Halley and longitude

If you’ve been following this blog about Halley’s voyages, you’re probably aware that 2014 is the 300th anniversary of the Longitude Act, which offered financial rewards for practicable methods of finding longitude at sea to specified degrees of accuracy.

Halley was involved with the quest for longitude throughout his long life: in 1675, aged 18, he was present when Flamsteed and Hooke visited the proposed site of the new observatory in Greenwich, being built by order of Charles II to help find longitude at sea; he was made a commissioner under the 1714 Longitude Act, courtesy of his position as Savilian Professor of Geometry (later also as Astronomer Royal), and around 1730 it was Halley who sent clockmaker John Harrison to see George Graham to discuss his ideas for a marine chronometer.

By the second half of the 18th century, there were two serious contending methods for finding longitude at sea, lunar distances and timekeepers, but in the late 17th and early 18th centuries, a diverse range of schemes were proposed, including finding longitude via magnetic variation.

Magnetic variation (or declination), the angle between magnetic and true north in a horizontal plane, was well known to the scientifically-minded, as too was the fact that it varied in different locations and also over time. It was thought that if an underlying pattern to the variation could be identified, it might offer a way of finding one’s longitude – and it was this that Halley was seeking to do on his voyage.

We’ll see Halley’s results in due course but for now we’ll consider one of the key difficulties with the theory, which is best illustrated by comparing data from four ships’ logs. [1]

At the start of Halley’s first voyage, he sailed from the Isle of Wight to Madeira in company with Admiral Benbow’s squadron and four of the five ships’ logs have survived, so we can compare their recorded latitude and longitude over several days:


1698 Falmouth Gloucester Lynn Paramore
Dec 2 47°28′ 47°39′ 47°24′ 47°23′
Dec 3… 46.28 46.30 46.13 46.20
Dec 14 32.39 32.36 32.43 32.25
Dec 15 32.22 32.26 32.19 32.15

Here, I’m showing the first and last two days that all four ships recorded data (leaving the English Channel and approaching Madeira) and you can see immediately that the latitudes are very similar – but the reported longitudes present a very different picture (first/last 5 days):


1698 Falmouth Gloucester Lynn Paramore
Dec 2 149.3 8°01′ 2°10′ W 8°00′
Dec 3 60.1 6.59 3.30 9.10
Dec 4 5.53 5.12 10.03
Dec 5 29.9 5.34 6.00 10.09
Dec 6… 51′-5/10 4.27 7.07 11.07
Dec 11 8.41 W 3.00 9.35 12.15
Dec 12 8.55 W 3.00 9.39 12.15
Dec 13 10.50 1.08 11.15 14.09
Dec 14 12.03 0.14 11.42 15.03
Dec 15 13.20 13.11 16.07

This table looks like a confused jumble, demonstrating that this is a problematic coordinate. Looking first at the Paramore, Halley always noted that his longitude position was measured west from London, and on December 15 he described himself as being to the south-east of Madeira, which is 16°55′ west of London, and so 16°07′ seems a respectable figure for his position.

The Gloucester does not specify where its longitude is measured from but apparently starts from the same longitude as the Paramore but then declines in value to zero as it approaches Madeira, and so that ship’s longitude is being measured east from Madeira (or possibly El Hierro in the Canaries, a common zero meridian of the time, in which case the final value is over a degree out).

The Lynn‘s figures increase like the Paramore‘s, but the values are quite different and I think these values are measured from Lizard Point as they depart from the English Channel (it isn’t specified). The later values for the Falmouth are similar to the Lynn‘s but the earlier ones are unlike any others and I’m assuming these positions are only partially calculated and represent the minutes travelled since the previous noon.

So these logs demonstrate one of the problems with longitude: even if you could accurately measure your longitude, where did you measure it from? (The prime meridian at Greenwich wasn’t agreed upon until the 1880s.) And how did this varying data affect the accuracy of the period’s maps and charts?

In other words, Halley didn’t really know where he was (his recorded longitude is often erroneous, sometimes considerably so) or even, strictly, where he was heading as many places were wrongly laid down in maps – and so how useful could a theory be that was founded on wrongly-placed locations?

