422 
NATURE 
opinion of our great physical astronomer, a datum is still wanting 
for the determination of a limit to geological time, according 
to Thomson’s argument. 
However, subject to this uncertainty, with the values used by 
Adams in his computation, and with the assumption that the rate 
of tidal friction has remained constant, then a thousand million 
years ago the earth was rotating twice as fast as at present. In 
the last edition of the ‘‘ Natural Philosophy ” the argument from 
these data runs thus :— 
“Tf the consolidation of the earth took place then or earlier, 
the ellipticity of the upper layers (of the earth’s mass) must have 
been zt, instead of about s4;, as it is at present. It must 
necessarily remain uncertain whether the earth would from time 
to time adjust itself completely to a figure of equilibrium adapted 
to the rotation. But itis clear that a want of complete adjust- 
ment would leave traces in a preponderance of land in equatorial 
regions. The existence of large continents and the great effec- 
tive rigidity of the earth’s mass render it improbable that the 
adjustment, if any, to the appropriate figure of equilibrium would 
be complete. The fact, then, that thecontinents are arranged along 
meridians, rather than in an equatorial belt, affords some degree 
of proof that the consolidation of the earth took place at a time 
when the diurnal rotation differed but little from its present value. 
It is probable, therefore, that the date of consolidation is con- 
siderably more recent than a thousand million years ago.” » 
I trust it may not be presumptuous in me to criticise the views 
of my great master, at whose intuitive perception of truth in 
physical questions I have often marvelled, but this passage does 
not even yet seem to me to allow a sufficiently large margin of 
uncertainty. 
It will be observed that the argument reposes on our certainty 
that the earth possesses rigidity of such a kind as to prevent its 
accommodation to the figure and arrangement of density appro- 
priate to its rotation. In an interesting discussion on subaérial 
denudation Croll has concluded that nearly one mile may have 
been worn off the equator during the past 12,000,000 years, if 
the rate of denudation all along the equator be equal to that of 
the basin of the Ganges (‘‘ Climate and Time,” 1885, p. 336). 
Now, since the equatorial protuberance of the earth when the 
ellipticity is 4, is fourteen miles greater than when it is z},, it 
follows that 170,000,000 years would suffice to wear down the 
surface to the equilibrium figure. Now let these numbers be 
halved or largely reduced, and the conclusion remains that denu- 
‘dation would suffice to obliterate external evidence of some early 
excess of ellipticity. 
If such external evidence be gone,! we must rely on the in- 
compatibility of the known yalue of the precessional constant 
with an ellipticity of internal strata of equal density-greater than 
that appropriate to the actual ellipticity of the surface. Might 
there not be a considerable excess of internal ellipticity without 
-our being c gnisant of the fact astronomically ? 
And, further, have we any right to feel so confident of the 
internal structure of the earth as to be able to allege that the 
earth would not through its whole mass adjust itself almost 
‘completely to the equilibrium figure ? 
Tresca has shown in his admirable memoirs on the flow of 
solids that when the stresses rise above a certain value the solid 
becomes plastic, and is brought into what he calls the state of 
fluidity. I do not know, however, that he determined at what 
stage the flow ceases when the stresses are gradually diminished. 
It seems probable, at least, that flow will continue with smaller 
stresses than were initially necessary to start it. But if this is 
so, then, when the earth has come to depart both internally and 
externally from the equilibrium condition, a flow of solid will set 
in, and will continue until a near approach to the equilibrium 
-condition is attained. 
When we consider the abuzdant geological evidence of the 
plasticity of rock, and of the repeated elevation and subsidence 
of large areas on the earth’s surface, this view appears to me more 
probable than Sir William Thomson’s. 
On the whole, then, I can neither feel the cogency of the 
argument from tidal friction itself, nor, accepting it, can I 
place any reliance on the limits which it assigns to geological 
history. 
* I find by a rough calculation that ths of the land in the northern 
hemisphere are in the equatorial half of that hemisphere, viz. between o° and 
30° N. lat. ; and that #8ths of the land in the southern hemisphere are in the 
equator.al half of that hemisphere, viz. between o° and 30° S. lat. ‘Thus for 
the whole earth, 4$}ths ofall the land lie in the equatorial half ofits surface, be- 
tween 30° N. and S. lat. In this computation the Mediterranean, Caspian, 
-and Black Seas are treated as land. 
