522 BESSEL ON BAROMETRICAL 



D </,D 



P Pi 



and 



' p+p!'''~ p+p! 



thus 



P+P, 

 or if, to avoid introducing a new sign, we denote the whole press- 

 ure {=zp +pi) hyp 



D'=d|i-^ (1-^,)} (7.) 



For moist air, therefore, the equation (3.) is changed into 

 h.E = {p-p,{i-d,)}B, 

 and its combination with (4.) gives 



^ , I dX (l-d) dX 



To integrate this equation, we must know the dependence 

 which Pi has on the other variable magnitudes. If in a parti- 

 cular case we have no observation determining the amount of 

 aqueous vapour contained in the air, we must found our calcu- 

 lation on the supposition either of a mean state of the atmo- 

 sphere, or of one which may appear more suitable to the actual 

 circumstances. I will first examine the case in which we may- 

 suppose that at every point of the atmosphere there exists a de- 

 terminate portion of the maximum quantity of vapour which 

 it can receive in accordance with its temperature. If this maxi- 

 mum of vapour exert the pressure {p^, I then assume 



P, = «- {Pi)> 

 where by a I understand a constant factor not greater than unity, 

 the value of which is to be determined hereafter. 



The expression for (pi), at the given t of the centesimal scale, 

 deduced by Laplace {Mec. Cel., iv. p. 273.) from the experiments 

 of Dalton, in the unit of pressure chosen in the foregoing article, 



= 10 (* ~ ^^"^ 00154547- {t - 100)2 0-0000625826. 



For which we may also write 



{p;) = 0-0067407 . 10 '•00279712 - .2 0-000062582C , , , (9.) 



We have thus, conformably to the supposition, 

 ;j, = «/3 10 "'-"', 



