SECTIONAL TRANSACTIONS.—A. 413 
own axis, to a stationary observer it appears twisted in the opposite sense to 
the rotation. This effect has been pointed out by R. W. Wood. 
The arrangement may act as aclock. It measures time on the same principle 
as the ideal clock, consisting of a beam of light reflected between two mirrors, 
with the addition that a disc fixed on the shait at any cross-section, and 
rotating with it, can indicate the local time there. _ 
In the latter part of the paper, the contraction in the shaft due to the 
motion of translation and the twist were considered as a strain-displacement in 
a thin tube or solid circular cylinder. One of the principal axes of strain is 
assumed to be the direction of resultant velocity /v* + u* (D). The prin- 
cipal contraction in the latter direction is found to be W/1—(v? + u*)/c?. 
Since the twist and longitudinal contraction are independent of the form 
of the shaft, the values of the contractions obtained for a thin tube hold also 
for a solid circular cylinder. In the limiting case of a disc rotating without 
any motion of translation, the circumferential contraction is equal to that of a 
rotating ring, viz. /[—w2/c2, where wu is the velocity at the rim. It follows 
that the contraction in the radius is of the same magnitude. 
At the end of the paper an application of the analysis was made to the 
Wiedemann effect. For the small strains of magneto-striction the formula 
agrees with that given by Knott, which has been experimentally verified. 
25. Prof. D’Arcy THompson.—Note on the Tetrakaidekahedron. 
26. Prof. A. S. Epprnaton, F.R.S.—Lecture on Hinstein’s Theory of 
Relativity. 
Tuesday, September 13. 
27. Joint Discussion With Sections C, D, and K on The Age of the 
arth. 
Rt. Hon. Lord Raytercu, F.R.S.—In view of the past history of this 
subject it seems particularly important to keep our eyes open to all possibilities, 
and to welcome evidence from any quarter. Lord Kelvin in the last generation 
attempted to set a limit of time to the duration of the sun’s heat. And also 
from consideration of the earth’s internal heat he argued back to the time when 
the surface was too hot for the presence of living beings. 
As regards the earth’s heat, it is now generally known that the premises of 
Lord Kelvin’s calculations, carefully particularised by him, are upset by the 
discovery of radioactive substances in the earth. In 1906 I made a determina- 
tion of the amount of radium in the superficial parts of the earth which are 
alone accessible. From the radium analysis we can calculate the amount of 
uranium and other associated substances, and the thermal output from them. 
The result is to show that if we suppose the same radium content to extend 
to a depth of some twenty miles, the whole output of heat would be accounted 
for, without assuming that any of it comes from primeval store as postulated 
by Lord Kelvin. It is surprising, in fact, that the output is not greater. 
We are puzzled at the present time to account for the existing state of things, 
and cannot use it as a firm basis from which to explore the past. 
Next, as to the sun’s heat. Lord Kelvin’s argument was that we knew of 
no source at all adequate to supply the existing output of solar energy except 
secular contraction; and even this was not enough to account for more than 
20 million years of solar heat in the past. Although we still do not know 
definitely of such a source, yet we are now compelled to admit that it must 
exist. Some of the stars (the giant red stars) are radiating energy at some- 
thing like 1,000 times the rate that the sun does. They ought, according 
to the contraction theory, to have expended an appreciable fraction of their 
total energy in historical times. No one will maintain that this has occurred, 
and if not, there must be some source of supply other than contraction, If 
this is admitted, Lord Kelvin’s argument from the sun’s heat fails. 
Modern knowledge in radioactivity, on the other hand, seems to give a 
firm basis for the estimation of geological time. Uranium, for example, goes 
