538 BESSEL ON BAROMETRICAL 



law, or corresponds to equation (3.), which, for the present 

 case, is 



8.E =p,I>d,', 



to which must still be added the condition requisite for equili- 

 brium, that the S resulting from this equation shall at no eleva- 

 tion exceed the maximum of density corresponding to the tem- 

 perature ; or, according to the notation in Sect. IV., that 



If we eliminate 8, we obtain 



dpi _ di dX 



'Yi ~ ~^' 1 + kt' 

 a similar differential has already been integrated in Sect. 2, 

 assuming the variation of temperature between the two heights 

 at which it was observed, to be that supposed by Laplace. With 

 this assumption, it follows that 



I + kt i 



and thence the integral, reckoned from the elevation h, where t 

 is the height of the thermometer, and P^ the pressure of the 

 aqueous vapour, is 



'°8f = 7 ¥('-'> ^ 



or 



p, = P, 10 ^' '• ^^ ' . . . . (16.) 



If we assume the pressure Py at the elevation h = oi<Pt, where 

 « cannot be greater than 1, the conditions to be fulfilled require 

 that for each value of t, 



d, 2k , 



r -^('^ — = 



or 



ri, 2A- _ -d, 2A 



ac;>r .]0~ '' ^^^4>^. 10 ^ "^'; 

 and if for c^ t, and <t> t, we substitute the expression (9.), 



/d, 2!: \ „ /d, 2 k \ 



« 10 V ' ' / ^ 10 V ^' » / 



If we suppose t to decrease without limit with increasing eleva- 

 tion, it would attain a negative value, for which, even Avith the 

 smallest value of «, the conditions would cease to be fulfilled ; 



