Captain James Cook and the Transits of Mercury and...

Captain James Cook and the Transits of Mercury and Venus*

CHARLES E. HERDENDORF

MERCURY BAY IS A SERENE INLET ON THE EAST COAST OF THE COROMANDEL PENINSULA.

Most New Zealanders know that Captain Cook anchored here to observe the Transit of Mercury, having come from Tahiti where he had observed the Transit of Venus. When the moon is full, illuminating the white bluff of Cathedral Rocks above Hahei and giving a sparkle to the gently rolling sea, it is easy to imagine the

Endeavour at anchor, busy with preparations to observe the transit at daybreak. But just what are the transits of these planets? And why were these events

important enough to send the King's navy around the world to measure them from the South Pacific? Most of us only have a vague notion of the underlying reasons for Cook's first voyage of discovery in 1769; but his story is a fascinating chapter in the history of modern scientific thought.l

Mercury and Venus have orbits which lie between the Sun and Earth's orbit. At rare intervals these planets pass across the face of the Sun in a movement known as a transit. The passage of these planets is the same phenomenon as the

more familiar eclipse of the Sun by the Moon except for the important difference that the apparent size of these planets is too small to cause any noticeable

diminution in the Sun's light. By aiming a telecope at the Sun during one of these vents and focusing the Sun's image on a white screen behind the eyepiece, the

planet will appear as a small black dot crossing the solar disc. Recording a

complete transit requires several hours of observation.

Mercury is never seen very far from the Sun and could never be seen overhead during the night. Thus the only times when Mercury can be observed

satisfactorily are just after sunset or just before dawn. Another consequence of

Mercury's orbit being closer to the Sun than the Earth's orbit is that it exhibits moonlike phases?crescent, half, and full. About 13 times each century, a Transit of Mercury across the face of the Sun can be observed.2

Venus resembles Mercury in several respects from an observational point of view. Venus appears both as a morning star and an evening star for the reason

* Research for this paper was undertaken while on sabbatical leave from The Ohio State University,

Center for Lake Erie Researcn, to conduct studies in New Zealand with the Ministry of Works and Development, Water Quality Centre. I wish to thank these organizations and the University of Waikato Library for their

support and assistance. Terry M. Hume and Robert J. Davies-Colley of the Centre reviewed the manuscript and provided helpful suggestions. The figures were drawn by Suzanne L. Abbati of the Ohio Sea Grant Program. 1 Authoritative account of Cook's first voyage to the South Pacific contained in J.C. Beaglehole (ed.), The

Journals of Captain James Cook on His Voyages of Discovery: Vol. J, The Voyage of the 'Endeavour' 1868-1771 (Cambridge 1955).

2 L. Warner, Astronomy for the Southern Hemisphere (Wellington 1975), 113.

39

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40 THE JOURNAL OF PACIFIC HISTORY

that it too is closer to the Sun than the Earth's orbit. It also exhibits phases as does the Moon. At crescent phase Venus is closer to the Earth and appears brighter than when showing a full disc. At its maximum brilliancy, Venus outshines all

other objects in the sky except the Sun and the Moon. At times it remains above the western horizon for several hours after sunset as the most conspicuous celestial body. Venus also transits the Sun's disc, but at much rarer intervals because of the planet's more inclined orbit. Since the earliest glimpse ofa Transit of Venus in 1631 only five more transits have been observed.3

In Cook's time the dimensions of the solar system were only crudely known. New theories held that accurate timing of a transit could provide the essential information necessary for calculating the precise distance between the Earth and the Sun, variously referred to as the 'solar parallax' or the 'astronomical unit'. If this distance could be determined, then using the formula which Kepler had

developed over a century earlier the distances to all the other planets could be found.4

This was one of the principal reasons why the accomplished navigator James Cook was dispatched on his voyage of exploration in 1769. A complete transit was predicted to be observable in the South Pacific. The transit did occur as

predicted, but the success of the observations was and still is a matter of debate and perspective.

An additional benefit of a transit is the ability to accurately calculate the observer's longitude, otherwise a particularly difficult and imprecise determination at that time. It was for this purpose that Cook landed at what is now called Mercury Bay, to observe the Transit of Mercury on 9 November 1769 and firmly fix the position of New Zealand.

the 18th century was an age of enlightenment in the arts and sciences that marks

the period when scientific observation replaced supposition as the method for

formulating and testing theories. Sir Isaac Newton and his contemporaries had articulated many of the physical laws which govern the dynamics of Earth and the solar system, but one measurement eluded them. That measurement was the 'solar parallax', or the mean distance between Earth and Sun. If this fundamental

unit were known, then Kepler's laws could be used to determine the dimensions of the solar system. Thus, in the 1760s, the scientific community turned its

attention to solving this 'final' problem of astronomy.5 In astronomy, the word 'parallax' means the angular difference between (1)

the direction to a celestial body as seen by an observer on the Earth's surface and

(2) the direction projected from a standard reference point (normally the centre of

3 S. Newcomb, Popular Astronomy (New York 1882), 177-8. 4 See endnote 'Note on Calculations Relating to the Transit of Venus: Kepler's Third Law.' 5 H. Woolf, The Transits of Venus, a Study of Eighteenth-century Science (Princeton 1959), vii.


