512 Mr. milner on the 
earth’s equator is impelled at the greateft diftance from 
the axis T, is to the fpace which would be defcribed 
in the fame time by any particle at liberty, the magnitude 
of which is reprefented by p, as p x kt x the radius of the 
equator to the fum of all the particles of the earth mul- 
tiplied into the fquares of their refpedtive diffcances from 
the faid axis. 
To compute this fum in the eafieft way, and by an 
approximation, which is quite fufficient when the polar 
and equatorial diameters differ little from one another; 
let dpe (fig. 3.) be a fphere whofe radius is unity, divided 
into an infinite number of thin cylindrical furfaces, 
whofe bafes are the circles naqj it is obvious, that all 
the particles in any one of thefe furfaces are at the fame 
diftance cx-x from the axis of motion perpendicular to 
the plane of the circle nac^. Call Ap,_y, and a, the area 
of the circle dpe and the fluent of ^.xxKxy, or of -4A xyy, 
becaufe xx — —yy gives the fum of all the particles in the 
fphere multiplied into the fquares of the refpedtive dif- 
tances from the axis. This fluent corrected is equal to 
— , and muft now be diminifhed in the ratio of 1 to 
*5 
1 — 2/), if we fuppofe the earth to be an oblate fpheroid 
whofe equatorial diameter is to the polar as 1 to 1 -p; 
4 and, 
