292 
MOVING FORCE. 
Cases of difii- to B*.— It would be too much to say that this explanation may 
docuin^^af applied to the action of water on a water-wheel, but it is 
moving force, remarkable that these conclusions agree very nearly with the 
results of Mr. Smeaton’s experiments. (Sec page lOo.) 
The exp«nditure of moving force in overcoming the cohe- 
sion of the particles of fluids is always exhibited under very 
complicated circumstances ; but the amount of it may in some 
instances be estimated with considerable exactness. When a 
jet of water issues from an orifice of a particular construction, 
it has very n«arly the same velocity which a body would acquire 
in falling freely through a height equal to the depth of the 
orifice under the surface of the water.-— In that case, therefore, 
a very small part only of the moving force is expended in 
changing the figure of the water before it reaches the most 
contracted part of the orifice.— But if the orifice be constructed 
so that any separation of the particles of the water from each 
other takes place, although they may be brought together again, 
and completely fill the most contracted part of the orifice, yet 
* To nit.tlicmatiral readers it may perhaps be acceptable to have 
tlie problem in a more general form. 
Problem. Given two non-elastic bodies, A and B, such that A, 
moving with a given velocity, v, shall overtake B, moving witli a vari- 
able velocity, .r, in the same right line ; it is required to tind x, such 
that the increase of moting force feund in the motion of B after the 
stroke may be a maximum. 
.Solution. Lety =» the velocity of B after the stroke. By meclianic* 
Ar-f-B.v 
A-PB 
-y ; and per question, By’— -Ba;^=maximum, That is, B. 
^ -Bx’ = 
3 I 
Ai-PB 
A+B 
maximum. 
In Unctions 2 Brx— (A-p2B)2xx 
maximHin. Reduced, 2 Bex — (A-p2B).r’ 
0 , or Be = (A+2B)x, & x 
n.Q.E. 
A-P2B 
r. 
Cor. 1. If Bbe indefinitely greater than A, then its velocity after the 
stroke will be the same as before, 8c x —iv, which is tlic case in the 
text. 
Cor. 2, If R »= A, then x *• 
Cor. 3. If A be indefinitely greater than B, then x =s o. 
there 
