the generalization of it depends upon our mentally shifting the several conditions into all their varieties. Thus, if we wish to convince a person previously acquainted with the 47th proposition of the first book of Euclid, that, in any circle, the square of the sine added to the square of the co-sine, is equal to the square of the radius, he has only to delineate on paper, or to conceive in his mind, a circle with a radius drawn to some particular point of the periphery, and the sine and co-sine applied. He will then immediately discover that the three lines form a right-angled-triangle. This proves the fact in the particular instance. In order to render the general deduction equally convincing, the next process would be to place the radius in different positions; or, which would be still more conclusive, to fancy it sweeping round with the sine and co-sine attached to it; he will then, and not before, have ascertained, by experiment, that this property belongs equally to any part of the circle." After having shewn, at large, the justice of his principle by the application of it to the first theorem, he proceeds to some remarks upon the definitions, which he complains are, by an unnecessary pursuit of extreme exactness, rendered almost incomprehensible It is certainly discouraging to the mind to impose upon it the task of comprehending impossibilities. Yet little less is required by the common definition of a point, a line, and a superficies. From the definitions, he proceeds to apply his principle to the elucidation of some of the axioms. To the twelfth in particular, he has added a long series of experimental illustrations of the nature of parallel lines. The fifth definition of the fifth book, is also accompanied by an explanation equally ample. u I am indebted for this elegant illustration of Dr. Beddoes's doctrine, to the gentleman to whom the work is dedicated. In a casual communication before the book had come into my possession, he made use of it, by way of stating the principle upon which its reasoning was founded. For the principal opinion stated and exemplified in this treatise, the Author observes in the dedication, that he has "the full evidence of intuition." And "what additional confirmation it was possible, under such circumstances, to receive, was afforded by the assent of his friend; whose uncommon proficiency in mathematical science, and no less uncommon discernment, perfectly qualified him to decide on such a question." The deduction from the principle which it is his object to establish is briefly this: that the sciences which have obtained the name of the abstract sciences, are, in fact, originally founded entirely in "What the experiment; that they absolutely depend upon sense. 66 they senses are so perfectly adequate to convey," he observes, have been supposed not to convey at all: just as we many times hardly perceive ourselves doing what we do with perfect ease. When the senses serve us imperfectly, and make us continually feel our dependence, we are ever ready to express the obligation; But, where they instantly deliver such full and clear perceptions to the memory, that we have no more occasion to recur to them, we forget or deny the service they have rendered us.” Having thus denied the claim of mathematics to the title of an abstract science, he is led, by an easy transition, to consider the origin of abstract terms, and the philosophy of language. Remarks upon these subjects are frequently introduced in the body of the work, and they are still further elucidated in the appendix, in which, the labors of the Dutch etymologists, of Mr. Harris and of Lord Monboddo, pass under his review. Wherever these topics are alluded to, he confesses his obligations to the ETEα ПITEроla of Mr. Horne Tooke; a work upon which he bestows the highest eulogium. He vindicates the Author's claim to originality, with ▾ So much was he gratified by this work, that it appears he had, at one time, meditated that generous warmth which an ingenuous mind is apt to feel, when a theory unassailable on the score of reasoning is attacked on the ground of its having been previously discovered. But such, he remarks, was the lot of the illustrious Hervey; and future discoverers can scarcely hope to escape a similar fate. The other work which appears to have divided his attention with that just noticed, during the closing period of his residence in the University, was his first original publication on medical subjects. It was entitled "Observations on the nature and cure of Calculus, Sea-scurvy, Consumption, Catarrh, and Fever; together with conjectures upon several other objects of Physiology and Pathology." It is easy to trace throughout this work, his prevailing bias for chemistry, and the outlines of most of those sentiments and opinions, which he afterwards more fully developed, and inculcated with still greater earnestness. In his dedication, he complains of "the infinitely small portion of genius that has hitherto been exerted in attempts to diminish the sum of our painful sensations," and anticipates, from the movements then taking place in the moral world, a great and important improvement. In the first division of