COOK AND THE TRANSITS 41

the Earth). Therefore the 'solar parallax' is the angle formed at the Sun by lines drawn from the centre of the Earth and from the observer's location on the circumference of the Earth (Fig.l). Because the radius of the Earth at 6,378 km

was reasonably well established in the 1760s, if the angle of parallax could be

measured, then the actual distance to the Sun could easily be found by simple

trigonometric calculations (altitude of a isosceles triangle).6 In practice the measurement of solar parallax is beset with numerous problems and requires the

intercession of one of the planets with an orbit between the Earth and the Sun,

namely Mercury or Venus.

I v\iy Sun

Earth X^X"

"

^t-- ? -^^

/ \ - -; - " "~

Solar Parallax (p)

1 Earth's j \ Ceilter /

I FIGURE 1. DEFINITION OF SOLAR PARALLAX

The usefulness of the transits of Mercury and Venus in determining the distance to the Sun was first demonstrated by Edmond Halley, popularly known as the discoverer of the periodic occurrence of the comet which bears his name.

(Halley's Comet will return in 1986 after a 76-year journey through the solar

system.) In 1677, at the age of 21, Halley persuaded the Royal Society of London to finance an expedition to St Helena, a tropical island off Africa's South Atlantic

coast, so that he could observe and catalogue the southern hemisphere stars. While there he also observed the Transit of Mercury across the Sun's disc. He

later compared his results with measurements of the same phenomenon made at

Avignon, France, and arrived at a rough calculation of the distance to the Sun. His

30,000,000 km estimate is only about one-fifth of the actual value, but it is of historic interest because it suggested to Halley the idea of utilizing a transit of the

larger planet Venus to obtain a more precise measurement. In the closing years of the 17 th and early in the 18 th century Halley published a series of papers encouraging his colleagues to plan for world wide observations of two transits of

Venus which he predicted would take place in the 1760s.7

Halley's calculations revealed that at very rare intervals the planet Venus would pass in front of the Sun. Through a combination of the motions of Venus

6 See endnote. 7 A. Armitage, Edmond Halley (London 1966), 101-5.

D



and of the Earth, favourable conditions happen at intervals of eight years, 121.5

years, eight years, and 105.5 years, after which the cycle is repeated. In 1716 he

predicted a Transit of Venus would take place in June 1761 and again in June 1769, after which it would not recur for over 100 years?1874.

Halley encouraged his fellow scientists to occupy as many observing stations as possible throughout the world to time the ingress and egress of the planet on

the solar disc. He reasoned that differences in the duration of time the planet appeared to spend in transit across the surface of the Sun would permit an accurate calculation of the solar parallax, yielding the true distance of the astronomical unit. Halley's idea sprang from the circumstance that the path of

Venus across the Sun is not the same for observers at different locations on Earth. Thus two observers at different latitudes will see Venus sweep across the Sun

along two different chords, the amount of difference depending on the degree of latitudinal spread on Earth (Fig. 2). Hence the distance to the Sun can be deduced if the difference between the chords can be measured with adequate

accuracy.8

._0-28 AU_0-72 AU_ ISiXe II rv^iobservations

Transit line of G&<^^^

>>. N. Hemisphere

observationsyQ^ ^\ Q'^v

Venus_^-~J~ ^v/ ^\A EarthQ^^--??- \f I ̂ ^XJ^

Overtaking Earth at \ Slin / \ \ relative speed ? 1.63 N. / ^

1.0 AU FIGURE 2. TRANSIT OF VENUS

Thus by the mid-1700s a major scientific aspiration was that of solving the

problem of the actual dimensions of the solar system. Since the early 1600s the 'relative distances' of the planets from the Sun were known by virtue of Kepler's third law of planetary motion. But not knowing what the actual distances were, astronomers of the day simply called the gulf between the Earth and the Sun an

astronomical unit or AU, having a value of one. This made possible the calculation of distances from the Sun to the other planets, but only on the basis of this arbitrary value. One might compare this to expressing the metric distance

between Auckland and Wellington without knowing the length of a

kilometre.

