APRIL 2, 1914] 
NATURE 
109 
LETTERS “LO THE EDITOR. 
[The Editor does not hold himself responsible for 
opinions expressed by his correspondents. Neither 
can he undertake to return, or to correspond with 
the writers of, rejected manuscripts intended for 
ihis or any other part of Nature. No notice is 
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The Doppler Effect and Carnot’s Principle. 
In my letter of Marck 19 I endeavoured to show 
that the latent heat absorbed in the production of unit 
volume of stationary vibration of a particular fire- 
quency in a mixed beam of radiation, is not equal to 
4q/c (where q is the energy stream per sq. cm. per 
sec., and c tne velocity), as would naturally be sup- 
posed, but, in consequence of the Doppler effect at the 
moving mirror or piston, takes the form T(dp/dT), 
as required by Carnot’s principle, where p is the pres- 
sure, or the mechanical work per unit volume, and is 
equal to 2q/c for a directly reflected beam under 
equilibrium conditions. The latent heat, T(dp/dT), 
may be represented as the sum (w+) of the intrinsic 
energy or internal latent heat u and the external work 
p. As a matter of interpretation, u was identified in 
my letter with some form of stationary vibration 
which continued to exist in the medium at the fre- 
quency at which it was emitted. Further analysis 
shows that this is not the case, but that the energy 
left in the medium conforms exactly to the, distribu- 
tion required by the theory of exchanges. The energy 
density is 2q/c in a directly reflected beam, and is 
equal to the pressure, but differs from the energy 
absorbed on emission or evolved on condensation, 
namely, the latent heat, T(dp/dT), which is the quan- 
tity measured experimentally, as previously explained 
een. Mag., October, 1913, p: 787). . 
Similarly in the case of full radiation where the 
energy stream is Q per sq. cm. per sec. in all direc- 
tions, the energy density is 4Q/c, and the pressure 
40/3c for each frequency, but the latent heat per unit 
volume is still T(dp/dT) (in place of 16Q/3c) on 
account of the Doppler effect, and the energy stream 
as measured experimentally is not Q but 47T(dQ/dT). 
With a slight change of viewpoint the consideration 
of the Doppler effect leads to the exact formula and 
numerical relations already detailed in my previous 
note (loc. cit.), which are now seen to be no longer 
in conflict with the electromagnetic theory as was at 
first supposed. H. L. CALLenpar. 
Imperial College of Science, South Kensington, 
March 30. 
Lead and the Final Product of Thorium. 
It is now practically certain that the final product 
of the uranium family of radio-elements is isotopic, or 
chemically identical, with lead. The constancy of the 
ratio between lead and uranium, Pb/U, in the case 
of primary rock-forming minerals of the same geo- 
logical age, and its sympathetic variation in the case of 
minerals of different ages, go far to establish this 
important conclusion. The recent discovery that all 
the final products of radio-active disintegration fall 
into Group iv. B of the periodic classification has 
naturally led to the further suggestion that each one is 
isotopic with lead. 
If lead, or one of its isotopic equivalents, is the final 
product of the thorium series, then the estimates of 
geological time hitherto based on the lead-uranium 
ratio stand in need of a ruthless revision. 
Fortunately this does not appear to be necessary, for 
mineralogical evidence clearly indicates that the pre- 
sence or absence of thorium in a uranium-bearing 
mineral does not affect the Jead content, which can 
NO: 2316, VOL. 93| 
generally be adequately accounted for by the uranium 
alone. 
It is easy to calculate the relative rates at which 
uranium and thorium generate their final products, 
and assuming that the latter are isotopic, to express a 
given amount of thorium in terms of uranium, and so 
to arrive at a ‘“‘total equivalent quantity of uranium,” 
U,, which also takes thorium into consideration. If 
then lead is, chemically speaking, the final product of 
thorium as well as that of uranium, the ratio Pb/U, 
ought to be constant for minerals of the same age, 
and ought to vary in sympathy with the ages if these 
should differ. I have examined a large number of 
analyses of radio-active minerals from this point of 
view, and neither of the above criteria is found to 
hold. In many cases a large percentage of thorium 
may be present, but unless uranium is also present, 
lead is nearly always absent. In the few examples 
where lead and thorium occur alone, the ratio Pb/Th 
is variable and bears no relation to the geological age 
of the minerals. 
However, more fully to demonstrate the bearing of 
evidence of this kind on the problem, Mr. R. W. Law- 
son, of the Radium Institute, Vienna, and myself are 
at present estimating the thorium content of a series 
of Norwegian minerals of Devonian age which had 
already been analysed for lead and uranium (Proc. 
Roy. Soc., A, vol. Ixxxv., p. 248, 1911). Other workers 
are busily engaged on determinations of the atomic 
weights of the lead from uranium and thorium bear- 
ing minerals respectively, and there is therefore some 
likelihood in the near future ot a final settlement of the 
question whether lead is an end-product of thorium or 
not. ARTHUR HOLMEs. 
Geological Department, Imperial College of 
Science, London, March 18. 
Thermions and the Origin of Solar and Terrestrial 
Magnetism. 
PREVALENT opinion seems to favour decidedly the 
hypothesis that the chief part of the magnetism of 
the earth or sun is due to the rotation of all, or a 
considerable portion of, the matter of which it is 
constituted. Theories of the magnetisation of matter 
by rotation fall into two classes: one (a) assuming 
that the substance is magnetic but not necessarily 
charged, the other (b) assuming that the substance 
is charged but not necessarily magnetic. 
(a) If the matter is magnetic, consisting of mole- 
cular systems with individual magnetic moments 
differing from zero, rotation about a given axis will, 
on the electron theory, produce a torque on each indi- 
vidual system, causing it to contribute a magnetic 
moment parallel to the axis of rotation, and thus 
magnetising the whole body, if originally neutral, 
along this axis. 
(b) Gravitation, or electrical forces, acting differen- 
tially on the positive and negative constituents of the 
matter, or differential centrifugal action, or some other 
cause, may give rise to a volume-density of electrifica- 
tion throughout the mass of a rotating body, in which 
case magnetisation, or at least a magnetic field, must 
result from the convection currents thus formed. 
The particular kinds of differential action just men- 
tioned have been proposed before, but I have seen no 
reference to the fact that an essentially steady electric 
volume-density must long ago have been produced by 
| the emission of negative electrons from the heated 
matter of which the earth and sun are composed, and 
the resulting internal electric field. As the emission in- 
creases with the temperature, which increases from 
the surface inward, it is clear that the volume-density 
must be of the proper size to account for the polarity 
of solar and terrestrial magnetism. 
