26 PHILOSOPHICAL TRANSACTIONS. [aNNO 1735. 



metico-Geometricum, published at Leipzig in 1727, after the author's death, 

 yet imperfect, as it is owned in the book itself. 



Besides these, the French journals show that Charles Pascal invented one. 



M. Gersten took, the hint of his from that of Mr. de Leibnitz, which put 

 him on thinking how the inner structure might be contrived. The structure is 

 then described, and the mode of performing the arithmetical operations; but 

 the whole so intricate and operose, as incapable now of exciting any attention. 



Of the Figure of the Earth, and the Variation of Gravity on the Surface. By 

 Mr. James Stirling, F. R. S. N° 438, p. 98. 



The centrifugal force, arising from the diurnal rotation of the earth, depresses 

 it at the poles, and renders it protuberant at the equator; as has been lately 

 advanced by Sir Isaac Newton, and long ago by Polybius, according to Strabo, 

 in the second book of his Geography, But though it be of an oblate spheroid- 

 ical figure, yet the kind of that spheroid is not yet discovered ; and therefore 

 we may suppose it to be the common spheroid generated by the rotation of an 

 ellipsis about its less axis; though by computation it appears, that it is only 

 nearly, and not accurately such. Let us also suppose the density to be every 

 where the same, from the centre to the surface, and the mutual gravitation of 

 the particles towards each other to decrease in the duplicate ratio of their dis- 

 tances; and then the following rules will follow from the nature of the 

 spheroid. 



1. Let adbe, fig. 5, pi. 2, be the meridian of an oblate spheroid, de the 

 axis, AB the diameter of the equator, and c the centre. Take any point on 

 the surface, as f, from which draw fc to the centre, fg, perpendicular to the 

 surface at f, meeting cb in g, and fh cutting the line cg, so that ch may be 

 to gh as 3 to 2. Then will a body at f gravitate in the direction fh ; and the 

 mean force of gravity on the surface, will be to the excess of the gravity at the 

 pole above that at p, as the mean diameter multiplied into the square of the 

 radius, is to -J- of the difference of the longest and shortest diameters multiplied 

 into the square of the co-sine of latitude at p. 



2. The decrement of gravity from the pole to the equator is proportional to 

 the square of the co-sine of latitude; or, which comes to the same, the incre- 

 ment of gravity from the equator to the pole, is proportional to the sqaure of the 

 sine of latitude. Hitherto we have considered the variation of gravity which 

 arises from the spheroidical figure, while it does not turn round its axis ; but if it 

 does, the direction of gravity will be in the line fg, perpendicular to the sur- 

 face; and its variation now arising from both the figure and centrifugal force, 

 will be 5 times greater than what arises from the figure alone; as will appear 



