494 Mr. Lubbock on the Heat of Vapours 



aF - sg =* %(1 - z) (1 + e 2 ss) 



An (x" - xf d x = 2 A n w" n +\\ + e 2 ) z n 



Vcos 2 + 2ix . J2~ix" 



f>- 



m m {m — 1) (m — 2) 1 





(w + 1) (n + 2 (n + m -f 1) 





» and m being whole numbers. Hence 



2 *(! + *) sin 6> J" >, lt /'2 ^ ^/ 3 ^ x // 4 ^ x m 1 



8ss 7f?p> |^^+-v+-v-+-V-+-V+ &c -[ 



+ 



jf lX "2 2 ^ 2 *" 3 3 ^ 3 a/' 4 x 4^ A ^s 

 2.3 + 3.4 + 4.5 



+^w 



{ 



(2.\A 2 x»* . 3.2A 3 x»4 , 4.3^ 4 ^ /5 , 5.4^ 5 *"6 , o ■* 

 + i 3.4.5 + 4.5.6 + 5.6.7 + 6.7.8 + &C ' J 



3.2.1A 3 x"4 4.3.2 J 4 x"* 5A.3A s x"e 6.5.4A 6 x"7 



[1] 



5.6.7.8 ' 6.7.8.9 ^ 7.8.9.10 



r+&e.} 



[ 3.2.1A 3 x 

 "*" \ 4.5.6.7 



+ &C.1 



A& A l9 Ac^ &c. are constants, the numerical value of which de- 

 pends upon the constitution of the atmosphere. 



A v A X X* A 2 X 3 Q 



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

 oo = 1, when oo = 0, X = X' — x n , therefore generally 



n ( "\ 



A x» + 



A, x"* A* x" 3 



+ &c. = 1. 



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



/d 2 «A 



»* Vd7?> 



/d 8 »\ 



then the quantities (-. — ), ( j— i) might be deduced from oo l9 oo 2 , 

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

 a d . (f xf a 2 d 2 . (f x) 3 



