Vening Meinesz, Felix Andries
VENING MEINESZ, FELIX ANDRIES
(b. Scheveningen, Netherlands, 30 July 1887; d. Amersfoort, Netherlands, 10 August 1966)
The son of Sjoerd Vening Meinesz, burgomaster of Rotterdam and later of Amsterdam, and Cornelia den Tex, Vening Meinesz studied civil engineering at the Technical University of Delft, obtianing a degree in 1910. Shortly afterward J. J. A. Muller of the Rijkscommissie voor Graadmeting en Waterpassing asked him to join that government bureau and participate in a gravimetric survey of the Netherlands. Vening Meinesz agreed immediately; the survey would take a few years at most, and after that there would still be time to go into practice as a civil engineer. Gravity, however, held him in its grip for life.
It is not surprising that Vening Meinesz, who never married, became enamored of geodesy. Imbued as a child with the importance of solemn governmental affairs, he felt at home among the geodesists’ formal courtesy in a tradition of international cooperation that was over a century old. In 1911 he participated in the measurement of a base near Lyons by the Service Géorgraphique de l’Armée. He was later elected president of the Association Géodésique Internationale (1933–1955) and of the International Union of Geodesy and Geophysics (1948–1951), in each case for his contributions to these sciences and for his continued efforts to bring order to their entangled relations. That both geodesy and solid–earth geophysics were needed to interpret the results of Vening Meinesz’ gravity measurements, and that geology had its role as well, became abundantly clear after his first cruises. His strenuous efforts to achieve scientific interplay, however, elicited only a meager response.
One is struck by a strictly logical line of development in Vening Meinesz’ scientific achievements; everything seems to follow a careful plan, although of course no one could have foreseen that grave obstacles would yield to ingenuity and perseverance, or that salient features of the field of attraction of the earth exist–the Vening Meinesz belts of negative anomalies.
Vening Meinesz’ first measurement of gravity in the Netherlands confronted him with what appeared to be an insurmountable obstacle. At many stations it proved impossible to find a stable support for the pendulums; the continuous vibration of the peaty subsoil would lead to unacceptable errors in the results. Vening Meinesz’ efforts to overcome this difficulty were typical of the manner in which he confronted a problem. Far from trusting to luck in trying modifications of the experiments, he started with the thorough theoretical investigation embodied in his doctoral dissertation Bÿdragen tot de theorie der slingerwearnemingen (1915). In the introduction Vening Meinesz disparaged the originality of his own work; most of the disturbances had already been investigated when various authors had been confronted with them. His work, however, presents a systematic treatment starting from the fundamental equation
Where S represents the sum of all disturbances (storingen) the squares and products (second–order corrections) of which generally are negligible, so that, for instance, it is not necessary to introduce the temperature-dependence of the correction for finite amplitude.
For practical observations the most important conclusion of this theoretical work is that the mean of the periods of two isochronous pendulums swinging in the same plane with equal amplitude in opposite phases is not affected by the troublesome S–term, ÿ, the horizontal acceleration in that plane. Vening Meinesz had to use an apparatus in which two pairs of pendulums swung in two mutually perpendicular planes. For each pair the above conditions could be fulfilled with sufficient precision; and, using this method, by 1921 he had measured gravity at fifty–one stations covering the territory of the Netherlands at intervals of about forty kilometers. It was claimed that the mean-square error of the difference of the values for g from that obtained at the central station at De Bilt was somewhat less than 2 milligals. Gravity at De Bilt was compared, both before and after the survey, with the absolutely determined value at Potsdam, where Vening Meinesz had been instructed in the practice of pendulum observations by the director of the Geodetic Institute, Ludwig Haasemann. During the survey the chronometers were compared with the clock at the Leiden astronomical observatory by telephone and after 1919 the radio time signals from Paris were used.
