The gravimeter of professor Vening Meinesz

On a cold winter day, 21 November 1934, professor Vening Meinesz turned on his pendulum apparatus. Just a few minutes ago, the submarine K-XVIII dived to a depth of 30 meters [1]. At these depths, the motion of the surface waves was dampened such that it did not influence the delicate measurements done by the professor. This particular observation would mark the 500th measurement, observing the tiniest changes in the Earth's gravity field. This new gravity dataset would reveal many new mysteries of our home planet and would be the life’s work of Vening Meinesz. It is all documented in scientific publications of four volumes called Gravity Expeditions at Sea, followed by a fifth volume with gravity observations done by his students. Along these expeditions, the professor had brought his specially designed pendulum apparatus, or folklorised by the sailors on board the many submarines: Het Gouden Kalf (the Golden Calf).

The pendulum apparatus of Vening Meinesz, also known as "Het Gouden Kalf" (the Golden Calf). Positioned on the left side is the protective casing with the recording instrument on top. On the right side is the pendulum apparatus with the three pendulums at the back. 

During the beginning of 1900, Earth's gravity field was only measured on land. The classical single-pendulum device needed a stable platform, which was impossible to achieve on ships. The swell and the shaking of the large engines made it impossible to keep the pendulum stable. Therefore, 73 percentage of the Earth's gravity field was yet unknown to the geodetic community. A young civil engineer from the Technische Hogeschool in Delft would change this. After his graduation in 1915, Felix Andries Vening Meinesz, son of a mayor of Rotterdam and Amsterdam, was given the task at the Rijkscommisie voor Graadmeting to set up Holland’s first gravimetric base station network. For this project he needed a device that could measure the gravity field with the highest accuracy possible, which in those days were pendulum instruments. Unfortunately, he found out that the soil of the Netherlands was very unstable. The waves of the North Sea, when smashed at the dunes of the Dutch coast, would generate solid waves in the soils that affect the motion of the pendulum when observing in Delft. 

Professor Vening Meinesz changed his location of research to a small town called de Bilt. In particular, he moved to the KNMI (Royal Dutch Meteorological Institute). Here, in the basement of the KNMI building at the Kloosterweg, underneath the office of the director of the institute, Van Everdingen, Vening Meinesz commenced his measurements and thorough calibrations with new type of pendulum instruments [2]. Evidence of his presence can still be found at the old KNMI building, where a historical plaque indicating the gravimetric base station is still present on the left rail of the concrete stairs on the west side of the building. The location at the KNMI was in particular useful for Vening Meinesz, because the geological subsurface made it a very stable environment for gravity observations. Due to the stable subsoil, external motions were dampened and the remote location would decrease the oscillation of lorries and inland shipping. The extreme stable surroundings made it possible for the professor to test and calibrate his equipment with extreme precision, resulting in very accurate measurements of the gravity field later during his expeditions at sea [3].

Geodetical plague of the gravity measurement at the old building of the KNMI, marking the location of the gravimetric reference point.

Due to the success of his work in the Netherlands removing external accelerations from the measurements, Vening Meinesz decided to try measuring on board a surface ship. Unfortunately, the motion of the waves and the shaking due to the steam engine were too severe and the observations were worthless. Vening Meinesz, slightly disappointed, presented his negative results in Maastricht at the 19th Nederlandse Natuur- en Geneeskundig Congres. After his presentation, Ir. F.K.Th. van Iterson (1877 - 1957), director of the Staatsmijnen, suggested to use submarines instead of surface ships [4]. Wave motion at 30 meters depth would be dampened and submarines use quiet electro-motors when diving. This touch of serendipity was the start of many submarine gravity expeditions at sea.

