THE MOTION OF STEAM VESSELS. 319 



2nd Class. Mean = -193. 



Number of Number requiied to 



strokes observed. give the Mean. 



Alban 2/ 28-3 



Pluto 26J 27*5 



Hermes 18 16*2 



Meteor 32 29*0 



Firebrand 24 23*6 



Carron 28 29-1 



Firefly 20 20*2 



Magnet 29j 29-1 



3rd Class. Mean = -546. 



Medea 22^ 21*9 



Firebrand . 28 28*2 



Firebrand . 27 27*1 



Flamer 27 267 



Flamer 24 24 



Columbia 24 24*4 



It thus appears, that the number of strokes required to give the mean in each class, 

 differs generally but a fraction of a stroke from the registered observations ; except in 

 a very few cases, and these can be accounted for by the vessel being particularly light 

 or deeply immersed. At all events, there is no doubt that the mean of each set will 

 approximate very nearly to the truth, the immersion of the paddle being also a mean. 



A striking difference is observable between the ratio of the resistance of the paddle 

 in a vertical position to the power of the engine in the common wheels, and in the 

 new wheels ; the former being '157 and '193 with the large and small boats, and the 

 latter '546. This difference arises from the nature of their action. In the new wheels 

 the vertical position is the most effective in propelling the vessel, and in the common 

 wheels it is the least so, as may be proved in the following manner. 



Let A B, fig. 3, be the position of the paddle-rod of a vessel in motion, V being the 

 velocity of the wheel, and v that of the ship, and (p the angle of inclination of the 

 paddle-rod with a vertical line : let C D represent the velocity V at right angles to 

 the paddle, and E C that of the vessel in a horizontal direction. Then it is evident 

 that C F, which is the resultant of these velocities, will represent the velocity and 

 direction of motion of the paddle with respect to still water. 



Resolve F C into the two velocities F G, C G, one at right angles to, and the other 

 in the direction of, the paddle, of which the latter is lost, while the former will repre- 

 sent the velocity with which the paddle meets the water in a direction at right angles 

 to its face ; then E G or H F = E F — E H = V — ?; cos <p. Consequently (V — t; cos (p)2 

 will represent the whole resistance which the paddle opposes to the engine at any 

 angle 9. 



2 t2 



