We will now show in what manner this whole apparatus of methods and tables may be dispensed with, and the Gregorian calendar reduced to a few simple formulae of easy computation.

And, first, to find the dominical letter. Let L denote the number of the dominical letter of any given year of the era. Then, since every year which is not a leap year ends with the same day as that with which it began, the dominical letter of the following year must be L - 1, retrograding one letter every common year. After x years, therefore, the number of the letter will be L - x. But as L can never exceed 7, the number x will always exceed L after the first seven years of the era. In order, therefore, to render the subtraction possible, L must be increased by some multiple of 7, as 7m, and the formula then becomes 7m + L - x. In the year preceding the first of the era, the dominical letter was C; for that year, therefore, we have L = 3; consequently for any succeeding year x, L = 7m + 3 - x, the years being all supposed to consist of 365 days. But every fourth year is a leap year, and the effect of the intercalation is to throw the dominical letter one place farther back. The above expression must therefore be diminished by the number of units in x/4, or by (x/4)_w (this notation being used to denote the quotient, _in a whole number_, that arises from dividing x by 4). Hence in the Julian calendar the dominical letter is given by the equation

L = 7m + 3 - x - (x/4)_w.

This equation gives the dominical letter of any year from the commencement of the era to the Reformation. In order to adapt it to the Gregorian calendar, we must first add the 10 days that were left out of the year 1582; in the second place we must add one day for every century that has elapsed since 1600, in consequence of the secular suppression of the intercalary day; and lastly we must deduct the units contained in a fourth of the same number, because every fourth centesimal year is still a leap year. Denoting, therefore, the number of the century (or the date after the two right-hand digits have been struck out) by c, the value of L must be increased by 10 + (c - 16) - ((c - 16) / 4)_w . We have then

L = 7m + 3 - x - (x/4)w + 10 + (c - 16) - ((c - 16) / 4)w;

that is, since 3 + 10 = 13 or 6 (the 7 days being rejected, as they do not affect the value of L),

L = 7m + 6 - x - (x/4)w + (c - 16) - ((c - 16) / 4)w.

x = 1839, (x/4)_w = (1839/4)_w = 459, c = 18, c - 16 = 2, and ((c - 16) / 4)_w = 0.

((26 + 11(N - 6)) / 30)_r. But the numerator of this fraction becomes by reduction 11 N - 40 or 11 N - 10 (the 30 being rejected, as the remainder only is sought) = N + 10(N - 1); therefore, ultimately,

J = ((N + 10(N - 1)) / 30)_r.

On account of the solar equation S, the epact J must be diminished by unity every centesimal year, excepting always the fourth. After x centuries, therefore, it must be diminished by x - (x/4)w. Now, as 1600 was a leap year, the first correction of the Julian intercalation took place in 1700; hence, taking c to denote the number of the century as before, the correction becomes (c - 16) - ((c - 16) / 4)w, which [v.04 p.0999] must be deducted from J. We have therefore

S = - (c - 16) + ((c - 16) / 4)_w.

With regard to the lunar equation M, we have already stated that in the Gregorian calendar the epacts are increased by unity at the end of every period of 300 years seven times successively, and then the increase takes place once at the end of 400 years. This gives eight to be added in a period of twenty-five centuries, and x/25 in x centuries. But 8x/25 = 1/3 (x - x/25). Now, from the manner in which the intercalation is directed to be made (namely, seven times successively at the end of 300 years, and once at the end of 400), it is evident that the fraction x/25 must amount to unity when the number of centuries amounts to twenty-four. In like manner, when the number of centuries is 24 + 25 = 49, we must have x/25 = 2; when the number of centuries is 24 + 2 x 25 = 74, then x/25 = 3; and, generally, when the number of centuries is 24 + n x 25, then x/25 = n + 1. Now this is a condition which will evidently be expressed in general by the formula n - ((n + 1) / 25)_w. Hence the correction of the epact, or the number of days to be intercalated after x centuries reckoned from the commencement of one of the periods of twenty-five centuries, is {(x - ((x+1) / 25)_w) / 3}_w. The last period of twenty-five centuries terminated with 1800; therefore, in any succeeding year, if c be the number of the century, we shall have x = c - 18 and x + 1 = c - 17. Let ((c - 17) / 25)_w = a, then for all years after 1800 the value of M will be given by the formula ((c - 18 - a) / 3)_w; therefore, counting from the beginning of the calendar in 1582,

M={(c - 15 - a) / 3}_w.

By the substitution of these values of J, S and M, the equation of the epact becomes

E = ((N + 10(N - 1)) / 30)_r - (c - 16) + ((c - 16) / 4)_w + ((c - 15 - a) / 3)_w.

It may be remarked, that as a = ((c - 17) / 25)_w, the value of a will be 0 till c - 17 = 25 or c = 42; therefore, till the year 4200, a may be neglected in the computation. Had the anticipation of the new moons been taken, as it ought to have been, at one day in 308 years instead of 3121/2, the lunar equation would have occurred only twelve times in 3700 years, or eleven times successively at the end of 300 years, and then at the end of 400. In strict accuracy, therefore, a ought to have no value till c - 17 = 37, or c = 54, that is to say, till the year 5400. The above formula for the epact is given by Delambre (_Hist. de l'astronomie moderne,_ t. i. p. 9); it may be exhibited under a variety of forms, but the above is perhaps the best adapted for calculation. Another had previously been given by Gauss, but inaccurately, inasmuch as the correction depending on ''a'' was omitted.

Having determined the epact of the year, it only remains to find Easter Sunday from the conditions already laid down. Let

P = the number of days from the 21st of March to the 15th of the paschal moon, which is the first day on which Easter Sunday can fall;

p = the number of days from the 21st of March to Easter Sunday;

L = the number of the dominical letter of the year;

l = letter belonging to the day on which the 15th of the moon falls:

then, since Easter is the Sunday following the 14th of the moon, we have

p = P + (L - l),

which is commonly called the number of direction.

The value of L is always given by the formula for the dominical letter, and P and l are easily deduced from the epact, as will appear from the following considerations.

When P = 1 the full moon is on the 21st of March, and the new moon on the 8th (21 - 13 = 8), therefore the moon's age on the 1st of March (which is the same as on the 1st of January) is twenty-three days; the epact of the year is consequently twenty-three. When P = 2 the new moon falls on the ninth, and the epact is consequently twenty-two; and, in general, when P becomes 1 + x, E becomes 23 - x, therefore P + E = 1 + x + 23 - x = 24, and P = 24 - E. In like manner, when P = 1, l = D = 4; for D is the dominical letter of the calendar belonging to the 22nd of March. But it is evident that when l is increased by unity, that is to say, when the full moon falls a day later, the epact of the year is diminished by unity; therefore, in general, when l = 4 + x, E = 23 - x, whence, l + E = 27 and l = 27 - E. But P can never be less than 1 nor l less than 4, and in both cases E = 23. When, therefore, E is greater than 23, we must add 30 in order that P and l may have positive values in the formula P = 24 - E and l = 27 - E. Hence there are two cases.

When E < 24, P = 24 - E; l = 27 - E, or ((27 - E) / 7)r, When E > 23, P = 54 - E; l = 57 - E, or ((57 - E) / 7)r.