In spite of this, Halley apparently found all the islands he states he will sail for, even though some are little more than large rocks in a vast ocean. Halley followed the customary practice of parallel sailing (sailing along a coast until you attained the latitude of the place you were aiming for and then sailing east/west until you reached it) but on his “Southern cruise” he was seeking tiny islands (Tristan da Cunha, Martim Vaz) from the middle of the Atlantic ocean – I think he must have had at least one very sharp-sighted crew member on board!

IMG_0165 - Version 2


[1] References for the logs are: Falmouth NA, ADM 51/341; Gloucester NA, ADM 51/401; Lynn NA, ADM 51/3892; Paramore BL, Add MSS 30398. The figures are (mostly) degrees/minutes but the notation differs in each log (I’ve used the Paramore‘s).

Return to St Helena

We last saw Halley encountering a storm as he sailed from Tristan da Cunha towards the Cape of Good Hope. A few days later he found the storm had blown him northwards of the Cape, and as his water supplies were low and he didn’t want to delay his voyage by heading back south, he decided to sail on to St Helena, arriving in Jamestown harbour on 12 March 1700.


Town of St James, Island of St Helena, 1794 (Wikimedia Commons)

Now I’ve mentioned before that one of the most disappointing aspects of Halley’s logbook is that he records very few observations about the places and peoples he encounters, and nowhere is this more frustrating than during his visit to St Helena – for this is not Halley’s first trip to the island, it was here that he acquired a Europe-wide reputation by the young age of 22.

Edmond was a nineteen-year-old undergraduate at Oxford when in July 1676 he sat down to write a reply to the Royal Society’s Secretary, Henry Oldenburg. He and Oldenburg had been corresponding about a paper that would be Edmond’s first appearance in the Philosophical Transactions and after some remarks about his paper, he asks if Oldenburg knows whether a work then in the press at Paris would contain a catalogue of the southern stars because:

if that work be yet undone, I have some thoughts to undertake it my self, and go to St Helena… by the next East Indie fleet, and to carry with me, large and accurate Instruments, sufficient to make a good cataloge of those starrs, and to compleat the Celestiall globe… I will willingly adventure my self, upon this enterprize, if I find the proposition acceptable, and that the East Indie company will cause me to be kindly used there, which is all I desire as to my self, and if I can have any consideracon for one to assist me; this Sr I propose to you desireing your advice as to what inconveniences there may be, and if you think my design may meet with sutable encouragement. [1]

The young and ambitious Halley was concerned that with Flamsteed, Hevelius and Cassini all at work on star catalogues, there would be no room for him to make his mark and so he decided to travel to the southern hemisphere to map the stars not visible from Europe, which had so far received little attention from astronomers.

His design did meet with “sutable encouragement” and through the influence of his patrons, Sir Jonas Moore and Sir Joseph Williamson, a letter was sent from the king to the East India Company requesting that they give free passage to Halley and his friend James Clark (Clarke or Clerke) on their next ship to St Helena, at that time under the Company’s governance.

Halley left Oxford without taking his degree, and he and Clark sailed from England around Edmond’s 20th birthday on board the East Indiaman, Unity, arriving at St Helena by early February 1677. Halley tells us he took a newly-made sextant, a new pendulum clock, an old quadrant, and several telescopes including his 24 footer, and on arrival he and Clark began building a basic observatory from which to deploy them. [2]

But things didn’t then go quite as planned owing to the continually adverse weather, and in November 1677 Halley wrote to Jonas Moore that:

such hath been my ill fortune, that the Horizon of this Island is almost always covered with a Cloud, which sometimes for some weeks together hath hid the Stars from us, and when it is clear, is of so small continuance, that we cannot take any number of Observations at once; so that now, when I expected to be returning, I have not finished above half my intended work; and almost despair to accomplish what you ought to expect from me. [3]

Oh dear, he’s travelled a long way to be thwarted by cloud-cover, but Halley’s not the type to be easily defeated and so to simplify the process and maximise the number of star positions he could observe, he based his own measurements on reference stars from Tycho Brahe’s catalogue, so that if Tycho’s star places (taken before the advent of telescopes) were rendered more accurate in future, his own positions could then be accordingly adjusted.

By the time he and Clark left the island in March 1678 on board the Golden Fleece, Halley had observed 341 stars, as well as a lunar and a solar eclipse, and a transit of Mercury – and by the autumn he’d produced a catalogue of his results, published the following year and the first to feature observations made using telescopic sights. [4] Halley also produced a planisphere in which he outlined a new constellation Robur Carolinum (Charles’s Oak), named to mark the occasion when King Charles had hid in an oak tree after his defeat at the Battle of Worcester.

