The Variation in Attraction Due to the Attracting Bodies, 201 



5. A sphere made up of laminae varying in density from lamina to 

 lamina is the same as a sphere composed of shells having densities corre- 

 sponding to the laminae. The sphere, then, made up of laminae attracts 

 an outside particle in conformity with the law for spherical shells or a 

 homogeneous sphere. 



6. When attracting sphere is condensed to a particle, the investigation 

 of Art. 3 applies to the case where atrracted particle P becomes a sphere. 

 Two spheres, therefore, attract each other with a force directly as product 

 of masses and inversely as square of distance from center to center. 



7. To find the attraction of a sphere on a particle placed within it. 



Diagram 2. 



Diagram 2 shows particle P within the sphere. It is evident from in- 

 vestigation of Art. 3 that that poi'tion of the sphere outside of the radius 

 distance C P attracts particle P equally in opposite directions. The only 

 uucounterbalanced attraction, then, on particle P is the attraction of that 

 portion of the sphere inside of radius distance C P. Homogeneous spheres 

 of same density vary in masses as cubes of radii. The attraction on par- 

 ticles inside of a homogeneous sphere vary, then, as their distances from 

 the center of the sphere. 



8. When the sphere is fluid and particle P becomes a small solid of less 

 density than the sphere, then body P placed at the surface of the sphere 

 floats, and when body P is more dense than the sphere at the surface it 

 sinks. Its place of equihbrium is at the center of the sphere, in case all 

 the laminae of the sphere are less dense than the body P, otherwise in a 

 lamina having the same density as body P. 



It is evident that the law of equilibrium requires a fluid mass acted on 

 only by the force of the mutual attraction of component particles to as- 

 sume a spherical figure, and in case the mass is composed of fluids of 

 varying densities the fluids must take positions in spherical laminae in 

 order of densities, with tlie most dense at the centei*. 



