Of BAROMETRICAL MEASUREMENTS. 125 



4/0. THE correction on account of the departure of the law 

 of the elafticity of air, from that of the direct ratio of the den- 



fity, ( 29.) = -^-p(i+m(- ' r)) log. x log. bp. In this 



equation, b and (3 muft be exprefTed in the fame meafure with 

 pi that is, in fathoms. 



5/0. FOR the diminution of the weight of the quickfilver in. 

 the upper barometer, there is an equation to be applied = 



6/0. ON account of the diminifhed gravity of the air in a- 

 fcending from the furface of the earth, there is a fixth correc- 



/ , ^, 



rection = + -(i + w( - -- 0) f^.y) . 



WHEN a depth below the furface is to be meafured, the fifth 

 equation becomes negative and lofes the multiplier 2 j the fixth 

 remains affirmative, bxit is divided by 2. 



40. THESE equations, even exclufive of the firft, may, in 

 the meafurement of great heights, amount to a confiderable pro- 

 portion of the whole. In the inftance of Cora9on, 15833 feet 

 above the level of the fea, the greateft height to which the ba- 

 rometer has ever been carried, the firft equation exceeds noo 

 feet, and the third appears not to be lefs than 300. The re- 

 maining corrections are, indeed, lefs confiderable ; but, being 

 all affirmative, they mufl not be entirely neglected. And, on the 

 whole, it is certain, that, though the firft equation alone will 

 give the height fufEciently exact, while it does not exceed 

 five or fix thoufand feet, yet, at greater elevations, the cor- 

 rections that have now been enumerated muft all be taken into a 

 account. To facilitate the computation by means of them, 

 they ought to be reduced into tables adjufted to their proper ar- 

 gtiments, after the values of p, m and r are accurately deter- 



mined,, 



