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



On the present position of the question of Himalayan Mountain- 

 Attraction, as affecting the Great Trigonometrical Survey. 



10. I will conclude this letter with some remarks on this subject. 

 The average form of the earth has been already determined with 

 so much precision, that the Great Trigonometrical Survey cannot be 

 expected to improve it. The only new information it can commu- 

 nicate on this subject is, the extent to which the different parts of 

 the Indian continent depart from this average spheroid. This is a 

 matter of no peculiar interest in itself. Unless as a record for 

 comparison in future ages it might be found of use; just as, at 

 present, it would be a matter of interest to know the exact changes 

 of level the surface has gone through in ages past, as these might 

 serve to verify and to fix the chronology of those elevations and 

 sub-mergings of extensive portions of the surface, the evidences of 

 which geologists see in the fossil remains. This, however, is labour- 

 ing for generations who may never exist. 



The real importance of knowing the exact form of Indian arcs is 

 seen in the effect which an erroneous determination of the curv- 

 ature may have upon that accuracy in the Mapping of the Country 

 which the Great Survey is supposed to ensure. 



11. In calculating this curvature, it is absolutely necessary to 

 determine and allow for the effect of mountain-attraction upon the 

 plumb-line in all places where the latitude is observed astronomi- 

 cally. Without this, the curvature cannot be ascertained. I pro- 

 pose now to show this. 



If the determinations in the Great Trigonometrical Survey are 

 correct, they must satisfy this test, that the computed amplitude 

 of every arc must be precisely equal to the observed amplitude. 

 Colonel Everest's work published in 1847 shows that this test is 

 not satisfied, for the great arc, Kaliaua (29° 30' 48") to Kalian- 

 pur (24° 7' ll' 7 ). His calculations show a discrepancy of 5 /; .236 

 in the upper portion. In this comparison there are two sources 

 of error which it is necessary to examine — one, in the com- 

 putation of the amplitude ; the other, in the astronomical observa- 

 tion of the amplitude. Eor computing the amplitude of an elliptic 

 arc, it is necessary to know (1) the length of the arc, (2) the lati- 