By substituting one or other of these values of P and l, according as the case may be, in the formula p = P + (L - l), we shall have p, or the number of days from the 21st of March to Easter Sunday. It will be remarked, that as L - l cannot either be 0 or negative, we must add 7 to L as often as may be necessary, in order that L - l may be a positive whole number.

By means of the formulae which we have now given for the dominical letter, the golden number and the epact, Easter Sunday may be computed for any year after the Reformation, without the assistance of any tables whatever. As an example, suppose it were required to compute Easter for the year 1840. By substituting this number in the formula for the dominical letter, we have x = 1840, c - 16 = 2, ((c - 16) / 4)_w = 0, therefore

L = 7m + 6 - 1840 - 460 + 2 = 7m - 2292 = 7 x 328 - 2292 = 2296 - 2292 = 4 L = 4 = letter D . . . (1).

For the golden number we have N = ((1840 + 1) / 19)_r; therefore N = 17 . . . (2).

For the epact we have

((N + 10(N - 1)) / 30)_r = ((17 + 160) / 30)_r = (177 / 30)_r = 27;

likewise c - 16 = 18 - 16 = 2, (c - 15) / 3 = 1, a = 0; therefore

E = 27 - 2 + 1 = 26 . . . (3).

Now since E > 23, we have for P and l,

P = 54 - E = 54 - 26 = 28,

l = ((57 - E) / 7)_r = ((57 - 26) / 7)_r = (31 / 7)_r = 3;

consequently, since p = P + (L - l),

p = 28 + (4 - 3) = 29;

that is to say, Easter happens twenty-nine days after the 21st of March, or on the 19th April, the same result as was before found from the tables.

The principal church feasts depending on Easter, and the times of their celebration are as follows:—

Septuagesima Sunday } { 9 weeks } First Sunday in Lent } is { 6 weeks } before Easter. Ash Wednesday } { 46 days }

Rogation Sunday { 5 weeks } Ascension day or Holy Thursday } { 39 days } Pentecost or Whitsunday } is { 7 weeks } after Easter. Trinity Sunday } { 8 weeks }

The Gregorian calendar was introduced into Spain, Portugal and part of Italy the same day as at Rome. In France it was received in the same year in the month of December, and by the Catholic states of Germany the year following. In the Protestant states of Germany the Julian calendar was adhered to till the year 1700, when it was decreed by the diet of Regensburg that the new style and the Gregorian correction of the intercalation should be adopted. Instead, however, of employing the golden numbers and epacts for the determination of Easter and the movable feasts, it was resolved that the equinox and the paschal moon should be found by astronomical computation from the Rudolphine tables. But this method, though at first view it may appear more accurate, was soon found to be attended with numerous inconveniences, and was at length in 1774 abandoned at the instance of Frederick II., king of Prussia. In Denmark and Sweden the reformed calendar was received about the same time as in the Protestant states of Germany. It is remarkable that Russia still adheres to the Julian reckoning.

In Great Britain the alteration of the style was for a long time successfully opposed by popular prejudice. The inconvenience, however, of using a different date from that employed by the greater part of Europe in matters of history and chronology began to be generally felt; and at length the Calendar (New [v.04 p.1000] Style) Act 1750 was passed for the adoption of the new style in all public and legal transactions. The difference of the two styles, which then amounted to eleven days, was removed by ordering the day following the 2nd of September of the year 1752 to be accounted the 14th of that month; and in order to preserve uniformity in future, the Gregorian rule of intercalation respecting the secular years was adopted. At the same time, the commencement of the legal year was changed from the 25th of March to the 1st of January. In Scotland, January 1st was adopted for New Year's Day from 1600, according to an act of the privy council in December 1599. This fact is of importance with reference to the date of legal deeds executed in Scotland between that period and 1751, when the change was effected in England. With respect to the movable feasts, Easter is determined by the rule laid down by the council of Nice; but instead of employing the new moons and epacts, the golden numbers are prefixed to the days of the full moons. In those years in which the line of epacts is changed in the Gregorian calendar, the golden numbers are removed to different days, and of course a new table is required whenever the solar or lunar equation occurs. The golden numbers have been placed so that Easter may fall on the same day as in the Gregorian calendar. The calendar of the church of England is therefore from century to century the same in form as the old Roman calendar, excepting that the golden numbers indicate the full moons instead of the new moons.

Hebrew Calendar.—In the construction of the Jewish calendar numerous details require attention. The calendar is dated from the Creation, which is considered to have taken place 3760 years and 3 months before the commencement of the Christian era. The year is luni-solar, and, according as it is ordinary or embolismic, consists of twelve or thirteen lunar months, each of which has 29 or 30 days. Thus the duration of the ordinary year is 354 days, and that of the embolismic is 384 days. In either case, it is sometimes made a day more, and sometimes a day less, in order that certain festivals may fall on proper days of the week for their due observance. The distribution of the embolismic years, in each cycle of 19 years, is determined according to the following rule:—

The number of the Hebrew year (Y) which has its commencement in a Gregorian year (x) is obtained by the addition of 3761 years; that is, Y = x + 3761. Divide the Hebrew year by 19; then the quotient is the number of the last completed cycle, and the remainder is the year of the current cycle. If the remainder be 3, 6, 8, 11, 14, 17 or 19 (0), the year is embolismic; if any other number, it is ordinary. Or, otherwise, if we find the remainder

R=((7Y+1) / 19)_r

the year is embolismic when R < 7.

The calendar is constructed on the assumptions that the mean lunation is 29 days 12 hours 44 min. 3-1/3 sec., and that the year commences on, or immediately after, the new moon following the autumnal equinox. The mean solar year is also assumed to be 365 days 5 hours 55 min. 25-25/57 sec., so that a cycle of nineteen of such years, containing 6939 days 16 hours 33 min. 3-1/3 sec., is the exact measure of 235 of the assumed lunations. The year 5606 was the first of a cycle, and the mean new moon, appertaining to the 1st of Tisri for that year, was 1845, October 1, 15 hours 42 min. 43-1/3 sec., as computed by Lindo, and adopting the civil mode of reckoning from the previous midnight. The times of all future new moons may consequently be deduced by successively adding 29 days 12 hours 44 min. 3-1/3 sec. to this date.

To compute the times of the new moons which determine the commencement of successive years, it must be observed that in passing from an ordinary year the new moon of the following year is deduced by subtracting the interval that twelve lunations fall short of the corresponding Gregorian year of 365 or 366 days; and that, in passing from an embolismic year, it is to be found by adding the excess of thirteen lunations over the Gregorian year. Thus to deduce the new moon of Tisri, for the year immediately following any given year (Y), when Y is

ordinary, subtract (10)(11) days 15 hours 11 min. 20 sec., embolismic, add (18)(17) days 21 hours 32 min. 431/2 sec.

the second-mentioned number of days being used, in each case, whenever the following or new Gregorian year is bissextile.

Hence, knowing which of the years are embolismic, from their ordinal position in the cycle, according to the rule before stated, the times of the commencement of successive years may be thus carried on indefinitely without any difficulty. But some slight adjustments will occasionally be needed for the reasons before assigned, viz. to avoid certain festivals falling on incompatible days of the week. Whenever the computed conjunction falls on a Sunday, Wednesday or Friday, the new year is in such case to be fixed on the day after. It will also be requisite to attend to the following conditions:—

If the computed new moon be after 18 hours, the following day is to be taken, and if that happen to be Sunday, Wednesday or Friday, it must be further postponed one day. If, for an ordinary year, the new moon falls on a Tuesday, as late as 9 hours 11 min. 20 sec., it is not to be observed thereon; and as it may not be held on a Wednesday, it is in such case to be postponed to Thursday. If, for a year immediately following an embolismic year, the computed new moon is on Monday, as late as 15 hours 30 min. 52 sec., the new year is to be fixed on Tuesday.

