264 THE STRUCTURE AND LIFE OF BIRDS CHAP. 
often long beyond all justification) we find a certain 
proportion maintained with no great deviation, that 
when their bulk has been trebled their wing surface has 
not at the same time been trebled, in defiance of the 
laws of symmetry and geometry. But, looked upon 
as flying-machines, why do small birds require larger 
wings, in proportion to their bulk, than big birds? 
Since, allowing for his greater weight, the big bird 
has less wing to support him than the small bird, we 
must see what advantages he has that enable him to 
do with less. To begin with, if we compare the sustain- 
ing powers of two wings of different lengths, we shall 
find that the superior power of the long one is altogether 
out of proportion to its superiority inlength. Suppose 
the shorter one to be one foot, the longer two feet, 
long. Then if the two are worked by muscles of 
equally rapid contraction,the extremity of the latter will 
move with a velocity that is far more than double that 
attained by the extremity of the former. And since 
the resistance of the air increases nearly as the square 
of the velocity, it is clear that to judge even by the 
comparative velocities of the extremities is to under- 
estimate by a great deal the superiority of the longer 
wing. Secondly, it has been found by experiment 
that the air passes lightly off the margins of a plane 
surface which moves through it, and so does not offer 
much resistance tothem.! The loss is proportionately 
greater with small planes than with large ones, since 
for each square inch of area they have more margin. 
The resistance of the air in the case of a square plane 
having an area of two square feet, moving ina direction 
' Marey, Vol des Ozseaux, p. 214. 
