ALBERT

Notes: The propagation of waves of Rayleigh type in a uniform semi-infinite elastic medium with two uniform surface layers is discussed. The waves are dispersive, and the wave velocity equation is obtained as a determinant of the tenth order.By making infinite the thickness of the surface sheet one can derive the velocity equation for waves in an internal stratum. By making the thickness of either sheet zero one can retrieve the known equation for the velocity of Rayleigh waves in a medium with a single surface layer. If the wave-length is very small the determinant reduces to the product of three determinants which, equated in turn to zero, are the velocity equations of very short Rayleigh waves at the free surface and of very short waves of Rayleigh type at the two interfaces.The results of a numerical solution of the wave equation and the application to the surface waves of earthquakes will be communicated in a later paper.

Notes: When account is taken of the angular momentum of surface masses moving relative to the solid Earth it is found that the equations governing the variation of latitude are not sensibly affected by changes in the rate of rotation and that the equations previously used are adequate if correction terms are added to account for the angular momentum which may be large enough to have an observable effect.

Notes: Part I of this paper contains the presentation of a new analysis of observational material, mainly from Eskdalemuir, and describes some unexpected properties of geomagnetic fluctuations. The chief of these are (a) that there is a change of type at sunset from a continuous flux of disturbance to a comparative quiet punctuated by short damped wave trains, and (b) that the daytime fluctuations have a spectrum with definite fine structure. Part II is a discussion of the probable origin of geomagnetic pulsations. By comparing the characteristics found in Part I with those reported by previous observers it is concluded that the effects have a common cause, and very general arguments are then put forward to show that their origin is terrestrial. A survey of possible physical models points, after elimination, to a magneto-hydrodynamical resonance in one or more of the ionospheric layers.

Notes: A split-beam radio-echo technique has been used to measure the heights of the reflecting points of meteor trails. The measured width of the distribution of heights has been used in conjunction with the theories previously developed by Kaiser to determine the atmospheric scale height. The observations of sporadic meteors have been divided into velocity groups and values of the scale height have been calculated for each. A value of the atmospheric pressure at the mean height of each group is calculated from the evaporation theory of meteors. For purposes of comparison these results are converted into atmospheric densities which are compared with those obtained from rocket flights and meteor photographs made in New Mexico and Massachusetts. The present results for scale heights and densities are in close agreement with those obtained in New Mexico. In view of this a latitude variation in the density profile, which has been suggested as an explanation of the difference between the New Mexico and Massachusetts results, now seems unlikely.

Notes: It is suggested that the coincidence of the period of rotation of the Earth and a natural period of vibration of the atmosphere is not fortuitous but due to the Earth being driven at a constant rate in synchronism with the vibration. An observation by Kelvin that the gravitational couple on the atmospheric tides accelerates the Earth's rotation is recalled, and the production of mechanical energy to balance the dissipation of the oceanic tides is discussed. The astronomical evidence supporting the current view that the rotation is being steadily retarded is reviewed and found to contain contradictions, and it is claimed that the high value of the angular momentum of the Earth-Moon orbit supports the hypothesis of equilibrium.

Notes: Astronomical observations have indicated that variations in the Earth's rotation by several parts per hundred million sometimes occur over periods of one or two decades. These irregularities may be caused by variations in the distribution of matter, or by variable motion relative to the Earth. It is found that processes in the atmosphere and ocean are inadequate to account for all of the observed irregularities, but that their effect is not necessarily negligible. Processes in the crust and mantle could barely do so, but such processes seem highly unlikely for a number of reasons. The irregularities can be accounted for by a variable motion in the core amounting to a fraction of the total motion indicated by the westward drift of the Earth's magnetic field.

Notes: Times of P in Mediterranean, Japanese and Californian earthquakes are analysed with the objects of testing the generality of the increase of the velocity at short distances found in Europe and the evidence for Gutenberg's layer of low velocity. The Mediterranean earthquakes do confirm the increase at short distances, but the Japanese ones agree with the tables in use, and there is clear evidence of a regional difference. The evidence from North American earthquakes is conflicting. It does not definitely indicate any change from the present travel times, but the uncertainties are larger than in the other regions, chiefly because there are rarely enough stations in approximately the same azimuth and at greatly different distances to give much information.The difference of the times at 2° and 25° is about the same in Europe and Japan, but in comparison with them the times in Europe at 8° are about 3° earlier. The time-curve in Europe is nearly liner up to 14°. There is evidence in both regions for a strong curvature of the time-curve between 15° and 20°, but it does not decide whether dt/dΔ is continuous or discontinuous in this interval.The curvature of the time-curve is in any case surprisingly small, because laboratory studies of the variation of elastic moduli with pressure indicate an increase of velocity with depth several times that given by any set of travel times. Increase of temperature with depth would presumably reduce the rate of increase but does not appear sufficient to account for the discrepancy.

Notes: Tidal observations have been performed in the I. C. I. Salt Mine at Winsford. The gravimetric factor has been determined both for the overall values and the principal harmonic constituents. Its value is G= 1.20 ± 0.04. The results are compared with former measurements.

Notes: The analysis of a large number of observations of North Sea surges by R. H. Corkan has enabled him to make a classification of them into types. One type of surge appears to be due to the passage of an atmospheric depression over the entrance to the North Sea. By simplifying the mathematical conditions it is possible to predict the results of the passage of such a depression. These are largely in conformity with the observations. In particular it is shown that the surge produced is a progressive one, passing from the entrance to the North Sea to the closed end and increasing uniformly in amplitude.

Notes: On the basis of the study of the consolidation of clays made by Skempton (1944) and others, estimates have been made of the gravitational attraction of a deposit of clay. Examples of the behaviour of some typical clays are given and a procedure for correcting gravity anomalies for the attraction of a deposit of clay is suggested.

