THE MOTION OP STEAM VESSELS. 



325 



while in the former the effective part of the power exerted is only -553, and this power 

 is itself only two thirds of the whole power ; so that when a vessel is deeply laden, 

 not above -368, or three eighths of the whole power of the engine, is employed effec- 

 tively, while the fuel expended is nearly the same as when light. It is not proposed 

 in this place to speak of a remedy for this evil, but to point it out, in order, if possible, 

 to obtain some means of improvement. 



Table IV. 



On the relation between the Diameter of the Wheel, Area of the Paddle, and the Velo- 

 city of the Vessel. 



When the area of the float of a paddle-wheel is so adjusted to any given diameter 

 that the engine is capable of performing its whole duty, it is evident that the same 

 duty might also be performed with a less paddle and larger wheel, or with a smaller 

 wheel and larger paddle ; but the velocity of the vessel will not be the same in the 

 two cases, and the question therefore is to determine what change must be made in 

 the area of the paddle, and what change would take place in the speed of the vessel 

 with a given change in the diameter of the wheel, so that the engine in both cases 

 may perform its whole duty. 



Let d = diameter of the first wheel. 



V = its circumferential velocity. 

 a = the area of paddle. 



V = the velocity of the vessel. 



r c? = the diameter of the second wheel. 

 r V = the circumferential velocity. 



MDCCCXXXIV. 2 u 