the work itself, he speaks of the great efficacy of alkaline remedies in calculus ; and after bestowing its due praise upon the aqua super-carbonatis potasse, he proceeds to mention a remedy, which he had devised in order to obviate the only objection which could be made to the impregnated water, the expence of preparing it. He candidly observes of his medicine, that though he knows not whether it be inferior to the water, he cannot suppose that it is superior; and were both equally easy to pro 66 applying the principles contained in it, to the construction of a philosophical dictionary; which should endeavour to ascertain the primary signification of our abstract terms. A brief specimen of his etymological inquiries is contained in a letter published in August, 1796, in the Monthly Magazine; and in a subsequent number, he has given some farther examples. cure for all patients, he should not think it worthy of public notice." The remedy in question is the carbonate of soda, of which the water of chrystallization has been dissipated by exposure to a warm dry air, or by being spread before a fire. This is combined with rather more than an equal weight of soap, and made into pills. One or two scruples of the powder are taken in the course of the day. A number of interesting cases are added which establish the efficacy of this simple remedy; especially in that form of calculous complaints to which the nosologists have given the name of nephritis calculosa." The section concludes with some speculations and queries as to its mode of operation. His considerations upon the sea scurvy, which is the subject of the next section, are prefaced by a slight sketch of those reflections upon the effects of oxygene air upon the animal œconomy, which had, for some time, occupied his mind. "It appeared likely, he observes, "that its abundance or deficiency would sensibly affect the health, and that the chemical composition of the fluids and solids of the living body would influence their properties, not less than the properties of dead matter; though not perhaps exactly in the same way. I had long supposed," he continues, “the scurvy to be owing to a gradual abstraction of oxygene from the whole system; just as death is produced in drowning, by withholding, all at once, the same substance, from that blood which is to pass to the posterior cavities of the heart." In these speculations he was further confirmed : w From my own experience of the efficacy of this remedy, I cannot forbear adding that the ardour of discovery had not led Dr. Beddoes in any degree to overrate its powers. Calculous complaints are, as is observed in this treatise, not less frequent among the poor than among the rich and the sufferings which they inflict, are often more intensely felt by those whose labours or occupations oblige them constantly to exert the muscles of the back, It appears also, that slight degrees of calculous affection are more frequently complicated in patients of this class, with dyspeptic and nervous complaints, than is commonly imagined, or, as far as I know, stated in practical books. by the livid colour of the blood, and the large livid spots which are so often spread over the surface of the body of the scorbutic patient; as well as, by the remedial effects produced by acids and a vegetable diet. There still remained, however, certain difficulties which withheld absolute conviction from his mind, and prevented him from publishing his opinions to the world. While he was pausing over these difficulties, and waiting for some further lights which should dissipate or confirm them, Dr. Trotter, in the second edition of his work on the sea scurvy, advanced a similar theory to account for its origin. But although their opinions coincided in this important particular, there were some material differences in the views which they entertained upon other parts of the subject. One of the most important was with respect to the occasional cause of the disease, which in Dr. Trotter's apprehension was " a deficiency of recent vegetable matter alone." To this Dr. Beddoes objects, that although it is possible that the system may imbibe oxygene by the medium of the stomach, yet it is evident, that "the blood in the first instance, and afterwards the solids, are oxygenated by means of the lungs." He considers, therefore, the want of pure air, to be a more powerfully exciting cause of scurvy, than the want of recent vegetable aliment; although he does not deny, to the last, a considerable share in its occasional production. Facts, however, have occurred, which, in his idea, decide the question of their relative importance. Under this head he refers to the uniform health enjoyed by the crews of Captain Cook's ships while engaged in his voyages of discovery, although they were frequently confined, for a long period, to salt provisions alone; and contrasts it with the great devastation produced by the disease under consideration in slave-ships, where, though the unhappy victims were plentifully supplied with vegetable aliment, they were confined below the decks in a contaminated atmosphere. Neither does the freshness of the vegetables made use of, appear to him so im |