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 :— 
e PtP p-ta 
= fath. se lly naw RS eed yh | 7 tn o'8 
H=10000 (1 +25) ae a aes mae Fi (V.) 
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,= 0, f'a=0, then since f,=f, fs=/'s 
we obtain the statical formula (II.); if we suppose f; = 07's = 03 
then since fu=/, fa=/’, we find (V.) reduced to (III.), 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 f to 
7 is less than of p to p’, and, consequently, that the ratio of 
p-f to p-/j’ is greater than of pto p’. In such cases, for- 
mula (IIT.) will give a greater height than (I.). 
ea 4 > - then fp > pf, or fp'—pf' >0, and pp— pf >pp'—fp; 
therefore Ps >. p~f 3; and vice versa, 
PPT 
Pe i Pp 
f — <=. 
‘he P 
