492 



Mr. Lubbock on the Heat of Vapours 



d 2 co f P- z 5 2 i z 3 cos 2 



z cos 4 



3 



2 2 3 5 



cr w f i*z* 

 ~(T7 2 \375 



d 3 co f i 2 z" 

 + d^L3.5.7" 

 -&c. 



3 * sin j J l fl d«j -I 



} 



cos 2 — cos' 3 



1 d c - 



CO 



2 d <2? 2 



CO 



COS*0 



dw Q „ 



1 + ss-r- cos 2 

 d<# 



} 



cos 4 



l_ 3 n d 3 c 



+ 3 L i d ar 



3.51 / d x' 

 Z 7 f I d b co 



d 2 co y . . dco 



f £ -*f— £*. €0S — 2 



d^ 



d x 



} 



[2] 



+ 



I d 4 co .. d 3 co 9 , . d 2 aTl 



"4 C0S4 * + * ,TT3 C0S 9 + * ^T 2 J 



d 



3.5,71 * 



A a d 4 co 



E COS 4 — 2T j 2 COS 2 



d x b d x 4 



CO 



d x s 



)} 



In order to take this quantity between the proper limits, it is only 

 necessary to write it first with two accents and then with one ac- 

 cent, and take the difference of the quantities so expressed. 



Instead, however, of employing the preceding expressions, I 

 shall now introduce the auxiliary quantity e employed by Mr. 

 Ivory. Let 



tan £ 



V<2, 2 x' 



tan <p = j- 



cos 



2e 



4> 



e = tan — - 



2 



(i - *) 



,2\2 



Vcos»» + 8i* = V ^f- \/(l - e*f + 



4 e 1 x 



x 



I assume with Mr. Ivory 



v 



(i-*T + 



d x 



4^ 2 x 



= 1 - e 2 + 2 e 2 z 



_ _ 2^x n d z 

 ^ cos 2 + 2 i x ~ ^Vlx" 

 then x = # f/ z — # ff £ 2 (^ — z" 2 ). 



Suppose d co contains any term of the form Ac~ occ d #, then 

 u sin d co 



— bx 



V cos 2 ■{- 2i x 



will contain the term 



