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Journal of Astronomical History and Heritage, 20(3), 264‒270 (2017).
Page 264
ANALYSIS OF FRENCH JESUIT OBSERVATIONS OF IO
MADE IN CHINA IN AD 1689‒1690
Lars Gislén
University of Lund, Dala 7163, 24297 Hörby, Sweden.
Email: LarsG@vasterstad.se
Abstract: The methods and quality of seventeenth century timings of immersions and emersions of the Galilean
satellite Io were studied. It was found that the quality of the observations was very good but that in the cases where
these observations were used for longitude determinations, the results were impaired by the inaccuracy of Cassini's
ephemerides that were used.
Keywords: geographical longitude, China, clock correction, Io immersion, Io emersion
1 INTRODUCTION
The rise of the colonial powers in Western
Europe during the seventeenth century fuelled
by travels to distant countries created a need for
methods to determine geographical longitude.
The methods available at the end of the sev-
enteenth century involved timings of astronom-
ical events that were simultaneous for all obser-
vers on the Earth, such as lunar eclipses or
immersions and emersions of the satellites of
Jupiter. Timing such an event at the local time
in two different locations and calculating the
time difference between the timings determined
the longitude difference between the two loca-
tions. These timings required a precise know-
ledge, preferably accurate to one second, of the
local times. In the seventeenth century, timings
were in general made with pendulum clocks
that, however, were not very reliable. During his
voyage to Siam the French Jesuit missionary-
astronomer Guy Tachard (1648‒1712; Orchis-
ton et al., 2016: 31‒32) found that his master
clock was slow by more than three minutes per
day (Tachard, 1686: 332). Consequently, these
clocks had to be rectified frequently by deter-
mining the apparent (true) local solar time from
some external source. Also needed were accu-
rate tables of times of lunar eclipses or tables
for calculating immersions and emersions of the
Galilean satellites, such as those issued by the
Paris Observatory Director, Giovanni Domenico
Cassini (1625‒1712) in 1683. Immersions and
emersions of the Galilean satellites were the
preferred events to use for determining the long-
itude because these events occur frequently
and could be used practically every day. Lunar
eclipses are not very frequent and the shadow
edge is not well defined, which makes accurate
timings difficult. Cassini (Goüye, 1688: 232)
wrote an extensive article on how to use obser-
vations of the Galilean satellites in order to de-
termine the longitude.
Jean de Fontaney (1643‒1710), a French
Jesuit, was asked by King Louis XIV to set up a
mission to China in order to spread French and
Catholic influence at the Chinese court. Father
Fontaney assembled a group of five other
Jesuits to accompany him, all highly skilled in
sciences: Joachim Bouvet (1656‒1730), Jean-
François Gerbillo (1654 ‒1707) Louis Le Comte n ,
(1655‒1728), Guy Tachard (1651‒1712), and
Claude de Visdelou (1656‒1737). Before sett-
ing out for the Far East, they were admitted to
the Roya Frenc Academ o Sciences and were l h y f
trained and commissioned to carry out astro-
nomical observations in order to determine the
geographical positions of the various places they
would visit, and to collect various types of scien-
tific data (see Udias, 1994; 2003).
After being provided with all the necessary
scientific instruments, the Jesuit Fathers sailed
from Brest on 3 March 1685 with Father Font-
aney as leader. After spending some time in
Siam,1 where Tachard remained (see Orchiston
et al., 2016), they finally arrived in Peking on 7
February 1688. The Jesuits were well received
by the Kangxi Emperor (Figure 1). Father Bou-
vet an Father Gerbillon stayed in Peking, teach-d
ing the Emperor mathematics and astronomy.
Françoise Noël (1651‒1729) was sent in
1684 as a missionary for Japan and arrived in
Macao in August 1685. After trying in vain to
reach Japan, he was sent to China where he
besides making astronomical observations also
translated the works of Confucius. He returned
to Europe in 1709 and published his work Sin-
ensis imperii libri classici sex in Prague in 1711.
A detailed account of the mission can be found
in the excellent paper by Landry-Derons (2001).
