Power by Dynamo-electrical Machines. 519 



time, and E the electromotive force ; i and v represent the 

 current -strength and the number of turns, while a, b, p, q, I, 

 p, a, and X are constants, of which those denoted by Greek 

 letters, and especially the two last, are small as compared with 

 the rest. If the two members in the first round bracket be 

 reduced to a common denominator, and the sign e be then 

 introduced with the signification 



-*+£ « 



the equations assume the following still simpler form : — 



Mc^w^^-K^)^- • • (ILi) 



These equations may be used in dealing with the trans- 

 mission of force ; that is, in treating the case in which two 

 dynamo machines are in conducting communication, and one 

 of them is driven by any mechanical motor, while the other is 

 set in motion by the electrical current in the common con- 

 ductor, and can thus do mechanical work. In order to make 

 the application of the equations to this case as convenient as 

 possible, it is advisable to introduce a little simplification in 

 reference to the sign. 



The second machine, which is set in motion by the current, 

 rotates in the opposite direction to that wdrich produces the 

 current ; and hence, if we wish to express this also in the 

 equation, we must assign a negative value v for the second 

 machine. Further, the ponderomocive force is overcome in 

 the motion of the first machine, while the second is set in 

 motion by the ponderomotive force ; hence if this also is to 

 be expressed, we must represent the work T in the first 

 machine by a negative magnitude, as has been done in the 

 above equations ; and in the second machine by a positive 

 magnitude. Finally, the induced electromotive forces in the 

 two machines are in opposite directions, and for a complete 

 determination they also must be represented by positive and 

 negative magnitudes. 



But it would be inconvenient in practice to speak always 

 of negative velocities of rotation in regard to one machine ; 

 and instead of this it is usual to express the velocities of rota- 

 tion in both machines simply by the number of turns, and 

 therefore by absolute magnitudes, and to regard it as a matter 

 of course that the rotations are in opposite directions. It is 



