Hartmut Frommert
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Last Modification: May 20, 2001
In the predictions of the heavenly phaenomena, which depend on the motion of the stars, two things are to be considered, viz. the time and the place. As to the time, when the velocity and direction of the stars in their motion both apparent and real are known, the time of their different appulses and aspects may always be foretold, and the accuracy of the calculation depends on the exactness with which their velocity and their several inequalities are ascertained. Now it is well known that all the former uncertainty, as to the exact time of the return of the comet foretold by Dr. Halley, was owing to the variations it must have undergone from its several situations and approximations to the planets in its progress thro' the solar system.
Dr. Halley, who was first aware of the unequal returns of this comet in its former appearances, which he found to have been alternately of 75 and 76 years, was likewise the first who assigned their true cause. He ascribed it, as I said above, to the nearer or more distant approaches of the planets of our system; and having observed that the comet we are speaking of came very near Jupiter in the summer of 1681, above a year before its last appearance, and remained several months in the neighborhood of that planet, he judged that circumstance alone sufficient to have considerably retarded its motion, and prolonged the duration of its revolution. Hence he concluded that its return was not to be expected till the latter end of 1758, or the beginning of the next year.
Dr. Halley observed, in confirmation of this opinion, that the action of Jupiter upon Saturn is alone sufficient to alter the duration of Saturn's period one full month; and he adds, how much greater irregularities must not a comet be liable to, which at its remotest distance gets near four times farther from the Sun than Saturn, and whose velocity in drawing near the sun needs but a very small increase to change its elliptic into a parabolic curve.
Dr. Halley does not determine more exactly the time of the return of the comet of 1682; neither could he do it but by determining exactly the effect of the neighborhood of Jupiter, which must very sensibly affect the velocity with which the comet was moving towards the sun. Besides, regard must be had, not only to this approach to Jupiter in 1681, but likewise to the other approaches to this and all the other planets, which act upon the comet, as they do upon each other. In short, it was necessary to consider all the different situations and distances of all the planets with regard to the comet, during the whole of its last revolution, and even during its former ones, when returns had been found unequal.
What immense labour ! and what geometrical knowledge did this task not require ? Mr. Clairaut, of the Royal Academy of Sciences, undertook it; and his results but differed one month from the observation. No small degree of exactness this, considering the immensity of the object. In November 1758, he published his conclusion, which allowed about 618 days more for the period that was to end in 1759 than the former, whence he inferred that the comet must be in its perihelion towards the middle of April. He added, however (Journal des Scavans, Jan. 1759) "Any one may think with what caution I venture upon this publication, since so many small quantities unavoidably neglected by the method of approximation may very possibly make a month diference, as in the calculation of former periods." It accordingly proved so, the comet having reached its perihelion on the 13th of March in the morning. Mr. Clairaut has since published the methods and calculations, by which he has arrived at this conclusion.
The impatience of astronomers, and their desire to prepare for verifying this prediction of Dr. Halley, had put them upon enquiring for several years in what part of the heavens this comet was likely to appear; but, being ignorant of the exact time of its return, they could not determine the spot where it might be expected to be seen, but by making various suppositions as to the time of its perihelium. This Mr. Dirck of Klinkenberg, a famous astronomer, Member of the Society of Sciences in Holland, and a correspondent to the academy of Paris, had attempted seven or eight years before, having taken the pains to calculate the principal points of forteen different tracts, which the said comet was to take, upon as many different suppositions relating to its passage thro' its perihelium, almost from month to month, from the 19th of June, 1757 to the 15th of May 1758. Messrs. Pingré and De la Lande proceeded much in the same manner in the calculations they published in the Memoirs of Trevoux for April 1759, first and second parts, with this difference, that the latter in their suppositions had taken narrower limits, and nearer to Mr. Clairaut's determination, who, as I said before, had fixed the return of this comet to the middle of April.
Mr. De L'Isle, being curious of seeing the comet on its first return, as soon as it could be discovered by means of refracting or reflecting telescopes, before it was visible to the naked eye, thought he must proceed in a different manner from what other astronomers had done, to find out in what part of the heavens it must be looked for. He considered that it was not necessary to know the place throughout its whole course, but only at the moment of its appearance, because, having once found it out, it would be an easy matter afterwards to trace it thro' its whole progress by observation and calculation.
