A description of a new ORRERY, planned, and now nearly finished, by David Rittenhouse, A. M. of Norriton, in the county of Philadelphia. Communicated by Dr. SMITH.

THIS machine is intended to have three faces, standing perpendicular to the horizon: That in the front to be four feet square, made of sheet brass, curiously polished, silvered and painted in proper places, and otherwise ornamented. From the center arises an axis, to support a gilded brass ball, in­tended to represent the sun. Round this ball move others, made of brass or ivory, to represent the planets: They are to move in elliptical orbits, having the central ball in one focus; and their motions to be sometimes swifter, and sometimes flower, as nearly according to the true law of an equable de­scription of areas as is possible, without too great a complica­tion of wheel-work. The orbit of each planet is likewise to be [Page 2] properly inclined to those of the others; and their Apbelia and Nodes justly placed; and their velocities so accurately ad­justed, as not to differ sensibly from the tables of astronomy in some thousands of years.

FOR the greater beauty of the instrument, the balls repre­senting the planets, are to be of a considerable bigness; but so contrived, that they may be taken off at pleasure, and others, much smaller, and fitter for some purposes, put in their places.

WHEN the machine is put in motion, by the turning of a winch, there are three indexes, which point out the hour of the day, the day of the month, and the year, (according to the Julian account) answering to that situation of the heavenly bodies which it then represented; and so continually, for a period of 5000 years, either forward or backward.

IN order to know the true situation of a planet, at any par­ticular time, the small sett of balls are to be put each on its respective axis, then the winch to be turned round 'till each index points to the given time; then a small Telescope, made for the purpose, is to be applied to the central ball, and di­recting it to the planet, its longitude and inclination will be seen on a large brass circle, silvered, and properly graduated, representing the Zodiac, and having a motion of one degree in 72 years, agreeable to the precession of the Equinoxes: So likewise by applying the telescope to the ball representing the Earth, and directing it to any planet, then will both the lon­gitude and latitude of that planet be pointed out (by an index, and graduated circle) as seen from the earth.

THE two lesser Faces are four feet in heighth, and 2 feet 3 inches in breadth: One of them represents and exhibits all the appearances of Jupiter, and his satellites, their eclip­ses, transits and inclinations: Likewise all the appearances of Saturn, with his ring and satellites. And the other repre­sents all the phaenomena of the Moon, particularly the exact time, quantity, and duration of her eclipses, and those of the [Page 3] Sun, occasioned by her interposition; with a most curious con­trivance for exhibiting the appearance of a Solar Eclipse at any particular place on the earth: Likewise the true place of the Moon in the signs, with her latitude, and the place of her Apogee and Nodes, the Sun's declination, equation of time, &c. It must be understood that all these motions are to correspond exactly with the celestial motions, and not to differ some De­grees from the truth, as is common in orreries.

THE whole may be adjusted to, and kept in motion by, a strong Pendulum Clock, nevertheless, at liberty to be turned by the winch, and adjusted to any time, past or future.

N. B. THE above machine is to be supported by a mahoga­ny case, adorned with foliage, and some of the best enrich­ments of sculpture. The part containing the mechanical astronomy of the Moon, has been sometime finished, and is found perfectly to answer, by many trials already made of it. The remainder of the work, is now almost compleated. The clock part of it may be contrived to play a great variety of Music.

The following CALCULATIONS and PROJECTIONS of the Transit of Venus were laid before the Society agreeable to their Dates, and claim a Place here, as it may be of use, in va­rious Respects, to compare them with the actual Observations of the Transit, afterwards made in this Province; and from thence to collect the Differences between Computation and Observation, together wit the Causes of those Differences.

PROJECTION of the ensuing TRANSIT of VENUS over the SUN, which is to happen June 3d, 1769. By David Rittenhouse, A. M.

ELEMENTS from Halley's Tables, for Lat. 40° N. & Long. 75 W. from Greenwich.

Communicated by Revd. Dr. Smith, June 21, 1769.

1769, June 3d, at 3 h. P. M Sun's place, 2^s. 13°. 21′. 37″
Heliocentric place of ♀ in ecliptic, 8. 13. 18. 11 Lat. ♀ N. 4′ 29″
♁ à ♀ 3′ 26″
At 8 Hours P. M. Sun's Place, 2^s. 13°. 33′ 35″
Place of Venus 8. 13. 38 [...]2 Lat. ♀ N. 3′ 18″
♀ à ♁ 4. 27
Log. ♁ à ☉ 5.006568 Distance 10152385
Log. ♀ à ☉ 4.861095 Dist. 7262652
Log. ♀ à ♁ 4.460858 Dist. 2889733
Diff. Log. .400237
Apparent Semidiameter of ☉ 15′. 51″ = 15′ 85
Apparent Semidiameter of ♀ 0′, 5719
Diminish'd ^* Semidiam. Of ☉ 6,3065 in Ratio of 7262 to 2889
Diminish'd Semidiam. of ♀ 0,2276
Beginning of the Transit, 2h. 16′
End 8. 50

But supposing the Sun's Horizontal Parallax but 8 Seconds, then for the above Lat. and Lon.

First External Contact will be at 2h. 11min.

[Page]

The following Paper by the Revd. Mr. EWING, was also com­municated, June 21, 1768.

AS you have taken under consideration, the proposal which I made to you the 19th of April last, of observing the ensuing Transit of Venus over the Disk of the Sun, which will be on the 3d of June, 1769; permit me to lay before you a projection of the Transit, as seen from Philadelphia, together with the elements of the projection, deduced from as accu­rate a calculation as I could make from Dr. Halley's tables. I find from the observations made on the last Transit in June, 1761, that the mean motion of Venus, for the year 1769, should be 21″ more than these tables make it, and that the place of the nodes of Venus, as stated in these tables, needs the following correction. At the time of the ecliptical con­junction of the Sun and Venus in June 1761, their place was 2^s 15° 36′ 33, and her geocentric latitude was 9′ 44′ .9 south. Then say, as 72626.3 the distance of Venus from the Sun: 28894.9 the dist. of Venus from the earth:: 584′ .9 her geocentric latitude: 3′ 52″ .71 her heliocentric latitude at that time. Then say, as the tangent of the inclination of her orbit with the ecliptic, is to rad, so is the tangent of her heliocentric latitude to the fine of her dist. from the node; i. e. as, T, 3° 23′ 20″: rad.:: T, 3′ 52′ .71: S, 1° 5′ 14″, which deduct from her place June 6th, 1761, at the time of the transit, viz. at 5h, 57′ 20″ at Greenwich; and the remainder viz. 2^s 14° 31′ 19″ is the place of her ascending node at that time. The motion of her nodes, as stated by Dr. Halley, is 31″ per annum; therefore, for 8 years, add 4′ 8′ to the abovementioned place of her node, and the sum, viz. 2^s 14° 35′ 27″ is the place of the node in the year 1769, June 3d. With these corrected elements, and others, as in the tables, the following calculations are made.

