MAYER: COLOR AND COLOR-PATTERNS. 
269 
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 3d only 0.919 as 
great as that of the 2d, 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-membrane 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 Natural 
Selection would operate to keep it unaltered. 
A wing of Sarnia cecropia cut so as to give it the same shape and 
dimensions as one of Morpho 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 Sarnia cecropia wing, that when 
it was vibrated in the position for “ cutting through ” the air, the ratio 
of damping was 0.991. It will be remembered that, Avlien 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¬ 
tion (4), K = 
-log d 
AT l log e 
Thus for fanning, 
= 0.917 and T t 
0.877 
Making A unity, 
K 
—log 0.917 
0.877 log e 
= 0 . 1 . 
In cutting through the air, ^ =:0.991 and T l as before = 0.877. 
—log 0.991 
—- - - 0 01 
“0.877 log e ~ * 
Hence in this case K 