A full description of this method is to be found in an ample memoir concerning this comet, which I have laid before the Royal Academy of Sciences at Paris, and which no doubt will be printed in their collection, together with a northern hemisphere, by means of which I have been enabled to look for this comet in the very place of the sky, where it ought to appear; and it was by the help of this planisphere that I actually discovered the comet from the marine Observatory at Paris on the 21st of January in the evening, after searching for it two years successively whenever the sky would permit. The weather was extremely clear the 21st of January the whole day and evening. I seized the opportunity, and as soon as the stars were visible after sun-set, I examined, thro' a Newtonian telescope of four feet and a half [FL], those places in the sky, where my planisphere showed that the comet was to be expected. After much pains, I perceived about seven o'clock a light resembling that of the comet I had observed the year before in August, September, October, and the beginning of November *. I immediately made a configuration of this new light with respect to the neighboring stars, in order to examine the next night whether it had any motion among the fixed stars. This light appeared pretty large; and in the middle I observed a nucleus, or bright spot, which was no proof as yet that it was a comet, as there are some nebulous stars, with a bright spot in the middle. By the drawing I took of this new light with respect to two neighboring stars, one of which was the 18th of Pisces, according to Flamstead's [sic] Catalog, 2d edition, of the 5th magnitude, markes with the Greek letter Lambda, the other a new star of the 8th magnitude, which I ascertained by observation, by comparing it with the above-mentioned star Lambda of Pisces, its right ascension for the present time being 352d.13'.5". and its declination 1d.6'.40" N. and is the 28th in the catalog of the stars which have served to find out he position of the comet, which is to be seen at the end of this memoir; at 6h.56' true time, the position of the comet in right ascension was estiamted at 352d.15'.47". and its declination 1s.32'.6". North.
Jan. 22, at the same hour as the day before, the sky being equally clear, I again saw the same light with the 4 1/2 foot telescope, and found it had sensibly changed its place, but its appearances were the same. From this second observation I no longer doubted of its being a comet; and from this very night I began to take notice of the situation of the nucleus, by comparing it with a small new star which is not to be found in the catalogs, nor in the celestial maps of Flamstead [sic], but is that whose position I have just now mentioned, and which stands No. 28 in the catalog annexed to this memoir. It was not without some difficulty that I could take the position of the comet with regard to this little star, because I was obliged to throw light upon the threads of a silk micrometer, which was adapted to the Newtonian telescope, four feet and a half long, and the least degree of light from the wax candle I made use of, presently made both the comet and the star disappear. The position of the comet may be seen in the second table hereunto annexed, and likewise all the other positions of it , which have been determined to the time of its disappearing.
The 23d, the sky being very clear, I again saw the comet; its appearances were the same as the two preceding days. I compared the nucleus with a very small star, only of the 10th magnitude, which I have settled by comparing it with the 46th star or Pisces of the 6th magnitude, according to Flamstead's catalog. See the position of this star in the first table, No. 27. The position of the comet is set down in the second table.
The 24th in the evening, the fog, thin clouds, and vapours about the horizon suffered me to take but an imperfect view of the comet; all I could do to get at its situation was to observe the differences of azimuths and heights of the comet, and the two stars of Pegasus called Algenib and Markab. These differences did not appear to me to be so exact as to depend upon the determination of the comet from them, so I shall give no account of them.
The 25th in the evening, the sky being clear at times, I again saw the comet; its light was increased, and the nucleus looked brighter than before, but without any appearance of a tail. I compared it directly with a star which is the 16th of Pisces, in the order of Flamstead's catalog. It was likewise compared with No. 26 of my table. The comet was sufficiently visible this night to be seen thro' a common two feet [FL] telescope, and even thro' one of a single foot [FL]. At four minutes past seven, the comet was still to be seen thro' the telescope at the height of 13 deg above the horizon.
The 26th, the cloudy weather prevented my seeing the comet; but the 27th, the sky being tolarably clear, tho' the air was not altogether free from vapours, I again saw the comet, but could form no judgement of its appearance. I compared the nucleus with a new star which is the 25th in my table, which I knew by comparing it with some stars in Flamstead's catalog. I also directly compared the nucleus with the 16th star of Pisces. See second table.
The 28th, the sky being pretty clear in the evening, I began to see the comet at 26 1/2 above the horizon; but the air was so much darkened by some fire-works which had just been played off at the Prince of Conde's, that I could neither judge its shape nor its brightness. All I could do was to compare it three times with the new star mentioned above, No. 25 of my table, and once with th 16th of Pisces.
