2l6 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. 



of terms in the equation of the densities, ^—^ = «, or ^^ = — a. 



^ ' p im ' p 115 *> 



by putting 288 for m, as has been long known. It is easily seen from this 



equation, that when a is determined, will be so too, which was the thing 



proposed to be proved. 



23. But from this equation there follows a very singular proposition, and 

 which, in some sort, is contrary to the sentiments of Sir Isaac Newton, page 

 430 of the 3d edition of his Principles. And this is, that if by observation it 

 shall be discovered, that the earth is flatter than according to the spheroid of 

 Sir Isaac, that is, if the diameter of the equator exceeds the axis by more than 

 the 230th part, the gravity will increase less from the equator towards the pole, 

 than according to the table which he has given for his spheroid, prop. 20 of the 

 3d book. And on the contrary, if the spheroid is not so flat, the gravity will 

 increase more from the equator towards the pole. 



24. It is thus that Sir Isaac Newton expresses himself about it, when he re- 

 lates the experiments made towards the south, concerning the diminution of 

 gravity, which experiments make it greater than his theory requires. He 

 affirms, that the earth is denser towards the centre than at the superficies, and 

 more depressed than his spheroid requires. But by the foregoing theory we 

 may easily perceive, that if the density of the earth diminishes from the centre 

 towards the superficies, the diminution of gravity from the pole towards the 

 equator will be greater than according to Sir Isaac's table; but at the same time 

 the earth will be not so much depressed as his spheroid requires, instead of be- 

 ing more so, as he affirms. Yet I would not by any means be understood to 

 decide against Sir Isaac's determination, because I cannot be assured of his 

 meaning, when he tells us, that the density of the earth diminishes from the 

 centre towards the circumference. He does not explain this, and perhaps in- 

 stead of the earth's being composed of parallel strata, its parts may be con- 

 ceived to be otherwise arranged and disposed, so as that Sir Isaac's proposition 

 shall be agreeable to the truth. 



25. As to Dr. Gregory, who has attempted to comment on this passage of 

 Sir Isaac, I think I have demonstrated, that he has committed a paralogism. 

 He says (Element. Astronom. lib. 3, § 8, prop. 52 schol.) that if the earth is 

 denser towards the centre, or if, for example, it has a nucleus of greater weight 

 than the other parts, the diminution of gravity from the pole towards the 

 equator shall be greater than if the whole were of the same density; and in this 

 he is right. But he is in the wrong, I think, immediately to conclude from 

 thence, that the earth has a greater flatness. Whence can he conclude this ? 



