MACHINES WITH VARIABLE CURRENT. 735 



For a very great resistance x that is to say, with a single appa- 

 ratus introduced we have e=DC. As this resistance diminishes 

 that is to say, as the number of apparatus increases the difference 

 of potential at first increases, then diminishes, and resumes its 

 original value for ,r = B / B 1 . Starting from this point, the addition 

 of fresh apparatus rapidly diminishes the work of each. 



Machines which are thus provided with a double winding are 

 often called compound. 



1280. MACHINES WITH VARIABLE CURRENT. The current pro- 

 duced by mechanical electromotors is of course alternating, and it 

 may be used in this form. 



Let: 



L be the coefficient of self-induction of the circuit, 



Q the flow of magnetic force which it traverses at the time /, 



R its total resistance; 



the induced current I (518) is defined by the equation 



It will, however, be remarked that if the induced coils contain 

 soft iron, the coefficient L is no longer constant unless the mag- 

 netisation is proportional to the magnetising force. In the general 

 case we must consider the flow of force LI as a function of the 

 current which tends towards a maximum with the magnetisation, 

 and replace the first term of equation (5) by 



_ d\\ dl 

 L + I-- ) . 

 dl) dt 



The following results can only then be applied with restriction 

 to machines with electromagnets. 



As the flow of force as well as its differential is periodical, the 

 current presents the same characteristics. If this flow of force is 

 sinusoidal, as for a frame which turned in a uniform field with a 

 constant velocity w (535), and if T is the duration of the period, 

 we shall have 



Q = Q cos27r- = 



</Q 

 E = - = Q o> sin 



