ATTRACTION OP BODIES. 263 



enough to fill half the hollow space ; it will all be accumu- 

 lated on one side, and that side the one next the sun ; conse- 

 quently the axis of rotation will be changed and will not pass 

 through the centre, or even near it, and will constantly be alter- 

 ing its position. Hence we may be assured that there is no 

 such hollow in the globe filled with melted matter, or any hol- 

 low at all, inasmuch as there could no hollow exist without 

 such accumulations, in consequence of particles of the internal 

 spherical surface being constantly thrown off by the rotatory 

 motion of the earth.* 



Eg.15. 



If AHKB be a spherical section (or great circle), PEK 

 and P I L lines from the particle P, and infinitely near each 

 other, S D, S E perpendiculars from the centre, and I q per- 

 pendicular to the diameter ; then, by the similar triangles 

 PIE, Pp D, we find that the curve surface bounded by I H, 



* The argument is here succinctly and popularly stated respect- 

 ing the supposition of a hollow in the centre of the earth, and several 

 steps are omitted. One of these may be mentioned in case it should 

 appear to have been overlooked. Suppose a mass m detached from the 

 hollow sphere M, and impelled at the same time with that sphere by an 

 initial projectile force, then its tendency would be to describe an 

 elliptic orbit round the sun, the centre of forces, and if it were detached 

 from the earth it would describe an ellipse, and be a small planet. But 

 as the accelerating force acting upon it would be different from that 



S + M S + m 



acting on the earth, the one being as ~> an< i the other as = - 



(D being the distance and S the mass of the sun), it is manifest that, 

 sooner or later, its motion being slower than that of the hollow sphere, 

 if m be placed in the inside, it must come in contact with the interior 

 circumference of the sphere, and either librate, or, if fluid, coincide with 

 it, as assumed in the text. Where parts of the spherical shell come off by 

 the centrifugal force, of course no such step in the reasoning is wanted ; 

 nor is it necessary to add that neither those parts nor any other within 

 the hollow shell can have any rotatory motion. 