Notes: When a hot gravitating sphere cools, gravitational potential energy is lost in contraction. We consider a sphere that can be taken as in continual hydrostatic equilibrium for slow changes of state, and, assuming radial symmetry, set up the modified Fourier equation for heat conduction. This contains two extra terms, one contributed by the heating effect of contraction, and another from the change of temperature gradients with shrinkage. This equation is checked by integration through time and through the sphere to give a comprehensive energy equation.For an initial parabolic temperature distribution in the Earth, the heating effect of contraction is small, and more than counteracted by the extra cooling provided by increased temperature gradients. Moreover, it is probable that the modifications to the first (uniform rigid sphere) approximation which are needed to allow for departures from uniformity in density, specific heat, and thermal conductivity in the Earth are greater than those which allow for contraction.

Notes: A knowledge of the densities of rock formations is important in the interpretation of gravity anomalies. This paper describes the results of field and laboratory experiments made on the rocks in the Midlands of England. Density measurements were made on nine geological formations from the Silurian to the Cretaceous and also on Metamorphic rocks from the Malvern area. A catalogue of densities has been prepared for general use based on the assumption that rocks in the field are saturated with water. A table of densities and porosities for a large number of rocks is also given. Among the conclusions drawn about the observed sampling variances, the most significant is that rock formations in the West Midlands do not appear to show any” regional variation” of density. The results of the field and laboratory methods are consistent within the experimental errors of each, in marked contrast to the results reported by S. Hammer from observations in some American mines, from somewhat different data.

Notes: The corrections for bending and stretching of a pendulum, used for making an absolute determination of gravity, are obtained by a simple process depending on the equation of angular momentum, the results agreeing with those recently given by Jeffreys. The source of error in Clark's work is pointed out, and also an error in Jeffreys' which has no effect on the result.

Notes: An expression is derived for the temperature distribution T(x, t) in a semi-infinite solid, accreting with constant velocity v, on whose rising surface there is impressed the temperature T(o, t)= A+B cos (wt-θ), where x is depth, t is time, and A, B, ω and θ are constants. This solution is applied to the problem of an accumulating snowfield. The annual temperature wave, if accompanied by the rapid accumulation of snow, is shown to produce considerably lower temperatures in the firn than if accumulation is lacking. The effect of a diffusivity which varies with depth is also discussed; it is found that this may be treated approximately as equivalent to a theoretical fictitious velocity of accumulation.

Notes: At a certain stage in the cooling of the Earth a type of circulation could arise, analogous to the cellular convection of H. Bénard. G. F. S. Hills has suggested this as an explanation of the distribution of continents. It is found that the easiest modes to excite are those in which the disturbances of temperature and radial velocity contain spherical harmonics of degree I, and the surface currents would tend to sweep floating matter to one side. The theory shows some prospect of providing an explanation of the land and water hemispheres, though there are some outstanding difficulties.An approximate solution is also derived for a spherical mass with a rigid boundary, heated from within. It is again found that the easiest modes to excite correspond to harmonics of degree I.

Notes: Calculations have been made of the partitioning of energy of P waves incident from above against the boundary of the Earth's inner core, and of P and SV waves incident against this boundary from below. In these calculations the inner core has been assumed to have rigidity as in an Earth model based on compressibility theory. The calculations have been applied to estimating the relative amplitudes of the phases PKJKP and PKIKP at various epicentral distances for a given earthquake. It is shown that, on the assumptions made, the phase PKJKP is most likely to be observed over a range 130°≫Δ≫ 155° of epicentral distance, the amplitude in this range being about one-fifth of that for PKIKP. It is suggested that readers of seismograms who find PKIKP strongly recorded in this range might also look for the phase PKJKP; the writer of this paper would much appreciate it if observational evidence supporting the existence of the phase PKJKP could be communicated to him for purposes of collation.

Notes: Geological data are used to contour the bottom of the Cuddapah Basin, which is found to slope down eastward to a maximum depth of over 18,000 feet below sea-level. Using these contours the geological effect on gravity at the surface due to the departure from normal density (2.67) of the pre-Cambrian sediments in the Basin is calculated. Gravity anomalies over the Basin computed for density 2.67 are strongly negative, and these are increased by the geological corrections, since the average density of the sediments in the Basin is 2.74. Since it is probable that the underlying rocks, like those surrounding the Basin, have normal density, the defect of gravity is ascribed to a downwarping of the crust, which is assumed to have a total thickness of 30 km. Computation of the effect of downwarping to 18,000 feet gives results consistent with the gravity data. Crustal warping is briefly discussed, and a modified method of topographical reduction of gravity data is suggested.

Notes: A review of current theories of the scintillation of stars on optical wavelengths shows that the refraction theory of scintillation requires excessive atmospheric density gradients, and fails to explain the observed scintillation in colour, whilst the physiological explanations are insufficient to explain all the observed phenomena. A new theory, in which the scintillation phenomena are attributed to Fresnel diffraction at a non-homogeneous atmospheric layer, is shown to explain the observed effects, and to require considerably smaller density gradients. A similar theory, taking into account the effect of a wave-length change of 107, is shown to explain the observed fluctuations in intensity of radio waves from the localized extra-terrestrial sources of radio noise.

Notes: The energy in various model primitive Earth-Moon bodies containing a normal phase X and two high-pressure phases Y and Z has been examined. In each model, the first high-pressure phase Y has been taken to be in agreement with the data for the outer central core of Bullen's Earth Model B. On certain simplifying assumptions, it is then shown that disappearance of the phase Z from the primitive body would be accompanied by the release of sufficient energy to eject a body of the Moon's mass, provided that the radius of the region occupied by the phase Z was at least about 1500 km and that the density of Z is at least about 18 g/cm3. This result gives some quantitative support to Bullen's theory of the origin of the Moon, provided that his suggested mechanism of resonance could lead to sufficient distortion to take the primitive body over a potential barrier into the state in which the phase Z has disappeared.

