104 CA USES ivhirb *Jia the ACCURACY 



whole height, the error committed in eftimating it will be 

 but of the former correction ; and, if that did not ex- 



Z OO 



ceed , the error in queftion will not exceed of the 



400 40000 



whole height. 



21. IN computing the effect of the fecond inequality of ex- 

 panfion, defcribed 8. we may, therefore, abftract from the laft 

 inequality, and may even fuppofe, with M. DE Luc, that the 

 temperature, which is a mean between thofe of the extremities 

 of a column of air, is uniformly diffufed through that column. 

 Let the excefs of that mean, above the temperature r, or* 



r f; and let (3, the height of the mercury in the up- 



permofl barometer, be confidered as variable. Then taking the 

 formula of 8. and fuppofing m to be the expanfion for i of 

 heat, when the mercury in the barometer is of a given height, 

 which we mall here call y *, (to avoid the confufion that would 

 arife from naming it, as in the art. above referred to) and 

 retaining all the other denominations as before, we have 



fyx 



y j > , 



j ~ f ~~ . 



/ ^\ & 



Hence py(i+-^--\ fyx, fo that, taking the fluxions, 



py 



* According to the experiments of General ROY, above quoted, the expanfion of air, 

 for 1 of heat, at the temperature 32, is .00245 nearly, that air being comprefled at 

 the fame time by the weight of a column of mercury 29.5 inches high. As we have 

 fuppofed m, in the preceding computations, to be .00245, we mu ft fuppofe y 29.5. 

 The formula fuppofed here to give the fpace occupied by the air, fo far as heat is con- 



cerned, viz, i-^-'-L ft , is changed from the exponential expreffion of 5 8. in confequence 



if 



of what has been juft obferved about the effedl of neglecting one inequality in the com- 

 putation of another. 



