THE FORMATION OF ICE CRYSTALS 
atmospheric layer near the earth’s surface. The course 
of formation is shown in Fig. 26c. In the early stage the 
condition is favorable for stellar development, then 
both 7, and 7, decrease to just outside Region I, and 
the crystal is kept under this condition for a considerable 
time. In general, when a crystal is kept under a nearly 
constant condition at a point near the lower border of 
Region I, the ends of branches show the tendency to 
develop into plate or sector form. This can be explained 
as the result of a decrease in the vapor supplied per 
unit area to the crystal surface. The crystal of the form 
shown in Fig. 26a seems to show that a slightly super- 
saturated, homogeneous layer exists near the earth’s 
surface with a thin layer suitable for dendritic develop- 
ment above it. 
Spatial Assemblage of Radiating Type. The condi- 
tions favorable to formations of this type are also clear. 
The early stage is obtained at lower T, and T,,. In the 
case of the crystal in Fig. 27b, T.. is approximately 
—20C and T,, is about +12C. After the formation of 
this primitive stage, 7, and T,, are increased to the 
condition of dendritic development, that is, 7, = —16C 
and 7’, = +15C. Dendritic branches grow rapidly in 
space, giving the crystal of Fig. 27b in about twenty 
minutes. We may interpret the natural crystal of Fig. 
27a as follows: In the upper atmosphere there exists a 
layer, at a temperature of —20C or lower, in which the 
erystal is born; this minute crystal falls through a layer 
characterized by ample moisture and a temperature of 
nearly —15C. The lower layer will be a few hundred 
meters in thickness. 
_ Dendritic Crystal with Small Plates Attached. The 
natural snow reproduced in Fig. 28a is a good example 
of this type. Many small plates are attached in a spatial 
manner to the base crystal of hexagonal type. An arti- 
ficial crystal similar to this is shown in Fig. 28b. This 
crystal is produced by a condition just the opposite of 
that for the preceding case. The base crystal is formed 
in Region I in about fifteen minutes. Then 7, is gradu- 
ally decreased to —24C m two hours. The supply of 
water vapor is also reduced. In this second step many 
small plates extend out in space from various points of 
the base crystal. As the rate of growth of these small 
plates is very small, the development takes nearly two 
hours in this example. When this type of natural snow 
is observed, we may expect a thick layer of temperature 
inversion. The layer near the earth’s surface must be at 
a temperature of nearly —20C and less supersaturated. 
The thickness of this layer is estimated from the data 
of falling velocity to be about 2 km, and above this cold 
layer there exists a warm, well-supersaturated layer 
at a temperature of nearly —15C. The warm layer may 
not be as thick as the cold layer, say, only several 
hundred meters. 
The foregoing descriptions demonstrate the possi- 
bility of inferring the structure of the lower atmosphere 
by a synthesis of the examination of crystal forms and a 
knowledge of artificial snow. In this article we did not 
consider the question of wind. The horizontal com- 
ponent of wind velocity has no sensible influence upon 
219 
our argument, but the vertical component and the tur- 
bulence will have a strong effect. 
CONCLUDING REMARKS 
In discussing the phenomenon of ice crystal forma- 
tion in the atmosphere, the most important factor is the 
problem of supersaturation. As Bennett said in 1934 
[2], “the evidence is merely negative as to whether 
supersaturation does or does not exist, and positive 
evidence is urgently required.” This question is still 
left unanswered. It is very unlikely that more water 
vapor than the critical value of saturation exists in a 
purely gaseous state in the natural atmosphere. Strictly 
speaking, the existence of ample supersaturation of 
water vapor in air cannot be expected, except in some 
special cases such as at the instant of adiabatic ex- 
pansion in a Wilson cloud chamber. Furthermore, in 
this special case the duration of the supersaturation is 
extremely short, say, 10~ or 10~ sec. Supersaturation 
observable in the natural atmosphere is considered to 
mean the existence of minute droplets in saturated air. 
In our artificial snow experiment, the supersaturation 
was defined as the excessive water content in the at- 
mosphere, including both water vapor and minute drop- 
lets. Values of supersaturation as high as 120 per cent or 
130 per cent, referred to in this article, can thus be 
understood. We learned that in a rising air current 
which appeared to be transparent by ordinary illumina- 
tion, a strong beam of light showed a Tyndall phenome- 
non. If a glass plate covered with oil film is exposed to 
the ascending air current for a short time, and then 
examined under a microscope of high magnification, 
a great many minute droplets can be observed in the oil 
film, many of them about 2 » in diameter, the smaller 
ones about 1 yp. These minute droplets are not frozen 
to a snow crystal in the form of droplets, but appear to 
spread on the crystal surface at the moment when they 
are brought in contact with the crystal. In helping the 
erowth of crystals, they act as if they were in a gaseous 
state. The larger droplets, 20-30 » in diameter, behave 
in a manner quite different from that of the minute 
ones. They freeze to the snow crystal as droplets, and 
give rise to a rimed crystal. High values of supersatura- 
tion can be expected in the natural atmosphere, if by 
the supersaturation is meant an excessive water con- 
tent, including water vapor and minute droplets of the 
order of 1-2 » in diameter. This is not unreasonable, 
since in the process of condensation these minute drop- 
lets act as if they were in a gaseous state. Larger droplets 
such as ordinary fog particles do not behave in the 
same manner as do these minute droplets. 
Another point is the relation between the air tem- 
perature and the crystal form. The apparently new 
result described in this article may be interpreted as 
follows: 7, is a factor controlling the rate of heat trans- 
fer liberated by the formation of the crystal and this 
rate of heat transfer determines the form of the crystal. 
Another explanation is that the vapor pressure dif- 
ference between ice and supercooled water at the same 
temperature is a function of temperature, and that this 
