LORÁND EÖTVÖS

THREE

FUNDAMENTAL PAPERS OF

LORÁND EÖTVÖS

Edited by Zoltán Szabó

Eötvös Loránd Geophysical Institute of Hungary

Sponsored by

Eötvös Loránd Geophysical Institute of Hungary Eötvös Loránd Geophysical Foundation Foundation for Hungarian Geophysicists

© ELGI Budapest, 1998

Associate Editors:

Éva Kilényi and Zsuzsanna Hegybíró

ISBN 963 7135 02 2

Published by

FOREWORD

Loránd Eötvös, one of the most prominent Hungarian scientists, was bom on 27th July 1848. Within the confines of this brief Foreword it would be extremely difficult to do full justice to the range and depth of his multifarious activities. After his early work in which he dealt with capillarity and which led to the establishment of the ‘Eötvös law’, his attention turned to gravitation. His investigations in the latter field proved to be of fundamen­

tal importance to the physical sciences. With his invention of the torsion balance, the foundation of applied geophysics was established accompanied by the era of oil exploration utilizing instruments. In fact, Eötvös’ ingenious instrument heralded a major breakthrough in prospecting for oil resulting in a great number of oil fields throughout the world being discovered in the

1920s and 1930s.

His experimental observations on the principle of equivalence fur­

nished evidence for Einstein’s general theory of relativity. The results of his experiments obtained at the beginning of the 20th century' are still of interest to the physicists of today and they have been used in formulating the hypothesis of the fifth force.

One of his discoveries, known as the Eötvös effect, plays an important role in the correction of gravity measurements on moving vehicles. Accurate determination of the velocity' and azimuth of moving platforms necessary for the Eötvös correction is still a basic problem of gravity measurements on ships and aircraft.

It might be appropriate here to reiterate the view that a surprising number of people seem to be unaware of the extent of Eötvös’ achievements.

Since his death, the Eötvös Loránd Geophysical Institute (ELGI) does its best to maintain the tradition of his intellectual heritage and acts as custodian of his original instruments and documents. On the 150th anniver­

sary of his birth ELGI wishes to highlight the achievements of Loránd Eötvös

by publishing a short biography and facsimiles of three fundamental papers together with their English translations to make them accessible to a wider readership.

Tamás J.Bodoky director, ELGI

EÖTVÖS THE MAN, THE SCIENTIST, THE ORGANIZER1

by Zoltán Szabó

TheAge ofEÖTVÖS

In order to get a belter understanding of Loránd EÖTVÖS’ human and scientific eminence, we should look briefly at the conditions existing in Hungary' in his time.

The Hapsburg dynasty ruled Hungary' during the eighteenth century', forcing the country' into semi-colonial dependency. Radical changes took place in the life of the country in the first half of the nineteenth century'. At the beginning of the century the enlightened concepts of the French revolution spread among the liberal minded members of the Hungarian nobility, increas­

ing national consciousness and intensifying feelings against the Hapsburg oppression and the absorption of Hungary by Austria. Influenced by revolu­

tions in Europe, social unrest in Hungary came to a head in the revolution of March 15th 1848, 17 months of inspiration and tragedy for the struggle for independence. Austria combined forces with the Russian Tzar and the na­

tional Hungarian fight for independence ended in bloodshed. In the reprisals following defeat the most outstanding people ended their lives by the hand of the executioner or languished in jail or bitter exile. Those who managed to survive this difficult period in their country estates, awaited more propi­

tious limes and boycotted measures taken by those in power.

Agreement was reached in 1867 between the reigning House of the Hapsburgs and those Hungarians willing to co-operate. As a result of this the Austro-Hungarian Monarchy was bom. Hungary' received an independent constitutional government. Economic growth of so far unknown dimensions

’Translated by Judy Elliott

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was accomplished in the fields of agriculture, industry* and science. This development was arrested when Hungary' was on the losing side of the First World War. As a result of defeat the Austro-Hungarian Monarchy disinte­

grated, Hungary' gained complete independence, but lost two thirds of her former territory' and one third of her Hungarian speaking population.

This gives a brief picture of the economic, social and political back­

ground in which Loránd EÖTVÖS was bom, studied and worked.

EÖTVÖS theMan

Loránd EÖTVÖS was bom in Buda on July 27th 1848, the year of the Hungarian revolution and fight for independence. His father József EÖTVÖS came from an impoverished noble family. As a writer and politician of great renown, he was one of the leaders of the movement for reform. Due to his eminence in the political field, he was elected minister of religion and education in the first independent government of Hungary after the revolu­

tion. As a reformer, EÖTVÖS was appalled by the violent path taken during the struggle for independence, and escaped with his family, only returning to Hungary in 1850. During his period abroad he interested himself primarily in matters of state and philosophy. On returning home he strove to establish peace between Hungary and the ruling Hapsburg dynasty. This policy did not at first gain undivided support. During the fifteen years that followed, those in favour of agreement managed to achieve a compromise. As a result in the Hungarian government established in 1867, the Ministry of Religion and Education was again awarded to József EÖTVÖS.

In recognition of his literary work, József EÖTVÖS became an associate member of the Academy in 1835, a full member in 1839 and in 1866 he was elected president.

From an early age his son Loránd was educated by private tutor and he later attended the Piarists’ high school, from where he matriculated in 1865.

In those days it was assumed that boys of aristocratic families who wished to receive higher education had to enter some branch of the law. The law studies failed to satisfy Eötvös, but he always managed to find time to attend lectures in natural sciences.

In March 1866 he wrote the following words to his father: 'I was born with ambition and a sense of duty not only to one nation but towards the whole of humanity. In order to satisfy these urges and to retain my own individual independence, my aim in life will be best achieved, as far as I can see at

EÖTVÖS THE MAN. THE SCIENTIST. THE ORGANIZER

present, if I follow a career in science.' Despite the fact that he completed his law studies, his dearest wish was to 'study at a university abroad under the guidance of enlightened professors' in order to fully understand the natural forces at work in the scientific field.

In 1867 with his father’s consent, he took the final decision to follow a career in natural sciences, and to this end he enrolled at Heidelberg University. There he became a student of KIRCHHOFF, BUNSEN and HELM­

HOLTZ. First of all he studied physics, mathematics and chemistry. The following six months he spent at the University of Koenigsberg, but found the lectures too abstract and returned to Heidelberg.

During his university years he kept up a regular correspondence with his father. These letters reveal the depth of understanding and sincerity in the relationship between father and son. Through his father’s letters we get an idea of what was happening behind the scenes in the political life of his time.

In December 1867 for example, he wrote the following to his son: 'For once my letter is overdue, a rare occurrence in our correspondence, if you were ever to become a minister yourself which heaven forbid, you would discover, particularly in Hungary, that you can never cany out those closest to your heart ... There are moments when I'm overtaken by the feeling that I'm confronted by a rock which I must lift, but am unable to do so by myself and cannot rely on the help of others. Indeed where could I find the people who would help me to change the system of education in our country? ’

Later on he writes/.... / console myself with the thought that you will continue my labours and so the establishment of Hungarian culture and science may not be credited to me alone, but to us both jointly. Recognition will be shared by us both.'

