300 
MOVING FORCE. 
Cases of cliffi. expended in producing change of figure j that is, in forcing the 
docYrinU* of through the tubes and through the orifice C ; and if the 
moving force, velocity of the machine be such that PC == 5AB, the issuing 
velocity will be equal to the velocity of the orifice, and the 
whole moving force of the water in descending from A to B 
will be expended in producing change of figure. 
For, the head due to V, the issuing velocity, will in this case 
be PR, which is also the head due to v, the velocity of the 
orifice. We shall therefore have V = v j and if CP represent 
the total moving force necessary to raise the water from C to P, 
CR = AB will represent that part of it which is expended in 
producing change of figure. The greatest velocity, therefore, 
that the orifice, when the machine meets with no resistance, can 
acquire, will be V4gx 4h. 
When the velocity of the orifice is less than that, V will be 
(treater than v : and V — v, the absolute velocity of the water 
& 
after it has left the machine, will be Vs (4"A+v*)— v. The 
head or the moving force expended in producing that velocity 
■will be ^/-s ^1 ' 
The moving force expended in producing change of figure 
will be 
Noisr when the sum of these two 
quantities, or V'S {4gh-\-v^)—v 
■ + ■2 
a mini' 
mum, we shall find v = —l)=:6 3056^'ir for 
the velocity of the orifice when the machine produces a maxi- 
mum of effect j and in that case the above sum becomes 
=■4472/1. 
We shall therefore have h— ’447211 = *5528 h for the 
maximum of effect, supposing k to represent the whole mov- 
ing force of a given quantity of w'ater descending from A to B. 
This effect is considerably greater than that which the same 
quantity of water would produce if applied to an undershot 
water-wheel, but less than that which it would produce if 
properly applied to an overshot water-wheel. 
Respecting 
