THEORY OF GRAMME'S MACHINE. 711 



Making the same assumptions, the angle of lead for an infinite 

 velocity would be 





We should still have to bring in other losses of work, such as are 

 due, for instance, to currents induced in the ring, to the action of 

 the field on the movable ring, if there is a retardation in the mag- 

 netisation, to the reaction of this ring on the external field, etc. 

 These various effects may be represented, at any rate approximately, 

 by a fictive increase of resistance proportional to the velocity and 

 comprised within the term a^ = mnl 



1267. If we represent the function /'(a) by the ordinates of a 

 curve C (Fig. 255), in reference to the semi -circumference AB 

 rectified, the flow of force /(TT) is represented by the total area ACB, 



Fig. 255. 



and the term 2/(<9) by the sum of the areas AMP and M'P'B, so that 

 the total electromotive force is proportional to the area PCP'. We 

 may moreover determine the curve /'() by experiment. 



i st. If a single coil is closed by a galvanometer, and this coil 

 is suddenly displaced through a very small angle Aa, the induced 

 discharge gives the corresponding flow of force ^/"'(a)Aa, that is 

 to say, the ordinate f'(o-) of the curve C. The operation being 

 repeated for a series of equal displacements Aa, from to a, we 

 can deduce f(a) by an integration or by the measurement of a 

 surface. 



2nd. If the coil passes rapidly from the angle a x to the angle 

 a 2 , the induced discharge gives /[/( 2 ) ~/( a i)] '> we mav tnus a l so 

 determine /(TT- 0) -f(0) =/(TT) - 2 /(0). 



3rd. Instead of insulating a coil, the brushes are connected with 

 the ballistic galvanometer. If they are first in the transverse plane, 



