232 On the Measure of 
in order that the greatest possible quantity of 
the moving force of A shall be transferred 
to B.*—It would be too much to say that this 
explanation may be applied to the action of | 
water on a water-wheel, but it is remarkable 
that these conclusions agree very nearly with 
the results of Mr. Smeaton’s experiments. 
(See page 160). 
The expenditure of moving force in over= 
coming the cohesion of the particles of fluids 
is always exhibited under very complicated 
 * To mathematical readers it may perhaps be acceptable 
to have the problem in a more general form. 
Problem. Given two non-elastic bodies; A and B, such 
that A, moving with a given velocity, 2, shall overtake B; 
moving with a variable velocity, 2, in the same right line ; 
itis required to-find 2, such that the increase of moving 
force found in the motion of B after the stroke may be a 
maximum. 
Solution. Let y= the velocity of B after the stroke. 
By mechanics, =y; and per question, By? —Bx?= 
Av+Bxr 
A+B $ 
maximum, That is, B. ae) —Bxr? = maximum. 
Reduced, 2 Boa—(A+-2B)x7= maximum. 
In fluxions 2Box—(A+2B)2xz—=o, or Bo=(A+2B)s, 
B 
& Snaant te 
Cor. 1. If B be indefinitely greater than A,’ thien its velo- 
city after the stroke will be the same as before, & r==10, 
which is the case in the text. 
Cor. 2. If B=A, then #=!0. 
Cor. 3. If A’be indefinitely greater than B, then r=o. 