8 See endnote.



by the turn of the 18th century Halley had been appointed the second Astronomer Royal and Director of the Greenwich Observatory. As such he was one of the most influential scientists in Europe. He knew that he would not live to observe the transits himself, but in his final years he continued to use his

reputation to bring attention to the importance of these events. After his death in

1742, Joseph-Nicholas Delisle, Astronome de la Marine in Paris, became the

champion of the transit concept. He shared Halley's enthusiasm for the project and was able to modify his method so that observations of contact at either

ingress or egress could also be used in the calculations of the solar parallax. It was

through Delisle's world wide correspondence that interest in the transits was solidified. His office served as a clearinghouse and the plans for major expeditions were laid.9

The observation of the transits of Venus in the 1760s represents the first international scientific endeavour undertaken on a global scale. Although the

English and the French took the lead in organizing the project, other nations

sponsoring observations included Holland, Russia, Denmark, Sweden, Germany, Spain, Italy, and Portugal, and colonists in Canada, America and India. The 1761

Transit of Venus was observed at over 60 locations throughout the then known

world, including Europe, Russia, India, China, South Africa, and Canada. The results were inconclusive, but the prospects for obtaining more refined

measurements for the 1769 transit were considered very good by the astronomers of the day.10

To get the maximum benefit from the transit of 17 69, deficiencies in the 1761 observations would have to be corrected. Improved telescopes were developed and plans made to locate stations at more widely separated latitudes. In 1764, the French astronomer Joseph Lalande published a map which divided the globe into areas in which the ingress and egress of the transit could and could not be seen. It became immediately obvious that a station would have to be occupied somewhere in the South Pacific in order to observe both the start and end of the transit. In Paris, one of Lalande's colleagues, Alexandre Pingre', drew up a

memoir on the choice of stations for the coming transit.11 He stressed the need for stations in the far north and in the southern hemisphere. Pingre' calculated that

from a station in the South Pacific the shortest complete transit could be observed. This information could then be compared with results from the longest duration station, which was predicted for Scandinavian Lapland, above the Arctic Circle. He believed his theoretical Pacific station (placed at about latitude 28?S and

longitude 120?W) was reasonable because explorers, such as Mendana and

Quiros, had spoken of groups of islands in the region, although no island was

0 Woolf, The Transits, 23.

10 Ibid., 150. 11 Ibid., 152.



then known to exist at this location.12 The Marquesas, discovered by Mendana in

1596, were to have been the venue for the transit observations until Captain Samuel Wallis returned to England in 1768 with news of the discovery of Tahiti,

only 2,000 km to the northwest of Pingre' 's calculated position. (Incidentally, there is an island very near the theoretical station?Pitcairn Island, where the

mutineers of the Bounty settled in 1790.) Thus, arrangements were made on an international scale to observe the 1769

transit from as many places as possible. To England fell the responsibility of

occupying a station in the little known South Pacific, largely due to the resolve of the Royal Society to make up for their relatively poor showing in 17 61. The Royal Society petitioned King George III to direct the British Admiralty to dispatch a

ship to the area identified by Pingre'. The Admiralty agreed to participate in the

expedition, although for somewhat ulterior motives.13 One of the most qualified navigators and cartographers in the Royal Navy at

this time was James Cook, not a line officer but only a warrant officer serving in Newfoundland. He had risen in the ranks from a seaman to ship's master in just two years. During the next 10 years he became a self-taught expert in

mathematics, astronomy and hydrographic surveying. Now it was 1768, and his abilities were recognized. He was commissioned as first lieutenant and appointed commander of the bark H.M.S. Endeavour. Because of his scientific expertise he

was also approved as an observer of the transit by the Royal Society.

the British Admiralty's orders to Lt James Cook in 1768 were brief and

uncomplicated. He was to sail the Endeavour to the island of Otaheite (Tahiti) in

the South Pacific, with a team of scientists from the Royal Society, to observe the Transit of Venus. In addition to this publicly announced mission, Cook carried with him sealed orders not to be opened until after the transit had occurred.

Pursuant to His Majesty's pleasure, so soon as the observation of the Transit of the

planet Venus shall be finished, you are to put to sea with the bark you command and

proceed to the southward to a latitude of 40?S in order to make discovery of a southern continent. But not having discovered it or any evident signs, you are to

proceed in search of it to the westward until you discover it, or fall in with the eastern side of the land discovered by Tasman and now called New Zealand.14

Cook was further instructed to make a detailed survey of the coastline of the

southern continent and document its flora, fauna, and inhabitants. He was to

cultivate friendship and alliance and attempt to establish trade. The orders

12 E. Newby, The World Atlas of Exploration (London 1982), 122-3. 1S W.R. Gray, Voyages to Paradise: Exploring in Wake of Captain Cook (Washington 1981), 34, quotes H.T. Fry,

James Cook University of North Queensland, concerning underlying reasons for the expedition, 'After the

Seven Years War, the English hoped to expand gready their sphere of influence. In particular, they wanted to

preclude French moves into the South Pacific' 14

Newby, The World Atlas, 134.



required him to obtain the consent of the natives before taking occupied territory or, if uninhabited, take possession for His Majesty. The secret orders concluded, 'You will upon falling in with New Zealand carefully observe the latitude and

longitude, and explore as much of the coast as the conditions of the bark, the health of her crew, and the state of your provisions will permit, having always great attention to reserve as much of the latter as will enable you to reach

England.' Cook himself can be counted among the scientists aboard the Endeavour. In

1766, while in command of H.M.S. Mercury, he charted the east coast of Canada, and observed a solar eclipse in Newfoundland, recording the details for the Royal Society.15 The other scientists were Charles Green, assistant to the Astronomer

Royal; Joseph Banks, a wealthy young naturalist and a Fellow of the Royal Society; and Daniel Carl Solander, a Swedish botanist and pupil of Linnaeus, the

developer of the binomial system for scientific naming of plants and animals. Alexander Buchan, a landscape painter, Sydney Parkinson, a natural history artist, and Herman Sporing, technical secretary, completed the scientific

contingent. William Monkhouse, the ship's surgeon, also assisted with some of the scientific observations.