After the dates of commencement of the successive Hebrew years are finally adjusted, conformably with the foregoing directions, an estimation of the consecutive intervals, by taking the differences, will show the duration and character of the years that respectively intervene. According to the number of days thus found to be comprised in the different years, the days of the several months are distributed as in Table VI.

The signs + and - are respectively annexed to Hesvan and Kislev to indicate that the former of these months may sometimes require to have one day more, and the latter sometimes one day less, than the number of days shown in the table—the result, in every case, being at once determined by the total number of days that the year may happen to contain. An ordinary year may comprise 353, 354 or 355 days; and an embolismic year 383, 384 or 385 days. In these cases respectively the year is said to be imperfect, common or perfect. The intercalary month, Veadar, is introduced in embolismic years in order that Passover, the 15th day of Nisan, may be kept at its proper season, which is the full moon of the vernal equinox, or that which takes place after the sun has entered the sign Aries. It always precedes the following new year by 163 days, or 23 weeks and 2 days; and Pentecost always precedes the new year by 113 days, or 16 weeks and 1 day.

TABLE VI.—Hebrew Months.

Ordinary Embolismic Hebrew Month. Year. Year. - - Tisri 30 30 Hesvan 29 + 29 + Kislev 30 - 30 - Tebet 29 29 Sebat 30 30 Adar 29 30 (Veadar) (...) (29) Nisan 30 30 Yiar 29 29 Sivan 30 30 Tamuz 29 29 Ab 30 30 Elul 29 29 Total 354 384

The Gregorian epact being the age of the moon of Tebet at the beginning of the Gregorian year, it represents the day of Tebet which corresponds to January 1; and thus the approximate date of Tisri 1, the commencement of the Hebrew year, may be otherwise deduced by subtracting the epact from

Sept. 24 after an ordinary Hebrew year. Oct. 24 after an embolismic Hebrew year.

[v.04 p.1001]

The result so obtained would in general be more accurate than the Jewish calculation, from which it may differ a day, as fractions of a day do not enter alike in these computations. Such difference may also in part be accounted for by the fact that the assumed duration of the solar year is 6 min. 39-25/57 sec. in excess of the true astronomical value, which will cause the dates of commencement of future Jewish years, so calculated, to advance forward from the equinox a day in error in 216 years. The lunations are estimated with much greater precision.

The following table is extracted from Woolhouse's Measures, Weights and Moneys of all Nations:—

TABLE VII.—Hebrew Years.

