204 The Great Indian Arc of Meridian, [No. 3, 



axis. The sole quantities, therefore, to be determined are the 

 semi-major axis, and the ellipticity or compression. In the Problem 

 of the Figure of the Earth, the ellipse is a convenient curve of 

 comparison for this further reason, that it was the exact form of 

 each meridian when the earth was fluid, or sufficiently fluid to 

 control the external figure. 



One of the results of my paper in the Philosophical Transactions 

 of 1855 is the comparison of the curvature of the great arc in 

 India, 800 miles long, lying between Kaliana (latitude 29° 30' 48") 

 and Damargida (latitude 18° 3' 15'') ; and I find that it coincides 

 most nearly with an ellipse of which the compression is l-426th ; 

 and not l-300th, the compression of the average meridian — that is, 

 if no cause can be discovered counteracting the attraction of the 

 Himalaya mountains. 



6. — Mr. Tennant's object, as announced in the heading of his 

 first paper,* is to test this result. But how does he test it ? He 

 there proceeds, not to examine my arc, and test it by some other 



* I am indebted to Mr. Tennant for having detected a numerical error in p. 98 

 of my paper. 



For a = — 0.00S9737— 0.0051426 u + 0.0016881 v. 



Read a = —00019203 + 0.0059576 u —0.0014564 v. This will change the 

 value of a (1 + a) in the next line but one. 



In the last page I have also detected an error. The formula for the height of 

 the middle point of a small elliptic arc above its chord is correct as there given. 

 But I should not have left it in terms of A, the amplitude, but of s, the length of 

 the arc ; as A is not the same, whereas * is, in the three cases to which the formula 

 is applied. This change will make the height above the chord 



= — j 1 + e ( - h —cos 2 ^ J I — 20 (1 + 1.512 e) miles, the same as 



before excepting the sign of e. 



The result of this is, that my arc is flatter by 157 feet in the sagitta and the 

 arc when mountaiu attraction is neglected is more curved by 281 feet, than the 

 mean curvature. 



These corrections have no effect upon the results of my paper. It is possible 

 that there may be other numerical errors, for when the paper was written I was 

 away from all means of employing a computer, as is usual in such cases, to 

 verify the long numerical calculations, not one-tenth of which appears in what is 

 printed. I feel convinced, however, that there is no material error : for I used 

 every precaution I could, and applied every test. The eirors mentioned above 