The Endeavour sailed from Plymouth in late August 1768. But political events, such as naval wars, hampered free travel in the 18th century. Cook knew well how hostile nations could endanger his mission; the vessel which carried the French astronomer Le Gentil to India had to make wide detours to escape English

men-of-war, and unfortunately he arrived in Pondicherry after the 1761 Transit of Venus was over.16 As a sign of the international importance of the 1769 observations in the South Pacific, the French government instructed all its men of-war to leave Cook's ship unmolested, because he was 'out on enterprises that were of service to all mankind'.17 Even so, the Portuguese viceroy at Rio de

Janeiro found it hard to believe that the Endeavour was sailing around the world

merely to make an astronomical observation. Cook was delayed nearly a month before the misunderstanding was resolved.18

It took five arduous weeks for the Endeavour to round Cape Horn at the tip of South America. It was late January 1769 before Cook entered the Pacific. He arrived at Matavai Bay in Tahiti in mid-April with only seven weeks to prepare for the Transit of Venus which was predicted to take place in early June. Cook decided to construct a fortification on a sand spit at the northeast end of Matavai

Bay to observe the transit. One of the prime reasons for constructing Fort Venus was to thwart the Tahitians' propensity for theft.

15 G.M. Badger, 'Cook the Scientist', in G.M. Badger (ed.), Captain Cook Navigator and Scientist (London 1969), 182.

16 Newcomb, Popular Astronomy, 182. 17 A- Pennekoek, A History of Astronomy (London 1961), 287. 18

J.C. Beaglehole, The Life of Captain James Cook (London 1974), 155-9.



In early May the astronomical instruments were taken ashore and installed in the fort. They included Gregorian reflecting telescopes (2 ft to 3 ft focus, 140

magnification), a Shelton astronomical clock, and a Bird astronomical quadrant.,9 There was good reason for Cook's caution. The heavy brass quadrant was stolen from its wooden case the first night. Cook immediately ordered the bay sealed off so that the culprit could not escape by sea. With some difficulty Banks and Green recovered the battered quadrant after a 10 km pursuit into the Tahitian hills. Some damage had been done and parts were missing but Sporing, who had

worked as a watchmaker in London, was able to make repairs in time for the transit. The quadrant was critical to the observation because it was used to check the rate of the astronomical clock.

On Saturday 3 June 1769 the weather was favourable on Tahiti, not a cloud in the sky the whole day. The winds were calm and the unshaded midday temperature rose to 48?C. Cook and his colleagues took advantage of the day to

observe the entire passage of the planet Venus over the Sun's disc. He, Solander, and Green made their measurements from Fort Venus on Tahiti, while

Monkhouse and Sporing observed the transit from neighbouring Moorea which Wallis had called York Island.20

Table i?Observations of the Transit of Venus at Tahiti in 176921

Contact Stage Greenwich Time (3 June 1769) No. Description Cook Green

1 Ingress, exterior contact 07:21:25 07:21:20 2 Ingress, interior contact

a. real 07:88:55 07:38:55 b. apparent 07:39:55 07:39:35

3 Egress, interior contact a. real 13:09:56 13:09:46

b. apparent 13:10:28 13:10:34 4 Egress, exterior contact 13:27:45 13:27:57

Total 6h:6m:20s 6h:6m:37s

The total difference in timing the complete Transit, as observed by James Cook and Charles Green, was 17 seconds (0.077%); 'black-drop effect' accounts for the difference between real and apparent times.

Although the observations were successful Cook was concerned by the differences among the five independent observers in the times of the inner contacts with the Sun's disc. He noted in his journal that they could very distinctly see a dusky haze around the body of the planet which disrupted the accurate

19 Badger, 'Cook the Scientist', 38.

20 Beaglehole, Journals J, 97-8.

21 R. Woolley, 'The Significance of the Transit of Venus', in Badger, Captain Cook, 127.



timing of the contacts. This so-called 'black-drop' effect caused Cook to record a

difference of 32 seconds between the real and apparent contact at egress, while Green found the difference to be 48 seconds (see Table 1). It was hoped that the various observers would agree within a second in order to provide the precision necessary to accurately measure the distance to the Sun.22

In addition to the measurements for solar parallax purposes, from the transit observations Cook was able to deduce the longitude of Point Venus, the most

northerly tip of Tahiti from which he made his observation. His longitude calculation is within 3' 45" (about 7 km) of what is accepted today.

