. The London, Edinburgh and Dublin philosophical magazine and journal of science. with those due to the direct actionof the charged sphere), we have „__ e d 1* ~~ 47r dx p = -i- A1 J~ 4=ir dy pj _ _ e d 147r dz p therefore d£_ _ ep d2 1dt~ kirdxd^pdg _ _ ep d2 1dt d% dy p dh_ e d2 1%dt~~ Airdtjdzp Effects produced by the Motion of Electrified Bodies. 231 hence 4f = *£-#_!, dt ~~ 4z7r dx2 pdg _ ep d2 1dt ~ (1) 47r dx dy pdh _ ep d2 1 dt 4tt dx dz p J Using Maxwells notation, let F, G, H be the componentsof the vector-potential at any point; then, byi Electricity andMagnetism/ § 616, F = fi
. The London, Edinburgh and Dublin philosophical magazine and journal of science. with those due to the direct actionof the charged sphere), we have „__ e d 1* ~~ 47r dx p = -i- A1 J~ 4=ir dy pj _ _ e d 147r dz p therefore d£_ _ ep d2 1dt~ kirdxd^pdg _ _ ep d2 1dt d% dy p dh_ e d2 1%dt~~ Airdtjdzp Effects produced by the Motion of Electrified Bodies. 231 hence 4f = *£-#_!, dt ~~ 4z7r dx2 pdg _ ep d2 1dt ~ (1) 47r dx dy pdh _ ep d2 1 dt 4tt dx dz p J Using Maxwells notation, let F, G, H be the componentsof the vector-potential at any point; then, byi Electricity andMagnetism/ § 616, F = fi^\y^dxdydz, G = H<)))-/dxdyck, H = /A JJ p 7 dx dy dz, where u, v, w are the components of the electric currentthrough the element dx dy dz, and p is the distance of thatelement from the point at which the values of F, G, H arerequired, /n is the coefficient of magnetic permeability. Inthe case under consideration, 7 -P substituting for -j- its value from equation (1), we get with similar expressions for G and H. Let us proceed to calculate the value of F at a point Let 0 be the centre of the sphere; then OQ = p, TQ = p/, S2 Mr. J. J. Thomson on the Electric and Magnetic dydz. (P 1 Y Now -= „ - = .,2, wliero Y2 is a surface harmonic of the secondax p pl order. And when p > R, 1 -1 + R0 + R2o + and when p < R, + TD2 Ql + B3 Q2 + • ?• 9 \ 1 1 P n , 9 PQ where Q1? Q2, {l>+ff} or, as it is more convenient to write it, _/^p/5R2_a2\ d2 15 V6 2/d^R Bj symmetry, the corresponding values of G and H are B = fiep(5B? a2\ d2 15 V 6 2 J da: As R These values, however, do not satisfy the condition d¥ c]G cm=Q dx dy dz If, howeve
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