Horizontal Moon, &c. The fixth chapter shows the me. thod of finding the distances of the sun, moon, and planets. The seventh contains an explanation of the different lengths, of days and nights; the viciffitudes of seasons; and the phænomena of Saturn's ring. In the eighth chapter we have the method of finding the Longitude by the eclipses of Jupiter's Satellites, and a demonstration of the amazing velocity of light by these eclipses; together with a table for converting mean solar time into degrees and parts of the terreftial Equator, and also for converting degrees and parts of the Equator into mean folar time. The ninth chapter treats of the phænomena of the heavens, as seen from different parts of the solar system; and the tenth of solar and fidereal time; the Equation of natural days; and Recession of the Equinoxes. In this chapter we have a table fhewing how much of the Celestial Equator passes over the Meridian in any part of a mean solar day; and how much the fixed the stars gain upon the mean solar time every day, for a month. This chapter likewise contains a table of the Equation : Time depending on the sun's place in the ecliptic; a tabiw on the Equation of Time, depending on the sun's anomaly; a table fhewing the Precession of the Equinoxes; a tebis exhi-, biting the difference between Sidereal, Julian, and Solar Fears a with tables of the Equation of Natural Days; al very ex and accurate. In the eleventh chapter Mr. Ferguson exptains the phænomena of the Harvest Moon, in a very clear and tisfactory manner; and in the twelfth he describes the moon's surface and her phases. In the thirteenth chapter Mr. Ferguson explains the theory of the tides on the Newtonian principles; and in the fourteenth treắts of eclipses, their number and periods. He likewise presents us with a large catalogue of ancient and modern ecliples, from Struyk and Ricciolus ; and endeavours to ascertain the true time of our Saviour's crucifixion, • There is a remarkable prophecy,' says he, 'in Daniel, chap. ix. ver. 26, 27. concerning the year in which the « Messiah should be cut off. off. And he fall confirm the covenant ? with many for one week; and in the midst of the week he shall cause the sacrifice and the oblations to cease. Now, as it is generally allowed, that by each of Daniel's prophetic weeks was meant seven years, the middle of the week must be in the fourth year. And as our Saviour did not enter upon his public ministry, or confirming the covenant, until he was Rev. Sept. 1756. R baptized, 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 ve ry year of his death; namely, the thirty-third year of his á age, or fourth year of his public ministry. Let us now try whether we can ascertain that year from astronomical prin• ciples and calculations. • The Jews measured their months by the moon, and their years by the revolution of the sun; which obliged them ei ther 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 almoft eleven days of twelve months measured by the fun. « In the year of the crucifixion, the Passover full-moon was on a Friday; for our Saviour suffered on the day next be fore the Jews Sabbath. Here we have the day of the week ! ascertained, St. Mark, chap. xv. ver. 42. St. Luke, chap. 6 xxiii. ver. 54. • As the lunar year falls eleven days short of the folar, the full moon in any given month must, at the annual return of that month, be eleven days sooner ; and, consequently, • cannot fall again upon the same 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 Passover full-moons must be on different days of the 6 week, unless when the Passover months themselves are dif• ferent: that is, when the full-moon happens between the Vernal Equinox and first day of April, the Paflover 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 Passover 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 most; that year on which the • Passover full-moon fell on a Friday, muft undoubtedly be the year fought. • In order to determine this, I first went to work with my correry; which, in two or three minutes may be rectified so a: to thew the days of the months answering to all the new < hundred years 6 6 and full moons and eclipses, in any given year, within the * limits of fix thousand years both before and after the Christian Æra: and when once set right, will serve for above three without any new rectification. I began with the twenty-first year after the common date of our Saviour's birth, and observing 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 Passover 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 supposed he was born near the end of that year, But that it might not be said I trusted to the mechanical performance of a machine, I computed all the Passover fullmoons (according to the precepts delivered in the following chapter) from astronomical 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 Paff 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 year of his public ministry, agreeable to the afore-mention• ed remarkable prophecy. "We shall here subjoin a table of the true times of all the conjunctions of the sun and moon (adapted to the Meridian of Jerusalem) which preceded the Paflover full-moons, from A. D. 28, to A. D. 36 inclusive, although it be