The right ascensions and declinations of the principal fixed stars in both hemispheres to year 1678

Halley’s planisphere of the southern stars. Robur Carolinum is right of centre below the Centaur’s hooves (© NMM, Image B4225). The work was engraved by James Clark, presumably the friend who accompanied Halley but I haven’t been able to confirm that.

The catalogue and planisphere were well-received, with Flamsteed dubbing Halley “our Southern Tycho”, and Halley was rewarded with an MA by royal mandate, election to the Royal Society, and the esteem of Europe’s foremost astronomers. [5]

* * *

And now Halley is back on St Helena, scene of his youthful ambition. What went through his mind as he sailed into Jamestown harbour? Did he enquire after old acquaintances? Go in search of the observatory built with his friend James Clark over 20 years previously? Did he reflect on the path his life had taken since that first visit? He gives us no hint whatsoever, he tells us only that it rained heavily – plus ça change…

If anyone from St Helena can confirm that Halley’s Mount is pronounced ‘Hawley’, please let me know via the comments. Thanks!


[1] Halley to Oldenburg, 8 July 1676, Royal Society EL/H3/38.

[2] The location of Halley’s observatory isn’t certain but there is a monument set up on what is thought the likely site on a ridge known as Halley’s Mount. You can see the monument here and the wider view here (the walls are probably from a later construction).

[3] Halley to Moore, 22 November 1677, in MacPike, Correspondence and Papers of Edmond Halley (London, 1937), pp 39-41.

[4] Halley, Catalogus Stellarum Australium (London, 1679); it was subtitled (in Latin) Supplement to the Tychonic Catalogue. The transit of Mercury on 28 October 1677 gave Halley the idea (subsequent to James Gregory) that a transit of Venus would be the most useful method of estimating the sun’s distance from the earth, a method he would later vigorously promote to those future astronomers who would be alive to observe the late C18 transits.

[5] Flamsteed, The Doctrine of the Sphere (London, 1680), Preface. How Flamsteed must later have regretted this remark! The context of it was more complex than can be covered here, but we might look at the toxic relationship between Halley and Flamsteed later this year.

Halley and the Principia

Aboard the Paramore today, it’s Halley’s 43rd birthday* and I thought I would celebrate it this year by writing about how I became interested in Edmond and the qualities that I like about him.

My interest began in the summer of 2010 when I visited the Royal Society’s 350th anniversary exhibition. I very much enjoyed the exhibition and it inspired me to read a couple of biographies of Isaac Newton, about whom I knew very little – but while I found Newton a fascinating character, it was Halley who stood out for me, because among such complex and difficult men as Newton, Hooke and Flamsteed, Halley shone out as well-balanced, well-adjusted and nice. [1]

His kindness and lack of envy at the achievements of others are, I think, most apparent in the part he played in the publication of Newton’s Principia and it’s that role that I’ll try to sketch today.

The story begins in January 1684 when the 27-year-old Halley met up with Robert Hooke and Sir Christopher Wren and discussed the nature of celestial motions. Halley said he’d concluded that “the centripetall force decreased in the proportion of the squares of the distances reciprocally” (the inverse square law**) but that he’d been unable to prove it; Hooke affirmed the law and claimed that he had proved it, but Wren apparently didn’t believe him and so offered a book of 40 shillings to whoever was able to give him a convincing demonstration within the next two months.

The prize was never claimed, and in Halley’s case he may have given it little further consideration as he was shortly afterwards beset by several domestic crises. First, his younger brother Humphrey died abroad, then on March 5 his father went missing and five weeks later was found murdered on the banks of the Medway, then about the middle of March, Halley’s wife Mary gave birth to a daughter, Katherine, who was not to survive. [2] If all that wasn’t enough, Halley’s father died intestate and a legal war immediately broke out between Halley and his stepmother that would rumble on for almost fifteen years. In the circumstances, it was unlikely that Wren’s challenge was at the forefront of Halley’s mind.

