Read Ebook: The Train Wire: A Discussion of the Science of Train Dispatching (Second Edition) by Anderson John Alexander

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PART FIRST.

DEFINITIONS--HISTORY.

PART SECOND.

MATHEMATICAL.

Some peculiarities concerning events which fall on the 29th of February 64

PART THIRD.

CYCLES--JULIAN PERIOD--EASTER.

ERRATA 149

OUR CALENDAR.

PART FIRST.

DEFINITIONS. HISTORY.

DEFINITIONS.

HISTORY OF THE DIVISIONS OF TIME AND THE OLD ROMAN CALENDAR.

The Roman day, from sunrise to sunset, and the night, from sunset to sunrise, were each divided at all seasons of the year into twelve hours, the hour being uniformly one-twelfth of the day or the night, of course, varied in length with the length of the day or night at different seasons of the year.

It will be seen by the table, and it is also recorded by Dio Cassius, of the second Century, that the Egyptian week commenced with Saturday. On their flight from Egypt the Jews, from hatred to their ancient oppressors, made Saturday the last day of the week. It is stated that the ancient Saxons borrowed the week from some Eastern nation, and substituted the names of their own divinities for those of the gods of Greece. The names of the days are here given in Latin, Saxon and English. It will be seen that the English names of the days are derived from the Saxon.

Quintilis was changed to July in honor of Julius Caesar, who was born on the 12th of that month 98 B. C. Sextilis was changed to August by the Roman Senate to flatter Augustus on his victories about 8 B. C. In the reign of Numa Pompilius, about 700 B. C., two months were added to the year, January at the beginning, and February at the end of the year. This arrangement continued till 450 B. C., when the Decemvirs changed the order, placing February after January, making March the third instead of the first month of the Roman year.

They made use of no intercalation, and by losing one-fourth of a day every year, the commencement of the year went back one day in every period of four years, and consequently made a revolution of the seasons in 1460 years. Hence the Egyptian year was called a vague or erratic year because the first day of the year in the course of 1460 years wandered, as it were, over all the seasons. Therefore 1460 Julian years of 365-1/4 days each are equal to 1461 Egyptian years of 365 days each.

The ancient Roman year consisted of twelve lunar months, of twenty-nine and thirty days alternately, which equals 354 days; but a day was added to make the number odd, which was considered more fortunate, so that the year consisted of 355 days.

This differed from the solar year by ten whole days and a fraction; but to restore the coincidence, Numa ordered an additional or intercalary month to be inserted every second year between the 23d and 24th of February, consisting of twenty-two and twenty-three days alternately, so that four years contained 1465 days, and the mean length of the year was consequently 366-1/4 days, so that the year was then too long by one day.

As the error amounted to twenty-four days in as many years, it was ordered that every third period of eight years, instead of containing four intercalary months, two of twenty-two and two of twenty-three days, amounting in all to ninety days, should contain only three of those months of twenty-two days each, amounting to sixty-six days, thereby suppressing twenty-four days in as many years, reducing the mean length of the year to 365-1/4 days.

Had the intercalations been regularly made the concurrence of the solar and the civil year would have been preserved very nearly. But its regulation was left to the pontiffs, who, to prolong the term of a magistracy or hasten an annual election, would give to the intercalary month a greater or less number of days, and consequently the calendar was thrown into confusion, so that in the time of Julius Caesar there was a discrepancy between the solar and the civil year of about three months; the winter months being carried back into autumn and the autumnal into summer.

A table of the order and the names of the planets in the Egyptian astronomy illustrating the origin of the names of the days of the week:

HISTORY OF THE REFORMATION OF THE CALENDAR BY JULIUS CAESAR.

In order to put an end to the disorders arising from the negligence or ignorance of the pontiffs, Julius Caesar, 46 B. C., abolished the use of the lunar year and the intercalary month, and regulated the civil year entirely by the Sun. With the advice and assistance of the astronomers, especially Sosigenes of Alexandria, he fixed the mean length of the year at 365-1/4 days, and decided that there should be three consecutive years of 365 days, and a fourth of 366.

In order to restore the vernal equinox to the 24th of March, the place it occupied in the time of Numa, two months, together consisting of 67 days, were inserted between the last day of November and the first day of December of that year. An intercalary month of 23 days had already been added to February of the same year according to the old method, so that the first Julian year commenced with the first day of January, 45 years before Christ, and 709 from the foundation of Rome, making the year A. U. C. 708 to consist of the prodigious number of 445 days, . Hence it was called by some the year of confusion; Macrobius said it should be named the last year of confusion.

