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The Collected Works of Sir Humphry Davy ...: Discourses delivered before the Royal society. Elements of agricultural chemistry, pt. I
by Sir Humphry Davy
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Excerpt:
There is certainly no branch of science so calculated to awaken our admiration as the sublime or transcendental geometry, not only as showing the wonderful powers and resources of the human mind, but likewise demonstrating the wisdom and beauty of the laws of the system of the universe. It is, perhaps, the highest triumph of human intelligence, that, proceeding from the consideration of mere unities or points, lines, or surfaces, it should, by gradual generalizations, substitutions, and abstractions, be able to arrive, not only at the knowledge of all possible conditions of number and quantity, but likewise of time and motion; and by employing its own pure intellectual creations, to anticipate the results of observation and experiment, and determine the movements, not only of the bodies which form permanent parts of our system, but likewise of those which seem only occasionally to visit it, and which belong, as it were, to the immensity of space.
Whether the importance of the subject be considered, or the glory that has been derived by the society from the labours of those amongst its members who have cultivated the higher branches of the mathematics, it must be very gratifying to you to hear that Mr. Herschel, after gaining, at a very early period of life, academical honours of the highest kind in that university where the exact sciences are most profoundly studied, has successfully continued his pursuit of this kind of knowledge: and not contented with understanding and illustrating the most elaborate works of his predecessors and contemporaries, has made additions to them, and that even in the most abstruse and difficult branches of analysis
Four papers of Mr. Herschel, on pure mathematical subjects, are to be found in your Transactions. The first, on a remarkable application of Cotes's theorem. The second, on the consideration of various parts of analysis, in which he has examined one of the most sublime points of the doctrine of fluxions, the calculus of generating functions, and makes a new application of them to the case of logarithmic transcendents, and derives from them the summation of one of the most important series which has ever received discussion. The third paper is on the development of exponential functions, together with several new theorems relating to finite differences. The fourth paper is on circulating functions, and the integration of a class of finite differences into which they enter as co-efficients.
I cannot attempt an analysis of these papers; that their merits may be understood, they must be deeply studied; and, by the best mathematicians, they are regarded as ingenious and profound.
The author, in treating of algebraical or fluxional instruments, as they may be called, of the relations of variable quantities or functions which may be supposed capable of indefinite diminution or increase, has indulged in no vague metaphysical abstractions. He has shown a great love of simplicity in his processes, appearing rather desirous of being intelligible and useful, than anxious to display the variety and extent of his acquisitions. In all these papers Mr. Herschel has proved himself intimately acquainted with the works of the great masters of analysis, and has exhibited equal powers of seizing particular applications of methods already known, and of developing new and general views; thus demonstrating himself the worthy associate of a Brinkley, a Woodhouse, an Ivory, and a Young, who have, in late times, travelled, with so much zeal and success, towards mathematical discoveries, in these noble paths of investigation opened by the unrivalled genius of Newton, and too long deserted by our countrymen, and occupied, almost exclusively, by illustrious foreigners.
But Mr. Herschel has not limited himself to the invention or development of formulae, to what may be called the construction of the instruments of the science of quantity, he has made important applications of them, which is perhaps the highest claim that can be made to the approbation of this Society; for though, as a mere exercise, the higher mathematics strengthen the reasoning faculties, and afford intellectual pleasure, yet it is by enabling us to solve the physical phenomena of the universe, and modify the properties of matter, that they have their grandest end and use. In these respects, they are really power; and they may be compared to that power which we witness in the vapour of water, which, passing into the free atmosphere, exhibits only a pleasing spectacle; but which applied in the steam-engine, becomes the moving principle of the most useful and extensive machinery, and the source of the most important arts of life.
There are two papers of Mr. Herschel's, in the last volume of the Transactions, on physico-mathematical subjects, and both of them connected with optical phenomena. All the Fellows must be acquainted with the beautiful discoveries of Malus, of that peculiar modification given to rays or particles of light, by their passage through certain transparent bodies, or by their reflection from certain surfaces, which has been called polarization; and the ingenious and elaborate researches of Biot, Arago, and Brewster, in consequence of the discovery, have been illustrated from this chair by your venerable and illustrious deceased President. But, notwithstanding the talents and industry of these distinguished philosophers, Mr. Herschel has been able to add to the subject some novel investigations; and, in reasoning upon the tints developed by polarized light, has reduced the explanation of the phenomena to one general fact—namely, that the axes of double refraction differ in their position in the same crystal, for the different-coloured rays of the spectrum, and that this element must enter into all rigorous formulas of double refraction; and, consequently, that the idea of the colours of thin plates being correspondent with the tints developed by polarized light, is not conformable to the facts.
