RELATION OF WINU SURFACE TO WEIGHT, 129 



Of this fact there can he no doiiht, and the question arises why 

 this is so. ]\Iii]leiiliotf and others who have interested themselves in 

 this inquiry liave answered it from the morp]iohj*>ical point of view. 

 From the entirtdy correct principle deduced from the position of 

 these investigators, that with increasing size the linear diminsions 

 increase in the first, the magnitude in the second, and the weight 

 in the third ratio, they conclude that the wing surfact^ i> not to l>e 

 compared directly with the weight, but the sfjuare root of this sur- 

 face with the vuIh' root of the weight. In fact, however, the figures 

 thus obtained show no constancy, even when comparing animals of 



the same mode of flight. Thus the fornuda ^~t^,^5 ffives in the 



'^ \' weight ^ 



l)artridge 4.08, in the sparrow 2.86, and in the buml)lebee I.;');'). 



If, however, such a constancy existed, which we see is not the case, 

 the paradox that lies in the relative increase of wing surface with 

 decreasing weight of body would by no means be set aside; but in 

 similarly formed flying creatures it is not so essential that they shall 

 be morphologicall}^ alike as that all shall perform the task of over- 

 coming weight equally well, and thus be functionally the same. 



In sustaining and propelling the bod\' it thus becomes a ({uestion 

 of the power of the wings to press down upon the air, and this 

 power depends not only on their size, but in a very great degree upon 

 the swiftness of their movement against the air and its consequent 

 resistance. Hence, as is evident, the flapping flyers, whose wings 

 move in a comparatively small angle, have greater lifting power 

 the longer their wings and the more strolvcs they make in a second. 



A sparrow has a wing length of about 10 cm. and makes about 12 

 wing strokes in a second; a bee with a wing length of approximately 

 (';.;] nmi. makes, as Marey has shown, about 190 strokes in a second. 

 G.3 times 190 about equaling 100 times 12. The slow wing movement 

 used by the sailing birds when needed shows the same. The stork 

 has a wing length of 68 cm. and makes 1| strokes in a second, and 

 the laughing gull with a wing length of 39 cm. makes 31 strokes in 

 the same time. In these instances also the results are not dissimilar. 

 In general, one ma}^ therefore say that the movement of the wings 

 against the air in many l)irds of the same mode of flight is of equal 

 rapidity, this being true of the flapping flyers as w'ell as the sailers. 

 Although the smaller flyers have relatively larger wings than the 

 greater, one can not for this reason assert that the movement of the 

 Aving surface against the air would be slower. 



In view of the biological principle that organs are not greater (han 



demanded by their function, we must conclude from the known facts 



that the smaller animals need relatively larger wings to accomplish 



what the larger and heavier attain with their relatively smaller ones, 



SM 1904 9 



