THE PROBLEM OF A FLYING-MACHINE. 



73 



and therefore the difficulty of propulsion of a flying animal, de- 

 creases 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 illus- 

 trate it by many familiar phenomena. The floating of dust and 

 smoke, the suspension of clouds, the slow settling of fine sedi- 

 ments, are examples. As the particles become smaller, the resist- 

 ance of the air or water to falling through it, decreasing as the 

 surface, i. e., as the square of the diameter of the particle (cZ^), 

 while the force of motion or weight decreases as the volume, i. e., 

 as the cube {d^) 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 in- 

 definitely 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 after- 

 glow 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 

 propidsioii, 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 in- 

 cessant 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. 



