20 THE FLIGHT OF BIRDS 
put big and small bird in this respect more or 
less on a level. They appealed to the elementary 
principles of geometry. If you take two cubes, 
a side of one of which is twice the length of the 
other, the larger one is in bulk eight times as great 
as the smaller one, but its surface area is only four 
times as great. This holds true of other figures 
of three dimensions that are not cubes. Magnify 
a bird till it is eight times its former bulk and you 
will only have multiplied its surface area by four. 
In order, then, to compare bird with bird correctly, 
you should take (so say these theorists), the cube 
root of its weight (for the weight is practically the 
bulk, i. three dimensions multiplied together) 
and the square root of its surface area (since that 
is two dimensions multiplied together). When we 
adopt this method we find the preponderance of 
the small bird in point of wing-area per pound 
weight not so very great. And we may, if we are so 
constituted, derive a certain comfort from feeling 
that we are following out geometrical principles. 
But these principles have, it must be owned, in the 
case of some species been widely departed from. 
What are we to make of the legs and neck of the 
Flamingo ? If any small bird of ordinary build 
were symmetrically enlarged, should we ever arrive 
at elongations so enormous ? It is, of course, true 
that if the bulk of a small bird were multiplied 
many times, and the area (not the bulk) of his wings 
increased in proportion, he would have a greater 
expanse of wing than his muscles could possibly 
work. If the Stork had a wing-area as great in 
proportion to his weight as the Swallow, then 