Notes: 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.

Notes: Simultaneous measurements of the vertical component and two perpendicular horizontal components of gravity have been made in the I. C. I. Salt Mine at Winsford (Cheshire) over the period 1951 April 16 to 24. Apart from the gravitational tide the measurements show a well-developed influence of the variations in the maritime loading, especially in the horizontal components. A common drift in all components indicates the influence of meteorological pressure variations over a large area. Furthermore, diurnal variations of presumably meteorological origin have been observed. The “load tilt” has been determined. It is elliptical with an azimuth of N. 47° W. of the main axis and has an amplitude of 1.65 millisec per foot tide at Liverpool (5.5 millisec/m). The load influences in the vertical component are only 2.4 per cent of those in the horizontal direction and indicate the influence of more distant oceanic areas.

Notes: The effect of winds is to vary the length of day by 0.7 milliseconds between February and August. The bodily tides result largely in a semiannual variation of 0.4 ms. The combined effect of winds and tides is not far out of line with astronomical measurements since 1950. The fluid core of the Earth hardly participates in these variations in angular velocity and there is a half-year slippage of 23 metres between core and mantle at the equator. Eventually the astronomical measurements may provide a basis for determining the Love number h.

Notes: In an earlier paper it was suggested that it was failure in the region between 250 and 600 km below the surface which determined the periodicity of orogenic phenomena. In this paper estimates of the cross-sectional areas of the oceanic troughs and of the mass deficiencies reflected in the strips of large negative gravity anomalies are given and it is inferred that the interval between successive periods of failure is 50 million years.It is pointed out that if the troughs are formed in the manner described in the earlier paper then a regression of sea-level of about 70 metres will occur as a result of their formation. Finally some aspects of the development of the trough regions into mountain ranges are discussed qualitatively.

Notes: The results are given of the harmonic analysis of the Admiralty magnetic charts of declination, horizontal intensity and inclination for the epoch 1942.5. Within the limits of observational error, the Earth's magnetic field appears to be entirely of internal origin. There is no evidence of a dipole field of external origin greater than 0-1 per cent of the field of internal origin. The intensity of the dipole field is at present decreasing at a rate of about 5 per cent per century. The geomagnetic poles have a westerly drift at a rate of 4°-5 per century; the north magnetic dip pole is moving in a direction a little to the west of north, but the south magnetic dip pole appears to be practically stationary. In consequence of the dearth of magnetic data over the oceans since 1929, magnetic charts are becoming less accurate and there is a great need for airborne magnetic surveys of ocean areas.

Notes: This paper, which was almost completed* by Dr Corkan just before his death in 1952, gives a method of analysing observations of the tilting of the Earth's surface. The method combines observations from two places and assumes only that the body tilt due to the direct yielding to the attractive forces is simply related to the equilibrium form, but with a constant phase lag, and that the semidiurnal constituents in the load tilt have the same ratios as in the loading tide. It is shown that these ratios are very stable over large parts of the oceans, and a useful table is given for the main seas and oceans. This method avoids the uncertainties of computation of the loading tide which have caused many difficulties in previous investigations, and it automatically eliminates the greater part of the secondary effects of the more distant oceanic tides.

Notes: The theory of the calculation of the detailed undulation of the geoid from gravity by Stokes's integral is usually given to first order, and there are some approximations which may be important in mountainous places. Some are trivial but the change of undulation with height is not. Discussion of this involves the definition of orthometric height and of the geoid. With suitable definitions the undulations of the geoid are the same as those of equipotential surfaces at external points, so that the latter may be calculated directly without additional correction for changes with height. The free-air correction to gravity is determined by these definitions and conditions; for geodetic purposes the fundamental quantity is not the change of gravity with height but the difference of geopotential. The correction derived in this paper thus differs slightly from those commonly in use and there are consequently some small errors in the figure of the Earth derived with the use of the letter.

Notes: The gravimeter surveys made by the Anglo-American Oil Company (now the Esso Petroleum Company), the Anglo-Iranian Oil Company, the Geological Survey, and the Department of Geodesy and Geophysics of Cambridge University depend on about 600 base stations, of which those in any one survey are connected by a strong network of first order measurements of gravity differences. There are sufficient connections between base stations of different surveys for all the surveys to be compared and combined into one uniform system. The largest discrepancies between surveys arise from errors in the calibration factors of the gravmeters and the surveys have therefore been adjusted to six precise pendulum observations at stations between Aberdeen and Southampton.The adjustment has been carried out in three stages, The first is the preliminary adjustment of sets of observations made with the same instrument. The second is the calculation of gravity values at 120 principal stations selected from all 600 base stations, many of the 120 being common to two or more surveys; pendulum observations are included and the gravimeter calibration factors are determined. The gravity values are expressed as differences from the value at the Pendulum House, Cambridge Observatory. In the third stage, which it is hoped to report elsewhere, the remaining base station values are revised to agree with the 120 principal stations and the calculated calibration factors. It is shown that the discrepancies between this procedure and the simultaneous adjustment of all 600 base station values are not serious.The standard deviations of single observations as determined from the internal errors of surveys range from 0.05 mgal to 0.27 mgal. Comparisons between different surveys indicate larger errors and it is possible that stations are not re-occupied exactly by different observers. Observations are weighted according to the variability between surveys, and the residuals of measured differences of gravity are generally consistent with this.Of the 300 observations between the 120 principal stations, 3 have residuals greater than three times the standard deviation. The values calculated for the 120 stations have standard deviations mostly between 0.1 and 0.2 mgal. Secular changes of heights of stations may in time lead to greater uncertainty.The difference between the value of gravity at the Pendulum House, Cambridge Observatory, and that at the site of the absolute determination at the National Physical Laboratory, Teddington, is 72.17 mgal, s. d. 0 008 mgal, and the value of gravity at Cambridge on the Potsdam system is therefore 981 268-5 mgal, assuming the value at Teddington to be 981 196.3 mgal (Cook, 1952 a). It is, however, recommended that gravity values within the British Isles should continue to be based on the value of 981 265 mgal at Cambridge (Bullard and Jolly, 1936).

