Royal Society. 231 



jegion beyond them, upon the Plumb-line in India." By the Vene- 

 rable John Henry Pratt, M.A., Archdeacon of Calcutta. 



The author commences by observing that it is now well known 

 that the attraction of the Himalaya Mountains, and of the elevated 

 region beyond them, has a sensible influence on the plumb-line in 

 North India. This circumstance was brought to light during the 

 progress of the great trigonometrical survey of that country. It 

 was found by triangulation that the difference of latitude between 

 the two extreme stations of the northern division of the arc, namely 

 Kalianpur and Kaliana, is 5° 23' 42" - 294, whereas astronomical ob- 

 servations show a difference of 5° 23' 37"058, which is 5"-236 less 

 than the former. 



That the geodetic operations are not in fault, appears from this ; 

 that two bases, about 7 miles long, at the extremities of the arc 

 having been measured with the utmost care, and also the length of 

 the northern base having been computed from the measured length 

 of the southern one, through a chain of triangles extending about 

 370 miles, the difference between the measured and the computed 

 lengths was only 0"6 of a foot, which would produce, even if wholly 

 lying in the meridian, a difference of only 0" - 006 in the latitude. 



The difference 5" - 236 must therefore be attributed to some other 

 cause. A very probable cause presents itself in the attraction of the 

 superficial matter which lies in such abundance on the north of the 

 Indian arc. It is easily seen that this disturbing force acts in the 

 right direction, that is, it diminishes the difference of astronomical 

 latitude between the two stations. Whether the cause here assigned 

 will account for the error in the difference of latitude in quantity as 

 well as in direction, is the question which the author proposes to 

 discuss in the present paper. 



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

 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 Cane, as the most advantageous with which to combine the 

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



