166 
MOVING FORCE. 
} 
Cases of diffi- these maxims to be inconsistent with the common theory. If ifi 
cultY in tlie , , , , .la 
clocirines of 't were admitted, according to the theory, that the pressure at [I 
moving force, the circuiTiference of the wheel is always as Ax(t- — v)®we ’ p, 
can hardly suppose Mr. Smeaton to have been so little ac- 
quainted with the principles of calculation as not to have been 
aware, that the maximum effect must consequenily be as ■ 
Axe®. The principle of the fis wm agn^es still more remark- 
ably with the common theory in cases of rotatory motion ge- ^ 
nerated about fixed axes, as I have already observed at page r 
117. But although the rotatory force of a body in motion is, t 
according to the common theory, as the squaie of its velocity, , 
I do not see why that agreement with the principle of the t 
vis viva should be brought as an objection against it. The chief « 
object in discussion is to ascertain upon which principle the 1 
most consistent explanation of the facts is to be obtained in 
cases where the two measures disagree. 
It appears to me, that Mr. Smeaton's four maxims on under- 
shot water-wheels may all be comprehended in one, expressed 
thus : T/iai in cases where the inaximum effect is produced, it is 
nearly as the quantity of water multiplied by the effective head*. 
But the theory is founded on the supposition, that, in all cases 
the pressure at the circumference of the wheel is as (c — v)®, 
and if it were so, the maximum effect would, no doubt, be 
produced when v = By the mere inspection, however, 
of the results which I have slated above, it will be seen, that 
the pressure at the circumference of the wheel is not as (c — u)® 
and therefore the maximum effect cannot be produced when 
the wheel moves with one-third of the velocity of the water. 
I have to regret that I cannot at present refer to M. Bossut’s 
experiments on water-wheels. It is observed, however, by 
M. du Buat, that, according to these experiments, the maxi- 
mum effect was produced when the velocity of the wheel was 
^ that of the water, which corresponds very nearly with Mr. | 
Smeaton’s conclusions. 
• It should be observed, that the niaximuiu effect was not always 
produced at the same relative velocity. 
From 