Notes: A rise in sea-level at the rate of 1 cm per century following a reduction in the extent of ice in glaciated regions results in an increase of the moment of inertia of the Earth about its axis of rotation sufficient to lengthen the day by 10-4 second per century provided there is no isostatic compensation. The consequent apparent secular acceleration of the Moon is 2 seconds of arc per century per century. The changes however are negligible if immediate and complete isostatic compensation occurs. A tentative discussion of climatic and glaciological evidence indicates that fluctuations of sea-level do occur and that their effect on the Moon's apparent acceleration may be appreciable. This re-opens the question of the cause of the Moon's apparent acceleration which is usually attributed to the deceleration of the Earth by tidal friction. The change in tidal friction due to a rise in sea-level is very small and has not been sufficient to produce the observed change in the Moon's acceleration.

Notes: The depth of the level of no strain and the stress distribution have been calculated using Jeffreys's temperature distribution. It is found that the depth of the level of no strain is 59 km, that the stress difference in the crust increases at the rate of 0.6 dyn/cm2 year and that the decrease in the radius in 200 million years is 0.6 km. A relation between the decrease in radius and the heat loss per unit area is derived and from this relation it is shown that the possible changes in the parameters will not bring the contraction into accord with geological estimates. It is pointed out that the stress differences increase much more rapidly in relation to the strength at depths of 250 to 600 km and that failure should begin in this region. On this basis the cross-sectional area of an ocean deep is found to be 1400 km2.The lower mantle and the core are compressed as a result of cooling between the surface and 700 km. This compression is relieved when deep-focus earthquakes occur. It is calculated that increases in the length of the day totalling about 31/2 sec will occur in a period of failure of the mantle. Using a formula of Lapwood it is shown that the heating effect associated with the compression of the core is of the order of 1017 erg/sec, and that during failure of the mantle the cooling effect is likely to be much greater. Finally it is shown that the present rate of dissipation of energy in earthquakes is very much greater than the rate of generation of strain energy as a result of cooling.

Notes: A critical examination is made of curves presented by W. M. Elsasser on the density and compressibility of materials at zero temperatures and pressures up to 30 million atmospheres, and of Elsasser's inference that the Earth's core consists of iron or nickel-iron. An argument leading Elsasser to suggest that the writer's Earth Models A and B may require adjustments because of discrepancies with Elsasser's results is shown to be invalid.New tables are presented which fit the data used by Elsasser at 30 million atmospheres and are also consistent with geophysical data. The calculations leading to these tables imply that the atomic number to be associated with the material of the outer central core should be at least six units less than the value derived using simple extrapolations from quantummechanical calculations for high pressures. If the reduction in the atomic number is no more than six units, the most probable composition of the material in question would still be nickel-iron, and to this extent Elsasser's main conclusion is supported. But there are other aspects of the new calculations which suggest that the needed reduction may be greater than six units; these aspects raise the probability that the outer central core consists of a modification of ultra-basic rock. A caution is issued against forming too definite conclusions on either of the two opposing theories on the whole evidence so far available.Some support is found for the view that the Earth's present inner core is more likely to consist of an accumulation of iron and denser materials than of ultra-basic rock that has undergone a second pressure transformation. Support is also found for the view that the density gradients of Model B require a progressive change of composition with increase of depth in the inner core. The hypothesis that the inner core is solid is strengthened. Strong support is given to Elsasser's argument against the presence of large amounts of compressed hydrogen in the central core.The new tables suggest that the density of uranium (Z=92) may be a fairly smooth function of pressure from zero pressure right through to 30 million atmospheres, but that, for elements of smaller atomic numbers, there are likely to be significant density jumps at specific intermediate pressures. Tables are presented which give newly computed densities of uranium from 0.1 to 30 million atmospheres, and may serve as a useful basis of discussion in other contexts.As an incidental to discussing Elsasser's arguments, an Earth model (Model X) has been constructed with the property that the density in the central core near its outer boundary is 6.5 g/cm3. The model has a density gradient in the mantle only a little steeper than that in Models A and B, and has somewhat greater densities in the inner core. The outer part of the central core (between depths of 2900 and 4980km), however, differs radically from that of Models A and B through having a far steeper density gradient. The new model has to be regarded as implausible inasmuch as the last property implies far greater changes of composition with depth in the fluid part of the core than anywhere in the mantle.

Notes: Two field gravity meters were read continuously for a period of 14 days, one at Peebles in South Scotland, the other at Kirklington near Nottingham. The experiments have shown that the observed variations of gravity were proportional to the predicted tide-raising force to within a standard deviation of 1/50, milligal. The factors of proportionality are 1.02 for Kirklington, and 1.10 for Peebles. There were no significant phase differences on the average; the individual phase differences were rather irregular.

Notes: Simultaneous tidal gravity measurements at Peebles and Kirklington over a period of 14 days have been analysed harmonically. The diurnal terms K1 and O1 give a ratio of observed to theoretical amplitude of G= 1.1 without significant phase difference. The semi-diurnal terms show a phase lag of about 10° and G= 1.2 at Kirklington and G= 1.1 at Peebles. This difference is explained as due to regional influences of sea-tides. G= 1.10 to 1.15 is regarded as the most probable value resulting out of these observations. The influence of temperature and pressure is discussed and the existence of a 24-hour period of non-gravitational origin (“thermal tide”) confirmed. The most probable values of Love's numbers “k” and “h” and the geophysical consequences as to the properties of the interior of the Earth are discussed.

