MEASUREMENT OF HEIGHTS. 531 



sidered it probable that each of the constituents of the air is 

 compressed by its own superior strata alone, and not by the 

 whole superincumbent mass ; consequently, that at different 

 heights each constituent possesses the density which it would 

 have if it existed alone. Hence it must result, that the propor- 

 tions of the mixture would vary with the altitude, and the rela- 

 tion of the atmospheric pressure at different heights would differ 

 from the older assumption adopted in Sect. 2. Barometrical 

 measurements of heights have been proposed as a means of de- 

 ciding between the two assumptions. The attention, which the 

 opinions of so eminent a physicist as Dalton deserve, requires 

 that I should follow out his supposition also. 



The formula (6.) then is no longer correct for the air generally, 

 but only for each of its constituents ; it applies to each of these 

 according as the specific gravity of each is taken instead of that 

 of the atmosphere itself. If we call the pressure exerted by 

 the three constituents of the air, at the elevations h and h, 

 — Pi Pn Pill ^i^^ P'i Pn Pin ^^^ their specific gravities D </, D d^, 

 D d^^, and if for brevity we denote by U, 



L H'-H 



/' • 1 + X: T ' 



then, according to formula (6.), 



p' =p .10-^'^ 



pI=P, .10 



p,l=p„. 10 

 and as 



^ =P+Pi+Pii 

 p' = y + pI + p< 



p = vF; Pi = v,F; Pii = v„P; 



therefore 



F = p{v.\0-^'^+v,.lO-^^'+v,AO-'^'^"} 

 or 



V = P.l0-''{vA0''^'-'^ + v,A0^^'-''^ + v,.l0''^'-'"^} 

 instead of which, we may write for brevity 



F = P.10-".4' (14.) 



The quantity 4', at all accessible elevations, differs little from 

 I, as is shown by the following table, calculated according to 

 tlic values given in the 1st Section, viz. 



