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It has been known for some thousands of years that the Moon keeps a nearly constant face to the Earth. Only one explanation has been offered of how this state can have come about, namely tidal friction in the interior of the Moon. Darwin made an extensive study of the effects of tidal friction in the Earth and other planets, with special reference to the apparent secular acceleration of the Moon. Mercury and known satellites appear to keep constant faces to their primaries (there seems to be some d,oubt now about Mercury, but the rotation still appears to be slow). Turbulence in tidal currents in shallow seas seems to account for most of the friction for the Earth; but the other bodies have probably never had shallow seas, and we must infer some imperfection of elasticity at strains of the order of It is very hard to detect such imperfection in the laboratory. Other types however are very conspicuous. Fracture in igneous rocks and well compacted metamorphic ones such as quartzites occurs at strains of the order of and there is a complicated non-linear behaviour when the elastic strains are somewhat less than this; this may lead to permanent deformation far exceeding the direct elastic one. It was shown by various geodesists that mountains produce far smaller disturbances of gravity than would be expected if they were simply added loads. An explanation was given by Airy, who postulated a lower layer of denser but weaker matter. Extra load on a thin crust would push the interface down, and the resulting lack of heavy matter would largely compensate for the extra attraction of the mountain. Later Suess made the crucial inference on geological grounds that most surface rocks are essentially derived from granite or similar rocks with densities about 2.7, and overlie a layer with a density of 3-0 or so. Then A. MohorovilSiC in 1909 detected a duplication of earthquake pulses, as if one pair, Pg and Sg, travelled in an upper layer but another, Pn and Sn, in a lower one with higher velocities. Curiously, none of the continental seismologists at the time appear to mention Suess or Airy. The first mention in geophysics of the geological inference was, I think, in the paper by Winch and me in 1922 on the Oppau explosion. Later comparison with experiment confirmed these early results except that the lower layer seemed to need a density more like 3.3 and the upper was a great deal more complicated. But this is still too simple. Hayford’s survey of the United States assumed exact uniformity of mass per unit area and greatly reduced the residuals in comparison with the hypothesis that extra mass on the surface is not accompanied by defect below. But Helmert noticed that successive residuals along a survey line tended to keep the same sign, and on this ground multiplied Hayford’s uncertainties by about 3. Barrel1 inferred hence that the lower layer cannot be completely weak; he supposed a layer about lOOkm down where the strength is much less than that of surface rocks, but still appreciable. He called this the asthenosphere. Again confirmation came from Turner’s discovery of deep-focus earthquakes in 1921. Earthquakes comparable with the strongest shallow ones occur to depths of about a tenth of the Earth‘s radius. They send out strong S pulses. This is definite evidence that a discontinuous change occurs in the stress-difference and the material must have been able to stand that until the earthquake took place. (Incidentallyl it is hard to

Summary A table is provided of the external and dynamical ellipticities of the Earth for different values of the ratio I/Mb2, I being the mean moment of inertia and b the mean radius, on the first order Radau theory. A simplified model is used to find the corrections for the slight inaccuracy of the Radau approximation and the terms of the second order. The dynamical ellipticity and J2 as given by artificial satellites are used to estimate I/Mb2, and it is shown that on the hydrostatic theory 106J2 would be 1072.1 ± 0.4, in contradiction to the direct determination 1082.78 ± 0.05. The departures from the hydrostatic state indicated by J2 and J3 imply stress differences of 4 × 107 to 8 × 107 dyn/cm2 in the interior.

It is shown that a certain differential form depending on the values of the parameters in a law of chance is invariant for all transformations of the parameters when the law is differentiable with regard to all parameters. For laws containing a location and a scale parameter a form with a somewhat restricted type of invariance is found even when the law is not everywhere differentiable with regard to the parameters. This form has the properties required to give a general rule for stating the prior probability in a large class of estimation problems.

Summary Absorptions are worked out for S waves of different periods, based on the constants found for the modified Lomnitz law. It seems likely that the small amplitudes about distance 10° require absorption at small depths to be much stronger than the average for the shell.

