492 Dynamical Theory of Currents [OH. xvi 



magnets at rest. These two facts can be reconciled only by supposing that 

 the energy of a system of magnets at rest is kinetic energy a suggestion 

 originally due to Ampere. 



Weber's theory of magnetism ( 476) has already led us to regard any 

 magnetic body as a collection of permanently magnetised particles. Ampere 

 imagined the magnetism of each particle to arise from an electric current 

 which flowed permanently round a non-resisting circuit in the interior of the 

 magnet. The phenomena of magnetism, on this hypothesis, become in all 

 respects identical with those of electric currents, and in particular the energy 

 of a magnetic body must be interpreted as the kinetic energy of systems of 

 electric currents circulating in the individual molecules. For instance two 

 magnetic poles of opposite sign attract because two systems of currents 

 flowing in opposite directions attract. 



We have seen that the mechanical forces in a system of energy E are 



P) Tf r\ T? 



-^Q- , etc., if the energy is potential, but are + -^- , etc., if the energy is 



kinetic. It might therefore be thought that the acceptance of the hypothesis 

 that all magnetic energy is kinetic would compel us to suppose all mechan- 

 ical forces in the magnetic system to be the exact opposites of what we have 

 previously supposed them to be. This, however, is not so, because accepting 

 this hypothesis compels us also to suppose the energy to be exactly opposite 

 in amount to what we previously supposed it to be. Instead of supposing 



?> V 

 that we have potential energy E and forces -^ , etc., we now suppose that 



7\ ( T?\ 



we have kinetic energy E and forces + ~^r^ etc., so that the amounts of 

 the forces are unaltered. 



To understand how it is that the amount of the magnetic energy must be 

 supposed to change sign as soon as we suppose it to originate from a series 

 of molecular currents, we need only refer back to 502. 



567. The molecular currents by which we are now supposing magnetism 

 to be originated must be supposed to be acted on by no resistance and by no 

 batteries, but if the assemblage of currents is to constitute a true dynamical 

 system we must suppose them capable of being acted upon by induction 

 whenever the number of tubes of force or induction which crosses them is 

 changed. In the general dynamical equation 



d fiT\ _<M = E __ pj. 

 dt\dx) da 



we may put E and R each equal to zero, and -= - is already known to vanish. 

 Thus the equation expresses that -^ remains unaltered. 



