THEORY OF GRAMME'S MACHINE. 709 



The electromotive force is nE l9 and the factor E 1 represents 

 the electromotive force for one turn per second. 



The ring is really magnetised afresh by the current which sur- 

 rounds it, so that the field is no longer symmetrical. It may, 

 however, be assumed, as a first approximation, that this mag- 

 netisation is added to the original magnetisation. In this case, 

 no change takes place in the electromotive force, for the sum of 

 the corresponding flow of force, cut by a ring from A' to B', is 

 null. 



The energy lost comprises, first, that which arises from the 

 heating of the circuit, or I 2 R. 



Moreover, every time a coil is short-circuited by the contact 



of the brush on two adjacent strips, the current is suppressed, and 



/ I 2 I 2 



the intrinsic energy is lost ; the loss is - - at each brush, or /. 



24 4 



for a rotation, or mntl 2 = a l 1? in a second for all the coils.* 



In conclusion, the excess of energy expended over the energy 

 lost, or the disposable energy U, is 



The effects of self-induction may thus be represented by a 

 fictive resistance proportional to the velocity. 



1265. The best angle of lead is practically defined by the 

 condition that no sparks are produced. But these sparks are 

 dangerous, not when the brush meets a strip, but when it leaves 

 it. Hence two successive strips, that which is in contact with the 

 brush, and that which escapes, should be at the same potential, or 

 that the corresponding coil should contain at this moment an 

 electromotive force capable of producing the mean current -. 



2 



This electromotive force comprises a part of flvf'(O) which is 

 due to the field, and a term in the opposite direction proportional 

 to the magnetisation of the ring to the velocity and to the number 

 of turns, and which may be written - o 



* JOUBERT. Comptes rendus, Vol. xcvi., p. 641. 1883. 



