524 MEASUREMENT OF RESISTANCES IN ABSOLUTE VALUE. 



As the terms which contain the coefficient of self-induction are 

 very small, we might express the value R in the form 



_ GSw Vk + cos a Leo "| L 2 w 2 

 ~1T sin a f If J "~R~' 



or, replacing k by , and the resistance R in the terms of cor- 

 rection by its approximate value R = 



, 



2 tana 



G 2 M a> L 2 o>2 



(9; R = R H h Lo> tan a - . 



2 H Sin a R Q 



1109. We may also make the frame turn about a horizontal 

 axis ; the component to be considered is then the projection of the 

 terrestrial action on a plane perpendicular to the axis. If a is the 

 angle of this plane with the magnetic meridian, the value of 

 the effective component is (305) 



2 cos 2 a = Z N /i+cot 2 Icos 2 a, 

 and it makes, with .the horizontal plane, an angle I' such that 



cot I' = cot I cos a. 

 The simplest conditions are those in which the axis of rotation 



7T 7T 



is in the meridian. In that case a = - , I' = , and the effective 



2 2 



force reduces to the vertical component. Apart from the effects 

 of self-induction, the change of the direction of the induced current 

 is in the horizontal plane ; and for an observer outside the frame, the 

 current retains the same direction in all azimuths. On the other 

 hand, the electromagnetic action on a pole placed at the centre 

 being at each instant perpendicular to the plane, the resultant is 

 a horizontal force perpendicular to the axis. So long as the hori- 

 zontal needle is in the meridian, there is no variation in the flow 

 from the needle relative to the frame ; and therefore there is no 

 induction on the part of the needle, whatever be its magnetic 

 moment. The effect of induction may be regarded as negligable 

 if the deflection continues to be small. 



