second case 500 − 200 = 300.
But, when one of the dates is B.C. and the other A.D, the number of years elapsed between them is equal to the difference between the figures, standing before B.C. and A.D., diminished by 1. For example, the years elapsed between 1 January 500 B. C. and 1 January 200 A.D. is 200 − (−500) − 1 = 200 + 500 − 1 = 699, because the real difference between the years 1 B.C. and 1 A.D. is only 1, whilst in the formula 200 − (−500) or 200 + 500 this difference is reckoned as equal to 2.
As the tropical Solar year is the fundamental year in the European calendar, the cardinal stations of the Sun in its orbit should always in all centuries coincide with the same days of the series of 365 or 366 days, or with the same days of the same months.
In the year 45 B.C. the Roman emperor Julius Caesar drew uр a Calendar, called after him the Julian Calendar or the Old style.
Until this epoch the ancient European and Western-Asiatic nations the Romans, the Greeks, the Hebrews etc. had regulated their Calendar, according to the Lunar-year of twelve months, brought from time to time into accordance with the course of the Sun by the intercalation of a thirteenth month; in a similar manner as the Chinese have done from a very remote period to the present time.
The emperor Julius Caesar, in order to remove the disorder, caused by imperfect intercalation, decreed that the Calendar should be constructed only in accordance with the fun's course, without regard to that of the Moon.
In the Julian Calendar the length of the tropical year is supposed to be exactly equal to 365,25 days and in the year 45 B.C., the vernal equinox happened about the 23th March.
However, as the exact length of the tropical year is 365,24224 days, the error of the Julian Calendar is in one year 0,00776 days, in 130 years 1,0088 days, in 400 years 3,104 days and in 3600 years 27,936 days, and the Julian Calendar by its uninterrupted intercalations of one day after three common years of 365 days, the years not divisible by 4 without remainder containing 365 and those divisible by 4 containing 366 days, must in 130 years be behind by one day, in 400 years by three and in 3600 years by 28 days. Thus the Julian date of the vernal equinox, having been in 45 B. C. about the 23th March, is at present about the 9th March and was 325 A.D., at the time of the celebrated council of Nice about the 21 March. In order to correct the error of the Julian Calendar, which was in the year 1582 A.D. nearly 10 days, Pope Gregory XIII directed, that the 15th of October 1582 A.D. should be written instead of the 5th October 1582 A.D., thus omitting 10 days intercalated in excess during 325 A.D. until 1582 A.D. And further, in order to avoid for the
