Galileo's clocks

di Paolo Galluzzi

Historians of the Scientific Revolution have rarely attended to the consequences of one of Galileo's most sensational discoveries, that of the four satellites of Jupiter, which he detected with his telescope on the magic night of 7 January 1610 in Padua, where he was teaching Mathematics at the local university.

As Galileo immediately realized, the satellites of Jupiter offered strong evidence in support of the heliocentric system, which, more than 60 years after the publication of Copernicus' De revolutionibus Orbium Coelestium (1543), was still largely considered an absurd cosmological hypothesis. Systematic observations of the satellites soon convinced Galileo that once the Sun, and not the Earth, was taken as Jupiter's centre of revolution the satellites' periods and their eclipses became perfectly regular.

Thanks to the observations of Galileo and many other gifted European scientists, this amazing celestial novelty stimulated, during the following decades, a process of radical reformation of traditional knowledge: from the continuous improvement of instruments to observe and compute celestial phenomena to the formulation of revolutionary hypotheses on the physical causes of the motions and the orbits of the planets; from the discovery of the finite velocity of light to the scientific foundation of geography and cartography; from the transformation of the traditional organisation of research (with the birth of the first State-founded scientific institutions) to the solution of important problems, such as the building of precision clocks, the detection of the cause of the variations of gravity with latitude, and - last but not least- the determination of longitude.

It must also be noted that Galileo's dedication of the Jupiter satellites to the Medici family introduced a new chapter in the history of Renaissance patronage. From then on, influential patrons considered the heavens a promising space for their political image and gave scientists hitherto unheard of possibilities of social promotion, high economic reward, and dignified employment.

After Galileo's discovery, the mysterious and moody satellites of Jupiter attracted the attention of the major protagonists of the Scientific Revolution: Pierre Gassendi and Isaac Newton, Christiaan Huygens and Giovan Domenico Cassini, Ole Roemer and John Flamsteed, Giovanni Alfonso Borelli and Robert Hooke.

Among many exciting possibilities, Jupiter's moons opened up new perspectives for the scientists and institutions that had been engaged for decades in the search for a satisfactory method of determining longitude at sea.

When Galileo pointed his telescope towards Jupiter, the quest for longitude was over a century old and had received a substantial number of proposals, none of which had proved satisfactory.

The difficulty in determining longitude was known to classical authors, but after the discovery of the New World, the solution of this problem became an urgent need. Since the first decades of the sixteenth century, an increasing number of ships had set out across the Atlantic where no fixed point of reference was available. For small-scale navigation in the Mediterranean or in the seas of Northern Europe, it was enough, in order to obtain one's beings, to have a good knowledge of coastal profiles (provided by special maps, called portolani), and to be able to determine latitude by measuring the altitude of the Sun at noon with a cross-staff or a nautical astrolabe or (from the XIII century) to have a magnetic compass on board. These techniques were not sufficient for oceanic navigation where precise determination of longitude was necessary.

The lack of an effective method for determining longitude had serious consequences for seamen and their vessels, often laden with precious goods. At the best of times, a sea voyage took many months. Food and fresh water became scarce, and poor hygienic conditions resulted in the spread of infectious diseases. Lack of fruit and fresh vegetables in the seamen's diet caused scurvy. Beyond the grave economical damage, the price paid in the loss of human life was so enormous that in order to assemble a crew it was necessary to resort to men who had been sentenced to imprisonment or to death for serious crimes. In a word, the exploitation of the Eldorado of the New World was seriously hindered by the inability to find a solution to the troublesome longitude problem.

Before a viable solution was found, the methods at hand were based on the experience and guesses of seamen. Columbus, Vespucci, and early ocean explorers practised "dead reckoning", which depended on a rough evaluation of the distance covered daily by the ship. This was obtained by estimating the speed of the ship by dropping from the prow of the vessel a log tied to a line with evenly spaced knots. The seamen counted how many knots of the line were passed by the ship within a given time (measured by a sand glass), and thus made an estimate of the ship's velocity. It may be worth remembering that this is the origin of the custom of giving a ship's speed in "knots"! Regular observations of the Sun and the stars, with the help of the quadrant, the cross-staff and the nautical astrolabe, helped to correct these empirical estimates.

Another common method relied upon the declination of the needle of the magnetic compass from true North. Because of the continuous variation with time at any given location of the magnetic North, this method never worked properly and it was progressively abandoned.

At the beginning of the 16th century, Johann Werner of Nuremberg, and some time later, the Imperial Astronomer, Peter Apian, suggested using the Moon as a clock and measuring its distance from known stars or from the Sun. The idea was excellent, but the impossibility of determining with accuracy the position of the Moon made "lunar distances" practically useless. Yet another lunar method depended on eclipses of the Moon, but these were too rare to provide a solution to a problem that demanded frequent checks and corrections.

