282 Obituary Notices of Fellows deceased. 



the science all accidental considerations peculiar to special types of 

 mechanism. In the wider ramifications of modern abstract dynamics, 

 in which, following the lead of Kelvin, Maxwell, and Helmholtz, its 

 generalised principles are now extended to the elucidation of electrical 

 and other recondite physical manifestations, the query is often put 

 to specify the reaction, to show that Newton's Third Law of Motion is 

 not violated ; and the convenient answer is to appeal to Newton's 

 own " Scholium," which practically asserts that, wherever the analysis is 

 based on an energy function, the compensation of action and reaction, 

 considered as work of intrinsic forces, is secured in advance; and 

 we may thus claim to have obtained permanent footing without the 

 necessity of exploration of the concealed working of the system in order 

 to trace out the exact mode of occurrence of this compensation. 



The general consideration of the motions generated in unbalanced 

 mechanical systems a subject the details of which Newton expressly 

 excluded from the " Principia " led directly, in the hands of Leibniz, 

 Huygens, the Bernoullis, and others, to the recognition that, in the 

 absence of frictional (i.e. irreversible) resistances, work that went uncom- 

 pensated reappeared as vis viva of the motion in corresponding amount ; 

 so that, by including the kinetic energy, the principle of compensation 

 or conservation still maintains its validity, unless friction is present. 

 We have Helmholtz's own statement that it was early familiarity with 

 these mathematical investigations of the previous century that 

 prompted him to extend the law of conservation into a far-reaching 

 conspectus of all physical phenomena, in his famous essay on the 

 "Conservation of Force" of 1847 waste energy being assumed to 

 take the unorganized kinetic or thermal form about the same time 

 that the irrefragable evidence for such a universal principle of trans- 

 mutation of energy had been supplied, unknown to him, by the 

 experiments of Joule. 



The whole of the statics of reversible (i.e. frictionless) mechanical 

 systems had thus been condensed into the law that the states of 

 equilibrium are defined by the energy being stationary, the criterion 

 of stability being that it is a minimum. A corresponding generalisa- 

 tion was now required for the wider science in which chemical and 

 other non-mechanical sources of power are in operation. Here again 

 the theory will be exhaustive only in its application to reversible types 

 of change. In fact, if the complex of possible transformations is to be 

 reducible to a theory involving analytical functions, reversibility must 

 be an essential feature ; without it the courses of individual trans- 

 formations may be traced, but their features cannot be interlaced into 

 a scheme of relations. The essay of Sadi Carnot, " Sur la Puissance 

 Motrice du Feu," of date 1824, had already pointed out the way, by 

 abstract reasoning based on the idea of complete cycles of processes; 



