This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1879 Excerpt: ...one case stated in the question, viz. when the potential is a linear function of x, y, z. Let U be the potential at any outside point due to a solid ellipsoid of uniform density, then I + n s the potential at an out side point due to an ellipsoidal shell of the first degree, viz. a shell formed by the coexistence of ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1879 Excerpt: ...one case stated in the question, viz. when the potential is a linear function of x, y, z. Let U be the potential at any outside point due to a solid ellipsoid of uniform density, then I + n s the potential at an out side point due to an ellipsoidal shell of the first degree, viz. a shell formed by the coexistence of two solid ellipsoids, of equal uniform densities, one attracting and the other repelling, whose centres are infinitely near and on the line whose direction cosines are I, m, n. If we suppose the matter composing this shell to be an electrical distribution, then the potential at any outside point due to the outside field and to the supposed distribution is 7dU dU dU Ax + By + Cz + I-j-+ m + n--=-, ax ay az that is, Ax + By + C + lM(lx + rndy+nd z). (See Thomson and Tait's Natural Philosophy, 522.) Inside the shell the potential will be zero at every point, provided the following relations hold good, viz. A + lMtg-0, tf + f JfmJ = 0, where j is the value of jt when e has the value zero, viz. at the surface of the ellipsoid. If then I, m, n, M are thus determined, the supposed distribution is in reality the distribution induced on the ellipsoid by the outside field. By putting and transforming the integral for f, we have 2 fTM" d9 a--b = Jo J(l-Wg)' Whne k2= a? 17. A copper wire in the form of a complete circle is suspended so that it can turn without friction about a diameter which is perpendicular to the direction of the earth's magnetic force; it is set in rotation and then left free, determine its subsequent motion, neglecting the self-induction of the wire. The energy of the wire consists of two parts: 1. Its energy of motion Mk'6', where Mk' is the moment of inertia about the axis of rotation, and 6 is the ang...
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