96 CAUSES which affeSl the ACCURACY 



expanfion which depends on preflure, we have the fpace occu- 

 pied by that fame quantity of air, 'when it is of the temperature 



32 

 H A#, equal to (i m) : Or, making 32 H r, we have 



the required fpace =: (i m) 



Now, if the given quantity of air, of which the bulk has 

 been fuppofed i, and the temperature = 32, be compreffed 

 by a column of air of the fame denfity and temperature with 

 itfelf, but of the height/, and if its denlity, in this cafe, be 

 alfo called i ; then, in the cafe of its having any other tempe- 

 rature, as H AX, and being comprefTed by any other force, as 



fyx, or the weight of the fuperincumbent air at the height *-, 



T /"vv 



we have i : y : : p : - TT^> an d likewife 



(i z). 



fvx 



y - " 



i m) 



No account is here taken of the diminution of gravity, any 

 more than of the departure of the law of the elafticity of air 

 from diredl proportionality to the denfity ( 8.), becaufe it is 

 convenient to confider the problem at firft under the more fim- 

 ple view, where only the two firft inequalities are intro- 

 duced. 



13. SINCE y T + /X 7 we have 



py(i m) = /yx, and 

 . i m) (i m 



py ' x 



Or, 



(i m) 



Hence 



