Elementary principles of the theories of electricity, heat, and molecular actions / Designed for the use of students in the University. By the Rev. R. Murphy... Part I. On electricity.

Murphy, Robert, 1806-1843.

Date:: 1833

Credit: Elementary principles of the theories of electricity, heat, and molecular actions / Designed for the use of students in the University. By the Rev. R. Murphy... Part I. On electricity. Source: Wellcome Collection.

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$we get as before (since k is here constant), Q = kf,Jc («' cos0 + b'cos0' + c cos 0) -JLL- - k hence A . Q = 4 7r k F(t), F(t) being the value of F' (t) when x\ y', z, are changed into x, y, z. 4 7rk d Also from the equations f = —-— a —— (F + Q), 3 d? &c. rfg dh kirk we get - ■{ ~ + 7 ay a# F (0 - A . Q — ~C-. F (t). Q V 7 But from the values of a b and c, we have da db dc r (dfY dg\ dh{ —r —j = ]t y (^ ~ T) {—I- —I- — i •> dx dy dz \dx dy dz J 8 7T k hence, F (t) =- fT F (t) . \[s' (t - t), from r = 0 to r = £, which it is easily seen can only be satisfied by F (t) - 0; da 'db dc we have thus,-b --b — = 0. dx dy dz , . . da Again, it we put —— df dy db dx = r, (o, we get in like manner dg 47rk dx 3 and therefore, \fs (t) = —(tF1{t) . \// (t — t),$