30 Mr. Davies Gilbert on the expediency of assigning 
I =. 16.0954 feet the log. 1.2067016 
If the angular velocity of a body in one 
second of time be expressed in whole 
revolutions in degrees, in minutes, or in 
seconds, the absolute velocity will be = . 
R X 2 cr = Rr X 6.2831853 . . . log. 0.7981799 
D°xX 0.0174533 . . log. 8.2418774 
M' X ' =: M'r x 0.00029089 . log. 6.4637261 
360 x 60 
S" X ^ =:S"rx0.00000484817 log.4.6855748 
360x60x60 
The first of these functions reaches the maximum, when y 
exceeds .75 or ^th by two or three thousandths ; and the 
second wheny is about .83. 
From an inspection of the Table, it appears that when the 
machine is moving with the velocity productive of its greatest 
relative effect, namely, at three quarter parts of the velocity 
with which the fluid would issue under a pressure equal to 
that of the actual head, that the duty exceeds by a mere 
trifle one half of the efficiency expended ; and from thence it 
obviously follows, that the recoil engine cannot in any case be 
y 
The Duty for a 
given expenditure 
of fluid, on the 
function 
V^l+y^Xy—1/3 
y 
The Duty performed 
by the actual 
expenditure of fluid, 
or the function 
.05 
.04994 
.05 
.05000 
.10 
.09950 
.10 
. 10000 
•15 
.14830 
•*5 
.14997 
.20 
.19596 
.20 
.19984 
.25 
.24207 
•25 
.24952 
•30 
.28621 
•30 
.29881 
•35 
•32794 
•35 
•34762 
.40 
.36681 
.40 
.38607 
•45 
.40234 
•45 
.41159 
.50 
.43402 
.50 
.48525 
•55 
•46132 
•55 
.52649 
.60 
•48371 
.60 
.56410 
.65 
.50062 
.65 
.59706 
.70 
.51146 
.70 
.62432 
•75 
.51563 
•75 
.64454 
.80 
.51250 
.80 
.65632 
.85 
.50145 
.85 
.65812 
.90 
.48183 
.90 
.64824 
•95 
•45297 
•95 
.62479 
1.00 
.41421 
1.00 
.58578 
1.05 
.36488 
1.05 
.52908 
I.IO 
.30427 
I.IO 
•45233 
1.15 
.23170 
1.15 
• 353 ” 
1,20 
. 14646 
1.20 
.22878 
1.25 
.04785 
1.25 
.07660 
1.28 
— .01803 
negative 
1.28 
—.02929 
negative 