While working to solve the problems of unstable support, Vening Meinesz was tempted to direct his efforts more boldly to the apparently overambitious plan of measuring gravity at sea. In his Theory and Practice of Pendulum Observations at Sea, he again began with the first equations of motion for two pendulums affected by the same horizontal accelerations:
then jubilantly exclaimed:
It is clear that ÿ can be eliminated from these two equations, and is the fundamental principle of the method. If the pendulums are isochronous. so that l1 = l2, the result of this elimination is very simple: the difference of the equations gives
which has the same shape as the equation of motion of an undisturbed pendulum of the same mathematical length l and an angle of elongation (ϑ1 – ϑ2). We reach in this way the important conclusion that the difference of the angles of elongation may be considered as the angle of elongation of a fictitious pendulum, which is not disturbed by the horizontal accelerations of the apparatus, and which is isochronous with the original pendulums.
A shipboard attempt proved a complete failure, however, for even tiny surface waves striking the hull cause fairly high accelerations. It was necessary to wait for so exceptional a calm that the method was totally impractical. Vening Meinesz gratefully acknowledged the suggestion of F. K. T. van Iterson, chief engineer of the state coal mines, who, while on a submarine training dive conducted by the Dutch navy, had been struck by the profound tranquillity during submersion. Waves are in fact damped exponentially with depth, so that only 2 percent of the amplitude remains at a depth equal to the wavelength. The brisk movements of shorter waves were therefore imperceptible at the moderate depth then attainable by submarines, while the disturbance caused by the longer waves was handled by the fictitious pendulum. (See Figure 1.)
The first voyage to measure gravity at sea, from the Netherlands to Java in 1923, began under adverse circumstances. The small submarines moved slowly when submerged and could cover only limited distances. As a rule dives were restricted to the demands of the gravity observations. A heavy six-day storm wreaked the usual hardships on a
Vening Meinesz’ Gravity Expeditions at Sea
|Year||Submarine H.M.S.||Route||Number of Observations|
|1925||K XI||Holland–Alexandria||10 (experiments with new pendulum apparatus)|
|1927||K XIII||Java Deep||26|
|1934–35||K 18||Holland–Buenos Aires–Cape Town–Freemantle–Java||237|
|20(experiments on wave motion and Browne term)|
boat of 630 tons, aggravated by the limited room, by water coming through the hatch, and by clothes refusing to dry. But, Vening Meinesz reported, “The worst thing of all was that the pendulum apparatus could not be used.” (The rolling at a depth of thirty meters was still heavy enough to endanger the pendulums.) Finally, off the coast of Portugal with a smooth sea, three dives afforded an opportunity for observations. It now became clear that the apparatus, if it was to operate under normal waves, would have to be fitted in a kind of cradle to counteract the roll of the boat.
The harbor of Gibraltar was entered, and Vening Meinesz quickly developed the pendulum records; they showed good results, suggesting that no difficulties would arise if the tilt of the instrument could be kept small enough. The British commander gave permission for the naval yard to construct a suspension about an axis parallel to the keel. On the voyage to Java this tenacity was rewarded with thirty successful observations.
The Sterneck apparatus dealt separately with each pendulum, and the horizontal accelerations gave rise to irregular records that required days to interpret. Vening Meinesz constructed an entirely new instrument that was admirable for its ingenuity as well as for exquisite craftsmanship. The fundamental principle, elimination of ÿ by subtraction,
is applied in a beam of light reflected from one pendulum mirror onto the opposite mirror of a second pendulum, thus recording the desired fictitious pendulum (Figure 1). This device proved highly successful; from an engagingly regular pattern the value of gravity can be derived in a few hours. Furthermore, the strictly regular records have the advantage of showing at a glance that some conceivable disturbances affecting amplitude do not exist. Actually there are three pendulums swinging in the same plane; the outer two, each combined with the middle one, yield the records of two fictitious pendulums. The amplitude of the middle pendulum is kept as small as possible, and therefore the periods of the outer pendulums enter preponderantly into the result. Hence their stability can be relied upon as long as the slight difference between the two fictitious periods remains the same. The small amplitude of the middle pendulum is recorded separately against a short auxiliary damped pendulum, and this record is used to evaluate the correction for finite amplitude. A second damped pendulum records the tilt of the swinging plane. (In the Sterneck instrument the latter expedient was unnecessary; each pair of pendulums indicated the tilt of the swinging plane of the other pair.)
