the induced magnetization I with the magnetizing force H he had given in a form equivalent to
Thomson now[1] showed that the nine coefficients a, b′, c′′ …, introduced by Poisson, are not independent of each other. kor a sphere composed of the magnecrystalline substance, iſ placed in a uniform field of force, would be acted on by a couple: and the work done by this couple when the sphere, supposed of unit volume, performs a complete revolution round the axis of x may be easily shown to be . But this work must be zero, since the system is restored to its primitive condition; and hence b′′ and c′ must be equal. Similarly c′′ =a′, and a′′ = b′. By change of axes three more coefficients may be removed, so that the equations may be brought to the form
,
where κ1, κ2, κ3 may be called the principal magnetic susceptibilities.
In the same year (1851) Thomson investigated the energy which, as was evident from Faraday's work on self-induction, must be stored in connexion with every electric current. He showed that, in his own words,[2] "the value of a current in a closed conductor, left without electromotive force, is the quantity of work that would be got by letting all the infinitely small currents into which it may be divided along the lines of motion of the electricity come together from an infinite distance, and make it up Each of these 'infinitely small currents' is of course in a circuit which is generally of finite length; it is the section of each partial conductor and the strength of the current in it that must be infinitely small."
