118 HELMHOLTZ ON THE CONSERVATION OF FORCE. 



that this is the only reduction of which the phaenomena are 

 capable. 



I. The principle of the Conservation of vis viva. 



We will set out with the assumption that it is impossible, by 

 any combination whatever of natural bodies, to produce force 

 continually from nothing. By this proposition Carnot and 

 Clapeyron have deduced theoretically a series of laws, part of 

 which are proved by experiment and part not yet submitted to 

 this test, regarding the latent and specific heats of various natural 

 bodies. The object of the present memoir is to carry the same 

 principle, in the same manner, through all branches of physics ; 

 partly for the purpose of showing its applicability in all those 

 cases where the laws of the phaenomena have been sufficiently 

 investigated, partly, supported by the manifold analogies of the 

 known cases, to draw further conclusions regarding laws which 

 are as yet but imperfectly known, and thus to indicate the course 

 which the experimenter must pursue. 



The principle mentioned can be represented in the following 

 manner : — Let us imagine a system of natural bodies occupying 

 certain relative positions towards each other, operated upon by 

 forces mutually exerted among themselves, and caused to move 

 until another definite position is attained ; we can regard the 

 velocities thus acquired as a certain mechanical work and trans- 

 late them into such. If now we wish the same forces to act a 

 second time, so as to produce again the same quantity of work, 

 we must, in some way, by means of other forces placed at our 

 disposal, bring the bodies back to their original position, and in 

 effecting this a certain quantity of the latter forces will be con- 

 sumed. In this case our principle requires that the quantity of 

 work gained by the passage of the system from the first position 

 to the second, and the quantity lost by the passage of the system 

 from the second position back again to the first, are always 

 equal, it matters not in what way or at what velocity the change 

 has been effected. For were the quantity of work greater in 

 one way than another, we might use the former for the pro- 

 duction of work and the latter to carry the bodies back to their 

 primitive positions, and in this way procure an indefinite amount 

 of mechanical force. We should thus have built a perpetuum 