Thirsty for adventure, in 1869 the young EÖTVÖS planned to join PETERMANN the German geographer on his expedition to the Spitzbergen.

His father disagreed with his son’s plans and wrote the following: 'On this occasion, however, I do see the need to warn you of my situation, which demands that economies be made by the whole family, including yourself For years I 've almost always been in a situation in which my expenses exceed my income ...I willingly give whatever is necessary to further your scientific studies ... but I must ask you to forgo certain luxuries for the sake of us all, and your planned expedition is one of them. I'm not referring to the Transyl­

vanian expedition but the one to the Arctic.'

At his father’s request EÖTVÖS gave up his plan to travel with PETER­

MANN and applied all his energy to preparing for his examinations. In his letter of July 8th, 1870 he says:4... / 've had the results of my doctorate today.

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And my greatest delight is that this news will bring you pleasure. I passed my finals with first class honours, a distinction envied by many?

Shortly after his return home in February, 1871, his father died 'the best and truest friend? On his death bed he warned his son once more that his future happiness depended on his devoting himself to science and keeping out of politics.

After his father’s death, EÖTVÖS successfully applied for the post of lecturer, advertised by the faculty of theoretical physics at the Pest University, this university' now bears his name. It was characteristic of the social climate of the time that the majority of the audience attending his inaugural lecture did so because they were curious to see a real baron giving a lecture on physics at the university'.

After a short period of lecturing, in 1872 he was publicly honoured by the king, who awarded him the chair of theoretical physics. In 1874 he was allowed to give lectures in experimental physics and four years later he became professor in this field. He was then given the task of uniting the departments of experimental and theoretical physics, and was appointed as director to the newly established Institute of Physics.

In 1873 he became associate member of the Academy, a full member in 1883, and in 1889 he was elected president. Amongst his offices he became minister of religion and education for seven months in 1894. In his inaugural speech as minister he addressed the ministerial staff as follows: ‘We must strive, gentlemen, to make the field of public education a true garden of flowers. To achieve this aim we must first create order in the garden, so that

every plant has its place. It is also necessary that each one receives the right nourishment, the soil and air that will allow its full development. In short, we have just two things we must do here, to make order and then to help. And gentlemen, I would like us to give more and more assistance and show more tolerance in our regulations?

EÖTVÖS was a modest scientist who shunned the limelight. He disliked noisy ceremonies and did not seek moral or financial reward. In spite of this he was acclaimed and received awards at home and abroad for his scientific work and skill as an organiser. The most important honours included the French Legion of Honour, the Franz Josef award from the Hungarian king, the Saint Sava award from the king of Serbia. He was also elected honorary member of the Prussian Royal Academy of Sciences in Berlin and was given honorary doctorates from the Jagello University in Cracow and the Norwe­

gian Royal Frederick University in Christiania (now Oslo). In addition to the above he received several major and minor awards during his lifetime and

EÖTVÖS THE MAN. THE SCIENTIST. THE ORGANIZER

was elected president or a leading member of various social and scientific societies.

EÖTVÖS was a well balanced individual. Besides his intensive mental work he always found time for relaxation and sport. He often went riding and regularly made the eleven kilometre journey from his home to the university on horseback. In the summer he often cycled and indulged in his passion for mountaineering. In the classic time of alpinism he ranked among the best. As an enthusiastic photographer, he took hundreds of pictures during his moun­

taineering expeditions. In his latter years his daughters accompanied him on his expeditions, and also became keen alpinists. EÖTVÖS’ climbing achieve­

ments in the southern Tirol made the ‘Hungarian professor’s name so well- known that in 1902 one peak of 2837 metres high in the Dolomites (Italy) was named after him Cima di Eötvös (Eötvös Peak). In the company of friends he often jokingly said that he was prouder of his mountaineering successes than his discovery' of the torsion balance. For many years as president of the Hungarian Touring Society, he achieved a great deal in the popularization of tourism in Hungary.

With advancing years, he strove to avoid prestigious appointments in order to devote himself entirely to research. This prompted him to give up his

Eötvös on his way to give a lecture at the University

o

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EÖTVÖS THE MAN. THE SCIENTIST. THE ORGANIZER

position as president of the Academy in 1905. The last years of his life were clouded by a severe illness, but he continued to lecture at the university as long as it was humanly possible.

Until the last moments of his life he followed torsion balance field work with great interest. In the beginning he asked his colleagues to inform him of the daily results of their survey by telegram because he was very anxious to know how far the results of the survey supported his theories. He had never been able to tear himself away from his research, even during his summer excursions to the Mountains. When on holiday he always kept up a regular correspondence with his co-workers. He continued his scientific work from his sick bed and sent his last paper to be published only a few days before he died on April 8th 1919.

The international scientific community and the whole of Hungarian society mourned his death. Hungary' had said farewell to one of the last great representatives of classical physics and to the country’s greatest natural scientist. Through his work, however, his name will live forever in the history of physics and geophysics.

EÖTVÖS theScientist

In his scientific research EÖTVÖS was not interested in those topics that were fashionable at that time, and would have brought him immediate public acclaim. Instead, he was concerned with capillarity, gravitation and magnet­

ism, phenomena so taken for granted that a superficial observer would fail to see the mysterious powers at work within them. He formulated his ars poetica as follows: ‘ The true natural scientist ...finds pleasure in research itself and in those results which help to increase the prosperity of mankind. ’

He was still a university student when he began to concern himself with capillarity under the guidance of F. NEUMANN. This force governs the shape of the surface of water in a glass, due to its effect drops of water are rounded and water is caused to rise in capillary tubes. EÖTVÖS worked out a new way of determining surface tension called the reflection method. This method made it possible to determine the exact surface tension of different liquids.

During his experiments EÖTVÖS found that there was a relationship between the surface tensions of liquids and their molar weight.

Based on this perception, the rule, later to become known as the EÖTVÖS rule could be concluded which states that the rate of change of molar

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surface energy with temperature is a constant for all liquids. For liquids this constant is as fundamental as the universal gas constant for gases.

After studying capillarity EÖTVÖS turned his attention to gravitation and magnetism. From then onwards for the nearly forty years until his death, he was concerned with these two fields. In his research on the spatial changes in gravitation, he used a modified version of Coulomb’s torsion balance. His research method was based on two fundamentals. One was the strict physical theoretical aspect of the process; the other was the construction of an unbelievably sensitive instrument for this research work.

Eötvös built two different types of torsion balances for carrying out his gravitational investigations. The first type was a light horizontal beam suspended on a torsion wire with platinum masses attached to each end, so that the masses were at the same level (curvature variometer). This type was identical in form with the instrument used by Cavendish. The curvature variometer measures the ‘curvature’ values which give the deviation of equipotential surfaces of gravity from spherical shape, and give the direction of the minimum curvature.

Curvature variometer, 1890

Horizontal variometer, the first Eötvös torsion balance, 1890

EÖTVÖS THE MAN, THE SCIENTIST. THE ORGANIZER

The second type has a platinum mass attached to one end of a horizontal beam, while on the other end a platinum cylinder hangs on a wire so that this cylindrical mass is at a lower level than the other one (horizontal variometer).

