An account of the observation of Venus upon the sun, the third day of June, 1769, at Providence, in New-England. With some account of the use of those observations.
West, Benjamin, 1730-1813., Hopkins, Stephen, 1707-1785, dedicatee.
Page  [unnumbered]Page  [unnumbered]

AN ACCOUNT OF THE OBSERVATION OF VENUS Upon the SUN, The Third Day of June, 1769, AT PROVIDENCE, in New-England. With some Account of the Use of those Observations.

By BENJAMIN WEST.

The Course of Nature is the Art of GOD.

PROVIDENCE: Printed by JOHN CARTER, at Shakespear's Head.

M,DCC,LXIX.

Page  [unnumbered]

To the HONOURABLE Stephen Hopkins, ESQUIRE, Member of the PHILOSOPHICAL SOCIETY in the City of Philadelphia, and CHANCELLOR of the COLLEGE in the Colony of Rhode-Island.

SIR,

AS your Honour was pleased to ac|company, and assist us the whole time that we were preparing for the observation of the TRANSIT OF VE|NUS; and considering with what ala|crity our work went on, when encou|raged by your actuating genius; and that your Honour must be very sensi|ble of the great pains which were taken, in order that our work might be rendered as accurate as possible; I think myself bound in duty to publish the following account of our observa|tion under your patronage.—Much Page  [unnumbered] might be said with respect to your Ho|nour's superior abilities in mathematics and natural philosophy; but, without flattery, these are the least of your acquirements, when compared with your profound skill in civil police, and the wise government of a people.

Your Honour very well knows, that these observations of the Transit of Venus give the solution to a problem, that is not only curious in itself, but at once opens to our view, and gives us a deeper insight into the amazing works of God.—From these observa|tions we expect to discover the distance of the Earth, the Planets and Comets, from the Sun; and consequently their magnitudes and quantity of matter will be known, as also their proportion of light and heat.—These things being once known, Astronomers in future will be able, from the like observa|tions, to discover whether the Earth and Planets approach the Sun, or re|cede Page  [unnumbered] from him; and whether the Sun be diminished by its constant expence of light and heat. From a knowledge of all these things, methinks we shall have such a demonstration of the ex|istence of a GOD, who made and governs all things, that even the re|formed atheist must tremble when he reflects on his past conduct.—I am

Your Honour's most obedient, And most humble Servant, BENJAMIN WEST.

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VENUS upon the SUN.

THE TRANSIT OF VENUS OVER THE SUN'S DISK, the third day of June, 1769, did much engage the attention of the Astro|nomers in all the polite nations of Europe, not barely because it was a rare phaenomenon, but because the noblest problem in all the celestial science is thereby expected to be resolved; to wit, that of discovering the Sun's horizontal parallax.

Kepler *, when he had constructed his Rudolphine tables (upon the observations of Tycho Brahe, a Danish nobleman) soon saw that the planets Venus and Mercury, at their inferior conjunctions with the Sun, would sometimes appear to pass retrograde over his disk. From his tables he predicted two transits of Venus to happen, one in the year 1631, the other in 1761, in a book he published in 1629, intituled, "Advice to Astronomers." Kepler did not live to the year 1631. In 1639 a transit of Venus happen|ed, which, according to those tables, was to be in|visible, and that which he predicted to happen in 1631 was looked for at Paris, by Gassendus, but none was to be seen. All this was owing to the im|perfection of Kepler's numbers.

Page  2 When our English Astronomer, Mr. Jeremiah Horrox, came upon the stage, though a youth of but 20 years of age, yet his ingenuity and strength of reason were such, that he was able from his own observations to point out the errors in Kepler's ta|bles, and immediately set himself to work in mak|ing such other observations as enabled him greatly to correct Kepler's numbers. By these numbers, thus corrected, he predicted the before mentioned transit, which happened the 24th of November, 1639.—He expected the conjunction would be at 3 h. 57 m. P. M. with 10′ south latitude. He waited with eager desire for the moment to see his prediction ve|rified, and so extraordinary a phaenomenon as that of Venus on the Sun. The day arrived, and agree|able to his expectation he saw Venus wholly entered upon the Sun at 3 h. 15 m. P. M.—The place of his observation was at Hool, about 15 miles to the northward of Liverpool. Mr. William Crabtree, of Manchester (an Astronomer, and particular friend to Mr. Horrox) was also looking for the transit, and first saw it at 3 h. 35 m; the Sun being in a cloud was the reason that he did not see it sooner. By a comparison of their observations they were found to coincide very well. This ingenious friend to Astro|nomy (Mr. Horrox) died the third of January, 1640-1, at the age of 25 years.

