A N

A C C O U N X"

OF THE

OBSERVATION

OF

V E N U S

Upon the

S U N,

The Third Day of yune> 1769*

A T

1

Providence, in New-England.

With fome Account of the Ufe of thofe Obfervations.

By BENJAMIN WEST,

The Courfe of ifo/ar* is the Art of G O D.

PROVIDENCE:

Printed by John Carter, at Shakefpear\ Head) M,DCC,LXIX.

To the Honouraeli

Stephen Hopkins,

E S E, Member of the Philosophical Society

in the City of Philadelphia, and Chancellor of the College in the Colony of Rhode-JJIand.

SIR*

AS your Honour was pleafed to ae- company, and affift us the whole time that we were preparing for the obfervation of the Transit of Ve- nus; and confidering with what ala- crity our work went on, when encou- raged by your a&uating genius ; and that your Honour muft be very fenii- ble of the great pains which were taken, in order that our work might be rendered as accurate as poffible ; I think myfelf bound in duty to publifh the following account of our obferva- tion under your patronage. — Much A z - inighfe

DEDICATION.

might be faid with refpecl: to your Ho- nour's fuperior abilities in mathematics and natural philofophy ; but, without flattery, thefe are the leaft of your acquirements, when compared with your profound fkill in civil police, and the wife government of a people.

Your Honour very well knows, that thefe obfervations of the Tranlit of Venus give the folution to a problem, that is not only curious in itfelf, but at once opens to our view, and gives us a deeper infight into the amazing works of God.— From thefe obferva- tions we expecl: to difcover the diftance of the Earth, the Planets and Comets, from the Sun ; and confequently their magnitudes and quantity of matter will be known, as alfo their proportion of light and heat. — Thefe things being once known, Aftronomers in future will be able, from the like obferva- tions, to difcover whether the Earth and Planets approach the Sun, or re-

rme* *zwmtt wwrr.w t it*taMMf

DEDICATION.

cede from him ; and whether the Sun be diminifhed by its conftant expence of light and heat. From a knowledge of all thefe things, methinks we mail have fuch a demonftration of the ex- iftence of a G O D, who made and governs all things, that even the re- formed atheift muft tremble when he refleds on his paft condud.— I am

Tour Honour s moft obedient \

And mofi humble Servant^

BENJAMIN WEST.

VENUS upon the SUN.

TH E Transit of Venus over the Sun's Disk, the third day of June, 1769, did much engage the attention of the Aftro- nomers in all the polite nations of Europe* not barely becaufe it was a rare phenomenon* but becaufe the nobleft problem in all the celeftial fcience is thereby expected to be refolved ; to wit, that o£ difcovering the Sun's horizontal parallax.

Kepler*, when he had conftructed his Rudolphine tables (upon the obfervations of Tycho Brahe, a Danifli nobleman) foon faw that the planets Venus and Mercury, at their inferior conjunctions with the Sun, would fometimes appear to pafs retrograde over hisdilk. From his tables he predicted two tranfits of Venus to happen, one in the year 1631, the other in 1 761, in a book he publilhed in 1629, intituled* Advice to Aftronomers." Kepler did not live to the year 1631. In 1639 a tranfit of Venus happen- ed, which, according to thofe tables, was to be in- vifible, and that which he predicted to happen in 1 63 1 was looked for at Paris, by Gaffendus, but none was to be feen. All this was owing to the im- perfection of Kepler's numbers.

When

* " Kepler was a native of Wittemburgh, in Germany;" he flourifhed in the beginning of the fixteenth century; was Ma- thematician and Allronomer to three Emperors ; was the full who difcovered the elliptic orbits of the planets, and that the fquares of their periodic times are as the cubes of their mean diftances from the Sun, and explained the general phenomena of folar eclipfes."

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When our Englim Aftronomer, Mr. Jeremiah Horrox, came upon the ftage, though a youth of but 20 years of age, yet his ingenuity and ftrength of reaibn were fueh, that he was able from his own obfervations to point out the errors in Kepler's ta- bles, and immediately let himfelf to work in makT ing luch other obfervations as enabled him greatly to correct Kepler's numbers. By thefe numbers, thus corrected, he predicted the before mentioned tranfit, which happened the 24th of November, 1639. — He expected the conjunction would be at 3 h. 57 m. P.M. with 10' fouth latitude. He waited with eager defire for the moment to fee his prediction ve- rified, and fo extraordinary a phenomenon as that of Venus on the Sun. The day arrived, and agree- able to his expectation he faw Ven'us wholly entered upon the Sun at 3 h. 1 5 m. P. M. — The place of his obfervation was at Hool, about 15 miles to the northward of Liverpool. Mr. William Crabtree, of Manchefter (an Aftronomer, and particular friend to Mr. Horrox) was alfo looking for the tranfit, and firft faw it at 3 h. 35 m ; the Sun being in a cloud was the reafon that he did not fee it fooner. By a comparifon of their obfervations they were found to coincide very well. This ingenious friend to Aftro- nomy (Mr. Horrox) died "the third of January, 1 640- 1, at the age of 25 years.