In both cases the beam turns around the torsion wire in a horizontal plane and is deflected from the torsion-free position of the wire by the horizontal components of the gravity forces. This seemingly insignificant modification was EÖTVÖS’ most important invention, in fact this second version is known as the Eötvös Torsion Balance.

The horizontal variometer gives the ‘gradient’ of gravity which is defined as the rate of change of gravity over a horizontal distance of 1 centi­

metre. The horizontal variometer also furnishes the curvature values if the instrument is set up in at least five azimuths. The unit of gradient and curvature are named after EÖTVÖS. 1 E= 10-6 mGal/cm; that is, if the hori­

zontal gradient is 1 E the gravity acceleration between two neighbouring points 1 cm apart differs by 10_I" part of its total value.

In principle, the torsion balance is very' simple. However, due to the extreme precision required it is a highly refined instrument. Its sensitivity can be illustrated by the following example. If a piece of metal weighing 1 gram were stretched out to encircle the Earth’s equator 25 times and 1 mm of the stretched wire were cut, the segment would weigh lxl0-12 grams. This weight is in the order of the magnitude of forces the Eötvös torsion balance could detect.

Of his instrument Eötvös himself said the following: ‘ The means I use is a simple, straight stick with masses attached to each end and encased in metal, so that it will not be disturbed by the movement of air or differences in temperature. All mass near or far has an attracting influence on the stick, but the fibre, from which it is hung, resists this effect and twists in the opposite direction, producing by its twisting the exact measurements of the forces imposed upon it. This is nothing but an adapted version of the Coulomb instrument. It is as simple as Hamlet 's flute, if you know how to play it. Just as the musician can coax entrancing melodies from his instrument, so the physicist, with equal delight, can measure the finest variation in gravity. In this way we can investigate the Earth 's crust at depths that the eye cannot penetrate and the rig cannot reach.'

EÖTVÖS’ instruments were realised in the Nándor SUESS Precision Tool Workshop - predecessor of the Hungarian Optical Works (MOM). The curvature variometer and the horizontal variometer were completed in 1890 and tested in the lab and in the field in 1891.

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The simple gravity variometer completed in 1898 was a modified version of the horizontal variometer and was specially designed for field work. It was shown and awarded at the world exhibition in Paris in 1900.

In order to increase the efficiency of field work, EÖTVÖS constructed a double instrument with two balances in antiparallel arrangement (1902).

In later years the above-mentioned two instruments were used in experiments carried out by Eötvös and his associates to investigate the problem of proportionality of the inertial and gravitational masses.

At the beginning EÖTVÖS experimented with his instruments in the laboratory' of the university then later in the garden of his summer house. He carried out his first field measurements on Ság Hill in Transdanubia in 1891, where he proved that errors had been made in the relative pendulum measure­

ments carried out by STERNECK, an Austrian geodesist in 1884 in the same

Single torsion balance designed for field work in 1898. This was an award winner at the World Exhibition in Paris

Double balance, 1902. EÖTVÖS and his colleagues used this instrument in their experiments to study the equivalence of inertial and gravitational mass

EÖTVÖSTHEMAN.THESCIENTIST.THEORGANIZER

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A sensation in the press. Scientists drifting on ice sheets on Lake Balaton. A sud­

den rise in temperature led to the ice breaking up and Eötvös and his colleagues found themselves falling into captivity of the ice. Thanks to brave fishermen they

were saved

EÖTVÖS THE MAN. THE SCIENTIST, THE ORGANIZER

Transport of observation hut and torsion balance during the first ever gravity survey on the frozen Lake Balaton in 1901

area. His first report on gravitation was written in 1888 for the Academy. In 1896 his fundamental paper, entitled, Studies in the Field of Gravitation and Magnetism, was published, in which he gave a theoretical and practical summary* of his experiments up to date.

The first experiments on a larger area using the Eötvös balance took place in the winter of 1901 on the frozen lake Balaton. Eötvös chose the mirror-like frozen surface of the lake to carry out his measurements so that he would not have to concern himself with the disturbing effect of topo-

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graphic masses. He continued his survey work in the winter of 1903, com­

pleting measurements in altogether forty different stations. From the results of his torsion balance survey it was established that parallel to the axis of the lake ran a tectonic line. The establishment of this fact was the first geological conclusion based on torsion balance measurements.

In the following years torsion balance surveys were carried out in an ever widening area. International attention was focused on EÖTVÖS’ gravita­

tional experiments when he gave a talk on the results of his research in Paris in 1900. The high degree of sensitivity of his instrument was received with doubt by some. And it was not until the XVth congress of the Internationale Erdmessung held in Budapest in 1906, where he spoke about his latest experiments that these doubts were entirely dissipated and EÖTVÖS’ claims received general recognition. He also made possible for interested foreign participants to observe his torsion balance measurements in the field — in the Arad region. The participants of the conference found Eötvös’ research

The double balance packed in the wagon used for field work

EÖTVÖS THE MAN. THE SCIENTIST. THE ORGANIZER

During observation, the oxen can have a rest

Trouble-shooting during field work, 1906

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Siesta between observations. Eötvös relaxing in front of the tent

Geological interpretation of the torsion balance survey in the region of Arad, 1906

EÖTVÖS THE MAN. THE SCIENTIST. THE ORGANIZER

An improved version — smaller and easier to handle — of the double balance, 1908

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Triple curvature variometer, for shortening the observation time of curvature determination, 1909

EÖTVÖS THE MAN. THE SCIENTIST. THE ORGANIZER

SO significant that they petitioned the Hungarian government requesting that increased financial help be given for gravitational research. The Hungarian government agreed to the suggestion and from 1907 onwards a separate fund was allocated for EÖTVÖS’ gravitational studies. From this time geophysical research was recognized in Hungary as a separate field in its own right.

At first EÖTVÖS’ gravitational measurements were carried out for geodetic purposes, but from the very beginning EÖTVÖS had wondered what geological conclusions could be deduced from the results of his work. At the XVIIth congress of the Internationale Erdmessung held in Hamburg in 1912 EÖTVÖS wrote the following in his report of the practical application of the torsion balance: 'Geologists seem to agree that the most substantial dis­

charges of gas occur in the immediate vicinity of gas-bearing anticlines, and overlying sediments. Experience gained in America (Ohio) and observations in Transylvania where the subsurface geological structures could be deter­

mined from superficial indications further endorse these assumptions. Such geological indications, however, are absent in the sand and humus-covered surface of the Great Hungarian Plain. He who searches for gas-bearing anticlines in this or similar areas should not fail to take note of conclusions drawn from torsion balance observations?

In 1916 on the initiative of Hugo BÖCKH, an eminent Hungarian geologist, torsion balance measurements were carried out in the region of Egbell (Gbely, Slovakia) where oil was produced from a recognized anticlinal

The results of the torsion balance survey carried out in the area around Kecskemét after the big earthquake of 1911. The epicentre (marked C) lies at the edge of a

large gravity minimum

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Gradient map in the re­

gion of Egbell (Gbely, Slovakia): the first suc­

cessful oil exploration project by torsion bal­

ance, 1916

structure. The aim of these measurements was to establish the extent to which the effect of the oil-bearing anticline is reflected in the results of torsion balance measurements. On the basis of the measurements carried out at 92 stations the contours of the anticlinal oil field were clearly ascertained. These results proved the efficacy of the torsion balance in oil exploration and paved the way towards world renown for EÖTVÖS and his balance. In the 1920s and 30s hundreds of oil fields were discovered throughout the world with the help of EÖTVÖS’ ingenious instrument.