THE apparent time of the ecliptical conjunction of the Sun and Venus, as seen from the center of the earth, 1769, [Page 6] June 3d, 5^h. 4′ 43″, as reckoned at Philadelphia, 5^h. 0′ 32″ west from Greenwich. The place of the Sun and Venus, at the time of the transit, is 2^s 13° 26′ 32″. The place of her descending node is 8^s 14° 35′ 27″ at that time. The geocen­tric latitude of Venus at that time is 10′ 16″. 295. The Sun's semidiameter is 15′ 45″. 65. The semidiameter of Venus 0″ 29″. Their sum 16′ 14″. 65; their difference is 15′ 16″. 65. Ve­nus's horary motion from the Sun 3′ 57″.43. The angle made by the axis of the earth and ecliptic, as seen from the Sun, 7° 3′ 16″. The angle made by the axis of Venus's vi­sible path and the axis of the ecliptic, is 8° 34′ 17″; the angu­lar point or node being 1° 8′ 55″ west of the Sun. The angle made by the earth's axis and the axis of Venus's visible path is equal to the sum of these 15° 37′ 35′. The horizontal pa­rallax of the sun on the day of the transit is 8″.5204, when his distance from the earth is 101521.2, his parallax at his mean distance 100000 being supposed to be 8″. 65, as found at the last transit 1761. The horizontal parallax of Venus on the day of the transit 29″.9348, when her distance from the Sun is 72626.3, her mean distance being according to her periodic time 72333. The difference of these, viz. 21″.4144, is the horizontal parallax of Venus from the Sun on the said day. The Transit begins, as seen from the earth's center, at 2^h. 17′. 20″.48, and ends at 8 [...]h, 41′ 46″.72. The total ingress at 2^h. 36′ 31. 38; the beginning of egress at 8^h, 22′ 35′ 82; so that the whole duration between the internal contacts will be 5^h. 46′ 4″. 44. But these times will be considerably altered by the parallaxes of Venus in longitude and latitude, as observed from different parts of the earth. The whole effect of the pa­rallaxes of longitude and latitude at the time of the external contact to hasten it, being 3′ 31″, the time of it, as seen from Philadelphia, is at 2^h, 13′ 49″ 28′″ P. M. And the time of total ingress at Philadelphia is 2^h, 32′ 27″; the total effect of these parallaxes to accelerate the internal contact being 4′ 4″.

THESE times depend upon the longitude of Philadelphia West of Greenwich, which in this calculation is supposed to be 5h, 0′ 32′, which is as near as I have yet been able to ascertain [...], by comparing a number of observations made on the eclipses [Page 7] of the first satellite of Jupiter, with Mr. Emmerson's tables. But these cannot be depended upon for the longitude, within a minute or two of time, which will by no means answer the de­sign of ascertaining the distances of the Sun and planets by the ensuing transit. I would therefore beg leave to propose to the Society, that provision be made, without loss of time, for erecting a small observatory in some convenient place, that the occultations of some known stars by the Moon, and the eclipses of Jupiter's satellites, may be noted, and compared with the corresponding observations made at Greenwich, and other places: And that some proper persons be appointed to make the observations, at the expence of the Society, that our lon­gitude may be ascertained with the precision that is necessary. It would be proper, that at least two setts of observers be ap­pointed to view the transit in this city, in order to guard against the fatal accident of losing the Sun out of the field of the telescope, in the critical and important moment; which I find happened to a good astronomer in the East-Indies, at the time of the last transit. It is very difficult to preserve a celes­tial object in the field of a telescope, that magnifies considerably.

THE expence of making these observations, with sufficient accuracy, must be considerable; but it is hoped that an op­portunity will not be neglected on this account, which, for its importance to the interests of astronomy and navigation, has justly drawn the attention of every civilized nation in the world, and which will not be presented again for more than a century to come.

THESE things are submitted, with all humility and deference, to the judgment of this respectable Society, by

N. B. The difference between some of these Numbers and those printed in the American Magazine, was occasioned by neglecting the 21″ of correction in the place of Venus, as incon­siderable; the effect of which is here taken into the computation, and the result is set down above. See the projection, plate 2.

An Account of the TRANSIT OF VENUS over the SUN's DISC, as observed at NORRITON, in the County of Philadelphia, and Province of Pennsylvania, June 3d, 1769. By WILLIAM SMITH, D. D. Provost of the College of Philadel­phia, JOHN LUKENS, Esq Surveyor-General of Pennsylva­nia, DAVID RITTENHOUSE, A. M. of Norriton, and JOHN SELLERS, Esq Representative in Assembly, for Chesten County— Being the Committee appointed for that Observation, by the AMERICAN PHILOSOPHICAL SOCIETY, held at Philadelphia, for promoting useful Knowledge. Communicated to the SOCIETY, July 20th, 1769, by Direction, and in Behalf of, the Committee; by Dr. SMITH.

AMONG the various public spirited designs, that have engaged the attention of this Society, since its first Insti­tution; none does them more honor than their early resolution to appoint COMMITTEES, of their own Members, to take as many observations, in different places, of that rare Phaenome­non, the TRANSIT OF VENUS over the SUN's DISC, as they had any probability of being able to defray the expence of, either from their own funds, or the public assistance they expected.

As the members of the Norriton-Committee live at some distance from each other, I am, therefore, at their request, now to digest and lay before you, in one view, the whole of our observations in that place; distinguishing, however, the part of each observer; and going back to the first prepara­tions. For I am persuaded that the dependence, which the learned world may place on any particular Transit-Account, [Page 9] will be in proportion to the previous and subsequent care, which is found to have been taken in a series of accurate and well conducted observations, for ascertaining the going of the time-pieces, and fixing the Latitude and Longitude of the places of observation, &c.

AND I am the more desirous to be particular in these points, in order to do justice to Mr. Rittenhouse, one of our Commit­tee; to whose extraordinary skill and diligence is owing what­ever advantage may be derived, in these respects, to our obser­vation of the Transit itself. It is further presumed, that Astronomers, in distant countries, will be desirous to have not only the work and results belonging to each particular Transit-Observation, but the materials also, that they may examine and conclude for themselves. And this may be more particularly requisite, in a New Observatory, such as Norriton, the name of which hath perhaps never before been heard of by distant Astronomers; and therefore, its latitude and longitude are to be once fixed, from principles that may be satisfactory on the present, as well as on any future, occasion.

OUR great discouragement, at our first appointment, was the want of proper apparatus, especially good Telescopes, with Micrometers. The generosity of our Provincial Assembly soon removed a great part of this discouragement, not only by their vote to purchase one of the best Reflecting Telescopes, with a Dollond's Micrometer; but likewise by their subsequent dona­tion of One Hundred Pounds, for erecting Observatories, and defraying other incidental expences. It was foreseen that on the arrival of this Telescope, added to such private ones as might be procured in the city, together with fitting up the instruments belonging to the Honorable the Proprietaries of the Province, viz. the equal Altitude and Transit Instrument, and the large astronomical Se [...]l [...]r, nothing would be wanting for the City-Observatory in the State-House Square, but a good Time-Piece, which was easily to be procured.

