RELATION OF \VIN(i SHUKACK TO WKIOHT. 129 



()!' this fact llicri' can !»(' no doulit. and the (jncstion arises why 

 this is so. MiiHcnholl' and otlici's who ha\(' interested theniseh'es in 

 this iiHjnirv have answered it from tlie niof|)hoh)iiieal point of \iew. 

 From the entirely coi'rect principle deduced I'l-onT the j)osition of 

 these in\ est i<ja tors, that with increasini'; size the linear diminsions 

 increase in the first, the ma<j;nitude in the second, and the weijiht 

 in the third ratio, they conclude that the win^j; surfacf^ is not to he 

 compared directly with the weii>ht, hut the s(iuare root of this sur- 

 face with the cube root of the weight. In fact, however, the fin^ures 

 thus obtained show no constancy, even when comparing- animals of 



the same mode 'of flio-ht. Thus the fornnila ^t/"".'"!; ffives in the 



l)artrido;e 4. OH, in the sparrow ii.8(), and in the binnblebee ].:>:>. 



If, however, such u 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 morphologically 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 body it thus becomes a question 

 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 strokes 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 

 G.3 mm. makes, as ^larey has shown, about 100 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 3^- strokes in 

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

 In general, one may therefore say that the movement of the wings 

 against the air in many birds of the same mode of flight is of equal 

 rapidity, this being true of the flapping flyers as well as the sailers. 

 Although the smaller flyers h:ive relatively larger wings than the 

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

 wing surface against the air would be slower. 



In view of the biological principle that organs are not greater than 



demanded by their function, we nuist 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 



