The Mathematical Theory of Electricity And Magnetism volume 2
The Mathematical Theory of Electricity And Magnetism volume 2
Henry William Watson
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: du dv dw IT + T-+ -7- = . . Ax ay dz at every point. If n, v, w be replaced by their equivalents p+f, q+g, r + /i respectively, this equation of continuity becomes ^4.^4.^*4.^ ^4.^4.^^-0 da dy "*" dz "*" dt \dx "*" dy dz / ~ dp da dr de i. E. -~ + -~ + + -=- = 0, dx dy dz dt the interpretation and truth of which are obvious. If u, v, w vary discontinuously over a surface S, the values on opposite sides of that surface being u, #'; v, v' -, w, w' re- spectively, the condition of continuity req...uires that l(u u) + m(v v) + n(w w') = 0. In all regions throughout which u, v, w are finite we have the equations V 2 F= -4-Tm, V 2
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