By early July Cook was anxious to put to sea and undertake the mission disclosed in the sealed envelope. Tupaia, a Raiatian priest, volunteered to

journey back to England with Cook and Banks and to serve as pilot among the

islands, reefs, and atolls of the tropical Pacific. For several weeks they sailed westward through the chains of volcanic islands, surveying their coastlines. On

Raiatea, Tupaia's birthplace, Cook raised the British flag and took possession of the entire group, naming them Society Islands 'as they lay continguous to one another. '23

Tupaia spoke of legends that voyagers from Raiatea had colonized a

large island to the southwest (possibly New Zealand). Obeying the secret orders Cook sailed southwest for nearly 2,000 km in search of the supposed southern continent (Terra Australis Incognita), although Tupaia's description reinforced his own opinion that there were only islands to be found.24

Tasman had only seen the west coast of New Zealand, therefore the question of whether New Zealand was part of a great continent was unresolved as Cook sailed southwestward. On 7 October Cook resolved this by sighting the east coast of the North Island. But he was uncertain of the longitude and would need to wait for the Transit of Mercury to confirm the position of New Zealand.25

The Royal Society had not asked that the Transit of Mercury be observed,

mainly because there was no sure knowledge of land in the area where it would be visible. But Cook knew that if a landing could be made and the transit

observed, 'the longitude of this place and Country will thereby be accurately determined'.26 From Poverty Bay to the Bay of Plenty and eventually to the coast of the Coromandel, Cook searched for a place where he and Green could make their observations. On 4 November, only five days before the predicted transit,

he found a deep, sheltered bay with high, cream coloured cliffs and wide sandy

22 J. Waldersee, 'Sic Transit: Cook's observations on Tahiti, 3 June 1969', Journal of the Royal Australian

Historical Society, 55 (1969), 115-23. 23

Beaglehole, Life, 194. 24

Newby, World Atlas, 138. 25. Discussions of Captain Cook in New Zealand are presented by A.C. Begg and N.C. Begg, James Cook and

New Zealand (Wellington 1969); S. Maddock, Far as a Man May Go, Captain Cook's New Zealand (Auckland 1969); and A.H. $eed and A.W. Reed, Captain Cook in New Zealand (Wellington 1951).

26 Begg and Begg, James Cook, 33.



beaches that faced the northeastern sky?an ideal vantage point to observe

Mercury's passage across the face of the Sun.

Fortunately, on 9 November 1769 the sun rose in a cloudless sky. Cook and Green went ashore early in the morning, landing at a point on the sand spit beach about 300 m west of the mouth of the Oyster (Purangi) River.27 There they observed the Transit of Mercury which began at 0721 hours. Green observed the

early stages of the passage on a white screen behind the telescope while Cook determined the Sun's altitude with a sextant in order to ascertain the apparent time.28 They both observed the egress some four hours later. From these

observations Green calculated the longitude of the site as being equivalent to 176?56\ The latitude, calculated by Cook from the altitude of the sun, was found to be 36?48' south of the equator. Although the calculation sheets showing the exact methods used by the observers have not survived, there is no doubt about their accuracy. The position of the observation point, today known as Cooks Bay, is now computed to be latitude 36?50T8"S and longitude 175?45'23"E. Carrying their measurements all the way from England, they only differed less than 11

minutes (equivalent to about 19.7 km) from what is accepted today. The primary instrument available to Cook for determination of latitude and

longitude was the Ramsden sextant. Latitude could be determined directly by sights from the Southern Cross, or the Sun, but longitude required a precise knowledge of Greenwich Royal Observatory time or rare astronomic events such as transits. On his 1769 voyage to New Zealand Cook did not have an accurate

way of maintaining correct time over long periods. But on his second voyage he took with him Larcum Kendall's replica of John Harrison's prize winning marine chronometer. The precision of this timekeeper enabled Cook to determine

precise longitude and to construct the charts of New Zealand and the South Pacific with astonishing accuracy. The voyage placed severe demands on

Harrison's chronometer. Extremes of temperature were frequent; H.M.S.

Resolution had not only crossed and re-crossed the Equator, but it penetrated and

probed deep into the Antarctic reaching as far south as 71?S latitude and only turned north when faced with unbroken pack ice. Mountainous seas, torrential

rains, fog and tropical humidity were all experienced during the voyage which lasted nearly three years. As Cook sighted land near Plymouth at the end of his

journey in July 17 75, he checked the accuracy of the chronometer by determining the longitude. He found an error equivalent to only 14 km. This was amazing

considering the chronometer had not been set since the beginning of the voyage in July 1772. Eight months after the Resolution docked, John Harrison died in

27 Ibid., 36; Reed and Reed, Captain Cook, 58-9. 28

Beaglehole, Journals, I, 195.