He has taken his tow* ring flight aloft,

To mingle'with his ftars.- •

It feems the grand difcovery which was to be made from thefe tranfits, was not intended for Mr. Hor- rox, but was referved for fome future genius. Ac- cordingly we find a paper in the Philofophical Tranf- actions, No. 348, wrote by the learned Doctor

Halley,

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Halley*, our late Royal Aftronomer, upon this matter ; wherein the Doctor mows, that by obferva- tions made of Venus on the Sun, the diftance of

the

* " Dr. Halley was born tke 29th of November, 1656, in the parilh of St. Leonard, Shoredich. He had an uncommon (kill in plane and fpherical trigonometry, and all the various parts of mathematics, before he was 17 years of age. — At 19 he publifhecl a geometrical method of finding the apheiia and eccentricity of the planets ; the want of which before was an op- probrium to Kepler's hypochefis. — He difcovered the time in which the Sun revolves on its axis by its maculae. He was au- thor of the geometrical method of con It rutting folar eclipfes, by which the parallactic method was fuperfeded. In the year 1676 (at zo years of age) he was fent at the coft of the governmenC to St. Helena, in the South Seas, with letters of recommenda- tion from King Charles the 2d to the Eaft-India Company, to make obfervations of the fixed ftars about the South Pole.— In 1678 he was made Mafter of Arts, and chofen a Fellow of the Royal Society. — In 168-+, from obfervation, he thought the forces of the planets towards the fun decreafed as the fquares of their diftances inverfely ; but not being able to demonftrate it, he applied to Mr. NEWTON, at Cambridge, who gave hint ample demonftration of the truth of what he fufpefted. About this time he fhewed a method of finding the elevation of moun- tains, fteeples, &c. by the barometer.— In 1686 he explained why the water in the Mediterranean Sea never rifes any higher, although the current is continually fetting in at the Straights mouth, befides a large fupply of water from nine large rivers, and many fmall ones. The folution of this phzenomenon gave the fociety fo much fatisfadtion, that he received their orders to profecute the enquiries. — In 1699 ne ^et out on a voyag« in a (hip, of which he had the command, in order to make obferva- tions of the variation of the compafs ; and after traverfing the Atlantic Ocean into both hemifpheres, as far as the weather would admit him to go, and having touched at many coafts aRd iflands, he arrived at England in September, 1700; and from his obfervations he publifhed a general chart, ftiewing at one view the variation of the compafs in all thofe feas where the Eng- lish navigators were acquainted. — In 1703 he was appointed Savilian Proftffor of Geometry at Oxford, in room ef Dr. Wai- ts lit,

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the Sun from the earth may be found to the five hundredth part of the whole. I fhall take the liber- ty in this place to quote fome of the Doctor's own words (as we find them tranflated into Englifh in the before mentioned tranfaftions) upon this fubjeft.

The Doctor, after a previous introduction, faith, " about 40 years ago, when I was at the ifland of St. " Helena, where 1 was employed in obferving the " fixed liars which furround the South Pole, I had *c an opportunity of obferving Mercury pafiing over " the Sun's difk, which I did with the greateit dih- " gence. I obtained moft accurately, with an ex- " cellent tube of 24 feet, the moment in which

Mercury,

lis, deceafed, and had the degree of Dottc* of Laws conferred upon him by that univerfity.— In 1713 he was made Secretary to the Royal Society, in room of Sir Hans Sloan.— In 1717 he wrote the paper in which he (hewed the method of inveftigating the Sun's parallax by the Tranfn of Venus over the Sun's difk.

