Geophysical Abstracts 152 January-March 1953

48 GEOPHYSICAL ABSTRACTS 152, JANUARY-MARCH 1953
Within certain limitations, the variations in radioactivity of the litttes&mes
appear to be the dominant factor in the cause of variations in therm^lumines-
cence. Author's Abstract
HEAT
GENERAL AND THEORETICAL STUDIES
14345. Lapwood, E. R. The effect of contraction in the cooling by conduction of
a gravitating sphere, with special reference to the Earth: Royal Astron.
Soc. Monthly Notices, Geophys. supp., v. 6, p. 402-407, 1952.
The equation of heat conduction is given for a contracting, gravitating sphere.
An associated energy equation is interpreted in terms of interchanges of gravi­
tational potential, strain, and heat energy. The heat equation is applied to the
case of the earth, and with some simplifications it has been solved by the method
of successive approximations. Three conclusions are offered: It is pnofe^ble
that the heating effect of contraction is more than counteracted by the speedier
outflow of heat due to increased temperature gradients. It is probable that the
corrections demanded by departures of the earth's crust from homogeneity as
regards density, specific heat, and thermal conductivity are larger than those
that allow for contraction. None of these effects is large enough to make funda­
mental changes in the picture of the earth's thermal history that is derived from
discussion of the cooling of a rigid uniform sphere, with allowance for radio­
activity. P. E. B.
14346. Chandrasekhar, S. The thermal instability of a fluid sphere heated
within: Philos. Mag., v. 43, no. 347, p. 1317-1329, 1952.
In this paper the problem of the thermal instability of an incompressible
fluid sphere heated within and in equilibrium under its own gravitation is
considered. A general disturbance is analysed into modes in terms of spherical
harmonics of various orders, I, and the criterion for the onset of convection for
the first fifteen modes is found both when the bounding surface is free and
when it is rigid; and it is shown that in both cases the mode 1=1 is the first
to be excited. Author's Abstract
14347. Chandrasekhar, S. The onset of convection by thermal instability iu
spherical shells: Philos. Mag., v. 44, no. 350, p. 233-241, 1953.
In this paper the problem of the thermal instability of an incompressible
sphere consisting of an inviscid core and a viscous mantle is considered, and it
is shown that the pattern of convection which sets in, at marginal stability, in
the mantle shifts to harmonics of the higher orders as the thickness of the
mantle decreases. Thus, when the mantle extends to a depth of half the radius
of the sphere, the harmonics of orders three and four set in about simultaneously,
while the harmonic of order five follows very soon afterwards. The bearing of
this result on the problem of convection in the earth's mantle and of the inter­
pretation of the earth's topographic features is indicated. Author's Abstract
14348. Urey, H. C. Comments on planetary convection as applied to the earth:
Philos. Mag., v. 44, no. 349, p. 227-230, 1953.
Chandrasekhar has shown that first order spherical harmonic convection in
a sphere can occur if the sphere has a liquid core with a diameter not larger
than 18 percent of the sphere diameter. Successively higher harmonies appear