ELECTRODYNAMOMETERS. 245 



864. These equations only hold if the apparatus is well adjusted. 

 Suppose that, in the original condition, the coils are not exactly 

 rectangular, but that the axis of the movable coil makes an angle a, 

 and the plane of the fixed coil an angle /?, with the magnetic 

 meridian. 



The deflections S x and S 2 , obtained by the two different directions 

 of the current in the movable coil, give, with a bifilar suspension, 

 equations 



II'GS' cos (8 l + a + ft) = C sin 8 l + I'S'H sin (8 l + a), 

 II'GS' cos (3 2 - a - ft) = C sin 5 2 - I'S'H sin (8 2 - a) . 



The deflections 8 3 and S 4 , for the change in direction of the 

 current in the fixed coil, give similarly 



II'GS' cos (8 S - a - /?) = C sin S 3 + I'S'H sin (8 3 - a), 

 II'GS' cos (8 4 + a + /3) = C sin S 4 - I'S'H sin (8 4 + a). 



If the conditions of adjustment are nearly satisfied, and the 

 coefficient C is great in respect of the product I'S'H, the angles 

 a and /3 are very small, and the values of the four deflections very 

 near each other. By combining these equations as above (834) and 

 neglecting the squares of small angles, we have 



C 



* 



or sensibly 



(3.) ir.un^V^. '' , 



In the preceding conditions, we may thus neglect the action of 

 the earth, and take as standard deflection the mean of four readings. 



With the method of torsion, we shall take as standard value the 

 mean of the four angles necessary to bring the needle back to its 

 original position. 



The experiment being somewhat long, alternate tests must be 

 made to get rid of variations in the current. 



865. With the electrodynamometer it would be difficult to attain 

 the same degree of sensitiveness as with the galvanometer. But as 



