MOVING FORCEi 
299 
The theory of this machine has occasionally occupied the 
attention of many distinguished mathematicians, and M. Euler doctrines of 
has given two elaborate treatises on its principles in the memoirs lorcc. 
of the Berlin Academy for 1750, p. 311, and for 1751, p. 27 1. 
His demonstrations relating to this subject are very compli- 
cated, and they do not appear to have been adopted by succeed- 
ing authors. 
Mr. Waring, of America, has given quite a different theory, 
twhich has been approved of by several good writers on 
[hydraulics. He concludes that the greatest effect will be pro- 
duced when the velocity of the orifice is half that of the issuing 
vwater ; and that this effect will be nearly the same as that of a 
V well -constructed undershot water-wheel*. 
The explanation which I have offered of the action of the 
'.water on this machine is different from any other that I have 
lhad an opportunity of consulting. I offer it, therefore, merely 
jas an attempt to solve an intricate problem. 
If it were possible for the water to issue with the velocity duo 
I to the pressure, it is obvious, if my explanation be right, that 
:although a very large proportion of the moving force of the 
Twater may be communicated to the machine, moving with a 
.moderate velocity, the maximum of effect can only be obtained 
tby an infinite velocity. But when the water issues with a 
vvelocity which is less than what is due to the pressure, as must 
jalways be the case in practice, the velocity at which the 
tmaximum of effect is produced, may be found as follows. It 
>should first be ascertained by experiment how near the issuing 
'.velocity can be brought to that which is due to the pressure. 
iFrom the experiments which I have made, I have been led to 
^conclude that no greater issuing velocity can possibly be obtain- 
ced from a machine of this kind than what is due to *8 of the 
{pressure. If this conclusion be correct, it follows that, 
\whatever may be the issuing velocity of the water, a moving 
t force, equal to ^ of the moving force which is necessary to 
{generate that velocity in the water, when falling freely, is 
• American Philos, Trans. voL 3. p. 191 and 192. 
expended 
