66 PHILOSOPHICAL TKANSACTIONS. [aNNO 1725. 



if it was once fluid, to have been an oblong spheroid at first, as a sphere ; and 

 that, in such a case, the centrifugal force of the several parts of the earth, 

 arising from its revolution about its axis, which might convert a sphere into an 

 oblate spheroid, would only change an oblong spheroid into one less oblong." 

 But if the earth was at first a fluid, supposed homogeneous, and of any given 

 form, and left to those laws which we find to obtain at present, it must put on 

 a spherical figure; for the same reason that drops of mercury, of water, and 

 other fluids, put on such a figure. And to suppose any change made in that 

 figure from the pressure of an external fluid, filling up all space, is contrary to 

 what has been demonstrated by Sir Isaac Newton, in his Principia, lib. 2, prop. 

 19, where he shows, that if any portion of a fluid be compressed by the same 

 or any other homogeneous fluid, that portion will not have its figure altered by 

 that pressure. 



Now, without considering the unreasonableness of the supposition, let us 

 imagine the earth to have been an oblong spheroid at first, and then to have a 

 diurnal revolution given to it, which should by degrees shorten its axis, to bring 

 it to what Messrs. Cassini and Mairan suppose it at present to be. If in such 

 a case the earth be supposed fluid enough to change its figure by the revolu- 

 tion about its axis, why should it stop when the equatorial diameter comes to 

 want just -J^ part of the length of the axis? since two powers act upon it to 

 shorten its axis, viz. gravity, and the centrifugal force; the first of which has 

 already been shown capable to reduce it to a sphere, and the centrifugal force 

 is acknowledged by M. Mairan to be, as Sir Isaac Newton has proved it, at 

 the equator equal to -^-iir F^rt of the gravity there. Certainly the alteration of 

 figure would not have stopped before the earth came to be a sphere; nay, and 

 it must have risen at the equator, and how much, has been already shown in 

 the former paper. 



Again, if we suppose the earth of an heterogeneous fluid, before the diurnal 

 revolution, the heaviest parts would go towards the centre, and the lighter 

 towards the surface ; and that way the terraqueous globe would also become a 

 sphere. Then if, when the central parts are fixed, and the superficial strata 

 are still fluid, the earth receives a diurnal motion; it will rise at the equatorial 

 parts, and that to a greater height than what has been shown in the former 

 paper, where the earth is supposed of uniform matter. And that something 

 like this must be the case, appears from what Sir Isaac Newton has said on this 

 subject. For after having shown, from supposing the earth of uniform matter, 

 that the centrifugal force of all its parts would bring it to be ]7i English miles 

 higher at tlie equator than at the poles, and after having given a table of the 

 proportionable decrease of the length of the degrees of a meridian of the earth, 



