. The London, Edinburgh and Dublin philosophical magazine and journal of science. that the total energy, viz. the volume integral of ^———, due to the motion of a charge on any surface, is W=ijM>„+2T, where ^o is the value of the convection-potential at thesurface of the body, and T is the magnetic part of the energy,viz., the volume integral of/iH2/87r. of an Electrified Ellipsoid. 339 Now in fig. 4 let the ellipsoid PQ be determined by A, nndthe ellipsoid RS by h + dh. Let the angular coordinate of Eur. P and S be (/>, and let that of Q and R be (p +dcf>. Then thearea PQRS d(x,p)
. The London, Edinburgh and Dublin philosophical magazine and journal of science. that the total energy, viz. the volume integral of ^———, due to the motion of a charge on any surface, is W=ijM>„+2T, where ^o is the value of the convection-potential at thesurface of the body, and T is the magnetic part of the energy,viz., the volume integral of/iH2/87r. of an Electrified Ellipsoid. 339 Now in fig. 4 let the ellipsoid PQ be determined by A, nndthe ellipsoid RS by h + dh. Let the angular coordinate of Eur. P and S be (/>, and let that of Q and R be (p +dcf>. Then thearea PQRS d(x,p) „.,. / dxdp dx dp\ „ ,, 7i2—I2 cos2 6 7J , - T dk dd>. Va \//?-l2 Now if the area PQRS revolve about the axis Ox the volumeof the ring traced out is 2,. #?£ dh # = toW-no**)** dh #. r d(n,(p) a. Thus for the magnetic part of the energy we have ixqhi? CC A2 sin3 0 dh dJ J {h2-t2){h2-P cos2 ) Since \ goes from 0 to co A goes from a to co. The limitsof are 0 and nr. Now J0 A2-/2cos2c/> ~ ~~ P LC0S ~~Jhf g A-/cos</J0 Hence 1 f A2-/?, A + H = K2 aT^a^ MvVr, a2+/2, A+zr= 4F L7i 2TloS/7=7J • 340 Mr. G. F. C. Searle on the Steady Motion When h is large the quantity in [ j -*-<Jf+1) ft+ »-) vanishing when 7* = co . Thus, making use of ijlKv2—\ we have for the magneticenergy m q2u2 fa? + l2, a + l a -) Now by (17) we have at the surface of the ellipsoidMr _ 9a C dli q<% , a + l Hence the total electromagnetic energy of the ellipsoid is Here we mu
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