more than 5 double the number that there is occasion to examine for our • present purpose. All these new moons fell in Pisces and Aries, which signs set at a greater angle with the horizon in the west than any others; and therefore, a few degrees of them take more time to go down. Now, the moon movès somewhat more than twelve degrees from the fun in twenty-. « four hours; and if two small patches be put twelve degrees ' asunder, upon any two parts of Pisces or Aries, in the eclip' tic of a common globe, and the globe rectified to the lati"tude of Jerusalem, the most eafterly patch representing the moon, will be an hour later of setting than the other which represents the fun: consequently, in that latitude the moon may be feen just setting about an hour after the sun, when . fhe is not above twenty-four hours old. And fourteen days • added to the day of this first appearance after the change gives the day of full-moon. I True Time of Conjuncti- Moon visible at Jewish Full on at Jerusalem. Jerusalem. Moon. A.D. D. H. M. D. 28 Mar. 15. Mar. 16. Mar. 31 Wednes. 29 April 2. Apr. 17 Sunday. 30 Mar. 22. 8 Apr. 6 Thurid. 31 Mar. 12. Mar. 1 13: Mar. 27 Tuesd. 32 Mar. 29. II 19 Afte. Apr. 14 Mond. *33 Mar. 19. 12 Afte. Apr. 3 Friday. 34 Mar. 9. 5 12 Mor. Mar. 24 Wednet. 35 Mar. 28. 6 20 Afte. Apr. 12 Tuefa. 36 Mar. 16. 6 30 Afte. Mar. 17. Mar.:31 Saturd. 4 Mor. 7 30 Afte. 45 Afte. I 51 Mor. April 3. Mar. 31. I Mar. 20. Mar. 29. « The above thirty-third year was the 4746th year of the Julian period, and the last year of the 2020 Olympiad; « which is the very year that Phlegon informs us an extraor• dinary eclipse of the fun happened. His words are, In the fourth year of the 2020 Olympiad there was the greatest eclipse • of the fun that ever was known: it was night at the fixth hour of the day, so that the stars of heaven were seen. This • time of the day agrees exactly with the time that the dark“ness began, according to Matihew, 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 un could not possibly happen at Jerusalem any time that year in the natural way. All this feems suficient to ascertain the true time of our « Saviour's birth and crucifixion to be according to our pre< sent computation; and to put an end to the controversy a• mong Chronologers on that head. From hence likewife may be inferred the truth of the prophetic parts of scripture, • since they can stand so strict a test as that of being examined • on the principles of Astroncmy.' The fifteenth chapter shews the method of calculating new and full moons, that of calculating and projecting solar and lunar eclipses, the use of the Dominical Letter, and contains feveral astronomical and chronological tables. In the sixteenth chapter we have a description of several astronomical machines, which serye to explain and illustrate the foregoing part of the treatise. These machines are—the Orrery, fronting the title-page, made by the Author; the Calculator, contrived by Mr. Ferguson to explain the harveft mcon; the Cometarium, a curious machine invented by Dr. Desaguliers, for for shewing the motion of a comet, or excentric body moving round the sun,ļdefcribing equal areas in equal times; the improved Celestial Globe; the Planetary Globe; the Trajectorium Lunare, for delineating the paths of the earth and moon, Thewing what sort of curves they make in the etherial regions; the Tide-Dial; and the Ecliplareon, a piece of mechanism that exhibits the time, quantity, duration, and progress of solar eclipses, at all parts of the earth. Having thus given our readers a general view of what is contained in this performance, we shall conclude with obserying, that though it is chiefly calculated for such as have not studied Mathematics, those who have even made a confiderable progress in mathematical studies will, nevertheless, find it worthy of their attentive perufal. The Method of Fluxions applied to a select Number of useful Problems : together with the Demonstration of Mr. Cotes's Forms of Fluents, in the second part of his Logometria ; the Analysis of the Problems in his Scholium Generale ; and an Explanation of the principal Propositions of Sir Isaac Newton's Philosophy. By Nicholas Saunderson, L. L. D. late Professor of Mathematics in the University of Cambridge, 8vo. 6s. Millar. F all the surprising phænomena that have, in different , one more difficult to be accounted for, than that of a blind man's excelling in the most difficult and sublime parts of the Mathematics. It seems, indeed, almost impossible ; and had not the present age afforded us the illustrious example of Profeffor Saunderson, we might, perhaps, have looked upon the instances of his kind, related by authors, as fictions ; or, at least, that they had greatly magnified the truth. The most remarkable of such instances, mentioned by historians, is that of Dydimus of Alexandria, who, “tho' blind* from his in“ infancy, and consequently ignorant of the very letters, ap peared so great a miracle to the world, as not only to learn “ Logic, but also Geometry to perfection, which seems the “ most of any thing to require the help of sight.” The case of this extraordinary person, is similar to that of our Author, who, “ when † twelve months old, was deprived by the small poxa |