He has taken his tow'ring flight aloft,
To mingle with his Stars.

It seems the grand discovery which was to be made from these transits, was not intended for Mr. Hor|rox, but was reserved for some future genius. Ac|cordingly we find a paper in the Philosophical Trans|actions, No. 348, wrote by the learned Doctor Page  3 Halley *, our late Royal Astronomer, upon this matter; wherein the Doctor shows, that by observa|tions made of Venus on the Sun, the distance of Page  4 the Sun from the earth may be found to the five hundredth part of the whole. I shall take the liber|ty in this place to quote some of the Doctor's own words (as we find them translated into English in the before mentioned transactions) upon this subject.

The Doctor, after a previous introduction, saith,

about 40 years ago, when I was at the island of St. Helena, where I was employed in observing the fixed stars which surround the South Pole, I had an opportunity of observing Mercury passing over the Sun's disk, which I did with the greatest dili|gence. I obtained most accurately, with an ex|cellent tube of 24 feet, the moment in which Page  5 Mercury, entering the Sun's limb, was seen to touch it within; and, in like manner, the moment in which, at going out, he touched the Sun's limb, making an angle of inward contact. Whence I was sure of the interval of time, in which the whole body of Mercury appeared at that time within the disk of the Sun, and that without the error of one second of time. For the thread of the solar light, intercepted between the obscure limb of the planet, and the bright limb of the Sun, slender as it was, appeared to strike the eye, and in striking the eye, the denticle made in the limb of the Sun by the entrance of Mercury vanished, as that made by his going out began as it were in a moment. When this was known, I was immediately assured, that the Sun's paral|lax might be truly determined from this kind of observations, if only Mercury being nearer the earth should have a greater parallax from the Sun. For this difference of parallaxes is so very small, that it is always less than that of the Sun which we enquire after. Wherefore Mercury, though often to be seen within the Sun, will not be thought very proper for this business.

There remains therefore the Transit of Venus over the Sun's disk; her parallax being almost four times as big as that of the Sun's, will make very sensible differences between the spaces of time in which Venus will be seen to pass over the Sun, in the different regions of our earth. Now from these differences, if observed after a due manner, I say the parallax of the Sun may be determined within a small part of a second.
In such observa|tions, the Doctor saith,
nothing more is necessary Page  6 than faithful observators, good telescopes, and common clocks, regulated to the revolutions of the heavens, and that the times be reckoned from the total ingress of Venus within the Sun's disk, to the beginning of its egress from the same; that is, when first the opaque globe of Ve|nus begins to reach the lucid limb of the Sun; which moments, as I know by my own experi|ence, may be obtained to a second of time.

The Doctor then proceeds to mention the transit of 1761, and to make some curious calculations thereon; represents it as a suitable opportunity for the before mentioned observations; and being fully con|vinced of the certainty of this method of discover|ing the parallax of the Sun, seriously recommend|ed it to the Astronomers that should be then living, with all the power and elocution of an orator, not to slip so favourable an opportunity of promoting the science of Astronomy; wishing them all possi|ble success, and that the magnitudes of the celestial orbs being then determined within more exact li|mits, may reward them with perpetual fame and glory.

The Doctor's credit was too great in the astro|nomic world, not to be taken proper notice of; and as this learned piece of his was wrote many years before the transit of 1761, and the Astrono|mers since his day having had time to fully weigh and consider the matter, found his reasoning too cogent to let pass, without due notice, what he had so earnestly urged upon them.

In consequence of which we find, at the approach of the transit of 1761, the Astronomers of almost every civilized nation in Europe, emulously enga|ged Page  7 in this affair, of so much importance to science, His late Majesty, King George the second, and the French King, though in the midst of a vehement war, yet (from a sense of the utility of those ob|servations) found time to consider of the matter, and each contributed largely towards carrying so noble a design into execution;

neither was the Empress of Russia inactive on this singular occa|sion.

