ANNUAL REPORT SMITHSONIAN INSTITUTION, 1948 
Millions of Years 
2000 
0 1000 
3000 4000 
Ficure 4.—The curve AB indicates the variation of x (primeval Pb) with assigned values 
of ¢ for the pair of lead samples 25 and 18. CD represents the corresponding variation for 
the pair 19 and 1. The intersection at P gives a solution for x, and ¢,. The lines joining 
P to the points representing the lead samples (a and ¢,, in each case) show the gradual 
increase of Pb2, relative to Pb24=1, from x, to a during the period ¢, to ¢,,. 
Pb’, and Pb*® are almost exactly 
what they would be if the lead original- 
ly present in the material of the outer 
earth had been slowly modified by 
additions of radiogenic lead. A few 
of the samples have a more or less 
abnormal constitution, but apart from 
these the evidence is clear that ore- 
lead represents a concentration of the 
lead that was dispersed through the 
crustal rocks of the region concerned, 
at the time when the ore deposition 
took place. 
The problem, then, is this: knowing 
the isotopic constitution of rock-lead 
as it was at various periods ranging 
from 1,330 million years ago (the 
Great Bear Lake sample) to 25 million 
years ago (the Tertiary samples), to 
find the relative abundances of Pb? 
and Pb”? in the earth’s primeval 
lead, and the time that has elapsed 
since that primeval lead began to be 
modified by radiogenic additions. 
This time, ¢,, is the required age of 
the earth. 
Using the following symbols, with 
tm for the age of the lead ore: 
Pb2o4! Ph206] PpHh207| Pp208 
Ore-lead (=rock- 
Mead) ie ers tras avcaniets 1 a b Cc 
Primeval lead... . 1 X y Zz 
Radiogenic lead 
Gromit Atort.) se laa ee 
we can write: 
No. of atoms of Pb?°7 generated 
from t, to tm 
No. of atoms of Pb?0 generated 
from t, to tm 
From the expression on the right, 7 
can be calculated (for each appropri- 
ate value of ¢,,) for various assigned 
values of t, from 2,000 to 5,000 million 