Upon the death of Mr. Flamilead, in 17 19, Dr. Halley was

appointed to fucceed him'by his Majefty King George the firft. —Queen Caroline honoured him with a vifit at the Royal Ob- fervatory, and being pleafed with the polite reception (he met with, and confidering he had formerly ferved the crown under commiffion of Captain of the Navy, (he obtained of his Maje- fty for him a grant of his half pay for that commi(Tion during his life.— In the fpace of nine years (half of one plenian period) he obferved the right afcention of the Moon, as (he patted the meridian, 1500 times, which was a greater number of obferva- tions than were made by Flamftead, Tycho Brahe, and Heve- lius, toge her. When the Emperor, Peter the Great, vifited England, upon difcourfing with Dr. Halley on Ship-Building, the Arts and Sciences, &c. he was fo well pleafed with the Doaor, that he made him one of his intimate friends during his flay in England.— The Do&or died the 14th of January, 174 1-2; and fince hi* death, in 1752, were publilhed his astronomical ta- bles, for computing the places of the Sun, Moon, Planets, and Comets : They were fupplied with precepts by Mr. Gael Mor- ris."

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¥ Mercury, entering the Sun's limb, was feen to touch ** it within and, in like manner, the moment in *' which, at going out, he touched the Sun's limb, *c making an angle of inward contact. Whence I

was fure of the interval of time, in which the " whole body of Mercury appeared at that time ** within the dilk of the Sun, and that without the <c error of one fecond of time. For the thread of *s the folar light, intercepted between .the obfeure " limb of the planet, and the bright limb of the « Sun, (lender as it was, appeared to ftrike the eye,

and in ftriking the eye, the denticle made in the M limb of the Sun by the entrance of Mercury M vaniflied, as that made by his going out began *' as it were in a moment. When this was known, f« 1 was immediately allured, that the Sun's paral-

* lax might be truly determined from this kind of " obfervations, if only Mercury being nearer the " earth mould have a greater parallax from the

* Sun. For this difference of parallaxes is fo very *' fmall, that k is always lefs than that of the Sun

which we enquire after. Wherefore Mercury, ** though often to be feen within the Sun, will not

be thought very proper for this bufmefs.

« There remains therefore the Tranfit of Venus ** over the Sun's difk ; her parallax being aim oft u four times as big as that of the Sun's, will make " very fenfible differences between the fpaces of time «• in which Venus will be feen to pafs over the Sun, " in the different regions of our earth. Now from *< thefe differences, if obferved after a due manner, «' I fay the parallax of the Sun may be determined w within a fmall part of a fecond." In fuch obferva- tions, the Do&or faith, " nothing more is nccefiary B 2 ' ihm

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" than faithful obfervators, good telefcopes, and " common clocks, regulated to the revolutions of *' the heavens, and that the times be reckoned " from the total ingrefs of Venus within the Sun's " difk, to the beginning of its egrefs from the " fame that is, when firft the opaque globe of Ve- u 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 fecond of time."

The ftoelor then proceeds to mention the tranfit of 1 761, and to make fome curious calculations thereon ; reprefents it as a fuitable opportunity for the before mentioned obfervations ; and being fully con- vinced of the certainty of this method of difcover- ing the parallax of the Sun, ferioufly recommend- ed it to the Aftronomers that mould be then living, with all the power and elocution of an orator, not to flip fo favourable an opportunity of promoting the fcience of Aftronomy ; wifhing them all pofli- ble fuccefs, and that the magnitudes of the celeftial 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 aftro- nomic world, not to be taken proper notice of; and as this learned piece of his was wrote many years before the tranfit of 1761, and the Aftrono- mers fince his day having had time to fully weigh and confider the matter, found his reafoning too cogent to let pafs, without due notice, what he had fo earneftly- urged upon them.

In confequence of which we find, at the approach of the tranfit of 17.61, the Aftronomers of almoft every civilized nation in Europe, emuloufly enga- " * gcd

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ged in this affair, of fo much importance to fcience. His late Majefty, King George the fecond, and the French King, though in the mid'ft of a vehement war, yet (from a fenfe of the utility of thole ob- fervations) found time to confider of the matter, and each contributed largely towards carrying fo noble a defign into execution " neither was the " Emprefs of Ruflia inactive on this lingular occa- sion."

