PHENOMLXA OF FLIGHT IN THE AXIMAL KINGDOM. 



261 



from the same fomily, in ortler that the only differences shall be those of 

 form, a somewhat constant relation Avill be fonud between the weight of 

 the bird and the surface of its wings. But the determination of this 

 relation should be based upon certain considerations, which have long 

 escaped the attention of naturalists. ]Mr. de Lucy sons'ht to measure 

 the surface of the winus and tfie weight of the body in all tlying 

 animals. Now, toestablish a common unit amonganimalsof such different 

 kinds and forms, he reduced all the measures to an ideal type, of which 

 tlie weight should always be one kilogram. Thus, after having proved 

 that the gnat, which weighs three milligrams, ])ossessed wings with a 

 surface thirty millimetres square, he concluded, in the types represented 

 by the gnat, the kilogram of animal was su[)i)orted by an alar surface of 

 ten square millimeters. By making a comparative table of the measures 

 taken from a great number of animals of different kinds and various 

 forms, he arrived at the following figures : 



From these measurements, in spite of variations in detail, the evi- 

 dent result is obtained, that animals of large size and great weight 

 sustain themselves with a much smaller proportional alar surface than 

 smaller animals. A similar result already shows that the office of the 

 wing in flight is not merely passive, for a sail or parachute should al- 

 ways have a surface i^roportioned to the weight which acts npon it ; 

 considered, on the contrary, from its true point of view, that is to say, 

 as an instrument for striking the air, the wing of the bird should, as 

 ■we shall see, present a relatively smaller surface in birds of large size 

 and great Aveight. The astonishment exhibited at the result of the de- 

 terminations nmde by Mr. de Lucy disappeared when it was remem- 

 bered that there was a geometrical reason wliy the alar surfiice could 

 not increase in proportion to the weight of the bird. In fact, if Ave 

 take two objects of the same shape, two cubes, for example, of which 

 one shall be twice as large in diameter as the other, each one of the 

 faces of the larger cube will be four times as large as the corresponding 

 face of the smaller, while the Aveight of the greater cube will be eight 

 times that of the lesser one. For all similar geometrically solids, the 

 linear dimensions having a stated relation to each other, the surfaces 

 are as the square and the weight as the cube of their similar linear di- 

 mensions. Two birds of similar form, but haA'ing, one of them, the 

 spread of the wings from tip to tip twice as great' as in the other, Avill 

 haA'e respective wing surfaces in the proportion of 1 : 4, and Aveight as 

 1 : 8. M. P. Demondesir, who applied these principles before me, 

 thought that he had found in them a reason for the smaller size of 

 birds are capable of flight, while those of a larger kind, such as os- 

 triches and cassowarys, do not fly; he observes that if these birds had 

 as large wings as the heron, in proportion to their weight, they could 

 not fold them completely, and would drag them as long and embarrass- 

 ing appendages. These observations would be correct according to the 

 theory of "sailing" flight, but in "rowing" flight, the anqylitude of the 