In England, it was observed at Greenwich by the Rev. Dr. Bliss, the then Royal Astronomer; at Sa|vile-House, in London, by the late Mr. Short, in presence of their Royal Highnesses the Duke of York, Prince William, and Prince Henry. Mes|sieurs Ellicott and Dollond observed it at Hacney; and Mr. Canton at Spital-Square, London. It was likewise observed at Leskeard, in Cornwall, by the Rev. Mr. Richard Haydon. Abroad it was ob|served at Paris, in France, by Mr. De la Lande; and by Mr. Ferner, at Conflans. It was observed at Torneo, in Lapland, almost under the arctic circle, by Mr. Hellant; and this was the farthest north that observation was made. At Stockholm, the capital of Sweden, it was observed by Mr. War|gentin; and at Harnosend, in Sweden, by Mr. Gi|ster. In Asia observation was made at Tobolsk, the capital of Siberia, by Mr. Chapp, a French Astronomer, sent thither at the request of the Aca|demy of Sciences at Petersburgh, and under the protection of the Czarina. At Madrass, or Fort St. George, in the East-Indies, it was observed by the Rev. Mr. Hirst, under direction of the East-India Company of London. Observation was also made at Calcutta, near the mouth of the Page  8 Ganges, by Mr. William Magee; this was the far|thest east. It was observed at the Cape of Good Hope, by Mr. Mason; and would have been ob|served at St. Helena (had not the intervention of clouds prevented) by Astronomers sent to those pla|ces, at the expence of his Majesty King George the second. It was observed nowhere farther south than at the Cape of Good-Hope. In America, it was only observed at St. John's, in Newfoundland, by JOHN WINTHROP, Esq F. R. S. at the expence of the Massachusetts colony; and this was the far|thest west.

These, and many more observations, to the num|ber of forty odd, being collected, were submitted to Mr. Short, F. R. S. who duly examined them, and with incredible assiduity and labour solved the difficult problem; and found the Sun's parallax, on the day of the transit, to be 8″, 55; the Sun being then nearly at his greatest distance from the earth. The parallax being always in a reciprocal proportion to the distance of the Sun, it follows from thence that the parallax, when the Sun is at a mean distance, is 8″, 68 *.

Page  9 By this observation of Venus passing over the Sun, a certain principle in Astronomy was settled, which Dr. Halley, from certain observations, sus|pected did obtain in the planetary system, which is, that the nodes in the primary planets have a slow motion in antecedentia, or contrary to the order of the signs. From whence Astronomers were ascer|tained that Venus would again transit the Sun's disk the third day of June, 1769. I say ascertained, because, according to the old hypothesis of the im|mobility of the nodes, it was doubtful; and by Dr. Halley's calculations * upon that hypothesis, the center of Venus, as she passed by the Sun, would appear to be in contact with its north limb. The Doctor said, if at the transit in 1761 the nodes should be found to go backwards, then it might be expected, that at the transit in 1769, the body of Venus would appear wholly within the orb of the Sun; and would afford a much better opportunity for investigating the Sun's parallax.—What diffi|culties in science are too great to be surmounted, when pursued by men of interest and understand|ing!

And now that nothing might be wanting to ren|der the observations of this transit as perfect as pos|sible, we hear that ample preparations were season|ably made, and skilful Mathematicians dispersed into those distant regions of the earth, to make observa|tion, where the transit was attended with the most favourable circumstances. So that whatever was wanting to render the observations in 1761 com|pleat, was now to be fully supplied. We are in|formed Page  10 that several observators were sent into the South Seas, by the Royal Society in London, in order to get an observation where the whole duration of the transit was shortest; and that the Empress of Russia sent several companies into those parts of her empire, where the visible duration was of the great|est length. The King of France did likewise send observers into foreign parts; but as yet we know not to what particular places.

It remains now to give an account of the prepa|rations that were made in PROVIDENCE, for the observation of this transit. In doing of which I shall be as particular as possible, that the reader may the better judge of the merit of our work.

When it became more generally known that there would be a Transit of Venus in 1769, and the advantages which were like to accrue to Astronomy, and consequently to Navigation and Chronology, from proper observations of it, Mr. JOSEPH BROWN, *, a very respectable merchant of Pro|vidence, Page  11 being very desirous, if possible, to obtain an observation of it, was pleased to advise with me, concerning an apparatus suitable for such an ob|servation, and to know if we should be able to observe the transit with the necessary precision for answering the important design?

