348 PROCEEDINGS OF THE AMERICAN ACADEMY 



XXII. 



CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL 

 LABORATORY. 



THE DYNAMIC ACTION OF AN ELECTRIC CURRENT. 



By Hammoxd Vixton Hayes. 



Communicated November 11, 1885. 



In the measurement of the strength of an electric current by a gal- 

 vanometer, the formula usually employed is 



Hr 



C = ^ — ■ tan e. 



This formula is strictly true only when the needle is upon the axis of 

 the coil, which must consist of a small number of turns of wire. If 

 the needle is not upon the axis of the coil, this formula no longer holds 

 good, and a new one must be determined by the use of elliptic inte- 

 grals or by zonal harmonics. The method by zonal harmonics is the 

 simpler of the two, but is rendered very difficult by Maxwell in his 

 Treatise on Electricity and Magnetism. Maxwell also devised a 

 method of approximation to find the potential at any point, when a 

 coil of large cross-section was employed. His treatment of this is 

 almost incomprehensible. It is hoped that in the following paper 

 the errors in Maxwell's formulae have been eliminated, and that the 

 subject has been brought within the grasp of all. 



Let us first take a current of electricity passing through a single 



turn of wire in the form of a 

 circle, and find the potential 

 due to this current at any 

 point. Since, by Ampere's 

 theorem, the magnetic action 

 of a closed current is equal to 

 that of a magnetic shell of 

 the same contour, we will for 

 simplicity replace the circuit 

 by that part of a spherical 

 Fig, 1.. shell which has the circuit 



