Of BAR OME TRICAL MEASUREMENTS. 1 1 9 



In this formula, the fecond term, viz. (i+m( OV <S"-7 



j- \ 2 Ib 



is juft half the correfponding term in the preceding formula, 

 ( 31.) with a contrary fign, fo that the correction for the di- 

 minution of the gravity of the quickfilver takes away from a 

 depth, as it adds to an elevation. The correction 



p 2 f H+b \* f (3 * 



( i+m( r) [log. -j- retains the fame fign in bc-th cafes, 



2J"V 2 / V t> J 



but in this is only half of what it was in the former. That 

 thefe laft corrections fhould be each half of the correfponding 

 one in the preceding cafe, might have been concluded from 

 this, that, by any fmall afcent above the furface of the earth, 

 the force of gravity is twice as much diminifhed as by an 

 equal defcent below it. The reafon of the change of the figns 

 in the fecond term is alfo fumciently obvious. 



34. THOUGH thefe corrections fuppofe that z is fmall in re- 

 fpect of /, yet they would afford a fufficient approximation to 

 the truth, were we to reafon concerning much greater depths 

 under the furface of the earth than any to which man can pe- 

 netrate. For example, on a fuppofition that the atmofphere 

 was continued downwards within the earth, its denfity being 

 always as its compreflion, and its temperature every where the 

 fame, (and, for the greater cafe of computation equal to r), 

 let it be required to find, at what depth its denfity would be- 

 come equal to that of mercury. To refolve this problem, it 

 muft be remembered, that the denfity of mercury, throughout 

 all this computation, has been fvippofed = i, and p equal to 

 the height of a column of mercury, which, gravitating every 

 where with the fame force as at the furface, would, by its pref- 

 fure, give to air the denfity i . If a barometer, therefore, were 

 carried down to the depth at which air was as denfe as mercu- 

 ry, the mercury in it would rife to the height p, or to 4343 

 fathoms nearly, fuppofing, at the fame time, that its own gra- 

 vity were not diminifhed. Now, on this fuppofition, (by 33.) 



any 