A cruise from Holland to Egypt to test the new apparatus (1925) gave satisfactory results. On the first cruise to Java the recording apparatus was separately mounted at the distance of one meter required for an easily measurable deflection of a light spot on the records. Thus a fixed direction was necessary for the registering beam of light, which therefore was directed through the axis of the cradle, made hollow for this purpose. This axis, being constantly perpendicular to the swinging plane, had to be kept horizontal with a tolerance of thirty minutes. This requirement demanded extremely careful trimming of the boat, and placed a great strain on the helmsman and the crew, who were not allowed to move about.
Suspension in gimbals seemed unavoidable, which necessitated rearrangement of the recording piece so that it could be joined firmly to the pendulum box. To retain its full length, the light path was “folded” by introducing more prisms. A good example of Vening Meinesz’ attention to details is seen in the length of this path’s being 1,162 millimeters, whereas the focal distance of the exit lens is 1,110 millimeters. This excess length compensates for the loss of convergence by refraction of the rays as they enter a prism. (For the collimator these figures are 653 and 616 millimeters.)
His equipment now being shipshape, Vening Meinesz strongly desired to take it to sea. Fortunately he combined technical skill with a rare gift for persuasion. His tenacious politeness succeeded in convincing government officials and the admiralty of the urgent need for gravity values on all oceans. He next inspired the Dutch submarine service to unhears-of achievements. At that time it was still though impossible for submarines to travel long distances without escort ships on the surface. K XIII, however, crossed both the Atlantic and Pacific oceans unescorted. Several longer and shorter cruises followed over the southern Atlantic and the Indian Ocean and the seas of Indonesia, yielding hundreds of observations (see Table 1).
While Vening Meinesz was on his 1937 cruise, B. C. Browne, a young geodesist at Cambridge, sent him a letter that might be summarized as “Dear Sir, you have made a mistake.” On studying Browne’s arguments, Vening Meinesz had to admit that the numerous regular corrections failed to cover some of the disturbances due to the motions of the boat. He made this admission gracefully, without vexation or excuses. It is even possible that he enjoyed the opportunity to work again with the mechanics of the pendulum and to produce in corroboration three papers on “Browne terms” and the second volume of Theory and Practice.
With the primitive cradle, the single axis of which was fixed in the direction of the keel, an acceleration , parallel to the axis and hence to the knife-edges, clearly could not affect the other component of horizontal acceleration, ÿ, had been dealt with by the fictitious pendulum device. On the other hand, it is equally clear that suspension in a complete gimbal system requires consideration of the resultant of gravity and acceleration given by vector addition: .
A piece of good luck–as Vening Meinesz put it–made it possible for the vertical acceleration to be recovered from the old records. Assuming a circular wave movement, as was concurrently deduced form several wave theories, the horizontal acceleration should be equl–and thus Browne’s correction could be introduced. For the future, however, a more direct determination seemed worth trying. If the angle between apparent gravity and the true vertical could be found, the horizontal accelerations would be known. This would be no easy task, for the whole apparatus in its gimbals follows apparent gravity.
