Horizontal Moon, &c. The fixth chapter fhews the method of finding the diftances of the fun, moon, and planets. The feventh contains an explanation of the different lengths, of days and nights; the viciffitudes of feafons; and the phanomena of Saturn's ring. In the eighth chapter we have the method of finding the Longitude by the eclipfes of Jupiter's Satellites, and a demonftration of the amazing velocity of light by these eclipfes; together with a table for converting mean folar time into degrees and parts of the terreftial Equator, and alfo for converting degrees and parts of the Equator into mean folar time. The ninth chapter treats of the phænomena of the heavens, as feen from different parts of the folar fyftem; and the tenth of folar and fidereal time; the Equation of natural days; and Receffion of the Equinoxes. In this chapter we have a table fhewing how much of the Celeftial Equator paffes over the Meridian in any part of a mean folar day; and how much the fixed the ftars gain upon the mean folar time every day, for a month. This chapter likewise contains a table of the Equation Time depending on the fun's place in the ecliptic; a table of the Equation of Time, depending on the fun's anomaly; a table fhewing the Preceffion of the Equinoxes; a table exhi-, biting the difference between Sidereal, Julian, and Solar years a with tables of the Equation of Natural Days; all very exact and accurate. In the eleventh chapter Mr. Fergufon explaina the phænomena of the Harvest Moon, in a very clear and f tisfactory manner: and in the twelfth he defcribes the moon's furface and her phases. In the thirteenth chapter Mr. Fergufon explains the theory of the tides on the Newtonian principles; and in the fourteenth treats of eclipfes, their number and periods. He likewife prefents us with a large catalogue of ancient and modern eclipfes, from Struyk and Ricciolus; and endeavours to ascertain the true time of our Saviour's crucifixion. There is a remarkable prophecy,' fays he, in Daniel, chap. ix. ver. 26, 27. concerning the year in which the Meffiah fhould be cut off. And he fhall confirm the covenant with many for one week; and in the midst of the week he shall caufe the facrifice and the oblations to cease. Now, as it is generally allowed, that by each of Daniel's prophetic weeks was meant feven years, the middle of the week must be in the fourth year. And as our Saviour did not enter upon his public miniftry, or confirming the covenant, until he was REV. Sept. 1756. • baptized, R baptized, which, according to St. Luke, chap. iii. ver. 23. ⚫ was in the beginning of his thirtieth year, or when he was ⚫ full twenty-nine years old; this prophecy points out the very year of his death; namely, the thirty-third year of his age, or fourth year of his public miniftry. Let us now try whether we can ascertain that year from aftronomical principles and calculations. The Jews meafured their months by the moon, and their years by the revolution of the fun; which obliged them either to intercalate eleven days at the end of every twelve ⚫ months; or a whole month (which they called Ve-Adar) every third year: for twelve lunar months want almost eleven days of twelve months measured by the fun. In the year of the crucifixion, the Paffover full-moon was on a Friday; for our Saviour suffered on the day next before the Jews Sabbath. Here we have the day of the week afcertained, St. Mark, chap. xv. ver. 42. St. Luke, chap. xxiii. ver. 54. As the lunar year falls eleven days fhort of the folar, the • full moon in any given month muft, at the annual return of that month, be eleven days fooner; and, confequently, cannot fall again upon the fame day of the week: for eleven . days measure a week, and four days over. Hence, if the April full-moon this year, for example, be on a Sunday, on the next year it will be on a Thursday; unless the next be a Leap-year, which will cause twelve days difference; and fo, counting backward, throw it on a Wednesday. Thus, it is plain, that in different neighbouring years, the Paffover full-moons_must be on different days of the week, unless when the Paffover months themselves are different: that is, when the full-moon happens between the Vernal Equinox and first day of April, the Paffover falls in March; but always in April when no full-moon happens within this limit. Now, if it can be proved, that there was but one Paffover full-moon on a Friday in the course of a few years, ⚫ about which we imagine the year of the crucifixion to have been, as it is generally allowed that our account is not above four or five years wrong at moft; that year on which the Paffover full-moon fell on a Friday, muft undoubtedly be the year fought. In order to determine this, I first went to work with my orrery; which, in two or three minutes may be rectified fo as to fhew the days of the months anfwering to all the new and and full moons and eclipfes, in any given year, within the limits of fix thousand years both before and after the Chriftian Æra: and when once fet right, will ferve for above three hundred years without any new rectification. I began with the twenty- -first year after the common date of our Saviour's birth, and obferving from thence, in every year to the fortieth, was surprised to find, that inthe whole course of twenty years fo run over, there had been but one Paffover fullmoon on a Friday: and that one was in the thirty-third year of our Saviour's age, not including the year of his birth, because it is fuppofed he was born near the end of that year. But that it might not be faid I trusted to the mechanical ⚫ performance of a machine, I computed all