I 



the Indian Meridian. 405 



tion of the plumb-line at stations between C and A, caused 

 by H, varies inversely as the distance from a certain pomt Q 

 about 260 miles north of A or Kaliana, and that at a distance 

 of 1000 miles it equals 7"'235. Mr. Tennant makes use of this 

 law to determine the effect the mountain-attraction has in alter- 

 ing the curve of level. He calculates it from the equator (sup- 

 posing that my law extends so far)j and shows that the curve 

 ascends continually higher and higher ; so that cb a being the 

 curve as affected by mountain-attraction, 0' (/ b' a' is the curve 

 which would mark the level if H did not exist, Mr. Tennant 

 makes cc'=327 feet. This is not to be depended upon, because 

 it is calculated on the assumption that my law applies between 

 the equator and C, which is not proved. The other results are 

 correct, — viz. that, if c^ebe di'awn parallel to c'b'a', db = 9S, 

 and ea = 271 feet. 



These measures enable me to show that cba and cde cannot 

 both be portions of ellipses of the kind described. For when 

 two concentric and coaxial ellipses of small ellipticity cut each 

 other in a point of which / is the latitude in either ellipse, the 

 distance between the ellipses at another point of which \ is the 

 latitude =i c(cos2/— cos2X), where c is the difference of the 

 minor axes. Hence if both the curves are ellipses, 



bd , , cos 36° 6' 30" - cos 48° 1 4' 22" _^ ^^ 



^"^^""''^ - cos 36° 6' 30"- cos 59° 1' 36" -^'^^' 



98 

 whereas this ratio = ^-y =0'36. 



It is clear that, if either be eUiptic, it miist be cde, which is 

 that obtained by eliminating the effect of H ; and the curve cba 

 cannot be elliptic, as assumed in the Great Survey. 



This shows the absolute necessity of calculating and allowing 

 for mountain-attraction. If after making this allowance the 

 curve does not become part of the mean elhpse, it shows that 

 there is some other cause of derangement which we have not de- 

 tected. 



7. There is another point I would mention as occurring to 

 me. We have been accustomed to think that, however much the 

 contour of the continents may vary and depart from the mean 

 form, the ocean must possess that figure. But I infer from the 

 following approximate calculation that this is not certainly the 

 case. 



I have shown that the Himalayan attraction may fairly be 

 considered to vary inversely as the distance from Q for all sta- 

 tions between A and C. Ueyond C the law has not been proved. 

 In fact it is clear that, from that point southwards, the attrac- 

 tion of the mass will be better represented by the inverse**/ ware 



