Moving Force. 243 
That this is the effective moving force, may 
be shownealso in another manner, as follows : 
The absolute velocity of the water after it 
has left the machine will be V—v, and (V—v)? 
ree 
will be the head which would produce ‘that 
velocity ; which being multiplied by aV, the 
quantity of water delivered in a second, gives’ 
a V (Y—)* for the moving force which re- 
4g 
mains with the water after it has left the 
machine. 
If that be deducted from aVh, the whole 
moving force of the water, there will remain 
i= 
aVh— aV ———_ Wah 
force, which wn be found to be equal to 
¢ ou) prowl yg oft dh. 
2av ht ap —2a agt e effective mov- 
for the effective moving 
ing force stated above. 
The theory of this machine has occasionally 
occupied the attention of many distinguished 
mathematicians, and M. Euler has given two 
elaborate treatises on its principles in the 
memoirs of the Berlin Academy for 1750, 
p- 311, and for 1751, p. 271. His demonstra- 
tions relating to this subject are very compli- 
Hh2 