Summary. Pacific earthquakes studied by Gogna, also three important explosions in the Tuamotu archipelago, are rediscussed. The results are very consistent, but those from Tuamotu are later than Gogna's by about 1 s in the times of P about 60°. Both sets of data give PKP residuals about -5 s about 140° - 142°, indicating that the observations there referred to the neighbourhood of the cusp of the travel-time curve but the ISS had compared them with the DEF branch. The corresponding difference in the 1940 tables is about 2 s. Analysis at intervals of 1° indicated that the cusp of PKP is about 141° instead of 143° as in the 1940 tables and the difference between it and the DEF branch at these distances is about - 5 s. Travel times of S under the Pacific were found but need more data, especially at distances under 10°. Times of PcP reported by Kogan and Carder were compared with those calculated from P in Gogan's explosions, and indicated a radius of the core of 3479.8 ± 1.8 km.

b Observations of P and S from deep earthquakes in the Hindu Kush region are analysed. They are reduced to a surface focus by a method of S. Mohorovicic. Cubic forms in Δ are found to fit the times of P satisfactorily up to 19|Mo and of S to 21|Mo. The coefficient of the cube term is less for S than for P, indicating that the S rays are much straighter than the P ones. A cubic from 21|Mo to 37|Mo and a quadratic from 37|Mo to 95|Mo fitted the times of P, with t and dt/dΔ continuous. Beyond 92|Mo it seems that the time curve becomes nearly straight, as had been suspected previously. For S cubics from 22.5|Mo to 37|Mo and from 37|Mo to 94|Mo fitted; there are few data beyond 95|Mo and a linear extrapolation was made to 105|Mo. For both P and S there are considerable drops in dt/dΔ about distance 20|Mo. Analysis for P at 1|Mo intervals showed that the times beyond 20|Mo vary smoothly with distance, and that the 20|Mo discontinuity cannot be smoothed over more than 2|Mo. The large amplitudes in this range strongly suggest that the variation of dt/dΔ is continuous and not due to the entry of an overtaking branch. The data for S are less clear but would suggest a similar strong d2dΔ2 about 22|Mo. There is evidence that the times of P, extrapolated to distance 0|Mo, are about 0.6 s more than those found by Willmore in the Heligoland explosion. The intervals between P and its near reflexion agree with this, and could be interpreted as an effect of the height of the region. If so it may be desirable at some stage to adapt the results to sea level.

Summary. Attempts are made to estimate the distribution of damping with depth, based on the observed damping of P waves, of free vibrations, and of surface waves and partly on a discussion by D. L. Anderson and R. S. Hart. Results are consistent in order of magnitude, but could easily be wrong by a factor of 2. Comments are added on the need for further work. Stress is laid on the damping of the free nutation, which indicates that α in the modified Lomnitz law is about 0.2 on an average.

Summary. Data for P and S beyond 85° are used for earthquakes in the four epicentral regions that travel times have been found for (Japan, Europe, Central and South Pacific). They seem to disagree seriously with suggestions of a considerable change in the times and dt/dΔ for S from the Jeffreys—Bullen tables of 1939–40. There are signs of a sharp drop in dt/dΔ for both Pand S in the range 93–95° except for the Southern Pacific.

Keith Edward Bullen was born in Auckland, New Zealand, the son of George Sherrar Bullen and Maud Hannah Bullen ( nee Burfoot). His father was born in New Zealand and his mother in England, both in 1875. His sister, Jean Maud Bullen, was a member of the research staff in the Ionosphere Section of the Department of Scientific Research, Christchurch, New Zealand, until her retirement. His father was a reporter on The Auckland Herald but was later put in charge of the illustrated section of The Weekly , until 1922, when he left for the quieter life in Whakatane in the Bay of Plenty, where he was coeditor of the local paper with Edgar Beckett. He returned to Auckland in 1930 and was re-engaged by the Herald .

Summary Most works on geophysics assume laws of damping according to which the creep under constant stress would be proportional to the time or to its logarithm. Both contradict strong geophysical evidence. The most direct evidence indicates that creep under small stresses increases about like to*'. This rule is tested by application to several geophysical and astronomical phenomena and leads to satisfactory explanations. The data, however, concern average properties of the Earth's shell and attention is needed to possible variation of the properties with depth.

Summary. Travel times for central Asia studied by Gogna, Jeffreys and Shimshoni are modified. Corrected surface times of P and S are tabulated and a structure is computed. We tabulate also full travel-time tables for all usual depths of focus.