There was also adopted at the same time a more commodious arrangement in the distribution of the days throughout the several months. It was decided to give to January, March, May, July, September and November each thirty-one days; and the other months thirty, excepting February, which in common years should have but twenty-nine days, but every fourth year thirty; so that the average length of the Julian year was 365-1/4 days.

Augustus Caesar interrupted this order by taking one day from February, reducing it to twenty-eight and giving it to August, that the month bearing his name should have as many days as July, which was named in honor of his great-uncle, Julius. In order that three months of thirty-one days might not come together, September and November were reduced to thirty days, and thirty-one given to October and December.

In the Julian calendar a day was added to February every fourth year, it being the shortest month, which was called the additional or intercalary day, and was inserted in the calendar between the 23d and 24th of that month. In the ancient Roman calendar the first day of every month was invariably called the calends. The 24th of February then was the 6th of the calends of March--Sexto calendas; the preceding, which was the additional or intercalary day, was called bis-sexto calendas , twice the sixth day. Hence the term bis-sextile as applied to every fourth year, commonly called leap-year. Appendix B.

True enough, the year in which Julius Caesar reformed the ancient Roman calendar was the last year of confusion, and the method adopted by him a commodious one, and answered a very good purpose for a short time; but as the years rolled on and century after century had passed away, astronomers began to discover the discrepancy between the solar and the civil year; that the vernal equinox did not occupy the place it occupied in the time of Caesar, namely, the 24th of March, but was gradually retrograding towards the beginning of the year, so that at the meeting of the Council of Nice in 325 it fell on the 21st. Appendix C.

The venerable Bede, in the 8th century, observed that these phenomena took place three or four days earlier than at the meeting of that council. Roger Bacon, in the 13th century, wrote a treatise on this subject and sent it to the Pope, setting forth the errors of the Julian calendar. The discrepancy at that time amounted to seven or eight days.

Thus the errors of the calendar continued to increase until 1582, when the vernal equinox fell on the 11th instead of the 21st of March. Gregory, perceiving that the measure was likely to confer great eclat on his pontificate, undertook the long desired reformation; and having found the governments of the principal Catholic states ready to adopt his views, he issued a brief in the month of March, 1582, in which he abolished the use of the ancient calendar, and substituted that which has since been received in almost all Christian countries under the name of the Gregorian calendar or New Style.

The edict of the Pope took effect in October of that year, causing the 5th to be called the 15th of that month, thus suppressing ten days and making the year 1582 to consist of only 355 days. So we see that the ten days that had been gained by incorrect computation during the past 1257 years, were deducted from 1582, restoring the concurrence of the solar and the civil year, and consequently the vernal equinox to the place it occupied in 325, namely, the 21st of March.

The Pope was promptly obeyed in Spain, Portugal, and Italy. The change took place the same year in France, by calling the 10th the 20th of December. Many other Catholic countries made the change the same year, and the Catholic states of Germany the year following; but most of the Protestant countries adhered to the Old Style until after the year 1700. Among the last was Great Britain; she, after having suffered a great deal of inconvenience for nearly two hundred years by using a different date from the most of Europe, at length, by an act of Parliament, fixed on September, 1752, as the time for making the much desired change, which was done by calling the 3d of that month the 14th , adopting at the same time the Gregorian rule of intercalation.

Russia is the only Christian country that still adheres to the Old Style, and by using a different date from the rest of Europe is now twelve days behind the true time. The discrepancy between solar and civil time does not effect the day, for, as has already been shown, the mean length of the day is twenty-four hours, and is marked by one revolution of the earth upon its axis.

Nor does it effect the week, for the week is uniformly seven of those days. But it effects the year, the month and the day of the month.

Russia, by adhering to the Old Style, has reckoned as many days and as many weeks, and events have transpired on the same day of the week as they have with us who have adopted the New Style; as Christian nations we are observing the same day as the Sabbath.

When it was Tuesday, the 20th day of December, 1888, in Russia, it was Tuesday, the 1st day of January, 1889, in those countries which have adopted the New Style. Columbus sailed from Palos, in Spain, on Friday, August 3d, 1492, Old Style, which was Friday, August 12th, New Style. Washington was born on Friday, February 11th, 1732, Old Style, which was Friday, February 22d, New Style.

