FUNDAMENTAL PRINCIPLES OF MATHEMATICS. 113 



analytical treatment led him to expressions from which the forces at a 

 distance completely disappeared and were replaced by the reactions of 

 the polarized medium. He thus verified the conceptions of Faraday 

 and Maxwell, who regarded the ether as the conveyer of tensions in 

 space empty of ponderable substance, and who saw in the motions of 

 electricity in conductors nothing else than the effects of the arisiug and 

 passing away of polarization in the insulators. Helmholtz accepted 

 these views still more completely in a memoir which appeared in 1882 

 "On systems of absolute measurement for electrical and magnetic 

 quantities." In this investigation the theory of Faraday- Maxwell was 

 given the preference over all other electro-dynamic theories which 

 assume direct action at a distance having a magnitude and direction 

 dependent on the absolute or relative motion of two electrical quanti- 

 ties. For these latter theories violate either the principle of the finite- 

 ness and constancy of energy or that of the equality of action and 

 reaction; and first of all, in order to make the theory the basis only of 

 conservative processes, exclude those phenomena in which, by reason 

 of friction, heat is created and electrical or magnetic energy lost. 



This research, in which, by reason of the observations of Faraday, 

 he was confronted with the question whether actions at a distance 

 really exist and must be taken into consideration, shows the wholly 

 new train of thought upon which he was engaged and whose results 

 were shortly to appear in discoveries of the greatest value for the 

 principles of mechanics. But it was first necessary to pursue investi- 

 gations in other branches of science in order to build thereon a treat- 

 ment of the principles of mechanics which should embrace the laws of 

 all the phenomena of nature. He therefore turned his attention to 

 theoretical chemistry and published in 1882 a treatise "On the thermo- 

 dynamics of chemical processes." In this the fundamental principles 

 of the mechanical theory of heat were applied to chemical processes, 

 and the generalized conception of the principles of mechanics is plainly 

 visible, though appearing completely in physical form. 



Since the loss of mechanical energy by friction creates heat, and a 

 gain in mechanical energy implies the loss of heat; and since, further, 

 the quantity of mechanical energy lost or gained is proportional to the 

 amount of heat correspondingly gained or lost, it becomes natural to 

 regard heat as a form of energy. The hypothesis may be made that 

 each particle of a warm body is continually moving with varying 

 direction and velocity in such a way that its place in the body remains 

 sensibly unchanged. If this be the case, a part of the energy of a 

 warm body must be in the form of kinetic energy, and energy of 

 whatever kind transformed into heat must be measurable in that form. 

 But the principle of the conservation of energy gives no indication 

 whether work may be completely transformed into heat and heat 

 retransformed into work without limit; and a similar uncertainty exists 

 for all forms of energy. It was to this point of great theoretical and 

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