as Floats for Paddle-wheels. 357 



the number of revolutions a minute must be 36. The efficiency 

 Uv -060871 v __ -060871 3 __ 

 Mo> -079837 X cor"" -079837 X 4 -* 57 ^ 

 (5) In the case of the flat float with paddle-wheels of the same 

 radius and making the same number of revolutions with the 

 same speed, the efficiency 



Rv _ -0234 v _ -0234 1 _ 

 Ma>" -021 X a>r~ '021 X 2 7; 



so that the flat float is not so advantageous as the screw-blade 

 with the portion nearest the axis cut away. 



Cases (4) and (5) may be compared with the case which fol- 

 lows, so as to determine whether it is more advantageous to 

 have screw-blades with the inner portions cut out, or complete 

 screw-blades of the same size, but having their axis at a distance 

 from the centre of the wheel greater than one-third of the 

 radius. 



Another point to be considered is, what should be the pitch 

 of the screw-blade at the circumference of the wheel ? If y be 

 the pitch, then the blade extends to a distance (a + r cot 7) from 

 the axis of the wheel, a-\-r being, as in the case already consi- 

 dered, the distance from the axis to the point where the pitch is 

 45°. Therefore for the superior limit of p in this case 



a 2 + p 2 + 2«/3COs0=(« + rcotY) 2 =r 2 cot 2 7(l+\) 2 



[where a=\r cot 7] , 



- = (x/l + 2\ + \ 2 cos 2 0-\ cos 6) . cot y. 



Considering the float to be a complete screw surface having 

 its axis at a distance «=r\cot 7 from the centre of the wheel, 

 the lower limit for p will be 0. 



Let 



Os/l + 2\ + A 2 cos 2 - X cos 6) cot y = q. 



Then the expressions for the resistance and moment on one float 

 are these : 



E,=4ftft>V 4 | ]Q cos 0d0+\\ cot y cos 2 log (1 +q 2 ) d0 



- ( (1 -X 2 cot 2 7 cos 2 0) cos . tan" J q . dO 

 _JLr c os 2 <91og(l + 2 2 )d0 



- — (%k cot y- i) fcos 3 . tan" 1 q . dd\ 