Jewish Number Commencement Jewish Number Commencement Year. of (1st of Tisri). Year. of (1st of Tisri). Days. Days. 296 Cycle. 302 Cycle. 5606 354 Thur. 2 Oct. 1845 5720 355 Sat. 3 Oct. 1959 07 355 Mon. 21 Sept. 1846 21 354 Thur. 22 Sept. 1960 08 383 Sat. 11 Sept. 1847 22 383 Mon. 11 Sept. 1961 09 354 Thur. 28 Sept. 1848 23 355 Sat. 29 Sept. 1962 10 355 Mon. 17 Sept. 1849 24 354 Thur. 19 Sept. 1963 11 385 Sat. 7 Sept. 1850 25 385 Mon. 7 Sept. 1964 12 353 Sat. 27 Sept. 1851 26 353 Mon. 27 Sept. 1965 13 384 Tues. 14 Sept. 1852 27 385 Thur. 15 Sept. 1966 14 355 Mon. 3 Oct. 1853 28 354 Thur. 5 Oct. 1967 15 355 Sat. 23 Sept. 1854 29 355 Mon. 23 Sept. 1968 16 383 Thur. 13 Sept. 1855 30 383 Sat. 13 Sept. 1969 17 354 Tues. 30 Sept. 1856 31 354 Thur. 1 Oct. 1970 18 355 Sat. 19 Sept. 1857 32 355 Mon. 20 Sept. 1971 19 385 Thur. 9 Sept. 1858 33 383 Sat. 9 Sept. 1972 20 354 Thur. 29 Sept. 1859 34 355 Thur. 27 Sept. 1973 21 353 Mon. 17 Sept. 1860 35 354 Tues. 17 Sept. 1974 22 385 Thur. 5 Sept. 1861 36 385 Sat. 6 Sept. 1975 23 354 Thur. 25 Sept. 1862 37 353 Sat. 25 Sept. 1976 24 383 Mon. 14 Sept. 1863 38 384 Tues. 13 Sept. 1977 —————————————————- —————————————————- 297 Cycle. 303 Cycle. 5625 355 Sat. 1 Oct. 1864 5739 355 Mon. 2 Oct. 1978 26 354 Thur. 21 Sept. 1865 40 355 Sat. 22 Sept. 1979 27 385 Mon. 10 Sept. 1866 41 383 Thur. 11 Sept. 1980 28 353 Mon. 30 Sept. 1867 42 354 Tues. 29 Sept. 1981 29 354 Thur. 17 Sept. 1868 43 355 Sat. 18 Sept. 1982 30 385 Mon. 6 Sept. 1869 44 385 Thur. 8 Sept. 1983 31 355 Mon. 26 Sept. 1870 45 354 Thur. 27 Sept. 1984 32 383 Sat. 16 Sept. 1871 46 383 Mon. 16 Sept. 1985 33 354 Thur. 3 Oct. 1872 47 355 Sat. 4 Oct. 1986 34 355 Mon. 22 Sept. 1873 48 354 Thur. 24 Sept. 1987 35 383 Sat. 12 Sept. 1874 49 383 Mon. 12 Sept. 1988 36 355 Thur. 30 Sept. 1875 50 355 Sat. 30 Sept. 1989 37 354 Tues. 19 Sept. 1876 51 354 Thur. 20 Sept. 1990 38 385 Sat. 8 Sept. 1877 52 385 Mon. 9 Sept. 1991 39 355 Sat. 28 Sept. 1878 53 353 Mon. 28 Sept. 1992 40 354 Thur. 18 Sept. 1879 54 355 Thur. 16 Sept. 1993 41 383 Mon. 6 Sept. 1880 55 384 Tues. 6 Sept. 1994 42 355 Sat. 24 Sept. 1881 56 355 Mon. 25 Sept. 1995 43 383 Thur. 14 Sept. 1882 57 383 Sat. 14 Sept. 1996 —————————————————- —————————————————- 298 Cycle. 304 Cycle. 5644 354 Tues. 2 Oct. 1883 5758 354 Thur. 2 Oct. 1997 45 355 Sat. 20 Sept. 1884 59 355 Mon. 21 Sept. 1998 46 385 Thur. 10 Sept. 1885 60 385 Sat. 11 Sept. 1999 47 354 Thur. 30 Sept. 1886 61 353 Sat. 30 Sept. 2000 48 353 Mon. 19 Sept. 1887 62 354 Tues. 18 Sept. 2001 49 385 Thur. 6 Sept. 1888 63 385 Sat. 7 Sept. 2002 50 354 Thur. 26 Sept. 1889 64 355 Sat. 27 Sept. 2003 51 383 Mon. 15 Sept. 1890 65 383 Thur. 16 Sept. 2004 52 355 Sat. 3 Oct. 1891 66 354 Tues. 4 Oct. 2005 53 354 Thur. 22 Sept. 1892 67 355 Sat. 23 Sept. 2006 54 385 Mon. 11 Sept. 1893 68 383 Thur. 13 Sept. 2007 55 353 Mon. 1 Oct. 1894 69 354 Tues. 30 Sept. 2008 56 355 Thur. 19 Sept. 1895 70 355 Sat. 19 Sept. 2009 57 384 Tues. 8 Sept. 1896 71 385 Thur. 8 Sept. 2010 58 355 Mon. 27 Sept. 1897 72 354 Thur. 29 Sept. 2011 59 353 Sat. 17 Sept. 1898 73 353 Mon. 17 Sept. 2012 60 384 Tues. 5 Sept. 1899 74 385 Thur. 5 Sept. 2013 61 355 Mon. 24 Sept. 1900 75 354 Thur. 25 Sept. 2014 62 383 Sat 14 Sept. 1901 76 385 Mon. 14 Sept. 2015 —————————————————- —————————————————- 299 Cycle. 305 Cycle. 5663 355 Thur. 2 Oct. 1902 5777 353 Mon. 3 Oct. 2016 64 354 Tues. 22 Sept. 1903 78 354 Thur. 21 Sept. 2017 65 385 Sat. 10 Sept. 1904 79 385 Mon. 10 Sept. 2018 66 355 Sat. 30 Sept. 1905 80 355 Mon. 30 Sept. 2019 67 354 Thur. 20 Sept. 1906 81 353 Sat. 19 Sept. 2020 68 383 Mon. 9 Sept. 1907 82 384 Tues. 7 Sept. 2021 69 355 Sat. 26 Sept. 1908 83 355 Mon. 26 Sept. 2022 70 383 Thur. 16 Sept. 1909 84 383 Sat. 16 Sept. 2023 71 354 Tues. 4 Oct. 1910 85 355 Thur. 3 Oct. 2024 72 355 Sat. 23 Sept. 1911 86 354 Tues. 23 Sept. 2025 73 385 Thur. 12 Sept. 1912 87 385 Sat. 12 Sept. 2026 74 354 Thur. 2 Oct. 1913 88 355 Sat. 2 Oct. 2027 75 353 Mon. 21 Sept. 1914 89 354 Thur. 21 Sept. 2028 76 385 Thur. 9 Sept. 1915 90 383 Mon. 10 Sept. 2029 77 354 Thur. 28 Sept. 1916 91 355 Sat. 28 Sept. 2030 78 355 Mon. 17 Sept. 1917 92 354 Thur. 18 Sept. 2031 79 383 Sat. 7 Sept. 1918 93 383 Mon. 6 Sept. 2032 80 354 Thur. 25 Sept. 1919 94 355 Sat. 24 Sept. 2033 81 385 Mon. 13 Sept. 1920 95 385 Thur. 14 Sept. 2034 —————————————————- —————————————————- 300 Cycle. 306 Cycle. 5682 355 Mon. 3 Oct. 1921 5796 354 Thur. 4 Oct. 2035 83 353 Sat. 23 Sept. 1922 97 353 Mon. 22 Sept. 2036 84 384 Tues. 11 Sept. 1923 98 385 Thur. 10 Sept. 2037 85 355 Mon. 29 Sept. 1924 99 354 Thur. 30 Sept. 2038 86 355 Sat. 19 Sept. 1925 5800 355 Mon. 19 Sept. 2039 87 383 Thur. 9 Sept. 1926 01 383 Sat. 8 Sept. 2040 88 354 Tues. 27 Sept. 1927 02 354 Thur. 26 Sept. 2041 89 385 Sat. 15 Sept. 1928 03 385 Mon. 15 Sept. 2042 90 353 Sat. 5 Oct. 1929 04 353 Mon. 5 Oct. 2043 91 354 Tues. 23 Sept. 1930 05 355 Thur. 22 Sept. 2044 92 385 Sat. 12 Sept. 1931 06 384 Tues. 12 Sept. 2045 93 355 Sat. 1 Oct. 1932 07 355 Mon. 1 Oct. 2046 94 354 Thur. 21 Sept. 1933 08 353 Sat. 21 Sept. 2047 95 383 Mon. 10 Sept. 1934 09 384 Tues. 8 Sept. 2048 96 355 Sat. 28 Sept. 1935 10 355 Mon. 27 Sept. 2049 97 354 Thur. 17 Sept. 1936 11 355 Sat. 17 Sept. 2050 98 385 Mon. 6 Sept. 1937 12 383 Thur. 7 Sept. 2051 99 353 Mon. 26 Sept. 1938 13 354 Tues. 24 Sept. 2052 5700 385 Thur. 14 Sept. 1939 14 385 Sat. 13 Sept. 2053 —————————————————- —————————————————- 301 Cycle. 307 Cycle. 5701 354 Thur. 3 Oct. 1940 5815 355 Sat. 3 Oct. 2054 02 355 Mon. 22 Sept. 1941 16 354 Thur. 23 Sept. 2055 03 383 Sat. 12 Sept. 1942 17 383 Mon. 11 Sept. 2056 04 354 Thur. 30 Sept. 1943 18 355 Sat. 29 Sept. 2057 05 355 Mon. 18 Sept. 1944 19 354 Thur. 19 Sept. 2058 06 383 Sat. 8 Sept. 1945 20 383 Mon. 8 Sept. 2059 07 354 Thur. 26 Sept. 1946 21 355 Sat. 25 Sept. 2060 08 385 Mon. 15 Sept. 1947 22 385 Thur. 15 Sept. 2061 09 355 Mon. 4 Oct. 1948 23 354 Thur. 5 Oct. 2062 10 353 Sat. 24 Sept. 1949 24 353 Mon. 24 Sept. 2063 11 384 Tues. 12 Sept. 1950 25 385 Thur. 11 Sept. 2064 12 355 Mon. 1 Oct. 1951 26 354 Thur. 1 Oct. 2065 13 355 Sat. 20 Sept. 1952 27 355 Mon. 20 Sept. 2066 14 383 Thur. 10 Sept. 1953 28 383 Sat. 10 Sept. 2067 15 354 Tues. 28 Sept. 1954 29 354 Thur. 27 Sept. 2068 16 355 Sat. 17 Sept. 1955 30 355 Mon. 16 Sept. 2069 17 385 Thur. 6 Sept. 1956 31 383 Sat. 6 Sept. 2070 18 354 Thur. 26 Sept. 1957 32 355 Thur. 24 Sept. 2071 19 383 Mon. 15 Sept. 1958 33 384 Tues. 13 Sept. 2072

Mahommedan Calendar.—The Mahommedan era, or era of the Hegira, used in Turkey, Persia, Arabia, &c., is dated from the first day of the month preceding the flight of Mahomet from Mecca to Medina, i.e. Thursday the 15th of July A.D. 622, and it commenced on the day following. The years of the Hegira are purely lunar, and always consist of twelve lunar months, commencing with the approximate new moon, without any intercalation to keep them to the same season with respect to the sun, so that they retrograde through all the seasons in about 321/2 years. They are also partitioned into cycles of 30 years, 19 of which are common years of 354 days each, and the other 11 are intercalary years having an additional day appended to the last month. The mean length of the year is therefore 354-11/30 days, or 354 days 8 hours 48 min., which divided by 12 gives 29-191/360 days, or 29 days 12 hours 44 min., as the time of a mean lunation, and this differs from the astronomical mean lunation by only 2.8 seconds. This small error will only amount to a day in about 2400 years.

