Section III, 1919 [153] Trans. R.S.C. 



The Mutual Potential Energies of Circular Coils and Small Magnets. 

 By A. Norman Shaw, D.Sc. 

 Presented by Prof. L. V. King, D.Sc, F.R.S.C. 



(Read May Meeting, 1919.) 



§1. Introduction. 



While determining certain small corrections in connection with 

 the use of the Weber type of electrodynamometer for absolute measure- 

 ments,^ the writer had to consider the mutual potential energies of 

 the dynamometer coils and the magnets of a small magnetometer; 

 and the following notes, arising from this, are reported with the hope 

 that they may be of service in connection with any problem which 

 requires the accurate consideration of the magnetic potential due to 

 small magnets. It will be observed that a number of points are 

 raised in the paper without reference to any authority; this is due to 

 the fact that the general method was derived from the lecture course 

 on the theory of electrical measurements given by Dr. G. F. C. 

 Searle at the Cavendish Laboratory, and apart from the well known 

 sections in MaxwelF and in Gray^ which deal with the application 

 of Zonal Harmonics to problems in potential, no other authorities 

 were consulted. A search in the literature on these subjects has been 

 made since, and led to the conclusion that these notes might be of 

 nterest. 



The main points of the paper are to show (1) that even in some 

 null methods it may be necessary to consider the influence of the 

 characteristic constants of a magnetometer, and (2) that these con- 

 stants may be determined with the aid of standard coils, in a com- 

 paratively simple manner. 



§2. The Significance of the Characteristic Constants of a Thin Magnet. 



The chief difificulty in the theory of electrical instruments which 

 involve the use of coils and magnets, lies in the exact calculation of 

 the couple on the moving system. In the usual symmetrical instru- 

 ments the axes of the two systems intersect, and the couple tending 



'A. N. Shaw, Phil. Trans., A, Vol. 214, pp. 147-198, (1914). 

 '^Maxwell, Electricity and Magnetism (third edition), Vol. 2, Ch. 14. 

 'Gray, Absolute Measurements in Electricity and Magnetism, Vol. 2, Ch. 1-6, also 

 Appendix, Vol. 2, pt. 2. 



Sec. Ill, Sig. n 



