Burgi

SUBJECT AREA: Horology

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Burgi entered the service of Duke William IV of Hesse in 1579 as Court Clockmaker, although he also assisted William with his astronomical observations. In 1584 he invented the cross-beat escapement which increased the accuracy of spring-driven clocks by two orders of magnitude. During the last years of the century he also worked on the development of geometrical and astronomical instruments for the Royal Observatory at Kassel.

On the death of Duke Wilhelm in 1603, and with news of his skills having reached the Holy Roman Emperor Rudolph II, in 1604 he went to Prague to become Imperial Watchmaker and to assist in the creation of a centre of scientific activity, subsequently becoming Assistant to the German astronomer, Johannes Kepler. No doubt this association led to an interest in mathematics and he made significant contributions to the concept of decimal fractions and the use of exponential notation, i.e. the use of a raised number to indicate powers of another number. It is likely that he was developing the idea of logarithms at the same time (or possibly even before) Napier, for in 1620 he made his greatest contribution to mathematics, science and, eventually, engineering, namely the publication of tables of anti-logarithms.

At Prague he continued the series of accurate clocks and instruments for astronomical measurements that he had begun to produce at Kassel. At that period clocks were very poor timekeepers since the controller, the foliot or balance, had no natural period of oscillation and was consequently dependent on the driving force. Although the force of the driving weight was constant, irregularities occurred during the transmission of the power through the train as a result of the poor shape and quality of the gearing. Burgi attempted to overcome this directly by superb craftsmanship and indirectly by using a remontoire. This device was wound at regular intervals by the main driving force and fed the power directly to the escape wheel, which impulsed the foliot. He also introduced the crossbeat escapement (a variation on the verge), which consisted of two coupled foliots that swung in opposition to each other. According to contemporary evidence his clocks produced a remarkable improvement in timekeeping, being accurate to within a minute a day. This improvement was probably a result of the use of a remontoire and the high quality of the workmanship rather than a result of the cross-beat escapement, which did not have a natural period of oscillation.

Burgi or Prague clocks, as they were known, were produced by very few other makers and were supplanted shortly afterwards by the intro-duction of the pendulum clock. Burgi also produced superb clockwork-driven celestial globes.

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See also: Briggs, Henry

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SUBJECT AREA: Electronics and information technology

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After education at Warley Grammar School, Briggs entered St John's College, Cambridge, in 1577 and became a fellow in 1588. Having been Reader of the Linacre Lecture in 1592, he was appointed to the new Chair in Geometry at Gresham House (subsequently Gresham College), London, in 1596. Shortly after, he concluded that the logarithms developed by John Napier would be much more useful if they were calculated to the decimal base 10, rather than to the base e (the "natural" number 2.71828…), a suggestion with which Napier concurred. Until the advent of modern computing these decimal logarithms were invaluable for the accurate calculations involved in surveying, navigation and astronomy. In 1619 he accepted the Savilian Chair in Geometry at Oxford University, having two years previously published the base 10 logarithms of 1,000 numbers. The year 1624 saw the completion of his monumental Arithmetica Logarithmica, which contained fourteen-figure logarithms of 30,000 numbers, together with their trigonometric sines to fifteen decimal places and their tangents and secants to ten places!

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SUBJECT AREA: Horology, Ports and shipping

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John Harrison was the son of a carpenter and was brought up to that trade. He was largely self-taught and learned mechanics from a copy of Nicholas Saunderson's lectures that had been lent to him. With the assistance of his younger brother, James, he built a series of unconventional clocks, mainly of wood. He was always concerned to reduce friction, without using oil, and this influenced the design of his "grasshopper" escapement. He also invented the "gridiron" compensation pendulum, which depended on the differential expansion of brass and steel. The excellent performance of his regulator clocks, which incorporated these devices, convinced him that they could also be used in a sea dock to compete for the longitude prize. In 1714 the Government had offered a prize of £20,000 for a method of determining longitude at sea to within half a degree after a voyage to the West Indies. In theory the longitude could be found by carrying an accurate timepiece that would indicate the time at a known longitude, but the requirements of the Act were very exacting. The timepiece would have to have a cumulative error of no more than two minutes after a voyage lasting six weeks.

