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As the extremity of the float-board muft have a 
certain velocity depending on the relation of the 
height a to the plunged part, and as the velocity of 
the weight rr — - z, it follows that if we would in- 
° a 
creafe the velocity of tt, we mud diminifh the height 
a and increafe the breadth ft, fothat the product /3 exa, 
and the relation of j to a. may be the lame as before ; 
for example, if the wheel be plunged as deep as the 
axle, to double the velocity of the weight, the 
height of the float-board muft be reduced one half, 
and its breadth be quadrupled. 
§ V. It may fo happen that the channel on which 
the wheel is placed (hall be fo (hallow and narrow, 
as not to allow the float-boards the neceflary dimen- 
fions, for raiflng the weight with a convenient ve- 
locity. In this cafe we are obliged to raife the axle 
of the wheel above the furface of the water, fo 
much that the lever on which the dream adls may 
be long enough to recompenfe the fmallnefs of the 
float- boards. Herein it is neceflary to folve the fol- 
lowing problem : 
The breadth b, and the height a, of the float-board 
AB being given ; to find the radius CA (r) of the 
wheel which fhall caufe the weight 7r to afee-nd with 
the velocity z. 
The exaft folution of this problem might be de- 
duced from the formula (§11.) which would render 
the operation tedious, the equation being of the fourth 
degree ; but it may be rendered far more Ample by a 
Juppofition which is but little wide of the truth when 
AB is but fmaflin companion of CA, and this is to 
con fid er 