To find if a year is intercalary or common, divide it by 30; the quotient will be the number of completed cycles and the remainder will be the year of the current cycle; if this last be one of the numbers 2, 5, 7, 10, 13, 16, 18, 21, 24, 26, 29, the year is intercalary and consists of 355 days; if it be any other number, the year is ordinary.

Or if Y denote the number of the Mahommedan year, and

R = ((11 Y + 14) / 30)_r,

the year is intercalary when R < 11.

[v.04 p.1002] Also the number of intercalary years from the year 1 up to the year Y inclusive = ((11 Y + 14) / 30)w; and the same up to the year Y - 1 = (11 Y + 3 / 30)w.

To find the day of the week on which any year of the Hegira begins, we observe that the year 1 began on a Friday, and that after every common year of 354 days, or 50 weeks and 4 days, the day of the week must necessarily become postponed 4 days, besides the additional day of each intercalary year.

Hence if w = 1 2 3 4 5 6 7 indicate Sun. Mon. Tue. Wed. Thur. Frid. Sat.

the day of the week on which the year Y commences will be

w = 2 + 4(Y / 7)r + ((11 Y + 3) / 30)w (rejecting sevens).

But, 30 ((11 Y + 3) / 30)w + ((11 Y + 3) / 30)r = 11 Y + 3

gives 120((11 Y + 3) / 30)w = 12 + 44 Y - 4((11 Y + 3) / 30)r,

or ((11 Y + 3) / 30)w = 5 + 2 Y + 3((11 Y + 3) / 30)r (rejecting sevens).

So that

w = 6(Y / 7)r + 3((11 Y + 3) / 30)r (rejecting sevens),

the values of which obviously circulate in a period of 7 times 30 or 210 years.

Let C denote the number of completed cycles, and y the year of the cycle; then Y = 30 C + y, and

w = 5(C / 7)_r + 6(y / 7)_r + 3((11 y +3) / 30)_r (rejecting sevens).

From this formula the following table has been constructed:—

TABLE VIII.

Year of the Number of the Period of Seven Cycles = (C/7)_r Current Cycle (y) 0 1 2 3 4 5 6 0 8 Mon. Sat. Thur. Tues. Sun. Frid. Wed. 1 9 17 25 Frid. Wed. Mon. Sat. Thur. Tues. Sun. *2 *10 *18 *26 Tues. Sun. Frid. Wed. Mon. Sat. Thur. 3 11 19 27 Sun. Frid. Wed. Mon. Sat. Thur. Tues. 4 12 20 28 Thur. Tues. Sun. Frid. Wed. Mon. Sat. *5 *13 *21 *29 Mon. Sat. Thur. Tues. Sun. Frid. Wed. 6 14 22 30 Sat. Thur. Tues. Sun. Frid. Wed. Mon. *7 15 23 Wed. Mon. Sat. Thur. Tues. Sun. Frid. *16 *24 Sun. Frid. Wed. Mon. Sat. Thur. Tues.

To find from this table the day of the week on which any year of the Hegira commences, the rule to be observed will be as follows:—

Rule.—Divide the year of the Hegira by 30; the quotient is the number of cycles, and the remainder is the year of the current cycle. Next divide the number of cycles by 7, and the second remainder will be the Number of the Period, which being found at the top of the table, and the year of the cycle on the left hand, the required day of the week is immediately shown.

The intercalary years of the cycle are distinguished by an asterisk.

For the computation of the Christian date, the ratio of a mean year of the Hegira to a solar year is

Year of Hegira / Mean solar year = 354-11/30 / 365.2422 = 0.970224.

The year 1 began 16 July 622, Old Style, or 19 July 622, according to the New or Gregorian Style. Now the day of the year answering to the 19th of July is 200, which, in parts of the solar year, is 0.5476, and the number of years elapsed = Y - 1. Therefore, as the intercalary days are distributed with considerable regularity in both calendars, the date of commencement of the year Y expressed in Gregorian years is

0.970224 (Y - 1) + 622.5476, or 0.970224 Y + 621.5774.

This formula gives the following rule for calculating the date of the commencement of any year of the Hegira, according to the Gregorian or New Style.

Rule.—Multiply 970224 by the year of the Hegira, cut off six decimals from the product, and add 621.5774. The sum will be the year of the Christian era, and the day of the year will be found by multiplying the decimal figures by 365.

The result may sometimes differ a day from the truth, as the intercalary days do not occur simultaneously; but as the day of the week can always be accurately obtained from the foregoing table, the result can be readily adjusted.

Example.—Required the date on which the year 1362 of the Hegira begins.

970224 1362 ———— 1940448 5821344 2910672 970224 —————- 1321.445088 621.5774 —————- 1943.0225 365 —— 1125 1350 675 ——— 8.2125

Thus the date is the 8th day, or the 8th of January, of the year 1943.

To find, as a test, the accurate day of the week, the proposed year of the Hegira, divided by 30, gives 45 cycles, and remainder 12, the year of the current cycle.

Also 45, divided by 7, leaves a remainder 3 for the number of the period.

Therefore, referring to 3 at the top of the table, and 12 on the left, the required day is Friday.

The tables, page 571, show that 8th January 1943 is a Friday, therefore the date is exact.

For any other date of the Mahommedan year it is only requisite to know the names of the consecutive months, and the number of days in each; these are—

Muharram . . . . . . . 30 Saphar . . . . . . . . 29 Rabia I. . . . . . . . 30 Rabia II. . . . . . . . 29 Jomada I. . . . . . . . 30 Jomada II. . . . . . . 29 Rajab . . . . . . . . . 30 Shaaban . . . . . . . . 29 Ramadan . . . . . . . . 30 Shawall (Shawwal) . . . 29 Dulkaada (Dhu'l Qa'da) 30 Dulheggia (Dhu'l Hijja) 29 ) and in intercalary ) years . . . . . . . . 30 )

The ninth month, Ramadān, is the month of Abstinence observed by the Moslems.

The Moslem calendar may evidently be carried on indefinitely by successive addition, observing only to allow for the additional day that occurs in the bissextile and intercalary years; but for any remote date the computation according to the preceding rules will be most efficient, and such computation may be usefully employed as a check on the accuracy of any considerable extension of the calendar by induction alone.

The following table, taken from Woolhouse's Measures, Weights and Moneys of all Nations, shows the dates of commencement of Mahommedan years from 1845 up to 2047, or from the 43rd to the 49th cycle inclusive, which form the whole of the seventh period of seven cycles. Throughout the next period of seven cycles, and all other like periods, the days of the week will recur in exactly the same order. All the tables of this kind previously published, which extend beyond the year 1900 of the Christian era, are erroneous, not excepting the celebrated French work, L'Art de verifier les dates, so justly regarded as the greatest authority in chronological matters. The errors have probably arisen from a continued excess of 10 in the discrimination of the intercalary years.