WE remained however still at a loss, how to furnish the Nor­riton Observatory. But even this difficulty gradually vanished. [Page 10] Early in September, 1768, soon after the nomination of our Committees, I received a letter from that worthy and honorable Gentleman, THOMAS PENN, Esq one of the Proprietaries of this Province, which he wrote at the desire of the Rev. Mr. Maskelyne, Astronomer Royal, expressing their desire, ‘That we would exert ourselves in observing the Transit, for which our situation would be so favourable;’ and enclo­sing some copies of Mr. Maskylyne's printed directions for that purpose.

THIS gave me an opportunity, which I immediately em­braced, of acquainting Mr. PENN what preparations we had already made; and what encouragement the Assembly had given in voting One Hundred Pounds Sterling, for the purchase of One Reflecting Telescope and Micrometer, for the City Observatory; but that we should be at a great loss for a tel­escope of the like construction for the Norriton Observatory, and requesting him to order a Reflector of two, or two and an half feet, with Dollond's Micrometer, to be got ready as soon as possible in London. It was not long before I had the pleasure to hear that Mr. PENN had ordered such a Telescope, which came to hand about the middle of May, with a most obliging letter, expressing the satisfaction he had in hearing of the spirit shewn at Philadelphia, for observing this curious Phoenomenon when it should happen; and concluding as follows—

‘I HAVE sent, by Capt. Sparks, a Reflecting-Telescope with Dollond's Micrometer, exact to your request, which I hope will come safe to hand After making your observation with it, I desire you will present it, in my name, to the Col­lege—Messrs. Mason and Dixon tell me, they never used a better than that ^* which I formerly sent to the Library Com­pany [Page 11] of Philadelphia, with which a good observation may be made, tho' it has no micrometer.’

WE were now enabled to furnish the Norriton Observatory, as follows, viz.

1. A GRICORIAN REFLECTOR about 2 f. focal length, with a Dollond's Micrometer. This Telescope hath four different magnifying powers, viz. 55; 95, 130, and 200 times; by means of two Tubes containing eye-glasses that magnify dif­ferently, and two small Speculums of different focal distances. Made by Nairne. Used by Dr. SMITH.

2. A REFRACTOR of 42 f. its magnifying power about 140. The glasses were sent from London with the large Reflector, and belonged to Harvard College, New England; but as they did not arrive time enough to be sent to that place before the Transit, they were fitted up here, by Mr. Rittenhouse; and—Used by Mr. LUKENS.

3. MR. Rittenhouse's REFRACTOR, with an object glass of 36 f. focus, and a convex eye-glass of 3 inches, magnifying about 144 times. Used by HIMSELF.

BOTH these Refractors, as well as the Reflector, were in most exquisite order.

4. An Equal-Altitude Instrument; its telescope three and an half f. focal length, with two horizontal hairs, and a vertical one, in its focus, firmly supported on a stone pedestal, and easily adjusted to a plummet wire 4 feet in length, by 2 screws; one moving it in a North and South, the other in an East and West, direction.

5. A TRANSIT-TELESCOPE, fixed in the Meridian on an axis with fine steel points; so that the hair in its focus can move in no other direction than along the meridian; in which, are two marks South and North, about 330 yards distance each; to which it can be readily adjusted in a horizontal po­sition by one screw, as it can in a vertical position by another screw.

[Page 12] 6. AN excellent TIME-PIECE, having for its pendulum­rod a slat steel-bar, with a bob weighing about 12 lb. and vi­brating in a small arch. It goes 8 days, does not stop when wound up, beats dead seconds, and is kept in motion by a weight of 5 pounds.

THESE three last articles were also Mr. Rittenhouse's proper­ty, and made by himself.

7. AN ASTRONOMICAL QUADRANT, two and an half f. radius, made by Sisson, the property of the East-Jersey Proprietors; under the care of the Right Hon. William Earl of Stirling, Sur­veyor-General of that Province; from whom Mr. Lukens pro­cured the use of it, and sent it up to Mr. Rittenhouse for ascer­taining the latitude of the Observatory. Thus we were at length compleatly furnished with every instrument proper for our work.

As Mr. Rittenhouse's dwelling at Norriton is about 20 miles North-West of Philadelphia, our other engagements did not permit Mr. Lukens or myself, to pay much attention to the necessary preparations; but we knew that we had entrusted them to a gentleman on the spot, who had joined to a compleat skill in Mechanics, so extensive an astronomical and mathematical knowlege, that the use, management, and even the construction, of the necessary apparatus, were perfectly familiar to him. Mr. Lukens and myself could not set out for his house till Thursday, June 1st; but, on our arrival there, we found every preparation so forward, that we had little to do, but to exa­mine, and adjust our respective telescopes to distinct vision. He had fitted up the different instruments, and made a great number of observations, to ascertain the going of his Time­Piece, and to determine the latitude and longitude of his Observatory. The laudable pains he hath taken in these mate­rial articles, will best appear from the work itself, which he hath committed into my hands, with the following modest in­troduction; giving me a liberty, which his own accuracy, care and abilities, leave no room to exercise.

[Page 23] THE difference of the above observations is greater than might be wished. All that can be offered to excuse them is the want of better instruments; though Mr. Rittenhouse thinks the differences chiefly arose from the action of the sun on the wooden frame which supported the quadrant. For he always observed that when the shutter in the roof was opened, the plummet-wire would, in a minute or two, leave the point, though it had stood over it quietly all the forenoon. Yet, not­withstanding those differences, a Mean, from so many, may be supposed very near the truth; since, if we leave out that of June 6th, which differs most from the others, the mean of the rest will be but 2″ greater than it is set down above.

So far I have given Mr.Rittenhouse's observations, previous and subsequent to the Transit, for ascertaining the going of his time­piece and fixing the latitude and longitude of the observatory, from February 15th to July 8th; by which it will appear what laudable diligence he hath used in these material articles. He hath taken many more observations since; but those given above, are judged fully sufficient to shew that both the latitude and longitude of the observatory may be ^* depended on, and also the times given on the day of the transit.

IT hath been mentioned before, that it was on Thursday af­ternoon, June 1st, that Mr. Lukens and myself arrived at Norriton, with a design to continue with Mr. Rittenhouse 'till the transit should be over. The prospect before us was very discouraging. That day, and several preceeding, had been generally overcast with clouds, and frequent heavy rains; a thing not very common for so long a period at that season of the year, in this part of America. But, by one of those sudden transitions, which we often experience here, on Thursday evening, the weather became perfectly clear, and continued the day following, as well as the day of the Transit, in such a state of serenity, splendor of sunshine, and purity of atmos­phere, that not the least appearance of a cloud was to be seen.

[Page 24] JUNE 2d, and the forenoon of June 3d, were spent in making the necessary preparations, such as examining and marking the foci of our several telescopes, particularly the reflector, with and without the micrometer. The reflector was also placed on a polar axis, and such supports contrived for resting the ends of the refractors, as might give them a motion as nearly parallel to the equator as such hasty preparations would admit. Several diameters of the Sun were taken, and the micrometer examined by such other methods as the short­ness of the time would allow.

