Upon reflection: The Hadley brothers.

This is not a post about a circus act, a Canadian punk band or a boy band from Tulsa, Oklahoma.  John (1682 – 1744), George (1685 – 1768) and Henry Hadley (1697 – 1771) were three mathematical inclined gentleman scholars active in England in the first half of the 18th century. This is really a post about John but as he states quite clearly in his publications that George and Henry were actively involved in the realisation of his two major contributions to the histories of science and technology I thought it only fair that they should also be mentioned at least at the beginning of this article. In reading up for this piece I also discovered that George made a major contribution to the history of meteorology, which I will briefly sketch at the end.

The three were the sons of a wealthy landowner George Hadley who owned properties throughout the Home Counties as well as a town house in Bloomsbury Square in London although it appears that the family seat was in East Barnet in Hertfordshire of which county George senior was a deputy-lieutenant and in 1691 High Sheriff.

John Hadley

John, the first born, was according to his father born, “16 April 1682, just half an hour past nine, before noon, Sunday, Easter-day; christened the 21st, by Dr. Sharp Dean, of Norwich; sponsors, Sir Harry Fitzjames, John Huxley, Esq., and Lady Fitzjames.” (Sharp would later become Archbishop of York). This should give a flavour of the circles in which John moved. Nothing is known about his education and he appears not to have attended university. According to the Newtonian physicist Desagulier he invented and was granted a patent for some sort of water lift for mill wheels sometime between 1700 and 1710. In 1717 he was elected to the Royal Society and attracted notice by commenting in the Philosophical Transactions on the work of Bianchini and Maclaurin, which shows that he had a high level of mathematical knowledge. It was in 1721, however, that he made the first of two technological contributions that were to establish his fame.

 Isaac, John and the Reflecting Telescope.

It is wrong to state, as is often claimed, that Isaac Newton invented the reflecting telescope. The basic principle behind this instrument, that a concave parabolic mirror focuses parallel beams of light falling onto its surface at a single point, thus forming an image, can already be found in the catoptrics of Hero of Alexandria in the 1st century CE and the same phenomenon is discussed in the works of Leonardo da Vinci. The Jesuit astronomer Niccolò Zucchi, a contemporary and friend of Galileo attempted to build one in 1616 and the Scottish mathematician and physicist James Gregory published the design of what is now known as the Gregorian telescope in 1663. Between the attempts of Zucchi and Gregory the polymath Marin Mersenne also published designs of several different models of reflecting telescope. Both Zucchi and Gregory stumbled over the difficulties of grinding and polishing a mirror for their telescopes; Mersenne apparently aware of the problems didn’t even try. It is six times more difficult to grind and polish a telescope mirror than a telescope lens and the errors produced in this procedure meant that the instruments of both Zucchi and Gregory were useless. It was Isaac Newton who in about 1666 first succeeded in producing a functioning reflecting telescope, which became his entry ticket to the Royal Society and the world of science. Newton’s telescope was very small, scarcely more than a toy, although it had a magnification factor of forty, and for the reflecting telescope to become practical it was necessary for somebody to scale up the mirror and telescope, all attempts to do so failed miserably; enter John Hadley.

In 1721 John Hadley succeeded where all others had failed and produced a comparatively large scale functioning Newtonian reflecting telescope, which he presented to the Royal Society whose President was of course Sir Isaac himself. This instrument was tested against the 120-foot (focal length) refracting telescope in Wanstead, a present to the Royal Society from Huygens, and found to be superior and so introduced the age of the reflecting telescope. Hadley also went on to build a functioning Gregorian telescope and more importantly was able to teach his method of grinding and polishing to the leading instrument makers of the time enabling the serial production of reflecting telescopes. Important though this breakthrough was, and it should be remembered that most of the important astronomical telescopes since then, including Hubble, have been reflecting telescopes, Hadley would go on to produce a second possibly even more important invention.

 John Hadley (almost) invented the sextant.

