494 Mr. Lubbock on the Heat of Vapours 



a" x = x n (1 z) (1 + e* *) 



A n (x" - x) d x 1A x" n+ (\ + e 2 ) *" 



__ ..^.^ rr- " 



^ ... (m - 1) (M - 2) ...... 1 



= 



and m being whole numbers. Hence 



2 (! + *) sin 9 



J ^7 j X i 2 _j_ _ 3 *^ I 4 *^ i^ .& L 3 



" 1 ~2T3~ H 3.4 4.5 5.6 ' I e ' 



+ j " l -^2 x i 3 x _i ' ' **< * , 4. . ' A 6 X ^ i &. 



\ 3.4.5 4.5.6 5.6.7 6.7.8 



+ { 4. 5. 6^7 *" 5. 6. 7! 8 h 6.7.8 5 .9 + 7.8.9!lO + &c - } e ' 

 + &c. I 



^ , A lt A zt &c. are constants, the numerical value of which de- 

 pends upon the constitution of the atmosphere. 



U> = 1 AQ X ^ ^ &C. 



the first term is necessarily equal to unity, because when X = 

 co = 1, when (a = 0, X = X 1 = #", therefore generally 



^ tf2 // -T//3 



y* f I ^.1 1 * ^4 O *** . Q | 



Let wj be written for brevity instead of (-: j, 



(si?/ 1 



0> 2 



\ 



d s w 



then the quantities (-T - j, f jp) might be deduced from eoj, o> 2 , 

 &c., in the following manner, without having recourse to the series 



__ d . (f xf a? d 2 . (fa-) 3 



T37 2 d^r 2 



