181 



The author then examines these values more minutely, and con- 

 siders the effect of various hypotheses for reducing them. 



In the first place, the density of the attracting mass may have been 

 assumed too large. The density assumed is 2' 75 that of distilled 

 water, the value assumed as the mean density of the mountain 

 Schehallien in the calculations of Maskelyne. This can hardly be 

 too great, but at any rate no remarkable supposition relative to the 

 density can reduce the attraction by more than a small fraction of 

 the whole. 



Next, the mass of the doubtful region may have been assumed 

 too great. This hypothesis is then examined by the author, who 

 concludes that even the extravagant supposition of the non-exist- 

 ence of that region will not reduce the difference of meridian de- 

 flexions at A and B lower than to 9"' 753. 



A third means of reduction may be looked for in the known region. 

 A large part of the attraction belonging to this region arises from 

 the Great Plateau. It would be necessary to cut down this plateau 

 as much as 6000 feet to reduce the deflexions at A and B to 5"'236, 

 even were the whole mass on the doubtful region non-existent ; so 

 that it appears to be quite hopeless, by any admissible, hypothesis 

 relative to heights, densities, &c., to reduce the calculated deflexion 

 so as to make it tally with the error brought to light by the 

 survey. 



After entering into some elaborate calculations confirmatory of 

 the previous results, the author concludes by calculating the form of 

 the Indian arc, that is, by determining what spheroid of revolution, 

 the axis of revolution being the earth's axis, would most nearly 

 coincide with that arc without reference to the rest of the earth, the 

 data employed being the lengths and amplitudes of the northern and 

 southern portions of the arc, and of course their sum, and likewise 

 the latitudes, or at least approximate latitudes, of the middle points 

 of the arcs. By using the amplitudes uncorrected for mountain 

 attraction, the author obtains for the value of the ellipticity deduced 

 from the Indian arc alone n^, nearly agreeing with nfF<i> which is 

 Col. Everest's result ; but by using the amplitudes corrected for 

 mountain attraction according to the author's calculation, the ellipti- 

 city is reduced to 4262. He concludes that the arc is more curved 

 than it would be if it had the mean ellipticity of the earth, and 



VOL. VII. T 