Vening Meinesz may well have been equally pleased with the opportunity to show that his skill in tackling such problems had not deteriorated during twelve years of making routine measurements. In close cooperation with Browne the “slow pendulums” were designed and used as a highly simplified but effective artificial horizon. A slow pendulum consists of a horizontal brass beam balanced on a knife-edge. The center of gravity being only a few tenths of a millimeter beneath this edge, the pendulum’s period amounts to about half a minute. Therefore, waves going round in less than ten seconds can set it in motion to only an insignificant degree. Keeping a steady position in space, two such pendulums thus afford a means for registering the tilt of the apparatus in the gimbals (or, rather, of the damped pendulums, which, because of their short periods, follow exactly the changing direction of apparent gravity). For recording the slow pendulums, three lenses and thirteen prisms had to be added to the four mirrors, four lenses, and twenty-three prisms already in use. The housing of the new pendulums could be fitted into the eighty millimeters left between the main box and the recording box, and the whole instrument now appeared to have been made all of a piece.
The instrument was used for only a short time, however, because the outbreak of World War II suspended the peaceful use of submarines. After the war the Royal Dutch Navy was again helpful although it had a greatly reduced number of submarines. Vening Meinesz, however, had to delegate the work to younger observers. For over thirty years his apparatus (of which some five copies are in existence) provided the only means for measuring gravity at sea, but in the late 1950’s it was superseded. Then spring gravimeters mounted on stabilized platforms on surface ships began to record gravity values along continuous profiles. American investigators used the Vening Meinesz method until 1959, the number of stations then amounting to nearly 3,000.
Vening Meinesz’ Observations in Relation to Geodesy . Geodesy seeks to ascertain the shape and dimensions of the earth. Altitudes and depths must refer to a certain curved surface called the geoid, which is the gravity-equipotential surface coinciding with the mean surface of the sea and its continuation on land. The geoid is approximately an ellipsoid of revolution, minor deviations being due to irregularities in the distribution of masses. These deviations are therefore closely linked to the values of gravity as measured by pendulum observations. If gravity is determined everywhere on the earth, the shape of the geoid with reference to the ellipsoid can be calculated according to a formula deduced by Stokes. This calculation greatly occupied Vening Meinesz. For instance, Gravity Expeditions at Sea, II , 13–17, concludes with “In the future it will become possible to apply the Theorem of Stokes in its full accuracy and to solve in this way the central geodetic problem: the determination of the Figure of the Earth.”
Values of gravity averaged over regions extending some tens of kilometers are appropriate for this purpose. Observations on land have the disadvantage that a nearby irregular mass may cause a severe deviation from the mean. At sea this problem does not arise, since no irregularity can be nearer than the sea floor. Through Vening Meinesz’ and English and American observations, approximation was already possible for about half the globe. Recently the central problem was solved by observing the trajectories of satellites. Their acceleration at any moment is that of gravity averaged over a region the radius of which is proportional to the distance of the satellite from the earth (about 100 kilometers).
Since the eighteenth century geodesists have asked whether the geoid, instead of being represented by an ellipsoid of revolution, should rather be seen as a triaxial ellipsoid–that is, whether the equator was a circle or an ellipse, the latter shape involving a systematic variation in the values of gravity. Having closed a ring of observations around the globe, Vening Meinesz could rule out the possibility of regular deviations and therefore establish that the equator must be represented by a circle.
Isostasy. The principle of isostasy is usually elucidated by analogy with blocks of wood or a mass of ice floating on stagnant water. The experiments by which we try to understand the origin of the geographic and geologic structure of the earth are perforce on a small scale. Small-scale models are very deceptive because of the strength of materials factor. In order to imitate real rocks on a continental scale the tensile strength has to be practically zero. Hans Cloos and P. H. Kuenen were among the first to experiment with wet clary or soft wax, but in general it is impossible to get all the mechanical parameters to scale and difficulties multiply. These problems do not affect Vening Meinesz’ numerous calculations in applied mechanics. For large nonplastic deformations and for disruptions, calculations are hardly possible. For small strains seismic data are very useful and allow fairly accurate estimates of the specific weight of materials at depth.