Notes: An extensive network of gravimeter stations has been observed by the Geological Survey of Great Britain using a Frost gravimeter. In the course of this survey gravimeter observations were made at recent pendulum stations in York, Newcastle-upon-Tyne, Edinburgh and Aberdeen. At these stations the gravimeter determinations gave values for differences in gravity from Pendulum House, Cambridge, which were consistent with the pendulum observations of Browne, Cook, McCarthy and Parasnis (1950). If the value of gravity at Pendulum House, Cambridge, is assumed to be 981.26500 cm/s2 the values at the other stations are found by combining the pendulum and gravimeter observations as:–York, Minster Crypt 981.41474 cm/s2± 0.00011Newcastle, King's College 981.50608 cm/s2± 0.00012Edinburgh, Royal Observatory 981.58014 cm/s2± 0.00013Aberdeen, Marischal College 981.69597 cm/s2± 0.00014From the observations at these pendulum stations an accurate calibration factor was obtained for the Frost gravimeter and this was found to differ significantly from the calibration factor determined from observations in the tower of Westminster Cathedral. Further measurements at Westminster Cathedral showed that the vertical variation in gravity is not linear but is distorted near the base of the tower, probably due to local terrain effects.

Notes: A definition of height is given in terms of the geopotential that will agree to the second order with the height determined by direct measurement along the vertical where such measurement is possible. The free-air reduction of gravity is carried to the second order so as to permit allowance for terms in eh and h2.

Notes: The magnetic properties of oriented rock samples from some Tertiary igneous intrusions in the Isle of Mull have been investigated. Analysis of the directions of natural residual magnetization, supported by some subsidiary experiments, shows that most of the natural magnetization could have been acquired by cooling in an ambient magnetic field. The analysis reveals two main directions of magnetization, one approximately in the direction of the present terrestrial field and the other in opposition to it. Various possible causes of the reversed magnetization are discussed and a suggestion is put forward that it may have been produced by reversals of the terrestrial field in the past.

Notes: Using the Cambridge pendulum apparatus the value of gravity at the National Physical Laboratory has been found to be 69.90 ± 0.16 mgal greater than that at the Ordnance Survey Office, Southampton. The result of a measurement with a Worden gravimeter was 70.36 mgal, and other indirect gravimeter measurements are in satisfactory agreement with the pendulum result.

Notes: The theory of thermal instability in a sphere is extended to the case of a viscous sphere with a fluid core, the radius of the core being half that of the outer surface. The easiest mode to excite no longer corresponds to a spherical harmonic of degree I in the temperature but probably to degree 3 or 4. A more satisfactory model from the petrological point of view is based on the idea of a magma percolating through a mass of incompletely consolidated crystals. Results are obtained for this case, both for a uniform sphere and for one with a core. The harmonics of degree I are not the easiest to excite in either case. From analogy with other hydrodynamical problems it does not appear that these results offer any objection to the theory of the origin of the land and water hemispheres by thermal instability. The essential point is that, given sufficient time, the most widespread disturbances will become dominant provided only that they can be excited at all, and this condition is satisfied in all cases.

Notes: Carbon dioxide and carbon monoxide: The rate of photo-dissociation of CO2 is appreciable only in the region above about 100 km. If local equilibrium prevails the carbon would occur mainly as the monoxide in this region, and as the dioxide below. However, oxidation may proceed so slowly that the life of a CO molecule is long compared with the characteristic time associated with atmospheric mixing effects. In this case the CO resulting from photo-dissociation would not be confined to above the 100 km level, but would extend much lower; its total abundance could scarcely be great enough to produce the observed absorption lines. It is estimated that the various forms of combustion taking place on the Earth would provide the CO content of the atmosphere within perhaps four years or even less. Methane: Dissociation of CH4 in the upper atmosphere is brought about mainly by collision processes. These prevent the existence of appreciable CH4 above the 100 km level and probably keep the concentration low even down to 70 km. The yield to date from oil wells and coal mines appears to be less than the amount of the gas now in the atmosphere. Seepage from fuel beds, and the anaerobic decay of vegetable matter, are the only obvious naturally occurring sources of significance. As far as can be judged at least ten years (and probably much longer) is required for the production of the atmospheric abundance. Nitrous oxide : Information on the necessary rate of formation of N2O is obtained by calculating the photo-dissociation rate. One hypothesis is that soil micro-organisms produce the gas, but it appears that the yield would only be sufficient if N2O were a major end-product of denitrification. Many of the homogeneous gas reactions suggested by earlier workers must be rejected, since there is an inadequate supply of the requisite parent particles. The only acceptable parent particles seem to be those arising directly or indirectly from the photo-dissociation of O2 in the Herzberg continuum. Various reactions involving O, O3 and N2 are discussed. Though they are very slow they might nevertheless give rise to sufficient N2O.

Notes: An analysis of the natural magnetic polarization of the basalt flows of Mull shows that many are adversely magnetized but the mean direction of magnetization of each flow, based on observations of a number of specimens, is not always significant. For such flows measurements of the magnetic stability, response to heat treatment, etc., suggest that the original intensities have been modified by later events. Finally, the observed natural intensities could be acquired by cooling in a field similar in magnitude to that of the Earth's present field.

Notes: Free air and Bouguer anomalies are given for 22 stations on Malta. A density of 2.25 g/c. c. is used for the Bouguer reductions on the basis of density measurements on five samples. In the second part of the paper discussion is made of the best Potsdam values for No. 3 dock Malta and at Tunis airport. The adopted values are shown to be consistent, within the rather low accuracy of the connections, with values accepted in Sicily.