In England, it was obferved at Greenwich by the Rev. Dr. Blifs, the then Royal Aftronomer; at Sa- vile-Houfe, in London, by the late Mr. Short, in pretence of their Royal Highneffes the Duke of York, Prince William, and Prince Henry. Mef- fieurs Ellicott and Dollond obferved it at Hacney ; and Mr. Canton at Spital-Square, London. It was likewife obferved at Lefkeard, in Cornwall, by the Rev. Mr. Richard Hay don. Abroad it was ob- ferved at Paris, in France, by Mr. De la Lande ; and by Mr. Ferner, at Conflans. It was obferved at Torneo, in Lapland, almoft under the arctic circle, by Mr. Hellant ; and this was the farther! north that obfervation was made. At Stockholm* the capital of Sweden, it was obferved by Mr. War- gentin ; and at Harnofend, in Sweden, by Mr. Gi- tter. In Afia obfervation was made at Tobolfk, the capital of Siberia, by Mr. Chapp, a French Aftronomer, fent thither at the requeft of the Aca- demy of Sciences at Peterfburgh, and under the protection of the Czarina. At Madrafs, or Fort St. George, in the Eaft-Indies, it was obferved by the Rev. Mr. Hirft, under direction of the Eaft-lndia, Company of London/ Obfervation was alfo made at Calcutta, near the mouth of the

Ganges,

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Ganges, by Mr. William Magee ; this was the far- theft eaft. It was obferved at the Cape of Good Hope, by Mr. Mafon ; and would have been ob- ferved at St. Helena (had not the intervention of clouds prevented) by Aftronomers fent to thofe pla- ces, at the expence of his Majefty King George the fecond. It was obferved nowhere farther fouth than at the Cape of Good-Kope. In America, it was only obferved at St. John's, in Newfoundland, by John Winthrop, Eiq; F. R. S. at the expence ©f the Maflac-hulects culony ; and this was the far- theft weft.

Thefe, and many more obfervations, to the num- ber of forty odd, being collected, were fubmitted to Mr. Short, F. R. S. who duly examined them, and with incredible afilcluity and labour folved the difficult problem ; and found the Sun's parallax, on the day of the tranfit, to be cv/,55; the Sun being then nearly at his greateft di^ancc irom the «arth. The parallax being always in a reciprocal proportion to the diftancc of the Sun, it follows from thence that the parallax, when the Sun is at a mean diftance, is S",68j-<. /

By

ft The horizontal parallax cf the Son being known, the ■diftance of the Sun from the canh is found by the following pro- portion.

As tang, of 8",68 5,6241119 is to j , o fo is radius tang. 45* io.coooooo

to 23763 femidiameters of the earth. ' 4,3758881 From the latefl meafurements, a mean femidiameter of the

earth is found to be 3957 miles. Then 23763 X 3957 ^940 50 191

miles the diftance of the Sun.

< $ 5

By this obfervation of Verrus paffing over the Sun, a certain principle in Aftronomy was fettled, which Dr. Halley, from certain obfervations, fuf- peeked did obtain in the planetary fyftem, which is, that the nodes in the primary planets have a flow motion in antecedentia, or contrary to the order of the figns. From whence Aftronomers were afcer- tained that Venus would again tranfit the Sun's dific the third day of June, 1769. I fay afcertaineel* becaufe, according to the old hypothefis of the ini- mobility of the nodes, it was doubtful ; and by Dr. Halley's calculations * upon that hypothefiSj, the center of Venus, as fhe paffed by the Sunv would appear to be in contact with its north limb. The Doctor faid, if at the tranfit in 1761 the nodes Ihould be found to go backwards, then it might be expected, that at the tranfit in 1769, the body of Venus would appear wholly within the orb of the Sun; and would afford a much better opportunity for inveftigating the Sun's parallax. — What dffi- culties in fcience are too great to be furmounted* when purfued by men of intereft and underftand- ing!

And now that nothing might be wanting to ren- der the obfervations of this tranfit as perfect as pof- fible, we hear that ample preparations were feaibn- ably made, and fkilful Mathematicians difperfed into thofe diftant regions of the earth, to make obferva- tion, where the tranfit was attended with the moft favourable circumftances. So that whatever was wanting to render the obfervations in 1761 corn- pleat, was now to be fully fupplied. We are in- formed

* Philo. Tranf. page 436, Lowthrop's Abridgment,

'"V '

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formed that fevcral obfervators were fent into thfc South Seas, by the Royal Society in London, in order to get an obfervation where the whole duration of the tranfit was fliorteft ; and that the Emprefs of Ruflla fent feveral companies into thole parts of" her empire, where the vifibie duration was of the great- efl: length. The King of France did likevvife fend obfervers into foreign parts j 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 obfervation of this tranfit. In doing of which I lhall be as particular as poffible, that the reader may the better judge of the merit of our work.

