526 MEASUREMENT OF RESISTANCES IN ABSOLUTE VALUE. 



1111. CONSTANT ELECTROMOTIVE FORCES. Finally, the use of 

 a sliding contact enables us to obtain a constant electromotive 

 force of induction. 



Suppose, for instance, as in Faraday's experiment (530), that 

 a conducting disc is rotated in a magnetic field, the centre of the 

 disc being joined by a connecting wire with a spring which presses 

 against the edge. 



If the field is uniform, and if F is the component parallel to 

 the axis, a the radius of the disc, the electromotive force for a 

 constant angular velocity w is 



If the field is not uniform, F being the value of the component 

 in question at a point at a distance r from the centre, we have 



\Yrdr, 

 Jo 



and therefore 



'" dt = 



When the distribution of the forces F forms a system of revo- 

 lution about an axis of rotation, the total flow of force across the 

 disc is expressed by 



Q=27r Yrdr, 

 Jo 



which gives 



MAS'. 



27T T 



If the field is produced by a current of strength I, which tra- 

 verses a coil having the same axis as the disc, the flow of force Q 

 is the product MI of the current by the coefficient of mutual 

 induction of the coil with the circumference of the disc, and we 

 have 



QMI 