London on his 83rd birthday, with the knowledge that his life's work had proven to be a complete success.29

But back to the first voyage. After observing the Transit of Mercury, Cook made a complete circumnavigation of New Zealand, charting most of the coast in

exceptional detail. This included a passage through the treacherous strait between the North and South islands which now bears his name. In March 1770 Cook made a momentous decision to return to England via New Holland (Australia) and the Cape of Good Hope. On 1 April the Endeavour left New

Zealand passing by Cape Farewell and crossed the Tasman Sea. Cook and Banks received a hero's welcome back in England. Cook was

promoted to Commander and then to Post-Captain in the Royal Navy (1775) and was elected a Fellow of the Royal Society. Banks eventually became the Society's President. Solander, also a Fellow of the Royal Society, resumed his post as

specialist on the staff at the British Museum where he was generally conceded to be the ablest botanist in England. But other members of the party did not fare as well. The artist, Buchan, suffered an epileptic fit on the bitterly cold shore of Tierra del Fuego during the passage around Cape Horn, and died in Tahiti. This left only Parkinson to record the landscapes and the hundreds of hitherto

unknown plants and animals. He produced over 1,500 drawings from the

voyage. On the return voyage to England, Cook sailed the Endeavour to the Dutch

colony of Batavia (Jakarta) for ship repairs. Notorious as one of the unhealthiest

places on earth, many of the ship's company contracted malaria and dysentery there. Monkhouse and Tupaia died on Batavia. In late December 1770 the feeble crew of the Endeavour set sail for home, but the worst was yet to come. By the end of January 1771 the astronomer, Green, the secretary, Sporing, and the artist, Parkinson, had all perished.

After a stop at Cape Town, on 10 July 1771 the Endeavour came into sight of the English coast. The person who first saw it was the same Nicholas Young who

had caught the first glimpse of New Zealand and for whom Cook named Young Nicks Head at the entrance to Poverty Bay.

the saga of the Transit of Venus is that of an 18 th century attempt to determine the dimensions of the solar system. Indeed, the rare Transit of Venus provided the incentive for the first world wide scientific venture, and thus the establishment of the modern international community in science. The 1769 transit was observed on an even grander scale than the 1761 event. Stations were selected ranging from Siberia to California, from Varanger Fiord, Norway (above the Arctic Circle) to Tahiti, and from Hudsons Bay to Madras. The values of the

29 J. QuiU. John Harrison, The Man who Found Longitude (London 1966), presents a comprehensive account of

marine chronometer development in the 18 th century.



parallax of the Sun deduced from the 1761 Transit of Venus ranged between 8" and 10"; while those obtained in 1769, though much more consistent, still varied between 8" and 9", corresponding to a variation of about 18 million km (see Table 2). Even so, as a result of Halley's plan the absolute scale of the solar system was established to within an accuracy of about 5%?a considerble improvement on the 20-30% error for the previous century.

Table 2?Distance to the Sun for Various Solar Parallax Angles30

Parallax in Mean Distance Parallax in Mean Distance

Seconds of Arc in Kilometres Seconds of Arc in Kilometres

8.0" 169,396,390 9.1" 144,524,270 8.1" 162,366,760 9.2" 142,953,370 8.2" 160,386,710 9.3" 141,416,270 8.3" 158,454,350 9.4" 139,911,790 8.4" 156,567,960 9.5" 138,439,070 8.5" 154,726,010 9.6" 136,997,020

8.6" 152,926,830 9.7" 135,584,640 8.7" 151,169,090 9.8" 134,201,120

8.8" 149,451,220 9.9" 132,845,570 8.9" 147,772,040 10.0" 131,517,120

9.0" 146,130,140

But how did the 18th century scientific community view the 1769 observations? Did the effort involving 151 observers from 77 stations world wide

produce a definitive solar parallax? The Royal Society of London would probably have answered 'no', because the precision in timing the beginning and ending points of the transit did not live up to their expectations.31 Despite this problem, the degree of accuracy was gready improved over earlier measurements when the complete data set from all the stations was assembled. The number of scientific papers dealing with value of solar parallax deducible from the 1769 transit was enormous?approximately 600.

Some of the best analyses were produced by the French. Alexandre Pingre' of the French Academie Royale des Sciences examined the results of the 1769

observations, particularly those obtained from the 'lands of the midnight Sun',

by comparing data from Norway (Lapland) and Canada (Hudson Bay). He

published a paper in 1770 giving a rather unsatisfactory solar parallax of 9.2 seconds. Two years later, when the observations of Cook in Tahiti and the French astronomer Jean Chappe in Baja, California, reached Pingre' in Paris, he was able to recalculate the parallax and obtained an angle of 8.8 seconds, very close to the

M Woolf, The Transits, 208. 31

Beaglehole, Journals, I, cvi, cxlv; Waldersee, 'Cook's Observations', 120.



value accepted today.32 The difference in angles appears small, but the 0.4 seconds represents a distance of nearly 6.5 million kilometres (see Table 2).