Jea d Fontaney returned to Europe in 1699 n e
but went back to China in 1701, then returned to
France in 1702 where he became Rector of the
Collèg Roya Henry-Le-Grand. Joachim Bouvet e l
later served as the Chinese Emperor’s envoy to
France and returned to his home country in
1697. In 1699 he arrived in China for the sec-
ond time and from 1708 to 1715, he was en-
gaged in a survey of the country and the prep-
aration of maps of its various provinces. Jean-
François Gerbillon remained in China working
for the Chinese Emperor among other things as
interpreter for a treaty with Russia regarding the
Lars Gislén French Jesuit Observations of Io, 1689‒1690
Page 265
boundaries of the two empires. Louis Le Comte
returned to France in 1691 as Procurator of the
Jesuits. In 1697 he published Nouveaux Mém-
oires sur l’État Présent de la Chine. Claude de
Visdelou acquired a wide knowledge of the
Chinese language and literature. In 1709 he
moved to Pondicherry in India where he remain-
ed until his death.
2 ADJUSTING A CLOCK FOR TRUE LOCAL
SOLAR TIME, THE 17TH CENTURY WAY
Two main methods were used to rectify the
clocks: using the altitude of a reference star and
using two identical altitudes of the Sun, before
and after noon. These will be investigated be-
low.
2.1 Using a Reference Star
This method had the advantage that it could be
used almost at any time of the day or night and
thus in rather close connection with the timing
observation. In most cases a star was used as
a reference; since stars are point-like objects,
well-defined location and altitude measurements
only had to be corrected for atmospheric refract-
ion. If the Sun was used, one of the solar limbs
had to be used to get a well-defined altitude and
you then also had to correct for the semi-
diameter of the Sun as well as for refraction.
Given quantities:
a = the known altitude of a reference star, meas-
ured and corrected for refraction.
= the known declination of the star from a star
catalogue.
= the known right ascension of the star from a
star catalogue.
Both the declination and right ascension of stars
are slowly varying quantities with time and a
reasonably up-to-date star catalogue had to be
used.
S = the known right ascension of the Sun,
computed for the given date or taken from a pre-
computed table.
= the known geographical latitude of the
location, measured earlier.
H0 = the measured local clock time of the ob-
servation. Time is reckoned from noon and
negative before noon.
We then have the following relation (after
Meeus, 1998):
sin a = sin
sin
+ cos
cos
cos H (1)
We use (1) to compute the hour angle H.
We choose the positive value of H if the ref-
erence star is west of the meridian and other-
wise the negative value. The sidereal time,
, is
then
= ±H +
. The hour angle of the true Sun
is HS =
–
S = ±H +
–
S. This is the
apparent local solar time. Comparing this with
the measured clock time will give the clock cor-
rection
= HS – H0. In case the Sun itself was
used as the reference star, HS = ±H.
As an example where the Sun’s altitude was
used, we can use one of the observations made
by Father Noël to determine the longitude of
Hoai-ngan (Huai’an) in China on 14 September
1689 (Mémoires, 1729: 779). The geographical
latitude was 33° 34′ 40″. The clock time was 1
hour 50 minutes after noon and the corrected
altitude of the Sun was then 52° 47′ 4″. The
declination of the Sun was 3° 11′ north. Using
the formula above we compute the true local
solar time as 1 hour 31 minutes 58 seconds,
thus the clock was 18 minutes 2 seconds fast.
Figure 1: The Kangxi Emperor (en.wikipedia.org).
The same observation also timed and meas-
ured the altitude of the stars Lyrae (Vega) and
Aquilae (Altair) just before the emersion. The
computation in this case gives a clock correction
of 20 minutes and 19 minutes 45 seconds re-
spectively. Unfortunately, Father Noël identified
what was the satellite Ganymede wrongly as Io
in this observation.
The right ascension of the Sun is a function
of time, changing by about 1 degree per day. In
order to determine the current value using tables
of the solar right ascension set up for instance
for Paris you needed to have some previous
idea of what the longitude difference to Paris of
Lars Gislén French Jesuit Observations of Io, 1689‒1690
Page 266
your location was, or use successive approxi-
mations in order to find the current solar right
ascension for your local time.
2.2 Using Two Altitudes of the Sun
The fundamental idea is to measure the clock
times when the Sun has the same altitude be-
fore and after noon. The clock noon will be the
average of these times. Often the upper limb of
the Sun was used. However, the afternoon tim-
ing has to be corrected for the change of the
Sun’s declination between the measurements
and the altitudes corrected for atmospheric re-
fraction. Sometimes the upper limb was used
before noon and the lower limb was used after
noon. Then you will then also have to correct
for the semi-diameter of the Sun. The drawback
with this method was that the computations
were quite involved and that the measurements
had to be made during daytime while the lu-
nar eclipse o immersion/emersio observation r n s
were normally made after sunset and thus there
could be a rather long time interval between the
determination of the clock correction and the
application of it during which the clock correction
could have changed.
