MOVING FORCE. 
593 
there is invariably a considerable loss of moving force. In 
other words, a portion of the moving force is expended in pro- 
ducing this separation of the particles of the water ; and that 
portion may be estimated by deducting from the whole moving 
force which the water would acquire in falling freely through 
the height of the head, that portion of moving force which is 
found to remain with the water after it has issued. 
The following important proposition relating to this subject, 
is laid down by Daniel Bernoulli, in his Hydrodynamics, page 
2/8. If a jet of water I (fig. 18l issue from the side of a 
vessel A, with the velocity which a body w’ould acquire in fall- 
ing freely from the surface B to C, he says the repuUion of the 
water in the opposite direction to the jet will be equal to the 
weight of a column of water, of which the base is equal to the 
section of the contracted vein, and the height equal to 2 BC. 
This question respecting the amount of what has been 
termed the " reaction of the effluent water," derives additional 
interest from the circumstance of its having particularly engag- 
ed the .attention of Sir Isaac Newton, and from his having 
given a solution of the problem in the first edition of the 
“ Principia,” which he materially altered in the succeeding 
I editions. In the first edition (book 2d, prop, 3/) he infers, that 
I the reaction is equal to the weight of a column of water of 
■ which the base is equal to the area of the orifice, and the height 
I equal to that of the surface of the water above the orifice. In 
Itbe succeeding editions, the subject is more fully discussed in the 
:30thprop. of the second book, where he infers (cor. 4.) that, 
>when the area of the surface B is indefinitely large compared 
>with that of the orifices, the reaction is, what it was afterwards 
in a different manner demonstrated to be by D. Bernoulli. Sir 
Ilsaac Newton further observes, that he found, by admeasure- 
:ment, the area of the orifiee in a thin plate to be to that of the 
^section of the contracted vein, at the point of its greatest con- 
ttraction, in the ratio of /TI I nearly. He takes the reaction, 
tlherefore, to be greater than what he understood it to be when 
Hie published the first edition, in the ratio of 1 nearlj*. 
He refers, however, more to experiment than to theory for a 
solution 
Ca?cs of difti- 
Ciiky in the 
docirines of 
moving force. 