The 29th and the 30th it was too cloudy to see the comet, but the 31st it cleared up a little; the comet appeared between the clouds, though not plain enough to judge of its increase, but only to compare it with two stars, which are not in Flamstead's maps, nor mentioned in his catalog, but are not far from the star k of Pisces of the 5th magnitude, with which I compared them. They are both set down in the first table, No. 23 and 24.
February 1, the sky being perfectly clear in the evening, the comet appeared, notwithstanding a strong twilight and the neighborhood of the moon. I compared the nucleus with the same two new stars, No. 23 and 24. The clearness of the air this night induced me tomeasure the diameter of the coma of the comet with the micrometer adapted to the Newtonian telescope, and I found it 2 min. and 1/2. I likewise determined the magnitude of the nucleus, which I found to be 20", having compared it with the thickness of one of the threads of the micrometer, which I afterwards reduced into parts of the micrometer. The twilight was then such as to favour this measuring and the other observations.
The 2d the clouds prevented my seeing the comet, but the 3d, about sevon o'clock, the sky being tolarably clear, the comet appeared, though but faintly, by reason of its nearness to the horizon and of the light of the moon; however, I compared it with a star of Pisces that is to be found in Flamstead's catalog. It is the 8th of that constellation, marked with the Greek letter Kappa'. The position of this star for the present time is shewn in the first table.
The 4th I was as much hindered as the night before by the comet's nearness to the horizon, and by the too great light of the moon, which made it impossible to judge of its increase. I compared the nucleus with the same star Kappa' of Pisces.
From the 4th to the 11th it was utterly impossible to make any observations, or even to see the comet, by reason of the clouds which darkened that part of the sky at the time it should have appeared. The 11th the sky was clear in the evening. I saw the comet, which was but 10 deg high, so that I could not judge of its appearance, from its nearness to the horizon, and the strong light of the moon, which was then at the full. I was likewise much obstructed by the height of the chimneys which stand between the horizon and the marine Observatory to the West. This prevented my comparing the comet with the neighboring stars for a quarter of an hour that it it continued visible. All I could do was to draw the configuration of these stars with the comet, both with the four feet and half [FL] telescope and with a little two feet refracting telescope, which was so flastened over the reflector in a parallel situation. From this configuration, I have estimated the position of the comet, as seen in the second table.
The 12th, the sky, which had been cloudy all day, cleared up a little in the evening. The comet appeared near the horizon for a few minutes, but was soon hid behind the chimneys. All I could do was to estimate its position relative to the neighboring stars.
The 13th, the sky was quite overcast,; but the 14th having cleared up in the evening, I could see the comet, but close to the horizon, at the height of 6 deg for a few minutes; and it soon disappeared, being intercepted by terrestrial objects too high above the horizon, and which I could not keep clear of. All I was able to do in the short interval it was visible, was to take a hasty estimate of its position with respect to the star A of Pisces. The brightness of the twilight prevented my seeing the comet earlier.
The 15th and the 17th, the sky was pretty clear in the evening; but I could not see the comet at all, because of the bright twilight, which continued till the setting of the comet.
The comet no longer being visible at night, on account of its getting into the sun's rays, Mr. De L'Isle and i examined the exactest observations I had made, which helped us to determine the time and the place in the sky, where it was to re-appear in the morning, when it should get clear of the rays of the sun. This was to happen towards the end of March; but the cloudy weather, which prevailed at Paris during that month, prevented our seeing it again. Besides this inconveniency, the marine Observatory did not stand high enough to see it at its first rising in the morning. We were obliged to look out for a more convenient place in the neighborhood, and met with one at the house belonging to the College of Lewis the Great, where there is a turret which overlooks all the horizon, and where Father Merville, Professor of Mathematics, makes his observations. The 31st of March I removed thither my 4 1/2 feet Newtonian telescope, and likewise a pendulum clock.