THE Sun was so intensely bright on the Day of the Transit, that instead of using the coloured glasses sent from England with the Reflector, I put on a deeply-smoaked glass prepared by Mr. Lukens, which gave a much more beautiful, natural and well-defined appearance of the Sun's Disk. The smoaked glass was fastened on the Eye Tube with a little bees-wax, and there was no occasion to change it during the whole day, as there was not the least cloud, or intermission of the Sun's splendor.

MR. Rittenhouse, in his previous projection (see p.4) had made the first external contact to be, June 3d, 2^h, 11′ for lat. 40° N. and long. 5^h. W. of Greenwich; on a supposition of the Sun's horizontal parallax being 8″. He happened to be very near the truth. For at 2^h. 10′ 33″ mean time, the 1st external contact was at Norriton, lat. 40°. 9′. 56″ N. and long. 5^h. 1′. 31″ west. Other calculations made it generally from 6′ to 8′ later for the same latitude and longitude.

THO' this calculation was not given, to be entirely depended on, yet it was sufficient to make us keep what, in the sea­phrase, would be called a good look-out; and therefore, at one o'clock, we took off the Micrometer, which had been fitted to the Reflector with a power of 95, and adjusted it to distinct vi­sion, with the^* same power to observe the CONTACTS. And [Page 25] during the hour that was to intervene from one to two, we resolved to keep an alternate watch through the Reflector, on that half of the Sun's limb, where Venus was certainly expected to touch; while the others, not thus employed, were fixing what more remained to be done, as follows, viz.

FIRST, That each of us might the better exercise our own judgment, without being influenced, or thrown into any agi­tation by the others, it was agreed to transact every thing by signals, and that one should not know what another was doing. The Situation of the Telescopes, the two Refractors being at some distance without the Observatory, and the Reflector within, favoured this design.

SECONDLY, Two persons, Mr. Sellers, one of our Committee, and Mr. Archibald Mc. Clean, both well accustomed to matters of this kind, were placed at one window of the Observatory, to count the clock and take the signal from Mr. Lukens. Two of Mr. Rittenhouse's family, whom he hath often employed to count the clock for him in his observations, were placed at another window to take his signal. My Telescope was placed close by the clock, and I was to count its beats, and set down my own time.

THESE Preliminaries being settled, we prepared at two o'clock to sit down to our respective Telescopes; or (I should rather say) lie down to the Refractors, on account of the Sun's great height.

As there was a large concourse of the inhabitants of the county, and many from the city, we were apprehensive that our scheme for silence might be defeated, by some of them speaking, when they should see any of the signals [Page 26] for the Contacts; and therefore we found it necessary to tell them that the success of our observation would depend on their keeping a profound silence 'till the Contacts were over. And to do them justice, during the 12′ that ensued, there could not have been a more solemn pause of silence and expectation, if each individual had been waiting for the sentence that was to give him life or death. So regular and quiet was the whole, that, far from hearing a whisper, or word spoken, I did not even hear the feet of the counters, who passed behind me from the windows to the clock; and was surprized when I turned from my Telescope to the clock, to find them all there before me, counting up their seconds to an even number; as I imagin­ed, from the deep silence, that my associates had yet seen nothing of Venus.

As the CONTACTS are among the most essential articles re­lative to this Phaenomenon, it is material, before we set down the times, to give a particular account of the manner in which each observer judged of them, and the circumstances attending them.

[Page 33] WHEN Venus was fully entered on the Sun's limb, and we had compared the different papers on which our contacts were written down, and entered them in our book, we prepared for the Micrometer and other observations.

THOSE of the Micrometer, reduced to apparent time, are as follow, viz.

Which gives ☉'s semidiameter 15′. 46,″ 94: that is, one second and [...] a second larger than the diameter given in the nautical almanack for the transit day. Yet, Venus's diameter, though taken with the utmost care by the same Micrometer and at the same focus (as the Sun's) comes out about one second less than it was expected, being 57″, 12; or about [...] of ☉'s diameter.

The vertical diameter of ☉ on the same day was 31′. 31″, 8 at 4^h. 40′. P. M.

OF the Micrometer measures, the 2d, 5th, and 18th distance of the nearest limbs of the Sun and Venus; the 1st in a chord parallel to the equator, the 1st and 6th of the diameters of Venus; and the 1st and 4th of the diameters of the Sun, were taken by Mr. Rittenhouse. The 3d and 16th distance of the nearest limbs, the 3d diameter of Venus and the 2d of the Sun, were taken by Mr. Lukens. All the other Micrometer measures were taken by myself, while Mr. Rittenhouse applied himself to take the appulses of the limbs of the Sun and center of Venus to the cross hairs of his equal altitude instrument, Mr. Lukens writing down the observations and their exact time.

THE Micrometer measures were all separately reduced to their value in minutes and seconds by Mr. Rittenhouse, and by myself, making the proper allowance for the error of adjust­ment [Page 35] of the instrument. Many more Micrometer measures might have been taken; but had we made the intervals between them much shorter than 8 or 10 minutes, they would have been of little use in the projection, and would have crouded it too much. Nor could we have bestowed the same care in setting the instrument, reading off the vernier, &c. if a much larger number had been taken.

IN order to judge of the error of the Micrometer (if any) Jupiter's diameter was not only taken with it both ways, viz. to the right and to the left, but Mr. Rittenhouse likewise took a mean to the right of 10 diameters of a white painted circle about 330 yards distant, and also a mean of as many to the left. This work was performed early in the morning before sun-rise; when the air was free from all tremulous motion; and the re­sult gave an error of adjustment of 1, 12 to be substracted from all the micrometer measures.

IT was once intended still further to confirm the work of the following delineation, by applying the observations of the ap­pulses of the limbs of the Sun and center of Venus, mentioned to have been taken above. But the lines necessary for this, would have confused the figure; and the Micrometer observations being found so exact, any further use of the others, than to try how well they would agree, was thought to be needless, espe­cial as the fractions of seconds in them could not be estimated, so as to come up to the accuracy of the Micrometer. For this reason, they are not set down.

THUS, Gentlemen, you have a faithful account of our whole work, which we could have wished to have reduced to less compass. Had our latitude and longitude been previously fixed, as they had been at Philadelphia by able mathematicians, a great part of our work might have been saved. But we thought it necessary (as hath been before hinted) to shew that such pains were taken in these material articles that they may [Page 39] be depended on. And as we were happily favoured at the transit, with advantages of weather, and other circumstances, which cannot have happened to the generality of observers in many parts of the world, it was thought we should be more readily excused, by men of science, for the insertion of things that might be superflous, than the omission of the least article material, in the account of a phoenomenon, that will never be observed again, by any of the present generation of men.

An Account of the OSERVATIONS on the TRANSIT OF VENUS over the SUN, on the 3d of June, 1769, by the COMMITTEE appointed to observe it at Philadelphia; drawn up, and pre­sented to the AMERICAN PHILOSOPHICAL SOCIETY, held at Philadelphia, for promoting useful Knowledge, By JOHN EWING.