TABLE IX.—Mahommedan Years.

43rd Cycle. 46th Cycle. (continued.) Year of Commencement Year of Commencement Hegira. (1st of Muharram). Hegira. (1st of Muharram). 1261 Frid. 10 Jan. 1845 1365 Thur. 6 Dec. 1945 1262* Tues. 30 Dec. 1845 1366* Mon. 25 Nov. 1946 1263 Sun. 20 Dec. 1846 1367 Sat. 15 Nov. 1947 1264 Thur. 9 Dec. 1847 1368* Wed. 3 Nov. 1948 1265* Mon. 27 Nov. 1848 1369 Mon. 24 Oct. 1949 1266 Sat. 17 Nov. 1849 1370 Frid. 13 Oct. 1950 1267* Wed. 6 Nov. 1850 1371* Tues. 2 Oct. 1951 1268 Mon. 27 Oct. 1851 1372 Sun. 21 Sept. 1952 1269 Frid. 15 Oct. 1852 1373 Thur. 10 Sept. 1953 1270* Tues. 4 Oct. 1853 1374* Mon. 30 Aug. 1954 1271 Sun. 24 Sept. 1854 1375 Sat. 20 Aug. 1955 1272 Thur. 13 Sept. 1855 1376* Wed. 8 Aug. 1956 1273* Mon. 1 Sept. 1856 1377 Mon. 29 July 1957 1274 Sat. 22 Aug. 1857 1378 Frid. 18 July 1958 1275 Wed. 11 Aug. 1858 1379* Tues. 7 July 1959 1276* Sun. 31 July 1859 1380 Sun. 26 June 1960 1277* Frid. 20 July 1860 1278* Tues. 9 July 1861 47th Cycle. 1279 Sun. 29 June 1862 1381 Thur. 15 June 1961 1280 Thur. 18 June 1863 1382* Mon. 4 June 1962 1281* Mon. 6 June 1864 1383 Sat. 25 May 1963 1282 Sat. 27 May 1865 1384 Wed. 13 May 1964 1283 Wed. 16 May 1866 1385* Sun. 2 May 1965 1284* Sun. 5 May 1867 1386 Frid. 22 April 1966 1285 Frid. 24 April 1868 1387* Tues. 11 April 1967 1286* Tues. 13 April 1869 1388 Sun. 31 Mar. 1968 1287 Sun. 3 April 1870 1389 Thur. 20 Mar. 1969 1288 Thur. 23 Mar. 1871 1390* Mon. 9 Mar. 1970 1289* Mon. 11 Mar. 1872 1391 Sat. 27 Feb. 1971 1290 Sat. 1 Mar. 1873 1392 Wed. 16 Feb. 1972 1393* Sun. 4 Feb. 1973 44th Cycle. 1394 Frid. 25 Jan. 1974 1291 Wed. 18 Feb. 1874 1395 Tues. 14 Jan. 1975 1292* Sun. 7 Feb. 1875 1396* Sat. 3 Jan. 1976 1293 Frid. 28 Jan. 1876 1397 Thur. 23 Dec. 1976 1294 Tues. 16 Jan. 1877 1398* Mon. 12 Dec. 1977 1295* Sat. 5 Jan. 1878 1399 Sat. 2 Dec. 1978 1296 Thur. 26 Dec. 1878 1400 Wed. 21 Nov. 1979 1297* Mon. 15 Dec. 1879 1401* Sun. 9 Nov. 1980 1298 Sat. 4 Dec. 1880 1402 Frid. 30 Oct. 1981 1299 Wed. 23 Nov. 1881 1403 Tues. 19 Oct. 1982 1300* Sun. 12 Nov. 1882 1404* Sat. 8 Oct. 1983 1301 Frid. 2 Nov. 1883 1405 Thur. 27 Sept. 1984 1302 Tues. 21 Oct. 1884 1406* Mon. 16 Sept. 1985 1303* Sat. 10 Oct. 1885 1407 Sat. 6 Sept. 1986 1304 Thur. 30 Sept. 1886 1408 Wed. 26 Aug. 1987 1305 Mon. 19 Sept. 1887 1409* Sun. 14 Aug. 1988 1306* Frid. 7 Sept. 1888 1410 Frid. 4 Aug. 1989 1307 Wed. 28 Aug. 1889 1308* Sun. 17 Aug. 1890 48th Cycle. 1309 Frid. 7 Aug. 1891 1411 Tues. 24 July 1990 1310 Tues. 26 July 1892 1412* Sat. 13 July 1991 1311* Sat. 15 July 1893 1413 Thur. 2 July 1992 1312 Thur. 5 July 1894 1414 Mon. 21 June 1993 1313 Mon. 24 June 1895 1415* Frid. 10 June 1994 1314* Frid. 12 June 1896 1416 Wed. 31 May 1995 1315 Wed. 2 June 1897 1417* Sun. 19 May 1996 1316* Sun. 22 May 1898 1418 Frid. 9 May 1997 1317 Frid. 12 May 1899 1419 Tues. 28 April 1998 1318 Tues. 1 May 1900 1420* Sat. 17 April 1999 1319* Sat. 20 April 1901 1421 Thur. 6 April 2000 1320 Thur. 10 April 1902 1422 Mon. 26 Mar. 2001 1423 Frid. 15 Mar. 2002 45th Cycle. 1424 Wed. 5 Mar. 2003 1321 Mon. 30 Mar. 1903 1425 Sun. 22 Feb. 2004 1322* Frid. 18 Mar. 1904 1426* Thur. 10 Feb. 2005 1323 Wed. 8 Mar. 1905 1427 Tues. 31 Jan. 2006 1324 Sun. 25 Feb. 1906 1428* Sat. 20 Jan. 2007 1325 Thur. 14 Feb. 1907 1429 Thur. 10 Jan. 2008 1326 Tues. 4 Feb. 1908 1430 Mon. 29 Dec. 2008 1327* Sat. 23 Jan. 1909 1431* Frid. 18 Dec. 2009 1328 Thur. 13 Jan. 1910 1432 Wed. 8 Dec. 2010 1329 Mon. 2 Jan. 1911 1433 Sun. 27 Nov. 2011 1330* Frid. 22 Dec. 1911 1434* Thur. 15 Nov. 2012 1331 Wed. 11 Dec. 1912 1435 Tues. 5 Nov. 2013 1332 Sun. 30 Nov. 1913 1436* Sat. 25 Oct. 2014 1333* Thur. 19 Nov. 1914 1437 Thur. 15 Oct. 2015 1334 Tues. 9 Nov. 1915 1438 Mon. 3 Oct. 2016 1335 Sat. 28 Oct. 1916 1439* Frid. 22 Sept. 2017 1336* Wed. 17 Oct. 1917 1440 Wed. 12 Sept. 2018 1337 Mon. 7 Oct. 1918 [v.04 p.1003] 1338* Frid. 26 Sept. 1919 49th Cycle. 1339 Wed. 15 Sept. 1920 1441 Sun. 1 Sept. 2019 1340 Sun. 4 Sept. 1921 1442* Thur. 20 Aug. 2020 1341* Thur. 24 Aug. 1922 1443 Tues. 10 Aug. 2021 1342 Tues. 14 Aug. 1923 1444 Sat. 30 July 2022 1343 Sat. 2 Aug. 1924 1445* Wed. 19 July 2023 1344* Wed. 22 July 1925 1446 Mon. 8 July 2024 1345 Mon. 12 July 1926 1447* Frid. 27 June 2025 1346* Frid. 1 July 1927 1448 Wed. 17 June 2026 1347 Wed. 20 June 1928 1449 Sun. 6 June 2027 1348 Sun. 9 June 1929 1450* Thur. 25 May 2028 1349* Thur. 29 May 1930 1451 Tues. 15 May 2029 1350 Tues. 19 May 1931 1452 Sat. 4 May 2030 1453* Wed. 23 April 2031 46th Cycle. 1454 Mon. 12 April 2032 1351 Sat. 7 May 1932 1455 Frid. 1 April 2033 1352* Wed. 26 April 1933 1456* Tues. 21 Mar. 2034 1353 Mon. 16 April 1934 1457 Sun. 11 Mar. 2035 1354 Frid. 5 April 1935 1458* Thur. 28 Feb. 2036 1355* Tues. 24 Mar. 1936 1459 Tues. 17 Feb. 2037 1356 Sun. 14 Mar. 1937 1460 Sat. 6 Feb. 2038 1357* Thur. 3 Mar. 1938 1461* Wed. 26 Jan. 2039 1358 Tues. 21 Feb. 1939 1462 Mon. 16 Jan. 2040 1359 Sat. 10 Feb. 1940 1463 Frid. 4 Jan. 2041 1360* Wed. 29 Jan. 1941 1464* Tues. 24 Dec. 2041 1361 Mon. 19 Jan. 1942 1465 Sun. 14 Dec. 2042 1362 Frid. 8 Jan. 1943 1466* Thur. 3 Dec. 2043 1363* Tues. 28 Dec. 1943 1467 Tues. 22 Nov. 2044 1364 Sun. 17 Dec. 1944 1468 Sat. 11 Nov. 2045

