ON THE GENERAL THEORY OF THE STEAM ENGINE. 193 



1. OLDHAM'S WHEEL. Here e = $-, and hence, the number of horses' power ex- 



pended, 



by the Engine 



on the Fluid 



on the Vessel 



cS 

 1000 



x -< 



, 



(V - vY C 

 o 

 a. 



(v - ) r 



cos. 3 



In which 



/J.L s $ _ o / 1 2 a i ^ \ a _ 5 + cos. a . a. _ 5+ cos. a /I cos. a 

 cos. ^ - cos. - - J - - 3 1- 2 ~ 3 2 



o 



= i \/ 1 may be very readily calculated. 



3 2 



The respective proportions of the whole power expended on the Fluid and Vessel are therefore 



2. THE COMMON WHEEL. Here e = o, and the number of horses' power expended, 



Co. 



by the Engine 

 on the Fluid 

 on the Vessel 



1000 



x < 



V (V - v cos. 



4>) 3 d4>. 



a, 

 C (V - v cos. 



a 

 / cos. <j> (V v cos. <f>} 2 d<f>. 



3. THE VERTICALLY ACTING WHEEL. Here e = <f>, and the number of horses' power 

 expended, 



by the Engine 

 on the Fluid 



on the Vessel 



cS 

 1000 



/ cos. 



(Vcos. <f>-v) 3 d<j>. 



, 

 v C (V cos. < - t)) 2 <fy>. 



