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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; 80 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,^[1] must acquire a magnetic moment of amount ${\frac {3}{4\pi }}\mathbf {F} \times$ 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 ${\frac {3}{4}}\pi \mathbf {I} =k_{p}\mathbf {F}$, and F denotes the magnetic intensity within a spherical cavity excavated in the body. This is Poisson's law 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.^[2] The physical interpretation assigned by Poisson to his formulae must therefore be rejected, although the formulae themselves retain their value.

Poisson's electrical and magnetical investigations were generalized and extended in 1828 by George Green^[3] (b. 1793, d. 1841). Green's treatment is based on the properties of the function already used by Lagrange, Laplace, and Poisson, which

F

1. In the present work, vectors will generally be distinguished by heavy type.
2. This objection was advanced by Maxwell in § 480 of his Treatise. An attempt to overcome it was made by Betti: cf. p. 377 of his Lessons on the Potential.
3. An 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. I.