However, in August 1684, while probably engaged on family business in the area, Halley remembered the celestial problem and decided to visit Isaac Newton in Cambridge, whom he’d met once before in London. After some pleasantries, he asked Newton what type of curve he thought would be described by the planets orbiting under the inverse square law, and Newton immediately replied it would be an ellipse – and that he had proved it. An astonished Halley asked to see the proof but Newton said he couldn’t find it but would redo the demonstration and send it to him.

Halley resumed his attendance at Royal Society meetings in November, having been absent during his domestic tribulations, and on December 10 reported that he’d seen Newton again in Cambridge, who had “shewed him a curious treatise, De Motu, which, upon Mr Halley’s desire, was, he said, promised to be sent to the Society to be entered upon their register.” This paper would develop into the three-book Philosophiae Naturalis Principia Mathematica over the next 18 months, a period during which the Society was obsessed with the publication of De Historia Piscium (History of Fishes), an impressive but poorly-selling book by Willughby and Ray, and Edmond and Mary welcomed a new daughter Margaret into their world (April 1685).

On 27 January 1686 Halley was elected to the new post of clerk to the Royal Society, defeating 3 other candidates – including Hans Sloane – despite not meeting some of the specified criteria (he was not a single man without children, and didn’t reside in Gresham College where the Society met) but the Society had reserved the right to waive any of the qualifications should they wish to do so.

Now it used to be thought that Halley was in severe financial difficulties after the death of his father and that that was why he’d sought the subordinate post of clerk with a salary of just £50pa, but Alan Cook has shown that Halley had a moderate income of about £150-£200pa from his father’s estate, (Flamsteed’s salary as Astronomer Royal was £100 and Pepys’s £350 as Clerk of the Acts, though Halley also had children to support), and that his interest in the position probably derived more from his interest in the Society and its activities than in the attendant salary. [3]

So with Halley now employed as the Society’s clerk, the next we hear of the Principia is on 28 April 1686 when Dr Nathaniel Vincent presented “a manuscript treatise intitled, Philosophiae Naturalis principia mathematica” to the weekly meeting, where the Fellows agreed to refer consideration of printing the book to the next Council meeting. But the Council didn’t meet again when expected and so at a regular weekly meeting on May 19, the Fellows agreed to go ahead and print the Principia at the Society’s charge, a decision which may have been pushed through by Halley. This didn’t go down well with the Council, not least because the Society’s finances were reeling from the cost of De Historia Piscium, and at the next Council meeting on June 2 we read:

It was ordered, that Mr Newton’s book be printed, and that Mr. Halley undertake the business of looking after it, and printing it at his own charge, which he engaged to do.

so the ‘lowly’ clerk has to foot the bill!

It says much about Halley’s admiration for Newton’s work and his recognition of its importance that he agreed to pay the cost of publication (and edit, print and promote it), especially as it meant neglecting his own concerns and jeopardising his employment at the Royal Society. One wonders what Mary Halley thought about the matter? I said in a previous post that I tend to think of Mary as being very supportive of Edmond and it’s these events I had in mind as it strikes me as improbable that Halley could have acted as he did without Mary’s support.

In any event, Halley’s troubles had barely begun: in April, his stepmother had taken him back to court over the settlement of his father’s estate, and at the Council meeting (on June 16) following the one where he was ordered to pay the cost of printing the Principia, his employment as clerk was challenged on the grounds that he didn’t meet the qualification that the clerk be single and without children. The challenge was dismissed by the Council since the Society had chosen to dispense with that requirement at the time of his election in January.

This attempt to remove him may have been because he was considered to have overreached himself in apparently bouncing a regular meeting of the Society into agreeing to print Newton’s book – or it may have been launched by Robert Hooke as the Newton-Hooke priority dispute was by now well underway, and Hooke would have been unhappy with Halley’s support of Newton.

The priority dispute and handling the temperamental Newton (and Hooke) was another problem that Halley had to contend with. After the presentation of the Principia in April, the Fellows adjourned to a coffeehouse where Hooke claimed that Newton had taken the idea of the inverse square law from him. Halley, who seems to have grasped Newton’s personality very early on, was concerned that he might hear an overly dramatic account of Hooke’s claim from another source and so wrote himself to Newton on May 22 giving a diplomatic report of the situation. Newton replied quite calmly on May 27 setting out what he recalled of his correspondence with Hooke, and then wrote again with further particulars on June 20.

