234 Royal Society. 



the portion to the south of the line first mentioned, and not included 

 in the known region, slopes at four times that rate. 



The author then proceeds to numerical summations replacing an 

 integration to be extended over the whole of the enclosed space. 

 The breadth of the lines employed in the calculation is taken at 30°, 

 which is shown not to be too large to give good results. The fol- 

 lowing are the results obtained : — 



Arising from 



| * » 



Known Doubtful 



Station A, Kaliana. re Si°n. region. Total. 



Deflexion of plumb-line in meridian 12-972 14-881 27'853 

 Correction of same for every 1001 n-TI9 O-^PO 



feet of change in heights . . . . / 

 Deflexion of plumb-line in prime 1 q.iof S-80P lf-94^ 



vertical J 



Station B, Kalianpur. 



Deflexion in meridian 3'219 8-749 1196S 



Correction for 100 feet 059 0-158 



Deflexion in prime vertical - 789 3-974 4'763 



Station C, Damargida. 



Deflexion in meridian 1*336 5-573 6-909 



Correction for 100 feet 0-022 0-100 



Deflexion in prime vertical 000 2" 7 23 2-723 



whence there results, 



Total deflexion at A=32-601, and in azimuth 31 18 East. 

 Total deflexion at B=1 2-880, and in azimuth 21 42 East. 

 Total deflexion at C= 7-426, and in azimuth 21 31 East. 



Difference of meridian deflexions at A and BzslS'SSS. 

 Difference of meridian deflexions at A and C = 20 - 944. 

 Difference of meridian deflexions at B and C= 5 - 059. 



The first of these differences is considerably greater than 5" - 236, 

 the quantity brought to light by the Indian Survey. 



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 