EÖTVÖS the physicist regarded the geological interpretation of his measurements with utmost interest, as the following citation proves: 'Beneath our feet stretches the open country of the Hungarian Plain, crowned with hills. Over the years this region has shaped itself naturally, as it wished. I wonder what it was like in former days. What sort of hills have been eroded and what valleys filled with loose deposits before this fertile area of golden grain came into being, this life-giving Hungarian Plain? As I walk upon it and eat its bread my mind dwells upon these questions which would give me such joy to answer. ’

Among EÖTVÖS’ gravitational instruments, his gravity compensator is also worthy of mention. This instrument is strictly speaking a curvature variometer provided at both ends with sector-shaped deflectors, whose posi-

EÖTVÖS THE MAN. THE SCIENTIST. THE ORGANIZER

tion can be changed by rotation about a horizontal axis. If the deflectors are in vertical position their attraction to the balance is zero, in a horizontal position their effect is maximum. If the beam of the balance is in the centre of its case, the attraction of the deflectors is zero because of the symmetrical disposition but if the beam is not in the central position because of deflection by some outside mass, the deflectors become effective since they are now unsymmetrically positioned with respect to the beam (astatization). Changing the position of the deflectors with respect to the horizontal direction, the sensitivity of the gravity compensator can be further increased up to the point of instability. With this instrument EÖTVÖS could register 1 cm changes of the water level of the Danube from a distance of about 100 m. Although best known for his torsion balance, EÖTVÖS also developed a gravimeter. It was completed in 1901, based on the bifilar principle. The experimental measure­

ments carried out with this instrument, however, failed to meet his expecta­

tions, so he did not publicize his activities in this field. His gravimeter still exists today, an indication of the wealth of his love for experimentation.

In 1890 EÖTVÖS worked out a method, namely the dynamic method for measuring the gravitational constant. The basis of his method was the concept that the period of oscillation of a pendulum placed between two parallel lead walls differed according to whether it oscillated parallel or perpendicular to the walls. Measuring the periods of oscillation in both positions and determining the exact mass of the attracting walls the gravita­

tional constant can be calculated.

In physics, mass can be defined in two ways as inertial and gravita­

tional. The inertial mass of a body determines the acceleration given by an applied force (Newton’s second law). The gravitational mass of the body determines the force it experiences due to the gravitational attraction of another body.

EÖTVÖS became concerned with the question of the proportionality of the inertial and gravitational mass as early as 1880. In order to examine this phenomenon, he used his sensitive torsion balance. He examined the state of equilibrium of the balance by attaching masses of different composition to each end of the arm of the balance. If the quantity of gravitational force depended on the composition of the mass, when placing bodies of different composition on to the balance, the state of equilibrium should change in each case. This phenomenon did not occur. In 1908 EÖTVÖS and his colleagues, Jenő FEKETE and Dezső PÉKÁR, perfected their measurements to such an extent that they were able to establish that the difference between the inertial and gravitational mass was at the most 1/200.000.000. Their paper on the

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subject won them the Benecke award at the Göttingen University. The experiments carried out by EÖTVÖS and his colleagues on the proportionality of the inertial and gravitational mass supports Einstein’s theory of relativity.

EÖTVÖS was also interested in the question of gravitational absorption.

His method was the following: the beam of a horizontal variometer is placed perpendicularly to the direction of the rising or setting Sun. Let us suppose that two straight lines are drawn from a fixed point on the Sun, one directed to the upper weight on the balancing rod, and one to the lower. If the Sun is just below the horizon, the parts of the two straight lines passing through the Earth will differ in length. For example if the straight line drawn to the upper weight just touches the Earth, then the line directed to the weight which is one meter below will pass through the Earth for seven kilometres. If this layer of the Earth could change the attraction of the Sun, deflection would be indicated by the variometer. The instrument did not show any definite deflection at sunrise or sunset. The degree of sensitivity of this instrument was such that EÖTVÖS could state that if the upper layer of the Earth changes the Sun’s attraction the effect was less than 1:100.000.000.

In the last years of his life, EÖTVÖS carried out experiments which showed that the weight of moving bodies on the Earth’s surface changed depending on the direction and speed at which they were proceeding. A clear explanation of this change can be given on the basis of the mechanics of Galilei and Newton. The gravitational force of the Earth is the resultant of two forces: the principal one caused by the attraction according to Newton’s law, the second one the centrifugal force caused by the Earth’s rotation. Since the distribution of the masses on the Earth’s surface and the speed at which the Earth rotates are constant, the weight of objects on the Earth’s surface is also constant. The situation is different, however, in the case of moving objects. As the Earth rotates from west to east, the centrifugal force on a moving object is greater if its motion on the Earth is towards the east than towards the west. As a result of this phenomenon the weight of a body moving eastwards will decrease, while that moving westwards will increase.

It is interesting to note the circumstances that initiated EÖTVÖS’

research on this topic. O. HECKER, an eminent researcher at the Institute of Geodesy in Potsdam led a team to the Atlantic Ocean in 1901 and then in 1904-1905 to the Indian and Pacific Oceans, to carry out gravity measure­

ments on moving boats. While studying Hecker’s results in the published report, Eötvös noticed that no consideration had been given to the forces developed by the motion of the boat. In a letter to HECKER, EÖTVÖS pointed out his error, but HECKER at first refused to give credence to this criticism.

EÖTVÖS THE MAN. THE SCIENTIST. Till-: ORGANIZER

His colleagues, however, persuaded him that EÖTVÖS was right and so in 1908 new measurements were carried out in the Black Sea to prove this phenomenon. Observations were made in two boats, one moving towards the east and one towards the west. The results substantiated EÖTVÖS’ claim. The international scientific world recognizes this phenomenon as the Eötvös Effect. The Eötvös Effect has special importance nowadays in the field of sea and air gravimetry.

In 1915 EÖTVÖS constructed a special instrument to demonstrate this phenomenon. The device is basically a balance with horizontal axis, where instead of pans, weights are attached to the ends of the arm. The balance stands on a tripod, which rotates evenly. When the balance is rotated the weight moving towards the west will become heavier, the one moving towards the east lighter. The balance will, therefore, deflect from its state of equilibrium.

If the balance is rotated at such a speed that the rotation period equals the period of its oscillation the impulses occurring during the rotations will cause the arms to make ever greater oscillations.

This experiment is yet another proof of the Earth’s rotation, and has even greater significance than Foucault’s famous balance experiment carried out in the Pantheon in Paris.

Parallel to field work with the torsion balance, EÖTVÖS and his col­

leagues determined the horizontal component and declination and inclination of the Earth's magnetic field at every* observation point. The extensive observational data available enabled him to give integrated geophysical interpretation of his measurements.

