492 Mr. Lubbock on the Heat of Vapours 



d 3 co r i~ z 5 2 i z 3 cos 2 9 



d* co r t 2 z a 



~ (T7 2 \3~75 " 



3 



d 3 r i* z- 2 i * 



2 COS 



cos 2 9 - 



.5.7 3.5 3 



-&c. 

 3 sin I i fid 



^3sin0 M rija^fll 



B ,/ f | * \ f che j 



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 = l x . e = tan 



cos 9 2 



<2e 



tan $ = 7- T^T 



__ _ 



\/ 2 i x" / , , o., 4 e 1 x 



2 



I assume with Mr. Ivory 



x 2 ex" d z 



V cos 2 + 2 i x ~ ^2 zV 

 then x = x" z x" e* (z z 2 ). 



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



a. sin 9 d co ... . , 



. will contain the term 



V cos 8 9 -I- 2 * a? 