IT doubtless must appear strange to many, that the parallax of the Sun, which is so important and fundamental an ar­ticle in Astronomy, has not been settled by Astronomers long ago, as so many things in that useful Science depend upon it. But this surprise is lessened by considering, that the smallness of the parallactic angle has eluded their most careful researches in all ages, as it is but about 8 or 9 seconds of a minute; so that the subtense of it, were it much larger than it is, must be invisible to the naked eye at the distance of 6 inches, and it is hardly possible to distinguish 10 seconds by instruments, let them be ever so skillfully made. Many methods have been devised by Astronomers, which shew the ingenuity of the in­ventors; but the disadvantage of them all was, that they de­pended upon observations to be made with a precision, which no instruments hitherto constructed could possibly accomplish. The Transits of Venus alone afford an opportunity of determining this problem with sufficient certainty, and these, from the strict laws of her motion, happen so seldom, that there cannot be more of them than two in one century, and in some centuries none at all. Three only have been observed since the creation, and the first of them by two persons only. The peculiar advantage of this phaenomenon for determining the parallax of the Sun with a precision which is not to be expected from any other method, consists in its being deduced from the absolute time that elapses between the instants of the contacts with the Sun's limb, as seen from different parts of the earth; or from the difference of total durations as noted by distant observers, properly stationed for that purpose. A second of time being easily distinguished by a well regulated clock, if the aforesaid absolute difference of [Page 43] time be carefully noted, in places where it will amount to 24 mi­nutes, it will give the parallax, small as it is, within the hun­dreth part of a second of a degree, and consequently the dis­tance of the Sun and planets within the seven hundredth part of the whole. In some Transits this difference of time will be greater, and in others less, in certain places on the earth, which renders those that happen on the northern part of the Sun's disc, in general, more favourable to our purpose, than those that happen on the southern hemisphere. Hence it is, that al­tho' much was done in this matter by the sedulity and care of Astronomers at the Transit in the year 1761, when Venus passed south of the Sun's center, yet our expectations could not be fully answered by the observations that were then made; as it was easily foreseen that much greater precision might be attained, from the advantageous circumstances that would attend the Transit in 1769. The great proficience, which the Astro­mers made in settling this fundamental element, beyond what was ever known before, has only raised their expectations and engaged their attention to improve every advantage, that can be derived from a careful observation of this Transit. If they have not been disappointed by unfavourable weather, we hope for the utmost certainty that can be gained in this matter, from the Observations they have made, when they shall be compared together. But after all, we must sit down with the disagreeable assurance that the distance of the Sun cannot be determined by them, let them be made with ever so great ac­curacy, within many thousand miles; which will not appear strange, when we consider that his distance is upwards of 94 millions of miles, and that an error of a single second in his parallax will give an uncertainty of 10 or 11 millions of miles in his distance.

THIS approximation, however, is so much greater than could be expected, from any other method, that has ever been proposed, that it has deservedly engaged the attention of every civilized nation in the world; and it must redound to the honor of our Society, that they have taken such effectual care to have proper Observatories erected, to furnish them with the necessary instruments, and to appoint proper persons, to use them on that occasion.

[Page 44] As the credit of our Observations, and the stress that will be laid upon them, in determining the parallax of the Sun, will greatly depend not only on the care and skill of the persons that made them, but also on the goodness of the instruments, with which we were furnished; it has been judged proper to give the public the following account of our apparatus, and of the pains we have taken to have it in the best order.

As the Society were pleased to appoint Joseph Shippen, Esq Dr. Hugh Williamson, Mr. Charles Thomson, Mr. Thomas Prior, and Myself, as a Committee to observe the Transit at the Ob­servatory, which they had erected in this city, we spared nei­ther time nor labor to have every thing necessary for the Ob­servation in readiness. We were provided with an excellent Sector of 6 feet radius, made by the accurate Mr. Bird, and an Equal Altitude and Transit Instrument, both belonging to the honorable Proprietaries of this province, which the Governor very generously lent to the Society on this occasion. Our Tele­scopes were, a large Reflector of 4 feet focus and 7 inches aperture, which magnified from 100 to 400 times with an excellent Mi­crometer of Mr. Dollond's construction fitted to it, which the Assembly of the province had ordered over at the request of the Society; a Refracting Telescope of 24 feet focus, belonging to Miss Norris; two Reflecting Telescopes of 18 inches focus, one the property of Mr. Hamilton, the late Governor of this pro­vince, and the other of Mr. Prior, together with another Reflec­tor of 12 inches focus. With these, and a good time-piece, we promised ourselves the pleasure of making accurate Observa­tions, if the weather should prove favourable. For this pur­pose we met frequently before the Day of the Transit, to ad­just our instruments, and to remove every local obstruction that might hinder our Observations.

SOME of us gave particular attention to the regulation of the time-piece, and therefore took the passage of the Sun's limbs over the [...] hairs of the Transit-instrument, both forenoon and afternoon for many days before and after the Transit, and particularly on that day. As it had 3 horizontal hairs fixed in the focus, it afforded us 6 setts of corresponding altitudes, which [Page 45] generally agreed in giving the time of apparent noon within 2 seconds of each other; so that by comparing them together daily, and applying the proper equations for corresponding altitudes, on account of the Sun's change of declination be­tween the forenoon and afternoon Observations, we were as­sured of the rate of our clock's going and the time of apparent noon to a single second. We did not think it necessary to burden our minutes, with the great number of Observations of this kind, that we made. Let it suffice to say, that they were made with the utmost care, and that our time piece was fixed to a large post sunk into the ground four or five feet, secured from shaking by a brick wall at the bottom, and no ways communicating with the sides of the building.

THE long expected Day of the Transit came, so favourable to our wishes, that here was not the least appearance of a cloud in the whole horizon from morning till night, and the sky was uncommonly serene. The Committee assembled in the morning at the Observatory, examined the adjustment of their Telescopes anew, and appointed two assistants to observe the clock, one to count the seconds with an audible voice, and the other to write down the minutes as they were compleated, to prevent a mistake in that article.

EVERY Observer being fixed at his Telescope, at least half an hour before the beginning of the Transit; we observed the contacts of the limbs of Venus and the Sun at the times mentioned in the following accounts, as they were drawn up separately by the Observers themselves, and are here inserted in their own words.

MR. PRIOR made his Observations with his own Reflecting Telescope, whose magnifying power he does not certainly know, but supposes it to be at least an hundred times. He gave the following account of his Observation of the Contacts, viz.

‘THE uncertainty where Venus would touch the Sun's limb made me take the following method. From 8 or 9 minutes past two o'clock I made it a rule to pass my eye from the lower edge of the field of my Telescope to the upper, many times in a minute, and examine the limb of [Page 50] the Sun strictly, in hopes of discovering the [...] here of Venus approach, so as to give an opportunity of taking the contacts of the limbs to a great certainty. In passing my eye along the limb of the Sun, I discovered a small imper­fection, which I thought must be the stroke of the at­mosphere, but in four seconds I discovered it to be the limb of Venus, the atmosphere not being visible on the Sun. The time therefore that I note for my external contact is, when I first discovered that imperfection on the Sun's limb, which was at 2^h.13′42″ apparent time. When the body of Venus was something more than one third on the Sun, I saw her eastern atmosphere very distinctly reflecting the light of the Sun so strongly on the limb of Venus, as to shew it well defined; but as it came on the Sun, it was entirely lost. The time, I note for my internal Contact, was, when the thread of light was distinctly seen all round the body of Venus, which was at 2^h.31′.28″ apparent time.’