TABLE X.—Principal Days of the Hebrew Calendar.

Tisri 1, New Year, Feast of Trumpets. " 3,[1] Fast of Guedaliah. " 10, Fast of Expiation. " 15, Feast of Tabernacles. " 21, Last Day of the Festival. " 22, Feast of the 8th Day. " 23, Rejoicing of the Law. Kislev 25, Dedication of the Temple. Tebet 10, Fast, Siege of Jerusalem. Adar 13,[2] Fast of Esther, } In embolismic " 14, Purim, } years, Veadar. Nisan 15, Passover. Sivan 6, Pentecost. Tamuz 17,[1] Fast, Taking of Jerusalem. Ab 9.[1] Fast, Destruction of the Temple.

[1] If Saturday, substitute Sunday immediately following.

[2] If Saturday, substitute Thursday immediately preceding.

TABLE XI.—Principal Days of the Mahommedan Calendar.

Muharram 1, New Year. " 10, Ashura. Rabia I. 11, Birth of Mahomet. Jornada I. 20, Taking of Constantinople. Rajab 15, Day of Victory. " 20, Exaltation of Mahomet. Shaaban 15, Borak's Night. Shawall 1,2,3, Kutshuk Bairam. Dulheggia 10, Qurban Bairam.

TABLE XII.—Epochs, Eras, and Periods.

Name. Christian Date of Commencement.

Grecian Mundane era 1 Sep. 5598 B.C. Civil era of Constantinople 1 Sep. 5508 " Alexandrian era 29 Aug. 5502 " Ecclesiastical era of Antioch 1 Sep. 5492 " Julian Period 1 Jan. 4713 " Mundane era Oct. 4008 " Jewish Mundane era Oct. 3761 " Era of Abraham 1 Oct. 2015 " Era of the Olympiads 1 July 776 " Roman era 24 April 753 " Era of Nabonassar 26 Feb. 747 " Metonic Cycle 15 July 432 " Grecian or Syro-Macedonian era 1 Sep. 312 " Tyrian era 19 Oct. 125 " Sidonian era Oct. 110 " Caesarean era of Antioch 1 Sep. 48 " Julian year 1 Jan. 45 " Spanish era 1 Jan. 38 " Actian era 1 Jan. 30 " Augustan era 14 Feb. 27 " Vulgar Christian era 1 Jan. 1 A.D. Destruction of Jerusalem 1 Sep. 69 " Era of Maccabees 24 Nov. 166 " Era of Diocletian 17 Sep. 284 " Era of Ascension 12 Nov. 295 " Era of the Armenians 7 July 552 " Mahommedan era of the Hegira 16 July 622 " Persian era of Yezdegird 16 June 632 "

For the Revolutionary Calendar see FRENCH REVOLUTION ad fin.

The principal works on the calendar are the following:—Clavius, Romani Calendarii a Gregorio XIII. P.M. restituti Explicatio (Rome, 1603); L'Art de verifier les dates; Lalande, Astronomie tome ii.; Traite de la sphere et du calendrier, par M. Revard (Paris, 1816); Delambre, Traite de l'astronomie theorique et pratique, tome iii.; Histoire de l'astronomie moderne; Methodus technica brevis, perfacilis, ac perpetua construendi Calendarium Ecclesiasticum, Stylo tam novo quam vetere, pro cunctis Christianis Europae populis, &c., auctore Paulo Tittel (Gottingen, 1816); Formole analitiche pel calcolo delta Pasgua, e correzione di quello di Gauss, con critiche osservazioni su quanta ha scritto del calendario il Delambri, di Lodovico Ciccolini (Rome, 1817); E.H. Lindo, Jewish Calendar for Sixty-four Years (1838); W.S.B. Woolhouse, Measures, Weights, and Moneys of all Nations (1869).

(T. G.; W. S. B. W.)

CALENDER, (1) (Fr. calendre, from the Med. Lat. calendra, a corruption of the Latinized form of the Gr. [Greek: kulindros], a cylinder), a machine consisting of two or more rollers or cylinders in close contact with each other, and often heated, through which are passed cotton, calico and other fabrics, for the purpose of having a finished smooth surface given to them; the process flattens the fibres, removes inequalities, and also gives a glaze to the surface. It is similarly employed in paper manufacture (q.v.). (2) (From the Arabic qalandar), an order of dervishes, who separated from the Baktashite order in the 14th century; they were vowed to perpetual travelling. Other forms of the name by which they are known are Kalenderis, Kalenderites, and Qalandarites (see DERVISH).

CALENUS, QUINTUS FUFIUS, Roman general. As tribune of the people in 61 B.C., he wa$ chiefly instrumental in securing the acquittal of the notorious Publius Clodius when charged with having profaned the mysteries of Bona Dea (Cicero, Ad. Att. i. 16). In 59 Calenus was praetor, and brought forward a law that the senators, knights, and tribuni aerarii, who composed the judices, should vote separately, so that it might be known how they gave their votes (Dio Cassius xxxviii. 8). He fought in Gaul (51) and Spain (49) under Caesar, who, after he had crossed over to Greece (48), sent Calenus from Epirus to bring over the rest of the troops from Italy. On the passage to Italy, most of the ships were captured by Bibulus and Calenus himself escaped with difficulty. In 47 he was raised to the consulship through the influence of Caesar. After the death of the dictator, he joined Antony, whose legions he afterwards commanded in the north of Italy. He died in 41, while stationed with his army at the foot of the Alps, just as he was on the point of marching against Octavianus.

