76 ELECTRICAL MEASUREMENTS 



tion of the two coils cannot be exactly calculated in this simple 

 manner, for to be exact, m must be expressed in the form of a series. 

 However, in this particular case, as pointed out by A. Gray, 14 



if the ratio of the radius of each coil to its length is = all the 



terms in the series between the first and seventh drop out and 

 all but the first term are so very small that they may be 

 considered as corrections, to be calculated if the accuracy of 

 the work demands it. 



The result of careful analysis shows that the turning moment 

 due to the mutual action of the two coils, if they are concentric- 

 ally placed with their axes perpendicular, is given, to a very high 

 degree of approximation, by 



or if the two coils are in series, by 

 M 



Va 2 + & 2 



Of course the field in which the movable coil is placed is not 

 uniform, but with coils proportioned as stated above, the instru- 

 ment acts as if a plane circuit having the net area of the movable 

 coil were suspended in a uniform field of strength, 



H = 



Secondary Electrodynamometer. Siemens Dynamometer. 

 A form of secondary electrodynamometer in common use is 

 shown in Fig. 38. The fixed coils are firmly supported from a 

 wooden pillar which carries at its top a torsion head provided 

 with a pointer which can be moved over a uniformly graduated 

 circle. 



The wooden frame effectually prevents any errors which might 

 be introduced in alternating-current work by currents induced 

 in the supports for the coils. 



The movable coil hangs freely from a pivot which rests in a 

 jewel carried by a stirrup attached to the graduated plate. The 

 torsion head is connected to the movable system by a loosely 