In order to study the characteristics of the Earth's magnetic field, Eötvös designed an instrument on the analogy of his torsion balance, called a magnetic translatometcr. It differed from the torsion balance in that the lower weight was replaced by a magnetic needle. The needle could be rotated around its horizontal axis, thus it could be positioned in the direction of the Earth’s magnetic field. The suspending wire of the magnet became the centre of the rotation axis of the instrument. Due to the high sensitivity of the instrument, Eötvös was able to determine the magnetic moment of rocks and other bodies of weak magnetism. He carried out similar measurements on old bricks and clay pots. During the baking and cooling of the bricks and pots, several hundred years earlier, they had acquired a remanent magnetization in the direction of the ambient magnetic field. Since it was easy to recognize the sides of the bricks and the bottoms of the pots on which they had rested during baking, it was possible to stand them up in the same position. After having determined the direction of their magnetization, the inclination of the mag-

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Magnetic translatometer, the magnetic equivalent of the torsion balance, 1891 netic field at the time of their cooling could be defined. In 1900 EÖTVÖS gave a lecture on his studies in this subject, entitled 'Magnetic Inclination in the Past'.

EÖTVÖSthe Organizer

In addition to activities as a researcher and lecturer, EÖTVÖS played an important role in organizational work, thus promoting the development of the natural sciences in Hungary.

In 1885 in the company of other university lecturers, he took part in discussions on the latest scientific results. This group later became known as the Mathematical Society, in its activity physicists played an ever increasing role. As a result, in 1891 the Mathematical and Physical Society was formed, with Eötvös as its president. The society’s journal was entitled the Mathe­

matical and Physical Papers. The society was split in the year 1949, the Physical Society took the name of Loránd EÖTVÖS and the Mathematical

EÖTVÖS THE MAN. THE SCIENTIST, THE ORGANIZER

Society was called after one of Hungary’s great mathematicians, János Bolyai.

In 1894, not long after EÖTVÖS was appointed Minister of Education, the Physical Society gave their president a festive welcome, and to honour the occasion they announced a mathematical and physical competition for secon­

dary school children, the winners of which would receive an Eötvös award.

During his career as a teacher EÖTVÖS quickly realized that a great number of talented and hard working students were forced to stop their studies, due to lack of financial support.. He wished to help to solve this problem and so during the time he was minister, he established a scientific residential college, which was named the József Eötvös College, after his father. Within the framework of the college future secondary school teachers received excellent tuition and took part in special tutorials to promote and develop individual scientific work. The Eötvös College trained numerous excellent researchers and teachers for Hungary in the following decades.

In order to assist the poorest students no fees were required for thirty of the one hundred places. The financial situation of some of the college students is characterized by the following story'. In 1918 on the seventieth birthday of the now seriously ill EÖTVÖS, the leaders and six of the students from the college visited him on his sick bed. During the conversation EÖTVÖS asked how the six representatives of the students had been chosen. One of the students gave this explanation: 'Honourable sir, it was a question of jackets.

It was only those with proper jackets who came.'

To promote natural sciences, EÖTVÖS convinced Andor SEMSEY, a great Hungarian patron of sciences, to establish a scholarship which was to be awarded to young graduates who wished to devote themselves to scientific studies.

EÖTVÖS kept a close connection with several international scientific organizations. The foremost of these was the Internationale Erdmessung, precursor to the IUGG (International Union of Geodesy and Geophysics).

Eötvös regularly attended the general meetings of this organization and on each occasion reported on his research. As already mentioned, the 1906 general meeting of the Internationale Erdmessung held in Budapest played an important role in the further development of geophysical research in Hungary.

EÖTVÖS maintained a regular correspondence with scientists and ex­

perts from other countries. As illustrations of this there is a letter written by Einstein to Eötvös, asking for his advice on the selection of a candidate to fill the post of director of the Institute of Geodesy in Potsdam.

ZOLTÁNSZABÓ

5. 1. 18.

Dear and Honoured Friend.

Following the death of Professor Helmert, the post of director of the Potsdam Institute of Geodesy is vacant. The Academy, University and Ministry are responsible for finding a successor. Several of my colleagues have asked me to obtain an objective opinion from someone who is eminent in this field. It seems to me honoured colleague, that you are the only person whose opinion carries sufficient weight in this matter. It is for this reason that I am requesting you to advise us.

Without wishing to prejudice your view to the smallest degree, I would be grateful of you could include in your assessment the following gentlemen:

Schumann (Vienna) Wiechert (Göttingen) Krüger (Potsdam) Kohlschütter (Potsdam) Schweydar (Potsdam)

since they have atready attracted the attention of the authorities. Observa­ tions on the scientific suitability of the last three would be welcome, even if they cannot be considered for the post.

I anticipate your highiy esteemed answer with the greatest possible in­ terest, and remain your very devoted

Einstein Haberland str. 5.

Berlin Schöneberg

Another letter from General ARTAMONOFF leader of the Russian military cartographic service in St. Petersburg, informed EÖTVÖS that his most important papers had been translated into Russian so that experts taking part in the cartographic service could study them in detail.

ZOLTÁN SZABÓ

Department of cartography Headquarters Ministry of Defence

St, Petersburg

26th January 1910 8th February No 123,

Most respected Professor,

In reply to your kind letter of December 28th, I have to report that your flattering suggestion of carrying out a series of observations here in Russia will he difficult to put into effect.

A simpler solution to the problem would be that we should send one or two of our surveyors to you, during the period of the autumn expedition. so that they may master the methods in the study of gravitational force, and practise under your guidance. In this way we could make use of your kind

offer, The realisation of this project will depend on our ability to appoint suitable staff for such an expedition.

Our surveyors are now studying your methods from a theoretical point of view, and with this in mind all your scientific works dealing with this field are being translated. Of course it goes without saying that your name will he referred to everywhere. Our journals where your papers will appear will not he available fie sate, but will be widely circulated among our scien­

tific societies, so that it will become possible for Russian scientists to fully understand your work.

I hope, most honoured Professor, that we shall not give you cause for dissatisfaction in our great efforts to speed up the translation of your papers in order that your methods he widely propagated and your name well known,

As you have informed me of the cost of the instruments and all ex­

penses connected with such an expedition I shall he able to provide financial support wherever necessary,

With the greatest respect and admiration, I remain your devoted

N. Artamonoff To Baron Loránd Eötvös

Professor of the Budapest University

EÖTVÖS THE MAN, THE SCIENTIST, THE ORGANIZER

From 1907 onwards work with Eötvös’ torsion balance was financed by a governmental fund. In 1919, after his death, geophysical research became financially independent from the University Institute of Physics, under the name: Eötvös Loránd Geophysical Institute (ELGI). This group of researchers, which during EÖTVÖS’ lifetime consisted of a few members, has developed into a research establishment of about a thousand members in the beginning of the 1980s. Due to drastic changes in the social and economic system of Hungary, ELGI was reduced to about a hundred members all striving in his name to further develop the science of geophysics.

The mostimportant publications ofLoránd EÖTVÖS

Über den Zusammenhang der Oberflächenspannung der Flüssigkeiten mit ihrem Molekularvolumen. Ann. d. Phys. u. Chem. Neue Folge. Vol.

