56 THE FLIGHT OF BIRDS 
is more conspicuous. The big bird, on the other 
hand, dare not lose al@f€ude in so reckless a way, 
since when he has once lost it he with difficulty 
recovers it. He ploughs steadily on, whereas the 
small bird with a few rapid strokes gains altitude, 
then, like a bicyclist utilising his free wheel, glides 
restfully and rapidly onward, not minding the loss 
of some of the height he had gained. His stroke 
is more rapid, but he is able to take frequent 
easies. * 
I have now compared and contrasted big birds 
and small, but even the biggest birds that fly are 
not very big; as compared with the larger mammals 
they are diminutive. Why, among all the birds 
that fly, are there none that weigh even half as 
much as, for example, a Zebra ? 
Helmholtz, dealing with this subject, produced a 
formula which, backed as it was by the authority of 
a great man, was too readily accepted, regardless of 
the fact that it was not founded on data obtained 
by experiment. There is nothing so misleading 
as mathematics when the premises are unsound. 
Helmholtz started with undeniable facts. Ifa bird’s 
linear dimensions be multiplied by 4, then the area 
is multiplied by 16 (4°), and the bulk, which must 
nearly correspond to the weight, by 64 (4°). So far 
good. He showed that the weight increased more 
rapidly than the supporting area. But when he 
went on to maintain that the power required to lift 
the bird increased at a still more rapid rate—that, in 
the case I have taken, it would be 128 (4+)—then he 
was building a theory without a proper foundation 
* On big birds and small birds see Chap. 1, pp. 18-22. 
