The concurrence of the solar and the civil year was restored by Gregory in 1582, or 1600 is the same in computation; but the discrepancy between civil and solar time is 11 minutes and 10.38 seconds every year, which in 100 years will amount to 18 hours, and 37.3 minutes; reckoned in round numbers 18 hours, and is represented on the chart, hours behind time 18.

The intercalary day or 24 hours being suppressed in 1700, causes the civil year to be 6 hours in advance of the solar, and is represented on the chart 6 hours in advance.

Now this discrepancy of 18 hours for the next 100 years, will cause the civil year in 1800 to be 12 hours behind; again suppressing the intercalation it will be 12 hours in advance. In 1900 it will be 6 hours behind, but the correction makes 18 hours in advance. The 18 hours gained the next 100 years restores the coincidence in the year 2000 and so on, the solar and the civil year being made to coincide very nearly every 400 years.

From close examination it will become evident that the solar and the civil year coincide twice every 400 years, though no account is made of it in computation. From 6 hours in advance in 1700, the civil year falls back to 12 hours behind the solar in 1800, consequently they must coincide in 1733.

Again from 12 hours in advance in 1800, it falls back to 6 hours behind the solar in 1900, consequently they must coincide again in 1867.

Discrepancy between Julian and solar time in—1 year is (365d. 6h.) - (365d. 5h. 48m. 49.62s.) = (11m. 10.38s.)

100years is(11m. 10.38s.) × 100 = (18h. 37.3.)
400"(18h. 37.3m.) × 4 = (3d. 2h. 29.2m.)
4,000"(3d. 2h. 29.2m.) × 10 = (31d. 0h. 52m.)
100,000"(31d. 0h. 52m.) × 25 = (773d. 21h. 40m.)

Discrepancy between Gregorian and solar time in—

1year is .373m.
100years is.373m. × 100 =37.3m.
400years37.3m. × 4 =2h. 29.2m.
4,000"(2h. 29.2m.) × 10 =1d. 0h. 52m.
100,000"(1d. 0h. 52m.) × 25 =25d. 21h. 40m.

Discrepancy between corrected Gregorian and solar time in—