1904; Laws, 1941; Blanchard, 1950; Magono, 
1954] and the calculations [Liznar, 1914; Spil- 
haus, 1948; Imai, 1951 and McDonald, 1954] 
that falling drops flatten more and more as the 
size increases (Fig. 2). The path of horizontal 
incident light through a drop of 2.4 mm radius 
is shown in Figure 3. The rainbow angle has de- 
creased to 25° from 42° for a sphere. It is also 
important that now some rays suffer total im- 
ternal reflection while in a spherical drop only 
partial reflections are possible. Probably such a 
rainbow is much less intense than that of spheri- 
cal drops. 
Figure 4 shows calculated changes of rainbow 
angle for an elliptical cross section [Moebius, 
1907] and measurements of this angle for a 
flattened drop as a function of the angle between 
the major axis of the drop and the incident light. 
From these results it is clear that flattened 
FRIEDRICH E. VOLZ 
drops with a low Sun will lead to rambows whose 
radii at the apex decrease as the drop size in- 
creases. This distortion of the rainbow is im- 
portant for drops greater than 0.25 to 0.6 mm 
radius (Fig. 2). Larger drops of different size 
can contribute nothing to the rainbow of small 
droplets. For sideways scattering, however, the 
drops have a circular cross section and hence the 
rainbow angle at the foot of the bow is the same 
regardless of the drop size. These statements 
agree well with the observations (Fig. 1). 
Raindrop oscillations—Of great imterest both 
to the physics of rain and to the theory of the 
rainbow is the problem of drop oscillations. 
Early photographie observations by Lenard 
[1887] show that drops falling down a tube os- 
cillate between vertically elongated and flattened 
ellipsoidal shapes, in addition to the flattening 
mentioned earlier. The oscillations of the drops 
—. DROP RADIUS r (mm) 
Sane u 1.0 i520 3.0 40 50 60mm 
270 600 |1000 pre—- 2000 3 Tie © 
at 
EDDY FREQUENCY 
_>>~_ (RIGID SPHERES) 
. 
~ 
x 
. 
\ BLANCHARD 
—* DROP DIAMETER (cm) 
04 06 Ale) (4 3 4 6 8  |Ocm 
6 
4 Vy 
= S= 5 
V,{cm sec™'] 2 7 INTERRUPTION 
WAVELENGTH 
{ 10% 
TERMINAL 
6 FALL VELOCITY 
A 
a 
a 
2 
Ww | i 10 10 102 
Wa 
Yea 
— > DROP MASS (mg) 
Fic. 5—Some properties of raindrops plotted against the drop size and 
the drop mass; upper part: oscillatio 
n frequency v by Rayleigh, and eddy 
frequency f behind a sphere by Moeller as a function of the Reynolds’ num- 
ber Np of falling water drops; lower part: terminal velocity vr of water 
drops, and spacing s = v;/y of interr 
uptions in raindrop illumination 
