Arthur Holmes—Radio-actwrty. 273 
The symbols are those employed in Part II (p. 108) except that 
V is the initial surface temperature of the earth, taken by Becker 
as 1,300°C., and 6 is the melting-point of diabase at the surface, 
taken on the authority of Barus as 1,170°C. Solving with Becker’s 
data and giving definite values to z,, the following are some of the 
results obtained :— 
%1, the depth of The proportion of the titheraceor the 
cate ean. aa eae ear earth in years. 
121 0-1425 68 million. 
180 0-43 200 a 
254 ‘ 0-59 600 a5 
300 0-6667 MSA Ay 
315 0-675 1,600 55 
Tf 2, is actually the depth of the level of isostatic compensation, 
as Becker believes, then the age of the earth is 68 million years 
according to this calculation, and only one-seventh of the earth’s 
heat can be maintained by radio-activity. -The impossibility of the 
latter result itself throws doubt, if indeed it does not disprove, 
the validity of the whole method. Curiously enough, however, the 
calculations show that if the level at which isostatic restoration most 
readily takes place is at a greater depth than 300 km., then the age 
is either about that required by radio-active minerals or is considerably 
higher. The work of Barrell on the strength of the earth’s crust, 
and of Schweydar on tides in the solid earth, suggest that the depth 
of flowage in question actually is greater than 300 km., and the quite 
independent results of this paper are in complete accord with such 
a conclusion. So far from disproving the great age of the earth 
imphed by radio-active methods, Becker’s analysis would seem to 
lead to an equally high or even higher age. But it may be noticed 
that the value of ¢ derived from any stated value of x, in equation 14 
is strongly affected by the value of V—b. Thus the results are vitiated 
at their very source, for the figure chosen for V, viz. 1,300°C., is 
a pure guess. Any other figure would give totally different values 
for ¢.° Moreover, the equation fails altogether to give a rational 
result if ( V—0) is not positive ; that is to say, unless the initial surface 
temperature of the earth were higher than the melting-point of 
whatever rocks are in place within the asthenosphere. Already 
Becker’s paper has been quoted as furnishing an argument against 
the radio-active methods of determining time. Clearly it fails to do 
so for the following reasons :— 
(1) The value assigned to Vis a pure guess. 
(2) The depth of the ‘‘ eutectic level’’ is said to be at the level of 
isostatic compensation instead of 200-800 km. below that 
level. 
(3) The proportion. of the temperature gradient maintained by 
radio-activity cannot, on the age favoured by Becker, be 
more than one-seyenth of the whole. 
(4) It is assumed that ‘ diabase’ can be present at a depth of 
Ao! Qi ema 
(5) If the method were valid it would imply that the earth had 
cooled for considerably longer than 1,600 million years. 
DECADE VI.—VOL. Il.—NO. VI. 18 
