268 
ZAHM. 
it is at once evident that the mileage cost is directly propor¬ 
tional to the load, and inversely proportional to the density 
of the medium, the area of the plane, and the square of its 
velocity. 
The propulsive power may be obtained directly from the 
last equation. Thus, 
11= Wv tan a 
W 2 
2 Ics Av‘ 
This shows that the power varies directly as the square of the 
load, and inversely as the density of the medium, the area 
and speed of the plane. 
This last relation, viz., that if W, ?, and A remain con¬ 
stant, IT varies inversely as v, has been more emphasized 
than the other relations by the various writers on aero¬ 
nautics. It was first proved, though in a different manner, 
by A. Du Roy de Bruignac,* and formally enunciated by 
him in 1875, as follows : “ Providing the angle of a heavy 
plane, moving in the air, be maintained at the minimum 
necessary to sustain its weight, the work of translation 
diminishes as the velocity increases.” Mr. Curtis f gives a 
different analytical proof, and Lord Rayleigh, in his inter¬ 
esting memoir on “ The Mechanical Principles of Flight,” 
demonstrates analytically that “ if frictional forces can be 
neglected, a high speed is all that is required in order to 
glide without energy. Mr. ChanuteJ has shown, by nu¬ 
merical computation, that De Bruignac’s statement may be 
applied to birds and flying machines moving at limited 
speeds, say thirty to forty miles an hour; and Professor 
Langley has concluded from his experiments that the pro¬ 
pulsive power of a material soaring plane diminishes with 
the speed up to at least 66 feet a second, if the edge resist¬ 
ance be left out of the account. 
Nearly identical with the expression for power is the equa- 
* “ Reeherches sur la Navigation Aerienne.” 
f “ Experiments in Aerodynamics,” Langley. 
t “Aerial Navigation.” 
