MOVING FORCE. 
293 
it to be divided into a number of different filaments, and I gave Cases of diffi. 
-culty in the 
up all hopes of ascertaining the actual area of the section of doctrines of 
the stream at that place by measuring its diameter. After force, 
repeated trials I found that when the water issued through a con- 
tracted hole, of the shape represented at G, the jet was quite 
transparent, and the reaction (taking the mean of 12 experi- 
ments with 4 different orifices) was less than the weight of a 
column of water of twice the height of the head and diameter 
of the smallest part of the hole, in the ratio of '665 to 1 . The 
least reaction was as '65 to 1, and the greatest as '86 to 1. By 
measuring the quantity of water delivered in a given time, I 
found the velocity of the jet, at the smallest part of the orifice, 
to be less than that which a body would acquire in falling freely 
from B to C, in the ratio of ‘Q-i to 1 . The highest ratio was 
as '95 to 1 , and the lowest '89 to 1 *. 
From these results it appears, that when the contracted vein 
is not opaque, and when its velocity is nearly equal to that which 
is due to the head, the reaction is nearly equal to what it was 
concluded to be by Sir Isaac Newton and M. D. Bernoulli ; and 
the great apparent difference between Sir Isaac Newton’s first 
and second conclusions arises from his having been misled by 
) f ome experiments to which he alludes. He says — “ Per 
I experimenta vero constat, quod quantitas aquae, quae, per foramen 
* circulare in fundo vasis factum, dato tempore effluit, ea sit, qus 
t cum velocitate praedicta,” [viz. the velocity due to the head] 
‘ non per foramen illud, sed per foramen circulare, cujus 
• diaraetrum est ad diametrum foraminis illius ut 21 ad 25, eodem 
I tempore effluere debetf.” We must presunrse, however, that he 
1 refers to experiments made by others ; for if be had made 
I them himself, he would, no doubt, have arrived at the same 
I results which have since been so well established by various 
• Although these experiments were made since this paper was read 
Ibefore the Society, I have taken the liberty to insert the results, because 
tthey afford a good illustration of the principle which I have endcavour- 
i«d to support, 
f Principia, edit. 3 lib- 2, prop. 3(5. 
authors. 
