224 
THE FLIGHT OF BIRDS AND INSECTS. 
Oct., 1889. 
wings, moving horizontally like those of an insect, but rotating 
always in the same direction (Sir G. Cayley’s model, in fact), 
forms, probably, the most economical flying arrangement, fora 
given wing surface, which is mechanically possible, the recipro¬ 
cating motion of the insect’s wings, though on the same 
principle, is the most wasteful of all methods of flight in use, the 
energy required to support a given weight being, as appears 
from some not-too-satisfactory experiments of mine, between 
three and four times the amount that would be necessary if 
the same wings could rotate always in the same direction. 
A method so wasteful must be confined to the smaller flying 
animals, whose wings, enormously large in proportion to 
their weight, are a source of economy which balances this 
waste. 
There is another reason why this method of supporting a 
weight in the air must be confined to small animals. Though 
this model with oscillating wings supports part of its weight 
when in motion, as shown by the rise of the scale-pan, it can¬ 
not be made to rise by itself, for even if made light enough, 
which would be difficult, the strokes are so slow that during 
each stroke the framework, which, of course, is acted on by 
a force equal and opposite to that which drives the wings, 
would acquire considerable velocity ; in fact, the framework 
would move and not the wings. That in the insect the 
opposite is the case results from the extremely rapid reversals 
of the motion of the wings, and this sets a limit to the size 
of the animals which use this method of flight. For since 
(as may be shown mathematically) the velocity of the tips of 
the wings cannot be increased without great waste of energy, 
and the strokes cannot be shortened without a similar waste 
arising from the springing back of the wing at the end of 
of each stroke, it follows that the larger the wings the slower 
must be their vibrations, and hence the greater must be the 
oscillations of the body of the animal compared with those of 
the wings. Hence, this method of flight must be confined to 
creatures of small size. 
The pressure of the air acts, of course, directly on the 
wings, which in their turn support the body, and the upward 
pressure on each wing increases with its increasing velocity 
from the beginning to the end of each stroke. So that, not 
being perfectly rigid, each wing rises a little during the stroke, 
and springs down again when it stops at the end, thus 
describing a kind of horizontal figure of eight ( v oo ). This 
has been illustrated by Dr. Pettigrew, in his “Animal 
Mechanism,” but it does not seem to have the importance he 
supposes—in fact, any wing not perfectly rigid must move in 
this way ; that of the model described above does so, as may 