One of the few scientific instruments that has, largely thanks to Hollywood, become a household name is the sextant. It serves as a guarantee of authenticity in movies about the sea to have the captain or first officer of a ship shoot the sun at noon in order to establish the ships latitude.

When we see this scene on the big silver screen we know we are in the hands of real sea dogs. This ritual is of course carried out using a sextant that instantly recognisable insignia of the navigator. John Hadley is credited with the invention of the sextant in 1731. It should be pointed out that the American glazier Thomas Godfrey invented an almost identical instrument in the same year a coincidence that led both men to being accused of intellectual theft by the supporters of the other. In fact the inventions were genuinely independent of each other but because it was Hadley’s instrument that went on to change history he is given the major share of the recognition as inventor. This attribution is slightly incorrect as Hadley’s original instrument was actually an octant and not a sextant and is confusingly often referred to as Hadley’s quadrant. I shall come to the story of how Hadley’s instrument became a sextant shortly but first we need to take a sort look at the history of navigation in the couple of centuries preceding Hadley’s invention.

It is a fairly easy task to determine ones latitude by measuring the altitude, that is height above the horizon, of either the pole star or the sun and then making some routine mathematical calculations. In the European history of navigation this was not done before the 15th century because seamen’s charts were not drawn with a latitude and longitude grid. This practice first came in after the rediscovery of Ptolemaeus’ Geographia in 1406. In fact using latitude determinations in sailing only began to become established in the 16th century and then only very slowly. At first altitudes were determined with a Jacob’s Staff an instrument   first described by the French Jewish astronomer Levi ben Gerson in the 14th century. This instrument had the disadvantage that the sailor doing the measuring was required to stare directly into the sun, which even with the use of a dark glass filter was not very healthy.

Using a Jacob’s Staff

In 1594 an English seaman John Davis invented the back staff, or as it was commonly know the Davis quadrant, an instrument with which the navigator stood with his back to the sun and a vane cast a shadow onto the measuring scale thus sparing the user the necessity of looking directly into the sun.

Simple Backstaff or Davis Quadrant

The next stage in the development was the invention of single reflecting instruments of which several prototypes were produced at the end of the 17th century, by Robert Hooke amongst others in which the image of the sun was reflected onto a measuring scale with a mirror. We are now ready for Hadley’s quadrant.

Hadley’s quadrant is a so-called double reflecting instrument here a small telescope is focused on the horizon through a half mirrored glass plate the mirrored half displaying an image of the sun reflected from a second mirror pointing behind the observer thus allowing the user to observe the horizon and sun simultaneously, the principle of the sextant.

Hadley’s Octant

Hadley’s instrument was only an octant because its measuring scale was only an eighth of a circle but because the readings are doubled creating the illusion that the scale is a quarter circle the instrument became known as Hadley’s quadrant. Although I have introduced the subject by talking about altitude measurements in navigation Hadley’s quadrant was originally conceived to make a completely different navigational measurement and in fact played a pivotal role in a much more difficult task the determination of longitude.

 Hadley’s quadrant, the sextant and the lunar distance method.

Regular readers of this blog and the Board of Longitude Blog will be well aware that the most pressing problem in navigation in the 18th century was the determination of longitude aboard ship. On land the problem had been largely solved by cartographers but their methods were not practicable on the rolling deck of a ship. Although not the only methods under consideration the two main competitors were the clock method first proposed by Gemma Frisius and the lunar distance method first proposed by Johannes Werner. Both methods depend on comparing local time with time at a known point elsewhere and then determining the time difference and thus the difference in longitude. The clock method depending on a clock carried on the ship displaying the time of the given distant point and the lunar distance method depending on accurate tables of the time of occurrence of astronomical phenomena, i.e. the distance of the moon from a given star, at the given distant point and comparing the time when the phenomena occur locally. In the 18th century nearly everyone doubted that anyone could build a clock that would remain accurate enough under the strenuous conditions of sea travel and so nearly all the leading astronomers backed the lunar distance method. This method, however, suffered from three major problems: 1) there existed no tables of the lunar orbit accurate enough to be used for this method, 2) there existed no table to correct for a whole collection of distorting factors that I wont go into here and 3) there existed no instrument capable of determining the lunar distances to the necessary accuracy of ± 1 minute of arc (astronomical and navigational distances are determined in degrees of separation). In the middle of the 16th century the French mathematicus Jean Rotz determined his longitude in the Atlantic Ocean west of Dieppe using a Jacob’s staff and the lunar distance method. The inherent inaccuracies of his instrument led him to an answer of 150 degrees and 30 minutes west of Dieppe, which would have had in the Pacific Ocean heading towards the International Date Line!

