. 8vo. Cambridge: 1835.

We saw the announcement of this pamphlet with no ordinary interest, from the subject,-from the place of publication,-and from the author.

The subject is one of great importance in the science of educa

• [In French by M. Peisse; in Italian by S. Lo Gatto; in German, as a separate pamphlet, under the title,-Ueber ben Werth und Unwerth der Mathematik, als Mittel der hochern geistigen Ausbildung, Cassel, 1836. To this last there is an able preface; and the translator publishes the paper from “an intimate and resistless conviction that the plan of study in some of our new gymnasia comprehends too great a variety of objects, and, especially, lavishes too much time and application on mathematical instruction ;-an instruction without interest to the majority of students, which, at the same time, pays no regard to the differences of natural disposition and future destination, overloads the memory and compromises the development of the higher mental and moral capacities, while, more especially, it stunts the evolution of that free and independent activity of thought on which a utility for life and a susceptibility for its noblest avocations depend."

This article was attacked in a pamphlet published by Professor Chevallier of Durham, in the course of the year; but his opposition being either mere assertion or mere mistake, I do not find it necessary to say anything in reply. in fact, his defence of "The Study of Mathematics as conducive to the development of the Intellectual Powers," may suffice to show how little, even

R

tion. Whether, and to what extent, the study of mathematics conduces to the development of the higher faculties, is a question which, though never adequately discussed, has been very confidently and very variously decided. The stream of opinions, and the general practice of the European schools and universities, allow to that study, at best, only a subordinate utility as a mean of liberal education;—that is, an education in which the individual is cultivated, not as an instrument towards some ulterior end, but as an end unto himself alone; in other words, an education, in which his absolute perfection as a man, and not merely his relative dexterity as a professional man, is the scope immediately in view. But, at the same time, it cannot be denied, that signs of a revolutionary tendency in popular opinion, touching the objects and the end of education, are, in this nation at least, becoming daily more and more obtrusive; and as the extended study of mathematics is that mainly proposed, in lieu of the ancient branches of discipline which our innovators would retrench, a professed inquiry, like the present, into the influence of this study on the intellectual habits, comes invested, independently of its general importance, with a certain local and temporary interest.

But the centre from which it proceeds, enhances also the interest of the publication. In opposition to the general opinion of the learned world,-in opposition to the practice of all other universities, past or present,-in opposition even to its oaths and statutes, and to the intention of its founders and legislators, the University of Cambridge stands alone in now making mathematical science the principal object of the whole liberal education it affords; and mathematical skill the sole condition of the one tripos of its honours, and the necessary passport to the other:thus restricting to the narrowest proficiency all places of distinction and emolument in university and college, to which such honours constitute a claim ;-thus also leaving the immense majority of its alumni without incitement, and the most arduous and important studies void of encouragement and reward. It is true,

by an able advocate, can be alleged in vindication of their utility in this respect at all.

Certain statements in the criticism have also been controverted by Professor Boole in his very able "Mathematical Analysis of Logic," in 1847. I shall consider these in a note. (P. 273.)

On Dr Whewell's rejoinder, see the end of the article.

One unimportant note appended by the Editor is omitted.]

indeed, that the effect of this contracted tendency of the public university is, in some degree, tempered by certain favourable accidents in the constitution of more than one of its private colleges; but with every allowance for petty and precarious counteraction, and latterly for some very inadequate legislation, the University of Cambridge, unless it can demonstrate that mathematical study is the one best, if not the one exclusive, mean of a general evolution of our faculties, must be held to have established and maintained a scheme of discipline, more partial and inadequate than any other which the history of education records. That no Cambridge mathematician has yet been found to essay this demonstration, so necessary for his university, so honourable to his science, has always appeared to us a virtual admission, that the thesis was incapable of defence. A treatise, therefore, apparently on the very point, and by a distinguished member of the university, could not fail of engaging our attention; and this, whether it proposed to defend the actual practice of the seminary, or to urge the expediency of a reform.

From the character of its author, the pamphlet before us likewise comes recommended by no mean claim to consideration. Mr Whewell has already, by his writings, approved to the world, not only his extensive acquirements in mathematical and physical science, but his talent as a vigorous and independent thinker. To a narrower circle, he is known as the principal public tutor of the principal college of his university; and in this relation, his zeal, and knowledge, and ability have concurred in raising him to an enviable eminence. Though more peculiarly distinguished by his publications in that department of science so exclusively patronised by the university, he has yet shown at once his intelligence and liberality, by amplifying the former circle of studies pursued in the college under his direction; and, in particular, we are informed, that he has exerted his influence in awakening a new spirit for the cultivation of mental philosophy; in which department he has already introduced, or is in the course of introducing, a series of more appropriate authors than those previously in use. In these circumstances it was with more than usual expectation that we received Mr Whewell's pamphlet. Its perusal-must we say it has disappointed us. The confession is unavoidable. Even the respect which we entertain for the character and talents of the author, compels us to be plain rather than pleasant with his work. As a writer, Mr Whewell has long out-grown the need