88 MATHEMATICS 



meaning of the great generalization known to us 

 as the law of the Conservation of Energy, emerged 

 as results of the development of the abstract side 

 of molar Mechanics, which determined the modes 

 in which the kinetic energy of moving bodies and 

 potential energy as work are defined as measurable 

 quantities. Only by the transference and extension 

 of these notions to the molecular domain did the 

 formulation of the modern doctrine become possible. 

 The doctrine of the conservation of energy for the 

 case of molar bodies had been established before 

 Joule and Mayer commenced their work, and was 

 a necessary presupposition of this further develop- 

 ment. Joule was able to determine the mechanical 

 equivalent of heat only owing to the fact that 

 mechanical work was already regarded as a measur- 

 able quantity, measured in a manner which had 

 been fixed in the course of the establishment of 

 the older Mathematical Mechanics. The notion of 

 Potential, fundamental in Electrical Science, upon 

 which the units employed by the Electrical Engineer 

 depend, was first developed as a mathematical 

 conception during the eighteenth century in con- 

 nection with the theory of the attractions of gra- 

 vitating bodies. It was transferred to the electrical 

 domain by George Green and others, together with 

 a good deal of detailed mathematics connected 

 with it which had previously been applied to the 

 gravitational potential function. 



The man of true Physical instincts, endowed 



