268 PROCEEDINGS: BOSTON SOCIETY NATURAL HISTORY. 
however, frictional resistances interfere, the formula becomes, 
(2) d = A e~ 
Kt 
27T 
sin — t 
A 1 
(3) 
Hence, K = 
—log d Tj 
A log e sin 27r t 2 
or if t = T x 
■—log; d 
K = ATj log e 
where K is a constant dependent upon the friction, e is the base of 
the Napierian system of logarithms and T x is the time of a complete 
vibration, which may be different from the T, representing the time 
of vibration when not under the influence of friction. 
The plan was, then, to attach the wing of some large butterfly or 
moth to the end of a short, light pendulum in such a way that it 
would either fan against the air, or cut through it, and then to 
observe the ratio of damping of the pendulum’s vibrations. A 
drawing of the pendulum with a wing attached is given in Plate 1, 
Fig. 3. The wing is here shown in the position for “cutting or glid¬ 
ing” through the air. It would be in the position for fanning against 
the air, if it were rotated 90°. The pendulum was made of brass 
and steel, the ends being of brass and the slender middle portion of 
steel. Its vibrations were read off upon an arc graduated in milli¬ 
meters. The readings were certainly accurate down to 0.5 mm. 
The pendulum was hung upon a steel knife edge (n, isr, Fig. 3), 
which rested upon Arm level glass bearings. The pendulum was 
24.21 cm. long, and weighed 19.61 grams. Its time of vibration 
(T x ) was 0.877 seconds. This rate of vibration was practically 
unaltered when a wing was fastened to the end of the pendulum, 
the reason being that the wings were very light, the heaviest, that of 
Sarnia cecropia, weighing only 0.038 grams. The wing to be experi¬ 
mented upon was fitted into a deep, narrow slot at the free end of 
the pendulum, and then cemented in by means of a little melted 
beeswax. It thus became a perfectly rigid part of the pendulum 
itself. 
The pendulum with wing attached was deflected through a known 
arc, read off upon the millimeter scale, and its reading at the end of 
the first swing carefully observed. Then if A be the initial deflec¬ 
tion, which we may call unity, and if d be the reading after the first 
swing, the ratio of damping is given by the expression -r. In experi¬ 
menting with a fore wing of Sarnia cecropia “fanning the air,” it 
