326 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1914. 
age to the rocks. If the radioactive estimate is correct, then we are 
now living in a time when the denudative forces ofthe earth are 
about eight or nine times as active as they have been on the average 
over the past. Such a state of things is absolutely unaccountable. 
And all the more unaccountable because from all we know we would 
expect a somewhat lesser rate of solvent denudation as the world 
gets older and the land gets more and more loaded with the washed- 
out materials of the rocks. 
Both the methods referred to of finding the age assume the prin- 
ciple of uniformity. The geologist contends for uniformity through- 
out the past physical history of the earth. The physicist claims 
the like for the change rates of the radioactive elements. Now the 
study of the rocks enables us to infer something as to the past history 
of our globe. Nothing is, on the other hand, known respecting the 
origin of uranium or thorium—the parent radioactive bodies. And 
while not questioning the law and regularity which undoubtedly 
prevail in the periods of the members of the radioactive families, it 
appears to me that it is allowable to ask if the change rate of uranium 
has been always what we now believe it to be. This comes to much 
the same thing as supposing that atoms possessing a faster change 
rate once were associated with it which were capable of yielding 
both helium and lead to the rocks. Such atoms might have been 
collateral in origin with uranium from some antecedent element. 
Like helium, lead may be a derivative from more than one sequence 
of radioactive changes. In the present state of our knowledge the 
possibilities are many. The change rate is known to be connected 
with the range of the alpha ray expelled by the transforming ele- 
ment; and the conformity of the halo with our existing knowledge 
of the ranges is reason for assuming that, whatever the origin of 
the more active associate of uranium, this passed through similar 
elemental changes in the progress of its disintegration. There 
may, however, have been differences in the ranges which the halo 
would not reveal. It is remarkable that uranium at the present time 
is apparently responsible for two alpha rays of very different ranges. 
If these proceed from different elements, one should be faster in its 
change rate than the other. Some guidance may yet be forth- 
coming from the study of the more obscure problems of radio- 
activity. 
Now, it is not improbable that the halo may contribute directly 
to this discussion. We can evidently attack the biotite with a 
known number of alpha rays and determine how many are required 
to produce a certain intensity of darkening, corresponding to that 
of a halo with a nucleus of measurable dimensions. On certain 
assumptions, which are correct within defined limits, we can calculate, 
as I have done above, the number of rays concerned in forming the 
