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time exactly; ist, because hitherto no account has been made of the four little equations, the sum of which may produce above three seconds of time ; 2dly, because it has been the practice to convert the equation of the sun's centre, and the difference between his right ascension and longitude into time of the Primum Mobile, instead of converting them into mean solar time, which, says he, may produce an error of two seconds and a half; 3dly, because the equation of the sun's centre was not known exactly before, every minute of which answers to four seconds in the equation of time.”
• I readily agree with M. Delalande, that the equation of time could not be had so exactly formerly as it may now, when we have a much more exact theory of the sun, and are lately made acquainted with new equations of his motion. I cannot, however, aflent to his position, 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 sun's motion, but arises from a motion of the equator itself; yet of such a kind as cannot accelerate or retard the coming of the sun, or any star lying within the tropics, to the meridian, by above a quarter of a second of time. This will, perhaps, appear in a good measure plain, if it be considered, that the diurnal motion of the earth round its axis is neither accelerated nor retarded by the action of the sun and moon in producing the precession of the equinoxes, and variations of the inclination of the earth’s axis to the ecliptic. The effect of these 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 celestial meridian passing through the sun or moon, or rather one between both; and, consequently, 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, observed in all ages, on which the continual preceflion of the equinoxes depends.
After giving a demonstration of what he has afferted, Mr. Maskelyne proceeds to fhew the true manner of computing the equation of time from the sun's right afcenfion; and also how to calculate the equation of time, as affected by the nutation of the earth's axis.
• But this, adds Mr. Maskelyne, is not the only mistake in the computation of the equation of time in the Connoiffance des Mouvements Celeftes, tho'it may exceed one second of time. M. Delalande says that the sum of the equation of the sun's centre, the difference between his longitude and right afcenfion, and the sum of the four little equations, must be converted into mean solar time, in order to find the equation of time; and adds, that no exact equation table could be had, before this time, for three reasons, one of which is, that it has always been the practice to convert the equation of the sun's centre and the difference between his longitude and right ascension into time of the Primum Mobile, instead of mean lolar time, which, says he, may produce an error of 2 seconds.
Now I must here freely own, that as I could not, without some reluctance, and only from the fullest proof, allow all the mathematicians and astronomers, 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 so from what has been cited above: on the contrary, from a full confideration of the subject, I apprehend the method hitherto used by the mathematicians to be just, and that the author has himself fallen into an equal mistake with that of which he accuses them.
• But, in order to set this matter in a clearer light, it will be first necessary to consider motion and time, relatively to each other; for, except this be done, it will be impossible to understand any thing precise from converting a certain number of mi-'. nutes and seconds into mean solar time, or time of the Primum Mobile.
“There are three different kinds of time used by astronomers, fidereal time, apparent solar 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 sidereal day, which is divided into 24. equal parts or hours, and the hours into minutes, &c. This time is thewn by a clock regulated to agree with the transit of the stars across the meridian. The interval between the transit of the sun across the meridian one day, and his transit the next day, is called an apparent solar 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 sun's motion, which is unequal. Therefore, astronomers have devised an imaginary time, called mean solar time ; which is what would be pointed out by the sun, 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 supposed to move uniformly in the cquator, with a motion equal to the mean motion of the sun in longitude, its distance from the first point of Aries (meaning hereby the mean equinox) being always equal to the mean longitude of the sun: and as apparent noon is the instant of the true sun's coming to the meridian, so mean noon is the instant 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 solar day, which is divided into hours, minutes, &c.
of mean solar time ; all which it is manifest will preserve chę fame length at all times of the year.
The equation of time, at the instant of apparent noon, or of the fun's paffing the meridian, being equal to the difference between mean time and 12 hours, is also equal to the interval between the mean and true sun's pafling the meridian expressed in mean solar time: to find which, we have the distance of the mean sun from the meridian, at the instant of apparent noon, equal to the difference between the sun's apparent and mean right ascension (both reckoned either from the mean or apparent equinox) which may be called the equation of right ascension. The question, therefore, comes to this, How many minutes and seconds of mean solar time doth the mean sun take to move this distance up to or from the meridian? Astronomers bitherto have allowed i minute of time to every 15 minutes of right afçension, and fo in proportion; and, l' apprehend, juftly too ; for does not the mean sun, in returning to the meridian, describe 360° about the pole in 24 hours of mean solar time? whence it is plain, that his departure from the meridian is at the rate of 150 to 1 hour, and 15 to one minute of mean solar time. Therefore astronomers have not converted the equation of right ascension into time according to the motion of the Primum Mobile ; for, the equation of time being mean solar time, and the motion of the Primum Mobile being compleated in 23 H. 56 M. 4 S. of mean solar time, therefore 15 motion of the Primum Mobile does not answer to 1 hour of mean solar 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 Connoisance des Mouvements Celeftes has been computed in this manner, and the table in the 79th page of the Connoissance for 1761 has been made use of, entitled, “ A table to convert into degrees the time of a clock regulated according to the mean motion of the sun.” The degrees of this table are evidently degrees of the Primum Mobile, 1 hour of mean I lar time giving 150 2 27,8", which answers to the motion of the stars 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 sun from the meridian ; an equal mistake to that of which he erroneously supposes former mathematicians to have been guilty, in computing the equation of time. So that the equation of time in this ephemeris, besides the mistake arising from the taking in the equation of the equinoctial points into the account, is conftantly too small in the proportion of 24 hours to 23 H. 56 M. 4 S. or of 366 to 365, or too small by i second upon every 6
minutes of the equation of time: and the mistake of 2 seconds,
By the same.