MR. JAMES PEARSON having observed the external Contact at 2^h. 13′. 50″ apparent time, with a small Telescope, belonging to the honorable [...] of this province, whose magnifying power i [...] about 60 times; Mr. CHARLES THOMSON observed the internal contact with the same Telescope, of which he gave the following account, viz.

‘AT 2^h.29′.11″ mean time, or 2^h.3′.26″ apparent time, I saw some tremulous rays of [...]ight pass from the up­per or eastern limb of the Sun to the eye, across, and so as just to touch the upper limb of Venus. Marking that down therefore as the time of Contact, I counted four seconds, at which time I saw a continued thread of light, like a silver lace, but still with a tremulous motion, round the eastern limb of Venus, whereby it appeared to me that the whole body of Venus was then within the disc of the Sun. The tremulous appearance of the rays of light, I at first attri­buted to my Telescope resting against the side of the Ob­servatory, but afterwards apprehended might be owing to their passing thro' the atmospere of Venus.’

[Page 51] THE Committee having desired me to use the large Reflec­tor abovementioned, I chose that power which magnifies [...]he diameters of objects 300 times: with which I observed a [...] 2^h.13′.48″ apparent time, an obscuration on the north-eastern limb of the Sun, gradually advancing forwards with a tremu­lous motion, which from its irregular and dusky appearance, I concluded was occasioned by the refraction of the Sun's rays thro' the atmosphere of Venus, which atmosphere soon after­wards became very observable to us all. From this I was led to conclude that the Contact did not happen till about 15 or 16 seconds afterwards, when there was a large and evident impres­sion made on the limb of the Sun; but as the precise moment of the external Contact cannot be noted by an Observer, the body of Venus not yet being interposed between the Sun's limb and the eye; this Contact must have happened about the time that her atmosphere made the above mentioned obscuration, and therefore I am of opinion that the true time of the Contact should be accounted at 2^h.13′.48″, or it may be 3 or 4 seconds sooner, when nothing but the atmosphere of Venus, which preceded her body, appeared on the limb of the Sun. About the time that the center of Venus approached the Sun's disc, I saw the whole body of Venus, her eastern edge being surrounded with a faint light, which was doubtless occasioned by her atmosphere re­fracting the Sun's rays. At 2^h.29′.11″ mean time, or 2^h.31′.26″ apparent time, I saw the internal contact, when the whole body of Venus was introduced within the disc of the Sun, and the thread of light had compleatly surrounded her, altho' not as bright as it became in two seconds afterwards.

FROM what has been said, it appears that the apparent times of the Contacts may be represented at one view in the following table, as they were noted by the different Observers.

[Page 52] AFTER the Observation of the Contacts, I applied myself to the Micrometer to measure the diameters of the Sun and Venus, and the distance of their limbs at sundry times during the Transit. I had indeed frequently measured the equatorial dia­meter of the Sun before the Day of the Transit, and always found it to be 6 seconds less than what is given in the Nautical Almanac. The mean of 6 measures on that day is 31′.31″.6, which differs but 0″.3 or three-tenths of a second from what is given in the said Almanac lessened as above. Therefore I have stated it at 31′.31″.3 in the following reductions and cal­culations.

SIX measures of the diameter of Venus on the Sun made it 58 seconds. I attempted to measure it both ways, with the beginning of the divisions of the vernier advanced on the scale of the Micrometer and the contrary, that the error of adjust­ment might have been thereby taken away. But the Micro­meter did not admit of it, the diameter of Venus being a small matter too large for this operation. However I took some measures this way, but they gave the diameter no more than 55″.4, which appearing too small were therefore rejected.

ABOUT 20 minutes after the Contacts, I began to measure the nearest distance of the limbs of Venus and the Sun, and continued untill the Sun [...]as so low, that the measures could not be made with sufficient accuracy any longer. Some of the measures appear to disagree too much with the others, and therefore should not be depended on; but I could not prevail upon myself to neglect the inserting of them; least the unusual agreement among so great a number should raise a suspicion in the minds of Astronomers that they had not been honestly transcribed from our minutes; especially as there are enough to answer all the purposes designed by them, which ag [...]e in giving the nearest distance of the centers with sufficient precision. Although these measures are set down in the fol­lowing table with the parts of a second, we would not therefore be supposed to affect an impossible accuracy in them, but they are such as the Micrometer has given them when properly reduced.

[Page 53] [Page 54]

THE foregoing nearest distances of their centers are deduced from the measured distances of their limbs, taking their dia­meters as they are stated above: And the parallaxes are not computed, but measured from a projection of the disc of the earth as seen from the Sun, the projection being 21 inches and an half in diameter.

THE latitude of our Observatory in Philadelphia is deter­mined from the Observations of Messrs. Mason and Dixon with the above mentioned Sector. From a mean of thirty Obser­vations of the passages of some stars over the Meridian, they found the latitude of the most southern point of the city of Philadelphia to be 39°.56′.29,″2. Our Observatory is North of this point, 25 seconds, and therefore its latitude is 39°.56′.54″.

IN order to determine the parallax of the Sun, from the foregoing Observations, it is necessary that our longitude from some fixed Meridian should be ascertained with the most rigor­ous precision. For this purpose we have observed various Eclipses of Jupiter's Satellites, that they might be compared with the correspondent Observations made at Greenwich and elsewhere, when we are furnished with them.

[Page 55]

SINCE the foregoing account has been drawn up, we have been furnished with some Observations of the eclipses of Jupi­ter's satellites, made by the Revd. Mr. Maskelyne, Astrono­mer Royal, at Greenwich. By comparing these with the like Observations made at Philadelphia and Norriton, we are en­abled to settle the longitudes of our Observatories. But as there are but two or three of them correspondent with ours, we must have recourse to another method; which is first to compare them with the calculations in the Nautical Almanac, which were made for the meridian of Greenwich, that the er­ror of the tables may be discovered by the mean of them; and then to compare ours with the same calculations, applying the errors of the tables to the longitude deduced from this com­parison. We may depend upon the result of this method with much more confidence, than upon any single observation.

[Page 56]

Now altho' the errors of the first satellite appear considera­ble, yet if we reject the Observation of the 16th of May as being too near to the time of Jupiter's opposition with the Sun; the mean of those, which give an eastern meridian corresponding with the calculations of the Nautical Almanac, exactly counter­balances the mean of those which give a western meridian cor­responding with them. Therefore we have nothing to do but to reduce all our Observations at Norriton and Philadelphia to the meridian of Philadelphia, and then compare them with the calculations in the Nautical Almanac.

Now if we compare the correspondent Observations at Phi­ladelphia and Norriton on the 16th of February, the 12th of April, the 5th of May, and the 7th of June 1769, the diffe­rence of our meridians will be found from the mean of them to be 57 seconds of time. This is farther confirmed by the Obser­vations we have made on the Transit of Mercury over the Sun, on the 9th of November, 1769, which being compleated before these sheets were printed off, we have judged proper to insert.