Now, the difference in styles during the 15th century is nine days; during the 16th and 17th centuries, ten days; the 18th century, eleven days, and the 19th, twelve days. In regard to the sailing of Columbus, the change is made by suppressing nine days, calling the 3d the 12th of August. In regard to the birth of Washington, the change is effected by suppressing eleven days, calling the 11th of February the 22d. As regards Russia, she could have made the change last year by calling the 20th of December, 1888, the 1st day of January, 1889, thereby suppressing twelve days, and making the year 1888 to consist of only 354 days, and the month of December twenty days. The methods of computation, both Old and New Styles, will be explained in another chapter.

To persons unacquainted with astronomy, the difference between Old and New Styles would probably be better understood by the diagram on the 25th page. The figures represent the ecliptic, which is the apparent path of the Sun, or the real path of the Earth as seen from the Sun, in her annual or yearly revolution around the Sun in the order of the months, as marked on the ecliptic.

Attention is called to four points on the ecliptic, namely, the vernal equinox, the autumnal equinox, the winter solstice, and the summer solstice. These occur, in the order given above, on the 21st of March, the 21st of September, the 21st of December and the 21st of June. It has already been stated that if the civil year correspond with the solar, the seasons of the year will always come at the same period. Julius Caesar found the ancient Roman year in advance of the solar; Gregory found the Julian behind the solar year; so one reforms the calendar by intercalation, the other by suppression. Appendix D.

Caesar restored the coincidence of the solar and the civil year, but failed to retain it by allowing what probably appeared to him at the time a trifling error in his calendar. The error, which was 11 minutes and 10.38 seconds every year, was hardly perceptable for a short period, but still amounted to three days every 400 years. Hence the necessity in 1582 of reforming the reformed calendar of Julius Caesar to restore the coincidence. Appendix E.

From the meeting of the Council of Nice, in 325, to 1582, a period of 1257 years, there was found to be an error in the Julian calendar of ten days. Now, in 1257 years the Earth performs 1257 annual and 459,109 daily revolutions, after which the vernal equinox was found to occur on the 21st of March, true or solar time; thus concurring with the vernal equinox of 325. But the erroneous Julian calendar would make the Earth perform 459,119 daily revolutions to complete the 1257 years, a discrepancy of ten days, making the vernal equinox to fall on the 11th instead of the 21st. It will be seen by the diagram that the ten days were deducted from October, in 1582, making it a short month, consisting of only twenty-one days.

The discrepancy between the Julian and Gregorian calendar amounts to thirty days in 4000 years; three months in 12,175 years. Hence, in 12,175 years the equinoxes would take the place of the solstices, and the solstices the place of the equinoxes. In 24,350 years, the vernal equinox would take the place of the autumnal equinox, and the winter solstice the place of the summer solstice.

And in 48,700 years, according to the Julian rule of intercalation, there would be gained nearly 365-1/4 days, or one entire revolution of the Earth. So, to restore the concurrence of the Julian and Gregorian years, there would have to be suppressed 365-1/4 days, calling the 1st day of January, 48,699, the 1st day of January, 48,700.

Thus would disappear from the Julian calendar twelve months, or one whole year, it having been divided among the thousands of the preceding years.

To make this subject better understood, let us suppose the solar year to consist in round numbers of 365 days, and the civil year 366. It is evident that at the end of the year of 365 days, there would still be wanting one day to complete the civil year of 366 days, so one day must be added to that year, and to every succeeding year, to complete the years of 366 days each, which would be the loss of one year of 365 days in 365 years. Hence, 364 years of 366 days each are equal to 365 years of 365 days each, wanting one day.

Again, let us suppose the civil year to consist of 364 days. It is evident that at the end of the supposed solar year of 365 days, there would be an advance or gain of one day in that year and every succeeding year, so that in 365 years there would be a gain of 365 days or one whole year. Hence, 366 years of 364 days each are equal to 365 years of 365 days each, wanting one day. Appendix F.

PECULIARITIES OF THE ROMAN CALENDAR.

The Romans, instead of distinguishing the days of the month by the ordinal numbers, first, second, third, etc., counted backwards from three fixed points, namely, the Calends, the Nones, and the Ides.

Calends was so denominated because it had been an ancient custom of the pontiffs to call the people together on that day to apprise them of the festivals, or days that were to be kept sacred during the month.

Nones the ninth day before the Ides.

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