But the ink was barely dry on that letter when what Halley had most dreaded, now occurred, and another Fellow gave Newton an incendiary account of Hooke’s behaviour and Newton duly exploded. He returned to his June 20 letter and added a postscript lambasting Hooke and threatening to suppress the third book of the Principia, its most important section and principal selling-point. Halley then wrote a masterly reply, judiciously constructed to pacify Newton and save the third book, which so far achieved its intention that Newton “wish[ed] I had spared ye Postscript in my last [letter]”.

Back at the Royal Society, Halley still wasn’t safe in his job. The June attempt to remove him had failed, but on 29 November 1686 we read that:

It was resolved, that there is a necessity of a new election of a clerk in the place of Mr Halley, and that it be put to the ballot, whether he be continued or not.

And at the next Council meeting of 5 January 1687, a committee was selected to examine the books and Halley’s performance – which reported on 9 February that the books and papers were “in a very good condition, and the entries made according to order”.

Shortly afterwards, Halley received a letter from Newton saying that he’d been “told (thô not truly) that upon new differences in ye R. Society you had left your secretaries place”, and Halley replied that all was well (!) but that “6 of 38, last generall Election day, did their endeavour to have put me by”. Halley then promised to do nothing else until Newton’s book was finished and on March 7 he wrote to say he now had a second printer at work on book 2 and that he would engage a third to print book 3 “being resolved to engage upon no other business till such time as all is done: desiring herby to clear my self from all imputations of negligence, in a business, wherin I am much rejoyced to be any wais concerned in handing to the world that that all future ages will admire”. Though happily his first printer was able to print book 3, having finished book 1 by that time, and on 5 July 1687 Halley wrote to inform Newton that the Principia was finally ready.

But Halley’s contribution didn’t stop there: he promoted the book to his correspondents in advance of publication; he composed an introductory Latin ode to the work; he reviewed it (anonymously) in the Philosophical Transactions; he distributed presentation copies (at his own cost) to key individuals; and he sent a presentation copy to King James II, accompanied by an essay written by himself on Newton’s theory of the tides, a subject carefully chosen by Halley to appeal to James, a former Lord High Admiral.

With his family misfortunes, his legal disputes, his work as clerk, his fight to retain his employment, his reading, editing and overseeing the printing of the Principia, and his management of the volatile Newton, Halley must have been under great strain throughout this period, yet he betrays no hint of that in his correspondence – although he did fail in one undertaking as he had no time to publish the Philosophical Transactions, which at that time provided a source of income for Halley.

So did Edmond receive any reward from the Royal Society for his hard work and the credit accruing to them from his publication of the Principia? After several applications by him to have his salary confirmed and paid (he’d received nothing after 18 months), on the 6 July – the day after the Principia was completed – the Council agreed to pay Halley a bonus of £20 in addition to the promised annual salary of £50, the whole amount to be paid to him … in the form of 70 unsold copies of De Historia Piscium, the very book that had prevented the Society from publishing Newton’s book in the first place. I doubt that Halley appreciated the irony.

Happy birthday, Edmond!

RS_9284 copy

Edmond Halley in his early 30s (the inscription is a later addition). This is how Halley would have looked around the time he was publishing Newton’s Principia. (© The Royal Society Image RS.9284)

* Halley’s birthday is 29 October (OS) or 8 November (NS)

** In essence, if two bodies move apart by 3 units the gravitational attractive force between them decreases by 9, if by 4, then by 16


[1] It should be noted that this was my early impression of Halley and I have encountered some less impressive behaviour since then (mostly relating to Flamsteed, their early friendship having turned quickly sour – well, toxic).

[2] The date of Humphrey’s death isn’t known but is generally given as 1684 as Halley applied for administration of his estate in autumn of that year, and he is known to have died before their father. Katherine was baptised on 27 March 1684 but again the date of her death isn’t known, though she had certainly died by 1688 when the name was used for another daughter. If she died shortly after birth, it may be that Halley lost his brother, father and daughter in the space of a few weeks.