In 1730 Harrison went to London with his proposal for a sea clock, supported by examples of his grasshopper escapement and his gridiron pendulum. His proposal received sufficient encouragement and financial support, from George Graham and others, to enable him to return to Barrow and construct his first sea clock, which he completed five years later. This was a large and complicated machine that was made out of brass but retained the wooden wheelwork and the grasshopper escapement of the regulator clocks. The two balances were interlinked to counteract the rolling of the vessel and were controlled by helical springs operating in tension. It was the first timepiece with a balance to have temperature compensation. The effect of temperature change on the timekeeping of a balance is more pronounced than it is for a pendulum, as two effects are involved: the change in the size of the balance; and the change in the elasticity of the balance spring. Harrison compensated for both effects by using a gridiron arrangement to alter the tension in the springs. This timekeeper performed creditably when it was tested on a voyage to Lisbon, and the Board of Longitude agreed to finance improved models. Harrison's second timekeeper dispensed with the use of wood and had the added refinement of a remontoire, but even before it was tested he had embarked on a third machine. The balance of this machine was controlled by a spiral spring whose effective length was altered by a bimetallic strip to compensate for changes in temperature. In 1753 Harrison commissioned a London watchmaker, John Jefferys, to make a watch for his own personal use, with a similar form of temperature compensation and a modified verge escapement that was intended to compensate for the lack of isochronism of the balance spring. The time-keeping of this watch was surprisingly good and Harrison proceeded to build a larger and more sophisticated version, with a remontoire. This timekeeper was completed in 1759 and its performance was so remarkable that Harrison decided to enter it for the longitude prize in place of his third machine. It was tested on two voyages to the West Indies and on both occasions it met the requirements of the Act, but the Board of Longitude withheld half the prize money until they had proof that the timekeeper could be duplicated. Copies were made by Harrison and by Larcum Kendall, but the Board still continued to prevaricate and Harrison received the full amount of the prize in 1773 only after George III had intervened on his behalf.

Although Harrison had shown that it was possible to construct a timepiece of sufficient accuracy to determine longitude at sea, his solution was too complex and costly to be produced in quantity. It had, for example, taken Larcum Kendall two years to produce his copy of Harrison's fourth timekeeper, but Harrison had overcome the psychological barrier and opened the door for others to produce chronometers in quantity at an affordable price. This was achieved before the end of the century by Arnold and Earnshaw, but they used an entirely different design that owed more to Le Roy than it did to Harrison and which only retained Harrison's maintaining power.

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See also: Burgi, Jost; Huygens, Christiaan

See also: INDEX BY SUBJECT AREA

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al-Jazari, Ibn al-Razzaz

Arnold, John

Bain, Alexander

Barlow, Edward

Breguet, Abraham-Louis

Burgi, Jost

Cady, Walter Guyton

Ctesibius of Alexandria

Dondi, Giovanni

Essen, Louis

Graham, George

Grimthorpe, Edmund Beckett, Baron

Guillaume, Charles-Edouard

Harrison, John

Harwood, John

Hetzel, Max

Hipp, Matthäus

Hooke, Robert

Huygens, Christiaan

Leonardo da Vinci

Le Roy, Pierre

Leschot, Georges Auguste

Lioret, Henri Jules

Marrison, Warren Alvin

Mudge, Thomas

Richard of Wallingford, Abbot

Riefler, Sigmund

Shortt, William Hamilton

Sinclair, Sir Clive Maries

Su Song

Tompion, Thomas

Warren, Henry Ellis

Yi-Xing

Zhang Sixun

SUBJECT AREA: Horology

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Huygens was born into a cultured and privileged class. His father, Constantijn, was a poet and statesman who had wide interests. Constantijn exerted a strong influence on his son, who was educated at home until he reached the age of 16. Christiaan studied law and mathematics at Ley den University from 1645 to 1647, and continued his studies at the Collegium Arausiacum in Breda until 1649. He then lived at The Hague, where he had the means to devote his time entirely to study. In 1666 he became a Member of the Académie des Sciences in Paris and settled there until his return to The Hague in 1681. He also had a close relationship with the Royal Society and visited London on three occasions, meeting Newton on his last visit in 1689. Huygens had a wide range of interests and made significant contributions in mathematics, astronomy, optics and mechanics. He also made technical advances in optical instruments and horology.

