On the General Law of the Transformation of Energy, 107 



' ;^\Let Q denote the quantity^ present in the substance, of the 

 kind of actual energy under consideration. It is required to find 

 how much of the potential energy of the kind U, developed by 

 a small increase of the state V, is produced by transformation of 

 actual energy of the kind Q, whose total quantity (to avoid com- 

 plication of the problem) is supposed to be maintained constant 

 by the communication of actual energy from external substances. 



The quantity of potential energy of the form U which is pro- 

 duced by transformation from the actual form Q, is the effect of 

 the presence of the total energy Q in the substance during the 

 change ^V. 



To find this effect^ let the total energy Q be conceived to be 

 divided into an indefinite number of indefinitely small parts c?Q, 

 and let the effect of one be computed separately. To do this, 

 let any one of the parts ^Q be abstracted from the total energy 

 Q ; and let the effect of this be to diminish the development of 

 power d\J by the quantity ^^U. Then 



is the effect, in development of potential energy, of the presence 

 in the substance of the small portion dQ, of actual energy ; and 

 as all the small portions of actual energy are similarly circum- 

 stanced, the potential energy which is developed by the change 

 d\j in consequence of the presence of the whole actual energy Q, 

 bears the same ratio to the whole energy Q which the above 

 quantity bears to the portion ^Q ; that is to say, the conversion 

 of energy from the actual form Q, to the potential form U during 

 the change d\, is represented by /, >. ;^^;^ p r; 



(3.) Next let us suppose, that not only the state V varies, but 

 the total quantity of energy Q also ; and let us investigate what 

 quantity of actual energy of the form Q must be communicated 

 to the substance to produce simultaneously the variations c?Q 

 and dY. 



First, there is the energy which remains in the actual form, 

 directly producing the increase c?Q in the total quantity Q. 



Secondly, there is the energy (not yet determined) which may 

 be transformed from the actual to some invisible potential form 

 in consequence of the change dQ, only. Let this be denoted by 

 Lc^Q. The nature of this quantity may be best conceived by 

 considering that the energy Q is itself a state of the substance, 

 to effect a change in which a resistance L may have to be overcome. 



Thirdly, there is the energy already determined and expressed 

 12 