As the proposal was new, and unexpected, my an|swer was not direct; as it required some time to consi|der of it. At length I gave him my opinion concern|ing an apparatus proper for such an occasion; and that I thought we could observe the transit with that accuracy as would render it worthy of notice, provi|ded we could have such an apparatus as was de|scribed. My answer gave him so much satisfaction in the matter, that he immediately sent his orders to his correspondent in London, to procure the in|struments; his orders were accordingly executed with fidelity and dispatch; they arrived in Providence about one month before the transit.—Our apparatus was made by Messieurs WATKINS and SMITH, Lon|don; it consisted of a three feet reflecting telescope, with horizontal and vertical wires for taking dif|ferences of altitudes and azimuths, adjusted with spirit-levels at right angles, and a divided arch for taking altitudes; a curious helioscope, together with a micrometer of a new and elegant construction, with rack motions, and fitted to the telescope.—Such a noble disposition in Mr. BROWN for promo|ting useful knowledge, certainly merits the applause of the public; and, in justice to him, I must ac|knowledge, our work could not have been done with equal accuracy, had it not been for his skill and contrivance therein.—Besides the before mentioned instruments, we had a sextant belonging to the go|vernment, Page  12 made in Newport, by Mr. BENJAMIN KING, under the direction of JOSEPH HARRISON, Esq now Collector of his Majesty's Customs for the port of Boston; its limb was divided to five miles, and by a vernier index to five seconds *.—We had two good clocks, one of which was made in Providence, by Mr. EDWARD SPALDING.

We had nothing to learn respecting the appara|tus, excepting our new catadioptric micrometer, which, I have lately learned, is of DOLLOND'S con|struction; not having any author by us, from which we could get the use of that curious instrument, we were obliged to have recourse to experiments.—When the micrometer was fixed upon the telescope, it was found by trial, that objects could not be seen with the same focal distance as when it was off, but were obliged to screw up the small speculum nearer to the eye; for which there is an optical reason.—From whence it was concluded, that objects should always be observed in the most distinct point of view, the same with the micrometer on as when it was off. The next thing to be done was to find the apparent diameter of an object (or the angle subtended at the eye by two objects) by this instru|ment. In order to this, we stretched a cord, as straight as possible, one thousand feet in length; which was measured several times over, in order to Page  13 avoid mistake. At the end of the cord was set two circular objects, made of white paper, in a line perpendicular to the cord, and exactly ten feet apart; standing at the other end of the cord, and by opening the micrometer, we could bring the two images into an exact coincidence, or could make one of the images appear like two, and by bringing their limbs into contact, the distance of their centers was shewn on the scale, to the five hundredth part of an inch. Now from the rules of trigonometry, the angular distance of the two objects was 34′ 22″, 58; from thence it was known, how many inches and parts of an inch were answer|able to that angle. These experiments were repeat|ed every fair day (for no other was suitable for these observations) till we could many times going find the diameter of a body to a second of a degree.—From these observations we were enabled to make a table for the micrometer, as far as the scale ex|tended.—These experiments were carried yet far|ther, for, by looking at two bodies whose distance from each other was known, we could tell their di|stance from the place of observation, to a critical exactness; and this was proved by accurate men|suration. These were certainly very diverting ex|periments to an inquisitive mind!—The gentle|men who assisted us through these experiments, and likewise in the rest of our work, were the Honour|able STEPHEN HOPKINS, Esq Mr. MOSES BROWN, Dr. JABEZ BOWEN, A. M. JOSEPH NASH, Esq and Capt. JOHN BURROUGH.

The regulation of our clocks, being of the ut|most consequence in this affair, was what next com|manded our attention. In this part of the work, Page  14 we endeavoured to arrive at as great a degree of certainty as the nature of the case would admit.—Several workmen, who were equal to the under|taking, were employed in laying a platform, of seasoned pine plank, as smooth and level as art could make it: This was secured from rain, or other moisture, that it might not warp when ex|posed to the Sun. We examined this platform three times a day (when the weather would admit of it) with a very long level, made for that purpose, in order to keep its position from altering. On the south side of the platform, and exactly perpendi|cular to it, we erected a stile ten feet high; this was likewise examined three times a day. We next per|forated a piece of board, into which was fixed the glass of a scioptic ball, so that the center of the glass was exactly in the center of the perforation; this board was so cut, and let in at the top of the stile, that it turned upon an axis, in such a manner, that the center of the glass did not alter its position. The Sun's rays were transmitted through the lens upon the platform, where they were formed into a bright spot, and very distinctly defined. From the center of the lens was let fall a perpendicular upon the platform; from that point, as a center, was drawn a great number of concentric circles, for taking correspondent shades, in order to trace a me|ridian line; and, as our wishes would have it, the weather proved favourable for this work. When the line was drawn *, I found, from calculation, it Page  15 reclined 3″ in time, east of the true meridian; this error arose from the increase of the Sun's declina|tion, between the times of forenoon and afternoon shades; this small equation of 3″ was allowed for in regulating the clocks.