2.2.1 Father Fontaney’s Method
Jean de Fontaney has described this method in
detail (Mémoires, 1729: 860) and applied it to
several observations. Following is my English
transIation:
Of all the methods that one uses to correct the
clock by observations of the Sun, observed be-
fore and after noon, I have chosen the follow-
ing as I am more used to it than to other
methods.
I take the difference between the times of
observation in the morning and in the after-
noon. I change the half of this difference to
degrees of the parts of the great circle that
gives me how much the Sun, at the morning
observation, is distant from the meridian, more
or less precisely. With this distance [H], the
complement of the altitude of the pole [
] and
the corrected altitude [a] of the upper limb of
the Sun, I find what is called the solar angle
[
], by this analogy: As the sine of the comple-
ment of the corrected altitude of the Sun is to
the sine of the complement of the altitude of
the pole; so is the sine of the distance of the
Sun from the meridian (the hour angle) to the
solar angle.
I then take the difference of the declination
of the Sun in 24 hours on the day of obser-
vation of which I take the part of the difference
in declination proportional to the interval of
observation before and after noon, to which,
as the Sun describes a parallel with the equa-
tor, I add (i.e. divide by cos
) the proportion
coming from the difference between the equa-
tor and the parallel of the day: and with this
difference of declination increased in this way I
have: As the sine of the solar angle is to the
part of the difference in declination, proportion-
al to the interval between the observations,
increased by the proportion of the equation to
the parallel of the day: so is the sine of the
complement of the solar angle to parts of 360˚
hour angle, which, reduced to time measure,
gives the correction to the time of observation
in the afternoon.
This correction, when the Sun is in the
descendant signs ha t be added to the hours , s o
in the afternoon and to be subtracted when the
Sun is in the ascendant signs.
With the time in the afternoon, thus corr-
ected, I take the difference between the times
in th mornin an th correcte afternoon time, e g d e d
I add half of this difference to the morning
observed time; the sum gives the hour that the
clock shows when the Sun at true noon, and
the difference between the time that the clock
shows and 12 hours, is how much it is slow or
fast. The demonstration of this practice is very
easy unless you think the movement of the
Sun would be pointless to take into account.
This method was also used by Tachard
(1686: 76, 78) when he determined the long-
itude of Cape Town in 1685, using the upper
and lower limbs of the Sun.
2.2.2 Mathematical Formulation
Expressed in mathematical language the first
statement is equivalent to
sin
= sin H cos
/ cos a (2)
where
is the ‘solar angle’,2 H the hour angle of
the Sun,
the geographical latitude, and a the
altitude of the Sun, corrected for refraction.
The second statement can be written
H = –(
/ cos
) / tan
(3)
where
H is the time correction due to the
change in declination,
is the solar declination,
and
the change in solar declination between
the morning and afternoon measurement.
Both of these formulae can be verified using
standard spherical trigonometry. If T1 is the time
of the altitude measurement before noon and T2
the time of the corresponding measurement
after noon, the formula for the clock correction in
hours is
= T1 + (T2 +
H – T1) / 2.
An example of this method is the determin-
ation of the longitude of Si-ngan-fu (Xi’an) on 12
July 1689 by Father Fontaney (Mémoires, 1729:
860). He used three pairs of observations of the
solar upper limb in the morning and afternoon to
set his clock. I have checked his calculations,
and they are correct to the seconds within round-
ing errors.
3 THE OBSERVATIONS
In my analysis I have used observations of im-
mersions and emersions of the Jupiter satellite
Lars Gislén French Jesuit Observations of Io, 1689‒1690
Page 267
Table 1: Observations from Hoai-ngan.
Date
Type
Observation Time
IMCCE Apparent Time (Greenwich)
Longitude
h
m
s
h
m
s
˚
'
1689-10-07
Emersion
23
13
58
15
16
03
119
29
1689-11-01
Emersion
18
01
20
10
03
07
119
33
1689-11-08
Emersion
19
56
14
11
58
11
119
31
1689-11-15
Emersion
21
50
30
13
52
34
119
29
1689-12-01
Emersion
20
05
00
12
07
33
119
22
1690-09-10
Immersion
22
12
20
14
18
29
118
28
1690-09-17
Immersion
24
12
23
16
15
28
119
14
1690-10-05
Emersion
19
16
08
11
16
43
119
51
1690-10-12
Emersion
21
13
00
13
13
19
119
55
1690-10-19
Emersion
23
08
50
15
10
02
119
42
1690-12-04
Emersion
23
30
40
15
31
48
119
43
Average
119
29
Io in 1689 and 1690 in China taken from Pingré
(1901), supplemented with information taken from
Mémoires (1729) and Goüye (1692). I have de-
leted two observations that are certainly other
Galilean satellites mistaken for Io.
