304 



OF STEAM NAVIGATION. 



[SECT. x. 



to produce the effect is, 



3r 



x -75 .3 bh = 



A somewhat greater power is required, because there is also a loss by oblique 

 action, and this will be expressed with accuracy enough for the object by multiply- 

 ing the power by, 



- h 



where r is the radius C B, and h the depth of the float boards D B. For the 



FIG. 27. 



JF. - 



centre of gravity, a of the immersed part A B D may be considered the actual 

 point where the whole force acts, instead of being distributed over the segment ; 

 and its mean direction will be E F, which is perpendicular to the line A C, drawn 

 from the centre of the wheel through the centre of gravity : and the direction of 

 this line will determine the loss by oblique action, for the power is to the effect 

 as A H : A D, and is nearly given by the multiplier above. 



An example may give a clearer idea of its effect. Let the radius of the wheel 

 be 8 feet, and the depth of the paddles 2 feet, then 



= 1-024, nearly. 



Hence, as it will not exceed one-fortieth part of the whole, it may be neglected. 

 The mean direction of the action is of greater importance to the motion, than the 

 loss of power. 



632. We have supposed the paddles to be of the same breadth every where, 