As we were willing to have every corroborating circumstance to prove our work, we made use of another method, which seems to be most approved of by all the celebrated Astronomers in Europe and America; this was the method of corresponding al|titudes of the Sun, forenoon and afternoon. The sextant and reflector were both employed in this bu|siness for several days preceding the transit (and the day following) in order to ascertain the going of the clocks. In the last method (as in that of corres|ponding shades) the equation of time, answerable to the increase of declination, ought by no means to be neglected. Through the whole process we conducted with the utmost caution, that no errors might escape our notice. We found, upon the whole, a surprizing agreement in these two methods of regulating clocks; they were seldom found to differ a single second.—In short, as truth was the point we aimed at, nothing was omitted by which it might be obtained.

Being in this readiness, the morning of the third of June was ushered in with that serenity the bu|siness of the day required; all was calm, and not a cloud to be seen. The gentlemen concerned in the business convened very early at the place of Page  16 observation, to see that every thing was in order; and at the sight of such a morning, the gladness of their hearts was visibly expressed, by a pleasant as|pect upon their countenance.

At noon we examined the going of the clocks, as the Sun passed the meridian, and found them very regular.

We began to look for the first contact of Venus with the Sun, at least 15 minutes before the time given by calculation, to get as early a sight of it as possible.—Venus was first perceived by making a dent upon the superior limb of the Sun at 2h. 29m. 43sec. P. M. apparent time. But, as it is likely the exterior contacts will be given different, by dif|ferent observators, they can be of but little conse|quence in this affair.—The greatest attention was given to the interior contact; this was at 2h. 46m. 35sec. apparent time *. From a mean of a number of good observations, the apparent diameter of the Sun was 31′ 40″, 66, and that of Venus 58″, 66; though I could not make it myself more than 58″, Page  17 which was the same we found it about a fortnight before the transit. The proportion of their dia|meters was nearly as 1 to 33. The nearest approach of their centers, at the middle of the transit, was taken with the micrometer, and found to be 10′ 5″.

The following TYPE will give the reader some idea of the appearance of Venus, at her several stages on the Sun.

[illustration]

In the figure, the circle Z E N C is the disk of the Sun, and S its center; the obscure line Z S N a vertical passing through the Sun's center; E S C Page  18 the ecliptic in its position at the middle of the tran|sit; A a M X the orb of Venus; A is Venus at her first contact; a the interior contact; M the middle of the transit; and X her place at sunsetting.

The proportion of the distances of the Sun and Venus from the earth, at that time, was as 3,5143 to 1; then (allowing the Sun's parallax to be the same it was found the 6th of June, 1761) the pa|rallax of Venus was 30″, 04; the difference of their parallaxes 21″, 49. The angle between the visible way of Venus and the ecliptic, 8° 34′ 17″; and the angle made by the axis of the ecliptic and equator, 7° 3′ 7″; their sum, 15° 37′ 24″, was the angle be|tween the axis of the visible way of Venus, and the earth's axis. The transit line, from total in|gress to the middle of the transit (measured in time by the visible motion of Venus) was 2h. 55′ 36″; but Venus was more accelerated in her orbit (by pa|rallax in longitude) at the middle of the transit, than at total ingress; this difference of acceleration was 1′ 33″; therefore from the total ingress to the middle of the transit was 2h. 54′ 3″.

Thence I conclude, that the

  h.  
* First contact was at 2 28 0 app. time.
Interior contact 2 46 35
Middle of the transit 5 40 38

Venus's parallax in longitude, at the middle of the transit, was 18″, 7; this was passed over by Ve|nus's visible motion in 4′ 44″; so that the middle Page  19 of the transit, as seen from the center of the earth, was at 5h. 43′ 8″ mean time. The true conjunction was 23′ 21″ before the middle of the transit, as seen from the earth's center; consequently the true conjunction was at 5h. 19′ 45″, mean time. At which time, the place of the Sun and planet was 11 13° 27′ 3″; and the geocentric latitude of Venus 10′ 19″, 8 north. But her heliocentric latitude was 4′ 6″, 51; and by the rules of spherical trigonometry, the ascending node of Venus was 1° 9′ 23″, 5 in consequence of the Sun, or in 11 14° 36′ 26″, 5.

From the foregoing calculation it appears, that the mean motion of Venus is 37″ forward of what it stands in Dr. HALLEY'S tables, and her ascending node 2′ 41″.

