Mathematical Theories of the Earth. — Woodward. 279 
sions were announced twenty-seven years ago, and were republished 
without modification in 1883. 
Recently, also, professor Tait, reasoning from the same basis, has 
insisted witli equal confidence on cutting down the upper limit of 
geologic time to some such figures as ten million or fifteen million 
years. As mathematicians and astronomers, we must all confess to a 
deep interest in these conclusions and the hypothesis from which they 
flow. They are very important if true. But what are the probabili- 
ties? Having been at some pains to look into this matter, I feel 
bound to state that, although the hypothesis appears to be the best 
which can be formulated at present, the odds are against its correct- 
ness. Its weak links are the unverified assumptions of an initial uni- 
form temperature and a constant diffusivity. A^ery likely these are 
approximations, but of what order we can not decide. Furthermore, 
if we accept the hypothesis the odds appear to be against the present 
attainment of trustworthy numerical result?, since the data for calcu- 
lation obtained mostly from observations on continental areas are far 
too meagre to give satisfactory average values for the entire mass of 
the earth. In short, this phase of the case seems to stand about 
where it did twenty years ago, when Huxley warned us that the per- 
fection of our mathematical mill is no guaranty of the quality of the 
grist, adding that, "as the grandest mill will not extract wheat- flour 
from peas-cods, so pages of formulae will not get a definite result out 
of loose data." 
When we pass from the restricted domain of quantitative results 
concerning geologic time to the freer domain of qualitative results of a 
general character, the contractional theory of the earth maj' be said to 
still lead all others, though it seems destined to require more or less 
modification, if not to be relegated to a place of secondary importance. 
Old as is the notion that the great surface irregularities of the earth 
are but the outward evidence of a crumpling crust, it is only recently 
that this notion has been subjected to mathematical analysis on any- 
thing like a rational basis. About three years ago ^Ir. T. Mellard 
Keade announced the doctrine that the earth's crust, from the joint 
effect of its heat and gravitation, should behave in a way somewhat 
analagons to a bent beam, and should possess at a certain depth a 
"level of no strain," corresponding to the neutral surface in a beam. 
Above the level of no strain, according to this doctrine, the strata will 
be subjected to compression, and will undergo crumpling, while below 
that level the tendency of the strata to crack and part is overcome by 
pressure which produces what Keade calls "compressive extension," 
thus keeping the nucleus compact and continuous. A little later the 
same idea was worked out independently by Mr. Charles Davison, 
and it has since received elaborate mathematical treatment at the 
hands of Darwin, Fisher, and others. The doctrine requires for its 
application a competent theory of cooling, and hence can not be 
depended on at present to give anything better than a general idea of 
