1872.] Natural and Artificial Flight. 29 
thus derive a power of ascension, there are geometrical 
reasons why the greater weight of the larger bird should 
not have a proportional wing-surface. Consider two objects 
similar in shape,—for instance, two cubes,—one having 
twice the diameter of the other, then each of the faces of 
the larger cube is four times the size of each face of the 
smaller cube, while the larger cube has a weight eight times 
that of the smaller. This is but a familiar illustration of 
the fact that all geometrical solids with linear dimensions, 
bearing a stated relation, have their surfaces proportioned 
as the square, and their weight as the cube, of their similar 
linear dimensions. So that two birds of the same form, but 
one having a width of wing from tip to tip twice that of the 
other, will have their wing-surfaces proportioned as I: 4, 
and their weight as 1:8. Applying these principles, Dr. 
Hureau de Villeneuve has endeavoured to determine the 
extent of wing that would enable a bat of the same weight 
as a man to fly, and he has found that each of its wings 
would be less than three metres, or a little more than three 
yards, in length. 
The most important points in the consideration of the ul- 
timate capability of man’s flight still remain. They are— 
can man exert sufficient force? and can that force be me- 
chanically employed to raise himself from the ground? 
The second of these questions is yet to be answered; the 
first has been solved by the experiments of M. Marey, of the 
College of France. It is evidently only necessary to con- 
sider the power of a bird to raise its own weight, because, 
when once in the air, by the simple extension of its wings, 
the bird is converted into a natural parachute, counteracting 
the direct action of gravity, so that it does not acquire even 
the descending velocity of nearly 17 feet in the first second, 
but traverses a much less space,—in fact, a space that does 
not increase as the square of the time. Therefore it follows 
that a bird has not, as calculated by Borelli and Navier, to 
employ force to countera¢t gravitation, because it finds a 
counter-balance in the resistance of theair. The force, then, 
to be expended is only that necessary to prevent the fall for 
a fraction of a second. Now, M. de Lucy asks, what is the 
space traversed in one-tenth of a second by a body left to 
itself? This space is 19°29 inches; but as a bird is supplied 
with a large surface of suspension the space may be esti- 
mated as much less, orat 25 centimetres, in English measure 
9°84 inches. The bird, then, has to expend a force sufficient 
to raise itself, say a weight of 1 kilogramme, or about 24 lbs., 
9 or Io inches at each flapping of the wing. Now, 
