NO. 2 DIMENSIONS OF FLYING ANIMALS — GREENEWALT 5 



ment of inertia of the wing muscles and whatever part of the skeleton 

 vibrates with them. If we assume br^ proportional to P (or the weight 

 of the animal) and / to P (the product of wing weight and the square 

 of a distance proportional to wing length) we see that the product fl 

 should be constant for a dimensionally similar series of animals. We 

 have seen, however, from figure 9 that for the whole roster of flying 

 animals the weight of the wing varies with the 3.3 power of the wing 

 length. Hence it should follow that the constant will be proportional to 

 f/i-i^nottof/. 



In figure 10 we have plotted all available data for wing-beat rate 

 against the corresponding wing length. We see that there is a limiting 

 boundary line which does indeed have the slope 1.15. Unfortunately 

 the data for birds are quite limited. I have obtained measurements for 

 hummingbirds and for a few small passerines using high-speed cinema- 

 tography, and Meinertzhagen gives data for a number of large birds 

 whose wing frequencies are sufficiently low to permit visual counting. 

 Even for insects there are insufficient data to show conclusively 

 whether the slope 1.15 is characteristic also for particular families or 

 genera of insects, or whether in these limited ranges a slope of 1.0 

 obtains. Figure 12 would appear to give some support to the latter 

 hypothesis. Here we have placed the insects in four arbitrarily selected 

 groups with decreasing values for // assumed to be constant. It is seen 

 that in quite general terms the various genera appear to fall on lines 

 for which the slope is unity. 



Whatever the proper exponent for / (and for a particular genus it 

 makes little difference) the product // appears to define the flying ability 

 of the animal. This would place the fruitflies at the bottom of the list, 

 with butterflies not much better. The best fliers would appear to in- 

 clude many of the Hymenoptera, certain Diptera genera, and a few 

 Coleoptera. The birds in general seem to be more proficient fliers than 

 the insects, with the hummingbirds at least equal to the best in both 

 groups. 



The hummingbirds again appear to be anomalous, but the data are 

 not good enough to establish quantitative relationships with sufficient 

 precision. Figure 11 is an expansion of the hummingbird region. The 

 best fit for the data appears to be a line whose slope is 1.25 and this 

 slope correlates well with what one would expect from the other dimen- 

 sional relationships for the family. 



It is to be hoped that many more data for birds will become available 

 in order that these relationships can be more precisely established. 

 Ideally, of course, one should have data on wing length, wing weight, 

 muscle weight, and wing-beat rate for each specific individual. Here 