When it became more generally known that there would be a Tranfit of Venus in 1769, and the advantages which were like to accrue to Aftronomy, and coniequently, to Navigation and Chronology, from proper obfervations of it, Mr. JOSEPH BROWN*, a very refpecfable merchant of Pro- vidence,

* Mr. Brown is a gentleman of a folid, aflive genius, ftrong- ly turned to the fluuy of mechanics and natural philofophy, which has induced him to conftruft and furnitti himfelf with ai curious ard compleat an apparatus for eleclrical experiments* as any perhaps in America; and of which he well knows the ufe. — Reading Mr. Wi. throp's account of the tranfit in 1761, was what fu(l occafioned him to fend for a telefcope, fitted in the manner Mr. Wir.throp there defcribes; afterwards, taking no- tice of ihe application of the American Philofophical Society to the AfTembly of Penr.fylvania, for an apparatus for obferving the Tranfit of Venus, he found the orders he had fent were in- c^mpleat: He then advifed with the author, as mentioned, and thceupon ordered a micrometer to be added. — Mr. Brown's ex- pence, in this laudable undertaking, was little lefs than One Hundred Pounds (lerling, befides near a month's time of him- felf and fervsnts, in making the necelTary previous experiments and preparations.

vidence, being very defirous, if poflible, to obtaia an obfervation of it, was plcafecl to advife with me, concerning an apparatus fuitable for fuch an ob- fervation, and to know if we fhould be able to obferve the tranfit with the neceffary precifton for anfwering the important defign ?

As the propofal was new, and unexpected, my an- fwer was riot direct •, as it required fome time to consi- der of it. At length I gave Him my opinion concern- ing an apparatus proper for fuch an occafion •, and that I thought we could obferve the tranfit with that accuracy as would render it worthy of notice* provi- ded we could have fuch an apparatus as was de- fcribed. My anfwer gave him fo much fatisfaction in the matter, that he imrhediately fent his orders to his correfpondent in London, to procure the in- ftruments ; his orders were accordingly executed with fidelity and difpatchj they arrived in Providence about one mohth before the tranfit. — -Our apparatus was made by Mefiieurs Watkins and Smith, Lon- don it confided of a three feet reflecting telefcope, with horizontal and vertical wires for taking dif- ferences of altitudes and azimuths, adjufted with fpirit-lcvels at right angles, and a divided arch for taking altitudes; a curious heliofcope, together with a micrometer of a new and elegant conftruction, with rack motions, and fitted to the telefcope.— Such a noble difpofition in Mr. Brown for promo- ting ufeful knowledge, certainly merits the applatife of the public ; and, in juftice to him, I muft ac- knowledge, our work could not have been done with equal accuracy, had it not been for his (kill and contrivance therein. — Befides the before mentioned mftruments, we had a fextant belonging to the go- C vernmcntj

f i| )

vernment, made in Newport, by Mr. Benjamin Kmc, under the direction of Joseph Harrison, Efqv nowCoIleftor of his Maidty's Cuftoms for the port of Botton; ks limb was divided to rive miles, and by a vernier index to five feconds * —We had two o-0od Clocks, one of which was made in Providence? by Mr. Edward Spalding. * We had nothing to learn refpecTing the appara- tus, excepting our new catadioptric micrometer, which, I have lately learned, ds of Dollond's con- duction; not having, any author by us, from which, we could get the me .of that curious inurnment, we

were obliged to have recourfe to experiments. .

When the micrometer was fixed upon the telefcope it was found by trial, that obje&s could not be feen with the fame focal diftance as when it was off bir were obliged to fcrew up the fmall fpeculum nearer to the -eye; for which there is an optical reafon.— *rom whence it was concluded, that objects mould always be obferved in the mod diftind point of view, the fame with the micrometer on as when it was off. The next thing to be done was to find the apparent diameter of an objed (or the angle iubtended at the eye by two objects) by this inurn- ment. In order to this, we ftretched a cord, as Itraight as poffible, one thoufand feet in length • whicn was meafured feveral times over, in order to

avoid

Kedvjood, Efq; of Newport, who, in order that Newport and: Province m,ght both be fupplied with a ftxtant, for This fi„- gular occafion ^de.ed one made at his own coft, for the "ft of the Rev r.Dr STILES 1 am fenfible Mr. Redwood, for fo

