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. 1899 Excerpt: ...the region inside, vt the normal to S drawn into 3i, and v2 the normal drawn into @a; then, if V be the potential due to M, by Art. 70, there is a function j such that j = V at S, and is of the order--at a point P at infinity, where R is the dis tance of P from the origin, and that v2# = 0 throughout @t, and a function ...
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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. 1899 Excerpt: ...the region inside, vt the normal to S drawn into 3i, and v2 the normal drawn into @a; then, if V be the potential due to M, by Art. 70, there is a function j such that j = V at S, and is of the order--at a point P at infinity, where R is the dis tance of P from the origin, and that v2# = 0 throughout @t, and a function p such that = V at S, and v2 = 0 throughout @-. Again, if P be a point in the region @lf and r denote the distance of any point from P, by Art. 59, we have Also, by Art. 58, we have )r dv2 ) dvr) Adding this equation.to the former, and remembering that at the surface 8 we have ip = j = V, and that d d--=---, we get avi av% Hence at any point in @i the function 0 expresses the potential of a surface distribution whose density is 1_ (d$ dP iir dvi dv2 In like manner ip is the potential in @a of the same surface distribution. Also, if M be situated in @2 we have j = V throughout @i, and if M be situated in @, we have p = V throughout @2. Hence the surface distribution is determined which produces the same potential on one side of S &s a, given mass distribution existing on the other side. When the mass M is inside 8 it is equal to the total mass of the surface distribution. It is obvious that we can show in a similar manner, that if space be divided by a boundary or set of boundaries into two regions, it is always possible to distribute mass over the boundary so as to produce in one region the same potential as that produced by a given distribution of mass existing in the other region. The density of the required surface distribution is determined in the same manner as before. Another theorem, in some respects more general than those given above, is the following: --It is always possible to distribute mass over a surface 8 closed or open..
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Add this copy of An Introduction to the Mathematical Theory of to cart. $53.36, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2011 by Nabu Press.