It is impossible to determine which of the
ephemeris tables issued by Cassini for the move-
ments of the four Galilean satellites were used
by the Jesuit observers in China. The tables
that I have been able to consult (Cassini, 1668;
1693) do not by my computation render the pre-
cise time values cited in the observations.
Another problem is that Cassini’s tables are
not accurate, having time errors of some min-
utes: “It is true that often there are still a few
minutes difference in time between the Ephem-
erides and the Observations.” (Mémoires, 1730:
180; my English translation).
Also, the immersion and emersion times com-
puted from the tables and cited by the Jesuits in
the Memoires are only given to one minute pre-
cision (or in one case, to half a minute precis-
ion). As I have been mainly interested in the
quality of the Jesuit observations, I decided to
use as a benchmark a modern ephemeris pro-
gram, available on the web at the Institute de
Méchanique Celeste de Calcul des Éphémer-
ides (IMCCE), in order to determine the immer-
sion and emersion times.
An immersion or emersion of a satellite is not
an instant in time; for Io, the event typically has
a duration of a little more than four minutes. A
time interval of four minutes corresponds to about
1° of longitude, thus it is important to define the
precise moments that are chosen to represent
the immersion or emersion respectively. For an
immersion, the modern definition is the time when
the satellite just disappears completely in the
shadow of Jupiter, the ‘last speck’, and for an
emersion, it is the first appearance, the ‘first
speck’. These are given in the IMCCE ephem-
eris in Universal Time (UT), with a precision of
seconds. In practice, for an observer the pre-
cise timing would to some extent depend on the
telescope’s magnification. With a stronger mag-
nification, one would expect to follow a dimin-
ishing satellite crescent a little longer and dis-
cover its appearance a little earlier. It is then to
be expected that the observed timing of an
immersion would be slightly too early and for an
emersion slightly too late as compared with the
ephemeris, resulting in a slightly-too-large longi-
tude difference for emersions and slightly-too-
small longitude difference for immersions. It
could also be expected that such timings would
be somewhat observer dependent, although the
Jesuit missionary-astronomers were trained
scientists.
There are six sets of observations for diff-
erent Chinese locations, and these are discus-
sed separately below. The modern Chinese
names are given in brackets.
In the following tables, the times given by
the observers are reckoned from noon and are
shown in the first column. I have added 12
hours to these times in order to have the
standard modern astronomical reckoning from
midnight. The observers also use apparent
local solar time as was standard during the
seventeenth century and used the terminology
‘true time’ for this. The second column shows
immersion/emersion times according to IMCCE
where I have converted the UT ephemeris time
into apparent solar time using the equation of
time as computed from the algorithm in Meeus
(1998). The last column shows the longitude
computed using the difference in time between
the observed immersion/emersion time and the
IMCCE time and the relation that 15° in
longitude difference corresponds to one hour in
time.
3.1 Observation Set 1
These observations (see Table 1) were made by
Father Noël from Hoai-ngan (Huai’an) in 1689
and 1690.
The official modern longitude of Huai’an is
119° 8′. As expected, the emersion longitudes
are larger than the immersion ones. There are
few immersion longitudes, a fact that will
increase the average longitude as the emersion
longitudes will dominate. Pingré notes that the
Lars Gislén French Jesuit Observations of Io, 1689‒1690
Page 268
Table 2: Observations from Si-ngan-fu.
Date
Type
Observation Time
IMCCE Apparent Time (Greenwich)
Longitude
h
m
s
h
m
s
˚
'
1689-06-03
Immersion
28
18
00
21
04
16
108
26
1689-06-19
Immersion
26
31
22
19
18
18
108
16
1689-07-12
Immersion
26
36
56
19
23
06
108
28
1689-08-04
Immersion
26
46
56
19
33
24
108
23
1689-10-23
Emersion
20
55
05
13
38
22
109
11
1689-11-08
Emersion
19
15
20
11
58
11
109
17
1689-11-15
Emersion
21
09
07
13
52
34
109
08
Average
108
44
Table 3: Observations from Canton.
