158 THE ROYAL SOCIETY OF CANADA 



§5. Three Examples of the Magnetic Constants in Common Formulae. 



(a) In the ordinary tangent galvanometer, the formula for the 



, 2TvniM sin , ^ i ^i 



couple, namely -, becomes at length 



r 



2TrniM sin 6 



1_ ^ til (5cos20-l) + 

 4 r^ 



— — (21 cos''0-14cos-e+l)+ (9) 



64 r" 



(&) The formula for the double tangent galvanometer follows at 

 once from equation (6). The correction, if expressed as in (9) has the 

 obvious advantage that the second term containing Li vanishes under 

 the conditions already mentioned. 



(c) The complete formula for the couple in magnetometric' tests 

 where x is the distance apart of the centres of two magnets with con- 

 stants M, Li, L2, and m, k, k respectively, is, in the case of the "sine" 

 or "side-on" method given by 



2Mm / 2L\-SPr 24LS-120LSh^-\-4lS \ 

 x^ \ _ x^ 8^4 ' "/ 



Summary. 



This paper discusses the significance of the characteristic con- 

 stants of small magnets and points out that the use of Zonal Har- 

 monics leads to an expression of their value in a determinable form. 

 The calculation of mutual potential energy in a special case is re- 

 viewed, and an application is made to the experimental determination 

 of the magnetic constants. The details of the procedure are outlined, 

 and the paper concludes with a brief reference to the occurrence of 

 these constants in common formulae. 



In conclusion the writer desires to repeat his indebtedness to Dr. 

 G. F. C. Searle for the general method of treatment, and to express 

 his thanks most heartily. 



Macdonald Physics Building, 

 McGill University. 