Ste&S* &th0n> Wl11 the °< P«k

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avoid miftake. At the end of the cord was fet -twp circular objects, made of white paper, in a line perpendicular to the cord, and exactly ten feet apart; Handing 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 diftance of •their centers was fftewn on the fcale, to the .five hundredth part of an inch. " Now from the rules of trigonometry, the angular diftance of the two obje&s was 34.' 22^,58 ; from thence it was knowrt, Jiow many inches and parts of an inch were anfwer- able to that angle. Thefe experiments were repeat- ed every fair day (for no other was fuitable for thefe obfervations) till we could many times going find the diameter of a body to a fecond of a degree.-— From thefe obfervatiens we were enabled to make a table for the micrometer, as far as -the fcale ex- tended.—Thefe experiments were carried yet far- ther, for, by looking at two. bodies whofe diftance from each other was known, we could tell their di- ftance from the place of obfervation, to a critical exactnefs ; and this was proved by accurate men- iuration. Thefe were certainly very diverting ex- periments to an inquifitive mind!' The gentle- men who affifted us through thefe experiments, and likewife in the reft of pur work, were the Honour- able Stephen Hopkins, Efq; Mr. Moses. Brown, Dr. Jabez Bowen, A. M. Joseph Nash, Efqj and Capt. John Burrough.

The regulation of our clocks, being of the ut- moft confequence in this affair, was what next com- manded our attention. In this part of the work,

C 2' .jyg

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we endeavoured to arrive at as great a degree of certainty as the nature of the cafe would admit — Several workmen, who were equal to the under!

£flng^WCrC ^P1^ in tying a platform, of fcafoned pine plank, as fmooth and level as art cpuld make it: This was fecured from rain, or other moifture that it might not warp when ex- pofed 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 purpofe, in order to keep its pofition from altering. On the fouth fide of the platform, and exactly perpendi- cular to it, we erected a ftile ten feet high, this was likewife examined three times a day. We next per- forated a piece of board/into which was fixed the g afs of a fcioptic ball, fo that the center of the glafs was exadly in the center of the perforation, this board was fo cut, and let in at the top of the Ihle that it turned upon an axis, in fuch a manner, that the center of the glafs did not alter its pofition! The Sun s rays were tranfmitted through the lens upon the platform, where they were formed into a bright foot, and very diftinclly 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 correfpondent fhades, in order to trace a me- ridian line •, and, as our wifiies would have it the weather proved favourable for this work. When the line was drawn * I found, from calculation, it

recline^

line, was found to differ from it 6° ± weft ward. -That our ob?

forehand to the people (whofe curiofity was excited by the pre-

parautniV

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reclined %n in time, eaft of the true meridian; this error arofe from the increafe of the Sun's declina- tion, between the times of forenoon and afternoon (hades this fmall equation of %° was allowed for in regulating the clocks.

As we were willing to have every corroborating circumftance to prove our work, we made ufe of another method, which feems to be mod approved of by all the celebrated Aftronomers in Europe and America this was the method of correfponding al^ titudes of the Sun, forenoon and afternoon. The fextant and reflector were both employed in this bu- finefs for feveral days preceding the tranfit (and the day following) in order to afcertain the going of the clocks. In the laft method (as in that of corref- ponding fhades) the equation of time, anfwerable to the increafe of declination, Ought by no means to be neglected. Through the whole procefs we conducted with the utmoft caution, that no errors might efcape our notice. We found, upon the whole, a furprizing agreement in thefe two methods of regulating clocks •, they were feldom found to differ a fingle fecond. — In ftiort, as truth was the point we aimed at, nothing was omitted by which it might be obtained.

Being in this readinefs, the morning of the third of June was ufhered in with that ferenity the bu- finefs of the day required ; all was calm, and not a cloud to be feen. The gentlemen concerned in the bufinefs convened very early at the place of

obfervation,

parations) that on the day before the tranfit, when the Sun came on the meridian, a cannon would be fired, which being donet moft of the inhabitants marked meridian lines in their windows, or on their floors.

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pbfervation to fee that every thing was in order- and « the : fight of fed, a ^ £ ™fy

Pea uoon rhWaS V'f!bly eXprCired' ^ * 2 pea upon their countenance.

verj regular Palkd the mendia"> a"d them

■ We began to look for the firft contact of Venus With the Son, at ieaft ,5 minutes bef^e g.ven by calculation, to get as early a figh of ™ poffible.-Venus wa, firft perce.ved by maki „*" » limb of the Sun at aT^r,

43 fee P. M. apparent time. But, as it is likelv the exterior contacts will be given different, by d! Cerent obfervators, they can^be of but lite e confe-

SrnV^ affair-The g^teft attention w« given to the mter.or contact; this was at ah 46m

H ■ APPuT'n "me *' From a me*r of a number of good obiervations, the apparent diameter of the

u" Vi 3 1 40//'66' and that of Venus .though 1 could not make it myfelf more than gfy

which

flantaneous as [ d,d expert it would be, but/the bright cufts of die S«, as they .ncompafled Venus, were much nfore obt ff and there Wd to be a faint junclion of their Jimbs for at cart 4' ; the »o«ent , „ p.„urabral ligament broke, I pro«i Che time; at firft I fufpecled the tel.fcope was no adjuftJdTo t l^TT ; by looking at the folate" &c!