Notes: The geophysicists who attempted to evaluate elastic anisotropy of some bedded formations most often gave but little information about recording and interpretating the measurements.May be they did not lay enough stress on the fact that any determination of the anisotropy factor is a critical operation and that, to have some certainty. it must be made under good conditions and then discussed.Due to the very favourable conditions offered: undisturbed tectonics and topography, relatively regular series the Berriane district in Northern Sahara, is rather well suited to accurate measurements and to an anisotropy study down to 1,250 meters. Since measurements have been carried out in the wildcat drilled at Berriane by S. N. Repal, it seems interesting to communicate the results obtained and to discuss them according to the influence of high velocity layers.It can be noted that in the clay and sand series which have been investigated, anisotropy coefficient amounts to 1.09 or so.To conclude, it seems desirable that determinations made by numerous operators should allow a more accurate knowledge of the anisotropy factor in the main types of rocks.

Notes: The aim of the present investigation is to examine the significance of the second derivative for the purpose of the prospective determination of the geological properties of the district of Offenburg, which are relatively wellknown as a result of both reflection seismic and bore profile findings.The calculation of the second derivative is carried out by means of three approximation formulae, which are compared with each other. In contrast to the isogam map the second derivative shows some additional characteristics, whose structural significance illuminates the comparison with the results of reflection seismics.A geological profile constructed on the basis of 6 wells completely confirms the geophysical findings.

Notes: It has been shown in a paper by L. Y. Faust that the wave velocity in rock depends on the depth below the ground surface according to a specified equation. It follows that the attitude of the planes of equal velocity is influenced by the topographic relief. Under these conditions the problem arises of how to place the reference plane in such a manner, that the fluctuations of the planes of equal velocity, that result from the fluctuations in the topography, shall not affect the results of the depth computations. In the present paper an analytical solution of this problem is given.

Notes: In a previous paper by the first author a method has been presented for computing the first vertical derivative of the gravity field or of the magnetic field. In the present paper an analysis is given of the errors in the first vertical derivative that result when the latter is computed by the above method. Two sorts of errors are considered. Firstly, the error in the first vertical derivative that results from the errors in interpolating between isogam lines on the Bouguer anomaly map. Secondly, the error in the first vertical derivative that results from the approximations upon which the computation method is based. The conclusion is reached that both sorts of error are only of minor importance.

Notes: The common notion, that the regional anomaly must be as regular as possible, can be translated into mathematical language by requiring that the regional anomaly shall be represented, over a not too large area, by a surface of the second or of the third degree. The residual anomaly is commonly defined by the requirement that its horizontal dimensions must be as small as possible. This implies that also its amplitude should be small. This requirement may be moulded into a mathematical form by stating that the square of the difference between the Bouguer anomaly and the regional anomaly, integrated over a certain area, must be a minimum. On these two definitions an analytic method is based for deriving the regional anomaly. Practical computation procedures are presented.

Notes: The different equations of elasticity concerning the departure of the behaviour of rocks from perfect elasticity are discussed. The theory of elastic afterworking and its significance for the propagation of elastic waves is studied in detail. It is found that this theory does not explain the observations on seismic waves in exploration geophysics so well as the theory of viscoelasticity suggested by Ricker.

Notes: The writer classifies problems of geophysical interpretation. He distinguishes four fundamental problems and indicates the methods of solving them. Among these methods he refers to classical methods and methods based on the writer's theoretical work.The geophysical examples are developed, as well as the very simple numerical examples. Methods of enumeration are also referred to. The whole object is to show that the practical application of the geophysical methods suggested will not give prospectors any difficulty.

Notes: The efficient production of “Geophysical Prospecting” depends upon the co-operation of the individual authors and this paper serves as a guide for them. Some suggestions are also made on the presentation of papers at meetings in the hope of promoting successful discussions.

Notes: A process is described whereby the interpretation of seismic reflection data is carried out by a preliminary two-dimensional plotting procedure followed by a three-dimensional migration. The concept of a surface of maximum convexity is introduced as an integral part of the process of migration. The procedures for deriving the necessary charts of curves are considered and a number of serviceable charts presented.

Notes: In the first part of the present paper we shall investigate the possibility of localising highly situated inclined faults with the aid of the vertical gradient and the second derivative in the direction of the vertical. Since these quantities have been computed from gravity values by means of formulae of approximation we shall have to study the question as to their applicability for possible quantitative interpretation. Particular caution should be exercised when making the usual comparison with theoretical test examples. For three effects have to be taken into account which result from the application of the formulae of approximation:〈list xml:id="l1" style="custom"〉1) The extreme values appear more or less smoothed out2) Extremal abscissae are being displaced3) The results are influenced by the orientation of the grid which forms the basis of the calculation.For a practical instance it was possible to locate a well under troublesome circumstances. This well is situated on the downthrown side of an inclined fault, the depth of the upthrown side being known as a result of another well.We shall show in the second part of the present paper how small, deeply situated structures may be recognised in the diagrams of the vertical gradient and of the second derivative. In the case of two practical instances the effect of these structures is rendered unrecognisable in the isogam map in view of regional influences. The results according to the formulae of Baranov, Elkins and Rosenbach are contrasted with each other.

Notes: The results obtained from a number of seismic velocity well-logging surveys and adjacent refraction sections are compared. The velocities derived by these two methods for a certain layer are found to differ appreciably. This is shown by presenting the time-depth relations of the well-surveys and the time-d stance relations of the refraction sections at three locations, plotted on graphs with sloping depth- and distance axes.

Notes: The gravity effect of earth tides was measured simultaneously at 26 stations, with 2 instruments at 3 of the stations. After a description of the stations, the corrections on the measurements are described. The results for the separate measurements are given and it can be stated that, within the accuracy of the measurements 〈inlineGraphic alt="inline image" href="urn:x-wiley:00168025:GPR82:GPR_82_mu1" location="equation/GPR_82_mu1.gif"/〉 is very probably constant and has a value of 1.22. If this value is combined with Nishimura's value 0.66 for (1 − h + k), it can be shown that Takeuchi's earth models fit these values provided a value of 2.7 is taken for the surface density of the earth. The importance of a constant value for 〈inlineGraphic alt="inline image" href="urn:x-wiley:00168025:GPR82:GPR_82_mu1" location="equation/GPR_82_mu1.gif"/〉 in gravity surveys is pointed out.