The Belgian mathematician and instrument maker, Gemma Frisius, was the first in 1530, to advance the much simpler idea of carrying standard time on the ships with a clock. In this way, the difference between local time (established by observing the altitude of the Sun at noon) and standard time would immediately give the longitude. The method, theoretically impeccable and easy to carry out, proved once again impractical: there was no clock (and there would not be one for a long time to come) capable of keeping standard time with sufficient precision over a long period and under variable weather conditions.

The increasing importance of navigation, and a series of maritime disasters due to uncertainty about longitude, made those nations most involved in world trade take important steps to solve the problem.

Philip II of Spain, in 1567, offered the inventor of a practical method of detemuning longitude a pension of 6000 ducats. This reward was increased in 1598 by Philip III. In 1600 the Dutch Republic established a prize of 5000 florins. The Kings of France and Portugal, and the Venetian Republic, offered huge rewards. But no practical solution was forthcoming. Everyone was frustrated when, at the beginning of 1610, Galileo observed, through the eye-piece of his telescope, Jupiter surrounded by 4 satellites, and realised that the moons of Jupiter could be used as a celestial clock in the determination of longitude.

This engraving from James Ferguson's Astronomy explained (mid-18th century) illustrates Galileo's idea of using the eclipses of the moons of Jupiter to determine the difference in longitude between two places on the Earth. Ferguson's illustration shows that the eclipse of the innermost satellite K (behind J - Jupiter) is observed from two points on the Earth (R and Q) at precisely the same moment. If the observer standing at Q has tables that allow him to compare the time of the eclipse at point R with his local time, he can easily find the difference in longitude between the two points. If the time at R is 4 p.m. and the local time at Q is noon, then, because of the difference of 4 hours, point Q is 45° west of R.

It was soon clear that for the success of this proposal three major conditions had to be met:

a) First, a good telescope to observe the Jupiter satellites;

b) Second, tables indicating the time the moons entered and left the shadow of the planet, and/or the times of their conjunctions, oppositions and occultations;

c) Third, an easy way of observing the satellites with a telescope on the rocking deck of a ship.

Galileo worked intensely during 1610 and 1611 to improve his telescope, and he achieved excellent results. For at least three decades, only his telescopes could guarantee a clear and distinct vision of Jupiter and its moons. Galileo devoted a great deal of time from mid-1611 to the systematic observation of the satellites of Jupiter in order to prepare accurate tables. By September 1612, he had determined the periods of the satellites, and his autograph records show that, during these months, he had taken into account the prostapheresis, that is the continuously varying angle between the Earth and the Sun as seen from Jupiter. as a consequence of the annual motion of the Earth. Prostapheresis causes the irregular appearance of the periods and eclipses of Jupiter's moons as seen from the Earth. Galileo invented a device, which he called a Giovilabio, to compute the prostapheresis. From Galileo's diagram, a neat brass instrument (a kind of analogic computer), was later made.

The quality of the data recorded by Galileo in his tables was more than acceptable. He believed that eclipses could be timed with an accuracy of about one minute (corresponding to an error in longitude of only 15'). An excellent result when compared with other methods that were often off by more than 4° .

Once he had prepared the tables, Galileo pondered the practical applications of his new method, and a new stimulus soon presented itself. In 1612, the Granduke of Tuscany, Cosimo II, discussed with the Spanish Crown the possibility of allowing Tuscan ships to trade with the West Indies, using as their base the harbour of Leghorn. To gain the King of Spain's favour, the Granduke offered to disclose Galileo's method of determining longitude, and to train Spanish seamen in its use. Galileo prepared a formal proposal in which he extolled the superiority of his method compared to those already in use, and offered to make one hundred telescopes that magnified "forty or fifty times" for the Spanish navy. He also promised to write out full instructions for the seamen.

The discussion with the Spanish authorities, which went on for several years, was conducted through the channels of Medici diplomacy. The Medici considered the satellites as their personal property (it must not be forgotten that they were internationally known as the Medici stars), and the Florentine princes acted as if they were selling exclusive rights for their practical exploitation.

