161 



NOTE. 



The argument in page 136. is succinctly and po 

 pularly stated respecting the supposition of a hollow in 

 the centre of the Earth, and several steps are omitted. 

 One of these may be here mentioned in case it should 

 appear to have been overlooked. Suppose a mass m de 

 tached 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 acting on the earth, the one being 



as pp } and the other as ^- y (D being the dis 

 tance 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 coine in con 

 tact 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. 



