1886.] On a New Scale for Tangent Galvanometers. 



499 



Fig. 2. 



that is to say, the angle through which the needle would have been 

 turned when the zero was 60° to one side of zero, would be twice 

 what it would be if it had been deflected from the ordinary zero. The 

 ratio of these angles, however, decreases in value, and at a certain 

 point becomes equal to 1 ; that is to say, the angular deflection from 

 the new zero is the same as it is from the old zero. 



Let 



sin (a° + /3°) 



= tan <%°, 



therefore 



or 



sin («°+y3°) sin «° 



cos oc° cos «° ' 



sinO° + /3°)=sW 



If the angle a is negative, that is to say, if the angular deflection 

 from the new zero is less than the angle then we have — 



or 



that is, 



sin (jS° — a°) = sin a. , 



r>o o O 



p — x =<x ; 



that is to say, whatever be the angle /3° (the angular distance of the 

 new from the old zero), then a current sufficient to move the needle a 

 distance of J/3° from the old zero would move it the same distance 

 from the new zero. If the deflection from the old zero be less than 



2 l 2 