the Pallover fullmoons (according to the precepts delivered in the following chapter) from aftronomical tables, which begin not with the year of our Saviour's birth, but the first year after it; ⚫ and found, as a thing very remarkable, that the only Paff6 over full-moon which happened on a Friday in all that time, "was in the thirty-third year of his age by the tables, or fourth 6 year of his public miniftry, agreeable to the afore-mentioned remarkable prophecy. "We shall here fubjoin a table of the true times of all the ⚫ conjunctions of the fun and moon (adapted to the Meridian of Jerufalem) which preceded the Paffover full-moons, from A. D. 28, to A. D. 36 inclufive, although it be more than <double the number that there is occafion to examine for our prefent purpose. All these new moons fell in Pifces and Aries, which figns fet at a greater angle with the horizon in the weft than any others; and therefore, a few degrees of ⚫ them take more time to go down. Now, the moon moves ⚫ fomewhat more than twelve degrees from the fun in twentyfour hours; and if two fmall patches be put twelve degrees afunder, upon any two parts of Pifces or Aries, in the ecliptic of a common globe, and the globe rectified to the latitude of Jerufalem, the most eafterly patch representing the moon, will be an hour later of fetting than the other which • represents the fun: confequently, in that latitude the moon may be feen juft fetting about an hour after the fun, when • she is not above twenty-four hours old. And fourteen days added to the day of this firft appearance after the change, · gives the day of full-moon. < The above thirty-third year was the 4746th year of the Julian period, and the last year of the 202d Olympiad; which is the very year that Phlegon informs us an extraordinary eclipfe of the fun happened. His words are, In the fourth year of the 202d Olympiad there was the greatest eclipfe of the fun that ever was known: it was night at the fixth bour of the day, fo that the ftars of heaven were feen. This time of the day agrees exactly with the time that the darknefs began, according to Matthew, chap. xvii. ver. 25. Mark, chap. xv. ver. 33. and Luke, chap. xxiii. ver. 44. But whoever calculates, will find, that a total eclipse of the • fun could not poffibly happen at Jerufalem any time that year in the natural way. All this feems fufficient to afcertain the true time of our Saviour's birth and crucifixion to be according to our prefent computation; and to put an end to the controverfy a6 mong Chronologers on that head. From hence likewife. may be inferred the truth of the prophetic parts of fcripture, fince they can ftand so ftrict a teft as that of being examined on the principles of Aftronomy.' The fifteenth chapter fhews the method of calculating new and full moons, that of calculating and projecting folar and lunar eclipfes, the ufe of the Dominical Letter, and contains feveral aftronomical and chronological tables. In the fixteenth chapter we have a defcription of feveral aftronomical machines, which ferve to explain and illustrate the foregoing part of the treatise. Thefe machines are-the Orrery, fronting the title-page, made by the Author; the Calculator, contrived by Mr. Ferguson to explain the harvest mcon; the Cometarium, a curious machine invented by Dr. Defaguliers, for for fhewing the motion of a comet, or excentric body moving round the fun, defcribing equal areas in equal times; the improved Celestial Globe; the Planetary Globe; the Trajectorium Lunare, for delineating the paths of the earth and moon, fhewing what fort of curves they make in the etherial regions; the Tide-Dial; and the Eclipfareon, a piece of mechanifm that exhibits the time, quantity, duration, and progrefs of folar eclipfes, at all parts of the earth. Having thus given our readers a general view of what is contained in this performance, we fhall conclude with obferving, that though it is chiefly calculated for fuch as have not ftudied Mathematics, those who have even made a confiderable progress in mathematical ftudies will, nevertheless, find it worthy of their attentive perufal. The Method of Fluxions applied to a felect Number of useful Problems: together with the Demonstration of Mr. Cotes's Forms of Fluents, in the fecond part of his Logometria; the Analysis of the Problems in his Scholium Generale; and an Explanation of the principal Propofitions of Sir Ifaac Newton's Philofophy. By Nicholas Saunderfon, L. L. D. late Profeffor of Mathematics in the University of Cambridge, 8vo. 6s. Millar. F all the furprifing phænomena that have, in different ages, appeared among the human fpecies, there is not one more difficult to be accounted for, than that of a blind man's excelling in the moft difficult and fublime parts of the Mathematics. It feems, indeed, almoft impoffible; and had not the prefent age afforded us the illuftrious example of Profeffor Saunderson, we might, perhaps, have looked upon the inftances of this kind, related by authors, as fictions; or, at leaft, that they had greatly magnified the truth. The most remarkable of fuch inftances, mentioned by historians, is that of Dydimus of Alexandria, who, " tho' blind* from his in infancy, and confequently ignorant of the very letters, ap"peared fo great a miracle to the world, as not only to learn Logic, but alfo Geometry to perfection, which feems the "moft of any thing to require the help of fight." The cafe of this extraordinary perfon, is fimilar to that of our Author, who, "when twelve months old, was deprived by the small Hieronymus de viris illeft. cap. CIX. + Colfon's Life of Profeffor Saunderfon. R 3. ❝ pox, |