Hence 



MEASUREMENT OF HEIGHTS. 525 " 



/3 = 0-0067407, 

 2 k (r-O _ H'-H 

 i ~ 1 + ytT' 



and we obtain, by the substitution of this expression in equa- 

 tion (10.), 

 , P H'-H f, 0-002561 «T-oTn 



^°gF = /'(i + /^T) |/-"-v7PF)^^ |--(n.) 



If we wish to found the calculation of the difference in height 

 of two points, where the pressures and temperatures of the air 

 have been observed, upon the supposition of a mean state be- 

 tween dryness and saturation, we must make « = |. But if we 

 have not an immediate determination of the quantity of aqueous 

 vapour on such occasions, we may obtain in particular cases, 

 by taking other circumstances into account, greater exactness 

 than by making « = |. If, for example, rain falls thi-oughout 

 the whole space between the two elevations, then « = 1. If 

 the two points are far distant from the ocean, and in a coun- 

 try known to be particularly dry*, it will be more suitable to 

 take a less than A. In order to give a direct view of the influ- 

 ence of aqueous vapour on barometric measurement, I will de- 

 velope it further. The increase, which is occasioned in a differ- 

 ence of elevation computed on the supposition of dry air, by 

 the introduction of the consideration of the aqueous vapour, 

 according to equation (11.), is 



= .^L^(H'-H) 



\ — uw ' 



where w is written for 



0-002561 «T-cP 

 \/(PP') ^ 

 If we neglect the square of this quantity, and make 



(H'-H 



P' = PlO-^'(i+/^T)^ 

 which can only occasion an error of the order lo'^, 



^ ^ OM0O2561 j^^TTTTTt) ^ ^^aT-cT* 



aIi^V*^''!-'" ^''^ ''"^^ '" * S""®^*^ P^""' °^ nortliern Asia, as we learn from 

 AdolpI.e hrniai. s Reisc, vol. ii. p. 67, where we have not only the fact, but the 

 geographical relations of which it is the consequence. 