I spent the night from the 31st to the 1st April in this turret with Mr. De L'Isle. At three in the morning, I began to trace a meridian upon the floor by the means of a sea-compass; and I likewise drew a line, which made an angle of about 74 deg with the meridian, from the South toward the East, in the direction of which the comet was to first appear. I directed the Newtonian telescope according to this line; and at 52 minutes past three I saw the comet, about two degrees above the horizon. It appeared much larger and brighter than in the middle of February; and indeed it was but 18 days past its perihelion. Now it is well known that cometsare much brighter after the perihelion than at the same distance before it. Besides, the comet after passing the perihelion was as near again to the earth as on the 14th of February, when I lost sight of it at night. When I saw this comet again on the 1st of April, I could very plainly discern its tail, but could not ascertain its length, because of the morning twilight which was then beginning, and soon increased much; it filled the field of the telescope, and must have extended far beyond. According to what I have observed, the tail of the comet must have spread to more than 25 degrees. The nucleus was considerable, but not well terminated, and it apparently exceeded the size [brightness] of a star of the first magnitude. It was of a pale whitish colour, not unlike that of Venus. The nebulosity which surrounded the nucleus, and went on lessening, shewed reddish colours, and these colours grew more vivid toward the brightest parts of the tail. The morning twilight, which increased apace, soon put an end to these appearances, and afterwards made the comet itself disappea; however, I had been able to perceive it with the naked eye when it was somewhat disengaged from the vapours of the horizon. In this short interval, I had but just time to observe the shape of the comet with the telescope, and to compare the nucleus with a star which I have since found to be the 30th of Aquarius, according to Flamstead's catalog, where it is set down as of the 6th magnitude. The difference of declination between the star and the comet was only estimated. The true time of this observation, which will be found in the second table, has been concluded only by means of a minute watch, which had to be set to the true time in the evening by the clock of the marine Observatory. This was likewise the case with respect to the observations made during the month of April, in the turret of the College of Lewis the Great, where there was a pendulum clock, as I said before, set by a watch which was regulated every day of observation.
More minute accounts of this comet will be seen in a memoir which I have presented to the Royal Academy of Sciences at Paris, together with two celestial maps shewing [sic] the tract of the comet through the fixed stars during its appearance, which I have traced exactly from my observations. There is likewise annexed to this memoir a collection of all the observations which have been made of this comet, by my own and Mr. De L'Isle's correspondents. These observations have been taken, at the Hague by Mr. Dirck de Klinkenberg, at Leyden by Mr. Lulof, at Montpelpellier by Mr. de Ratte, at Avignon by Father Morand, at Vienna by Rev. Father Hell, at Leipsick at Rome, at Cadiz by Mr. Godin, at Lisbon by Father Chevalier, and at Pondicherri in the East Indies by Father Coeurdoux.
Footnotes:
The second table contains all the places of the comet, as well in right ascension and declination, as in longitude and latitude, concluded from its situation observed relaticely to the stars, whether new ones or already known. These are the titles of each column: The 1st points out the day of the month; the 2d, the true time for each observation; the 3d, the right ascensions of the comet observed; the 4th, the declinations; the 5th, the longitudes observed; the 6th, the latitudes; the 7th, the differences ofpassage in right ascension of the comet and the stars, marked with the sign "-" [Minus] when the comet preceded the star or was to the West of it, and with "+" [Plus] when it followed the star or was to the East. This difference, according to the sign, being either added or substracted from the right ascension of the star set down in the first table, with which the comet was compared, will give its right ascension. The 8th column shews [sic] the differences of declination between the comet and the stars, marked likewise with "+" [Plus] and "-" [Minus], and which, being accordingly either added to or taken from the declination of the star with which the comet was compared, will give its declination. The 9th column contains the magnitude of the stars; and the 10th, which is the last, has Bayer's letters, and the numbers of the stars, either new or taken from Bayer's catalog, according to their order in each constellation.
The following are the elements of the comet, as computed by Messrs. de la Caille, Maraldi, and De la Lande.
Mr de la Caille Mr. Maraldi Mr. de la Lande
S. D. M. S. S. D. M. S. S. D. M. S.
Place of the ascending node 1 23 49 0 1 23 49 41 1 23 45 35
Inclination of the orbit 17 39 0 17 35 20 17 40 14
Place of the Perihelion 10 3 16 0 10 3 16 20 10 3 8 10
Logarithm of the distance
at the perihelion 9.766039 9.766115 9.7670848
March h ' h ' " h ' "
Time of the Perihelion 12. at 13 41 at 12 57 36 at 13 59 24
Mean time, at the meridian of Paris, the motion of the comet was retograde.
