prior to the Introduction of the Potentials. 65 



This memoir also contains a discussion of the magnetism 

 temporarily induced in soft iron and other magnetizable metals 

 by the approach of a permanent magnet. Poisson accounted for 

 the properties of temporary magnets by assuming that they 

 contain embedded in their substance a great number of small 

 spheres, which are perfect conductors for the magnetic fluids ; so 

 that the resultant magnetic intensity in the interior of one of 

 these small spheres must be zero. He showed that such a sphere, 

 when placed in a field of magnetic intensity F,* must acquire a 



magnetic moment of amount -.- F x the volume of the sphere, 



in order to counteract within the sphere the force F. Thus if 

 k p denote the total volume of these spheres contained within a 

 unit volume of the temporary magnet, the magnetization will be 

 I, where 4-TrI = k p F, 



and F denotes the magnetic intensity within a spherical cavity 

 excavated in the body. This is Poisson s laiv of induced magnetism. 



It is known that some substances acquire a greater degree 

 of temporary magnetization than others when placed in the 

 same circumstances : Poisson accounted for this by supposing that 

 the quantity k p varies from one substance to another. But the 

 experimental data show that for soft iron k p must have a value 

 very near unity, which would obviously be impossible if k p is to 

 mean the ratio of the volume of spheres contained within a 

 region to the total volume of the region.f The physical inter- 

 pretation assigned by Poisson to his formulae must therefore be 

 rejected, although the formulae themselves retain their value. 



Poisson's electrical and magiietical investigations were 

 generalized and extended in 1828 by George Green* (b. 1793, 

 d. 1841). Green's treatment is based on the properties of the 

 function already used by Lagrange, Laplace, and Poisson, which 



* In the present work, vectors will generally be distinguished by heavy type. 



t This objection was advanced by Maxwell in 430 of his Treatise. An attempt 

 to overcome it was made by Betti : cf. p. 377 of his Lessons on the Potential. 



J A.n essay on the application of mathematical analysis to the theories of electricity 

 and magnetism, Nottingham, 1828 : reprinted in The Mathematical Papers of the late 

 George Green, p. 1. 



F 



