OPTICAL GALVANOMETER. 30! 



When the magnetic field is produced by a current, the mean 

 magnetic force F m is equal to the product of the intensity by a 

 more or less complex function of the dimensions of the circuit. 



If the luminous ray traverses the axis of a coil for instance, we 

 shall have 



F TX 



x ~ Ay 



m 



and the factor X m will be calculated by the integral of the values 

 (729) relative to the different windings of the coil. Equation (43) 

 of (742), for example, will give this factor for a coil of great length 

 compared with the thickness e of the body if we suppose it near the 

 centre. 



If V and V are the potentials for unit current, we have generally 



(58) I<o(V-V) = <9. 



Other things being equal, the intensity is proportional to the rotation 

 of the plane of polarization, which will enable us to determine the 

 ratio of two currents. 



915. In order to know the absolute value of a current, we must 

 first know the constant w for the body observed, and the elements 

 of the coil which would enable us to calculate V - V ; but we may 

 choose such conditions of experiment as will enable us to get rid 

 of measurements of dimensions. We need only remember that when 

 we pass from one point to another in the field of a current, the 

 change of electromagnetic potential V V should be increased by 

 as many times 471-! as the surface of the circuit has been traversed 

 in a direction opposite that of the field (452). 



If the ends of the medium in question are on either side of the 

 coil, and are so far that the values of the potentials V and V are 

 insensible, the rotation produced by each winding will be (0477-1. A 

 coil of n windings will give then the rotation 



(59) ^ = W47TI. 



This expression depends neither on the shape, nor on the size, nor on 

 the relative direction of the windings, nor, again, on the direction of 

 the radius in respect of their mean plane ; it is sufficient to know the 

 number of windings. 



916. We may first utilise equation (59) to determine the con- 

 stant w relative to a very active body, which would then serve as 

 galvanometric apparatus. Bisulphide of carbon is the best substance. 