[Page 57] THEREFORE the mean of both these makes the difference of our meridians 56 seconds of time, which must certainly be more accurate than what is deduced from a few corresponding Observations of the eclipses of Jupiter's satellites; both because they afford 24 comparisons, all nearly agreeing among them­selves, and because these Transits, in the judgment of most astronomers, afford the best opportunities of settling the lon­gitudes of places. Hence if we add 56 seconds to the time of the Norriton Observations of the eclipses of Jupiter's satellites, they will be reduced to the meridian of our Observatory in Philadelphia, and may be used in fixing our longitude from Greenwich, in the following manner.

[Page 58] Now if we take the mean of all the 21 foregoing determina­tions of our longitude from Greenwich, by the eclipses of the first satellite, rejecting only those of March 1st, and April 9th, 1768, which differ most from the others, the result will be 5^h.0′.35″ for the difference of our meridians. These ought evidently to be rejected, as they differ near twice as much, from the mean of the rest, as any other of the determinations do, yet the retaining of them will make no difference in the result. If the mean determination of the longitude be taken from the immersions alone, rejecting that of the 1st of March, 1768, it will be 5^h.0′.36″, and if from the emersions alone, it will be 5^h.0′.34″, when the Observation of the 9th of April, 1768, is excluded. Therefore the mean of both, (which should always be preferred,) is 5^h.0′.35″.

As a farther confirmation of this conclusion; if this dif­ference of meridians be applied to the Greenwich Observations, of the first satellite, rejecting that of the 16th of May, to re­duce them to the meridian of Philadelphia, and if they are then compared with the calculations in the Nautical Almanac; we shall have the same result from them also.

THE mean of these determinations of the longitude, from the Greenwich Observations of the first satellite, is 5^h.0′.35″. But farther if we take the mean of all the determinations, derived from the eclipses of the second satellite, it will be found to be 5^h.0′.37″. And lastly, if the mean of all the determinations from the eclipses of both first and second satellite be chosen, [Page]

[Page]

[Page 59] the deduced longitude will be 5^h.0′.35″. So that we may safely conclude, that the difference of meridians between Phi­ladelphia and Greenwich, is 5^h.0′.35″.; and that Norriton is 56″ of time west of Philadelphia, and its longitude is 5^h.1′.31″. west. With this determination we must be con­tented until farther observations are made, by which it may be confirmed, or rendered liable to exception.

THESE Observations are sufficient to determine every thing relative to the theory of Venus, and the parallaxes of the Sun and planets, as may be seen by the annexed projection of the Transit, and the following calculations Altho' the parallax of the Sun may be obtained from the observed nearest distance of the centers of the Sun and Venus, yet this method cannot be so much depended on, as the comparison of the contacts of the limbs observed in proper places, where the absolute dif­ference of time is considerable. Nevertheless, as the public seem very impatient to know the result of what was done in this place; I have endeavoured to deduce it from our Obser­vations alone; and flatter myself, that, in the conclusion, it will be found pretty accurate; as it is nearly the same, with what I had before found it to be, by an hundred and forty determinations of it, from the Observations of Astronomers on the Transit of 1761; and also from another method, the invention of the celebrated Mr. Stuart, of Glasgow; both which I have now annexed to the following calculations.

HAVING thus collected together all the elements necessary for the ensuing calculation; before I proceed to it, I must, in justice to Dr. Williamson and Mr. Prior, observe, that of the Micrometer measures, the 2d, 3d, 19th, 20th, 21st, 22d, 23d, 24th, and 25th were made by Mr. Prior, and the 35th, 43d, 44th, and 54th by Dr. Williamson, with the same adjustment of the focus, that I used in the others.

I HAVE taken the trouble of making above fifty determina­tions of the middle of the Transit, and find from a mean of them, that the nearest approach of their centers was at 5^h.21′.27″ mean time, or 5^h.23′.41″,7 apparent time, which [Page 60] was hastened by parallax 4′.48″ at Philadelphia; and there­fore, that the central apparent time of the middle of the Tran­sit was 5^h.28′.29″,7, according to our meridian.

BY comparing together eighteen determinations of the near­est distance of the center of the Sun and Venus, I find the mean of them to be 10′.3″,58, as seen in Philadelphia. But she was then depressed 6,″91 by parallax; and therefore, the geo­cent. nearest distance of the centers was 10′.10″,49=610″,49. Therefore say,

As 72626,45 the dist. of ♀ from ☉ ∶ 28879,55 her dist. from ♁ ∷ 610″,49 ∶ helioc. dist. of their centers.
4.861,0949
4.460,59 [...]4
2.785,6785
7.246,2689
2.385,1740=242″,7583=4′.2″,7583 the helioc. dist. of their cent.

As S, 3°.23′.20″ the incl. of ♀ orbit to the eclip. ∶ R ∷ S, 4′,2″,758 ∶ Sine of ☉'s dist. from the node of ♀
8.771,6803
10.
7.070,2506
8.298,5703=1°.8′.20″,23☉ dist. from the node of ♀

As S, 1°.8′.20″,23 ∶ R ∷ S, 10′.10″,49 ∶ S, of the angle of her visible path with the eclip.
8.298,5703
10
7.470,9623
9.172,3920=8°.33′.11″,5 the angle of her visible path.

If AB represent the horary motion of ☉=2, ′392375. See P1. IV. [...]ig. 2d.

BAC the inclination of the orbit of ♀ with the ecliptic=3°.23′.20″

DBC the angle of ♀ visi. path with the eclipt.=8°.33′.11″,5

Then AC will represent the horary motion of ♀ and may be found by the following proportion;

As S, A C B ∶ A B ∷ S, D B C or A B C ∶ A C.

As S, 5°.9′.51″,5 ∶ 2′,3922357 ∷ S, 8°.33′.11″,5 ∶ the hor. mot. of ♀
8.954,3008
0.378,8292
9.172,3920
0 596,9204=3′,952942=237″,17652 the hor. mot. ♀ whose log. is 2.37 [...],0716.

[Page 61] 916,65=the diff. of the semidiameters of ☉ and ♀
610,49=the geo. nearest dist. of their centers.
Sum, 1527,14=3. 183,8789
Diff. 306,16=2. 485,9484
5.669,8273 the log. of the square of half the transit line between the internal contacts.
2.834,9136=the log. of half the transit line between the
2.375,0716=the log. of ♀ hor. mot. [int. cont.=683″,776
0.459,8420=2^h.882982=2^h.52′.58″,7=the semidu­ration between the int. contacts.

974,65=the sum of the semidiameters of ☉ and ♀
610,49=the geo. nearest dist. of their centers.
Sum, 1585,14 3.200,0677
Diff. 364,16 2.561,2922
5.701,3599
2.880,6799=the log. of half the transit line between the
2.375,0710=the log. of ♀ hor. mot. [ext. co.=759″,766
0.505,6083=3^h.20338=3^h.12′.12″,168=the semidu­ration between the ext. contacts.