Notwithstanding Galileo's optimism, the Jupiter clock turned out to be moody and capricious, and this for several reasons. Galileo's tables could not predict the eclipses of Jupiter's moons with sufficient accuracy. Furthermore, the modest quality of the telescopes available at the time made observation of the occultation of the satellites difficult and uncertain. This was mainly due to the fact that these instruments had a very small field of view, which meant that it was difficult to spot the planet and the satellites, and almost as difficult to keep them within the field of view. Galileo erroneously believed that the orbits of the satellites were circular and that they moved at a constant velocity. Hence the problem of accurately timing their aspects. He also ignored the inclination of the moons' orbits with respect to Jupiter's plane. Finally, Galileo was unaware of the alterations of Jupiter's appearances produced by atmospheric refraction, and equally unaware of the perturbing factor of the speed of light in the exact timing of eclipses when viewed from the periodically varying distance of the Earth.

Galileo had also underestimated other technical problems. When the longitude dealings with the Spanish Crown were revived in 1616, Galileo had to face a major objection that was raised against his method and was communicated to him directly by the Tuscan Ambassador in Madrid, the Count d'Elci: "In order to put your method into practice it is compulsory and necessary first to see the said stars and their aspects. 1 do not know how this can be done at sea... For, leaving aside the fact that the telescope cannot be used on ships because of their motion, and allowing that it could be used, it could serve neither during the day when the weather is overcast nor at night".

Galileo felt the blow. But he did not give up. To enable the telescope to be used on the deck of a rocking ship he designed a special headgear, which had to be fixed to the neck and probably to the shoulders. It was meant to neutralise, by a kind of Cardan suspension, the movement of the ship. A short telescope was fitted to the headgear in such a way that it remained in line with one of the eyes, while the other eye was left free to find Jupiter. This device, of which no illustration survives, was tested to the sailors' satisfaction on Medicean galleys in Leghorn. Galileo applied to the celatone (the Italian name given by Galileo to the device) a special micrometer, which made it easier to measure, in Jupiter diameters, the distance between the planet and the four satellites. Notwithstanding Galileo's claims of having provided the solution to the problem of longitude, the Spanish Crown did not grant him the prize. Later on, in 1620, and again in 1629 and 1631, negotiations with the Spanish Crown were revived, but always with negative results.

This disappointing conclusion did not put an end to attempts by Galileo and other scientists to improve Jupiter's clock. Galileo's method might have been difficult to apply at sea, but it was well suited to determine longitude on land. This was not a trivial matter since an accurate knowledge of the longitude of the coastal profile would offer considerable help to navigators.

Thus Galileo continued to observe the satellites in order to improve the accuracy of his tables. But new problems kept him from continuous research in this field, and he had to face the Church's opposition to the Copernican system. The matter was delicate since he had been warned in 1616 against presenting heliocentrism as a realistic description of the world. He tried nonetheless to push the Roman Church to assume a more open attitude towards the heliocentric hypothesis, and he undertook basic work on the nature of the laws of motion in the hope of finding a decisive confirmation of the Copernican system. His efforts, which produced the great masterpieces that are the Essayer, in 1623, and the Dialogue on the Two Systems of the World, in 1632, ended in the dramatic trial of 1633 where Galileo was accused by the Tribunal of the Inquisition and condemned for being - as a Copernican - strongly suspected of heresy.

A few months after his condemnation Galileo was allowed to return to his Florentine house, the Villa Il Gioiello at Arcetri where he was kept under house arrest. With the help of a young assistant, the Olivetan monk Vincenzo Renieri, he returned to his "longitude method". Prevented from celestial observation by the poor state of his eyesight (he was soon to become completely blind), Galileo instructed Vincenzo Renieri to revise his earlier tables. Unfortunately these revisions were lost after his sudden death in 1647. After 1633, Galileo was immersed in the preparation of his last work, the Discourses and Demonstrations on Two New Sciences, which was published in Leyden in 1638. Galileo also took up his early experimental work on pendulums. According to his last disciple, Vincenzo Viviani, Galileo had observed that pendulums of the same length are isochronous (no matter what the amplitude of their oscillations) as early as 1584. In 1602, he provided an indirect geometrical demonstration of this isochronism, and a little later, he discovered the proportion between the length and the periods of a pendulum.

Galileo had known since 1627 that a prize of 30,000 scudi had been promised by the States General of the United Provinces of the Netherlands to anyone who could find a correct method of finding longitude. Galileo was initially reluctant to contact the Dutch probably because he believed that the Spaniards would come round, but when he realized that the Jury of the Dutch prize was made up of first-rate scientists, he decided, in 1636, to compete. He may also have been tempted to leave Italy where he was living the life of a prisoner, in order to enjoy the freedom, the prosperity and the bustle of Amsterdam. The proposal of the longitude method sent to Amsterdam extolled the high quality of Galileo's telescopes and the accuracy of his ephemerides of Jupiter's satellites. In order to facilitate observations on the deck of a ship Galileo suggested a special chair that would float in a bath of water or oil to eliminate the perturbing effects of the agitation of the sea.

