THEORY OF GRAMME'S MACHINE. 



707 



sign in respect of the transverse plane AB perpendicular to the 

 first that is to say, that the forces F on one side are directed 

 towards the transverse plane, while the symmetrical forces F' 

 are directed from this plane. The ring of soft iron introduced 

 into the field does not modify this kind of symmetry. The flow 

 of force is absorbed on one side of the ring; an equal flow is 

 emitted from the other, and a part of the total flow, the least 

 possible, proceeds from one half of the ring to the other by the 

 internal void space. The figure given by iron filings well illus- 

 trates this distribution. 



It will be assumed that the magnetisation of the ring by the 

 field is the same in motion as at rest that is to say, there is no 

 retardation in the magnetisation. 



When a winding moves from A to M, it cuts a flow of force 

 which is a function /(a) of the angle a which its plane makes 



with the transverse plane. The flow of force cut by a coil, the 

 mean plane of which has traversed this same angle, is 



q =//(<*) 



For a displacement afa, the electromotive force induced in the 



ring is 



If 6 is the angle of lead of the brush that is to say, the 

 angle of the diameter A'B' of the contacts with the transverse 

 plane the flow of force cut by the ring from A' to B' comprises 



zz 2 



