STUDIES,

PERPETUAL CALENDAR

FOR FINDING THE DAY OF THE WEEK ON WHICH ANY DAY OF ANY MONTH FALLS IN ANY YEAR BEFORE

OR AFTER CHRIST, OLD STYLE OR NEW.

EXAMPLE 1. To find the day of the week for July 4th, 1881. Opposite Century 19, New Style, and over year 81, is Saturday. Therefore, July 2d is Saturday; and the line of week-days in which Saturday falls under July (which is the second line), with the days of the month above, constitutes the entire Calendar for July, 1881, according to which the 4th falls on Monday.

EXAMPLE 2. To find the day of the week on which Columbus discov ered America, October 12, 1492, Old Style. Opposite Century 15, Old Style, and over 92 in black letter (it being leap year), is Monday. Therefore, October 8th was Monday; and the line of week-days in which Monday falls under Mondays (which is the sixth), with the days of the month above, constitutes the entire Calendar for October, 1492, Old Style, and the 12th, as seen falls on Friday.

Copyright, 1875, by Jos. P. Bradley

9 10

40

44 45

50 51

60

61

62

66

67 68

72

72

73

77

78

82 83 84

forms

the

entire

TABLE

FOR FINDING MEAN TIME OF NEW MOON FOR ANY MONTH
AND YEAR IN A PERIOD OF THIRTY CENTURIES.

DIRECTIONS -Add together time of Centurial New Moon and Moon's advance for the year, applying correction; deduct retardation for the month, adding a lunation (29d. 12h. 44m.) if necessary; or casting out a lunation if the result exceeds the number of days in the month; the remainder will be the time of mean New Moon for the month required. For mean Full Moon, add or subtract half a lunation (14d. 18h 22m.) EXAMPLE: Required mean New Moon for October, 1879. Here, Centurial New Moon for 1801 N. S. is 14d. 14h. 31m.; Moon's advance for 79, 8d. 6h. 21m.: sum, 22d. 20h. 52m. Correction for Cycle V.,-5h. 55m.; remainder, 22d. 14. 57m. Retardation for October, 7d. 5h 24m.; which deducted, leaves 15d. 9h. 33m. That is, Mean New Moon October 15, at 9h. 33m.A.M.

THE NEW CALENDAR PROPOSED.

[From The Nation of April 29, 1875.]

The National Academy of Sciences has just concluded its April meeting in Washington, which was held at the Smithsonian Institution, under the presidency of Professor Henry. The attendance was not large, either of members or of the public, but a respectable number of papers were read, of which a very full report has been given by the Tribune. Of the more strictly scientific papers that of Professor Loomis of Yale College on the results to be reached from a discussion of the signal service maps, and Professor Langley's account of Solar phenomena observed at Allegheny Observatory, were of most general interest whilst President Barnard's Report for the Committee on Weights, Measures and Coinage, and Mr. Justice Bradley's (of the Supreme Court) proposal for a reform of the Gregorian Calendar, referred most directly to practical questions. The reform of the calendar has been somewhat fully discussed lately, and a bill setting forth that "the Gregorian year pays no proper respect to the cardinal points in the earth's orbit," and proposing to secure such respect, was laid before the House of Representatives at its last session. Mr. Justice Bradley's plan proposes to fix the beginning of the year at the winter solstice (December 21) and to divide it into four unequal parts of 90, 93, 93 and 89 days. In leap years the last part is to have 90 days. In the remarks on this paper a much better plan was mentioned, which had been previously discussed by the Philosophical Society of Washington. This was to begin the year with 21st December, and

to divide it into six parts of two months each, each part to have sixty-one days in leap years, and the last part to have but sixty days in common years.

The scheme would be somewhat as follows for a common year of both systems:

Gregorian 31 28

Ideal

Jan. Feb. Mch. Apl. May Jun. July Aug. Sep. Oct. Nov. Dec.
31 30 31 30 31 31 30 31 30 31
31 30 31 30 31 30
30 31 30 30

31 30

Thus, only February, August and December would be altered by this ingenious plan, which is due to Mr. E. B. Elliott, the statistician.

[From The Nation, May 13, 1875].

An esteemed correspondent writes us from Washington: "In noticing Mr. Justice Bradley's proposed arrangement of the calendar, you did not explain the manner in which, by his plan, the year would be divided into four quarters of three months each, exactly corresponding with the four natural divisions of the year made by the sun's arrival at the two equinoxes and two solstices. Thus, beginning at the winter solstice, when the sun is at the extreme southerly point reached by him, where he commences his return to the north, Judge Bradley would place the new year, or January 1st, on the present 21st day of December. Then giving to January, February and March each thirty days, the 1st of April, or beginning of the second quarter, will, in common years, fall on the 21st of March, and in leap year, on the 20th of March, or exactly at the vernal equinox, when the sun is on the equinoctial line and the days and nights are equal. Then, giving to the next six months, each thirty-one

days, the 1st of July, or the beginning of the third quarter will fall in common years on the present 22d of June, and in leap years on the 21st, which is the summer solstice, when the sun is at his farthest point north, and the days are longest; and the 1st of October, or beginning of the fourth quarter, will fall in common years on the 23d September, and in leap years on the 22d, which is the autumnal equinox, when the sun recrosses the line and the days and nights are equal again. Then giving to October and November each thirty days, and to December twentynine in common years and thirty in leap years, the 1st of January will again fall on the present 21st of December in all cases. This allotment of days to each month is easy to remember; is as convenient as any, and makes them correspond to the great natural phenomena of the sun's annual circuit. It is a lesson in astronomy in itself, and is generally approved as the best plan that has been proposed. The placing of the intercalary day of leap year at the end of the year would be a great advantage in all astronomical calculations and arrangements of the calendar. And the conformity of the entire civil year to the natural year would, of course, be an advantage amply sufficient to compensate for any temporary inconvenience arising from the change. No alteration in the recurrence of leap years from the arrangement of the Gregorian Calendar is proposed. That is sufficiently accurate for many centuries to come. The law prepared by Judge Bradley to effect the proposed change, and which was read to the National Academy of Science, is extremely simple and comprehensive, and would obviate all inconveniences of a business character that could possibly arise.