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XVIII. On the General Law of the Transformation of Energy, 



By William John Macquorn Rankine, C.E., F.R.S.E., 



F.R.S.8.A. ^c* 

 (1.) TN this investigation the term energy is used to compre- 

 'iro X. hend every aiFection of substances which constitutes or 

 is commensurable with a power of producing change in opposi- 

 tion to resistance, and includes ordinary motion and mechanical 

 power, chemical action, heat, light, electricity, magnetism, and 

 all other powers, known or unknown, which are convertible or com- 

 mensurable with these. All conceivable forms of energy may be 

 distinguished into two kinds; actual or sensible^ and potential 

 or latent. 



Actual energy is a measurable, transferable, and transformable 

 affection of a substance, the presence of which causes the sub- 

 stance to tend to change its state in one or more respects ; by 

 the occurrence of which changes, actual energy disappears, and 

 is replaced by 



Potential energy y which is measured by the amount of a change 

 in the condition of a substance, and that of the tendency or force 

 whereby chat change is produced (or, what is the same thing, 

 of the resistance overcome in producing it), taken jointly. 



If the change whereby potential energy has been developed be 

 exactly reversed, then as the potential energy disappears, the 

 actual eJtiergy which had previously disappeared is reproduced. 



The law of the conservation of energy is already known, viz. 

 that the sum of the actual and potential energies in the universe 

 is unchangeable. 



The object of the present investigation is to find the law of 

 the transformation of energy ^ according to which all transforma- 

 tions of energy between the actual and potential states take place. 



(2.) To reduce the problem to its simplest form, let us in the 

 first place consider the mutual transformation of one form only 

 of actual energy, and one form only of potential energy. 



Let V denote one measurable state, condition, or mode of 

 existence of the substance under consideration, whose magnitude 

 increases when the kind of potential energy in question is de- 

 veloped. 



Let U denote this potential energy. 



Let P be the tendency or force whereby the state V tends to 

 increase, which is opposed by an equal resistance. 



Then when the state V undergoes a small increase dY, the 

 potential energy developed or given out is 



^^ L (A) 



so that P— ^ 



* Communicated by the Author, having been read to the Philosophical 

 Society of Glasgow, January 5, 1853. 



