146 
PHYSICS: I. LANGMUIR 
nucleus formed by applying liquid air for one minute causes a visible de- 
posit to grow more rapidly (with the lower part of the bulb at 170°). 
But the nucleus obtained with temperatures above about 78° are not 
any more effective than those formed at 78°. 
A calculation similar to that above shows that the deposit formed in 
one minute at 78° contains 2 . 5 X 10^^ atoms per square centimeter, or 
enough to cover 25/1000 of the surface. If we consider that the surface 
of the glass contains elementary spaces each capable of holding one 
cadmium atom, the chance that any given cadmium atom will be ad- 
jacent to another is 1 —(1 — 0.025)^, or 0.16. When the surface is 
allowed to warm up, the single atoms evaporate, but the pairs remain. 
The surface is then covered to the extent of 16% of 25/1000, or 4/1000. 
About 2% of the atoms striking such a surface will fall in positions 
adjacent to those atoms already on the surface. With cadmium vapor 
at 170°, 1.4 X 10^^ atoms per square centimeter strike the surface 
each second, so that 2.8 X 10^^ would condense in the first second 
around the 4 X 10^^ atoms remaining on the surface. Thus in only a 
few seconds the whole surface becomes covered with a layer of cadmium 
atoms. This explains why a surface only partially covered with cad- 
mium atoms can serve so effectively as a nucleus. If a much smaller 
fraction than 0.025 of the surface is covered, however, there is a long 
delay in completing the first layer of atoms, so that the visible deposit 
is formed much more slowly. 
The above experiments prove that the range of atomic forces is very 
small and that they act only between atoms practically in contact with 
each other. Thus a surface covered by a single layer of cadmium 
atoms behaves, as far as condensation and evaporation are concerned, 
like a surface of massive cadmium. This absence of transition layer 
is in accord with my theory of heterogeneous reactions.^" 
One of the best proofs of the correctness of the condensation-evap- 
oration theory was obtained in experiments in which nuclei formed at 
liquid air temperature, were not allowed to warm up to room tem- 
perature, but only to — 40°C. In this case the nuclei were formed in 
one minute from cadmium vapor at 54° C. The nuclei which were 
kept at — 40°C. developed rapidly into cadmium mirrors in cadmium 
vapor at 170°, while those at room temperature developed extremely 
slowly. A still more striking demonstration of the theory was ob- 
tained when one of the nuclei was allowed to warm up to room tem- 
perature and then cooled to —40° before exposure to cadmium vapor 
at 170°. This nucleus did not develop nearly as rapidly as that which 
had not been allowed to warm up to room temperature. 