XXVIII. pp. 448-459. 1886.

Untersuchungen über Gravitation und Erdmagnetismus. Ann. d. Phys. u.

Chem. Neue Folge. Vol. LIX. pp. 354-400. 1896.

Bestimmung der Gradienten der Schwerkraft und ihrer Niveauflächen mit Hilfe der Drehwaage. Verhandl. d. XV. alig. Konferenz der Interna­

tionalen Erdmessung in Budapest, 1906.

Die Niveauflächen und die Gradienten der Schwerkraft am Balaton-see. Wien, 1908. 64 p.

Über geodätischen Arbeiten in Ungarn, besonders über Beobachtungen mit der Drehwaage. Budapest, 1909. 42 p.

Experimenteller Nachweis der Schwereänderung, die ein auf normal ge­

formter Erdoberfläche in östlicher oder westlicher Richtung bewegter Körper durch diese Bewegung erleidet. Annalen der Physik Vol. LIX.

pp. 743-752. 1919.

Beiträge zum Gesetze der Proportionalität von Trägheit und Gravität (with co-authors). Annalen der Physik Vol. LXVIII. pp. 11-66. 1922.

Roland Eötvös gesammelte Arbeiten (edited by P. SELÉNYI) 1953. Akadémiai Kiadó, Budapest. 385 p.

ZOLTÁN SZABÓ

Publications on Loránd EÖTVÖS

Fröhlich I. (edit.) 1930: Memorial volume on Baron Loránd EÖTVÖS (in Hungarian). Special issue of the Hungarian Academy of Sciences, Budapest. 319 p.

PEKÁR D. 1941: Baron Loránd EÖTVÖS. For the 50th jubilee of the torsion balance (in Hungarian). Kis Akadémia Budapest, 340 p.

KÖRNYE1 E. 1964: A selection from the works of Loránd Eötvös the scientist and cultural politician (in Hungarian with 678 references). Gondolat Kiadó, Budapest. 425 p.

BODÓ B. 1980: A selection from the papers of Loránd Eötvös on science and cultural politics (in Hungarian). Criterion Könyvkiadó, Bucharest. 287 p.

SZILÁRD J. 1983: Loránd Eötvös, his youth, education and preparations for his profession (in Hungarian). Fizikai Szemle, XXXIII. 6. pp. 213-225.

Budapest

Budai T. and Budai-Mosonyi K. 1986: The life and activity of Loránd Eötvös the prominent physicist (in Hungarian). Magvető Kiadó, Bu­

dapest. 422 p.

Tomb of Loránd Eötvös in Kerepes cemetery (Budapest, Hungary)

MATHEMATIKAI

ÉS

TERMÉ SZETTUDO MÁNYI ÉRTESÍTŐ.

A M. TUD. AKADÉMIA III. OSZTÁLYÁNAK FOLYÓIRATA.

SZERKESZTI

KÖNIG GYULA

OSZTÁ LYTTTKÁR.

Különlenyomat a XIV. kötet 4. füzetéből.

VIZSGÁLATOK

A GRAVITATIO ÉS MÁGNESSÉG KÖRÉBŐL.

B. EÖTVÖS LORÁND

r. tagtól.

BUDAPEST.

KIADJA A MAGYAR TUDOMÁNYOS AKADÉMIA.

1896.

VIZSGÁLATOK

A GRAVITATIO ÉS MÁGNESSÉG KÖRÉBŐL.

(Elöleges jelentés.) B. EÖTVÖS LORÁND r. tagtól.

E jelentésemben a tárgyalt anyag terjedelméhez mérten rövi­

den foglalom össze azon kutatásaim eredményét, melyeket immár nyolcz év óta a gravitatióra és a földi mágnességre vonatkozólag végeztem. Azok a rendkívül érzékeny módszerek, melyeket különö­

sen az erők változásainak mérésére megállapítanom sikerült, lehe­

tővé tették a foglalkozást olyan feladatokkal, melyek eddig úgy­

szólván hozzáférhetlenek voltak. így történt az, hogy a kutatás folyamán mindig újabb kérdések megoldására törekedvén, a már elért eredmények közzétételére, egyéb sokféle teendőm mellett, alig maradt időm. A m. t. akadémiának tettem ugyan időről-időre rövid előterjesztéseket munkám állásáról, de ez a néhány szó és még kevesebb sor nem volt elég arra, hogy annak eredményét biztosítsa és másoknak is hozzáférhetővé tegye. Addig is tehát, míg e feladatnak teljes mértékben eleget tehetni időm lesz, ezt az össze­

foglaló jelentést bocsátom közre, a mely, bár mellőztem benne az elméleti tárgyalások és számítások, valamint a kísérleti adatok részletes felsorolását, talán mégis elég lesz arra, hogy érthetővé tegye azt, a mi kutatásomban lényegesen új.

Kötelességet mulasztanék, ha, a midőn a magam munkás­

ságáról szólok, említetlenül hagynám munkatársaim nevét. Éveken át buzgó segédem volt dr.

K

övesligethy

R

adó

,

ma egyetemi rend­

kívüli tanár úr, és kutatásaim egész idején át, kezdetben mint tanuló, utóbb mint egyetemi tanársegéd velem együtt dolgozott dr.

T

angl

K

ároly úr. Fogadják ma közreműködésükért hálás köszönetemet.

Az új eszközöket, melyekre vizsgálataimhoz szükségem volt, mind Süss

N

ándor úr, az állami mechanikai tanműhely igazgatója

1

2 B. EÖTVÖS LORÁND.

itt Budapesten készítette, avval a kiváló gonddal, pontossággal és csínnal, a mely keze munkáját jellemzi.

I. A nehézség térbeli változásainak méréséről.

1. A feladat.

Ismereteink a nehézség térbeli változásaira vonatkozólag, a felismerésükre szolgáló módszerek elégtelensége miatt, mindeddig nagyon hiányosak. Az inga e változások kicsinységéhez mérten ki nem elégítő érzékenységével csak nagy távolságokban teszi lehe­

tővé azoknak felismerését, a mérleg pedig, úgy a mint azt J

olly

használta, ugyan érzékenyebben, hanem csak egy kiváltságos irány­

ban, t. i. lefelé tárja fel a változás nagyságát. Azok a módszerek és azok az eszközök, melyekről e jelentésemben fogok szólni, lehe­

tővé teszik e változások lemérését kicsiny, néhány decimeternyi távolságokban és külömböző irányokban. Sőt az e módszerek sze­

rint tett mérések az ingával és JoLLY-féle mérleggel tett megfigye­

léseket úgy egészítik ki, hogy ezekkel együtt a nehézség nagyságát és irányát teljesen ismertté teszik, nemcsak egyes pontokban, ha­

nem a térnek egy olyan nagy kiterjedésű részében, a melyben ez erőt egyenletesen változónak feltételezhetjük. Ezt a czélt állítván magam elé, mindenekelőtt a megoldandó feladatokat fogom ki­

jelölni.

