26 G. H. KNIBBS. 



from certain spatial and dynamic considerations based on chemical 

 data (?). The differences of his values from the best deductions 

 are about the same order as their uncertainty. 



But it is quite impossible even to enumerate the developments 

 of the great applications of mathematics to physical science, and 

 we must be content to take what has been mentioned as illustra- 

 tive of the whole. 



We have already said that mathematics lies behind physics-. 

 When one regards descriptions of the development of these sciences, 

 however, they perhaps appear, at first sight, merely theoretical 

 and unpractical — matters rather of curiosity than of utility. This 

 arises from the fact that the links by which conceptual or abstract 

 truths are united, and by which they guide and control the oper- 

 ation of the human will upon the material world, are non-material. 

 Day by day the truth is being forced upon us, with ever-increasing 

 impressiveness, that all knowledge is inter-related ; and more and 

 more do we perceive that the secret of our power in controlling, 

 the great energies of Nature, and in handling her material, lies 

 in the acquisition of abstract truth. The mathematician supplies 

 us with the subtlest and most far-reaching relations, with truths 

 entirely general, of universal adaptation. His discoveries are 

 revelations of the way in which, by the very constitution of 

 our being, we must think, if we are to have intelligent existence 

 at all. The physicist takes the splendid instruments furnished 

 by the mathematician and applies them both in observing and in 

 interpreting the phenomena of Nature ; and is often richly 

 rewarded, not only by the discovery of physical facts of great 

 significance, but also by being able to shew the inherent wealth 

 of mathematical conceptions, with a fulness unknown even to the 

 pure mathematician. 



The relation of the physicist to the material world, is akin to 

 that of the mathematician to the conceptual world : his it is to 

 study the world of matter in its generality, and in detail only with 

 a view to the development of general conceptions, the interest of 

 which, in the main, as with the truths of mathematics, is self- 



