2 Trans. Acad. Sci. of St. Louis. 
Hence I use the familiar hydraulic formula 
vy? = 2gh 
in which 2g is approximately 64 and h is the “‘ dynamic head”’ 
of the current whose value is 
OS NON II 
A a ES ape ES Ton p Ure Ye [IT] 
yap f « Bepepets 
Hence v = aoe ORCI ue ine Pere ig 
if A = mr’, and w = 0.08. 
Substituting for » in the expression for the kinetic energy, 
we have the Kinetic Energy of the air-current, and hence the 
work done per second by the motor-driven propeller is 
Pee Pe oe [IV] 
2 
Kg =e (el 
29 \Aw/ ~ ¢ 
so that we have for the net horse-power actually exerted, 
dividing by 550, the horse-power-work in one second, 
DP. Sr si 
FL ea gee LG ay UN tea es [V] 
approximately. 
This formula gives the horse-power required by means of a 
propeller of radius r to maintain a steady pull or thrust of P 
Ibs. If there are two or more propellers acting without the least 
interference, then their combined area is represented by 
Arar. 
In the formulas [III], [IV], and [V] r is the radius of the 
circle equivalent in area to the combined area of all the propellers. 
The above case may be illustrated by a suspended frame 
carrying a motor and propellers with horizontal shafts in a yard 
or a large laboratory. The frame should be anchored by a 
cable attached to a spring balance, or, passing over a light and 
easily running pulley be attached to an adjustable weight P. 
