520 Prof. R. Clausius on the Transmission of 



also looked on as a matter of course that work is expended in 

 one machine and is gained in the other, and that the electro- 

 motive forces induced in them are in opposite directions ; and 

 accordingly, in determining the values of the work and the 

 electromotive forces, we are content with giving their absolute 

 values. We shall follow this custom, and in accordance there- 

 with shall represent by v 1 and v 2 the two numbers of turns 

 without reference to the directions of rotations, by T a and T 2 

 the absolute values of the work, and by E x and E 2 the absolute 

 values of the electromotive forces. 



The equations referring to the first machine are then as 

 follows : — 



In order to form the corresponding equations for the second 

 machine, a remark must be made as to the sign of the mem- 

 bers which have v 2 as factor, and of the member pv. Dis- 

 regarding for the present the member pv, the following holds 

 for the other members. If the signs of T and E are to be 

 determined, then, in order to pass from the equations refer- 

 ring to the first machine to those which hold for the second 

 machine, we must replace vi by — v 2 . The members of the 

 first order would thereby change their sign, while those of 

 the second order would retain theirs unaltered. If, on the 

 contrary, the absolute values only of T and E are to be 

 determined, then in those cases in which the previous method 

 would have given negative values of T and E, we must change 

 all signs on the right hand. The consequence of this would be 

 that, in the equations which refer to the second machine, the 

 members of the first order acquire the same sign as in the 

 equations referring to the first machine, while those of the 

 second degree acquire the opposite sign. As to the member 

 pv, which we have hitherto disregarded, the electromotive 

 force represented by the product pvi acts always in that direc- 

 tion which is opposed to the direction of the current i : hence 

 in the first machine, in which the whole induced electromotive 

 force has the direction of the current i } it must diminish its 

 absolute value, which agrees with the minus sign prefixed to 

 pv (IV.) ; in the second machine, on the contrary, in which 

 the whole electromotive force is opposed to the current i, the 

 electromotive force represented by that product must increase 

 the absolute value, and hence the member pv must have the 