The solution to the problem of instrument accuracy was Hadley’s quadrant and he actually presented it to solve exactly this problem. His first instrument was subjected to a trial on the yacht Chatham under the supervision of Hadley himself, his brother George, the somewhat aged Astronomer Royal Edmond Halley and his successor the astronomer James Bradley. The instrument despite being new and the testers unskilled in its use preformed excellently and the first step had been taken along the road to the realisation of the lunar distance method. What were now necessary were accurate lunar tables and these were supplied by the German astronomer Tobias Mayer who sent them to the Board of Longitude in the 1750s. Mayer was convinced that the problem lay, not as had long been supposed in an inadequate lunar theory, but in inaccurate observations and equally inaccurate calculations both suppositions he proved right with his own diligent work. It was clear to him that for the lunar distance method to work the shipboard measurements would also have to be highly accurate and so he conceived a new measuring instrument, based on surveying instruments, called a reflecting circle. He sent drawings and a model of his new instrument along with his tables to the Board. James Bradley now Astronomer Royal recommended testing Mayer’s tables and a London instrument maker was commissioned to construct his reflecting circle.

Reflecting circle (not from Mayer)

This instrument together with the tables were tested by Captain John Campbell who found them to function well he however compared the readings of Mayer’s instrument with those made with his Hadley Quadrant. The quadrant proved to be as accurate as Mayer’s circle and because it was already established and being smaller easier to use than Mayer’s instrument it became the recommended instrument for the lunar distance method. However Campbell found some advantage in the 360° scale of the Mayer circle and so he had an instrument maker produce a double reflecting instrument with a sixth of a circle scale, as opposed to Hadley’s eighth, giving him because of the doubling effect 120° and so the sextant was born. Not long after mariners were able to determine longitude using the Campbell/Hadley sextant and Maskelyne’s simplified version of Mayer’s tables (Maskelyne simplified the calculations necessary by pre-calculating the steps between measurement and determination).

As I said at the beginning John Hadley explicitly credited his brothers George and Henry with the realisation of his two groundbreaking optical instruments so one should also give them credit along with John for these achievements. However George established his own scientific reputation in a completely different field and it is to his work that I will now briefly turn.

 The Hadley Cell 

Unlike John who inherited the family fortune George earned his living as a lawyer but like his elder brother he was interested in things natural philosophical and like his brother, who in the meantime had become a vice president of that august body, he became a member of the Royal Society in 1735. His main interest was in meteorology and he became responsible for handling the societies meteorological correspondence. One of the open questions of the age was the cause or origin of the so-called trade winds that were so vital to trans-Atlantic sailing George provided the first largely correct answer in that the winds are a product of the temperature gradient between the equator and higher or lower latitudes and the earth’s rotation. In recognition of this important achievement in the history of meteorology the section of the globe in which the trade winds are generated is called a Hadley Cell. This is a Hadley Cell and not the Hadley Cell because as well as for the earth the Hadley Cell for Venus has also been determined something that George Hadley almost certainly never imagined.

Next time you are contemplating significant 18th century natural philosophers alongside the Newtons and Halleys, the Watts and the Huttons, the Priestleys and the Lavoisiers spare a thought for the Hadley Brothers who also made some not insignificant contributions.

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Filed under History of Astronomy, History of Optics, History of science, Newton

8 responses to “Upon reflection: The Hadley brothers.

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