It is probable Dr. HALLEY'S solar numbers need some correction likewise; the following may not be far from truth, viz. add to Dr. HALLEY'S mean motion of the Sun, for any year of the Christian aera, 25″, and to the apogee 6′ 18″; for each cen|tury after 1700 add 14″, 666 to the mean motion, and to the apogee 3′ 53″; then by making use of the Parisian * equation of the Sun's center, his place may be had within a small matter of truth.

By taking the mean of a number of observations, the latitude of our observatory was found to be 41° 50′ 41″ north *. The longitude was obtained by Page  20 observing the emersions of Jupiter's satellites, com|pared with the corresponding observations made at Cambridge, in New-England, by Mr. WINTHROP, which he was so kind as to favour us with; and for which we return him our sincere thanks.—Provi|dence was found to be 16′ in longitude west from Cambridge; Mr. WINTHROP has hitherto found the longitude of Cambridge to be 71° 0′ west from the Royal Observatory at Greenwich; so that the longitude of Providence is about 71° 16′ from the Royal Observatory.

It is to be hoped the Commissioners, sent abroad to observe that interesting phaenomenon, were fa|voured with a suitable air for that purpose, as there will not be another opportunity, for making the like observations of Venus, for more than a century to come. The next transit of Venus will be in the month of December, in the year 1874, at the as|cending node; and that will be succeeded by ano|ther, at the same node, in 8 years after it; then there will pass 122 years without a transit, which will bring it to the year 2004, in the month of June.

I shall now give the reader a short account of the parallax herein mentioned, and how the planets are affected thereby.

The horizontal parallax of the Sun is that angle at the Sun's center, which is included between two lines supposed to be drawn, one from the Sun's cen|ter to the center of the earth, the other from the Page  21 Sun's center to the surface of the earth. Or, in other words, it is the angle, under which the semi|diameter of the earth would appear to an eye, at the center of the Sun.—The way that parallax af|fects the Sun and Planets is, it makes them appear below their true places in the heavens, except they be in the zenith of the observer; in that case, pa|rallax has no effect at all; and the reason is, because the observer is in that right line which joins the cen|ters of the earth and planet. Parallax may affect the planets places several ways; as if the observer should view the planet upon a vertical, cutting the ecliptic at right angles; in this case, parallax will affect its place in respect to latitude only; but if the observer be situated in the plane of the ecliptic, it will then alter its place, in respect to longitude on|ly; and if the planet be viewed in an oblique po|sition, with respect to the ecliptic, parallax will affect its place both in longitude and latitude.—The horizontal parallaxes of the planets are to each other in a reciprocal proportion to their distances; that is, the planets which are nearest have the great|est parallax, and those which are most remote, the least.—Thence it follows, if two planets are view|ed together, that which is nearest will appear just so much below the other, as what the difference of their parallaxes is.—The nearer a planet is to the horizon of the observer, the greater is its parallax, and in the horizon it is the greatest possible; and is then called the horizontal parallax.

Hence comes the method of investigating the Sun's parallax, from observations of Venus on his disk. At the time of the transit, the third day of June, Venus was much nearer to the earth than the Sun was, and, of consequence, was much more af|fected Page  22 by parallax.—This effect was produced in a two-fold manner, in respect to us in the northern regions of our earth.—First, Venus was depressed upon the Sun, by parallax in longitude, bringing her to a conjunction with the Sun sooner to our point of view, than to a spectator at the center of the Earth; in the second place, she was carried nearer to the center of the Sun, by parallax in latitude, thereby lengthening the transit-line; both which effects conspired to accelerate the time of first interior contact. Now to an observer in Great-Britain, pa|rallax had a still greater effect, by what is said be|fore:—That is, some minutes passed after the con|tact was formed to the observer there, before it was seen by us.—Now the difference of longitude, be|tween the two places of observation, being accurate|ly known, the effect of parallax, between the two places, is likewise known; for the difference of lon|gitude, by these observations, while considerably less than the true difference.

The method of calculating the Sun's parallax, from these observations, is by trial; the parallax will be supposed of that quantity, which the observations found it in 1761; hence the total effect of parallax, at each place of observation, must be computed; and if it should be the same as given by observation, it will prove the assumption to be just; but if, by observa|tion, it should be greater or less than by calculation, the Sun's parallax will turn out to be greater or less in the same proportion.—When the Sun's parallax is known, the distance of the earth, and of all the pla|nets, from the Sun, will be known likewise.

FINIS.