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certain portion of the works of Newton, or of some other of the writers who treat of pure or mixed mathematics in the synthetic method, is prescribed to the pupil, which the candidate for academical honours must study day and night. He must study it, not to learn the spirit of geometry, or to acquire the δυναμις ευρητίκη by which the theorems were discovered, but to know them as a child does his catechism, by heart, so as to answer readily to certain interrogations. In all this, the invention finds no exercise; the student is confined within narrow limits; his curiosity is not roused; the spirit of discovery is not awakened. Suppose that a young man, studying mechanics, is compelled to get by heart the whole of the heavy and verbose demonstrations contained in Keil's introduction, (which we believe is an exercise sometimes prescribed,) what is likely to be the consequence? The exercise afforded to the understanding by those demonstrations, may no doubt be improving to the mind; but as soon as they are well understood, the natural impulse is to go on; to seek for something higher; or to think of the application of the theorems demonstrated. If this natural expansion of the mind is restrained, if the student is forced to fall back, and to go again and again over the same ground, disgust is likely to ensue; the more likely, indeed, the more he is fitted for a better employ

ment of his talents; and the least evil that can be produced, is the loss of the time, and the extinction of the ardour that might have enabled him to attempt investigation himself, and to acquire both the power and the taste of discovery. Confinement to a regular routine, and moving round and round in the same circle, must, of all things, be the most pernicious to the inventive faculty. The laws of periodical revolution, and of returning continually in the same track, may, as we have seen, be excellently adapted to a planetary system, but are ill calculated to promote the ends of an academical institution. We would wish to see, then, some of those secular accelerations, by which improvements go on increasing from one age to another. But this has been rarely the case; and it is melancholy to reflect, how many of the universities of Europe have been the strong holds where prejudice and error made their last stand-the fastnesses from which they were latest of being dislodged. We do not mean to hint that this is true of the university of which we now speak, where the credit of teaching the doctrines of Locke and Newton is sufficient to cover a multitude of sins. Still, however, we must take the liberty to say, that Newton is taught there in the way least conducive to solid mathematical improvement.

Perhaps, too, we might allege, that another public institution, intended for the advancement of

science, the Royal Society, has not held out, in the course of the greater part of the last century, sufficient encouragement for mathematical learning. But this would lead to a long disquisition: And we shall put an end to the present digression, with remarking, that though the mathematicians of England have taken no share in the deeper researches of physical astronomy, the observers of that country have discharged their duty better. The observations of Bradley and Maskelyne have been of the utmost importance in this theory; their accuracy, their number, and their uninterrupted series, have rendered them a fund of immense astronomical riches. Taken in conjunction with the observations made at Paris, they have furnished Laplace with the data for fixing the numerical values of the constant quantities in his different series; without which, his investigations could have had no practical application. We may add, that no man has so materially contributed to render the formulas of the mathematician useful to the art of the navigator, as the present astronomerroyal. He has been the main instrument of bringing down this philosophy from the heavens to the earth; of adapting it to the uses of the unlearned; and of making the problem of the Three Bodies the surest guide of the mariner in his journey across the ocean.






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