Despite the efforts of Burgi there had been no significant improvement in the performance of ordinary clocks and watches from their inception to Huygens's time, as they were controlled by foliots or balances which had no natural period of oscillation. The pendulum appeared to offer a means of improvement as it had a natural period of oscillation that was almost independent of amplitude. Galileo Galilei had already pioneered the use of a freely suspended pendulum for timing events, but it was by no means obvious how it could be kept swinging and used to control a clock. Towards the end of his life Galileo described such a. mechanism to his son Vincenzio, who constructed a model after his father's death, although it was not completed when he himself died in 1642. This model appears to have been copied in Italy, but it had little influence on horology, partly because of the circumstances in which it was produced and possibly also because it differed radically from clocks of that period. The crucial event occurred on Christmas Day 1656 when Huygens, quite independently, succeeded in adapting an existing spring-driven table clock so that it was not only controlled by a pendulum but also kept it swinging. In the following year he was granted a privilege or patent for this clock, and several were made by the clockmaker Salomon Coster of The Hague. The use of the pendulum produced a dramatic improvement in timekeeping, reducing the daily error from minutes to seconds, but Huygens was aware that the pendulum was not truly isochronous. This error was magnified by the use of the existing verge escapement, which made the pendulum swing through a large arc. He overcame this defect very elegantly by fitting cheeks at the pendulum suspension point, progressively reducing the effective length of the pendulum as the amplitude increased. Initially the cheeks were shaped empirically, but he was later able to show that they should have a cycloidal shape. The cheeks were not adopted universally because they introduced other defects, and the problem was eventually solved more prosaically by way of new escapements which reduced the swing of the pendulum. Huygens's clocks had another innovatory feature: maintaining power, which kept the clock going while it was being wound.

Pendulums could not be used for portable timepieces, which continued to use balances despite their deficiencies. Robert Hooke was probably the first to apply a spring to the balance, but his efforts were not successful. From his work on the pendulum Huygens was well aware of the conditions necessary for isochronism in a vibrating system, and in January 1675, with a flash of inspiration, he realized that this could be achieved by controlling the oscillations of the balance with a spiral spring, an arrangement that is still used in mechanical watches. The first model was made for Huygens in Paris by the clockmaker Isaac Thuret, who attempted to appropriate the invention and patent it himself. Huygens had for many years been trying unsuccessfully to adapt the pendulum clock for use at sea (in order to determine longitude), and he hoped that a balance-spring timekeeper might be better suited for this purpose. However, he was disillusioned as its timekeeping proved to be much more susceptible to changes in temperature than that of the pendulum clock.

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SUBJECT AREA: Electronics and information technology

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Born into a family of Scottish landowners, at the early age of 13 years Napier went to the University of St Andrews in Fife, but he apparently left before taking his degree. An extreme Protestant, he was active in the struggles with the Roman Catholic Church and in 1594 he dedicated to James VI of Scotland his Plaine Discovery of the Whole Revelation of St John, an attempt to promote the Protestant case in the guise of a learned study. About this time, as well as being involved in the development of military equipment, he devoted much of his time to finding methods of simplifying the tedious calculations involved in astronomy. Eventually he realized that by representing numbers in terms of the power to which a "base" number needed to be raised to produce them, it was possible to perform multiplication and division and to find roots, by the simpler processes of addition, substraction and integer division, respectively.

A description of the principle of his "logarithms" (from the Gk. logos, reckoning, and arithmos, number), how he arrived at the idea and how they could be used was published in 1614 under the title Mirifici Logarithmorum Canonis Descriptio. Two years after his death his Mirifici Logarithmorum Canonis Constructio appeared, in which he explained how to calculate the logarithms of numbers and gave tables of them to eight significant figures, a novel feature being the use of the decimal point to distinguish the integral and fractional parts of the logarithm. As originally conceived, Napier's tables of logarithms were calculated using the natural number e(=2.71828…) as the base, not directly, but in effect according to the formula: Naperian logx= 107(log e 107-log e x) so that the original Naperian logarithm of a number decreased as the number increased. However, prior to his death he had readily acceded to a suggestion by Henry Briggs that it would greatly facilitate their use if logarithms were simply defined as the value to which the decimal base 10 needed to be raised to realize the number in question. He was almost certainly also aware of the work of Joost Burgi.

No doubt as an extension of his ideas of logarithms, Napier also devised a means of manually performing multiplication and division by means of a system of rods known as Napier's Bones, a forerunner of the modern slide-rule, which evolved as a result of successive developments by Edmund Gunther, William Oughtred and others. Other contributions to mathematics by Napier include important simplifying discoveries in spherical trigonometry. However, his discovery of logarithms was undoubtedly his greatest achievement.

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SUBJECT AREA: Electronics and information technology

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Whilst Directeur of the Bureau du Cadastre, Prony was made responsible for a project to determine the trigonometric functions of the centesimal units of 90°, i.e. the right angle was successively divided into 100 grades containing 100 minutes, which in turn each consisted of 100 seconds. This work produced tables (known as the Table de Cadastre) of the natural sines to twenty-two decimal places and the logarithms of sines and tangents to fourteen places. Although the tables as calculated were never published, tables based on them (presumably derived for the more familiar degree, minute and second sub-divisions of a right-angle by interpolation) have since appeared.

See also: Briggs, Henry; Burgi, Jost; Napier, John