A nehézségnek egyenletesen változó terében ez erő gyorsulá­

sainak derékszögű összetevőit a következő egyenletek adják:

1)

ezekben X, Y,Z& gyorsulás összetevőit az x, y, z pontban, xo, Yo, ZQ pedig ugyanazokat a tengelyrendszer kezdetpontjában jelölik.

A nehézséget mint a földi tömegek vonzásának és a föld for-

VIZSGÁLATOK A GRAVITATIO ÉS MÁGNESSÉG KÖRÉBŐL. 3

fásából eredő középpont futó erőnek eredőjét állítván elő, ha 7-vel a föld tömegének potentiál függvényét, w-val a föld forgásának szögsebességét, /7-val az x, y, z pont forgás-sugarát és t7-val a nehézség erőfüggvényét jelöljük, akkor írhatjuk:

2)

E szerint:

3)

•és

4) Ha most a coordináta-rendszert úgy választjuk, hogy Z tengelye egyirányú legyen a nehézséggel a coordináták kezdő­

pontjában, akkor:

Az 1) egyenletek a nehézség gyorsulását az egész egyenlete­

sen változó térben tizenkét állandó segélyével fejezik ki, ez állan­

dók közül a függőn a Z tengely irányát jelölvén ki, kettőnek Ar0 és y0 null értékét állapítja meg, egynek, a harmadiknak Z0-nak értékét pedig az inga adja meg. A többi kilencz, a változás arányát kifejező állandó között a 3) és 4) egyenletek négy összefüggést állapítanak meg, úgy hogyr a feladat teljes megoldására még öt adatot kell mérés által meghatározni. Mielőtt az erre szolgáló módszerekről szólanék, előre bocsátom azon egyszerű vonatkozások felsorolását, melyekben az itt szereplő mennyiségek a nehézség niveau-felületé- hez, az U= C felülethez állanak. Ha ugyanis px e felület normál

1*

4 B. EÖTVÖS LORÁND.

metszetének görbületi sugarát jelenti az x tengely irányában, py pedig ugyanazt az y tengely irányában, akkor:

tengelyrendszerünket azonban úgy is választhatjuk, hogy A’ és Y tengelyei a főgörbületek irányába essenek, s akkor pt és />2-vel a főgörbületi sugarakat jelölvén, leszen:

és

Az ezeken kívül itt meghatározandó differen

­

cziál-hányadosoknak kettős jelentősége van. Ha írjuk:

úgy látjuk, hogy e mennyiségek a nehézség változásának arányát az X, illetve Ytengely irányában állítják elő. Tegyük még:

ds-sel a nehézség niveau-felületén az állandó nehézség görbéjére me­

rőleges ívelemet jelölvén, akkor a meghatározását a

VIZSGÁLATOK A GRAVITATIO ÉS MÁGNESSÉG KÖRÉBŐL. 5

és az

a

szög meghatározásával pótolhatjuk. A — nem egyéb mint a nehézség változásának aránya magában a niveau-felületben, az a pedig az e változás irányát meghatározó szög.

A fenti mennyiségek második értelmezéséhez akkor jutunk, ha teszszük

ebből t. i. azt következtethetjük, hogy z-vel a kezdetpont alatt

dX dY

fekvő pontban —

z

és

—z

gyorsulások járulnak hozzá a

z

irá-

az az

nyába eső

g

gyorsuláshoz, úgy hogy az eredő nehézség e pontban

szögekkel hajlik el a Z tengelytől. így tehát:

azokat a szögeket jelentik, melyekkel a nehézség iránya, a hossz­

egységgel lefelé haladva, az

XZ,

illetőleg

YZ

síkokban a

Z

ten­

gelytől eltér. Ez a nehézség irányváltozásának aránya lefelé.

A feladatunk teljes megoldására szükséges öt adat e szerint meg lesz határozva, ha ismerjük egyrészt a főgörbületek irányát és nagyságát, másrészt a nehézség változásának irányát és nagysá­

gát magában a niveau-felületben. Mivel pedig a JoLLY-féle mérlege- 1 1

lés a 4) egyenlet értelmében az--- 1--- értékét adja, azért a fő­

görbületi sugarak ismeretére elégséges lesz az---értékének meghatározása, a melyről alább fogok szólni.

(> B. EÖTVÖS LOBÁND.

2. A módszer.

A fent körvonalozott feladat megoldására a CouLOMB-féle- mérleget használtam.

Az előbbi fejezet 1) és 3) egyenleteinek értelmében a C

oulomb

- féle mérlegrúd nehézségének forgásmomentumát a felfüggesztő drót tengelyébe helyezett Z tengely körül a kővetkező alakban feje­

zem ki:

a hol az integrálás kiterjesztendő a dróton függő összes töme­

gekre.

Ha pedig a mérlegrúd tömegelemeinek helyzetét egy szilár­

dan e rúdhoz kötött tengelyrendszerre vonatkoztatjuk, mely­

nek C tengelye a z forgási tengelylyel összeesik, $ tengelye pedig á- rúddal együtt forogván, az x tengelylyel a szöget képez, akkor a forgá8momentum értéke:

Ez az egyenlet a mérlegtestnek bármely alakjára vonatkozó­

lag érvényes. Czélom elérésére két alakot használtam. Az első alak egyszerű hengeres rúd volt, végén golyó vagy hengeralakú töme­

gekkel, a második alak ettől annyiban külömbözött, hogy a rúd egyik végén a golyó vagy henger fonálra függesztve, mélyebben volt elhelyezve. A f tengelyt a rúd geometriai tengelyébe helyez­

vén, mindkét esetben:

VIZSGÁLATOK A GRAVITATIO ÉS MÁGNESSÉG KÖRÉBŐL. 7

az első esetben ezenkívül a másodikban ellenben:

a hol

l

a felfüggesztett golyó karját, m tömegét,

h

pedig függélyes távolát jelöli a rúdtól, illetőleg az annak másik végén megerősített golyótól.

Vizsgáljuk most meg a CouLOMB-féle mérleg mechanikai viszonyait külön-külön e két esetre.

Az első esetben, t. i. a rúd két végén egy magasságban meg­

erősített golyók esetében, az 5) egyenlet szerint lesz :

ha pedig az

X, Y

tengelyeket úgy választjuk,

hogy

X

és

Y

a főgörbületek irányai legyenek (lásd fent), akkor:

K

a rúd tehetetlenségi momentumát fejezi ki, hosszúkás rúd eseté­

ben az e kicsiny, sőt a legtöbb esetben elhanyagolható lesz.

A nehézségnek forgásmomentuma

F

a CouLOMB-mérleg drót­

ját vagy fonalát

d

szöggel megcsavarja úgy, hogy:

B. EÖTVÖS LORÁND.

T&

a drótnak csavarás ellenében ható forgásmomentumát állít­

ván elő.

A szöget a mérleg rúdjának egy7 egyetlen állásából ugyan nem olvashatjuk le, de ha a mérleg szekrényét torsio fejével együtt függélyes tengely körül úgy forgatjuk, hogy a rúd középvonala az

x

tengelylyel az előbbitől eltérő

a

szöget képezzen, akkor a drót csavarási szöge is megváltozik, s ez a változás (#'—ö) a rúdhoz és a szekrényhez erősített mutatóknak vagy7 jobban tükröknek viszonyos elfordulásából felismerhető és mérhető lesz.