In the latter half of the nineteenth century the earth came to be seen as originally a molten sphere, which at an early stage of cooling came to be enclosed in a strong crust of consolidation. Vening Meinesz constantly had in mind an earth model with an elastic crust on a viscous substratum. This led to his preference for interpretation in terms of regional isostasy, reducing observed gravity by applying the so-called regional isostatic compensation. For such a calculation a number of assumptions are tried regarding the thickness of the crust (twenty or thirty kilometers) and its strength, resulting in a bend area with a radius of 232, 174, 116, 58, or 29 kilometers (also 0 kilometers: local compensation). An assumption resulting in a complete reduction of the anomaly may be true–at least it cannot be said to be wrong. The great drawback of gravity measurements, however, is that although a value can be calculated from a given repartition of masses, the reverse calculation is impossible. A given set of gravity values can result from a wide range of depth configurations that depart in many ways from a simplified assumption. In addition, in some instances none of the regional isostatic assumptions made by Vening Meinesz can be said to give satisfactory results.
The Vening Meinesz Belts. The most striking feature shown by the earth’s gravity field was discovered by Vening Meinesz during his earlier cruises. The “Vening Meinesz negative gravity anomaly belts of island arcs,” as they were called by H. H. Hess (Gedenkboek, 183), with their bold, steeply descending lows of gravity, are not reduced to zero by any of the common suppositions. Winding for thousands of miles in gentle curves, along deepsea trenches and rows of mostly volcanic islands, the belts often follow the outcrop of a roughly stratiform cluster of shallow and deep earthquake foci dipping at about forty-five degrees landward.
The regular concurrence of these conspicuous phenomena challenged every inventive mind to discover their significance. Vening Meinesz directed his attention chiefly to the gravity anomalies; his explanation of them by means of the buckling hypothesis brought strong reactions from geologists. Throughout he used the classic tool of compression in a rigid crust. Strong enough to overcome the resistance of the crust, the compression would cause a thickening along a line of weakness that apparently coincides with the frontier between a continent or shallow sea and the ocean. This thickened part of the crust, representing increased mass, naturally sinks to restore isostasy, thus causing the compressive forces to deviate downward. On further compression the crust will be folded and the folded parts pressed downward, thus causing light crustal rocks to take the place of heavy mantle materials. This process explains the observed negative gravity anomalies. The Dutch geologist Kuenen, who often did model experiments to explain geological phenomena, illustrated this buckling by compressing a floating layer of soft wax, which behaved exactly as Vening Meinesz had predicted. The downward buckling was soon interpreted as a geo syncline receiving sediments because of the compensating rise of the borders, which led to emergence of land at the continental edge and its subsequent attack by erosion. The resulting sediments, filling in the depression, would then be folded by continued pressure. The deepsea trenches often are situated somewhat farther from the continent than the most strongly negative anomaly; this situation is explained by the sediments’ having filled part of the trench.
A strong departure from isostasy cannot be of unlimited duration. In due course the base will be buoyed, thus producing an elevated strip of folded sediments. In Vening Meinesz’ view, folded mountain chains, such as the Alps, represent buckles of an older period that now reach great altitudes because of an older period that now reach great altitudes because of isostatic compensation by the remnants of a base of crustal rocks. The view that the Indonesian archipelago was comparable with an initial stage of Alpine mountains had long been considered by geologists. This view, joined with Kuenen’s experiment, secured a favorable reception for the buckling hypothesis.
Areas of strong anomalies are necessarily of limited size, at least in breadth. A large, round domain could not depart from isostasy to a degree comparable with the negative anomaly belts, unless one accepted an exorbitant value for the strength of the crust. An example of an extensive area about 1,000 kilometers across having moderate negative anomalies is in Scandinavia and is readily interpreted in connection with the thick ice cap formerly present there. That ice cap would have been brought into isostatic equilibrium during the long glacial epoch by weighing down the crust of the earth. It melted rather suddenly, a short geological time (6,000 years) ago. In correspondence with the remaining negative anomaly, the land is now rising. In combination these two facts, numerically assessed, enabled Vening Meinesz to calculate the resistance of the substratum, which, expressed in terms of viscosity, yields a value of 1022 poises. He used this value for calculations concerning the velocity of the movement that other departures from isostatic equilibrium may cause.
