DEVELOPMENTS IN PHYSICAL SCIENCE 453 
theory. If one wishes to explain it by assuming the diffusion of ordi- 
nary gases through the glass walls of the tube, he must explain the fact 
that in many cases it was the heavy and least volatile substances that 
escaped fastest. 
3. In the third place the element of time has been overlooked. Mat- 
ter may be disintegrating, but at such a slow rate that in the limited 
time over which experiments have been extended the balance has failed 
to detect the change. As far as our experience goes the time of rotation 
of the earth is constant; but we know that it can not be absolutely con- 
stant. The moon has slowed down until it takes a month to make 
one turn. ‘To an ephemeral insect almost everything would appear to 
be eternal. 
With due respect for the balance and the wonderful work it has 
enabled chemists to do, it must be admitted that it is, comparatively, a 
very crude instrument. Let me prove it. 
Suppose we fix the limit of sensibility of the chemical balance at 
one one-thousandth of a miligram. Our books on chemistry tell us 
that 1 c.c. of gas, say hydrogen, at ordinary pressure contains 4 « 1019 
molecules. The density of H being 896 « 10-", then 1 gm. of H 
would consist of (4 * 101°) + (896 & 10-7) molecules. Taking 112 
as the ratio of the molecular weights of radium and H, then 1 gm. 
of radium would consist of [(4 X 10*) + (896 & 10-7) ] + 112=— 
4% 107? molecules. Therefore .001 mgm. of radium would consist of 
4 >< 10° molecules, and this would be the smallest possible number 
that our most sensitive balance could detect. If the gram of radium 
were disintegrating and its molecules escaping at the rate of a million 
per second it would require 4 X 10’ seconds = 463,000 days = 1,270 
_years for that gram of radium to lose in weight only the one-thousandth 
part of one milligram, all the while its molecules trooping away at the 
rate of a million per second. 
The population of the earth is about 1,500 millions. The smallest 
number of molecules a balance will detect is 4 X 10**, or about 26,600,- 
000 times the population of the earth. We wonder if Mars is inhabited. 
If a Martian were to come to the earth to make an experiment to deter- 
mine whether or not the earth is populated and he had no better instru- 
ment “for the detection of the existence of a man” than ig the balance 
for a molecule, he would be obliged to go back and report the earth 
uninhabited. In fact his instrument for the man test would need to be 
#6,600,000 times as sensitive as the balance to give him even a hint of 
the probability of an earth population. 
Thomson says that the smallest quantity of unelectrified matter ever 
detected is probably neon, and this was discovered by the spectroscope 
—not the balance. But the number of molecules of neon required to 
give a spectroscopic effect is about ten million million, or about 7,000 
times the population of the earth. It has been shown that the presence 