A rúdnak három állása elég már arra, hogy7 a drót csavaro­

dásában előálló változások észlelése alapján úgy7 az

a

szög érté­

két,

jobban áttekinthető s a számításban egyszerűbb lesz azonban eljá­

rásunk, ha négy állást létesítünk, úgy7 hogy7 az állások közül kettő­

kettő egymásra merőleges legyen, e két pár pedig egymással 45 foknyi szöget képezzen.

így7 lesz az eredeti állásban:

VIZSGÁLATOK A GRAVITATIO ÉS MÁGNE8SÉG KÖRÉBŐL. 9

az e-nak amúgy is kicsiny értéke, a mérlegrúd méreteiből, pedig annak lengési idejéből határozható meg.

Légüres térben végtelen kicsiny amplitúdókkal egyedül a drót rugalmassága által okozott lengések esetében volna:

A levegő ellenállása és a nehézség változásaiból eredő forgásmo­

mentum befolyása azonban különös megfontolást követel. A rúd mozgásának differencziálegyenletét ismert alakjában írjuk:

itt

aj

a szögkitérést,

H

a levegő súrlódásától függő állandót,

K

mint előbb a tehetetlenségi momentumot jelenti. Ebből folyólag a rúd eg^7 pontjának kitérése:

10 B. EÖTVÖS LORÁND.

ha pedig a helyébe a+ -y értéket teszünk, a mi a rúd merőleges állításának felel meg, akkor:

ezekből kapjuk:

s így kiszámíthatjuk-gr értékét.

Ez okoskodásunkból kitűnik még az is, hogy a lengési idők észlelése már egymagában is elég az elcsavarodások által lemérhető adatok meghatározására. Két egymásra merőleges helyzetre nézve ugyanis az előbb megállapított értékekből nyerjük :

tehát úgy a főgörbületek iránya a, mint

meg vannak határozva.

Ha az általam használt mérlegrudakra vonatkozólag amúgy is kicsiny e mennyiséget elhanyagoljuk, és a lengési idő értékét egyedül a drót rugalmassága folytán T0-al jelöljük, akkor közelítés­

ben a következőleg mondhatjuk ki okoskodásunk eredményét: a CouLOMB-féle mérleg drótja a mérlegszekrény és torsiofejnek együt­

tes forgatása közben megcsavarodik, e csavarodás nagysága a rúd­

nak 90 fokkal egyenlő elforgatásánál:

VIZSGÁLATOK A GRAVITATIO ÉS MÁGNES8ÉG KÖRÉBŐL. 11

a mérlegrúd lengési ideje ugyanilyen forgatásnál megváltozik^

90 fokos forgatásnál e változás:

—d

maximum lesz, mikor a=45° és =135°

T'—T

maximum lesz, mikor a=0 és =90°, (T'~ 7’)raax = ?o(^,”^)“ax-

A CouLOMB-féle mérlegnek még azon második alakjáról kell most szólanom, melynél a rúd együk végén a fonálon felfüggesz­

tett tömeg mélyebben áll, mint az ellensúlyozó tömeg a rúd másik végén. Erre vonatkozólag már tudjuk, hogy

s így az 5) egyenlet tetszőlegesen irányított

X

tengelyre vonatkoz­

tatva, adja:

Ha a mérlegrudat előbb az

X

tengely irányába állítjuk, úgy hogy a=0 legyen s azután az eszköz szekrényét és vele a torsio- fejet átforgatjuk addig, amíg a=;r, akkor a mérődrót szög­

lettel csavarodik meg, e szögletnek értéke az

F

értékéből kiszá­

mítva :

és ha a rudat előbb a= -77- azután

2 a te

2

állásba hozzuk, akkor e két helyzet között a csavarodás

az — mennyiséget vagy az eszköz méreteiből, vagy a függő súlyra

lm

12 B. EÖTVÖS LORÁND.

kívülről liató vonzó tömegek által okozott kitérésből könnyen meg­

határozhatjuk. így aés a vízszintes irányú változásoknak, vagy eredőjüknek és ez eredő irányának ismeretéhez jutunk. Tud­

juk már, hogy

g ds

a nehézség irányváltozását lefelé méri.

A CouLOMB-féle mérleg e két alakjában és e két módon hasz­

nálva, az előadottak szerint lehetővé teszi azt, hogy meghatározzuk egyrészt a nehézség niveau-felületének főgörbületi irányait és e fő­

görbületek külömbségét ---—) , másrészt a nehézség változását

'/?i

PJ

a niveau-felület érintő síkjában (a vízszintesben) és e változásnak irányát. Feladatunkat tehát teljesen megoldhatjuk, mert a JoLLY-féle mérlegelés a értékét adja s így a 4) egyenletből folyó

egyenlet segélyével az (--- —) értékével együtt magukat a fa és

'/^í Pz'

p±

görbületi sugarakat is kiszámíthatjuk.

Megjegyzem még, hogy a függélyes síkban lengő inga me­

chanikáját abban a modorban tárgyalva, mint azt itt a C

oulomb

- féle ingára vonatkozólag röviden előadtam, az elmélet a meg­

esz határozására a JoLLY-féle eljárásnál előnyösebb módszerekkel ke­

csegtet, azoknak megvalósítása azonban a vízszintes forgási ten­

gelyeket létesítő szerkezetek tökéletlensége miatt nekem mindeddig nem sikerült.

3. Az eszközök.

A tervbe vett mérések kivitelére Qlyan eszközökről kellett gondoskodnom, melyeknek érzékenysége a lemérendő igen kicsiny erőknek megfelelő legyen. A megkívánt érzékenység fokának meg­

ítélése végett közlöm itt a lemérendő adatoknak értékeit egy olyan

VIZSGÁLATOK A GRAVITATIO ÉS MÁGNESSÉG KÖRÉBŐL. 13

mintaszerű földre vonatkozólag, a minőt közelítésben a föld alak­

jának s rajta a nehézség változásainak előtüntetésére szoktunk használni. Ilyen például L

isting

forgás-ellipsoidja. Ennél:

a=637 736 500 C.

&=635 529 800 C.

és

</,p=978 0728 (1 +0,005 201 3 sin3?)

A számítás ez adatokból p>=47° 30' szélességre vonatkozólag, azaz Budapest helyzetére, a következő értékeket adja:

(/=980,838 g{--- -) =4 836.10'12

'Pi P°'

^-=7 960.10-12 uS

dg_

j?= — =8 115.10-15 vágj’

E—0,000 001 673 másodpercz

=3 080.10-®.

dz

A két végén golyókkal ellátott mérlegrúd drótjának elcsava- rodása a legnagyobb akkor lesz, a mikor e rúd tengelye a meridián­

nal 45 foknyi szögletet képez, a meridián két oldalán fekvő két ilyen állás között az elcsavarodás

8 ha teszszük To=lOOO s, akkor:

10002

fl'-d = . 4 836.10~12=0,000 490 azaz 1,7 perez.

Ha pedig a lengési időt a meridián körül T-vel, arra merő­

legesen T'-gyel jelöljük, akkor: