The Variation in Attraction Due to the Attracting Bodier. 197 



THE VARIATION IN ATTRACTION DUE TO THE 

 FIGURE 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 law 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, "witliout form and void." 



In finding the attraction of an ellipsoid on any outside 

 particle or body I avoid the use of the expedient of 



