Historical astronomy
Lieutenant Cook and the
transit of Venus, 1769
One of the first international scientific expeditions took place more than 200 years ago.
Derek Howse and Andrew Murray describe the part played by Cook in the observations of the transit of Venus.
W
ith the Australian-built replica of
the bark HMS Endeavour visiting
many British ports this summer,
Cook’s first Pacific voyage (1768–1771) has
been much in the news. His discoveries in New
Zealand and Australia are well known. However, what is not so well known is that the official reason that Cook was sent in the first place
was not for geographical discovery, but for
astronomy, as part of Britain’s contribution to
a vast international project – to observe the
transit of Venus across the face of the Sun.
Cook, then only a lieutenant, was to take the
Endeavour to make this observation from the
island of Tahiti in the Pacific.
It was only after the transit had been successfully observed on 3 June 1769 that Cook
opened his sealed orders, directing him to
search for a great southern continent in the
south Pacific, and then to chart New Zealand
(discovered by Abel Tasman in 1642) and to
take possession of any new land he might discover. He found no great continent, but he carried out a detailed running survey of both
islands of New Zealand. He then went on to
discover and, in the name of King George III,
take possession of the east coast of Australia,
which he named New South Wales.
Fig. 1: The Endeavour replica in
Doubtful Sound, New Zealand,
1996. (Photo: John Longley.)
The quest for the solar parallax
The linear scale of the orbits in the Solar System is the mean distance from the Sun to the
Earth, or astronomical unit. This is related to a
terrestrial measure of distance through the
solar parallax, which is the ratio of the equatorial radius of the Earth to the astronomical
unit, and is expressed in arc seconds. There are
several independent methods of measuring the
solar parallax, and its value is now known to
very high accuracy from interplanetary radar.
However, in the 18th century the only method
was the direct geometrical measurement of the
distance to a planet. In practice, Venus and
Mars were the only objects that could come
close enough to the Earth for this purpose.
Since the time of Kepler the relative sizes of
the planetary orbits had been expressed in
terms of the astronomical unit from the
observed orbital periods. Kepler thought that it
was about one minute of arc, but in 1679
August/September 1997 Vol 38 Issue 4
Flamsteed showed, from telescopic observations of Mars, that it could only be about 10″
(Forbes 1975). Halley (1716) proposed a
method of measuring the distance to Venus,
and hence determining the solar parallax, by
means of observations made from widely separated stations of the duration of the transit of
Venus across the disk of the Sun (figure 2). As
was customary at the time, this paper was written in Latin, but fortunately a translation with
commentary was published by Martin (1761).
Transits of Venus are very rare phenomena
that occur in pairs about eight years apart, but
the pairs are sometimes separated by more
27
Historical astronomy
than a century. Assuming a value of 12″.5 for
the solar parallax, Halley made predictions for
the transit in 1761 for two stations, one in
India and the other in North America. He concluded, somewhat optimistically, that from the
difference between the durations at these two
stations the solar parallax could be measured
to within about 1 part in 500. Though Halley
knew that he would not live to see the next
pair of transits (in 1761 and 1769), he urged
that every advantage should be taken of these
opportunities, and that observations should be
planned for as many different places on the
globe as possible to mitigate the effects of bad
weather in any one place.
“Therefore,” wrote Halley, “I strongly urge
diligent searchers of the Heavens (for whom,
when I shall have ended my days, these sights
are being kept in store) to bear in mind this
injunction of mine and to apply themselves
actively and with all their might to making the
necessary observations. And I wish them luck
and pray above all that they are not robbed of
the hoped-for spectacle by the untimely gloom
of a cloudy sky; but that at last they may gain
undying glory and fame by confining the
dimensions of the celestial orbits within the
narrower limits” (Halley 1761, p460).
Unfortunately, Halley’s calculations were
flawed, mainly because he made no allowance
for the retrograde motion of the node of
Venus’s orbit, the result being that, instead of a
difference in durations of more than 15 minutes, it would be rather less than 5 minutes.