Date
Type
Observation Time
IMCCE Apparent Time (Greenwich)
Longitude
h
m
s
h
m
s
˚
'
1690-09-10
Immersion
21
49
03
14
18
27
112
39
1690-09-17
Immersion
23
46
14
16
15
34
112
40
1690-10-12
Emersion
20
46
25
13
13
18
113
17
1690-10-19
Emersion
22
42
49
15
10
02
113
12
1690-10-28
Emersion
19
06
46
11
34
17
113
07
1690-11-04
Emersion
21
02
38
13
29
24
113
19
Average
113
02
Figure 2: Si-ngan-fu (BnF).
location for the observations were a little to the
east of Huai’an. The standard deviation of the
emersion longitudes is 11′. Father Noël used the
Figure 3: The old city in Xi’an (Google Map Pro).
five first observations (Mémoires, 1729: 779) to
determine the longitude from Paris as 116° 30′,
i.e. 118° 50′ from London. The time errors (all
positive) from the cited Cassini ephemerides
have an average of 2.6 minutes.
3.2 Observation Set 2
These observations (Table 2) were made by
Father Fontaney from Si-ngan-fu (Xi’an) in 1689.
Figure 2 shows a contemporary map of Si-ngan-
du, while Figure 3 shows the still existing old city
layout in Xi’an.
The official modern longitude of Xi'an is 108°
54′. The standard deviations of the immersion
and emersion groups are both 5′. Father Font-
aney used observations number 3, 5, and 7
(Mémoires, 1729: 855) for his longitude deter-
mination and got an average of 108° 44′, ident-
ical to the average result in the table. This is a
pure coincidence, as the cited Cassini ephem-
erides are in error by about –1.4, 1.8, and 2.1
minutes respectively.
3.3 Observation Set 3
These observations (Table 3) were made by Fat-
her Fontaney from Canton (Guangzhou) in 1690.
The official modern longitude of Guangzhou
is 113° 16′. The spread is very small within the
immersion and emersion groups separately, ind-
icating that Fontanay was a very good observer.
The emersion longitudes have a standard dev-
iation of 5′. Father Fontaney used the first and
third observations each with three clock corr-
ections where he used his method with pairs of
equal solar altitudes. He arrived at the same
longitude value as the average in the table (Mém-
oires, 1729: 870). Again this is sheer luck al-
though in this case the errors in Cassini’s ephem-
erides are –0.8 and 0.35 minutes respectively.
Lars Gislén French Jesuit Observations of Io, 1689‒1690
Page 269
Table 4: Observations from Shanghai.
Date
Type
Observation Time
IMCCE Apparent Time (Greenwich)
Longitude
h
m
s
h
m
s
˚
'
1689-07-28
Immersion
25
42
49
17
38
48
121
00
1689-08-06
Immersion
22
06
24
14
02
11
121
03
1689-08-31
Emersion
19
07
12
11
01
05
121
32
1689-09-07
Emersion
21
04
07
12
57
51
121
34
Average
121
17
Table 5: Observations from Nankin.
Date
Type
Observation Time
IMCCE Apparent Time (Greenwich)
Longitude
h
m
s
h
m
s
˚
'
1689-10-16
Emersion
19
37
27
11
42
04
118
51
1689-10-23
Emersion
21
33
50
13
38
22
118
52
1689-11-01
Emersion
17
59
12
10
03
07
119
01
1689-11-08
Emersion
19
54
00
11
58
08
118
58
1689-11-15
Emersion
21
48
13
13
52
29
118
56
1689-12-01
Emersion
20
03
06
12
07
34
118
53
Average
118
55
Table 6: Observations from Peking.
Date
Type
Observation Time
IMCCE Apparent Time (Greenwich)
Longitude
h
m
s
h
m
s
˚
'
1690-09-10
Immersion
22
03
29
14
18
29
116
15
1690-10-12
Emersion
21
00
00
13
13
19
116
40
1690-10-19
Emersion
22
56
15
15
09
29
116
41
1690-10-26
Emersion
24
51
14
17
05
25
116
27
1690-11-04
Emersion
21
16
42
13
29
24
116
49
1690-12-13
Emersion
19
39
24
11
52
01
116
51
Average
116
37
3.4 Observation Set 4
These observations (Table 4) were made by Fat-
her Fontaney from Chang-hai (Shanghai) in 1689.
The official modern longitude of Shanghai is
121° 30′. Again, Jean de Fontenay’s emersion
longitudes are larger than the immersion ones.
The spread is extremely small for both the im-
mersion and emersion longitudes: 2′ –3′.
3.5 Observation Set 5
These observations (Table 5) were made by
Father Fontaney from Nankin (Nanjing) in 1689.
