MAGNETIC MOMENT OF A COIL. \ 50! 



determined by comparison with the value X' of a standard coil, as in 

 the preceding paragraph. 



In the case of a cylindrical coil, the channel of which is of such 

 small dimensions that we may neglect powers higher than the square 

 of the ratios of these dimensions to the mean radius, the action X at 

 a point P on the axis, at a distance x from the mean plane, may be 

 written 



28 



-f!_ + ^! ^- + ^ a -- i. 



4 a 2 x> 2X* 2.3*4 



or, denoting by i + e, the quotient of the bracket by i + y, 



If the point P were in the mean plane at a distance r from 

 the centre, we should have 



3* 



which may be written 



X = ?3 



Taking, as term of comparison, a single circle of radius R, with 

 a small magnetic needle at the centre, and traversed by the same 

 current as the coil, we find* 



T*I+0 



xr^8 (I 



These two arrangements have the drawback of requiring a very 

 exact measurement of the distances x and r, the cubes of which 

 occur in the principal factor. The difficulty might be got over by 

 making two observations at two different distances from the needle, 

 as the displacement of the frame could be determined with great 

 accuracy. The experimental errors acquire then great importance. 



* F. KOHLRAUSCH. Gottinger Nachrichten, No. 20, p. 654. 1882. 



