Takleton — The Relation of Mathematics to Physical Science. 167 



ture in a time of two dimensions. There is, however, little doubt that 

 Poincare would say that our time is the most convenient. 



As the result of the considerations with which we have been occupied, we 

 may, I think, be satisfied that Mathematics is more certain than any other 

 part of our knowledge, and that mathematical truths condition the whole of 

 experience. If, however, Mathematics could be applied only to the number 

 and apparent relative positions of objects, its value would be comparatively 

 small ; and the student of nature might pass it by with but little attention. 

 Far different is the actual state of things. It has been held from the earliest 

 times — apparently without much evidence — strongly insisted on by Locke, 

 and abundantly confirmed by modern research, that the sensible qualities 

 of bodies depend on their primary qualities, that is, their relations to space 

 and time. A change of these relations for the permanent in space constitutes 

 bodily motion. Thus the science of motion, or dynamics, in the widest sense, 

 is the root-science of nature. Completing and perfecting the discoveries of 

 his predecessors, ISTewton showed that the laws of motion could be expressed 

 with simplicity and accuracy in a mathematical form. He thus brought the 

 whole theory of motion under the control of Mathematics, and laid the 

 foundation of the great edifice of Mathematical Physics which has since 

 attained such colossal dimensions. Astronomy, in a way always mathema- 

 tical, was no longer concerned merely with the distances and observed motions 

 of the heavenly bodies, but was able to account for these motions, and predict 

 them with a precision never attained before. As time went on, the 

 phenomena of Light, Heat, and Electricity were brought into the domain 

 of Mathematics. Many and great were the difficulties which were sur- 

 mounted. The problems which nature presents are in their details so 

 complicated as to baffle the most accomplished mathematician ; but the 

 genius of Lagrange, aided by the subsequent developments of Hamilton, 

 Eouth, and Helmholtz, has enabled mathematicians in many cases to deal 

 with the most important features of a moving system when a knowledge of 

 details is quite impossible. 



The greatest discoveries are usually made originally by accident, but to 

 follow up a new discovery, ascertain its true import, and develop its con- 

 sequences requires the most patient investigation and the highest genius ; 

 nor is it possible to do this with any approach to completeness without the 

 aid of Mathematics. How incomplete would be the discoveries of Malus 

 without Fresnel, MacCullagh, and Maxwell ; of Black, Boyle, Watt, Gay- 

 Lussac, and Piegnault, without Carnot, Clausius, and Gibbs ; of Joule without 

 Helmholtz ; of Oersted without Ampere ; of Arago and Faraday without 

 Maxwell and Hertz. 



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