The Cambridge Pendulum Apparatus J. E. Jackson “A golden bud set on a leafless stem leads to my result”-E. Bramah, Kai Lung Unrolls his Mat. Summary Downloaded from https://academic.oup.com/gji/article/4/Supplement_1/375/650518 by guest on 24 September 2021 The three-pendulum method, developed and used by Lenox- Conyngham, was superseded in 1930, on the arrival of a new vacuum box for swinging two pendulums. With three invar pendulums taken over from the earlier apparatus and three new ones acquired in 1931, this box is the centrepiece of the apparatus which has been in use up to the present day, for geophysical investigations and for establishing gravity reference stations in many parts of the world. This article describes briefly the apparatus and the various modifications of pro- cedure and changes of auxiliary gear that have taken place in the past 30 years. A list of the work done with the apparatus is given. I. Introduction For two and a half centuries, geodesists have been studying the Figure of the Earth. Methods of investigation in this field are divisible into two classes, the geometrical and the physical. In the nineteenth century, surveyors with their triangulation and astronomical observations, helped by the utility of their work as a contribution to map-making, got away to a good geometrical start and produced a great many “Figures of the Earth”, each one of them closely fitting a small part of the geoid surface. Geodesy, in the modern sense of the word, stems from Newton’s law of gravitation. The variation of gravity with latitude, in a way involved with the Figure of the Earth, and expressed in the famous formula of Clairaut, was the basis for the physical methods of investigation. However, instruments and obser- vations developed slowly on this side. Two reasons for this are obvious enough: the techniques available were inaccurate and tedious, and the results had scarcely any utility value. The practical method for measuring gravity was the reversible pendulum. Many early observations were made with such instruments. It was soon realized, however, that the direct measurement of gravity acceleration in the field was beset by great difficulties, and that for most geodetic purposes the interesting feature of gravity was its variation from place to place, rather than its actual value anywhere. Out of this came the “invariable pendulum” method. If a pendulum of any kind is taken from place to place and its period of oscillation is measured, the variation of gravity is calculable from the elementary formula g2T22 = glT12. 375 376 J. E. Jackson The essential condition is that the pendulum shall not change: more realistically, any change, as that due to a different temperature for instance, is known and can be allowed for. The pendulum may be of quite conventional design, for no linear measurement is needed: indeed, grandfather clocks have been used as instru- ments for measuring gravity differences. Special pendulum apparatus for measurement of gravity differences in the field was in use quite early in the nineteenth century. The work was described as “finding the length of the seconds pendulum”. Remembering that the range of variation of gravity over the Earth‘s surface is about 5ga1, we see that an Downloaded from https://academic.oup.com/gji/article/4/Supplement_1/375/650518 by guest on 24 September 2021 accuracy of a few milligals is required if the physical method is to be comparable in accuracy with the geometrical method for finding the flattening of the Earth’s figure. Early differential pendulum work achieved this standard, and the past fifty years have seen a considerable improvement of accuracy, particularly due, of course, to the introduction of radio signals and the use of electronic auxiliary equipment. Gravity observations have now played their part in the determination of the Figure of the Earth, and this investigation has reached its consummation in Sir Harold Jeffreys’s studies and in the International Gravity Formula. (Maybe, the last word has not yet been said on this theme!) However, the observations also detected the anomalous gravity fields connected with structural features of the Earth’s crust. Thus, pendulums were swung for geophysical exploration. We recall the discovery of the interesting features of under-sea structure in the East Indies by Vening Meinesz, and the investigation of rift-valley structure by Bullard, as examples. The co-operation of pendulums with the geological hammer came to an end, however, about twenty years ago when the job of tracking local gravity anomalies was taken over by the much more convenient gravity meters. One might have been tempted to forecast a decline in pendulum swinging, but events have proved to the contrary. Developments during the past twenty years have brought forward the