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Transactions of the Wisconsin Academy of Sciences, Arts and Letters
volume VI (1881-1883)

Blackstone, D. P.
The variation in attraction due to the figure of the attracting bodies,   pp. 197-254


Page 197


The Variation in Attraction Due to the Attracting Bodies. 197
THE VARIATION IN ATTRACTION DUE TO THE
      FIGTURE OF THE ATTRACTING BODIES.
          By D. P. BLACKSTONE, A. M., C. E., Berlin, Wis.
                      INTRODUCTION.
  1. This paper is a part of the investigations that I have
nearly completed on the subject, The Variation in Figure
and in Attraction of a once Fluid Body, due to Rotation,
Law of Density, and Contraction. The portion of the in-
vestigations on that subject pertaining to attraction, herein
given, is abbreviated by the omission of some of the mathe-
matical demonstrations, and some evident deductions. The
results attained by my method give numerical exactness to
any power of the eccentricity of the ellipsoid.
  This paper develops by geometrical methods the law of
attraction for spheres, each of homogeneous mass, or each
or either composed of fluid masses of heterogeneous dens-
ities. It also develops by the same methods the variation in
attraction due to ellipsoidal figure, where one of the attract-
ing bodies is an ellipsoid of homogeneous mass, the stand-
ard for measuring the variation being the attraction of the
mass of the ellipsoid condensed at its own center.
A part of my investigation on attraction, not herein
given, develops the variation in attraction due to ellipsoidal
figure where the ellipsoid is composed of fluid masses of
heterogeneous densities. In this paper I take it as granted
that a fluid mass under the la. of the mutual attraction of
its own component particles, takes on the form of an oblate
ellipsoid. In my investigation pertaining to fluid equilibri-
um I demonstrate under what conditions of rotation the
fluid mass assumes the form of an oblate ellipsoid, and also
under what conditions of rotation the fluid mass has not de-
fined mathematical figure, but would go back if expanded
by heat, to nebula, "without form and void."
In finding the attraction of an ellipsoid on any outside
particle or body I avoid the use of the expedient of


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