Improving during submarine expeditions - the true engineering spirit

The Golden Calf did not have its final form from the beginning. Vening Meinesz, being a true engineer, modified the apparatus many times during his numerous submarine voyages, always improving the design. During his work on gravimetric reference network of the Netherlands, the professor used the Von Sterneck-Stückrath gravimeter (1887), but it proved to be difficult to operate during the long K-II submarine expedition (1923). Vening Meinesz decided to design a new gravimeter from the experience during this expedition. He ‘cannibalised’ the pendulums of the old Von Sterneck gravimeter (the casing of the old Von Sterneck was in 2015 still in possession of the KNMI). Vening Meinesz used the principle of the Von Sterneck gravimeter to acquire high precision. However, his mathematical analyses of the pendulum motion showed that he only needed three pendulums for two independent measurements instead of four [5]. The pendulums were placed in an along-direction pair-wise configuration. One pair of pendulums would produce an independent gravity observation. This was done to eliminate any external horizontal motion. The differential equation to describe a pendulum’s motion attenuated by a horizontal acceleration is as follows:

The angle of deflection of the pendulum is represented by θ, whereas the length is l and gravity is noted by g. The horizontal acceleration is given by a_y. With one pendulum it is impossible to decouple the value of g from the external accelerations acting on the instrument. Therefore, two pendulums are used, where the difference of their deflection angles is measured. The external acceleration, which is similar for both pendulums, is then mitigated by subtraction.

The pair θ₁-θ₂ is observed by an ingenious design of light rays, mirrors and prisms on the top of the pendulum apparatus. This second-order differential equation is easy to solve. For small initial amplitudes of the virtual pendulum, this will result in the famous pendulum relation of Christiaan Huygens:

The period of the virtual pendulum (T_1-2) can be determined from the recordings of the light rays. The recording instrument, a small ‘dark chamber’ with photographic roll of paper, was situated on top of the pendulum casing. A clockwork contraption unrolled the photo paper during the observations, such that the defections of the pendulum pair were recorded. 

Top view of the pendulum apparatus illustrating the locations of the three pendulums. The coloured dashed lines depict the path of the light rays from the recording apparatus. Red and green show the recording of the motion of two paired-pendulums, whereas blue depicts only the recording of the middle pendulum. The yellow light ray was observing the tilt and temperature changes of the instrument.

This unrolling of the photographic paper was not accurate enough, so Vening Meinesz designed another approach to accurately determine the time periods of the pendulum. The professor always took the state-of-the-art chronometers on board the submarine expeditions. One chronometer, the Nardin 212, was taken on almost all the expeditions and was accurate up to 0.04 sec/day. He asked for alternations made to the chronometers, such that they were able to open and close an electrical circuit every 0.5 seconds. The electric pulse was then used to control a shutter in the recording instrument to shortly interrupt the light ray. This resulted in small 0.5 markings in the final recording sheets and could be used to determine the time period with extreme accuracy.

During the submarine expeditions, Vening Meinesz always kept alternating the device and improving on its accuracy. The smallest details were taken into account. For example, when the submarine dived to 30 meters depth, the pressure of the air inside the enclosed vessel increased with sudden temperature changes of a few degrees. Because the Golden Calf had thermal insulation in the form of sheep’s wool, the air temperature inside the pendulum apparatus did not experience these sudden changes. However, during the 45 minute long observations, gradually the temperature would change due to leakages in the cover. In turn, this would effect the very sensitive measurements. A small electric heater in the bottom of the device would be turned on before the dive to heat up the air a few degrees to simulate the temperature of the air after dive. In this way, during the dive there would be no temperature offset between the air in the submarine and inside the pendulum device. It needed some practice of the operator, but it was effective.

A 3D computer model of the submarine Hr. Ms. K-XVIII made from the old engineering drawings of the shipyard Fijenoord

The name "Golden Calf" was given to the pendulum apparatus by the submarine crew. The story goes that during the gravity observation all the non-essential personnel had to lie down in their bed-bunk to create a very stable submarine. The Dutch Navy declared that this was a degradation of personnel life and well-being and therefore paid the submarine crew 1 guilder (currency of the Netherlands at the time) per dive extra wage for compensation. So, when the crew members saw the pendulum apparatus carried on board, they rubbed their hands and cheered on the coming of the Golden Calf, because this meant good wages. Of course, the bronze platting will have had some influence in the creation of the name. The abundant use of bronze in the casing has given it a gold colour, which could also lead to the name Golden Calf.

Results and legacy

One of the well-known theories of Vening Meinesz is his model to explain the stable situation of continents, mountains, and volcanic islands. Previous researchers assumed that these large masses were floating on a liquid mantle, like an iceberg floats in the water. From the observations with the Golden Calf, Vening Meinesz could deduce that the solid crust was partially responsible for holding up the mountains. Gravity observations of coastal regions and volcanic islands showed that the crust acted as a plate and experienced elastic bending due to the loading of the extra topography. This theory is now called Vening Meinesz isostasy and is especially successful in explaining the gravity field of oceanic islands.