possibility, and the necessity, for a study of the Earth’s gravity field as a whole and in some detail. A basic requirement for this study is a world-wide cover of gravity reference stations with values determined to the highest possible accuracy -one milligal or better-for use in calibrating gravity meters and controlling local gravity surveys. The direct measurement of gravity acceleration, to the desired accuracy, is still a slow and costly operation, and pendulum observations are con- sidered to be the most reliable method for measuring large differences of gravity. Establishment of the primary stations is a keen concern of the International Geodetic Association. Several pendulum equipments have contributed to this work, and one such apparatus, the Cambridge Pendulum Apparatus, is the subject of the present article. Gravity measurement has been actively studied and practised at Cambridge University since 1921, when the Committee for Geodesy and Geodynamics made proposals for the inauguration of a research and teaching branch in these subjects. Sir Gerald Lenox-Conyngham, on his retirement from the Survey of India, brought the “know-how” of his experiences with the three-pendulum apparatus. Much thought and research were devoted to the improvement of method and the design of apparatus, and a new three-pendulum equipment, made by the Cambridge Instrument Company, came into use in 1926. In 1929, a light-alloy box for swing- ing two pendulums was made by the same firm: this may be regarded as the birth of the apparatus which is still in use. The Cambridge pendulum apparatus 377 The basic principle of the method is the determination of the natural periods of two pendulums which swing in antiphase to avoid the sway which would affect the period of a single pendulum: ef€ects of ground motion also are reduced to insignificance by their opposite actions on the two pendulums. For timing the swings and for other necessary observations some auxiliary apparatus is required. Most of this has been designed and constructed in the workshop at Cambridge. It has been modified or rebuilt from time to time, under the expert hands of Mr Leslie Flavill, along with changes of experimental procedure, changes which in some cases led to improvements in accuracy. Downloaded from https://academic.oup.com/gji/article/4/Supplement_1/375/650518 by guest on 24 September 2021 The chronological list which follows, makes reference to all the observations done with the Cambridge apparatus, so far as the present author has been able to ascertain. After the list, further details are given about the equipment, methods and results of the work. The photographs of the vacuum box and pendulum (Figure I) were supplied by the Cambridge Instrument Company. The other photograph, reproduced by permission of the Director de Cartograjia Nacional, was taken in Caracas when the apparatus was set up in the Seismological Observatory there (Figure 2). A plan of the arrangement of the apparatus for observations is seen in Figure 3. 2. Chronological list of the work of the Cambridge two-pendulum apparatus, with some relevant details 1930 Observations by Jolly and Willis, using pendulums 1.A and 1.C in the new vacuum-box, at Cambridge, Greenwich, Sevenoaks, Wych Cross, Oxford and Bembridge ; timing by flash box and chronometer rated against rhythmic time signals : period of 1.A apparently increased by about 10-6 s during the series. 193I Observations by Lennox-Conyngham and Willis at Cambridge, Edin- burgh and Leith. Observations by Jolly, Fryer and Cowan in West Scotland and the Isles : 20 stations. Observations by Willis and Bullard at Greenwich, Southampton and Paris : photographic recording introduced : motor-car accident upset 1.C by about 10-5s but it almost recovered in a few days. New pendulums VI.A, VLB, V1.C received and adjusted. Observations by Bullard at Cambridge and Norwich, using V1.A and v1.c. 1932 Observations by Bullard at Cambridge, Bristol, Repton and Mithian, using V1.A and V1.C. Bullard made extensive tests on the effects of magnetization of pendu- lums. Observations by Jolly and others in N. Scotland, Orkney and Shetland using LA and 1.C: 17 stations: period of 1.A apparently decreased by about 10-6s. Tests of new timing method invented by Bullard for comparing the periods of pendulums swung simultaneously at a base station and in the field: pendulum V1.A at Cambridge, 1.A and 1.C in fields: 4 stations. Pendulum carrying cases and the vacuum box were lined with thin mu-met a1 . 378 J. E. Jackson 1933 Observations by Bullard in N. Wales: 9 stations: pendulums VIA and V1.C at Cambridge base station, LA and 1.C in field: rather large changes of periods of 1.A and 1.C were noticed. Observations by Jolly and Bullard at Cambridge, Greenwich and Southampton: large changes in 1.A and 1.C noticed.