232 
present reading is not inconsistent with 
an oceanic age of a few thousands of 
millions of years. 
What we need for the accurate meas- 
urement of such immense periods is a 
natural process that has operated 
throughout geological time and has 
produced measurable results at a 
known rate, of which the law of varia- 
tion with time is also known. The 
decay of the radioactive elements is 
the only known process that fulfills 
these stringent conditions. The radio- 
active methods depend on the trans- 
formation of uranium and thorium 
into helium and lead, and on the ac- 
cumulation of these stable end products 
in minerals and rocks that contain the 
parental elements. Helium, being a 
gas, is liable to escape, but the lead is 
much more likely to be retained and so 
to serve as an index of age. Provided 
a radioactive mineral such as pitch- 
blende or uraninite has remained un- 
altered by weathering or other changes, 
then the amount of radiogenic lead 
now found within it is a function of 
(a) the amounts of uranium and/or 
thorium now present and (b) of the 
time elapsed since the mineral first 
crystallized. Fortunately it is possible 
to discriminate between the radiogenic 
lead and any ordinary lead that may 
have been present as an initial impur- 
ity in the mineral. The parental ura- 
nium contains two chemically insep- 
arable isotopes, UI (or U**) and AcU 
(or U5), in atomic proportions hav- 
ing the present value: ACU/UI=1/139. 
Since AcU decays much more rapidly 
than UI, this ratio was progressively 
higher in the past. The material re- 
sults of the atomic transformations can 
be summarized as follows: 
U8>Pb”*-+8 He 
U®5_>Pb””--7 He 
Th#2->Pb*8- 6 He 
It will be noticed that in each case a 
specific isotope of lead is generated. 
Ordinary lead is a mixture of the same 
three istopoes, together with a fourth, 
Pb2, which is not known to be an 
end product of radioactive decay. 
Thus, if the lead separated from a 
ANNUAL REPORT SMITHSONIAN INSTITUTION, 1948 
radioactive mineral is isotopically 
analyzed (e. g., by means of the mass 
spectrograph) and found to contain 
Pb24, the proportion of the latter 
provides an index of the amount of 
ordinary lead that was initially present. 
The present rates of production of 
radiogenic lead are known with a 
remarkable degree of accuracy, but 
the question naturally arises, can we 
be reasonably sure that these rates 
have remained constant throughout 
geological time? apart, of course, 
from the inevitable slowing down due 
to the wearing-out of the parents. In 
other words, can we be sure that the 
physical constants concerned have 
not varied with time? Fortunately, 
pleochroic haloes provide us with an 
unambiguous affirmative. Certain 
granites contain flakes of brown mica 
which, under the microscope, can be 
seen to be sprinkled with dark circular 
spots (pl. 2, fig. 2, right). These are 
known as pleochroic haloes and some 
of them, when highly magnified, re- 
veal a beautifully developed pattern 
of concentric rings (pl. 2, fig. 2, left). 
A minute radioactive crystal lies at 
the center of each halo and the dark- 
ening of the surrounding mica is pro- 
duced by the helium ions (e-par- 
ticles) that are shot out in all direc- 
tions. The radius of each ring corre- 
sponds to the range of the a-particles 
from one particular radioactive ele- 
ment. Careful measurements by Prof. 
G. H. Henderson show that the rings 
in Pre-Cambrian haloes over 1,000 
million years old are just as sharply 
defined as those in younger rocks, and 
that the corresponding radii and 
ranges are identical. Since the range, 
in turn, depends on the rate of dis- 
integration of the radioactive element 
concerned, it follows that the radio- 
active constants have not varied ap- 
preciably for at least 1,000 million 
years. 
At any given time the rate of produc- 
tion of a particular lead isotope de- 
pends only on the disintegration con- 
stant and amount of the parental ele- 
ment then present. Thus the age of 
a mineral, tm, can be readily calcu- 