Summary. Several regional seismological travel times, mainly for P but also for S are compared with the Jeffreys and Bullen Seismological tables. The regions included in the study are ‘Japan’, ‘Hindu Kush’, ‘Pacific’ and ‘East North America’. Wherever available explosion data are used. Differences in crustal structures are considered as well.

Summary. The theoretical treatment of tidal friction in The Earth is modified to take account of non-tidal effects. Recent determinations of the Moon’s tidal acceleration are reviewed and estimates are found by combining them. The observed acceleration of the Moon before the introduction of atomic clocks is affected by fluctuations in the Earth’s rotation. These are discussed and can be explained by changes of mean sea-level of the order of 20 cm, the water being transferred to and from the polar regions as ice. Difficulties in the Ramsey-Lyttleton theory of the core are pointed out and an improvement in the thermal contraction theory is described. A theory of the origin of continents and the possible separation of America in the Earth’s history is described. 1 The acceleration of the Moon and of the Earth’s rotation Spencer Jones (1939) concluded that when the Earth’s rotation was taken as the standard of time the difference between observation and Brown’s tables without the empirical term for the longitude of the Moon could be expressed as a quadratic function of the time plus a term B which he defined as the fluctuation; further he showed that the departures of the longitudes of the Sun and planets (in particular Mercury and Venus) from those given by Newcomb’s tables could each be expressed as a quadratic function of the time plus a term whose ratio to B was that of the mean motion of the body to that of the Moon. For the bodies other than the Moon he found that the coefficients of the squared term in the time were also in the same proportion as their mean motions. Spencer Jones’s method is based on the following principle. If the mean motions of the Moon, Sun and a planet referred to dynamical time are n, n’ and n”, and the secular accelerations h, h‘ and ti”, then the apparent accelerations when observations are made using universal time, which depends on the rate of rotation of the Earth, a, will be given by a, a’, a”, where

The geostrophic relation between the wind and the surface pressure gradient is incapable of accounting for any variation whatever with time in the pressure distribution. All changes in this arise f...

1. In a recent paper I obtained a numerical solution of some problems concerning the stability of a layer of incompressible fluid when the temperature decreases upwards. The results depended on the solution of the sixth-order differential equation ( d 2 / d ζ 2 - a 2 ) 3 Z = -λ a 2 Z. (1) In this solution the co-ordinates were x , y and z , the last being taken vertically. The depth of the fluid is h , and ζ = z / h . (2) Z is the factor of the disturbance of temperature that involves Z. The other factor is supposed to be of the form sin lx sin my , and a 2 = ( l 2 + m 2 ) h 2 . (3)

Gauss gave a well-known proof that under certain conditions the postulate that the arithmetic mean of a number of measures is the most probable estimate of the true value, given the observations, implies the normal law of error. I found recently that in an important practical case the mean is the most probable value, although the normal law does not hold. I suggested an explanation of the apparent discrepancy, but it does not seem to be the true one in the case under consideration.

It is well known that in certain circumstances a type of instability may arise at the surface of separation of two fluids when there is a finite difference between the velocities on the two sides of the surface. Some disturbances of the surface, of simple harmonic type, may increase exponentially in amplitude until the customary simplifying assumption, that the terms of the second degree in the displacements from the undisturbed state can be ignored, breaks down. One would naturally expect that in the case, for instance, of a wind blowing over the surface of water, waves would be first formed when the velocity of the wind is just great enough to make one particular type of wave grow; thus the critical wind velocity and the wave-length of the waves first formed will constitute checks on any theory of wave formation. The problem for frictionless fluids has been solved by Lord Kelvin, subject to the restriction that the disturbances considered are two-dimensional, no horizontal displacement occurring across the relative velocity of the fluids. Since, however, the possible initial deformations of a horizontal surface will not as a rule satisfy this condition, an investigation of the growth or decay of deformations of other types is desirable. 1. Hypothesis of Irrotational Motion . Let the two fluids be incompressible (a legitimate approximation so long as the wave velocity is small compared with that of sound in either fluid) and of great vertical extent. Let the origin be in the undisturbed position of the surface of separation and the axis of z vertically upwards. Let ζ be the elevation of the surface, and suppose the two fluids to have initially velocities U and U' parallel to the axis of x , accents referring to the upper fluid. Let the densities of the fluids be respectively ρ and ρ', and the velocity potentials in them Ф and Ф' . Let the operators ∂/∂ t , ∂/∂ x , ∂/∂ y , ∂/∂ z be denoted by σ, p , q , and ϑ respectively. Putting r 2 for — ( p 2 + q 2 we see that ∇ 2 Φ = 0 (1) is equivalent to (ϑ 2 — r 2 ) Ф = 0, (2) whence Ф = U x + e rz A, (3) where A is a function of x and y , determined by the value of Ф where z is zero.

