540 BESSEL ON BAROMETRICAL 



-^- dX= {a-2ct) [1+ ki) dt. 

 Hence follows by integration, 



for which we may also write 



X - H = ~S{a -2ct) {l+kr) {r- t) 



-(^-c + 2cAT)(T-0^-|-cA(r-0^} . (22.) 



If we introduce into this equation the values of /', d^, a, c, k 

 already employed, we obtain the law of the decrease of tempera- 

 ture, which, on Dalton's supposition, is alone reconcilable with 

 an atmosphere everywhere saturated with aqueous vapours. 



X - H = 424^-0 (1-T. 0-00447) (1 + r. 0-00375) (x - t) 

 + 0^-15 (1-T. 0-0463) (t-^)2- 0^-003 {r-ty. 

 If, further, according to Sect. 2, we put 



2k _ H'-H 1 



— - t-t' ' I + kV 



and designate by (t) the value of t at the extreme limit of the 

 atmosphere, the condition (19.) becomes 



m:z3^I^{l + kT){a-c (t+ it))} 

 T — r di 



> {424T-0-0T-95 (r + (0)}(1 + kT). 

 The actual change of elevation, which produces a decrease of 1° 

 in the height of the thermometer, is much less, or about 

 = 85 toises ; this is irreconcilable, under Dalton's supposition, 

 Avith the saturation of the atmosphere with aqueous vapour at 

 the surface of the earth. But if the condition (20.) be fulfilled, 

 or if 



^' -^ < (424^-0-1 -Or) (1 + ^T); 



T — T 



then, according to formula (21.), after substituting in it the ex- 



. . 2 k 

 pression tor -r-. 



H»<{7^? r^-|^--+^(-+W)}(' 



■W), 