WaS conv'^^ ^ the contrary. During the time we fa" Ve »u. upon the bun, (he appeared to be Grounded by rfL ^ *>-ello*,fli .countenance; its width was about on^enth07tht

which was the fame we found it abont a fortnight feefore the tranfjt. The proportion of their dia- meters was nearly as i to 33. The neareft approach or their centers, at the middle of the tranfit, was taken with the micrometer, and found to be 10' 5* The following TYPE will give the reader fome idea of the appearance of Venus, at her feveral ttages on the Sun.

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»

the ecliptic in its pofition at the middle of the tran- fit •, A a M X the orb of Venus ; A is Venus at her firft contact; a the interior contact; M the middle of the tranfit ; and X her place at funfetting.

The proportion of the diftances of the Sun and Venus from the earth, at that time, was as Z">SlA.Z to i ; then (allowing the Sun's parallax to be the fame it was found the 6th of June, 1761) the pa- rallax of Venus was 30^,04 •, the difference of their parallaxes 2i//,49. The angle between the vifiblc way of Venus and the ecliptic, 8° 34' ij" and the angle made by the axis of the ecliptic and equator, 7" 3' 7^1 their fum, 150 37' 24^, was the angle be- tween the axis of the vifible way of Venus, and the earth's axis. The tranfit line, from total in- grefs to the middle of the tranfit (meafured in time by the vifible 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 tranfit, than at total ingrefs ; this difference of acceleration was 1' 33*5 therefore from the total ingrefs to the middle of the tranfit was 2h. 54' 3^.

Thence I conclude, that the

h. ' *

* Firft contact was at 2 28 o]

Interior contact 2 46 3 5 > app. time.

Middle of the tranfit 5 40 38 J Venus's parallax in longitude, at the middle of the tranfit, was 18^,7 •, this was paffed over by Ve- nus's vifible motion in 4' 44// ; fo that the middle

of

* When I calculated this tranfit, I fuppofed the longitude of Our place to be much lefs than we have fmce found it by obferva- tion. — By correcting that error, the error in calculation will ap- pear to be inconfiderable.

oT the tranfit, as feen from the center of the earth,1 was at 5 h. 43' 8^ mean time. The true conjunction, was 23' 21 7 before the middle of the tranfit, as feen from the earth's center ; confequently the true conjunction was at §h. 19' 45^, mean time. At which time, the place of the Sun and piahet was n 130 27' 3'y i and the geocentric latitude of Venus 10' 19^,8 north. But her heliocentric latitude was 4' 6,'/,5i j and by the rules of lpherical trigonometry, the afcending node of Venus was i° 9' 23^,5 in coniequencc of the Sun, or in n 140 36' 26^,5.

From the foregoing calculation it appears, that the mean motion of Venus is forward of what it ftands in Dr. Halley's tables, and her afcending node 2' 41''. ,-,

It is probable Dr. HaLley's folar numbers need fome correction likewife jj the following may hoc be far from truth, viz. add to Dr. Halle y's mean motion of the Sun.; for any year of the Chrift'iart sera,- i$f\ and to the apogee 6' i8/y ; for each cen- tury after 1700 add 1 4^,666 to the mean motion; and to the apogee 3' 53^ • then b'y making ufe of the Parifian * equation of the Sun's center, his place may be had within a fmall matter of truth.

By taking the mean of a number of obfer vatic;]? , the latitude of our obfervatory was found to be 41 0 50' 41^ north J. The longitude was obtained by D obferving

* According to the Parifian hypothefis, the eccentricity of the earth's orb is 1680 parts, of which the mean diftance of the earth from the Sun is 100,000.

