the best classics when joined to the classics themselves, and without which juncture vain the hope to pierce beyond the husks, or to reach, through the language, the literature, much less the general mind, of a country. In the more educated countries of the Continent large provision for education in Art, as an essential accompaniment to all intellectual cultivation, is made; not only in the more professional schools, but in every school, and of every grade, each in proportion to its grade and object. In the elementary school-the purely people's school-elementary drawing, fitted for the people's purposes, is taught; in the district, provincial, secondary school, this preliminary instruction is further developed; in the College and University, whilst opportunity is given for its manual cultivation, a higher object is aimed at the philosophy on which it rests, and by which it is regulated, both intrinsically and in its relations to other departments of human thought and action, is pursued. There is scarcely an University without its regular Chair of Esthetics, without Professors, whose province it is to give lectures and illustrations on the theory, principles, and history of Art. There is scarcely an University which has not, like that of Bonn, either its gallery of casts, drawings, engravings, &c. as well as library, or opportunity of easy and frequent access to one, to which the student can refer from the pages of his author for illustration, whenever he needs. It is [q. c. LEC.]

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something to study antiquity in this double mirror; one day dwelling upon the fatal fortunes of Laocoon and his sons in the impassioned lines of Virgil, and the next, pursuing and completing the poem in the still more powerful production of Statuary.

And who can read the poetical descriptions of our own Thompson, our own Shakespeare, with so great a pleasure as the painter of our own landscapes-the watchers of our ever-varying atmosphere, beautiful as it is in all its untiring changes? Let me then advise my young friends to hasten and prepare themselves by a little study and application in well-based theory and wholesome practice; that when the sunny Springdays come, they may be early afield, pencil in hand. The traveller's best and most interesting journal is a well-filled Sketch-book.

Thus much have I said, because thus much I feel, in praise of the Art which I follow. I have lived among its enjoyments for many years, and I can say with truth, in the words of a great continental artist, "I would not barter the power, feeble though it be, of this hand to draw out what this poor head contains, for the wealth of half the sovereigns of Europe;" for to me my years of Art have been, throughout, years of pleasure. I have feasted on the delights of Art, and would willingly invite all to partake with me of the rich banquet which Nature, through the bountiful Creator, has so unsparingly spread before us.

XVI.

ON MATHEMATICS.

BY THE

REV. T. G. HALL, M.A.

PROFESSOR OF MATHEMATICS IN KING'S COLLEGE, LONDON.

AD the Lecture which I am about to deliver

HAD

been introductory to the Course of scientific instruction given in these walls, I might have thought it needful, and due to my hearers, to attempt some more elaborate proof than I now find necessary, in order to shew that the study of Mathematics is not uninviting; and may in fact be rendered attractive to a class of pupils so different from that which now for 25 years I have been occupied in teaching. But the continued attendance of a considerable number of Ladies has shewn that there is nothing wanting on their part, and nothing very formidable in the nature of the subject, in whose principles and applications they here seek instruction. I know it has been said, and that too on no mean authority, that the study of Mathematics tends to unfit the mind for application to the purposes of life; that the unbending rigour of its demonstrations, and the never-failing

accuracy of its processes, harden the understanding, and force it into an habit of demanding from other subjects of inquiry a kind of proof incompatible with the nature of the investigation. That there is some truth in this statement, it would be vain for me to deny; but the objection only applies with full force to those who exclusively study Mathematics, and who, enamoured by their favorite pursuit, render themselves by that exclusiveness unfit to enter upon any other train of thought or inquiry. The objection will equally apply to the mere painter or musicianequally to the philologist and the metaphysician. But remember, that while it applies to the student, it does not to the science. The rules of Mathematics are strictly true; and if there were always proper and sufficient data, it would not fail to expound the difficulties of political, economical, or moral science. But in this Institution, no hesitation on such a ground as that just alluded to need exist; the instruction given here is so varied, that no consequences of the kind to which I have referred can possibly ensue. In fact, it is not the aim of this Institution to confine the attention of those who come here for instruction, to a particular object of study or to a particular class of subjects. The prospectus opens a wide field of instruction-the flowers of literature and science are invitingly offered; and each may cull or reject as the taste or the convenience of each may choose. Least of all is undue prominence given to that class,

the interest of which I am now permitted to represent.

This being the case, I may now safely recommend my hearers to bestow at least a short time, in order that they may acquire some knowledge of a science which is unequalled in the precision of its language— the correctness of its logic-the simplicity of its details and the unerring accuracy of its conclusions. Surely the knowledge of the elements of such a science must be beneficial to the female mind, and it will be my duty to lay before you to-day, that which any one may easily acquire; which will not only add to your stores of knowledge, but which may be a source of profit and of pleasure. I shall not ask you to attempt the higher and more difficult paths of this science, but which have been reached and firmly trod by an Agnesi and a Somerville. I shall content myself, to use the same simile, with the plain, and with humble heights; assuring you, at the same time, that the more extensive the horizon is, the greater will be the beauties of the landscape.

Mathematics has been defined to be the science, which treats, 1st, of the abstract relations of Number and Magnitude; and 2ndly, their application, through the medium of observed laws, to the useful purposes of life and the explanation of natural phænomena.

From this description it immediately follows, that