On the attractions of homogeneous ellipsoids / [Sir James Ivory].

  • Ivory, James, Sir, 1765-1842.
Date:
1809
Catalogue details

Licence: Public Domain Mark

Credit: On the attractions of homogeneous ellipsoids / [Sir James Ivory]. Source: Wellcome Collection.

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    2. Let a, b, c, be three co-ordinates, that determine the po¬ sition of a point attracted by a solid: and let dM denote a molecule, or element of the mass of the solid, whose position is fixed by the co-ordinates a*, y, z, respectively parallel to a, b, c: then, supposing the invariable density to be denoted by unity, if we put/= | {a — x)' + (b ~ yY + (r — the distance of the molecule from the attracted point, the di¬ rect attraction of the molecule on the point will be = This force of attraction is next to be decomposed into other forces, having fixed directions independent on the position of the attracting molecule; and the directions most naturally sug¬ gested for this purpose, are the three axes respectively paral¬ lel to the co-ordinates. When the direct attraction is thus decomposed, the resulting forces, acting parallel to the axes, and directed to the planes from which the co-ordinates are reckoned, will be respectively, Para^e^ t0 axis of x, dM{jfy), parallel to the axis of y, parallel to the axis of z. Let A denote the accumulated amount of all the attractions, parallel to the axis of x; and, in like manner, let B and C denote the same things for the attractions parallel to the axes of y and %: then, by restoring the value of/, and writing dx . dy . dz for its equivalent dM, there will be obtained.