No of Right Mag.
the ascension Declination of the
Stars deg ' " d ' " Stars
1 149 48 55 6 7 45 S 6 A new Star, the Comet compared May 18 and 19 at night
22 151 25 27 6 52 25 6 A Star of the Sextant, Comet compared May 14, 15, 16, and 17
2 153 25 25 5 50 36 7 A new Star, Comet compared May 17, 18, 19, and 20
3 153 33 8 5 12 52 8 A new Star, Comet compared May 20, 21, 22, 23, and 24
27 153 35 49 3 10 3 6 A Star of the Sextant, Comet compared June 3
4 153 42 34 4 28 35 10 A new Star, Comet compared May 24, 25, 26, 27, and 28
5 153 42 34 5 21 5 10 A new Star, Comet compared May 20
6 153 46 21 7 58 55 8 A new Star, Comet compared May 14
7 153 47 22 7 12 32 10 A new Star, Comet compared May 14
8 153 57 40 8 19 29 10 A new Star, Comet compared May 13
9 154 7 39 4 13 20 10 A new Star, Comet compared May 30
10 154 47 30 12 21 11 7 A new Star, Comet compared May 7
11 154 52 21 11 52 46 9 A new Star, Comet compared May 8
12 154 57 2 13 39 6 7 A new Star, Comet compared May 6
1 156 8 56 15 5 53 6 A Star of the Hydra Phi2, Comet compared May 5
13 156 8 15 11 1 27 7 A new Star, Comet compared May 9
2 156 43 56 15 37 38 5 Phi3 of the Hydra, Comet compared May 5
14 156 58 8 19 36 31 9 A new Star, Comet compared May 13
15 157 40 41 9 21 39 8 A new Star, Comet compared May 3
16 159 25 32 8 34 41 6 A new Star, Comet compared May 12
17 159 26 5 25 31 55 7 A new Star, Comet compared May 1
17.1 160 0 28 25 36 24 9 A new Star
18 322 3 15 20 52 19 8 A new Star, Comet compared April 17 in the Morning
19 322 25 3 20 41 56 7 A new Star, Comet compared April 17 in the Morning
49 323 25 38 17 12 5 3 Delta of Capricorn, Comet estimated April 14 and 15 in the Morning
20 325 10 5 11 26 3 7 A new Star, Comet compared April 7 and 8 in the Morning
21 326 12 50 9 42 0 7 A new Star, Comet compared April 6 in the Morning
30 327 41 29 7 40 52 6 A Star of Aquarius, Comet compared April 1 in the Morning
22 329 11 24 8 41 31 7 A new Star, Comet compared April 2 in the Morning
5 344 4 32 0 48 0 N 6 A of Pisces, Comet compared and estimated February 14
23 348 33 20 1 7 28 8 A new Star, Comet compared January 31 and February 1
8 348 38 36 0 3 40 S 5 Kappa' of Pisces, Comet compared February 3 and 4
24 348 49 10 0 32 29 N 8 A new Star, Comet compared February 1
25 349 40 54 1 1 14 8 A new Star, Comet compared January 27 and 28
26 350 44 16 0 50 56 10 A new Star, Comet compared January 25
27 350 52 16 1 5 8 10 A new Star, Comet compared January 23
16 351 0 1 0 44 48 6 A Star of Pisces, Comet estimated January 25, 27, and 28
28 352 13 5 1 6 40 8 A new Star, Comet compared January 21 and 22
18 352 26 6 0 25 53 5 Lambda of Pisces, Comet estimated January 21
Tr. Tim. r.ascension Declinat Longitude Latitude Diff in r Differ in M No
observed. observed observed observed ascension Declin. of of
Northern Northern from the * from the * * *
1759 h ' " deg ' " d ' " d ' " d ' " d ' " d ' "
Jan.21 6 40 0 352 15 28 1 32 58 Cap 23 30 48 4 29 44 0 2 53+ 0 26 18+ 8 28 New *. Com. estim.
6 56 0 352 15 47 1 32 6 23 39 37 4 31 26 0 10 19- 1 5 13+ 5 18 Lambda of Psc. Com. estim.
22 6 51 20 351 51 5 1 29 33 23 6 32 4 36 26 0 22 0- 0 22 53+ 8 28 Star above
23 7 5 37 351 26 31 1 25 28 22 42 16 4 42 23 0 34 15+ 0 20 20+ 10 27 A new Star
7 10 9 351 26 1 0 33 45+ 10 27 the same
25 6 58 54 350 38 9 1 13 57 21 53 10 4 50 53 0 21 52- 0 29 9+ 6 16 of Pisces
7 6 9 350 39 1 0 21 0- 6 16 the same
7 6 9 350 39 1 1 14 30 21 54 8 4 51 0 0 5 15- 0 23 34+ 10 26 New
27 6 22 31 349 54 47 1 4 48 21 9 31 4 59 34 0 13 53+ 0 3 34+ 8 25 New
June 3 10 1 31 154 26 50 3 26 11 7 36 22 13 5 21 0 51 1+ 0 16 8+ 6 27 of the Sextant
Last Modification: May 20, 2001