With respect to the method submitted to the Spanish authorities, Galileo's proposal now included a totally new element, the description of a working time-piece that was less subject to external alterations than any other such instrument. This device was intended to keep the local time between two successive astronomical measurements. Galileo's idea of a new time-piece exploited the isochronous oscillations of the pendulum, and opened a promised land. It has to be stressed that Galileo did not think of the construction of a true clock, capable of transporting standard time across the ocean as Gemma Frisius had suggested one century earlier. Galileo intended his invention to serve for very short time intervals and only in order to keep local time. It was meant to work in combination with, and not as an alternative to astronomical methods, which would still be used to make the tables to check and compare standard time with local time. He had spent so many years of accurate and patient observations, and he had promoted so intensely the virtues of the moons of Jupiter that he did not realise that the pendulum offered an entirely novel solution that rendered complicated astronomical measurements superfluous. He did not see that a transportable clock like the one he was proposing to the Dutch was the long-sought after solution to the problem of longitude. In any case, a few years later, in 1641, one year before his death, Galileo improved his device with a pin-wheel escapement that made it possible to record the regular oscillations of the pendulum with a counter. Galileo's son, Vincenzio, made a sketch of his father's invention, and built a working model of it.

The Dutch affair had a less agreeable side. Galileo had to face the suspicion of the Church, which did not view with favour the fact that he was dealing with representatives of a Protestant country. Moreover, after making promising noises, the Dutch turned cool, and rejected the proposal after the death of the members of the Jury who had shown a genuine interest. It seems that longitude was a curse, not only for the poor seamen, but also for those engaged in the search for a solution!

As the final resolution of the States General recites, their main concern was, again, the impracticality of the method at sea. Galileo's proposal required accurate observations and refined computation. On the ships' deck there are no scientists, stressed the members of the Jury, "but sailors, who are rude people, men only superficially acquainted with mathematics and astronomy, who are satisfied with those few propositions that are useful to their needs. Men, moreover, who still find insuperable the problem of using this invention on a moving ship that is continuously tossed about".

The failure of this second negotiation on longitude did not stop the improvement of Galileo's ephemerides of Jupiter's moons and the time device he developed.

Both the celestial and mechanical clocks witnessed dramatic improvements during the decades following Galileo's death.

The observation of Jupiter's satellites went on thanks, above all, to the Bolognese Gian Domenico Cassini. In 1668 he published improved ephemerides based on the Bologna meridian. The favourable reception of his work by astronomers throughout Europe led to the offer of a high salary and a permanent position in Paris at the court of Louis XIV, the Sun King, in 1669. In Paris, Cassini continued his research and organised expeditions to observe celestial phenomena at the same time, from different places, with the help of competent assistants. He was appointed Director of the Paris Observatory, the first permanent astronomical institution founded by Louis XIV in 1667, with the specific goal of enhancing geographical studies and finding the definitive solution for longitude. During his long life Cassini continuously referred to the moons of Jupiter as the best clock to determine longitude, at least on land. During the second half of the 17th century, continuous improvement of the Galilean method contributed to a better knowledge of geography.

Cassini relied on the cooperation of outstanding scholars. Jean Picard, for instance, helped him redraw the map of the coastal regions of northern France, a project that did not rejoice King Louis XIV who had promoted it. It is reported that the Sovereign, on seeing that the new coast line reduced the surface of France lamented that he had lost more territory to his astronomers than to his enemies!

When studying the ephemerides of the moons of Jupiter made by Cassini, the Danish mathematician Ole Roemer realised that errors in the tables were caused by the finite velocity of light. In a paper read in November 1676 in Paris at the Acadėmie des sciences, Roemer explained the perturbing role of the finite velocity of light in the prediction of the eclipses of the satellites of Jupiter. When Jupiter was at its maximum elongation from the Earth, eclipses were seen later than predicted by the tables. Working on the estimated distance between Jupiter and the Earth and on the difference in time between ephemerides, Roemer arrived at the conclusion that the velocity of light is about 140,000 miles per second (roughly 20% less than its actual value). Let us note that this remarkable deduction was a consequence of the discovery of the moons of Jupiter. Another major discovery of the workings of Nature had been derived from the observation of the Galilean Jupiter clock!

Fortune smiled on Galileo's other great idea: the application of the pendulum to the clock. The consequences were of considerable importance.

As everybody knows, the Dutch scientist, Christiaan Huygens, put Galileo's invention into practice. He not only made and progressively perfected the pendulum-regulated clock, which Galileo had simply thought of. Huygens showed also that the oscillations of the Galilean circular pendulum are not really isochronous, and that the real isochronous pendulum describes a cycloidal arc. After this important discovery, Huygens used cycloidal pendulums as time regulators.