The Royal Society was by no means pleased with Cook's report and data from the Transit of Venus (see Table 1). It was true that the Tahiti observers had had

difficulties in the timing of the stages, but so had every other observer. The stages consist of contacts: first contact, when the dark dot (Venus) just touches the outside edge of the Sun; second contact, when the dot is just completely within the disc of the Sun near the point of entry; third contact, when the dot, having crossed the Sun's disc, just touches the opposite edge of the Sun; fourth contact,

when the dot is completely outside the Sun but still just touching the outer edge. Just after the second contact the planet appears to draw a tiny area of blackness after it, the 'black drop' or haze that Cook noted in his journal. By the time the black drop has disappeared the planet has already separated from the Sun's inner

edge and the moment for recording the time of the second contact has been lost.33

When the Society sought to lay the blame on the dead astronomer Green, Cook responded with a sharp rebuke that contained such strong language that it was struck from the official proceedings of the Society. It soon became obvious that the numerous other observations taken elsewhere around the world were

equally unsuccessful for the same reason?the nebulous haze which surrounds Venus when viewed through a telescope precludes the precise timing of the

beginning and ending of the transit. In a 1771 paper published by the Royal Society, Nevil Maskelyne (fourth Astronomer Royal) commented that Green's observations differed more from one another than they ought to, or than those

made by other observers with quadrants of the same size and construction.34 In the journal of his second voyage Cook pointed out that the quadrant had been

pulled apart by natives and mended in the 'best possible manner'. He denounced

Maskelyne for not considering this fact and also for not realizing that Green had not had an opportunity to present his data in a final report; he asked Maskelyne if he would 'publish to the world all the observations he makes, good or bad, or did he never make a bad observation in his life'.35

The next Transit of Venus will occur on 7 June 2004. It is unlikely that it will be observed specifically for measurement of the solar parallax. Technology has

made great strides. In April 1961, 200 years after the first transit expeditions, powerful radars were for the first time trained on the Sun and planets. It took the

equivalent of 8.3 minutes for a signal to reach the Sun travelling at

299,793 km/sec. When confirmed by a series of observations throughout the

32 Woolf, Transits, 190-1. 53 Newcomb, Popular Astronomy, 179-84. 84

Beaglehole, Journals I, cxlv. 35 Ibid.



year, a mean solar distance of 149,597,000 km was determined.36 This value,

corresponding to a solar parallax of 8.7943", is in good agreement with the classical determinations of the 18 th century (particularly those of the French astronomer Pingre'), but has superior accuracy. Viewed from the perspective of 200 years of scientific advances, the efforts of our 18th century astronomers were a success and, moreover, were extremely important in unifying the scientific

community. But what of the Transit of Mercury? Cook once wrote that he hoped ambition

would lead him 'not only farther than any other man had been before, but as far as it is possible for man to go'.37 This is one of the few remarks in his journals that

exposes the tremendous drive which brought him to New Zealand and the Pacific

again and again. At Mercury Bay he used the occasion of the transit to firmly fix New Zealand's position on his chart of the Pacific Ocean. In a way, this observation was a tribute to Halley who conceived the concept of determining the dimension of the solar system from a transit of Mercury measurement nearly a hundred years earlier in the South Adantic.

The last transit of the planet Mercury occurred with litde note on 9 May 1973. The next one is predicted for 9 November 1986. Will anyone stand on the shore of Mercury Bay and focus a telescope skywards to watch a small black dot transit the solar disc; will they also ponder the achievements of the man who went as far as man may go?

Note on Calculations Relating to the Transit of Venus

Kepler's Third Law

The noted German astronomer and mathematician, Johannes Kepler (1571-1630) formulated three laws of planetary motion. Kepler's third law (also known as the harmonic law) is useful in

determining the dimensions of the solar system.38 The law states that for any two planets the

squares of the periods of revolution are proportional to the cubes of their mean distances from the Sun. Expressed mathematically:

?7 =

57 re'

Pi and P2 = respective periods for one revolution around the Sun for planet 1 and 2

Di and D2 = respective distances from the Sun to the two planets.

When the Earth is used as one of the planets, and the period of the Earth's revolution is taken as one

year and the distance from the Earth to the Sun is defined as one astronomical unit (AU =1), then

Kepler's formula reduces to:

56 F. Hoyle, Astronomy and Cosmology (San Francisco 1975), 433-4. 37

J.C. Beaglehole (ed.), The Journals of Captain James Cook on His Voyages of Discovery, Vol. II, The Voyage of the 'Resolution and 'Adventure' 1772-1775 (Cambridge 1961), 322.

S8 D.H. Menzel, F.L. Whipple and G. De Vaucouleurs, Survey of the Universe (Englewood Cliff 1970), 109-11.



(2) D - ^F where,

P = other planet's period in Earth years D = mean distance from the Sun to that planet in astronomical units.

