136 NEWTON S PRINCIPIA. 



being opposite they destroy one another. In like manner, 

 any particle of the spherical surface on one side of P, 

 acting in the direction of a P, is equal as well as opposite 

 to the attraction of another particle acting on the opposite 

 side, and so the whole action of every one particle is de 

 stroyed by the opposite action of some other particle ; and 

 P is not at all attracted by any part of the spherical sur 

 face; or the sum of all the attractions upon P is equal 

 to nothing. So of a hollow sphere ; for every such sphere 

 may be considered as composed of innumerable concentric 

 spherical surfaces, to each of which the foregoing reasoning 

 applies ; and consequently to their sum. 



We may here stop to observe upon a remarkable in 

 ference which may be drawn from this theorem. Sup 

 pose that in the centre of any planet, as of the earth, 

 there is a large vacant spherical space, or that the globe is 

 a hollow sphere ; if any particle or mass of matter is at any 

 moment of time in any point of this hollow sphere, it 

 must, as far as the globe is concerned, remain for ever 

 at rest there, and suffer no attraction from the globe itself. 

 Then the force of any other heavenly body, as the 

 moon, will attract it, and so will the force of the sun. 

 Suppose these two bodies in opposition, it will be drawn 

 to the side of the sun with a force equal to the dif 

 ference of their attractions, and this force will vary with 

 the relative position (configuration) of the three bodies ; but 

 from the greater attraction of the sun, the particle, or 

 body, will always be on the side of the hollow globe next 

 to the sun. Now the earth s attraction will exert no in 

 fluence over the internal body, even when in contact with 

 the internal surface of the hollow sphere ; for the theorem 

 which we have just demonstrated is quite general, and 

 applies to particles wherever situated within the sphere. 

 Therefore, although the earth moves round its axis, 