at Willoughby Fort; and at the Observatory on Constitution-
Both these are very useful papers, containing a great number of very accurate astronomical observations; but are, from their very nature, incapable of abridgement.
There are, likewise, in this publication, three articles relating to literary antiquities, viz. Nos 16, 22, and 60. The first of these contains observations on two Etruscan coins, never before illustrated.'-By the Rev. John Swinton, B. D. &c. The second consists of remarks on the first part of Abbé Barthelemy's Memoir on the Phænician Letters, relative to a Phænician inscription in the Isle of Malta. By the same. And the third, from the same hand, contains also remarks on the said Abbé's Reflections on certain Phoenician Monuments, and the Alphabet resulting from them.-But it is time to conclude this article.
For MAR CH, 1766.
M I S C E L L A NE OU S.
I2mo. 1 s. 6 d. Becket.
man of sense and observation, treats his subject in so vague and desultory a manner, with so little accuracy and precision, that (if we may judge from our own experience) the discerning reader will have very little pleasure in the perusal of his essay,
He fets out with the following definition of Luxury :-Luxury, fays he, is the use which ue oake of riches and of industry, in order to procure an agreeable existence.- Now, as the idea of what renders ex
ilence agreeable.is very different in different persons, luxury, according to this definition, may be applied to very different and even opposite characters. The man, for inttance, who employs his riches in relieving the indigent, in aslifting the induftrious poor, in encouraging genias, and promoting schemes of public utility, may be denominated luxurious, though he is extremely temperate and frugal, and far from being expenfive in his table, equipage, dress, or furniture. Such characters, it must be acknowledged, are but rare; this is nothing, however, to our Author's definition, which, at first sight, appears to be extremely inac-, curate.
Luxury, indeed, may be considered either as innocent or vicious, and though it is difficult, perhaps impossible, to determine exactly where it ceases to be innocent and begins to be vicious, yet it is reasonably expected of every author who writes upon the subject, that he should avoid confusiou and ambiguity as much as possible, both for the benefit of his readers and his own reputation.
• Luxury, says Mr. Pinto, is excellive in all those occasions, when individuals sacrifice to their oftentation, to their convenience, to their fancy, their duty, and the interests of the public; nor are individuals led into this excess but by some desecis in the constitution of their country, or by some faults in the adminiftration. In this case, it does nog fignify whether the nations are rich or poor, civilized or barbarous : when the love of country, and the useful passions are not kept up among them, their manners will be depraved, and luxury will assume the character of the current manners.'
This affertion must appear strange to those who are acquainted with human nature, or the history of mankind, as it must be evident to all such, that under the best administrations, under the most perfect forms of governnient that human wisdom hath as yet been able to plan, there have been always found individuals who have sacrificed their duty and the interests of their country, to ostentation and private convenience. A well-modelled government and upright administration, it is readily allowed, are absolutely necessary to form and support public spirit and public virtue ; buc human nature must be new-modelled, before the selfish passions lose their influence, or are made conducive to the public good.
The desire of acquiring and enjoying riches, our Author says, are passions natural to men in a Itate of society; all great focieties are maintained, enriched, and animated by them: luxury, therefore, he concludes, is a good ; contributes to the greatness of states, and the happiness of mankind; and the great point, he tells us, should be to encourage, enlighten, and direct it.
The abuses that may be made of luxury, and the excesses to which it may rise, are owing, he apprehends, to faults or defects in the adminiltration, or the constitution, and will be reformed, when such defects are reformed.
To conclude; as far as we are able to collect Mr. Pinto's meaning frony ghe confused manner in which he writes, the principal design of his effay is to fhew, that luxury has no natural tendency to beget venality and corruption, and that it has often been assigned as the cause of disora ders, which, in reality, have proceeded from an ill-modelled government. But this is no new discovery. The Reader will meet with the same len