Huygens' clock represents a considerable advancement in the history of time measurement. The Dutch scientist was convinced that he could now solve the problem of longitude by purely mechanical means (that is, by keeping standard time on the ship, thanks to his clock). No more observations of lunar distances, lunar eclipses or eclipses of the Jupiter satellites would be necessary, only the routine checking and readjusting of the clock.

Huygens' clocks were tested many times in actual navigation. Notwithstanding the care with which they had been designed and built, the results were disappointing. First of all, Huygens' clock suffered from humidity and change of temperature on the deck of ships. Moreover, it was soon discovered that the periods of pendulums (even of cycloidal pendulums) change in different regions of the Globe. This convinced Huygens that gravity varies with latitude, another great discovery we owe to the quest for longitude. A few years later Newton would explain why this occurs.

It is common knowledge that the final solution to the dramatic search was provided, not by one of the many outstanding scientists who confronted these problems, but by a modest and almost unlettered craftsman, a British clock-maker named John Harrison, who followed in the footsteps of Galileo and Huygens. He studied Galileo's pendulum and Huygens' proposal to use the cycloidal pendulum as time regulator. He managed to make a chronometer insensitive to the physical stress suffered on ships. Hamson clashed on many occasions with famous astronomers of the Royal Observatory at Greenwich (an institution founded by Charles II in 1675, like the Paris Observatory, with the aim of developing observational astronomy for practical purposes and especially to solve the problem of longitude). The Royal Astronomers would not admit that an effective solution could be devised by a craftsman poorly trained in mathematics and ignorant of astronomy. They strongly opposed Harrison's proposal, stressing that only Astronomy could offer the final answer.

Harrison had perfectly understood the reason why Huygens' pendulum clocks failed at sea and he put all of his energy into finding the technical solutions to neutralise the perturbing effects on the regular working of the clock caused by alterations in temperature and humidity, and by the rolling of the vessels. The first Harrison marine time-keeper was completed in 1735 (the construction took 5 years). It was tested by the Royal Navy and gave excellent results. But Harrison was not satisfied and went on to devise a new project. A few years later, his second marine time-keeper was ready. It was a totally new conception and much more compact. But the outcome of his personal tests was not encouraging, and Harrison did not want the clock taken on board ship. He dedicated himself to the construction of a third chronometer, a project that took 19 years and was completed in 1757.

Several parts of the clock were of a totally new conception, and the main pieces were made of bi-metallic components in order to automatically compensate for any changes in temperature. Great effort went into making the clock compact (considering the unusual complexity of its parts). This led to a fourth chronometer, completed in 1759. At last perfection had almost been reached!

The clock was tested by a British ship during a long transoceanic trip from Portsmouth to the Caribbeans and back. William Hamson, the son of John, was aboard and took care of the clock. The chronometer surpassed John Harrison's expectations. Back in Portsmouth after a little less than three months, the clock had lost only 5 seconds. The time had now come for the elderly John Harrison to cash the first half of the 20,000 pounds prize (an enormous sum!) put aside in the Longitude Act of 1717 for the inventor of an effective method of determining longitude. A few years later Harrison put his hands on the rest of the prize.

As we have seen, the early development of time-measurement occurred on the border between theoretical knowledge and practical expertise. The long quest for longitude clearly shows these characteristics. Galileo's clocks did not work well, neither the astronomical nor the mechanical one, but he had clearly foreseen the two major avenues to be explored, and he had paved the way for both the astronomer-mathematician and the clock-maker.

The re-proposal of the crucial role of the satellites of Jupiter, the planets that Galileo dedicated to the Medici family, in the history of time measurement is particularly fitting in this city of Florence, and in the context of an International conference on atomic physics and clocks. The fitting character of this evocation is emphasized by this room, which embodies the spirit of Cosimo I, the founder of the Great Duchy of Tuscany, who entrusted his distinguished architect, Giorgio Vasari, with the task of transforming this marvellous Salone into a huge, effective propaganda machine. Playing on the derivation of his own name, Cosimo (from the Greek word Cosmos), the Duke wanted to suggest that he was destined to become the Lord of the Universe. One could say that he foresaw what was to happen a few decades later when Galileo discovered and dedicated to the Medici the moons of Jupiter. The Medici now had the exclusive privilege of being the only dynasty to have a kingdom in the heavens, a privilege much envied by the most powerful monarchs of Europe. Thanks to Galileo's brilliant discovery of the Jupiter clock, the Medici could also claim the no less impressive title of Lords of Time.