344 



This latter formula (IV.) is the formula proposed by Dr. Ap- 

 john (Proc. Royal Irish Academy, vol. ii. p. 561). 



The dynamical formula may be thus written down, al- 

 though unfortunately it cannot be used : — 



H = 10000**- ( 1 + £=) *t* t ■*, kg 1 r 1 ¥' ( V -) 



V 4:93) p+p'-fs-fj b p-fd 



The statical part of the elastic force of the vapour appearing 

 in the hygrometric coefficient, and the dynamical part under 

 the logarithm. 



If in (V.) we make f d = 0, f d = 0, then since f s =/, /, =/', 

 we obtain the statical formula (II.); if we suppose f s = 0/ s = 0; 

 then since f d =f,fd=f, we find (V.) reduced to (III.)j the 

 hygrometric coefficient disappearing, as it ought, for we have 

 implicitly supposed that no expansion has yet taken place in 

 the column of air. Equation (III.) may therefore be con- 

 sidered as the barometric formula corresponding to the state 

 of incipient expansion. The heights calculated from (III.) 

 will be in general smaller than those calculated from (I.) with- 

 out hygrometric correction, because the elastic force of the 

 vapour diminishes faster than that of the dry air, and there- 

 fore* the ratio of p to p' will be greater than of p -/ to p' -/' ; 

 consequently, the heights calculated from (III.) will be smaller 

 than those deduced from (II.). The two corrections used in 

 (IV.) tend to counteract each other, one increasing and the 

 other diminishing the height, so that it sometimes happens 

 that the heights calculated from (I.) and (IV.) are absolutely 

 equal. It frequently occurs, however, from the irregular de- 

 velopment of vapour at particular places, that the ratio of/ to 

 f is less than of p to p', and, consequently, that the ratio of 

 jo-/ to p'-f is greater than of ptop'. In such cases, for- 

 mula (III.) will give a greater height than (I.). 



*I — >-V, then fp' > pf , or fp'-pf>0, andpp' - pf>p p' -fp', 



v v— f f v 



theroforo -=-7 > —, — —,; and vice versd, if ^— < -*-;. 

 P P ~f f P 



