HYDRAULICS. 221 



where r is the radius of the horizontal arm, mea- 

 sured from the axis of motion to the centre of the 

 perforation, and r> the radius of the perpendicular 

 tube, g being put for the force of gravity, or 32.J 

 feet. 



As % * r is the circumference described by the centre 



Q /' 

 of each perforation, is the time of a revolu- 



tion in seconds. 



The quantity V hg is also the velocity of the efflu- 

 r ' 



ent water ; therefore, when the machine is working 

 to the greatest advantage, the velocity with which 

 water issues is equal to that with which it is car- 

 ried horizontally in an opposite direction; so that, 

 on coming out, it falls perpendicularly down. 



The effect of this machine is equal to A h, or the mo- 

 mentum of the water expended ; so that it could, if 

 there were no force lost by friction, raise up the 

 whole of the water to the height from which it fell, 

 and in an equal time. It is therefore, in theory, 

 the most advantageous application of water that is 

 known ; but, on account of the friction, which must 

 be great, as the whole body of the water has to 

 turn on the axis CD, (fig. 24.), it will probably be 

 found in practice, that the overshot-wheel is, in ma- 

 ny cases, preferable. In the construction of this 

 machine for practical purposes, the water is made 



to 