[Sepé. 2, 1886 
The second argument concerning geological time is derived 
from the secular cooling of the earth. 
We know in round numbers the rate of increase of temperature, 
or temperature gradient, in borings and mines, and the conduc- 
tivity of rock. These data enable us to-compute how long ago 
the surface must have had the temperature of melting rock, 
and when it must have been too hot for vegetable and animal 
life. 
Sir William Thomson, in his celebrated essay on this subject (re- 
published in Thomson and Tait’s ‘‘Natural Philosophy,’’Appendix 
D), concludes from this argument that ‘‘for the last 96,000,000 
years the rate of increase of temperature underground has 
gradually diminished from about /;th to about ;;thof a degree 
Fahrenheit per foot. . . Is not this, on the whole, in harmony 
with geological evidence, rightly interpreted? Do not the vast 
masses of basalt, the general appearances of mountain-ranges, 
the violent distortions and fractures of strata, the great prevalence 
of metamorphic action (which must have taken place at depths of 
not many miles, if so much), all agree in demonstrating that the 
rate of increase of temperature downwards must have been much 
more rapid, and in rendering it probable that volcanic energy, 
earthquake shocks, and every kind of so-called plutonic action, 
have been, on the whole, more abundantly and violently ' 
operative in geological antiquity than in the present age?” 
Now, while I entirely agree with the general conclusion of Sir 
William Thomson, it is not unimportant to indicate a possible — 
flaw in the argument. This flaw will only be acknowledged as 
possible by those who agree with the previous criticism on the 
argument from tidal friction. 
The present argument as to the date of the consolidation of 
the earth reposes on the hypothesis that the earth is simply a 
cooling globe, and there are reasons why this may not be the 
case. The solidification of the earth probably began from the 
middle and spread to the surface. Now is it not possible, if not — 
probable, that, after a firm crust had been formed, the upper 
portion still retained some degree of viscosity? If the interior 
be viscous, some tidal oscillations must take place in it, and, 
these being subject to friction, heat must be generated in the 
viscous portion ; moreover the diurnal rotation of the earth must 
be retarded. Some years ago, ina paper on the tides ofa spheroid, 
viscous throughout the whole mass (P22/. Zrans., part ii. 1879), 1 
estimated the amount and distribution of the heat generated 
whilst the planet’s rotation is being retarded and the satellite’s 
distance is being increased. It then appeared that on that hypo- 
thesis the distribution of the heat must be such that it woald only 
be possible to attribute a very small part of the observed tem- 
perature gradient to such a cause. Now, with a more probable 
internal constitution for the earth in early times, the result 
might be very different. Suppose, in fact, that it is only those 
strata which are within some hundreds of miles of the surface 
which are viscous, whilst the central portion is rigid. Then, 
when tidal friction does its work the same amount of heat is 
generated as on the hypothesis of the viscosity of the whole planet, 
but instead of being distributed throughout the whole mass, and 
principally towards the middle, it is now to be found in the more 
superficial layers. 
In my paper it is shown that with Thomson's data for the con- 
ductivity of rock and the temperature gradient, the annual loss 
of heat by the earth is 1/260,009,090 part of the earth’s kinetic 
energy of rotation. 
Also, if by tidal friction the day is reduced from Jy hours to 
D hours, and the moon’s distance augmented from MI, to TI 
earth’s radii, the energy which has been converted into heat in 
the process is 
(4y -1- 884 (ce =a) times the earth’s kinetic energy 
LY 
of rotation. 
From these data it results that the heat generated in the 
lengthening of the day from twenty-three to twenty-four hours is 
equal to the amount of heat lost by the earth, at its present rate 
of loss, in 23,000,000 years. : : 
Now if this amount of heat, or any sensible fraction of it, was 
actually generated within a few hundred miles of the earth’s 
surface, the temperature gradient in the earth must be largely 
due to it, instead of to the primitive heat of the mass. ; 
Such an hypothesis precludes the assumption that the earth is 
simply a cooling mass, avd would greatly prolong the possible 
extension of geological time. It must be observed that this view 
is not acceptable unless we admit that the earth can adjust itself 
to the equilibrium figure adapted to its rotation. 