If the length of the astronomical unit from transit measurements, and the period of revolution around the Sun from Mercury and Venus are known, it is possible to calculate the distance from the Sun for these two planets. Mercury has a revolution period of 88 days (0.24 years) and Venus has a

period of 225 days (0.62 years). Therefore, for Mercury:

D - y(0.24)2

- 0.39 AU

Then using the approximate dimension of 1 AU = 149,600,000 km2, the distance from the Sun to

Mercury equals:

0.39 X 149.6 X 106km - 58.3 X 106km

The distance to Venus and the other planets can be calculated in a similar fashion.39 Therefore, Venus with a period of revolution equal to 0.62 Earth years is 0.72 AU from the Sun.

Astronomical Unit and Solar Parallax

The Earth travels in an elliptical orbit around the Sun, therefore its distance from the Sun varies a

little in the course ofa year. The mean distance is equal to one half of the major axis of the Earth's orbital ellipse. This is a quantity of great significance in astronomy. Known as the 'astronomical unit' or AU, it established the scale upon which the solar system is constructed, serving as the unit in terms of which the mean distance of the other planets from the Sun are expressed as well as a

baseline for surveying the distance to the nearer stars. For the past 300 years astronomers have been striving to determine this fundamental constant with all attainable accuracy.

Astronomers define 'solar parallax' as half the angular equatorial diameter of the Earth as seen from the Sun (Fig. 1). The solar parallax amounts to about 1/400 of a degree of arc, and

consequently it is difficult to measure with high precision. The relationship between the solar

parallax and the distance to the Sun (1 AU) is shown by the expression:

(3) D==RxIJ^ian where, P

D - distance to the Sun (1 AU) in km R = radius of the Earth (6378.2 km) P = the measured parallax in seconds of arc

360? 1 radian - -? = 57.296? - 3437.75' = 206,264.8"

Therefore, if a solar parallax of 8.7943 is measured, then the distance to the Sun equals:

D - 6,378.2 X 2^61^1'8 = 149,595,690 km

8.7943

Thus, approximately 149.6 X 106 km = 1 AU (astronomical unit).

Halley's Transit Method

Halley's plan was to have the Transit of Venus measured by two observers (N and S in Fig. 2) stationed in widely different latitudes.40 Venus will appear to describe different paths across the face

59 Data on solar system dimensions are presented by Warner, Astronomy, 152, App.H. 40 G.B. Airy, Popular Astronomy, A Series of Lectures (London 1866), 144-75.



of the Sun for each observer. The observers record the times taken by the planet in traversing these

paths; then, knowing the rate at which Venus is overtaking the Earth in its orbit and the ratio of the Earth-Venus distance to the Venus-Sun distance (from Kepler's third law), it is possible to calculate the length of the two paths in degrees of arc (angular measurement). The Sun's angular diameter (as viewed from Earth) being known, the two paths can be located on the Sun's disc and the angular distance between their mid-points (S'-N' on Fig. 2) can be calculated.

The linear distance between the mid-points of the chords (S'-N') can also be obtained from the similar triangles VNS, VS'N', the length NS on Earth and the ratio (VN:VN') being known. Dividing the linear by the angular measure of S'-N' gives the distance to the Sun. In practice, the daily rotation of the Earth and other factors add some complications to the problem. However, all the

equipment needed by an observer in the 1760s was a telescope and a good clock.

Figure 2 illustrates how the observation ofa planet's passage across the face of the Sun can yield the information necessary to calculate the distance to the Sun. Two observations of the Transit of

Venus are depicted, one in the northern hemisphere (N) and one in the southern hemisphere (S). If the linear distance between the observing stations is known, the distance on the Sun's surface

between the transit lines (S'N') can be determined. From Kepler's third law, if the Earth is one astronomical unit from the Sun, then Venus is 0.72 AU from the Sun and 0.28 AU from the Earth. If observation stations on the Earth are selected at 10,800 km apart, then the distance between the transit lines on the Sun's disc can be found by the ratio:

NS VENUS ? EARTH AU S'N'

* VENUS ? SUN AU

Solving for the above example:

10,800 0.28

S'N' : 0.72

SN' ^ noJ-

= 27,700 km (distance on Sun)

At this point in the calculation, the timing of the transit at the two locations becomes important. The northern station (N) would yield a longer passage time than the southern one (S). For example in 1769 Cook's transit observation in Tahiti was about 22 minutes shorter than the one measured

above the Arctic Circle in Norway. The time required for the transit as observed at N and S is

proportional to the length of the chords on the Sun's disc (S' and N'). This information permits the

position of the two chords on a diagram of the Sun. It is then possible to scale the perpendicular distance between the observation chords in relation to the total diameter of the Sun. For the above

example an approximate proportion of 1/50 would be obtained, yielding a Sun's diameter of about

1,392,000 km Once the diameter of the Sun is known it is a relatively simple matter to measure, by sextant, the

arc subtended by the solar disc (^32') and use this information to calculate the distance to the Sun or the absolute size of one astronomical unit (Fig. 3):

qo* ^^L~-^- / o \

Earthy s/2l 149.600,000 km I rS I

"""??^___^jv Sun/

FIGURE 3. EARTH SUN DISTANCE (1AU)


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