[3] The assessment of Halley’s income from his father’s estate can be found in: Alan Cook, Edmond Halley: Charting the Heavens and the Seas (Oxford, 1998), Appendix 3

All references to Royal Society minutes are taken from: Thomas Birch, The History of the Royal Society of London…, Vol IV (ECCO print edition)

All quotations from Newton-Halley correspondence are taken from: HW Turnbull (ed), The Correspondence of Isaac Newton, Vol II (CUP, 2008 edition)

Mrs Mary Halley

On the 6 April 1699 a baptism is taking place at the church of All Hallows on the Wall on the northern perimeter of the City of London. The child – a boy – is named Edmond after his father, but his father – Captain Edmond Halley – is unaware of his son’s existence…

Boundary mark for St James's Dukes Place, where Edmond and Mary were married in 1682

Boundary mark for St James’s Dukes Place, where Edmond and Mary were married in 1682 (© Kate Morant)

Edmond Halley married Mary Tooke on 20 April 1682 at St James’s Dukes Place, a short walk from his father’s house in Winchester Street. The marriage took place less than 3 months after Halley returned from his Grand Tour and it isn’t known whether he and Mary were acquainted before he left, or if the marriage was arranged while he was abroad, or after his return, or whether Edmond or Mary had any involvement in the decision.

What is known, is that the marriage was a great success. They were married for almost 54 years until Mary’s death in 1736, which Edmond described as “the saddest day of my life” and that he had lived “in great contentment” with Mary. [1]

At the time of Edmond’s departure, they had two daughters, Margaret, born 1685, and Catharine, born 1688. The Biographia Britannica says they had several children who did not survive, but I have only found a record for one, Katherine, born while they were living in Islington, where they’d set up home after their marriage. [2]

There are very few glimpses of Halley’s personal life but those few give the impression of a close and happy family. Flamsteed describes a visit in 1712 by the entire Halley family at a time when relations between Halley and Flamsteed were at their nadir, and one senses the cheery Halleys working together to make the visit less of an ordeal for Edmond (and Flamsteed).

Halley’s gravestone, now set into a wall at the Greenwich Observatory, was erected by his daughters (his son had already died) and dedicated to Edmond and Mary as the “best of parents” (optimis parentibus) and all four are buried together, along with Catharine’s second husband, Henry Price.

Yet despite their long and happy marriage, Mary hardly makes an appearance in the written records. The Biographia Britannica describes her as “a young lady equally amiable for the gracefulness of her person and the beauties of her mind” but we know nothing else about her character or personality. [3]

In spite of this, it’s Mary I most often think of when reading Halley’s logbook. I tend to think of her as being the type of person who was very supportive of Edmond’s various projects – that’s speculation but even if it’s correct, she must have been gravely apprehensive about his voyage.


St Benet Paul’s Wharf, where Halley’s daughter Margaret was baptised in 1685 (© Kate Morant)

Besides her concern for Edmond’s safety, she must have worried about what would happen to her and her two daughters if he didn’t return – and then shortly before Halley finally set sail, she found she was pregnant again – a hazardous event in itself.

We don’t know of any letters Edmond wrote to Mary from his ship, but he must surely have written at every opportunity to let her know he was safe and well. He was unable to write to the Admiralty between December and early April, and so presumably Mary had no word either and at the time of giving birth to their son, would not have known whether her husband was still alive. It must have been some sort of comfort to be able to name the child after Edmond.

And what of Halley’s own concerns for his family? We know he wrote a will shortly after the voyage was proposed and so was not blind to the fact he might not survive it, but I wonder how much consideration he gave to what would happen to his wife and young daughters if he didn’t return? I don’t doubt Halley would have been concerned for his family but I do wonder if his optimistic personality may have led him to underestimate the dangers of a long sea voyage.

Perhaps it’s more pleasing to reflect on the scene when Halley does return to his family: the relief of his wife, the joy of his daughters, his own delight at finding he has a son. For Mary, however, the relief will be short-lived as Halley will set off on his next voyage just two months after his return – and Mary Halley will have to spend another year wondering if she will ever see her husband again.


[1] The remarks by Halley about his wife are quoted in several books but I can’t locate the original source

[2] The spelling of Catharine’s name varies, ‘Catharine’ is used on the gravestone so I have opted for that. Biographia Britannica, Vol IV (1757) p 2517 note RR for the remark about his having several children. Catharine and Katherine were two different daughters as the latter was born before Margaret but Catharine is described as Halley’s younger daughter on the gravestone

[3] Biographia Britannica, Vol IV (1757) p 2500