Il6 Mr. W. J. M. Rankine on the General Law of 



are, the nature and value of the function /TQ) for each kind of 



JTJ 



actual energy of -j^ for each kind of potential energy, and o| 

 ir^,Y and ^^^2 for each combination by pairs of an actual with a 



potential energy. 



(5.) Abstract and metaphysical as the principles and reasoning 

 of this paper may appear, they are of immediate practical utility. 



When applied to the mutual transformation of visible motion 

 with the power arising from attractive and repulsive forces, the 

 equation 3 becomes identical. 



It is in the theory of those forms of energy which manifest 

 themselves to us only by their effects, such as heat and elec- 

 tricity, that this law becomes useful. It enables us, when power 

 is produced by the consumption of one or more of those energies, 

 to analyse the effect produced, to refer each portion to the kind of 

 energy by which it is caused, and thus to determine how much 

 of any given kind of energy must disappear in order to produce 

 a given change in the condition of a substance. 



An important consequence of the formula (1) is as follows : — 



If the tendency, ^, of the state V to increase is proportional 

 simply.to the actual energy present, Q, then 



dQdY" Q'dY* 



q£^-^^=^U' (^) 



thkt is to say, when the tendency to the production of potential 

 energy is simply proportional to the actual energy present, then is 

 the actual enej-gy converted into potential energy the exact equiva- 

 lent of the whole potential energy produced. 



(6.) Another important consequence of the formulae (1) and 

 (3) is as follows : — If a substance be made to undergo a change 

 of condition, and be brought back to its primitive condition by 

 a process not the exact reverse of the former process, then will 

 there be a certain amount of permanent conversion of energy 

 between the actual and potential forms. That the permanent 

 conversion from the actual to the potential form may be the 

 greatest possible in proportion to the actual energy supplied 

 from without, the changes of condition must be so regulated 

 that none of the actual energy received or given out by the sub- 

 stance shall be employed in changing the total actual energy 

 present in it, the whole being consumed or produced by trans- 

 formation to or from the potential form. 



and consequen^ty 



