as obtained from Geodetic Data. 



11 



must be defective, as the omission of local attraction may intro- 

 duce an error of serious importance. In a communication to the 

 Royal Society, which was printed in the ' Proceedings/ No. 64, 

 I proposed a means of rectifying this. But in so doing I, 

 knowingly, left out of account another source of error, because I 

 did not then know how to take account of both, and that which 

 I omitted in my method appeared to be of much inferior im- 

 portance to that overlooked by Bessel. The method I am now 

 going to give and work out into formulae, as it seems to me, 

 solves the problem entirely ; that is, it leads to formulae for the 

 axes, taking into account the effect of local attraction, and over- 

 looks no source of error. 



To obtain formula to calculate the axes of the ellipse which best 

 represents a given arc. 



3. In the accompanying diagram, let A B C D be the level- 

 curve or arc, A, B, C, D being the stations at which the latitudes 

 are observed, the lengths of the intermediate curves being mea- 



sured by the Trigonometrical Survey. Suppose otS is an ellipse 

 of small ellipticity and variable axes, not differing much from 

 the arc AD in form and position. Let a and b be the semiaxes 

 of this ellipse, and e its ellipticity. Since the mean radius of 

 the earth does not differ much from 20890000 feet, and the 



