518 Gravitation and the Soaring Birds, [June, 
plane into those forces in the same ratio that the direction of the 
force bears to those directions. 
To illustrate these propositions we will suppose a force, e f, in- 
clined 18° from ¢ d, to operate on the plane A B, with a value of 
sixty foot pounds per second. The plane would instantly resolve 
/ _ this force into twelve foot pounds in its own plane in the direction 
2, and forty-eight foot pounds in the direction ¢-d, at right angles 
to it, when it would be reasonable to suppose that the twelve 
pounds would drive the plane against friction of air with far 
greater velocity than forty-eight pounds would against air com- 
pression. 
If motion in the direction 2 were resisted to the point of pre- 
vention, all the force, e f, would do work in the direction ¢ æ, 
when the entire sixty pounds would be setting up air pressure, 
and the plane would be in equilibrium in the direction I 2. 
very small force, say one or two pounds, would now drive the 
plane in any direction, say towards 1, with considerable velocity. 
| It is obvious that the sixty pounds of air pressure would be 
enough to supply the twelve pounds needed to balance the force 
acting towards 2, and the one or two pounds additional needed to 
drive the plane towards 1 with a velocity we will suppose of 150 
feet per second. If we suppose the motion of the plane in the 
direction e f to be at the rate of thirty feet per second, it will 
= move in opposition to the direction of the force as fast as it does 
= with its direction, and we will have the anomalous case of a force 
= developing enough force in moving a body to move several such 
bodies through the same space in the same time diametrically 
| Opposite to its own direction ! 
. This seems absurd, and needs rectification to make it tolerable. 
We have entirely overlooked the fact that the moment e f began 
the task of working it abandoned the direction in which 1t re- 
_ sided, and four-fifths of it went over 18° to c d, and one-fifth 
-went over 108° to A B. The direction e f is vacated, it is without 
significance. For all the influence it has on the plane it mightas 
well not exist. There is zow no movement of the plane against 
_ the direction of the force whatever. Vow, the forces working 0° 
_air, and driving the plane towards t, are at right angles to each 
other and do not resist each other. The problem is, the ger 
of a force to drive a plane faster edgeways than flatways throug 
ee E R EREET 
PENA: 
