Mathematical investigations concerning the laws of the equilibrium of fluids analagous to the electric fluid / by George Green.
- George Green
- Date:
- 1833
Licence: Public Domain Mark
Credit: Mathematical investigations concerning the laws of the equilibrium of fluids analagous to the electric fluid / by George Green. Source: Wellcome Collection.
25/64 page 25
![By multiplying the last expression by 1 , and taking the sum of all the resulting values which arise when we make successively t' = 0, 1, 2, 3, 4, 5, 6, &:c. in infinitum, we shall obtain the value of the term contained in the expression + + F<^> + F(=^) + F(^> + &c. Hence, 3.5 4-1 ..X „ n- 1.« + 1 w + 2^ + 2^' — 3 (e)2 1.2 i ^“3.5 2/ + 2^' + l n-2.n n + 2t' — 4! 2.4 2t' \r the finite integral extending from t' = 0 to t'= cc. But by the known properties of functions of this kind, we have by substituting for F^'^ its value 1 —« f.]d^ (<■) (i - (*•). F® 3.5.7 2z + l ,, + l n + 2i + 2t'-3 = 1.2.8 3-. 5-:: 2^+^+r~ n — 2.n ra + 2^' —4 2.4 2if' 1.2.3 i —l.w + l w + 2e + 2/'—3 1.3.5 2i-l^ 3 . 5 2i + 2t' + 2 n — 2.n ;^ + 2^' —4 f = 2 2.4 2t' since by what Laplace has shown (Mec. Cel. Liv. iii. No. 17.) 2 /I. 2.3 i 2i + l Vl.3.5 2e-l/ ’ D VoL. V. Part I.](https://iiif.wellcomecollection.org/image/b28754207_0027.jp2/full/800%2C/0/default.jpg)