Old gravity results from Vening Meinesz of Indonesia (top) compared with current knowledge of the gravity field (bottom) from combined ground, seaborne, airborne, and satellite gravimetry. Please appreciate the accuracy that Vening Meinesz already obtained almost 100 years ago.

The Golden Calf revealed many secrets of the deep ocean. For example, the gravity signal at the Mid Atlantic Ridge differs from the gravity anomalies at the famous Vening Meinesz belts (now known as subduction zones). Vening Meinesz found strong negative and positive gravity anomalies situated parallel to the volcanic arc in the East Indies (Indonesia), which could not be explained by isostasy. This indicated a dynamic process along the southwest shore of the East Indies. Similar gravity anomalies were found in the West Indies, where Harry Hess, a young American scientist, was responsible for most of the gravity surveying. Harry Hess is mostly known for the founding father of the geophysical model for the spreading ridge, which occurs at the Mid Atlantic Ridge [6]. This model is believed to be the first step in accepting the tremendous powerful theory of plate tectonics. At the time of Vening Meinesz this was not yet known and both subsurface structures showed similar volcanic geology and seismic activity, but because of the different gravity anomalies Vening Meinesz and Harry Hess knew that different geological processes were at play. Other results thanks to the Golden Calf and Vening Meinesz were the first gravity measurements of a transform fault, the Romanche Trench (at the time theorised as volcanic craton). Also, the gravitational signatures of subsurface structures like the Walvis Ridge and the Rio Grandes Rise were observed during the submarine expeditions. 

Up until 1960, the Golden Calf was the only instrument that could measure the gravity field with such precision. One of the last scientific expeditions with the instrument was made in 1960 [7], to measure the gravity field in the South Atlantic and Indian Ocean. The instrument was succeeded by the Graf-Askania gravimeter, which was a spring gravimeter on a stable platform [8]. Overall, the Golden Calf was responsible for 37 years of ocean gravimetry.

The original Golden Calf is now in possession of the TUDelft Library, section Heritage. The apparatus is loaned to the museum of TUDelft, the Science Centre, where it will be placed in the geodesy section, such that the public can enjoy the beauty of this incredible contraption. In 2014-2015, a project group from TUDelft documented and studied the voyage of Vening Meinesz on board the K-XVIII, where special attention was given to the Golden Calf and its measurement principle. The project was developed under the larger Expedition Wikipedia project. The results of that project can be found on an interactive website: expeditiewikipedia.nl/#vening-meinesz

References

[1] Wytema, M.S. (1935), Klaar voor onderwater - Met Hr. Ms. K XVIII langs een omweg naar Soerabaja, Andries Blitz, Amsterdam.

[2] Gedenkboek F.A. Vening Meinesz (1957), Verhandelingen van het Koninklijk Nederlandsch Geologisch - Mijnbouwkundig Genootschap, Geologische serie deel XVIII, Drukkerij v/h Mouton & Co, ’S-Gravenhage. 

[3] Vening Meinesz, F.A. (1921-1945), Gravity expeditions at Sea Vol. I-IV, publication of the Netherlands Geodetic Commission, Drukkerij Walkman, Delft.

[4] van Hengel, TJC, (2014), The Diving Dutchman: het marien-gravimetrisch onderzoek van F.A. Vening Meinesz (1887-1966), PhD Thesis, University of Leiden, Leiden.

[5] Vening Meinesz, F.A. (1929), "Theory and practise of pendulum observations at sea”, publication of the Netherlands Geodetic Commission, Drukkerij Waltman, Delft.

[6] Hess, H. (1962), History of Ocean Basins, In A. E. J. Engel, Harold L. James, and B. F. Leonard. Petrologic studies: a volume in honor of A. F. Buddington. Boulder, CO: Geological Society of America, 599–620.

[7] Talwani, M. (1962), Gravity Measurements on HMS Acheron in South Atlantic and Indian Oceans, Geological Society of America Bulletin, 73, 1171-1182.

[8] Graf, A. (1958), Das Seegravimeter, Z. Instrumentenkd., 60, 151-162.