A Treatise on Electricity and Magnetism Volume 1 12+

📘 This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1892 edition. Excerpt: ...functions of the auxiliary angles, they will be periodic functions of the quantities a, /3, y. the periods of x and A3 are 4.F(k), and that of X2 is 2F¥). Particular Solutions. 150. If V is a linear function of a, /3, or y, the equation is satisfied. Hence we may deduce from the equation the distribution of electricity on any two confocal surfaces of the same family maintained at given potentials, and the potential at any point between them. The Hyperboldds of Two Sheets. When o is constant the corresponding surface is a hyperboloid of two sheets. Let us make the sign of a the same as that of x in the sheet under consideration. We shall thus be able to study one of these sheets at a time. Let at, a2 be the values of a corresponding to two single sheets, whether of different hyperboloids or of the same one, and let V, T£, be the potentials at which they are maintained. Then, if we make = a,-a2Tf + a(Kj al-Q2 the conditions will be satisfied at the two surfaces and throughout the space between them. If we make V constant and equal to in the space beyond the surface alt and constant and equal to in the space beyond the surface a2, we shall have obtained the complete solution of this particular case. (18) The resultant force at any point of either sheet is, ...