652 PHILOSOPHICAL TRANSACTIONS. [aNNO 1742-3. 



and that the forces with which equal particles at the surface tend towards the 

 spheroid, will be in the same proportion as perpendiculars to its surface, termi- 

 nated either by the plane of the equator, or by the axis. Because the centri- 

 fugal force with which any particle of the spheroid endeavours to recede from 

 its axis, in consequence of the diurnal rotation, is as the distance from the 

 axis, it appears that if the earth, or any other planet, was fluid, and of a uni- 

 form density, the figure which it would assume would be accurately that of an 

 oblate spheroid generated by an ellipsis revolving about its 2d axis. 



Afterwards the gravity towards an oblate spheroid is accurately measured by 

 circular arcs, not only at the pole, but also at the equator, and in any inter- 

 mediate places ; and the gravity towards an oblong spheroid is measured by 

 logarithms. The gravity at any distance in the axis of the spheroid, or in the 

 plane of the equator produced, is likewise accurately determined by like mea- 

 sures, without any new computation or quadrature, by showing that when two 

 spheroids have the same centre and focus, and are of a uniform density, the 

 gravities towards them at the same point in the axis or plane of the equator pro- 

 duced, are as the quantities of matter in the solids. 



This theory is applied for determining the figure of the earth, by comparing 

 the force of gravity in any given latitude, derived from the length of a pendu- 

 lum that vibrates there in a second of time, with the centrifugal force at the 

 equator, deduced from the periodic time of the diurnal rotation, and the ampli- 

 tude of a degree of the meridian ; or by comparing the lengths of pendulums 

 that vibrate in equal times in given unequal latitudes; or by comparing different 

 degrees measured on the meridian. By the best observations it would seem, 

 that there is a greater increase of gravitation, and of the degrees of the meridian 

 from the equator towards the poles, than ought to arise from the supposition of 

 a uniform density. Therefore the author supposes the density to vary from the 

 surface towards the centre ; and, in several cases he has considered, he finds 

 that a greater density towards the centre would account for a greater increase of 

 gravitation towards the poles, but not for a greater increase of the degrees of 

 the meridian ; and that the hypothesis of a less density towards the centre 

 would account for the latter, but not for the former, supposing (after Sir Isaac 

 Newton) the columns of the fliuid to extend from the surface to the centre, and 

 there to sustain each other. On this account he determines the gravitation to- 

 wards the earth, when it is supposed to be hollow with a nucleus included, ac- 

 cording to the hypothesis advanced by Dr. Halley, with the difference of the 

 semidiameters that might arise from such a disposition of the internal parts. But 

 in this case, and when the density is supposed variable, the spheroidical figure 

 is only assumed as an hypothesis. He adds, that by imagining the density to 



