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L. Obfervations on the Tranfit of Venus, June 6, 1761, at St. John's, Newfoundland. By the fame.

Mr. Winthorp appears to have taken every precaution in his power to render his observation useful to astronomers; but not being able to determine the longitude of his obfervatory, it cannot be depended upon. Mr. Short has however calculated the fun's parallax, from a comparison between Mr. Winthorp's Obfervation and that made at the Cape of Good Hope, and the refult is, 8", 25.

LII. A Demonftration of the second Rule in the Essay towards the Solution of a Problem in the Doctrine of Chances, published in the Philofophical Tranfactions, Vol. LIII. Communicated by the Rev. Richard Price, in a Letter to Mr. John Canton, M. A. F.R.S.

This demonftration being very long, and not capable of. abridgement, we must refer the Reader to the paper itself, which is extremely fubtile and curious, and cannot fail of pleafing those who are fond of fuch enquiries.

LIV. Extract of a Letter from Mr. John Horley, fourth Mate on board the Glatton East-India Ship, to the Rev. Mr. Nevil Mafkelyne, F. R. S. dated Batavia, Nov. 16th, 1763, giving an Account of his Obfervations at Sea, for finding out the Longitude by the Moon.

It appears from this ingenious navigator's account, that the method of finding the longitude at fea, by the moon, may be ufed to great advantage; and there is no reafon to doubt, but if thofe who have the care of fhips would affiduously apply themfelves to this useful ftudy, they would be able at all times to know the place of their fhip, and confequently to prevent the effects of thofe fatal mistakes that too often attend the common practice of navigation.

LVI. Some Remarks upon the Equation of Time, and the true Manner of computing it. By Nevil Mafkelyne, A. M. &c.

This is one of the most curious papers we ever remember to have seen on this fubject. The ingenious Author has here corrected two mistakes of that able mathematician Mr. Delalande, who has afferted, in the Connoiffance des Mouvements Celeftes, for the year 1760, That "to calculate exactly the difference between mean and true time (that is to fay the equation of time) at the inftant of apparent noon, the fum of the equation of the fun's centre, the difference between his longitude and right afcenfion, the lunar equation, the equation of Jupiter and Venus, and that of the preceffion of the equinoxes, with their proper figns, must be converted into mean folar time. He adds, that it was impoffible, before this time, to obtain the equation of

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time exactly; ift, because hitherto no account has been made of the four little equations, the fum of which may produce above three feconds of time; 2dly, because it has been the practice to convert the equation of the fun's centre, and the difference between his right afcenfion and longitude into time of the Primum Mobile, inftead of converting them into mean folar time, which, fays he, may produce an error of two feconds and a half; 3dly, because the equation of the fun's centre was not known exactly before, every minute of which aufwers to four feconds in the equation of time."

I readily agree with M. Delalande, that the equation of time could not be had fo exactly formerly as it may now, when we have a much more exact theory of the fun, and are lately made acquainted with new equations of his motion. I cannot, however, aflent to his pofition, that the equation of the equinoctial points is to be taken into this account, together with the other equations, fince this is not an inequality in the fun's motion, but arifes from a motion of the equator itself; yet of such a kind as cannot accelerate or retard the coming of the fun, or any ftar lying within the tropics, to the meridian, by above a quarter of a fecond of time. This will, perhaps, appear in a good measure plain, if it be confidered, that the diurnal motion of the earth round its axis is neither accelerated nor retarded by the action of the fun and moon in producing the preceffion of the equinoxes, and variations of the inclination of the earth's axis to the ecliptic. The effect of thefe actions is, that the terrestrial pole, each day, describes a small arc of a circle about the centre of the earth, in the plain of a celeftial meridian paffing through the fun or moon, or rather one between both; and, confequently, the equator of the earth has its motion in its own plane neither accelerated nor retarded, but obtains a new motion, whose axis is one of its own diameters. This is the true origin, as well of the minuter and periodical nutations, as of the regular and perpetual motion of the earth's axis about the pole of the ecliptic, obferved in all ages, on which the continual preceffion of the equinoxes depends.'