Notes: A ruler has been constructed to solve seismic refraction problems with horizontal or slightly inclined layers.

Notes: The main features of the gravimetric map of the Gharb can be related to the shape of the basement, covered by cretaceous and miocene layers, with a total maximum thickness of 13,000 feet. For the interpretation of local features, in the northern part of the basin, first a regional anomaly has been drawn, then the map of the first derivative has been established.Both maps are compared with geological maps and seismic and electrical surveys. The results are the following:As for method, the advantages and limitations of both processes are outlined.As for geological interpretation, it is suggested that most of the local features of the gravimetric map are due to the preriffan tectonics.

Notes: In the Cannock Chase Coalfield the rocks of the overburden are heavily waterlogged, thus constituting a source of difficulty and even danger to the miner. In order to ensure maximum safety with the maximum use of reserves, the area has been investigated by boreholes and by resistivity surveys.In this paper a short summary of the resistivity work is given, with especial reference to electrode arrangement and methods of interpretation used. Where applicable, comparison between resistivity evidence and borehole data is shown.

Notes: This paper summarizes and extends the published information on the theoretical design of electromagnetic geophones. Both moving-coil and moving-armature instruments are considered, their behaviour compared and various design criteria established.

Notes: After a short introduction, some examples of obliques multiple reflexions are treated and possible solutions given.

Notes: When a rather extensive network of short distance refraction profiles was shot the following two observations were made. Firstly, the wave velocity in the weathered layer showed a quite considerable fluctuation in horizontal direction, the extreme values being of the order of 300 and 700 m/sec. A practical result of this scattering of the velocities is that an uncertainty of about 10% is introduced in the computation of the weathering corrections. The second observation is that, in the majority of cases, the travel time curve does not pass through the origin. It could be ascertained that this observation was not caused by errors in the method of observation. A probable explanation of the phenomenon is found in a theory that has been developed by Gassmann, who derived the velocity distribution for a hexagonal packing of spherical solid bodies. According to this theory extremely low velocities would occur in the first few centimeters of the crust of the earth. Qualitatively, our observations are in agreement with the theory of Gassmann.

Notes: The formulas derived by the author in a preliminary paper for taking into consideration refraction when dealing with the problem of a vertical plane are extended to the three-dimensional case. Vector analysis is extensively applied. Among others it is shown that in the general case the 3 horizontal twodimensional vectors, i.e.〈list xml:id="l1" style="custom"〉1) the gradient of the time of reflection2) the direction of true dip3) the vector from the shot point to the projection of the reflecting point, point into 3 different directions.

Notes: The article is based on data from 74 seismic well velocity surveys in N.W. Germany.The effect of overburden is illustrated by means of diagrams representing interval velocities against depth. To eliminate observational errors and lithological variations from well to well, interval velocities from about the same depth are averaged. Thus, relatively uniform curves are obtained for lower Tertiary, Upper Cretaceous, and Lower Cretaceous (Albian), making the effect of overburden better evident than from individual observations. The vertical gradient of velocity for these geological sections are given. Furthermore, they are compared with curves for Lower Tertiary and Cretaceous obtained in N. America. Due to its high lime content, the Upper Cretaceous of N.W. Germany has a much higher velocity than that observed in the Cretaceous of N. America. The curves for shales of the Lower Tertiary and Lower Cretaceous (Albian), however, are similar in both countries. In older formations, on the other hand, e.g. Jurassic and Triassic, lithologic character has the dominant influence and the effect of overburden is rather small and often scarcely noticeable.The data considered cover a depth range down to 2,700 meters. The interval velocities are generally based on the use of various equal intervals.

Notes: When refraction time signals are transmitted over a radio link between shooter and observer there is a serious risk of interference from electrical storms. This risk can be minimised by sending a series of signals at fixed time intervals and the paper describes a simple device which will do this with the required accuracy.

Notes: Seismic reflection, telluric and gravity results are given for the lifted area of Ferrara, in Northern Italy. The agreement is shown between the available shallow seismic data and the gravity evidences. For a portion of the above area where seismic results are particularly poor the vertical gradients method gives a resolution of a gravity anomaly and confirms the telluric information. The residual gravity values, the vertical gradients and the telluric data along a seismic line crossing the zone are compared with seismic results and with evidences from adjacent wells.

Notes: Investigations into reflection seismic on the salt structure of Heide raised the following questions:〈list xml:id="l1" style="custom"〉1) How can the different directions of trend of a series of layers be established?2) How are the contour maps of reflecting horizons to be constructed if there is no general trend of the layers?To answer these questions, the case of the subsoil consisting of a series of layers with plane reflecting beds and constant layer-velocities is treated strictly. The strike lines of the reflecting planes may be at any angle whatever. However, formulas for constructing contour maps of the reflecting planes have been derived. With these formulas, the problem quoted under 1) has also been solved.The construction of contour maps is given.For special cases, formulas are obtained which have already been proved by others.

Notes: The triple integral for the attraction of a mass on a point is transformed in a double sum. This double sum serves to construct a graph for the rapid determination of the gravimetric influence of structures given by depth contours. The influence of topography can also be computed with this graph.

Notes: The dependence of the apparent resistivity on the distance between the potential electrodes is examined and a numerical method is described permitting quantitative calculations. Such a numerical relation is also established for the transformation of Wenner graphs into Schlumberger graphs.In addition it is shown, in which manner the jumps in observed Schlumberger curves, that result from changing the probe spacing, must be smoothed out.

Notes: The luni-solar corrections are considered under the three following aspects:Quality of results: the application of tidal corrections to all stations is pointless as long as the operations do not substantially exceed two hours.Working conditions: it seems possible to increase the duration of programs without any loss of precision, but operating in such a way requires particular care.Behaviour of gravity meters: the introduction of tidal corrections allows to separate three kinds of instrumental drifts; a good knowledge of the mean operational drift enables to appreciate the quality of a given set of measurements.An example is given to show the possibility in some cases to detect small errors which are close to the limit of precision of the instrument.

