296 
MOVING FORCE. 
Cases of diffi- authors, and he would have stated the above ratio to b« as IQ'S 
culty in the 
doctrines of nearly. 
moving force. jjjg demonstration of the reaction requires that the velocity 
at the contracted vein shall be equal to that which is due to the 
head. Now that velocity cannot be determined by measuring 
the imperfectly contracted -vein in cases of water spouting 
through a hole in a thin plate. 
We may safely indeed infer, that, in such cases the velocity 
is considerably less than what is due to the head. For, the jet 
being opaque, some moving force must be expended in separat- 
ing the particles from each other, and the distance to which the 
jet from such an orifice is projected on a horizontal plane, con- 
firms that inference. The demonstration, therefore, of the 
reaction can be properly applied to such cases only 'as those 
where the water, issuing through a tube properly contracted, 
acquires the velocity nearly which is due to the head, and in 
those cases the experimental results agree, as I have slated, 
remarkably well with the demonstration. 
These results agree also with the explanations which have 
been given of moving force. If we suppose the velocity of the 
jet to be equal to that which is due to the head, and the vessel 
to move uniformly in the opposite direction CD with the same 
velocity, the water will be at rest as it issues. 
Let a represent the area of the smallest section of the orifice. 
Then while the vessel has moved through a space = 2 BC, a 
quantity of water represented by ox2BC has descended from 
B to C, and has been brought to rest. But the reaction is = a 
X 2 BC, and this multiplied by 2 BC, the space through Avhich 
it has acted, gives ax '2 B Cl* for the amount of the moving 
force produced, which is exactlj' the quantity of moving force 
necessary to raise the column a x 2 BC to the height BC, and to 
project it with the velocity 2 BC. For, a moving force 
=ax2BCxBC will raise that column from C to B, and an 
equal moving force will generate the velocity 2BC in the same 
column, therefore 2a x 2BC x BC =a x 2 B CP is the whole 
moving force necessary to restore that column to the place and 
condition 
