THE PROBLEM OF A FLYING-MACHINE.
and therefore the difficulty of propulsion of a flying animal, decreases in the same ratio. The one varies directly, the other inversely, as the size.
This is a principle of very wide application, and I stop to illustrate it by many familiar phenomena. The floating of dust and smoke, the suspension of clouds, the slow settling of fine sediments, are examples. As the particles become smaller, the resistance of the air or water to falling through it, decreasing as the surface, i. e., as the square of the diameter of the particle (d 2), while the force of motion or weight decreases as the volume, i. e., as the cube (d 3) of the diameter—evidently the force decreases much faster than the resistance, and therefore the ratio of force to resistance, or the effective force of motion, becomes less and less, until in very small particles it is a vanishing quantity. For this reason it matters not how great the specific gravity of a substance may be, if the particles are only small enough they will float indefinitely in air or in water. Particles of gold may be made so small by precipitation from solution that they will require months to settle. Krakatoa-dust (if that be the true cause of the afterglow and of Bishop's ring) remained suspended in the air for more than two years. The perennial blue of the sky and of mountain-lake water is due to suspended particles.
Now, this principle applies not only to resistance of the air to the force of gravity in falling bodies, but also to resistance of the air to the force of propulsion in flying bodies. As a flying animal becomes smaller (as in the smaller birds and in insects), a larger and larger proportion of the whole flight-energy is consumed in propulsion, and a less and less proportion is necessary for rising. On the other hand, as a bird becomes larger, a progressively larger portion of the whole flight-energy is necessary for rising, and less and less is necessary for propulsion, until finally at the limit the whole is necessary for rising. Beyond this, of course, flight is impossible. This explains why large birds like the condor rise with difficulty; but once up they sail with ease and grace, while small birds and insects rise with ease, but require rapid and incessant fluttering in progressing.
5. Application to a Flying-Machine.—Many readers who have followed me thus far with entire assent will probably object right here that, while all this may be true of flying animals, it may not be true at least to the same extent—i. e., the limit may
- Marey has lately ("Nature," vol. xxxvii, p. 369, 1888) shown that there is still another reason for the greater ease of flight after the bird is well on its way. In starting, the wing, except at the very beginning of the stroke, pushes against air which is already in motion in the same direction as the wing itself; but in swift flight the whole stroke is against dead air, for the air beneath the wing is continually renewed by the motion of the bird.