178 Prof. Thomson on the Tlieory of Magnetic Induction 



out a mathematical theory of magnetic induction is obvious. On 

 the other hand, in the present state of science, no theory founded 

 on Poisson^s h}^othesis of " two magnetic fluids " moveable in 

 the " magnetic elements " could be satisfactory, as it is generally 

 admitted that the truth of any such hj^othesis is extremely 

 improbable. Hence it is at present desirable that a com- 

 plete theory of magnetic induction in ci-ystalline or non-crystal- 

 line matter should be established independently of any hypo- 

 thesis of magnetic flmds, and, if possible, upon a purely experi- 

 mental foimdation. With this object, I have endeavom'ed to 

 detach the hypothesis of magnetic fluids from Poisson's theory, 

 and to substitute elementaiy principles deducible from it as the 

 fouudation of a mathematical theory identical with Poisson's in 

 all substantial conclusions. In the present communication I 

 shall state these principles, and point out what modifications of 

 them may be required by a more complete experimental investi- 

 gation of the subject than has yet been made ; and, adopting 

 them temporarily as axioms of magnetic induction, I shall give 

 an account of some important practical conclusions deduced 

 fi'om them, by mathematical reasoning which I propose to pub- 

 lish on a future occasion. 



Some explanations and definitions are prefixed to show the 

 signification in which certain extremely convenient terms and 

 expressions, occasionally employed by Faraday and other writers, 

 will be used in what follows. 



Definition. — The foi-ce at any point due to a magnet is the force 

 which it would exert on the north pole of an infinitely thin, 

 uniformly and longitudinally magnetized bar of unit strength 

 placed at that point*, if it experienced no inductive action from 

 the latter magnet. 



* " If two infinitely thin bars be equally, and each uniformly and longi- 

 tudinally, magnetized, and if, when an end of one is placed at a unit of di- 

 stance from an end of the other, the mutual force between these ends is imity, 

 the magnetic strength of each is imity." (Phdosophical Magazine.Oct. 1850, 

 pp. 241, 242.) The definition of magnetic force in the text will agree pre- 

 cisely with the definition of " magnetic force in absolute measure " adopted 

 by the Royal Society, in its Instructions for making obser\ations on 

 terrestrial magnetism, if, m the definition of a unit bar, the unit of length 

 understood be one foot, and the unit of force, a force which, if acting 

 on a grain of matter, would in one second of time generate one foot per 

 second of velocity. (See Admiralty Manual of Scientific Inqiuiy, pp. 16, 



33, 37.) It may be remarked, that this unit of force will be the fraction - 



9 

 of the weight, in any locality, of one grain of matter, if g denote the velo- 

 city acquired in one second by a falling body in that locaUtj' ; and that it is 



therefore verj- nearly — -- of the weight, in any part of Great Britain or 

 Ireland, of a grain. 



