Mr. Sharpe on the Figure of the Earth. 



443 



ones at Madras and Bellary, with the several altitudes deduced 

 from them ; but I have not been able to accomplish my in- 

 tention. 



Colonel Lambton's base line near Gooty is nearly 1200 feet 

 above the sea, and he assumed this as the mean altitude of 

 the interval between that station and Bellary ; an inference to 

 which he was perhaps led by the plain, open appearance of 

 the intermediate country. The barometer, however, stood on 

 the 2d June at 



Guddicul, 28600 m. 99° Goontacul, 28528 m. 91° 



29920 92£ 29910 87 



Feet. 



making Sntc u ;i:s}-^ b - th -- 



Madras, July 1823. W. CuLLEN. 



Although the section referred to above, is not given in the Madras 

 Transactions, we have thought it right not to suppress the Postscript, in 

 which some of the altitudes in question are stated.— Edit. 



LXX1II. On the Figure of the Earth. By S. Sharpe, Esq. 



F.G.S.* 



TVTOST of the investigations into the figure of the earth 

 -*•*-*• have been on the supposition that its section through the 

 poles were an ellipse, which, however, several mathematicians 

 have shown not to be exactly true. 



Thomas Simpson has shown, that in an elliptical globe, with 

 a given axis major, and a given period of rotation on its axis 

 minor, its ellipticity is given also. 



There is water enough on our earth to show that its shape 

 is that which it would take if liquid, therefore the plumb-line 

 is every where perpendicular to the tangent. 



Let PT be perpendicular to the tangent at P on the ellips e 

 jENQS : then if the earth were 

 at rest, the plumb-line would 

 point nearer to the centre, as 

 PL ; and the angle LPT is the 

 measure of the centrifugal force 

 caused by the rotation on its 

 polar axis NS. Hence the con- 

 nection between the ellipticity 

 and velocity of rotation 



Mi 



I have gone over Thomas Simpson's work, and find : 



1st, If the pendulum at the equator be 39*014 inches, a 



* Communicated bv the Author. 

 3L2* 



body 



