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.
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![Now by adding the repulsion due to the inner sphere which is given by the formula (16), we obtain, (since it is evidently indifferent what variable enters into a definite integral, provided eacli of its limits re- main unchanged) iTT-v/TTP'r/''’';- ] +n 2 —w J'\x'(lx{\-x')^ (l- -x-\ — a «■ - / — jjx’‘(lx{\-x-) ^ • (l 4 TT -y/TT . P rt' ” r )l^x'‘dx{\ -X-) ^ . r for the value of the total repulsion upon a' particle of positive fluid situate within the sphere A and exterior to P. We thus see tliat when P' is positive the particle j) is always impelled by a force which is equal to zero at P’s surface, and which continually increases as p recedes farther from it. Hence, if any particle of positive fluid is separated ever so little from P’s surface, it has no tendency to return there, but on the contrary, it is continually impelled therefrom by a regularly increasing force; and consequently, as was before observed, the equilibrium can not be permanent until all the positive fluid has been gradually abstracted from P and carried to the surface of A, where it is retained by the non-conducting medium with which the s])here A is conceived to be surrounded. I.,et now q represent the total quantity of fluid in the inner sphere, then the repidsion exerted on p by this will evidently be qr~, when r is supposed infinite. Making therefore r infinite in the expression (1.5), and equating the value thus obtained to the one just given, there arises <7 = - 4 TT -v/TT. P d' b ^ fj'dx.x (I - a--) . When the equilibrium has become permanent, q is equal to the total quantity of that kind of fluid, which we choose to consider negative, originally introduced into the sphere A; and if now </, represent the](https://iiif.wellcomecollection.org/image/b28754207_0046.jp2/full/800%2C/0/default.jpg)
