The Variation in Attraction Due to the Attracting Bodies. 199 



INVESTIGATION. 

 I. 



SPHERICAL ATTEACTION. 



It is proved under Heading I. by demonstration and deduction: 

 First. — That two homogeneous spheres, or two spheres, each made up in 

 lamince varying in densities from lamina to lamina, attract each 

 other directly as product of masses, and inversely as square of 

 distance from center to center. 



Second. — That a mass composed of fluids under the laio of the mutual 

 attraction of component particles, arranges itself, in order of 

 the densities of the fluids, in a sphere made up in lamince ivith 

 the most dense at the center. 



3. To find the resultant attraction of an assemblage of particles consti- 

 tuting a homogenous sphere on an outside particle. 



Diagram 1. 



In Diagram 1 let C be the center of the sphere, having radius C A, and 

 P the attracted particle. Also let C B P be a circle described on C P 

 as diameter, From P draw any two lines, P g and P e cutting the sphere; 

 also cutting the circumference C B P in points a and b, making the angle 

 g P e infinitesimal. On the radius C A perpendicular to P C, take C 1 

 equal to chord C a, and C n equal to C b. Through 1 and n draw chords 

 h k and o p, parallel to C P. Then chord h k equals chord g d, and o p 

 equals e c. Per law of ultimate ratio when the angle e P g beconies infiii- 



