1882.] General Walker — Error in Spirit-Ievdlin^^ operations. 70 



higher than other points, as referred to a hypothetical geometrical surface, 

 or, say, to the earth's centre. The differences of height, however con- 

 siderable, must be insensible, because they cannot be measured by instru- 

 mental means ; for the causes by which they would be produced must 

 equally affect both the spirit-levels of the instruments and the water-levels 

 of the ocean, whenever both are subjected alike to the same influences. 

 Thus if in the present instance the sj^irit-levels had been carried, without 

 error, along the coast line, from Bombay round via Cape Comorin to 

 Madras, they must have shown identity of mSan-sea level at Bombay and 

 Madras, just as has been met with in the Red Sea and the Mediterranean 

 on opposite sides of the Isthmus of Suez, and in the Atlantic and the 

 Pacific Oceans, on opposite sides of the Isthmus of Panama. And this 

 identity would be obtained even if there were actually a considerable 

 difference of height, as is very possible ; for the Western Ghats, and the 

 generally greater elevation of the western as compared with the eastern 

 half of the peninsula, are sources of attraction which, if not counteracted, 

 must raise the mean-sea level at Bombay no less than 31 feet (as computed 

 by Mr. Hennessey) above the mean-sea level at Madras. 



The spirit-levels, however, were taken across the continent and not 

 along the coast-line ; they were carried from Bombay up the short and 

 abrupt ascent to the crest of the Western Ghats, and then down the long 

 and gentle decline to the east coast. Thus, while subject to the same 

 general attractive influence of the continental masses as the ocean levels, they 

 are also subject to the more proximate influences of local irregularities in 

 the configuration of the ground passed over. The closing discrepancy of 

 8 feet at Madras is materially greater — both absolutely, and relatively to 

 the distance levelled from Bombay — than any error previously met in the 

 course of the levelling operations of this survey, which have been carried 

 over many thousand miles and tested at a number of closing points and 

 junctions of circuits, and have been conducted with special precautions to 

 guard against errors of all kinds, whether accidental or cumulative. More- 

 over, a very similar discrepancy, almost identical in sign and magnitude, is 

 stated to have been met with at the close of the railway levels between 

 Madras and Bombay. Thus it has been surmised that the dis- 

 crepancy maj^ be due to the proximate and local attractions of the hills and 

 table-lands over which the lines of level were carried, and which must 

 exercise some influence on the instrumental levels, over and beyond the 

 general influence that is exerted alike on both the instrumental and the 

 ocean levels. Problems of this nature have been investigated mathemati- 

 cally by Colonel A. R. Clarke, C. B., R, E., and formulae for their calcula- 

 tion are given in his recent valuable treatise on Geodesy. Mr. Hennessey 

 has calculated the attractions with these formulae, making such assump- 



