MAGNETIC MOMENT OF A COIL. 503 



appreciably that which would correspond to coils centred on the 

 axis of rotation. 



When the coils are eccentric, it is evidently better to place the 

 needle in the second principal position that is to say, in the mean 

 plane of the coils. 



1091. The ratio of the surfaces of two coils is also obtained by 

 comparing the discharges induced under the action of the same 

 external field. Suppose, for instance, that the terrestrial field is 

 utilised. The coils are mounted on the same vertical axis, and 

 situate first in a plane perpendicular to the magnetic meridian. 

 When the system is suddenly turned through 180 about a vertical 

 axis, the flow of magnetic forces across the two coils are then 

 2HS and 2HS' (258). Their ratio is that of the surfaces S and S', 

 and this ratio is independent of the angle of rotation. The case is 

 the same if the system turns about a horizontal axis in the magnetic 

 meridian, the variation of the flow of force is produced then by the 

 vertical component Z of the terrestrial field. 



Instead of rotating the system of coils, they may be left sta- 

 tionary, and the direction of the field changed. For this it is 

 sufficient that the field be produced by an external current, the 

 direction of which is reversed. The ratio of the flow of force 

 across the two coils is then equal to the ratio of the surfaces 

 multiplied by the ratio of the mean actions (753). If the coils 

 are not of exactly the same diameter, the corrections for calculating 

 the ratio of the mean actions are rather complicated, even in the 

 case in which the induced coils are in the plane of the inducing 

 current. It is better then to use as inducing circuit, a system of 

 two, three, or four frames (749 to 751), the mean diameters of 

 which, the distances, and the numbers of windings are so chosen 

 as to form a sensibly uniform field. 



1092. Whatever be the method used, the problem reduces in 

 all cases to comparing two flows of force Q and Q'. 



We might in the first case, as with permanent currents, connect 

 the two induced coils in the same circuit containing a ballistic gal- 

 vanometer, and observe the swings a and a which correspond to the 

 cases in which the two flows of induction act in the same or in 

 contrary directions. The quantities of induced electricity m and m ', 

 being proportional to the swings as well as to the flows of force, we 

 shall have, when all corrections are made (883), 



Q-Q" 



