WITH MAGNETISM AND ELECTRICITY. 181 



sin udu, and let the integral be taken within the limits ^ = and 

 w=7r. This integral value, multiplied by the number n of the 



molecular currents and divided by / sinw^M=2, gives the re- 



quired moment y, 



n r-^ . , 

 y=- / x^\nudu. 



By carrying out the integration we obtain for y the following 

 expression, 



X XN4XXDD + |p4 



2'-^^^(XX-fDD)' X4-fXXDD + D4 



The force which acted upon the iron, and by which the moment 

 y was generated, was =X. Let n denote the number of mole- 

 cular currents in the unit of volume, then the ratio of the 

 moment y to the force X, in the theory of molecular currents, 

 has the same meaning as the magnetic constant which Neumann 

 has denoted by k, in the theory of separable magnetic fluids. 

 Substituting, therefore, for k in the formula of Neumann given 



above, , 7™,~5rj the variable value just found ^, we obtain the 



'l+49r^S' '^ X^ 



sought magnetic moment of a variable magnet of the form of an 



cUipsoid of revolution, to which the formula of Neumann refers, 



_ vy 



l+47rS|' 



where S denotes the factor already determined from the ratio of 

 the axes of the ellipsoid. 



This result, referring to the dependence of the variable mag- 

 netism on the strength of the magnetizing or electro-magnetizing 

 force derived from the view of Ampere in contradistinction to 

 that usually assumed, is actually corroborated by the experiments 

 described by Miiller in PoggendorfTs Annalen, 1851, vol. Ixxxii. 

 p. 181. 



II. Experiments, 



Having in the foregoing pages, for the sake of obtaining a 

 simpler general view, stated, under the title of a theory, the 

 results obtained with regard to the connexion of diamagnetism 

 with magnetism and electricity, we shall, in the present section, 



SCIEN. MEM.— iS^a/. Phil. Vol. I. Part II. o 



