Chapter XXXIV: A Perpetual Calendar

BY HERR H. F. L. MEYER.

EXPLANATIONS.

Various perpetual calendars have been published, but some of them are very elaborate, and others incorrect; therefore, by the editor’s invitation, I now present one in a most handy form. Table 1 shows the centuries, with the key numbers; Table 2, the last two figures of the year, and the seven key numbers below; Table 3, the months; and Table 4, the days. The key numbers are printed thick, the leap years in italics. January and February have two keys each, 3 and 6 for common years, 2 and 5 for leap years. The eleven days from September 3rd to 13th, 1752, were omitted. Every year which divides by 4 without a remainder is a leap year, except the centenaries, which are printed upright.

---------------+----------------------------------+-----------------+
TABLE 1. | TABLE 2. | TABLE 3. |
---------------+----+----+----+----+----+----+----+-----------------+
First =2= | 00 | 01 | 02 | 03 | |_04_| 05 |Jan. =3= _2_[C]|
_100_ =1= | 06 | 07 | |_08_| 09 | 10 | 11 |Feb. =6= _5_[C]|
_200_ =0= | |_12_| 13 | 14 | 15 | |_16_|Mar. =6= |
_300_ =6= | 17 | 18 | 19 | |_20_| 21 | 22 |Apr. =2= |
_400_ =5= | 23 | |_24_| 25 | 26 | 27 | |May =4= |
_500_ =4= |_28_| 29 | 30 | 31 | |_32_| 33 |June =0= |
_600_ =3= | 34 | 35 | |_36_| 37 | 38 | 39 |July =2= |
_700_ =2= | |_40_| 41 | 42 | 43 | |_44_|Aug. =5= |
_800_ =1= | 45 | 46 | 47 | |_48_| 49 | 50 |Sept. =1= |
_900_ =0= | 51 | |_52_| 53 | 54 | 55 | |Oct. =3= |
_1000_ =6= |_56_| 57 | 58 | 59 | |_60_| 61 |Nov. =6= |
_1100_ =5= | 62 | 63 | |_64_| 65 | 66 | 67 |Dec. =1= |
_1200_ =4= | |_68_| 69 | 70 | 71 | |_72_|
_1300_ =3= | 73 | 74 | 75 | |_76_| 77 | 78 |
_1400_ =2= | 79 | |_80_| 81 | 82 | 83 | |
_1500_ =1= |_84_| 85 | 86 | 87 | |_88_| 89 |
_1600_ =0= | 90 | 91 | |_92_| 93 | 94 | 95 |
_1700_{=6= [A] | |_96_| 97 | 98 | 99 | | |
{=2= [B] +----+----+----+----+----+----+----+
1800 =0= | =0=| =1=| =2=| =3=| =4=| =5=| =6=|
1900 =5=
_2000_ =4=
2100 =2=
2200 =0=
2300 =5=
_2400_ =4=

[A] 6 till Sept. 2, 1752.
[B] 2 from Sept. 14, 1752.
[C] _for leap years._

---------------------------------------+
TABLE 4. |
----+----+----+----+----+----+----+----+
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 8 | 9 | 10 | 11 | 12 | 13 | 14 |
| 15 | 16 | 17 | 18 | 19 | 20 | 21 |
| 22 | 23 | 24 | 25 | 26 | 27 | 28 |
| 29 | 30 | 31 | | | | |
=0= | S | M | T | W | Th | F | S |
=1= | M | T | W | Th | F | S | S |
=2= | T | W | Th | F | S | S | M |
=3= | W | Th | F | S | S | M | T |
=4= | Th | F | S | S | M | T | W |
=5= | F | S | S | M | T | W | Th |
=6= | S | S | M | T | W | Th | F |

EXAMPLES.

Example No. 1.--What day of the week was the 21st of June, 1581?

1500--key 1 in Table 1.
81--key 3 in Table 2.
June--key 0 in Table 3.
---
Total 4, the three keys added.

This 4 is the key for Table 4, where, on the right-hand side of this key, under the 21 st day, we find Wednesday.

If the three keys together make more than 6, seven is subtracted; and if more than 13, fourteen is deducted, and the remainder is the key to Table 4.