After giving a demonftration of what he has afferted, Mr. Mafkelyne proceeds to fhew the true manner of computing the equation of time from the fun's right afcenfion; and alfo how to calculate the equation of time, as affected by the nutation of the earth's axis.

But this, adds Mr. Mafkelyne, is not the only mistake in the computation of the equation of time in the Connoiffance des Mouvements Celeftes, tho' it may exceed one fecond of time. M. Delalande fays that the fum of the equation of the fun's centre, the difference between his longitude and right afcenfion, and the fum of the four little equations, must be converted into mean folar time, in order to find the equation of time; and adds, that no exact equation table could be had, before this time, for three

reafons,

reafons, one of which is, that it has always been the practice to convert the equation of the fun's centre and the difference be tween his longitude and right afcenfion into time of the Primum Mobile, instead of mean folar time, which, fays he, may produce an error of 2 feconds.

Now I must here freely own, that as I could not, without fome reluctance, and only from the fulleft proof, allow all the mathematicians and aftronomers, before this time, to have been mistaken in the manner of converting the quantities above-mentioned into time, so I can find no reason to conclude fo from what has been cited above: on the contrary, from a full confideration of the fubject, I apprehend the method hitherto used by the mathematicians to be juft, and that the author has himself fallen into an equal mistake with that of which he accuses them.

But, in order to fet this matter in a clearer light, it will be first neceffary to confider motion and time, relatively to each other; for, except this be done, it will be impoffible to underftand any thing precife from converting a certain number of mi-'. nutes and seconds into mean folar time, or time of the Primum Mobile.

There are three different kinds of time ufed by aftronomers, fidereal time, apparent folar time, and mean folar time. The interval between the tranfit of the first of Aries across the meridian one day, and its return to it the next day, is called a side- ́ real day, which is divided into 24 equal parts or hours, and the hours into minutes, &c. This time is fhewn by a clock regulated to agree with the tranfit of the ftars across the meridian. The interval between the tranfit of the fun acrofs the meridian one day, and his tranfit the next day, is called an apparent folar day, which is divided into hours, minutes, &c. of apparent time. The folar day, it is manifeft, and its hours, minutes, &c. are of different lengths, at different times of the year: on account of which inequality, a good clock, which keeps equal time, cannot long agree with the fun's motion, which is unequal. Therefore, aftronomers have devised an imaginary time, called mean folar time; which is what would be pointed out by the fun, if his motion in right afcenfion from day to day was uniform, or, in other words, it is what would be pointed out by a fictitious fun or planet fuppofed to move uniformly in the equator, with a motion equal to the mean motion of the fun in longitude, its diftance from the first point of Aries (meaning hereby the mean equinox) being always equal to the mean longitude of the fun and as apparent noon is the inftant of the true fun's com-.. ing to the meridian, fo mean noon is the inftant at which this fictitious planet would come to the meridian. The interval between its coming to the meridian on any two fucceffive days is a mean folar day, which is divided into hours, minutes, &c." of

of mean folar time; all which it is manifeft will preferve the fame length at all times of the year.