Notes: Exploration of the Catania region was carried out for over a year by means of electrical soundings. The thickness of the overburden (lava and alluvium) was thus computed and the contour map of the blue clays basement shows the existence of several buried channels where new wells were drilled, all of them successful.

Notes: The paper consists of an account of a resistivity investigation into an old river valley in Coal Measure strata. This valley denuded several of the upper coal seams leaving behind unconsolidated material and it was the purpose of the work to be described to investigate how far the extent and nature of this material could be determined by resistivity methods conducted at the surface.As such the survey fits into a wider programme of research instigated by the National Coal Board.The feature, which is quite well known geologically, was surveyed by conventional methods and the results obtained are discussed in relation to the above project.Thus, the investigations succeeded in tracing the approximate centre line of the feature and in yielding some information on the nature and order of thickness of the deposits. Limitations of the method and its future application are also discussed.

Notes: Using a comprehensive theory of the vertical force variometer, it is shown that the mean of the two readings taken in azimuths 180 degrees apart only eliminates the error of misorientation and of inclination of the knife edge if these factors are sufficiently small. The necessary accuracy in the 180 degree rotation and in the readjustment of the levels are investigated and a practical test is developed to allow the initial adjustments to be determined. Finally, a brief description of a new variometer tripod is given.

Notes: It is known that good use can be made of calculating the second vertical derivative of gravitational and magnetic fields. The first derivative, or Vertical Gradient, has the same properties, Like the second derivative, it does not depend on the locally linear regional anomaly. Moreover, the gradient is less affected by experimental errors.The report gives a practical method of calculating the vertical gradient. Its application is identical to that in general use for calculating the second derivative, except that the numerical coefficients are different. The method also allows the establishment of formulae for downward extension of the field and its derivatives.

Notes: In the region covered by the paper, electrical methods have been applied in four different zones:〈list xml:id="l1" style="custom"〉a) Ales-Maruejols Basin (resistive lower Oligocene blanketed by conductive Upper Oligocene);b) Ledignan and Vaunage-Lunel anticlines (faulted structures in the marly and limy Cretaceous, with different resistivities;c) Camargue (thick series of conductive sediments);d) Beziers Basin (highly complicated structures in the Mesozoic, widely blanketed by conductive Miocene).It may be assumed that electrical methods can yield valuable information enabling one to define the rugged subsurface topography of resistive strata burried under a reasonably thick cover of conductive sediments especially when a part of the lower formation outcrops even if the part exposed be small. Faults may be delineated and much, more information is obtainable than can be expected from gravity meter survey at a price not very much higher.

Notes: The measurement of well velocity data in the well of Scheibenhardt I has shown that it is possible to observe a well noticeable measurable increase of the travel time of seismic waves when approaching a disturbance. The tectonic event of the disturbance is combined in this case with a disorder (shattering) of the layers without subsequent cementation.The significance of these anomalies for reflection seismics is discussed. When existing they will then overlap the diffraction, treated by Th. Krey.

Notes: For the treatment of the problems involved in the interpretation of gravity pictures this paper gives a formula that holds generally for any potential function. It provides an extended applicability of the relation used by Elkins for the computation of the second derivative, and also yields an analogous relation to derivatives of higher order of the gravity field.This relation has not been utilized to determine in details the course of the derivatives of higher order in a plane, but is merely applied to points of comparatively extreme curvature of the isogams where the differential values present a ratio favourable to the “noise level”. By this method the values of the derivatives of higher order will not be determined themselves but only the ratio's responsible for the depth of divergence in comparison with the course of an anomaly of masses replaced by points.It is shown by examples of intercalated masses that the divergence points are important and by law related to the form and position of the density contrasts themselves.An analysis of the total gravity picture is made possible by progressing from elements close to the surface to deeper ones. In this way the fundamental features of the earth's crust will be obtained. The application of the analysis process to a gravity anomaly actually measured in Northwest Germany is given.

Notes: The supply of drinking water and water for general use in the towns and communities of Western Germany is in many cases insufficient. In order to eliminate the difficulties in the supply of water, geophysical methods have been applied to a large extent since the end of the war.The most important hydrological problems, which were solved successfully by geo-electrical measurements, are as follows:〈list xml:id="l1" style="custom"〉1Search for, and delimitation of, areas with salty ground water.2Investigation of the geological situation in catchment areas for large waterworks, and the finding of suitable places for the establishment of new plants, and in particular.3Search for and determination of the thickness and nature of water-bearing sands and gravels and of the relief of the underlying impervious strata.Some typical examples are presented herewith.

Notes: Supersonic pulses are transmitted into rock samples and cylindrical drill cores of about 10 cm to about 100 cm in length by a magnetostrictive driver attached to one end. The pulses are received at any chosen distance along the core by a small crystal geophone resting on the specimen. The beginning of the supersonic pulse and the wave form of the received disturbance, together with the marks of an accurate timer by a quartz clock, are made visual and stationary on the screen of a cathode-ray oscillograph and the travel-time is measured. Thus the core is picked up at different distances and a travel-time curve is drawn from which the velocity of the waves is determined.The method is interpreted and the measuring device described. Graphs give several travel-time curves of different rock samples, drill cores, metal rods and rods of other solid materials. The elastic moduli E of the samples are communicated, and an example is given for determining Poisson's ratio S from longitudinal and transversal velocities on two cores of sandstone.

Notes: Two geometric methods are given: one for estimating the position of mass distributions from the gravity anomalies, the other for determining the position of a thin plate of magnetized material from the magnetic anomalies. Finally a computational form of Nettleton's method for the determination of density is given.