177 



It might seem at first sight that if mountain attraction were eo 

 influential as is here supposed, it would disturb the geodetic opera- 

 tions, since in observing the altitude or depression of one station as 

 seen from another, the error in the plumb-line must come into cal- 

 culation. The author shows, however, by mathematical calculation, 

 that the effect of mountain attraction on the geodetic operations is 

 perfectly insensible, so that it is clearly the astronomical operation 

 of finding the difference of latitude that requires the correction. 

 This is further apparent from the results obtained by Colonel Everest 

 on attempting to determine the azimuths of the arc at seven stations 

 astronomically. 



To show the importance of considering mountain attraction in the 

 delicate problem of the figure of the earth, the author investigates the 

 effect of a small error in the difference of latitude of the extremities 

 of an arc on the deduced value of the earth's ellipticity. As two 

 unknown quantities occur in the determination of the spheroid of 

 revolution which most nearly agrees with the earth, namely a the 

 equatorial radius and e the ellipticity, two arcs are required in order 

 to determine them. The author selects the Russian arc, measured 

 near North Cape, as the most advantageous with which to combine the 

 northern portion of the Indian arc, and shows that an error of 5"'23G in 

 defect in the amplitude of the latter would diminish the value of the 

 ellipticity resulting from the two by about the -^th part of the 

 whole. If the effect of mountain attraction be as great as the author 

 calculates it to be, (15' r- 885 in the northern portion of the Indian 



arc,) the ellipticity would be diminished by - e, and even by as much 



8 



as e if the whole Indian arc from Kaliana to Damargida were 

 6 



employed. 



The author then proceeds, first to develope his method of calcula- 

 tion, and then to reduce his formula to numbers, according to the 

 best data which he was able to collect. 



An expression is first investigated for the horizontal attraction of 

 a prism of the earth's crust standing on a given small base, having a 

 small height, and situated at a given angular distance (measured 

 from the centre of the earth) from the station, A, at which the at- 

 traction is sought. In the cases to which this expression is employed 



