294 A. TANAKADATE 



The values of Fq for any actual case are to be obtained by divid- 

 ing the above number by the number expressing half the height' of 

 the coils in centimetres, and multiplying by the number of turns of 

 wire in the coil. From the table it is seen that when the length c 

 exceeds 5 times the height b the action of the coils is not far from 

 that of the four infinite parallel currents already treated. This justifies 

 the experiment described at the close of the first section of the paper. 

 Further we see that the assumption for a large magnetic shell made 

 in the beginning of the paper is practically correct, if the straight part of 

 the circuit extends more than 5 times the distance between the upper 

 and lower magnets (c/6 = 10) on each side of the instrument, and if 

 the length of each magnet is not less than be. 



In practice however the coils are of finite section whereas the 

 above results refer to coils of infinitesimally small section. So long 

 as the depth and width of the sections of the coils are small fractions 

 (say l/lO) of the height of the coils or of their distance apart, we may, 

 without sensible error take the centers of the sections for the posi- 

 tions of simple equivalent coils of infinitesimal section. 



If the depth of the section is small and the width finite the force 

 at the center of the coils is got by a process of ordinary integration. 

 Thus if the number of turns of wire per centimeter be ??, we have with 

 the same notation as before 



=2r 



. -ndx 

 ox 



2:»[^]:: 



Avhere a^ and a^ are the distances of the internal and external faces of 

 either coil measured from the point half way between the two coils. 

 Hence in order that the effect of eccentric displacement may be small 

 we have 



