THE MACHINERY OF FLIGHT 77 
is not far to seek. The small bird would gain but 
little in lightness by the aeration of his bones, since 
each bone consists almost entirely of its exterior 
shell. The big bird, with his stout, bulky bones, 
will gain far more. Here is a case in which we may 
appropriately quote some geometrical facts. We have 
seen above that if we take two cubes, the side of one 
_ of which is twice that of the other, then a face of the 
larger one is four times the area of a face of the 
smaller one, and the cubic content of the larger is 
eight times that of the smaller. Thus an increase 
in the length and girth of a bone means a far greater 
increase of the space within the outer shell. Obvi- 
ously,then, a big bird stands to gain more in lightness 
by the hollowing of the bones. How he manages 
to do with so very little marrow —the bones having 
only a very thin lining—is another question to which 
I hope to return (see Chap. x1). 
How much the bigness of the bone has to do with 
pneumaticity is made clearer by the facts which 
follow. If we make measurements of the humerus 
of a Skua, or other Gull—the Gulls have very little 
aeration—and of an Eagle as the representative of 
the birds which have a great deal, we find that the 
girth of the Eagle’s bone is disproportionate to the 
bird’s superiority in length of wing. And the 
explanation, no doubt, is this; the Eagle requires 
much greater strength in his wing-bones than does 
the Gull. Even a small increase in length of wing 
means a considerable increase in the pace at which 
the extremity will move. And, as we have seen, the 
resistance of the air increases as the square of the 
velocity. It is easy to see, then, that the Eagle and 