The official modern longitude of Nanjing is
118° 46′. The longitudes are very consistent,
with a small standard deviation of 4′. Also here
Pingré notes that Fontaney was located to the
east of Nanjing.
3.6 Observation Set 6
These observations (Table 6) were made by
Fathers Bouvet and Gerbillon from Peking (Bei-
jing) in 1690.
The official modern longitude of Beijing is
116° 23′. The standard deviation of the emer-
sion longitudes is 9′.
4 CONCLUDING REMARKS
From the data we can conclude that the
longitudes derived from the emersions are in
general a little too large and that those derived
from the immersions are a little too small. This
is to be expected, as explained above. Father
Fontaney’s observations clearly show that he
must have been a very skilled observer, given
the very good internal consistency in his timings
of the immersions and emersions.
In general, all the observations are quite con-
sistent and of good quality, the standard devi-
ations are with one exception very small and the
computed average longitudes above agree quite
well with the actual longitudes. Looking at the
whole data set, the Jesuit fathers had a timing
difference of about 20 seconds relative to the
IMCCE first and last speck times. Due to the
time errors in Cassini’s ephemerides that were
of the order of two minutes, the contemporary
longitude determinations had an inherent error
of at least half a degree. Actually, this is not
bad, as the Longitude Act, issued on 8 July
1715 by Queen Anne of England, stipulated a
prize of £20,000 for a method to determinate
longitude to an accuracy of half a degree of a
great circle. However, the Jesuit observations
were made on firm ground with rather large in-
struments that had been extensively calibrated.
On the heaving deck of a ship you could not ex-
pect very accurate results using their methods.
5 NOTES
1. While temporarily in Siam they observed a to-
tal lunar eclipse on 11 December 1685 (see
Gislén, 2004; Orchiston et al., 2016).
Lars Gislén French Jesuit Observations of Io, 1689‒1690
Page 270
2. When we consider a spherical triangle P is
the North Pole, Z the zenith and S the Sun,
the angle PSZ is the ‘solar angle’.
6 ACKNOWLEDGEMENTS
I am grateful to Dr C.J. Eade (Canberra, Aus-
tralia), Dr Yukio Ôhashi (Tokyo, Japan) and Pro-
fessor Wayne Orchiston (National Astronomical
Research Institute of Thailand, Chiang Mai) for
reading and commenting on the manuscript.
7 REFERENCES
Cassini, G.D., 1668, Ephemerides Boniensis Medi-
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Cassini, G.D., 1683. Les Hypotèses et les Tables des
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Gislén, L., 2004. Analysis of the astronomical infor-
mation in Tachard: “Voyage to Siam in the Year
1685”. Centaurus, 46, 133‒144.
Goüye, P. (ed.), 1688. Observations Physiques et
Mathématiques ... Paris, L’Imprimerie Royal.
Goüye, P. (ed.), 1692. Observations Physiques et
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Institute de Méchanique Céleste de Calcul des
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en Chine par Louis XIV en 1685. Archive for History
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VII.2, Paris, La Compagnie des Libraires (1729).
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X, Paris La Compagnie des Libraires (1730).
Orchiston, W., Orchiston, D.L., George, M., and Soon-
thornthum, B., 2016. Exploring the first scientific ob-
servations of lunar eclipses made in Siam. Journal
of Astronomical History and Heritage, 19, 25‒45.
Pingré, A.G., 1901, Annales Célestes du Dix-septième
Siècle. Paris, Gauthier-Villars.
Tachard, G., 1686. Voyage de Siam des Pères Jés-
uites, Avec Leurs Observations Astronomiques, etc.
Paris, Arnould Seneuze and Daniel Horthemels.
Udias, A., 1994. Jesuit astronomers in Beijing, 1601‒
1905. Quarterly Journal of the Royal Astronomical
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Udias, A., 2003. Searching the Earth and the Sky.
The History of Jesuit Observatories. Dordrecht, Klu-
wer.
Dr Lars Gislén is a former lector in the Department of
Theoretical Physics at the University of Lund, Swe-
den, and retired in 2003. In 1970 and 1971 he studied
for a Ph.D. in the Faculté des
Sciences, at Orsay, France.
He has been doing research in
elementary particle physics,
complex systems and appli-
cations of physics in biology
and with atmospheric physics.
During the past fifteen years
he has developed several com-
puter programs and Excel
spreadsheets implementing
calendars and medieval astro-
nomical models from Europe, India and South-East
Asia (see http://home.thep.lu.se/~larsg/).
