Principle of the Screw to the Floats of Paddle-wheels. 261 

 Resistance on a pair of floats 



==jp / G)V(-513256- — x -234563-— x^^x -259202 j; 

 zr ' I cor o)r cor J 



and the moment of the resistance on them 



= Jr/v»v{-573869-— x -513256 + -^ x -493765). 



zri I cor co lr r- J 



The angular velocity should be such that v, the rate of the 

 steamer, is not greater than — . Let v — -~- : 

 then the resistance 



=ip /ft > 2 r 4 x -149092 



=!rtft>*(rad) 4 x '029450; 



and the moment 



=|p i ft>Vx -184054 



=i / o / o> 2 (rad) 5 x -024238. 



The corresponding expressions may be obtained for the flat 

 float by taking (cop—v)' 2 for the square of the actual velocity of 

 a point of the surface, instead of co^p 2 ; and the results obtained 

 are : — 



Resistance 



= i /0/W/ V 4 {-1314--x -153+-^- 2 x -18T 

 2 ri ' L co t r cofr z J 



i-1314- — x -051 + 4 x '02"V > 

 L W/ ©/ J 



1140- -1314 x -+-^- 2 x '153^ 

 cof cofr' J 



1 2 



r 4 x - 



Moment 





1 2 



=2 w 



*{• 





r 5 r, 



^ x . 438+^ 



G). 0), 



2 x-017T, 



the velocities being the same in both cases. If the relation 

 between the angular velocities be such that the resistances are 

 the same, then the moment in the case of the new wheel will be 

 less than in the old, the ratios being as 96*88 to 100; so that 

 not only can the same hold be obtained on the water by means 

 of the new floats, and so the speed be kept up, but the power of 



