122 Prof. R. Clausius on the 



shape of a rotating body the axis of which coincides with the 

 axis about which it turns. But if the two moving forces do 

 not set the core in motion, it follows from this that they have 

 equal and opposite moments of rotation. As, now, the latter is 

 again equal and opposite to the moment of rotation exerted by 

 the iron core on the coil, it follows further that the moment of 

 rotation exerted by the fixed electromagnet on the iron core is 

 equal and in opposite direction to the moment of rotation exerted 

 by the iron core on the coil. 



Hence the work which, in the case where the iron core also 

 rotates, produces the force exerted by the fixed electromagnet 

 on the iron core, has the same value as the work previously 

 determined which, when the iron core is at rest, produces the 

 force exerted by it upon the coil. 



In the mathematical representation of these two magnitudes 

 we arrive at expressions which are apparently different. The 

 latter magnitude must, as expressed in the former paragraph, 

 be proportional to the magnitudes N and P 1? and we have 

 expressed them by 



in which k is an undefined constant. The former, on the con- 

 trary, must be proportional to the magnitudes M and P 2 , and 

 may therefore be expressed in a corresponding manner by 



-A'MP 2 v, 



in which k f may for the present be regarded as a second 

 undefined constant. These expressions seem externally very 

 different ; but if we replace in them for P x and P 2 their values 

 as given in (16), they change into 



7 CMN . 7 ,CMN 

 — k———.v and —k' T -- 7r .v, 

 1 + pi 1 + fit 7 



and from this it appears that it is only necessary to make the 

 constant k f , which was previously introduced as a second un- 

 defined constant, equal to k, in order to bring into agreement 

 the two expressions which, from the foregoing considerations, 

 represent equal magnitudes. 



That part of the work of the ponderomotive force, in deter- 

 mining which it is alone important to consider whether the 

 iron core does or does not rotate, has thus been shown to be 

 equal ; it follows thence that the entire work done by the pon- 

 deromotive force is the same in both cases, and hence, under 

 the supposition we have made as to the position and strength 

 of the poles, we may use the expression deduced (19) for the 

 determination of T also for the case in which the iron core 

 likewise rotates. 



