PECULIARITIES OF THE ROMAN CALENDAR.

The Romans, instead of distinguishing the days of the month by the ordinal numbers, first, second, third, etc., counted backwards from three fixed points, namely, the Calends, the Nones, and the Ides.

Calends (Latin Calandae, from Calare, to call,) was so denominated because it had been an ancient custom of the pontiffs to call the people together on that day to apprise them of the festivals, or days that were to be kept sacred during the month.Nones (Latin nonae, from nonus, the ninth,) the ninth day before the Ides.

Ides (Latin idus, supposed to be derived from an obsolete verb iduare, to divide,) was near the middle of the month, either the 13th or the 15th day.

The first day of each month was invariably called the Calends. The Nones were the fifth, and the Ides the thirteenth, except in March, May, July, and October, in which the Nones occurred on the seventh day and the Ides on the fifteenth.

From these three points the days of the month were numbered—not forward, but backward—as so many days before the Nones, the Ides, or the Calends, the point of departure being counted in the reckoning, so that the last day of every month was the second of the Calends of the following month.

It will be seen by the Roman and English calendar found on the following pages, that there are six days of Nones in March, May, July and October, and four of all the other months; also that all the months have eight days of Ides. The number of days of Calends depend upon the number of days in the month, and the day of the month on which the Ides fall.

If the month has thirty-one days and the Ides fall on the thirteenth, there are nineteen days of Calends; but if the Ides fall on the fifteenth, there are only seventeen days of Calends. As the Ides fall on the thirteenth of all the months of thirty days, they have eighteen days of Calends. February, the month of twenty-eight days, has only sixteen, except in leap-year, when the sixth of the Calends is reckoned twice.

It may also be seen from the calendar that the Romans, after the first day of the month, began to reckon so many days before the Nones, as 4th, 3d, 2d, then Nones; after the Nones, so many days before the Ides, as 8th, 7th, 6th, etc., and after the Ides, so many before the Calends of the next month, the highest numbers being reckoned first.

In reducing the Roman calendar to our own, it should be remembered that in reckoning backward from a fixed point, that the point of departure is counted; also, that the last day of the month is not the point from which the Calends are reckoned, but the first day of the following month. We have then this rule for finding the English expression for any Latin date:

RULE.

If the given date be Calends, add two to the number of days in the month, from which subtract the given date; if the date be Nones, or Ides, add one to that of the day on which the Nones or Ides fall, from which subtract the given date, and you will have the day of the month in our calendar. To find the Latin expression for any English date, the preceding method is to be reversed, upon the principle that if 5 - 3 = 2, then 5 - 2 = 3.

But in reducing a Roman date to a date of February in leap-year, for the first twenty-four days, proceed according to the preceding rule as if the month had only twenty-eight days, and to obtain the proper expression for the remaining five days, regard the month as having twenty-nine days, taking the Roman date from 31 instead of 30. Thus 31 - 6 = 25, while 30 - 6 = 24; the former corresponding with sexto calendas, the latter with bis-sexto calendas of the Julian calendar. By referring to the table on the 35th page, one may easily learn how to find the English expression for any Latin date, or the Latin expression for any English date.

It has already been stated that in January the Nones fall on the 5th, and the Ides on the 13th, January then having thirty one days, the number from which to subtract the Roman date to obtain the corresponding day of the month is, for Nones, 5 + 1 = 6; for Ides, 13 + 1 = 14; for Calends, 31 + 2 = 33. Hence the first column in the table under January are the numbers 6, 14 and 33. February is the same as January for Nones and Ides. For Calends in leap-year, for the first 24 days, it is 28 + 2 = 30; for the remaining 5 days it is 29 + 2 = 31. Hence for the first column under February are the numbers 6, 14, 30 and 31. March is the same as January, except that the Nones fall on the 7th and the Ides on the 15th, consequently we have for Nones, 7 + 1 = 8, and for Ides, 15 + 1 = 16; hence, for the first column under March we have the numbers 8, 16, and 33.

In the table the three months are taken to illustrate how easily the change may be made from Roman to English, or from English to Roman date. A complete calendar for 1892, both in Roman and English, which will be very convenient for reference, may be found on the four following pages.

The first seven letters of the alphabet, used to represent the days of the week, are placed in the calendar beside the days of the week. The letter that represents Sunday is called the dominical or Sunday letter. The letter that represents the first Sunday in any given year represents all the Sundays in that year, unless it be leap-year, when two Sunday letters are used. The first represents all the Sundays in January and February, while the letter that precedes it represents all the Sundays for the rest of the year.

The reason of this is, the day intercalated, or thrust in, between the 28th day of February and the 1st day of March so interrupts the order of the letters that D, which always represents the 1st day of March, now represents the 29th day of February, so that in 1892 it represents Monday, the 29th day of February, also Tuesday the 1st day of March. As it represented all the Mondays in January and February, it will now represent all the Tuesdays for the rest of the year, while C, the letter preceding, represented all the Sundays, will now represent all the Mondays, and B all the Sundays. For January and February we have then C, Sunday; D, Monday; E, Tuesday; F, Wednesday; G, Thursday; A, Friday, and B, Saturday. For the rest of the year we have B, Sunday; C, Monday; D, Tuesday; E, Wednesday; F, Thursday; G, Friday, and A, Saturday. See Part Second, chapters IV and V.

PART SECOND.

MATHEMATICAL.