Convection Currents in the Mantle . In the 1920’s Arthur Holmes, among others, had used convection currents to explain continental drift. By general agreement, however, the geoscientists of the northern hemisphere had also dismissed the sound arguments offered by Wegener, bluntly denying the possibility of wandering continents. For Venning Meinesz the crust was so rigid that he had no choice but to state that the continents were firmly fixed, while the interior of the earth became the site of great activity. He often thought in terms of a cooling earth and accepted an increase in temperature with depth greater than the adiabatic gradient. The resulting departure from equilibrium led to convection currents, about the velocity of which the Scandinavian viscosity could give information. The drag of the currents on the crust, in Vening Meinesz’ view, led to no more than a buckle here and there, notably along the Vening Meinesz belts–which, therefore, had to be located near a descending branch of the currents.
Vening Meinesz was strongly convinced that he had derived an unshakable argument for the reality of convection currents from a regularity apparent in the development of the earth’s relief in spherical harmonics. He showed this regularity to be present, at first, in the development calculated in 1922 by Adelbert Prey up to the sixteenth order, which, at his request, was extended to the thirty–first order by the Mathematical Center of Amsterdam. Its numerical result reflects mainly the contrasting heights of oceans and continents, whereas it is their distribution on the globe that must be closely linked with the system of convection currents: around sinks in this system patches of light continental rocks had floated together in the formation of the land on the surface of the globe. This all had taken place in a primordial stage, when the earth was still largely molten. Through cooling, the crust soon became so rigid as to resist further rearrangement; throughout the whole of geological time the continents retained their shapes and relative positions despite continued convection underneath. (When, in the early 1960’s, continental drift was held to be established by paleomagnetism, the currents were still there, serving as a motor.)
Convection had been challenged; and seismic data led to the view that a lower part of the mantle, because of higher specific weight, could not be involved in those currents. Vening Meinesz argued that the high density at depth was probably due to the presence of olivine in the spinel modification. The reversible transition between the olivine and the spinel phases could not be an obstacle, yet the boundary between them ought to be sharp–and, according to the seismologists, it was not. This objection was met by the plausible assumption of a fayalite component that caused phase equilibrium to persist through a certain range of pressures. These ideas were worked out with the physico–chemists J. L. Meijering and C. J. M. Rooymans, and were likewise taken up by A. E. Ringwood.
Problems like these, clearly needing information from many different fields, strengthened Vening Meinesz’ conviction that interdisciplinary cooperation is necessary when fundamental principles are involved. He felt this to be especially the case in geophysics and geology, and he had some success. Certain chapters in volume II of Gravity Expeditions at Sea written by the prominent Dutch geologists J. H. Umbgrove and Kuenen resulted in a genetic interpretation of the Indonesian archipelago. Twenty years later B. J. Collette submitted a doctoral dissertation concerning the effect of gravity on the geology of the Sunda Islands. In 1955–1957 Collette measured gravity on the North Sea, the shallower parts with a static gravimeter lowered to the bottom and the deeper northern part, up to 61° north latitude, with the Vening Meinesz instrument.
Vening Meinesz maintained a keen interest in the ocean floor. Later investigators did not forget the grand old pioneer: his honors steadily increased, culminating in the Vetlesen Prize in 1962. In 1963 the new institute for geophysics and geochemistry at Utrecht University was named for him.
I. Original Works. A list of Vening Meinesz’ publications to 1957 is included in the jubilee volume, Gedenkboek F. A. Vening Meinesz, which is Verhandelingen van het Nederlandsch geologisch–mijnbouwkundig genootschap, Geol. ser., 18 (1957), with portrait. His most important works are Theory and Practice of Pendulum Observations at Sea, 2 vols. (Delft, 1929–1941), with illustrations of apparatus and records: The Gravity Measuring Cruise of the U.S. Submarine S–21 (Washington, 1930), written with F. E. Wright, which includes illustrations of apparatus and records as well as a full explanation of the instruments and method; and Gravity Expeditions at Sea, 5 vols. (Delft, 1932 – 1960; II, repr. 1964), vol. II written with J. H. Umbgrove and P. H. Kuenen.