As R ∶ Sec, 8°.33′.11″,5 ∷ 610″,49 ∶ geo. latitude of ♀
10.
10.004,8572
2.785,6785
2.790,5357=617″,356=10′.17″,336=the geo. lat. of ♀

As 72626,45 ∶ 28879,55 ∷ geo. lat. ∶ hel. lat. of ♀
4.861,0949
4.460,5904
2.790,5357
7.251,1261
2.390,0312=245″,4885=4′.5″,4885=the hel. lat. of ♀
610,49
617,356
1227,846 3.089,1440
96,866 0.836,7038
3.925,8478
1.962,9239
2.375,0716=the log. of hor. mot. of ♀
9.587,8523=0^h.387126=23′.13″,6536=the time between the mid [...] and eclip. conjunction.

[Page 62] FROM the apparent time of the middle of the Transit, viz. 5^h.28′.29″,7 deduct 23′.13″,65, and the apparent time of the ecliptical conjunction will be 5^h.5′.16″,05, when the Sun's place given in the Nautical Almanac was 2^•.13°.27′.18″.7, making the difference of our meridian from Greenwich 5^h.0′.35″, as found above. To his place in the ecliptic add his distance from the node of Venus, found above, viz. 1°.8′.20″,23, and the sum gives the place of her ascending node, 2^•.14°.35′.38″,9.

FROM the middle of the Transit, as seen at the center of the earth, viz. 5^h.28′.29″,7 apparent time, deduct the semidura­tion between the internal contacts, viz. 2^h.52′.58″,7, and there remains 2^h.35′.31″ the apparent time of the first inter­nal contact, without parallax. This I observed at 2^h.31′.26″ apparent time; the difference between these is the total effect of parallax in longitude and latitude, which is 4′.5″. But upon the supposition that the Sun's horizontal parallax, on the day of the Transit was 8″,5204, the total effect of parallax should have been 4′.4″. Therefore say,

As 4′. ″4.=244″ ∶ 4″.5″=245″ ∷ 8″,5204 ∶ 8″,555=the hor. par. of the Sun on June 3d, 1769. Then

As 100000=his mean dist. from the earth ∶ 101506=his dist. on the day of the Transit, ∷ 8″,555 ∶ 8″,6838 his hori­zontal parallax at his mean distance from the earth.

THIS is nearly the same, with what is deduced from the best of the Observations made on the Transit of 1761: And ac­cording to this parallax of the Sun, the mean distances of the planets from the Sun will be, as they are exhibited in the fol­lowing table, taking a mean semidiameter of the earth 3985 English miles.

[Page 63] ON account of the difficulty of ascertaining the precise mo­ment of the middle of the Transit, from the mensurations of the nearest distances of the limbs of the Sun and Venus, and the small difference of time between the contacts happening, at the center of the earth, and at any particular place on its surface; Astronomers have generally preferred the comparison of two Observations at proper places, where the effects of parallax will be contrary to each other, retarding the contacts at one place and accelerating them at the other, for the purpose of deducing the parallax and distance of the Sun from them. We have an opportunity of confirming the former conclusions, by com­paring our Observations with those that have been made at the Royal Observatory at Greenwich, as they have lately come to hand. They differ indeed considerably among themselves, pro­bably owing to the various methods, which the Observers took to judge of the contacts, the account of which is not yet ar­rived here; yet they give a mean parrallax of the Sun nearly the same that we have deduced from our own Observations at Philadelphia. I have therefore inserted them in this account of the Transit, as they serve to shew that we have not lost our la­bour and expence on this occasion. The method I have used is first to reduce the Greenwich Observations of the contacts to the meridian of our Observatory in Philadelphia, by deducting from them the difference of longitude converted into time; and then to calculate the effect of parallax for both places at the apparent times of the contacts, upon the supposition of the Sun's horizontal parallax being 8″,5204 on the day of the Tran­sit. From this, the Sun's horizontal parallax is found either greater or less, as the calculated effect of parallax is greater or less, than what is observed.

THE parallax of Venus in longitude at Greenwich, at the time of the first external contact was 16″,9, which hastened the contact there 4′.16″,5, and her parallax in lat. at the same time was, 12″,97, which depressed her on the disc of the Sun, lengthened her visible path, and accelerated the contact 2′.34″,5, so that the total effect of her parallax was to hasten the contact 6′.51″ of time. In like manner her parallax in longitude at the internal contact was 16″,6, which hastened [Page 64] it 4′.12″ of time; and her parallax in latitude being 13″,42 at that time, for the same reason hastened the said contact 2′.40″; and therefore the total effect of parallax to accelerate the inter­nal contact at Greenwich is 6′.52″.

AT Philadelphia her parallax in longitude being 10″,74 at the external contact, hastened it 2′.43″; and her parallax in latitude being 4″,43, lengthened her visible path on the Sun and hastened the contact 53″ of time; whence its total effect was 3′.36″ of time. In like manner her parallax in longitude at the internal contact being 11″,95 hastened it 3′.1″ of time, and her parallax in lat. being 4″,49 lengthened the transit line, and hastened the contact 1′.3″; and therefore the total effect of her parallax at that time to hasten the internal contact was 4′.4″.

Now as the total effect of parallax both at Greenwich and at Philadelphia conspired to hasten the contacts at both these places, with respect to the center of the earth, their difference is the whole effect they have on absolute time, viz. 3′.15″ at the external contact, and 2′.48″ at the internal contact.

THE contacts were observed at Greenw. at the apparent times mentioned in the following table, according to their meridian.

THESE times are reduced to the meridian of Philadelphia, by substracting 5^h;.0′.35″ from them in the following manner.

[Page 65] THE mean of all the times of the external contacts at Philadelphia is 2^h.13′.46″,6, and of the internal contacts 2^h.31′.28″, as appears by pag. 51, and the difference be­tween these means is the observed effect of parallax.

the observed effects of parallax, at the ext. and int. contacts. Therefore say,

As 3′.15″=195″ the calculated effect of parallax at the ex­ternal contact is to 3′ ∶ 16″,6=196″,6 ∷ So is the assumed ho­rizontal parallax of the Sun on the day of the Transit 8″,5204 ∶ to his true parallax on that day. And in like manner, as 2′.48″=168″ ∶ 2′.47″,4=167″,4 ∷ 8″,5204: the Sun's par. on that day.

2.290,0346 2.225,3093
2.293,5835 2.223,7555
0.930,4600 0.930,4600
3.224,0435 3.154,2155
0.934,0089=8″,59031 ☉ hor par. 0.928,9062=8″,48997 ☉ hor. par.
8″,48997
2) 17″,08028
8″,54014 the mean hor. par. of ☉ on the day of the Transit.

As 100000 ∶ 101506 ∷ 8″,54014 ∶ the Sun's horizontal parallax at his mean distance from the earth.
5.000,0000
5.006,4917
0.931,4650
0.937,9567=8″,66875 the Sun's hor. par. at his mean distance from the earth.

THE parallax of the Sun being fixed by the mean of such comparisons as these, it is an easy matter to ascertain not only the distances of the bodies, which compose the solar system, but also their real diameters; that of the earth being previously known from the actual mensuration of some degrees on its surface. For

As the rectangle of the parallax of the Sun, and his distance from the earth, is to the real diameter of the earth; so is the rectangle of the parallax and distance of any other planet from the Sun, to its real diameter.