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The equation of time, at the inftant of apparent noon, or of the fun's paffing the meridian, being equal to the difference between mean time and 12 hours, is alfo equal to the interval between the mean and true fun's paffing the meridian expreffed in mean folar time: to find which, we have the distance of the mean fun from the meridian, at the inftant of apparent noon, equal to the difference between the fun's apparent and mean. right afcenfion (both reckoned either from the mean or apparent equinox) which may be called the equation of right ascension. The queftion, therefore, comes to this, How many minutes. and feconds of mean folar time doth the mean fun take to move this diftance up to or from the meridian? Aftronomers hitherto have allowed i minute of time to every 15 minutes of right afcenfion, and fo in proportion; and, I apprehend, juftly too; for does not the mean fun, in returning to the meridian, describe 360° about the pole in 24 hours of mean folar time? whence it is plain, that his departure from the meridian is at the rate of 15° to 1 hour, and 15 to one minute of mean folar time. Therefore aftronomers have not converted the equation of right afcenfion into time according to the motion of the Primum Mobile; for, the equation of time being mean folar time, and the motion of the Primum Mobile being compleated in 23 H. 56 M. 4 S. of mean folar time, therefore 15 motion of the Primum Mobile does not answer to 1 hour of mean folar time (though it does to 1 hour of fidereal time) but to the 24th part of 23 H. 56 M. 4 S. or 59 M. 50% S. And it appears, that the equation of time in the Connoiffance des Mouvements Celeftes has been computed in this manner, and the table in the 79th page of the Connoiffance for 1761 has been made ufe of, entitled, "A table to convert into degrees the time of a clock regulated according to the mean motion of the fun." The degrees of this table are evidently degrees of the Primum Mobile, I hour of mean f lar time giving 15° 2′ 27,8", which answers to the motion of the ftars from the meridian, but not to the mean motion of the fun from thence, which is 15° to 1 hour of mean folar time: whence it appears, that this writer hath evidently fell into the mistake of taking motion or space of the . Primum Mobile, instead of the mean motion of the fun from the meridian; an equal mistake to that of which he erroneously fuppofes former mathematicians to have been guilty, in computing the equation of time. So that the equation of time in this ephemeris, befides the miftake arifing from the taking in the equation of the equinoctial points into the account, is conftantly too fmall in the proportion of 24 hours to 23 H. 56 M. 4 S. or of 366 to 365, or too fmall by 1 fecond upon every 6

minutes

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minutes of the equation of time: and the mistake of 2 feconds, which was fuppofed to be found in the old manner of reducing the equation of right afcenfion into time, really takes place in this new method; which, added to 1 fecond of time, arifing from the mistake in taking the preceffion of the equinoxes into the account, produces 3 feconds, an error which, I apprehend, the aftronomical equation tables ufed fince Mr. Flamftead's time have but rarely exceeded.'

LVII. Aftronomical Obfervations made at the Ifland of St. Helena. By the fame.

LIX. Aftronomical Obfervations made at the Ifland of Barbadoes; at Willoughby Fort; and at the Obfervatory on ConstitutionHill, both adjoining to Bridge-Town. By the fame.

Both these are very ufeful papers, containing a great number of very accurate aftronomical obfervations; but are, from their very nature, incapable of abridgement.

There are, likewife, in this publication, three articles relating to literary antiquities, viz. No.s 16, 22, and 60. The first of thefe contains obfervations on two Etrufcan coins, never before illuftrated.'-By the Rev. John Swinton, B. D. &c. The fecond confifts of remarks on the firft part of Abbé Barthelemy's Memoir on the Phoenician Letters, relative to a Phoenician infcription in the lfle of Malta. By the fame. By the fame. And the third, from the fame hand, contains alfo remarks on the faid Abbé's Reflections on certain Phoenician Monuments, and the Alphabet refulting from them.-But it is time to conclude this article.

B.

MONTHLY CATALOGUE, For MARC H, 1766. MISCELLANEOUS.

Art. 7. An Efay on Luxury. Written originally in French, by Mr. Pinto*. 12mo. 1 s. 6d. Becket.

HE Author of this fuperficial performance, though apparently a man of fenfe and obfervation, treats his fubject in fo vague and defultory a manner, with fo little accuracy and precifion, that (if we may judge from our own experience) the difcerning reader will have very little pleasure in the perufal of his effay.

He fets out with the following definition of Luxury :-Luxury, fays he, is the ufe which we make of riches and of industry, in order to procure an agreeable existence.- Now, as the idea of what renders ex

A merchant of confiderable character in Holland.

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