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. xi). 



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 



