1859.] Mr. Pratt's Second Letter on the Indian Arc. 27 



of revolution,) and therefore its parts, at any rate near the surface, 

 do not exert the same amount of attraction as if it were a spheroid, 

 For example ; mountains rise up on the North of India, and the 

 Ocean spreads to the South. These, no doubt, we may conceive to 

 be removed — the mountains to be pared down to the sea-level, and 

 the density of the sea to be increased to that of rock. Were this 

 done, the plumb-line might hang all right, in the true vertical or 

 normal belonging to the surface of a spheroid. But since we cannot 

 actually cut down the mountains, nor fill up the ocean, the plumb- 

 line will not hang right for this purpose. If, therefore, we wish in 

 imagination to remove the mountains and to fill up the ocean, we 

 must do it by calculating their amount of influence, and allowing 

 for this amount in our calculations. Then we may use the plumb- 

 line, with this correction, as the true vertical or normal to an elliptic 

 surface, but not before. 



6. My object in writing these papers has not been to detect and 

 expose flaws in the operations of the Great Trigonometrical Survey 

 — very far from it ; but to assist in pointiug out the sources of 

 error, and the further observations and surveys which are necessary 

 to remedy the evils which must inevitably follow if these sources 

 of error are not attended to. The elaborate and well-executed 

 survey must be utterly useless in determining with accuracy the 

 curvature of the Indian Continent, and therefore of mapping the 

 country with higli scientific nicety, unless this is done. Except to 

 suggest a remedy in so important a work, after my attention had 

 been called to it in 1852 by the present Surveyor General, I could 

 never have devoted the time which has been necessarily occupied 

 on this highly interesting subject, even with the relief which the 

 assistance of a practised computer has afforded. The difference in 

 the views which Mr. Tennant and I take of the subject must arise 

 from some misconception which I am unable to fathom. 



J. H. Pratt. 



Calcutta, November Oth, 1858. 



P. S. — Since the above was written, Colonel E. Strachey has 

 favoured me with some information regarding heights in Tibet. 1 

 have given the results of these new data in a third paper to the 

 Royal Society. They do not at all meet the difficulty. 



