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
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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