4 Prof. R. Clausius on the Relations between the 



and with the aid of this quantity he forms the following equa- 

 tion : — 



d ^ OT V [f ^ dJJ it k\ dV , t N dV ~] 



This is very similar to equation (1); in some relations it is 

 more general. First, Lipschitz has given it a more general sig- 

 nification, as he advances it not merely for free systems, but also 

 for systems which are subject to certain conditions; and, secondly, 

 for each point a special defined position is assumed, which is 

 subject to further arrangement, while in (la) the corresponding 

 position marked out for each point is the initial point of the 

 coordinates. In other relations, on the contrary, it is more 

 limited, as in it the forces are presupposed to have a force-func- 

 tion, which is not the case in (la). 



Further than this equation (numbered 6 in his memoir) the 

 agreement of Lipschitz's considerations with mine does not ex- 

 tend, as from this point he gives quite another turn to the inves- 

 tigation. While even equation (1), which is more general than 

 (1 a), I have applied to stationary motions, and for these have 

 derived equation (2), Lipschitz proceeds as follows. First he 

 gives to his equation another form, in that he eliminates from it 

 the vis viva by means of the relation which subsists between this 

 and the force-function. Then he goes on to further specialize 

 his equation by making definite suppositions concerning the 

 nature of the forced unction, particularly this — that it is an alge- 

 braic homogeneous function of the elements x a — a a ,y a — b aJ z a —c a . 

 For the cases limited by these presuppositions, he then inquires 

 what condition is necessary and sufficient in order that the mo- 

 tion may be stable. This investigation is, on account of the 

 subject on which it treats, as well as the treatment itself, of high 

 interest; but it is altogether different from my considerations, 

 and accordingly the result which I have derived, and expressed 

 by the theorem of the virial, does not appear in it. 



The circumstance that no one before me put forth this theorem, 

 although equation (2) is so easily obtained from the funda- 

 mental equations of motion, must, I think, be accounted for by 

 this, that hitherto they had less inducement to turn their atten- 

 tion to stationary motions as such. But since the newer view 

 of the nature of heat has become current we have, in the theory 

 of heat, to do with a stationary motion of the minutest consti- 

 tuents of bodies ; and as we knew (and still know) very little 

 about the nature of this motion, it lay near to draw at least the 

 conclusion which could already be drawn from the condition 

 that the motion is stationary; and indeed the theorem thus 

 gained is of peculiar importance for the theory of heat. 