Some of the principal theories of the origin of the planets and satellites are discussed. The principal topics are the nebular theory (Roche’s form), tidal theories, collision theories; disk theories; densities of the planets; fission theories of the origin of the moon; origin of small bodies; initial temperatures; constitutions of the planets; the moon’s surface features.

1. We consider a small cube of the solid, of edge l, in the actual strained position. If the stresses were removed and the cube cooled to the absolute zero, the displacements of its particles would be (−u, −v, −w). Then the particles may be considered to have displacements (u, v, w) from a standard position; and the cube has strain components of the usual forms

Mr. Hills’s paper suggests a number of questions, some of which can be fairly definitely answered, while others seem to me to be worth recording on the principle that the best way to get a question answered is to ask it. The separation of the granitic material into limited regions of the earth’s surface to form the continents could clearly not occur when the earth was fluid, and after the earth solidified any mechanical cause would meet formidable difficulties. Explanations seem to be restricted to (1) a failure or partial failure of magmatic differentiation in the oceanic regions, so that the granite has separated out since solidification in the continental regions, but remained dissolved in the oceanic ones, (2) some mechanical process arising during solidification. There are difficulties about both possibilities. Mr. Hills’s theory belongs to the second class, and I think needs serious consideration.

Summary The times of P in six Japanese and five “European” earthquakes, selected because good determinations of epicentres are possible from stations within 30°, are studied. Revised tables for earthquakes in Europe and Japan are constructed. Evidence concerning differences of the times at distances over 30° is some what conflicting; if there are any they do not exceed 28, but a difference of the order of I part in 300 between the velocities under the eastern and western halves of Eurasia is possible.

Theories giving the properties of the general aerofoil of small camber and negligible thickness have been given by Munk, Birnbaum, and Glauert. Allowance for some thickness is desirable, however, since for most aerofoils the thickness is comparable with the camber. The method used is an extension of that of Munk and of Glauert in his first account. 1. If the circle C given by ∣ z ∣ = a is transformed by the equation z ' = z + a 2 / z , (1) we get the two sides of a flat plate C' extending from 2 a to —2 a and back. If we first transform the circle by ζ = z { 1+ Σ A n (a/z) n }, (2) where the A n ’s are small complex quantities, we get a curve S differing slightly from a circle, and if we then put ζ' = ζ + a 2 /ζ

IN the February number of the Geological Magazine, Mr. A. J. Bull illustrates an interesting experiment on a type of deformation in a sheet of elastic material subject to a contraction. The inferences he draws from it, however, need further discussion. An elastic solid, under sufficiently great stress, will develop a permanent deformation either by continuous yield or by fracture, according to the nature of the material. The stress needed to produce such deformation may conveniently be called thestrength. But in certain circumstances it is possible for a stress to produce a considerable change of shape before the strength is reached, and such phenomena are common in engineering practice. A simple example is provided when a rod of india-rubber is compressed longitudinally. So long as the force applied is not too great the rod remains straight; but at a certain critical value of the compression it suddenly buckles sideways into an arc. The straight form is still a possible position of equilibrium, but it is no longer stable, and the slightest disturbance grows until the rod has become strongly bent, giving a new and stable position of equilibrium. It is easy to verify in this case that the strength has not been reached; we need only remove the thrust on the ends, when the rod returns to its original straight form. Another example is provided by a flywheel on a long shaft. Steady rotation is possible at all speeds; but there is a critical speed at which instability develops. Then it becomes possible for the rod to bend and to carry the centre of the flywheel around a circle of finite radius; the tendency of the rod to recover its form provides just enough force to keep the centre of the wheel moving in a circle. Any further increase of the speed of rotation will make the shaft bend through a considerable angle, with disastrous consequences. Other known cases arise in the collapse of tubes under external pressure or longitudinal thrust.1