649 



stations at the extremities of the arc, he demonstrates that no change 

 in the curvature of the arc, within reasonable and indeed within 

 wide limits, can have any appreciable effect on the calculated am- 

 plitude. The author's conclusions from the whole investigation re- 

 garding the Indian Arc are thus summed up : 



(1) Colonel Everest discovered that the astronomical amplitudes of 

 the two portions of the Indian Arc between Kaliana and Kalianpur, 

 and between Kalianpur and Damargida, are, the first less by 5" -24, 

 and the second greater by 3"'79, than the geodetic amplitude calcu- 

 lated with the mean semi-axes and ellipticity of the earth. 



(2) The geodetic amplitudes of these two portions of the arc, 

 calculated from the measured lengths and with the mean axes, will 

 be sensibly exact, even should the curvature of the arc differ from 

 that of the mean meridian within reasonable but wide limits a thing 

 which geology teaches us to be very likely the case. 



(3) Hence the geodetic measurements of the survey being without 

 sensible error, as is known by the tests applied, the discrepancy in 

 (1) can only arise from local attraction affecting the vertical line, and 

 so changing the astronomical amplitudes. 



(4) Two great visible causes of disturbance of the vertical by at- 

 traction are, the Mountain Mass on the north of India, and the Ocean 

 on the south. The influence of both of these is felt all over India ; 

 the first producing a northerly deflection, varying from 2 7"' 9 8 at 

 Kaliana to a sensible angle (probably about 3", but this the author 

 has not calculated) at Cape Comorin ; the second producing also a 

 northerly deflection, varying from about 19"' 71 at Cape Comorin 

 to 6"* 18 at Kaliana. 



(5) The combined effect of these two visible causes is to make the 

 astronomical amplitude of the upper arc 13"'l 1 too small, and of the 

 lower 3" f 82 also too small. They are therefore insufficient to ac- 

 count for the discrepancies pointed out by Colonel Everest. Some 

 other cause must exist tending to increase the upper astronomical am- 

 tude by 13"'ll 5"'24=7"'87, and also to increase the lower am- 

 plitude by 3"-82 + 3"-79=7"'61. 



(6) It has been demonstrated that a slight but wide-spread varia- 

 tion in the density of the crust, from that deduced from the fluid- 

 theory, either in excess or defect, such as there is no difficulty in 

 conceiving to exist, is sufficient to account for deflections such as 



