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the same course over again with respect to the days of the week on which the days of the month fall.

The cycle of the Moon is a period of 19 years, after which period the conjunctions, oppositions, and other aspects of the Moon return to the same state as they were at the commencement of this period, and happen within about an hour and a half of the same time. The Roman indiction is a period of 15 years, established for the purpose of indicating the time of certain payments due to the republic. This indiction was established in the 312th year of the christian

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The christian era commenced in the 9th year of the solar and the 1st of the lunar cycle; therefore to find the year of the solar cycle at any time, add 9 to the given year of the christian era, and divide the sum by 28; the quotient will be the number of cycles, and the remainder the cycle for the given year. If there be not any remainder, the cycle is 28. Thus, if the cycle were required for 1819, we should have 1819 +91828, which divided by 28, gives 65 for the number of complete cycles, and 8 for the year of the present cycle. To find the lunar cycle, add 1 to the year of Christ, and divide by 19; the tient will be the number of cycles elapsed in the interval, and the remainder will be the state of the cycle at the given time. Hence for the present year we have 1819 +1=1820, which divided by 19, gives 95 for the number of complete cycles, and 15 for the year of the present cycle. Again, if the Roman indiction were required, 312 must be subtracted from the given year of the christian era, and the remainder divided by 15. For the present year we have 1819-3121507; and 150715 100, with 7 for the remainder, which is therefore the indiction for this year. The cycle of Easter, or the Dionysian period, is a space of 532 years, produced by multiplying the two former cycles of 28 and 19 years together. The Julian period is another division of time, which

was anciently much used, and is now occasionally referred to, especially in some works on astronomy. This period embraces a duration of 7980 years, and is equal to the continued product of the three preceding periods; for 28 × 19 × 157980. As the christian era commenced in the 4713th year of this period, whenever the Julian year is required, it will be sufficient to add this number to the current year. For example, if it were required to find the Julian year answering to 1819, we have 4713 + 1819 = 6532, the year required.

The principal application, however, of modern astronomy to the purposes of chronology is in ascertaining the uncertain dates of ancient events; and in this respect the powers of Newton conferred the greatest service on that science. The following specimen will show the manner in which his astronomical knowledge was employed for this purpose.

The sphere was formed by Chiron and Musæus at the time, and for the purpose of the Argonautic expedition, as is evident from the reference which several of the asterisms have to that event. At this time the cardinal points of the equinoxes and solstices were placed in the middle of the constellations Aries, Cancer, Libra, and Capricorn. Newton establishes this point by a consideration of the ancient Greek calendar, which consisted of 12 lunar months, and each month of 30 days, and therefore required an intercalary month, began sometimes a week or a fortnight before or after the equinox or solstice; and hence the first astronomers were led to the preceding disposition of the equinoxes and solstices; which is also confirmed by the direct testimonies of Eudoxus, Aratus, and Hipparchus. This being established as a basis, Sir Isaac reasons in the following manner.

At the end of the year 1689, the equinoctial colure cut the ecliptic in 6° 44′ of Taurus, and by this reckoning the equinox was then gone back 36° 44′

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since the Argonautic expedition. But it recedes 54" in a year, or 1° in 72 years, and consequently 46° 44′ would require 2645 years; which reckoned backward from the beginning of 1690, will place this expedition about 25 years after the death of Solomon. But, as there is no necessity for allowing that the middle of the constellations, according to the general account of the ancients, should be precisely the middle between the prima arietis and ultima caudæ, Newton then endeavours to determine the stars through which Eudoxus made the colures pass in the primitive sphere, and by this means to fix the position of the cardinal points. From the mean of five places he finds that the great circle, which in the primitive sphere described by Eudoxus, or at the time of the Argonautic expedition, was the equinoctial colure, did, at the end of 1689, cut the ecliptic in 6° 29′ 15′′ of Taurus. In this manner, he likewise determines the mean place of the solstitial colure to be 6° 28′ 46′′ of Leo; and as this is so nearly at right angles with the former, the difference being less than half a minute of a degree, he concludes that it is rightly drawn. From this con clusion, he also infers that, from the Argonautic expedition to 1689, the cardinal points had receded from the colures 1 sign 6° and 29'; which amounts to 2627 years, allowing 72 to a degree; and these reckoned backward, as in the former case, will place the Argonautic expedition 43 years after the death of Solomon. Newton also employs other methods of a similar nature, and, by thus establishing this epoch, reduces the supposed age of the world about 500 years.

Historians and astronomers of different countries and ages employ various epochs in fixing the dates of the events they record. The creation of the world; the first Olympiad; the building of Rome; the era of Nabonassar; the birth of Christ; and

the flight of Mahomet, are the principal of these epochs.

Many ancient authors date the occurrence of events from the Creation of the world; but the opinions of the learned relative to this primitive event do not agree with each other. This uncertainty renders the Julian period highly advantageous as a general standard to which to refer the dates of other systems, and one by which all this difference of opinion is avoided. Notwithstanding the various opinions of the learned on this subject, it should be remarked that, according to some of the most esteemed biblical critics, the sacred scriptures assign 4004 years for the interval between the creation and the birth of Christ. It is therefore easy to reduce any date of the Christian era, or of any other era when its relation to this is known, to that of the creation of the world, by means of simple addition or subtraction.

The Olympiads were used by the Greek writers, as epochs to which they refer the recurrence of events. The commencement of every fourth year was the signal for the celebration of magnificent games in honour of Jupiter Olympus, at which all the states of Greece were assembled, near Olympia, a city of Peloponesus. These games were instituted by Iphitus, and the first year of the first Olympiad corresponds with the year 3938 of the Julian period, and consequently with the 776th year before the Christian era. This year was therefore the 18th of the solar cycle; the 5th of the lunar cycle; and the 8th of the cycle of indiction. From these data, any year indicated in Olympiads may easily be brought either to the Julian period, or the Christian era. we take the second year of the 87th Olympiad, which is distinguished in the history of Greece by the commencement of the Peloponesian war, as an example, we have eighty-six complete Olympiads,

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which multiplied by 4, is 344 years, to which the 2 being added, we have 346 years since the commencement of the first Olympiad; but as this corresponded with the 3938th year of the Julian period, if 345 be added to this last we have 4283 for the year required. To transfer the same event to the Christian era; as the first Olympiad was 776 years before that era, we have 776-345-431 years before the birth of Christ for the date required.

The Founding of Rome is the era at which the Latin writers commence their series of dates, and is therefore of general utility. According to Varro, this was the 21st of April 3961 of the Julian period, and 753 before the birth of Christ. Any year, therefore, dated according to this series, is easily brought to either the Julian or the Christian period, in the same manner as in the preceding example.

The era of Nabonassor, King of the Chaldeans, is another epoch celebrated for its astronomical observations; and for having been referred to by several ancient writers on scientific subjects, particularly Hipparchus and Ptolemy. The commence

ment of this era corresponds to the 26th of February, of the 3967th year of the Julian period; and consequently 747 years before the Christian era. Its commencement answers to the Egyptian month Thoth; and it was then that they began their year of 365 days.

The Birth of Christ is now the era adopted by all Christendom as the common point of time to which they refer the commencement of their series of dates. This is the most extensively used of any of the epochs that have been mentioned, and the dates of the one may readily be reduced to the other by means of the relations already specified.

The last era abovementioned is the Hegira, or the flight of Mahomet, from which the Arabs, Saracens, Turks, Tartars, and other Mahometan writers, commence their series of dates, and corresponds to

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