Fortunately, Halley’s plea did not fall on deaf
ears. Many scientific expeditions were dispatched to remote parts of the world for the
transits of 1761 and 1769, particularly by the
British and French governments.
Outline theory
The instant of a particular contact, i, measured
by observer, j, can be expressed by the equation
Tij = ti + (1+ ε)∆tij , where ti is the time for a geocentric observer, ∆tij depends on the location of
the observer, using some assumed value of the
solar parallax, and ε is a correction factor to
the assumed parallax, which is, of course, the
same for all observers. Although all observed
times are expressed in apparent solar time, the
geocentric duration, t3 – t2 , is the same for all
observers since it depends only on the orbits of
the Sun and Venus, and their radii. In Halley’s
method, by taking the difference between the
durations observed at two stations, the geocentric duration cancels out and we are left with a
simple equation for 1+ ε. More generally, if the
same phase is observed at a number of stations,
the observations can also be combined in a
similar fashion provided that the longitudes
are known. Thus even if one contact is not
observed due to bad weather, the other can be
used. Although the principle is quite straight28
forward, the actual estimation of the time of
contact is difficult because of the well known
“black drop” phenomenon in which the disk
of Venus is apparently elongated towards the
Sun’s limb at the point of contact. The instant
of contact is taken to be the first appearance of
a luminous thread separating the black drop
from the Sun’s limb.
The transit of 1761
For Britain in 1761, Nevil Maskelyne, the
future Astronomer Royal went to St Helena
with Robert Waddington, but their observation was frustrated by cloud. However, Charles
Mason and Jeremiah Dixon (the surveyors of
the Mason–Dixon line in North America a few
years later), having failed to reach Sumatra
because of an attack by a French frigate, were
Fig. 2: Venus on the disk of the Sun, Honolulu,
1874. (Photo: Royal Greenwich Observatory.)
able to observe one phase of the transit at the
Cape of Good Hope. However, most of the
chosen sites were in Europe and Asia, where
the differences in durations were rather small,
but the transit was partially observed at
another site in the Southern hemisphere:
Rodrigues Island in the Indian Ocean. However, the results of the 1761 transit were disappointing, due partly to the cut and thrust of the
Seven Years War and partly to the weather.
The observations of this transit were discussed by Thomas Hornsby (1763). To the
modern astronomer a natural procedure would
be to form a conditional equation for each
observation with the parallax correction factor,
ε, and a bias, b, to allow for a systematic error
in timing due to the black drop, as unknowns,
and to solve for these by least squares. However, such concepts were not known in the mid18th century, and Hornsby arrived at his solution by adopting one station, Tobolski in
Siberia, as a standard, and differencing observations made at all other stations from that
made at Tobolski, where the duration was
shortest. In all he used 13 observations of the
duration and obtained 12 values for the solar
parallax, which ranged from 8″.4 to 12″.1. The
rather unsatisfactory result arises primarily
because of the very small differences between
the durations at all stations, which ranged over
less than 3 minutes. Hornsby then made a new
solution in which the calculated geocentric
duration was subtracted from each observation, and he was left with 13 independent
estimates of the solar parallax that were reasonably accordant, but were clearly liable to
systematic bias because of possible uncertainty
in the adopted geocentric duration.
Hornsby was well aware of the limitations of
this solution. His most satisfactory solution
used only the times of third contact observed at
stations whose longitudes could be estimated
with some accuracy. He was therefore able to
use the observation of this phase made by
Mason and Dixon at the Cape of Good Hope,
which gave time differences from the other stations of between 3 and 10 minutes in the coefficient of 1+ ε. Apart from a discordant result
from Rodrigues Island, which he attributed to
a transcription error of 1 minute in the recorded time, the values of the solar parallax on the
day of the transit, obtained from 13 stations,
only ranged between 8″.5 and 8″.9, compared
with the true value of 8″.66! Hornsby was not
satisfied with this result, since all other determinations derived from various differences of
timings of third contact at these stations,
excluding the Cape, clustered around 9″.7.
