84 
Proceedings of Royal Society of Edmlurgli. 
[SESS. 
W 
Since must in all practical cases be a small quantity com- 
pared to y, the velocity of the object will be almost equal to that 
of the wind in a few seconds. 
In the example of the bird treated as an inclined plane, and just 
supported by a constant relative velocity of wind, the horizontal 
acceleration is g tan a, where a, as before, is the inclination of the 
plane to the horizontal. For the ratio of the horizontal to the 
vertical pressures, due to the wind, is 
GA . . . 
sin^ a cos a 
GA 
tan a 
Vr Sin*^ a 
Therefore since the latter force is by hypothesis equal to the weight 
of the bird, and its acceleration under that would be g, its accelera- 
tion under the former will be g tan a. 
When a is given, the value 54° 44' required to bring about the 
least value for the relative velocity u — 
g tan a = 45 feet per second. 
There is no way out of this difficulty. 
Plenty of energy is in the air, enough to support many flying 
machines, but one must be very quick to seize it. 
Such things as upward currents in the air no doubt exist, and 
birds continually make use of them ; to currents like this must be 
attributed the more inexplicable feats of sailing, which Gheel some- 
times perform, round the tops of hills. 
The vertical velocity of these currents in order to support the 
bird should be ; 1 7 feet per second for these, at least ; being 
a velocity equal to their ultimate rate of falling. Such currents 
cannot often occur. 
In cyclonic weather there is supposed to be a general upward 
current of the air, but it probably does not exceed 6 inches per 
second, and birds notoriously fly best in anticyclonic weather, 
when the very opposite conditions prevail. 
