MAYER: COLOR AND COLOR-PATTERNS. 195 



was found, as the mean of many trials, that this ratio of damping 

 was 0.919, that is to say, the amplitude of the 2d swing was 0.919 

 as great as the amplitude of the 1st, that of the od only 0.919 as 

 great as that of the "id, and so on. The scales were then carefully 

 removed from the wing-membranes, by means of a camel's hair brush, 

 and by again testing the vibrations it was found that the new ratio of 

 damping was 0.917. This is so near the value of the ratio of damp- 

 ing with the scales on (0.919), that it may be considered identical, 

 the difference being due to errors of experimentation. 



Hence we must conclude that the presence of the scales upon the 

 wing-raembrane has not altered, appreciably, the co-efficient of fric- 

 tion which would exist between scaleless wing-membranes and the 

 air. The results indicate rather, that when the scales appeared upon 

 the wings of the scaleless, clear-winged ancestors of the Lepidoptera, 

 the co-efficient of friction remained unaltered. This tempts one to 

 the further conclusions, that the co-efficient of friction between the 

 air and the wings was already an optimum in these clear- winged an- 

 cestors before the appearance of the scales, and therefore that Xatural 

 Selection would operate to keep it unaltered. 



A wing of Samia cecropia cut so as to give it the same shape and 

 dimensions as one of ]\lorpho menelaus, gave an identical damping 

 ratio. I conclude that the co-efficient of friction may be the same 

 for both moths and butterflies, at least for those which move their 

 wings at about the same rate in flight. 



It was found in the case of the Samia cecropia wing, that when 

 it was vibrated in the position for " cutting through " the ah, the ratio 

 of damping was 0.991. It will be remembered that, when the wing 

 " fanned" the air, this ratio was 0.917. We may find the ratio be- 

 tween the resistance encountered in " fanning " and that encountered 

 in "gliding" through the air by substituting these values in equa- 



— loff d 

 tion (4\ K = ,^ , • 

 ^ ^ ATj log e 



d 

 Thus for fannuig, -r^ = 0.917 and Tj =z 0.877. Making A unity, 



—log 0.917 



K= ..^-f, = 0.1. 



0.8/ / log e 



d 

 In cuttms: through the air, -r- ^0.991 and T, as before = 0.877. 



,r . . —log 0.991 



Hence m this case K = .. ^^- , = 0.01. 



0.8/ / log e 



