28G 
M-R. J, LAR:\rO'R OX A OYXAMTCAL THEORY OF 
energy and the dissiiiation being supposed known. Substituting from the kinematic 
relation i-n-u = dyidy — d^/dz, and integrating by parts, 
dT/dt = d^jdt — (47r)~^J[/ (/3 Pl — yQ) + (yP — + n (“Q — /^P)} f^S 
+ {47r)“\f(a + ^dhldt + ydcjdt) dr. 
This equation of energy can however only apply to the case in which the energy of 
magnetic, as well as of electric, polarization is completely organized, and not mixed 
up with other molecular energy of the material, as it wmuld be if there were hysteresis 
or permanent magnetism. When this condition is satisfied, the negation of perpetual 
motion requires that a da ^ dh y dc shall be an exact differential, say d\\j ; thus 
we may tentatively assume T = (47r)“\fi/;(:?r, when the surface Integral wall remain as 
the value of cZE/dA In the case usually considered, in which the law of induced 
magnetization is linear, this gives Maxwell’s formula for the distribution of the 
energy, T = (87r)"\f(«a + +cy) cZt ; while the value of d^jdt expresses Poyxtixg’s 
law of flux of electric energy corresponding to that hypothesis. 
70. That this law of distribution of electrokinetic aethereal energy, for a magnetic 
medium of constant permeabilit}^ falls in with the present scheme may be verified as 
follows. Let [a, /3', y) be proportional to the velocity of the irrotational flow of the 
aether, due in part when there is magnetism to the Amperean aethereal vortices, in 
such wise that the total kinetic energy is (Stt) (a'® + 1^'^ + y^)dT ; this is equal 
to (87r)“^{ IvdYjdnd'^ — S^\dYIdnda}, where 8cr is an element of a barrier surface 
closing a magnetic vortex of strength fe, and SS is an element of the outer boundary 
of the region under consideration. As T is to include only the organized energy, it 
is given by this expression when in it V is restricted to be the potential of the mag¬ 
netic force as ordinarily defined. In that case for an element of volume Sr, 
jdndcT — S(kZcZV/c?.T -f- jdy -|- )^indVldz )(7 = — Airi^Kct -(- B/3 -|- Cy) dr; 
and therefore 
T = ( 877 )“’f {cd + 4 - y4 dr -f- (Aa -f -f Cy) dr = (87r)”\f(aa -}- + Cy) dr. 
But although this expression locates the energy correctly as regards distribution 
throughout space, it still ignores the essential distinction between the energy of the 
translatory motions of electrons which constitute the current and that of their orbital 
motions which involve the magnetism ; in a complete and consistent theoiw these two 
parts must be kept separate ; cf. foot-note, § 38 supra. 
On the Nature of Paramagnetism and Diamagnetism, as indicated, by their 
Temperature Relations. 
71. As a result of an extensive investigation of the magnetic properties of matter, 
the law has recently been formulated by Curie'" that in all feebly paramagnetic sub- 
P. Curie, ‘ Annales de Cliimie,’ 1895. 
