260 Mr. W. G. Adams on the Application of the 



Hence if these wheels be of the same breadth as in the first 

 case, the resistance and moment are not so great as in the other 

 case, but are nearly in the same proportion. If the breadth of 

 the wheel be three-fourths of the radius, then the same resistance 

 will be produced by the same power as in the first case considered. 



It will now not be difficult to arrive at the expressions for the 

 resistances and moments, taking into account the velocity of the 

 steamer. If v be this velocity, the expression for the resistance 

 when the float is in a vertical position is 



$ 



2 Pi ' ~t^ — ^f~~ cos 0- Mi + a cos 0) — v cos 0} *dp.' &Q 



Also the moment 



/ cos 



1 co(p + a cos 6) — v cos 6l 2 dp dO. 



— i/ / 3 \ \ - g a , C °2 {<°{p + aco$6)—v cos 6} Hp dd. 



Hence the resistance on one float becomes 



i 9. q CC(p + fl cos #) 2 cos ® j jq 

 iPl JJ r^T? P 



_1 



2 P COS * d dpd0 



C C cos 3 6 

 i pi r 3 v{2coa-v)^-—2dpd0. 



And the moment on one float becomes 



3 rr(p +« cos ^) 2 cos ^ , J,, 



- ft r* . n»j J v ^ y3+p i dp dd 



+ y i r*v*.a.^°^JLdpd0. 



These integrals are the same as those which have already been 

 found : and the results arrived at are these : — 