Thus we find June 6th, 1839, through 0 + 6 + 0 = 6, = Thursday.

August 9th, 1732, through 6 + 5 + 5 = 16, - 14 = 2 = Wednesday.

Columbus sailed from Palos on Friday, August 3rd, 1492, and discovered America on the 12th of October, 1492, which was also a Friday.

* * * * *

Example No. 2.--In what years will Christmas Day fall on a Sunday? Table 4 shows, below the 25th, the Sunday on the side of key 4; subtract the key of December, which is 1, there remains, for the present century, the key 3 of Table 2, showing the years 1887, 1892, 1898 and as this 4 for the next century will come from 5 + _x_ + 1 minus 7, it follows that _x_ means the key 5 in Table 2, which contains the years 1904, 1910, 1921, and the other years in that column.

We found the 6th of June, 1839, to be a Thursday, and see from the last column of Table 2 that it was again on a Thursday in 1844, 1850, 1861, etc.

Any one born on the 29th February, 1864, will have his birthday again on the same day of the week, a Monday, in 1892, that is, after an interval of 28 years, as is seen in the middle column of Table 2; and after that he will have it again on a Monday in 1904, 1932, etc.

HISTORICAL NOTES.

Romulus, the founder of Rome, established a year consisting of ten months, named Martius, Aprilis, Maius, Junius, Quintilis, Sextilis, September, October, November, and December; but in the succeeding reign, that of Numa, two months were added, called Januarius and Februarius.

Julius Cæsar, aided by Sosigenes, an Alexandrian astronomer, instituted the Julian Calendar, which has come down to our own epoch. It was then decided to give an additional day to every fourth year. The date of the reform was 45 B.C., which was the Roman year 708, dating from the foundation of Rome. The Julian year began on the 1st of January, 708 A.U.C., and ended on the 31st of December, 709 A.U.C. In the first 48 years of the reform there prevailed some confusion about the bissextile or leap years, because during the first 36 years every third year was reckoned a leap year (12 intercalations had taken place instead of 9); but, in order to rectify the error, the next 12 years (_i.e._ 9 B.C. to 3 A.D. inclusive), elapsed without an intercalary day, by decree of Cæsar Augustus, who also changed the names of Quintilis and Sextilis into Julius and Augustus, in honour of his uncle and himself. Thus the Roman years, 757, 761, 765, 769, etc., which were the years A.D. 4, 8, 12, 16, etc., were counted as leap years, and about all succeeding dates there is no doubt.

‘It was probably,’ writes Mr. Bond, of the Record Office, in his valuable work, ‘the original intention of Cæsar to commence the new year with the shortest day, the winter solstice at Rome, in the year 46 B.C. (common era), occurring on the 24th December of the Julian calendar. His motive for delaying the commencement for seven days longer, instead of taking the following day, was no doubt the desire to gratify the superstition of the Romans, by causing the commencement of the first year of the reformed calendar to fall on the day of the new moon, for it is found that the mean new moon occurred at Rome on the 1st of January, 45 B.C. (common era), at 6 h. 16 m. p.m.’

The Christian era was introduced in Italy, in the 6th century, by Dionysius the Little, a Roman abbot, and began to be used in Gaul in the 8th, though it was not generally followed in that country till a century later. From extant charters it is known to have been in use in England before the close of the 8th century. ‘At first, in A.D. 533,’ says Mr. Bond, ‘the era began with the 25th of March, but was subsequently reckoned from Christmas Day, the 25th of December, and in the 13th century, in some countries, was reckoned from the 1st of January according to the Julian era.’

