522 MEASUREMENT OF RESISTANCES IN ABSOLUTE VALUE. 



1108. MEAN FIELD OF A ROTATING FRAME. We may observe, 

 in the experiment of the rotating frame, that the current has always 

 the same direction in a given azimuth, although its direction changes 

 in reference to the circuit at each half -turn ; the magnetic action 

 of the -current induced at each point varies periodically, but the 

 resultant action is not null. As the intensity of the current is a 

 maximum, except for a retardation due to secondary effects, when 

 the frame is parallel to the external field, this resultant is almost 

 perpendicular to the component H, of the field normal to the axis 

 of rotation ; a magnetic needle placed in the interior of the frame 

 will then' be deflected from its original position. 



Let a be the deflection of the needle, the magnetic moment of 

 which is M, and x that of the frame. If we take into account the 

 true direction of the current and of the field of the needle, the 

 differential of the flow of force across the circuit is 



</Q dx 



dt dt 



= - wHS cos x + cos (x - a) , 

 L Hb J 



and the equation of the current is 



dl V MG 1 



L - + Rl = Hb(o cos 3H cos(x-a) 



dt |_ HS 'J 



dl dl MG 



We have further - = to ; putting = /e, we get 



dt dx HS 



T di R T r c\ 



L 1 I = HS cos x + k cos (x - a) 



**..*[ 'J 



If the movement is uniform, and rapid enough, in comparison 

 with the time of oscillation of the needle, for this to be permanently 

 deflected when the condition is established, the quantities w and a 

 are constants, and the integral of the equation is of the form 



I = A cos x + B sin x . 



