=1553.= The effects of heat are subject to constant laws which cannot be discovered without the aid of mathematical analysis. The object of the theory is to demonstrate these laws; it reduces all physical researches on the propagation of heat, to problems of the integral calculus, whose elements are given by experiment. No subject has more extensive relations with the progress of industry and the natural sciences; for the action of heat is always present, it influences the processes of the arts, and occurs in all the phenomena of the universe.--FOURIER, J. _Theory of Heat [Freeman], (Cambridge, 1878), Chap. 1, p. 12._ =1554.= Dealing with any and every amount of static electricity, the mathematical mind has balanced and adjusted them with wonderful advantage, and has foretold results which the experimentalist can do no more than verify.... So in respect of the force of gravitation, it has calculated the results of the power in such a wonderful manner as to trace the known planets through their courses and perturbations, and in so doing has _discovered_ a planet before unknown.--FARADAY. _Some Thoughts on the Conservation of Force._ =1555.= Certain branches of natural philosophy (such as physical astronomy and optics), ... are, in a great measure, inaccessible to those who have not received a regular mathematical education.... --STEWART, DUGALD. _Philosophy of the Human Mind, Part 3, chap. 1, sect. 3._ =1556.= So intimate is the union between mathematics and physics that probably by far the larger part of the accessions to our mathematical knowledge have been obtained by the efforts of mathematicians to solve the problems set to them by experiment, and to create “for each successive class of phenomena, a new calculus or a new geometry, as the case might be, which might prove not wholly inadequate to the subtlety of nature.” Sometimes, indeed, the mathematician has been before the physicist, and it has happened that when some great and new question has occurred to the experimentalist or the observer, he has found in the armoury of the mathematician the weapons which he has needed ready made to his hand. But, much oftener, the questions proposed by the physicist have transcended the utmost powers of the mathematics of the time, and a fresh mathematical creation has been needed to supply the logical instrument requisite to interpret the new enigma.--SMITH, H. J. S. _Presidential Address British Association for the Advancement of Science, Section A; Nature, Vol. 8 (1873), p. 450._