198 



ellipticity y^g. These two values are on opposite sides of the mean 

 elliptieity for the whole earth, from which they differ by about f ths 

 and -ths of the mean. 



In these calculations the ellipses are found which exactly accord 

 with the measured lengths and the corrected latitudes in the one case, 

 and in the other the latitudes uncorrected for deflection. A more 

 correct method has been followed by Captain A. Clarke, R.E., in the 

 volume of the Ordnance Survey just published by Lieut. Colonel 

 James, R.E. Captain Clarke takes the latitudes of the three stations 

 mentioned above, as corrected for mountain attraction by Archdeacon 

 Pratt, and supposing the corrected latitudes as well as the elements 

 of the mean ellipse subject to error, he determines, according to the 

 method of least squares, the ellipse which best corresponds with the 

 mean ellipse and with the three corrected latitudes. The resulting 

 ellipse depends of course upon the height attributed to the mean 

 ellipse, which is left arbitrary, to be assigned at the end of the cal- 

 culation. In this way Captain Clarke shows that it is possible to 

 obtain an ellipse which differs much less from the mean ellipse, and 

 yet which makes the differences between the three latitudes cal- 

 culated from the ellipse and the observed latitudes corrected for 

 deflection, very small. 



Since this calculation was made by Captain Clarke, the author 

 communicated to the Royal Society an approximate estimate of the 

 effect of the deficiency of matter in the ocean south of Hindostan, 

 on the plumb-line. On seeing Captain Clarke's result, he felt anxious 

 to ascertain what effect this new disturbing cause would have upon 

 it. The present paper contains a repetition of the calculations of 

 Captain Clarke, with the additional corrections to the latitudes due 

 to the defect of attraction of the ocean introduced into them. Capt. 

 Clarke's result, the author finds, is thereby improved, the ellipse 

 obtained coming out somewhat nearer to the mean ellipse, while the 

 errors in the latitudes, which already were very small, are still further 

 reduced. The following are the values of the semi-axes a b (infect) 

 and of the reciprocal of the ellipticity corresponding, I. to the mean 

 ellipse, as determined by Captain Clarke ; II. to the first of the two 

 ellipses (corresponding to two different degrees of importance assigned 

 to the mean ellipse) obtained by Captain Clarke by combining the mean 

 ellipse with the Indian Arc ; III. to the ellipse II. recalculated by 