The exact length of the mean solar or civil year is

365 d. 5 h. 48 m. 46 s.,

therefore the Julian year, being 365 days and 6 hours, departs from the course of the seasons at the rate of 11 m. 14 s., and consequently Aloysius Lilius, from Calabria, a physician and mathematician of Verona, projected a plan for amending the calendar, which induced Pope Gregory XIII. to introduce the plan on the 5th October, 1582, according to the former style, which day was decreed to be called the 15th October. These 10 days rectified the error of the past, in accordance with the day of the equinox, the 21st March. The error of the future, which was that an additional day every fourth year was too much, but that 129 years must elapse before the redundance would cause the equinox to be one day behind its time, was rectified thus: Adding 129 years to the year 1582 there results the year 1711, and it was decreed that the year 1700, which would, by the Julian Calendar, be a leap year, should be a common year, but, as stated below, it was still kept as a leap year in England, and appears as such in Table 1. In like manner 1800 was made a common year, and as in 1969 the 21st March would be a day behind the vernal equinox, it will be set right by making 1900 a common year. Another period of 129 years would extend to 2098, which will be remedied by making 2100 a common instead of a leap year.

Thus the equinox will be kept right by making three successive secular years common years; and the secular leap years will be those of which the first two figures are divisible by 4 without a remainder, as 2000, 2400, 2800, etc.

The keys or index figures in accordance with the Gregorian reform are these:--

CENTURIES. KEYS.
_1400_ =2=
_1500_ { =1= till October 4, 1582.
{ =5= from October 15, 1582.
_1600_ =4=
1700 =2=
1800 =0=

The Papal decree of October, 1582, was adopted in France in December, 1582, in Poland in 1586, in the Catholic States of Germany in 1583, in the Protestant German States, through Weigel’s Calendar, in 1700, in Denmark and Switzerland soon after the adoption in Germany, in England in September, 1752, whereas Russia still adheres to the Julian Calendar. Thus the Russian legal equinoxes are now twelve days in advance of the real equinoxes.

In England the years used to begin upon the 25th March, but it was declared that 1752 should end on the 31st December, and 1753 begin on the day formerly called the 1st January, 1752. At that time the people in England used to write the new style under the old, thus:--

30th June,
---------- 1753.
11th July,

25th February, 1753.
--------------------
8th March, 1754.

The death of Charles I. took place on Tuesday, January 30, 1648, as written at that time, but it is now written January 30, 1649, and often expressed by historians thus:--January 30, 1648-9.

In Scotland, the day after 31st December, 1599, was called 1st January, 1600.

The 4th August, 1581, was a Friday in all parts of Europe, but from 1582 to 1752 there was a variance in various parts, as there still is at present, between the east and the west of Europe. The variance was in the days of the month; the days of the week never changed. The 2nd September, 1752, was a Wednesday in England and in Russia, but a Saturday in the other States of Europe. Thus we find the 20th December, 1647, for England and Russia, through 0 + 2 + 1 = 3 = Monday, but for Italy, France, Spain, etc., through 4 + 2 + 1 = 7 - 7 = 0 = Friday. The 14th September, 1752, was a Monday in Russia, but a Thursday in England and the other European States. The 21st June, 1887, was a Tuesday in England, but in Russia it was twelve days later, that is, a Sunday, namely, the Sunday on which we had the 3rd of July. The Russians had the 9th June, 1887, on a Tuesday, that is the day on which we had the 21st June; and in writing to us they express that day thus:--

9
June --, 1887.
21

They have the key 6 for _1700_, and 5 for _1800_.

The Turks use the Mohammedan Calendar, from the Hegira, July 16, A.D. 622, and it is lunar like the Jewish.

The following historical dates agree with our calendar:--

The battle of Hastings was fought on Saturday, Oct. 14th, 1066.

The Magna Charta was signed on Sunday, May 24, 1215.

Edward II. was crowned on Sunday, 25th February, 1308 (1307 in the old style).

The battle of Crecy took place on Saturday, August 26th, 1346.

The battle of Towton, Yorkshire, occurred on Palm Sunday, March 29, 1461.

THE KEY NUMBERS.

The keys for the centuries and months can be arranged at pleasure, therefore the key 0 is chosen for the present century to calculate readily the dates of our time. To make the reckoning easy in the next century it will be well to have the key 0 for 1900, then the keys for the months must all be reduced by 2, and the tables will be:--

Jan. 1 and _0_ May 2 Sept. 6
1800 2 Feb. 4 and _3_ June 5 Oct. 1
1900 0 Mar. 4 July 0 Nov. 4
_2000_ 6 Apr. 0 Aug. 3 Dec. 6