He remarked: “And in this Quantity of the
Sun’s parallax we must either acquiesce or
remain as ignorant of the true quantity as we
were before, till we can have recourse to the
next transit on June 3rd 1769, when the planet
Venus will again pass over the Sun’s disk, having something more than 10 minutes of North
latitude; and will be so favourably circumstanced, that, if the errors in observing each
contact do not exceed 4s or 5s, the quantity of
the Sun’s parallax may be determined within
less than 1/100th part of the whole.”
Plans for the transit of 1769
This was the state of knowledge of the solar
parallax when plans for observation of the
transit in 1769 were being formulated. The
planners were determined to apply the lessons
learned in 1761 – and this time the world was
at peace. The importance of having a wide
variation in the parallactic coefficient, ∆tij , was
evident, and the distribution of stations over
the Earth was much better than in 1761. The
key observing site in this respect was Tahiti,
where the duration was more than 22 minutes
shorter than at the high latitude northern sites.
The observations were planned on a truly
international basis. The observers were chosen
and dispatched in good time and were provided with the best available instruments.
Global coverage was planned in the hope that
this would provide the necessary insurance
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Historical astronomy
against bad weather and other factors.
It was the Royal Society that took responsibility for planning Britain’s contribution. Having obtained the promise of a grant from the
King – it was eventually £4000 – it set about
planning for home and overseas, much of the
work being done by the Astronomer Royal, by
now Nevil Maskelyne. Thus it was that in
August 1768 Lieutenant James Cook sailed in
the Endeavour from Plymouth for Tahiti, discovered by Captain Samuel Wallis in the Dolphin as recently as 1767. Also in the Endeavour were the astronomer Charles Green (who
would die before the ship returned to England), recently assistant to Maskelyne’s predecessors at Greenwich and now appointed as
one of the Royal Society’s observers, the other
being Cook; the young naturalist Joseph
Banks; and the naturalist Dr Solander, Banks’s
friend. Other British expeditions were sent to
Hudson’s Bay in Canada, to the North Cape of
Norway, to Northern Ireland and to the Lizard
in Cornwall, the last being sponsored by the
Board of Longitude to find out the accurate
longitude of the headland that was the departure point for so many voyages from England.
Fig. 5: The Endeavour at anchor off
Fort Venus, Tahiti, 1769, detail from the
engraving View of Matavai Bay from
One Tree Hill after a drawing by
Sydney Parkinson, 1769. (Photo:
National Maritime Museum.)
Cook’s voyage was thus, overtly at least, part
of a major scientific programme, one of the
earliest to be organized internationally.
Before the expedition sailed, the Royal Society – and particularly Maskelyne – gave a great
deal of thought to the equipment that would be
needed. For the transit, the main observations
required were the times of first and last contact
of the planet with the limb of the Sun, or, more
technically, the times of internal and external
contact at both ingress and egress. In addition
the diameter of Venus and the angular distance
between the limbs of Venus and the Sun were
to be measured during the course of the transit. These observations
required a telescope fit3 A 2 foot-focus Gregorian
ted with a micrometer,
telescope of the type used to
observe the transit in Tahiti,
and an accurate pendu1769. Photo: National
lum clock, in some form
Maritime Museum.
of observatory ashore to
keep out the weather
and the natives. All
British expeditions were
supplied with similar
4 A 1 foot radius astronomical
Gregorian telescopes, of
quadrant by John Bird, and an
2 feet focus and 43⁄4 inch
astronomical clock by John
aperture (figure 3).
Shelton, of the types used to
Cook’s clock was by
observe the transit in Tahiti,
1769. The clock here was
John Shelton, almost
used at the North Cape of
certainly the one now
Norway for the transit of 1769
preserved in the Nationand is today in the library of
al Museum of Scotland
the Royal Society, London.
in Edinburgh (figure 4).
(Photo: National Maritime
Museum.)
