Two years later Thomson presented to the Royal Society a memoir[1] in which the results of Poisson's theory of magnetism were derived from experimental data, without making use of the hypothesis of magnetic fluids; and this was followed in 1850 by a second memoir,[2] in which Thomson drew attention to the fact previously noticed by Poisson,[3] that the magnetic intensity at a point within a magnetized body depends on the shape of the small cavity in which the exploring magnet is placed. Thomson distinguished two vectors;[4] one of these, by later writers generally denoted by B, represents the magnetic intensity at a point situated in a small crevice in the magnetized body, when the faces of the crevice are at right angles to the direction of magnetization; the vector B is always circuital. The other vector, generally denoted by H, represents the magnetic intensity in a narrow tubular cavity tangential to the direction of magnetization; it is an irrotational vector, The magnetic potential tends at any point to a limit which is independent of the shape of the cavity in which the point is situated; and the space-gradient of this limit is identical with H. Thomson called B the "magnetic force according to the electro-magnetic definition," and H the "magnetic force according to the polar definition"; but the names magnetic induction and magnetic force, proposed by Maxwell, have been generally used by later writers.
It may be remarked that the vector to which Faraday applied the term "magnetic force," and which he represented by lines of force, is not H, but B; for the number of unit lines of force passing through any gap must depend only on the gap, and not on the particular diaphragm filling up the gap, across which the flux is estimated; and this can be the case only if the vector which is represented by the lines of force is a circuital vector.