II. Secondary Literature. See B. J. Collette, “In Memoriam Dr. Ir. Felix Andries Vening Meinesz,” in Geologie en mijnbouw, 45 (Sept. 1966), 285 – 290, in English, with portrait and complementary bibliography to that in the jubilee volume (see above); J. L. Meijering and C. J. M. Rooymans, “On the Olivine–Spinel Transition in the Earth’s Mantle,” in Proceedings of the K. nederlandsche akademie van wetenschappen, Ser. B. 61 (1958), 333 – 344; and J. Lamar Worzel, “Pendulum Gravity Measurements at Sea, 1936 – 1959,” Contributions. Lamont Geological Observatory, no. 807 (1963), which contains the most important continuation of Vening Meinesz’ observations and interpretations.
Felix Andries Vening Meinesz
Felix Andries Vening Meinesz
The Dutch geodesist and geophysicist Felix Andries Vening Meinesz (1887-1966) pioneered in the field of gravity measurements.
On July 30, 1887, F. A. Vening Meinesz was born in Scheveningen. He attended the public schools in Amsterdam, the city in which his father was the burgemeester, and in 1910 obtained his diploma in civil engineering from the Technical University in Delft. He was first employed with the Geodetic Commission of the Netherlands, his task being to continue the gravimetric survey of the country with the aid of the contemporary pendulum instruments. The unstable soil of the Netherlands proved a serious handicap, and it was impossible to attain the desired accuracy. Vening Meinesz tried to eliminate the disturbing movements of the soil by using two pendulums swinging from the same support. His experiments, combined with a mathematical analysis of the sway of the entire system, proved very successful. Further experiments, carried out aboard submarines, resulted in the construction of the improved Vening Meinesz pendulum apparatus, which, for the first time in the history of geodesy, made possible the precise measurements of gravity on the oceans.
During the years 1923-1939 Vening Meinesz made 11 long journeys in submarines with his apparatus, cruising all oceans and especially in the East Indian Archipelago. At the same time, he expanded the mathematical theory which was used to convert the physical information about the gravity field to geometric information about the shape of the earth. In this way, the solution of the fundamental problem of scientific geodesy, that is, the mapping of the entire earth in one comprehensive system, was made possible both theoretically and practically. Only the use of artificial satellites can rival, to some extent, the gravimetric method initiated by the efforts of Vening Meinesz.
Meanwhile, Vening Meinesz's scientific interest was directed into deeper things. From his gravity maps of East India he found a long narrow strip of negative anomalies which he interpreted to be the first visible sign of a future mountain range. His investigations of this dealt with the internal structure and currents of the earth, the isostatic compensation of topographic formations, and the upheaval of the mountain ranges. Other, later discoveries in the field of geophysics gave plenty of support to his theories.
Vening Meinesz taught geodesy, cartography, and geophysics at the State University in Utrecht and at the Technical University in Delft. He was also the director of the Institute of Meteorology (1945-1951) and the president of the International Union of Geodesy and Geophysics (1948-1951). On Aug. 12, 1966, he died in Amersfoort, Netherlands.
The Gedenkboek F. A. Vening Meinesz (1957), honoring Vening Meinesz on his seventieth birthday, contains, mainly in English, a description and evaluation of his achievements and a complete bibliography of his publications, together with articles by his colleagues. His contributions to geodesy are discussed in general books such as Guy Bomford, Geodesy (1952; 2d ed. 1962), and Weikko A. Heiskanen and Helmut Moritz, Physical Geodesy (1966). □