It was also necessary to
know the observer’s latitude and longitude to the
best possible accuracy,
and this demanded two
other pieces of equipment: an astronomical
quadrant (figure 4) of
1 foot radius for measuring the altitudes of heavenly bodies to obtain latitude, and for use as
an equal-altitude instrument to check the going
of the clock (also in the
observatory because its
accuracy depended on a
plumb line, which is dif-
August/September 1997 Vol 38 Issue 4
ficult to settle in the open air); and the finest
available Hadley reflecting sextants, to find
longitude by lunar distance both ashore and
afloat. Ashore, longitude was also determined
by observations of the eclipses of Jupiter’s
satellites and by occultations of the stars by the
Moon, using the telescope and clock. On this
first voyage, Cook had no marine timekeeper.
Observations at Tahiti
Endeavour anchored in Matavai Bay, Tahiti,
(figure 5) on 13 April 1769, a good six weeks
before the transit (Cook 1771): “Fixed upon
the North point of the bay, which is the most
Northern point of the island, for the place of
observation; here we built a small fort, to
secure us against the natives, which we called
fort Venus: it was not finished and the instruments set up in proper order until the 10th of
May”.
The clock was set up on a wooden frame in a
tent and 12 feet away was the observatory with
the telescopes and the astronomical quadrant,
which “stood upon the head of a large cask
fixed firm in the ground, and well filled with
wett heavy sand. A centinal was placed continually over the tent and observatory, with
orders to suffer no one to enter either the one
or the other, but those whose business it was”.
However, despite all precautions, the day
after the instruments were landed and placed
in the newly erected Fort Venus, there occurred
an incident that could have had a serious effect
on the observations. On 2 May, to the consternation of all, the astronomical quadrant was
found to be missing. With no spare and the
base more than 10 000 miles away, this was a
serious situation. Cook describes in his journal
(Beaglehole 1968) the steps taken:
“Tuesday 2nd. This morning about 9 oClock
when Mr Green and I went to set up the
Quadt. it was not to be found, it had never
been taken out of its Packing case (which was
abt 18 Inches square) sence it came from Mr
Bird the Maker, and the whole was pretty
heavy, so that it was a matter of astonishment
to us all how it could be taken away, as a
Centinal stood the whole night within 5 yards
of the door of the Tent where it was put together with several other Instruments but none of
them was missing but this. However it was not
29
Historical astronomy
long before we got information that one
of the natives had taken it away and
carried it to the Eastward...I met Mr
Banks and Mr Green about 4 miles
from the Fort returning with the Quadrant, this was about Sunset and we all
got back to the Fort about 8 oClock”.
After this drama – one wonders what
happened to the sentinel – all went well.
The clock was set up and checked: the
latitude was found with great accuracy
by observations of the zenith distances
of the Sun and stars, using the astronomical quadrant; and the longitude
was found to somewhat less accuracy
by lunar-distance observations with the
Hadley sextant and by observations of
the eclipses of Jupiter’s satellites with
the reflecting telescope.
The day of the transit, 3 June,
dawned fine, and Cook and Green
made their observations exactly as
planned. The first contact was seen just
after 9.20 a.m. and both observers
used the 2 foot Gregorian telescopes
for judging the moments of contact.
Green then fitted his telescope with a
Dollond object-glass micrometer and
measured Venus’s diameter and its distance from the Sun’s limb as it crossed
the disk, Cook doing the same with his
privately owned 18 inch reflector.
Venus passed off the Sun’s disk soon
after 3.30 p.m. Despite near-perfect
conditions – “for every wished-for
favourable circumstance attended the
whole of that day, without one single
impediment, excepting the heat, which
was intolerable: the thermometer
which hung by the clock and was
exposed to the sun as we were, was at
one time as high as 119°” – the black
drop made the timing of the exact
moments of contacts difficult.
The standard error of unit weight is that
of the difference between two observed
times, hence the standard error of a single contact time is ±5s.4, which is about
what Hornsby had expected.
The solar parallax corresponding to
the value of e derived here is
8″.74 ± 0″.05,
whereas
Hornsby
obtained 8″.78 by his method of combinations. He remarks that, by his result,
“the accuracy of the observation made at
the Cape of Good Hope in 1761, by
Messieurs Mason and Dixon, is abundantly confirmed”.