Caesar, B.G. viii. 39; B.C. i. 87, iii. 26; Cic. Philippicae, viii. 4.

CALEPINO, AMBROGIO (1435-1511), Italian lexicographer, born at Bergamo in 1435, was descended of an old family of Calepio, whence he took his name. Becoming an Augustinian monk, he devoted his whole life to the composition of a polyglott dictionary, first printed at Reggio in 1502. This gigantic work was afterwards augmented by Passerat and others. The most complete edition, published at Basel in 1590, comprises no fewer than eleven languages. The best edition is that published at Padua in seven languages in 1772. Calepino died blind in 1511.

CALES (mod. Calvi), an ancient city of Campania, belonging Originally to the Aurunci, on the Via Latina, 8 m. N.N.W. of Casilinum. It was taken by the Romans in 335 B.C., and, a colony with Latin rights of 2500 citizens having been established there, it was for a long time the centre of the Roman dominion in Campania, and the seat of the quaestor for southern Italy even down to the days of Tacitus.[1] It was an important base in the war against Hannibal, and at last refused further contributions for the war. Before 184 more settlers were sent there. After the Social War it became a municipium. The fertility of its territory and its manufacture of black glazed pottery, which was even exported to Etruria, made it prosperous. At the end of the 3rd century it appears as a colony, and in the 5th century it became an episcopal see, which (jointly with Teano since 1818) it still is, though it is now a mere village. The cathedral, of the 12th century, has a carved portal and three apses decorated with small arches and pilasters, and contains a fine pulpit and episcopal throne in marble mosaic. Near it are two grottos [v.04 p.1004] which have been used for Christian worship and contain frescoes of the 10th and 11th centuries (E. Bertaux, L'Art dans l'Italie meridionale (Paris, 1904), i. 244, &c.). Inscriptions name six gates of the town: and there are considerable remains of antiquity, especially of an amphitheatre and theatre, of a supposed temple, and other edifices. A number of tombs belonging to the Roman necropolis were discovered in 1883.

See C. Huelsen in Pauly-Wissowa, Realencyclopaedie, iii. 1351 (Stuttgart, 1899).

(T. AS.)

[1] To the period after 335 belong numerous silver and bronze coins with the legend Caleno.

CALF. (1) (A word common in various forms to Teutonic languages, cf. German Kalb, and Dutch kalf), the young of the family of Bovidae, and particularly of the domestic cow, also of the elephant, and of marine mammals, as the whale and seal. The word is applied to a small island close to a larger one, like a calf close to its mother's side, as in the "Calf of Man," and to a mass of ice detached from an iceberg. (2) (Of unknown origin, possibly connected with the Celtic calpa, a leg), the fleshy hinder part of the leg, between the knee and the ankle.

CALF, THE GOLDEN, a molten image made by the Israelites when Moses had ascended the Mount of Yahweh to receive the Law (Ex. xxxii.). Alarmed at his lengthy absence the people clamoured for "gods" to lead them, and at the instigation of Aaron, they brought their jewelry and made the calf out of it. This was celebrated by a sacred festival, and it was only through the intervention of Moses that the people were saved from the wrath of Yahweh (cp. Deut. ix. 19 sqq.). Nevertheless 3000 of them fell at the hands of the Levites who, in answer to the summons of Moses, declared themselves on the side of Yahweh. The origin of this particular form of worship can scarcely be sought in Egypt; the Apis which was worshipped there was a live bull, and image-worship was common among the Canaanites in connexion with the cult of Baal and Astarte (qq.v.). In early Israel it was considered natural to worship Yahweh by means of images (cp. the story of Gideon, Judg. viii. 24 sqq.), and even to Moses himself was attributed the bronze-serpent whose cult at Jerusalem was destroyed in the time of Hezekiah (2 Kings xviii. 4, Num. xxi. 4-9). The condemnation which later writers, particularly those imbued with the spirit of the Deuteronomic reformation, pass upon all image-worship, is in harmony with the judgment upon Jeroboam for his innovations at Bethel and Dan (1 Kings xii. 28 sqq., xvi. 26, &c.). But neither Elijah nor Elisha raised a voice against the cult; then, as later, in the time of Amos, it was nominally Yahweh-worship, and Hosea is the first to regard it as the fundamental cause of Israel's misery.

See further, W.R. Smith, Prophets of Israel, pp. 175 sqq.; Kennedy, Hastings' Dict. Bib. i. 342; and HEBREW RELIGION.

(S. A. C.)

CALGARY, the oldest city in the province of Alberta. Pop. (1901) 4091; (1907) 21,112. It is situated in 114 deg. 15' W., and 51 deg. 41/2' N., on the Bow river, which flows with its crystal waters from the pass in the Rocky Mountains, by which the main line of the Canadian Pacific railway crosses the Rocky Mountains. The pass proper—Kananaskis—penetrates the mountains beginning 40 m. west of Calgary, and the well-known watering-place, Banff, lies 81 m. west of it, in the Canadian national park. The streets are wide and laid out on a rectangular system. The buildings are largely of stone, the building stone used being the brown Laramie sandstone found in the valley of the Bow river in the neighbourhood of the city. Calgary is an important point on the Canadian Pacific railway, which has a general superintendent resident here. It is an important centre of wholesale dealers, and also of industrial establishments. Calgary is near the site of Fort La Jonquiere founded by the French in 1752. Old Bow fort was a trading post for many years though now in ruins. The present city was created by the building of the Canadian Pacific railway about 1883.

* * * * *

Corrections made to printed original.

p. 795, Buelow, Hans Guido von: "married in his twenty-eighth year": 'twenty-eight' in original.

p. 843, Internal Communications: "a great deal of road construction": 'constuction' in original.

p. 854, "Italian work Saggi sul Ristabilimento...": 'Saggj' in original.

p. 884, 6th para: "Throughout the whole of the Analogy it is manifest": 'manfest' in original.

p. 894, Buys Ballot's Law: "takes its name from C.H.D. Buys Ballot": 'Ballott' in original.

p. 904, 4th para: "additions to already existing types": 'exsiting' in original.

p. 905, Biographies etc: Prisoner of Chillon and other Poems, edited by E. Koelbing (1896): '1869' in original, the place in this list implies 1896 and other sources support this.

p. 914, Cabasilas, Nicolaus: "a speech against usurers": 'againt' in original.

p. 970, 3rd para: "coloured by cobalt": 'colbalt' in original.

p. 976, 1st equation: "P = 1/2 l squared/c w": the = sign is printed vertically in original.

p. 979, 11th piece of text: "A_2 is proportional to the roll of W_2": 'roll of w_2' in original: but properly W_2 is the wheel, w_2 is the measure of its roll.

p. 996, Table III: column 11 begins 20-17-19-17-16 in original, this should be 20-19-18-17-16 (as described earlier, the columns are arranged in the order of the natural numbers, beginning at the bottom and proceeding to the top of the column.)

p. 997, Table IV: Nov 27. contains "25'24" in original: according to the text, 25 beside 24 should not be accented.

p. 999 Condition "When E < 24": 'When < 24' in original.

p. 1000, Table VII: 5620 shown starting "29 Sept. 1858" in original: must be 1859.

THE END