392 Mr. W. J. Macquorn Rankine on the Science of Energetics. 



When the law of variation of potential energy, by a change of condi- 

 tion of a substance, is known, the system of external efforts corresponding 

 to any system of independent accidents is found by means of this principle: 



Each effort is equal to the rate of variation of the potential energy with 

 respect to the independent accident which that effort tends to vary; or 

 symbolically 



ExTEEXAL PoTEKTiAL Equilibeium of a suhstancc takes place, when 

 the external effort to vary each of the independent accidents is null; that is 

 to say, when the rate of variation of the potential energy of the substance 

 with the variation of each independent accident is nidi. 



For a given substance, there are as many conditions of equilibrium, of 

 the form 



(3.) ^=0, 



as there are independent accidents in the expression of its condition. 



The special application of this law to motion and motive force consti- 

 tutes the principle of virtual velocities, from which the whole science of 

 statics is deducible. 



Xir. Intebxal Potential EQUiLiBBirii. 



The internal potential equilibrium of a substance consists in the equili- 

 brium of each of its parts, considered separately ; that is to say, in the 

 nullity of the rate of valuation of the potential energy of each part with 

 respect to each of the independent accidents on which the condition of 

 such part depends. 



Examples of particular cases of this principle are, the laws of the 

 equilibrium of elastic solids, and of the distribution of statical electricity. 



XIII. Thibd Axioir. 



The Effort to Perform Work of a Given Kind, Caused hy a Given Quantity 

 of Actual Energy, is the Sum of the Efforts Caused by the Paris of thai 

 Quantity. 



A law equivalent to this axiom, under the name of the " GenebaIi 

 La-w or THE TEAirsFOE:MATio>' OF E>'EBGT," formed the principal 

 subject of the previous paper already referred to. 



This axiom appears to be a consequence of the definition of actual 

 energy, as a capacity for performing work possessed by each part of a 



