Magnetic Field of Circular Currents. 377 



at which the gas begins appreciably to dissociate has been 

 indicated, and a theory, based on the assumption that the 

 molecules of a gas are decomposed by the deposit atoms 

 during their recoil, has been given to explain the behaviour 

 of the deposit atoms. 



I have to thank very sincerely Mr. E. M. Wellish, a 

 suggestion of whose led to this work being undertaken, 

 for his continual interest and advice. 



The Physical Laboratory, 

 The University, 



Sydney, N.S.W., 

 October 13, 1920. 



XXXTII. Magnetic Field of Circular Currents. By H. 

 Nagaoka, Professor of Physics, Imperial University, 

 Tokyo*. 



[Plate VI.] 



MANY years ago 1 1 have shown how -^-functions are 

 suited for calculating the strength of the magnetic 

 field due to a circular current. By means of the same 

 functions, the inductances of circular coils can be easily 

 expressed by formulae developed in ^-series, which are 

 rapidly convergent. In the present paper the expansion 

 in ^-series is applied to obtain expressions for the magnetic 

 force of a single coil and of Gaugain-Helmholtz coils, at 

 points not far distant from the axis, in powers of the 

 coordinates. 



It is usual to have recourse to expansion in spherical 

 harmonics for expressing the magnetic force of circular 

 currents ; but as each harmonic contains different powers 

 of coordinates calculated from the centre of a single coil, 

 or from the middle point of the axis of double coils, the 

 calculation of the deviations of the magnetic force from 

 that at the middle point cannot be easily expressed in 

 power series of the coordinates. By the expansion in q- 

 series, we can arrange terms giving the deviations according 

 to their importance in disturbing the field, and map out the 

 distribution of these perturbations. The study of the curves 

 of equal deviations will be of practical use for finding 

 to what degree of accuracy the field can be assumed as 

 uniform. 



* Communicated by the Author. 



+ Phil. Mag. vi. p. 19 (1903); Ball. Bureau Stand, xiii. pp. 269-893 

 1911) ; Phil. Mag. xxxv. p. 13 (1918). 