This simple analysis illustrates the
accuracy achieved, which was rather better than the 1% that Hornsby predicted,
despite the difficulties in interpretation
of the actual observations.
Conclusion
There have been several discussions of
the transits of 1761 and 1769, culminating in the memoir by Newcomb (1891),
who analysed nearly 500 individual timings by more than 100 observers of each
transit, from eight different nations –
and these included both amateurs and
professionals. From these he obtained
Fig. 6: How Cook and Green say they saw the transit on Tahiti, taken
the value for the solar parallax of
from Cook, 1771, Table 14, page 410.
8″.79 ± 0″.051. While the exact agreement, to the quoted precision, with the
modern value (8″.794148) is no doubt
Table 1: Analysis of the 1769 transit
fortuitous, it demonstrates the wisdom
of the planners and the skill of the
Station
Observed Calculated
O–C
f
(h m s)
(h m s)
(s)
(s)
observers in what is surely a magnifiWardhus
5 53 14.0
5 53 18
–4.0
676
cent example of international co-operation – and it happened more than 200
Kola
5 53 19.0
5 53 26
–7.0
684
years ago.
Hudson’s Bay
5 45 23.7
5 45 37
–13.3
215
In spite of this great achievement, one
California
5 37 32.4
5 37 25
7.4 –277
wonders if the phrase “transit of Venus”
K George’s Island 5 29 52.5
5 29 54
–1.5 –728
would be quite so well known today if
Cook had not taken the opportunity, on
The 1769 Transit observations compared with modern ephemerides.
the way home after the transit, to take
possession of New Zealand and New South
observed duration, as adopted by Hornsby,
Determining the solar parallax
Wales on behalf of King George III. ●
and the duration computed from modern
ephemerides using the coordinates of the
Although observations were made at many difobserving stations given by Hornsby. In the last
ferent places, the second and third contacts
Andrew Murray and Derek Howse are grateful to
column, f = ∆t3j – ∆t2j , which is the excess of
were observed at only five: Cape Wardhus;
A T Sinclair of the Royal Greenwich Observatory
Kola in Lapland; Prince of Wales’ Fort on
for providing ephemeris data from JPL DE404 relduration at the station, j, over the duration at
Hudson Bay; San José in California; and Tahating to these two transits, and to Peter Hingley,
the geocentre.
iti. Cook and Green observed both second and
Librarian of the Royal Astronomical Society.
A simple least squares solution for parallax
third contacts, and Solander observed only the
correction factor, e, to the modern value of the
second contact. The observations at these five
solar parallax, 8″.794, and a systematic bias, b,
References
Beaglehole J C 1968 The Journals of Captain James Cook 1 87
sites were analysed by Hornsby (1771), by the
in the timings, giving equal weight to each sta(Cambridge University Press for the Hakluyt Society).
same method which he used for the earlier
tion, gives:
Cook James 1771 Phil. Trans. Roy. Soc. London 61 397.
transit, that is by comparing the observed dure = –0.0061 ± 0.0062
Forbes E G (ed) 1975 The Gresham Lectures of John Flamsteed p99
s
s
ations made in various combinations of pairs
b = –3 .0 ± 3 .5
Mansell.
of stations. For some reason Hornsby used
neither of which is significantly greater than
Halley Edmund 1716 Phil. Trans. Roy. Soc. London 29 (348) 454.
Hornsby Thomas 1763 Phil. Trans. Roy. Soc. London 53 467.
only Cook’s observation of second contact.
zero. The standard error of unit weight comHornsby Thomas 1771 Phil. Trans. Roy. Soc. London 61 574.
s
Nevertheless, it is of interest to reanalyse his
puted from this solution is ±7 .6, whereas the
Martin Benjamin 1761 Venus in the Sun (W. Owen, London).
data by least squares.
rms value of O–C is ±7s.7. The observations
Newcomb Simon 1891 Astronomical Papers of the American
Table 1 gives for each of the five stations the
are thus entirely consistent with modern data.
Ephemeris II part V.
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