X The latitude of the place being of great confequerce, and the fextant and ftile not giving it exactly alike, the perfeve- rinjg Mr. Brown contrived to make ufe of the micrometer ?s a lens, which he placed on his houfe, twenty-feven feet high, and exaftly perpendicular to a center on a horizontal platform be'icw* on which was drawn a meridian line; the San's image on this

platforrii

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pbfejrving the emerfions of Jupiter's fatcllitcs, com- mr;ed with the correfpoading obfervations made at Cimbridge, in New-England, by Mr. Winthrop, which he was fo kind as to favour us with ; and for which we return him our fincere thanks.— Provi- dence was found to be 16' in longitude weft from Cambridge; Mr. Winthrop has hitherto found the longitude of Cambridge to be 71 ° o' weft from tne Royal Obfervatory at Greenwich fo that the longitude of Providence is about 71 ° 16' from the Royal Obfervatory.

It is to be hoped the Commiffioners, fent abroad to obferye that interefting phenomenon, were fa- voured with a fuitable air for that purpole, as there will not be another opportunity, for making the like obfervations of Venus, for more than a century to come. The next tranfit of Venus will be in the month of December, in the year 1874, at the af- cending node > and that will be fucceeded by ano- ther, at the fame node, in 8 years after it • then there will pafs 122 years without a tranfit, which will bring it to the year 2004, in the month of June.

I mall now give the reader a fhort account of the parallax herein mentioned, and how the planets are affeftcd thereby.

The horizontal parallax of the Sun is that angle at the Sun's center, which is included between two lines fuppofed to be drawn, one from the Sun's cen- ter to the center of the earth, the other from the

Sun's

platform was feen to move very fenfibly.— By this the latiiude was finally determined. The SunV meridian altitude, being taken ior fey.cral days by this long Itilc, the latitudes thence found did not differ from each other more than 15 fccondi.— At the i»:ne tins was done, we had f«en no account that a glafs had been made u.c cf, as here defcrihed ; but fince this went to the prefs, we learn from Dr. Long> aftronomy, that he found the latitude cf Vambnd-e, in England, by the fame meihed.

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Sun's center to the furface of the earth. Or, in other words, it is the angle, under which the femi- 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 obferver in that cafe, pa- rallax has no effect at all 5 and the re,afon is, becaufe th* obferver is in that right line which joins the cen- ters of the earth and planet. Parallax may affect the planets places feveral ways as if the obferver mould view the planet upon a vertical, cutting the ecliptic at right angles •, in this cafe, parallax _ will affect its place in refpect to latitude only 5 but if the obferver be fituated in the plane of the ecliptic, it will then alter its place, in refpect to longitude on- ly I and if the planet be viewed in an oblique po- rtion, with refpect 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 diftances,; that is, the planets which are neareft have the great- eft parallax, and thofe which are mod remote, the lead. — Thence it follows, if two planets are view- ed together, that which is neareft will appear juft fo much below the other, as what the difference of their parallaxes is. — The nearer a planet is to the horizon of the obferver, the greater is its parallax, and in the horizon it is the greateft poffible and is then called the horizontal parallax.

Hence comes the method of inveftigating the Sun's parallax, from obfervations of Venus on his difk. At the time of the tranfit, the third day of June, Venus was much nearer to the earth than the Sun was, and, of confequence, was much more af- fected

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fefted by parallax.— This effed was produced in i two-fold manner, in refpeft to us in the northern regions of our earth.— Firft, Venus was depreffed upon the Sun, by parallax in longitude, bringing her to a conjunction with the Sun fooner to our point of view, than to a fpectator at the center of the earth ; in the fecond place, flic was carried nearer to the center of the Sun, by parallax in latitude, thereby lengthening the tranfit-line ; both which Bffe£s confpired to accelerate the time of firft interior contact. Now to an obferver in Great-Britain, pa- rallax had a ftill greater effect, by what is faid be- fore : — That is, fome minutes paffed after the con-x tad was formed to the obferver there before it was feen by us,.— Now the difference of longitude, be- tween the two places of obfervation, being accurate- ly known, the effect of parallax, between the two places, is hkewife known ; for the difference of lon- gitude, by thtfe obfervations, will be confiderably lefs than the true difference.

The metbro of calculating the Sun's parallax, from thefe obfervations, is by trial ; the parallax will be fuppoled of that quantity, which the obfervations found it in 1761 5 hence the total effect of parallax, at each place of obfervation, mult be computed ; and if it mould be the fame as given by obfervation, it will prove the affumptiaa to bejuft-, but if, by obferva- tion, it mould be greater or lefs than by calculation, the Sun's parallax will turn out to be greater or lefs in the fame proportion. — When the Sun's parallax is known, the diftance of the earth, and of all the pla- nets, from the Sun, wijl be known likewife.

FINIS.

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